Read the following and answer the adjoining questions.


John's family is planning a road trip to Florida.

John is using the following information to help plan the trip:


- total distance (one way): 1,023 miles

- average driving speed: 60 miles per hour

- driving time on first day: 10 hours.


The question is, write an equation John can use to represent the relationship between distance traveled, in miles, d, and driving time, in hours, t

Answers

Answer 1

The relationship between distance traveled, in miles, d, and driving time, in hours, t. The Equation is 60 miles × 10 hours = 1023 miles

Distance:

Distance is a numerical or sometimes qualitative measurement of the distance between objects or points. In physics or common usage, distance can refer to a physical length or an estimate based on other criteria. Since spatial cognition is a rich source of conceptual metaphors in human thought,  the term is also often used metaphorically to refer to a measure of the amount of difference between two similar objects or some degree of separation.

Most of these concepts of distance, whether physical or metaphorical, are formalized in mathematics using the concept of metric spaces.

According to the Question:

total distance (one way): 1,023 miles

average driving speed: 60 miles per hour

driving time on first day: 10 hours.

Now,

Average driving speed = 60 miles per hour

Driving time on first day = 10 hours.

Total distance on first day = 60 miles × 10 hours

                                           = 600 miles/ Hour.

and,

The relationship obtained from the Given equation is:

60 miles + 10 hours = 1023 miles

Learn more about Distance:

https://brainly.com/question/15172156

#SPJ4


Related Questions

Help I got logged out of my account and forgot the password and the email I used to sign up is not an real to receive the code

Answers

If locked out of an account due to forgotten password and invalid email, try password recovery options or contact customer support, or create a new account.

If you've been locked out of your account. If you've forgotten your password and the email you used to sign up is not valid, it can be difficult to regain access to your account. Few steps you can try to recover your account:

Check if there's any password recovery option: Depending on the website or platform you've signed up for, there may be a password recovery option that doesn't rely on email verification. For example, some sites may allow you to answer security questions or use your phone number to reset your password.Contact customer support: If there's no password recovery option or it's not working for you, try contacting the customer support team for the website or platform. Explain the situation and provide any relevant information you can. They might be able to assist you in getting your account access back.Create a new account: If all else fails, you may need to create a new account with a valid email address. Make sure to choose a strong, unique password and consider enabling two-factor authentication to help secure your account in the future.

It's important to note that in some cases, it may not be possible to regain access to your account. Always be cautious about the information you provide when signing up for online services and make sure to keep your login credentials in a safe and secure location.

Learn more about number here:

https://brainly.com/question/17429689

#SPJ4

WILL GIVE BRAINLEIST TO THE BEST ANSWER PLUS A LOT OF POINTS!!!!!!!!!!
if (x-2)^2 =2 what values of x make the quadratic equation

Answers

The values of x make the quadratic equation (x-2)² =2 is 2 + √2.

To find the values of x that make the quadratic equation (x-2)² = 2 true, we need to solve for x.

First, we can take the square root of both sides of the equation:

x - 2 = ±√2

Next, we can add 2 to both sides of the equation:

x = 2 ± √2

Therefore, the two solutions for x are:

x = 2 + √2

x = 2 - √2

These are the two values of x that make the quadratic equation (x-2)^2 = 2 true.

To check these solutions, we can substitute each value back into the original equation:

[(2 + √2) - 2]² = 2

Simplifying:

√2² = 2

2 = 2

This solution works. Now let's check the other solution:

[(2 - √2) - 2]² = 2

Simplifying:

-√2² = 2

-2 = 2

This solution does not work, so we discard it. Therefore, the only value of x that makes the quadratic equation (x-2)² = 2 true is: x = 2 + √2.

Learn more about the quadratic equation at

https://brainly.com/question/30098550

#SPJ4

please help me please

251^5+8-(9x20+3)=

Answers

Answer:

  996,250,626,076

Step-by-step explanation:

You want the value of the numerical expression 251^5+8-(9×20+3).

Calculator

Your calculator will evaluate this properly if you enter it as shown. See the attachment.

If you're doing this in parts, the Order of Operations tells you to start with the parentheses, then do the exponentiation.

  251^5 +8 -(9·20 +3)

  = 251^5 +8 -183

  = 996,250,626,251 +8 -183 = 996,250,626,076

__

Additional comment

You can use a spreadsheet (or an on-line calculator) if your calculator only displays 10 digits.

which expression is equivalent to 6 divided by 2/5

Answers

Answer:15

Step-by-step explanation:

Final answer:

Dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore, 6 divided by 2/5 is the same as multiplying 6 by 5/2, which equals 15.

Explanation:

The expression 6 divided by 2/5 is equivalent to 6 multiplied by 5/2. This is because dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 2/5 is 5/2. Therefore, 6 divided by 2/5 is the same as 6 multiplied by 5/2, which gives you the result 15.

Learn more about Dividing by a fraction here:

https://brainly.com/question/26389562

#SPJ2

If it takes John 5/12 of an hour to work on a fence, how many minutes will it take him to finish the job?

Answers

Answer:

Step-by-step explanation:

Which statement best compares and contrasts the two formats?

The infographic shows the movement of water visually, while the text describes it.

The infographic would be less appealing to visual learners than the text.

It is impossible to understand the infographic without the text.

The text is more accurate than the infographic.

a side of an apartment building is shaped like a steep staircase. the windows are arranged in columns. the first column has 3 windows, the next has 6, then 12 and so on. how many windows are on the side of the apartment building if it had 10 columns

Answers

Answer:

3069 windows on the side of the apartment building if it has 10 columns.

Step-by-step explanation:

We can notice that the number of windows in each column is double the number of windows in the previous column. So, we can write down the number of windows in each column as a sequence of powers of 2:

3, 6, 12, 24, 48, 96, 192, 384, 768, 1536

We can see that this is a geometric sequence with a common ratio of 2. We can use the formula for the sum of a geometric sequence to find the total number of windows:

Sn = a(1 - r^n)/(1 - r)

where

a = 3 (the first term)

r = 2 (the common ratio)

n = 10 (the number of terms we want to sum)

Substituting these values into the formula, we get:

Sn = 3(1 - 2^10)/(1 - 2)

= 3(1 - 1024)/(-1)

= 3(1023)

= 3069

Therefore, there are 3069 windows on the side of the apartment building if it has 10 columns.

What is the distance in units between the points (1, 0) and (8, 0)?

Answers

In response to the stated question, we can state that As a result, there coordinates are 7 units between the points (1, 0) and (8, 0).

what are coordinates?

When locating points or other geometrical objects precisely on a manifold, such as Euclidean space, a coordinate system is a technique that uses one or more integers or coordinates. Locating a point or item on a two-dimensional plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y coordinates are used to describe a point's location on a 2D plane. a collection of integers that indicate exact locations. The figure often has two numbers. The first number denotes the front-to-back measurement, while the second number denotes the top-to-bottom measurement. For example, in (12.5), there are 12 units below and 5 above.

The distance formula can be used to determine the separation between two points in a two-dimensional Cartesian coordinate system:

[tex]\sqrt[(x2 - x1)2 + (y2 - y1)2] = d[/tex]

and d .

As both of the points in this instance have y-coordinates of 0, we may condense the expression to:

[tex]d = \sqrt[(8 - 1)^² + (0 - 0)^²]\\d = \sqrt[(7)^² + (0)^²]\\d = \sqrt[49]\\ d= 7[/tex]

As a result, there are 7 units between the points (1, 0) and (8, 0).

To know more about coordinates  visit:

https://brainly.com/question/27749090

#SPJ1

For the function f(x)=3x2 +3x+8, evaluate and fully
simplify each of the following.
f(x+h)= ?
f(x+h)-f(x) / h = ?

Answers

By evaluating and simplifying f(x)=3x2 +3x+8, we get  f(x + h) = 3x² + 6xh + 3h² + 3x + 3h + 8 and  (f(x + h) - f(x))/h = 6x + 3h + 3.

Given function is, f(x) = 3x² + 3x + 8

Evaluate f(x + h)

Expanding f(x + h) => f(x) + hf′(x) + h²/2f″(x)

Applying formulae in the given function f(x + h) = 3(x + h)² + 3(x + h) + 8=> 3x² + 6xh + 3h² + 3x + 3h + 8Now, f(x + h) = 3x² + 6xh + 3h² + 3x + 3h + 8

Evaluate (f(x + h) - f(x))/h

Expanding both the terms f(x + h) and f(x) and simplifying, (f(x + h) - f(x))/h = [3x² + 6xh + 3h² + 3x + 3h + 8 - (3x² + 3x + 8)]/h=> [3x² + 6xh + 3h² + 3x + 3h + 8 - 3x² - 3x - 8]/h=> [6xh + 3h² + 3h]/h=> 6x + 3h + 3

Therefore, the required value is f(x + h) = 3x² + 6xh + 3h² + 3x + 3h + 8and (f(x + h) - f(x))/h = 6x + 3h + 3.

You can learn more about function at: brainly.com/question/12431044

#SPJ11

mpho takes 140 km trip to visit his unclevon his motorbike.THE motorbike has a fuel capacity of 16 litres.He stops for lunch break after 5/7 of the journey.how many kilometers did he travel before he stopped for lunch?​

Answers

Answer:

40Km

Step-by-step explanation:


Total Distance of Journey  = 140KM

5/7 of the journey:
[tex]\frac{5}{7 } * 140 = 100km[/tex]

Distance travelled before stopping: Total Distance - 5/7 of Total Distance

=
140 - 100KM = 40KM

Find the shaded area. Round your answer to the nearest tenth, if necessary.

Example: 103.45 rounded to tenths place is 103.5

Use 3.14 for pi in finding the area of the semicircle.
Area of semicircle =


Area of rectangle =


TOTAL area of composite figue =

Answers

Answer:

The answer to your problem is, Area = 104.1 square feet.

Step-by-step explanation:

Area of semicircle = 1/2 the area of a circle:

[tex]A_{sc} = \frac{1}{2} tt r^{2}[/tex]

Radius is half the diameter of 6ft.

[tex]A_{sc} = \frac{1}{2} tt ( 3^{2} ) = 14.13ft^{2}[/tex]

Area of the rectangle:

[tex]A_{r} = lw = 15 * 6 = 90ft^{2}[/tex]

Add them:

[tex]90 + 14.13 = 104.13[/tex]

Round to the nearest tenth (one decimal place)

Which is 104.1

Thus the answer to your problem is 104.1 of 104.13

Tom and Gwen have an adjusted annual gross income of $111,480. Their monthly mortgage payment for the house they want would be $1,725. Their semi-annual property taxes would be $3,660, and the homeowner’s insurance premium would cost them $685 per year. They have a monthly $154 car payment, and their credit card monthly payment averages $2,021.



What is the front end ratio?


What is the back end ratio?

Answers

Tom and Gwen have an adjusted annual gross income of $111,480. Their front end ratio, which measures how much of their income is dedicated to housing costs, is 5.19%. Their back end ratio, which measures how much of their income is dedicated to all debt obligations, is 11.72%.

The front end ratio is a measure of how much of an individual’s gross income is dedicated to housing costs. It is calculated by taking the total housing costs, which includes mortgage payments, property taxes, and homeowners insurance premiums, and dividing it by the annual gross income. For Tom and Gwen, this would be:

Front End Ratio = (Mortgage Payment + Property Taxes + Homeowner’s Insurance Premium) / Annual Gross Income

Front End Ratio = (1,725 + 3,660 + 685) / 111,480

Front End Ratio = 5.19%

The back end ratio is a measure of how much of an individual’s gross income is dedicated to all debt obligations, including housing costs and other debts. It is calculated by taking all debt obligations, which includes mortgage payments, property taxes, homeowner’s insurance premiums, car payments, and credit card payments, and dividing it by the annual gross income. For Tom and Gwen, this would be:

Back End Ratio = (Mortgage Payment + Property Taxes + Homeowner’s Insurance Premium + Car Payment + Credit Card Payment) / Annual Gross Income

Back End Ratio = (1,725 + 3,660 + 685 + 154 + 2,021) / 111,480

Back End Ratio = 11.72%

Learn more about end ratio here:

https://brainly.com/question/29467965

#SPJ4

Multiply: (6a³3b³) (5a² + 46²)
O 11a³ + 10a³b² + 2a²b³ + b³
O 30a5 +24a³b² - 15a²b³ - 1265
O 30a5 +9a5b5 - 1265
O30a6 +24a³ b² - 15a² b3 - 1266

Answers

The correct answer is:

30a^5 + 24a^3b^2 + 15a^2b^3 + 1386a^3b^3

Step by step explanation:

To get this answer, we need to distribute the terms of the first expression (6a^3b^3) to the terms of the second expression (5a^2 + 46^2) using the distributive property:

(6a^3b^3) (5a^2 + 46^2) = 30a^5b^3 + 276a^3b^3 + 15a^2b^4 + 1386a^3b^3

We can simplify this expression by combining like terms, which gives us:

30a^5 + 24a^3b^2 + 15a^2b^3 + 1386a^3b^3

Therefore, the correct answer is 30a^5 + 24a^3b^2 + 15a^2b^3 + 1386a^3b^3.

Please help, will mark as brainlest

Answers

Answer:

Step-by-step explanation:

we should do multiplications first:

1)

[tex]1)12a^{2}*3ba=12a^{3}b\\2)2ab*3ab^{2}=6a^{2}b^{3}\\3)11aba=11a^{2}b\\4)12a^{3}b+6a^{2}b^{3}+11a^{2}b=a^{2}b(12a+6ab^{2}+11)[/tex]

2)

[tex]1)1.5xy^{2}*(-4)xyz=-6x^{2}y^{3}z\\2)-4mnk*5m^{2}n^{3}k=-20m^{3}n^{4}k^{2}\\3)-6x^{2}y^{3}z-20m^{3}n^{4}k^{2}[/tex]

A local hamburger shop sold a combined total of 441 hamburgers and cheeseburgers on Tuesday. There were 59 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Tuesday?

Answers

Accοrding tο given cοnditiοns, 250 hamburgers were sοld οn Tuesday.

What is algebra ?

Algebra is a branch οf mathematics that deals with symbοls and the rules fοr manipulating thοse symbοls. It invοlves sοlving equatiοns and manipulating variables tο find unknοwn values.

Let's use algebra tο sοlve the prοblem.

Let x be the number οf hamburgers sοld.

Then the number οf cheeseburgers sοld is x - 59.

The tοtal number οf hamburgers and cheeseburgers sοld is 441, sο we can write an equatiοn:

x + (x - 59) = 441

Simplifying the left side, we get:

2x - 59 = 441

Adding 59 tο bοth sides, we get:

2x = 500

Dividing by 2, we get:

x = 250

Therefοre, accοrding tο given cοnditiοns, 250 hamburgers were sοld οn Tuesday.

To know more about algebra visit :

https://brainly.com/question/953809

#SPJ1

Claude is covering the lateral surface of bug spray cans with labels. Each can is cylindrical with a height of 12. 7 centimeters and a radius of 3 centimeters. If he places labels on 5 bug spray cans, how many square centimeters of labeling material will he use?

Answers

Claude will use 1197 square centimeters of labeling material to cover the lateral surface of 5 cylindrical bug spray cans.

Laminar surface area: what is it?

A three-dimensional object's lateral surface area is its total surface area minus its top and bottom surfaces. The lateral surface area of a cylinder, for instance, would be the area of the curved side of the cylinder. In geometry and engineering, the lateral surface area is frequently used to determine how much material is required to cover or build an object's sides. Depending on the geometry of the item, many formulae may be used to compute the lateral surface area, which is often expressed in square units (such as square centimetres or square feet).

Given the dimensions of the cylindrical can we have the lateral surface area of cylinder as:

Lateral surface area = 2πrh

Substituting the value r = 3 and h = 12.7 we have:

Lateral surface area = 2π(3)(12.7) = 239.4 square centimeters

A total of 5 cans need to be covered thus,

Total labeling material = 5 x 239.4 = 1197 square centimeters

Hence, Claude will use 1197 square centimeters of labeling material to cover the lateral surface of 5 bug spray cans.

Learn more about lateral surface area here:

https://brainly.com/question/29007884

#SPJ1




Figure 2 shows the lawn ABCDEF, where ABDE is a rectangle of length y metres and width 2x metres.


Each end of the lawn is a semi-circle of radius x metres.


The lawn has perimeter 90 m and area S m ²


d. S


dx


= 90 - 2


Given S = 90x-x², then


The value x = 14. 32 gives a maximum value of S


Find, to the nearest whole number, the maximum value of S

Answers

The nearest whole number, the maximum value of S is equivalent to approximately 323 m², which is the area of the lawn.

We are given that the perimeter of the lawn is 90 m. Therefore, we can write:

2y + 4x + 2πx = 90

where π is the constant pi. Simplifying this equation gives:

y = 22.5 - 2x - πx

The area of the lawn is given by:

S = y(2x) + πx²

Substituting y in terms of x gives:

S = (22.5 - 2x - πx)(2x) + πx²

Simplifying this expression gives:

S = 45x - 2πx² - 4x²

We are asked to find the maximum value of S. To do this, we can differentiate S with respect to x and set the derivative equal to zero:

dS/dx

= 45 - 4πx - 8x = 0

Solving for x gives:

x = (45 - 4π)/8

Substituting this value of x into the expression for S gives:

S ≈ 323 m²

Rounding this value to the nearest whole number gives:

S ≈ 323 m².

Therefore, the maximum value of S is approximately 323 m².

To know more about area as a whole number, refer:

https://brainly.com/question/25092270

#SPJ4

Complete question is:

Figure 2 shows the lawn ABCDEF, where ABDE is a rectangle of length y meters and width 2x meters. (Refer the image)

Each end of the lawn is a semi-circle of radius x meters.

The lawn has perimeter 90 m and area S m ²

dS/ dx= 90 - 2

Given S = 90x-x², then

The value x = 14. 32 gives a maximum value of S

Find, to the nearest whole number, the maximum value of S

The frequency table shows Sam's record in swimming

Year

Number of medals

2008

2009

2010

2012

2013

Based on this record, what is the probability of picking up a medal won by him in the years 2009 or 2012

Answers

The probability of picking a medal won by Sam in the years 2009 or 2012 is 5/6.

The probability of picking a medal won by Sam in the years 2009 or 2012 can be calculated using the formula P(A∪B) = P(A) + P(B) - P(A∩B). In this case, P(A) equals the probability of picking a medal won by Sam in 2009, which is 1/3, and P(B) equals the probability of picking a medal won by Sam in 2012, which is 1/2. P(A∩B) would be the probability of picking a medal won by Sam in both years, which is 0, since he did not win a medal in both years. Therefore, the probability of picking a medal won by Sam in the years 2009 or 2012 is P(A∪B) = P(A) + P(B) - P(A∩B) = 1/3 + 1/2 - 0 = 5/6.

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ4

Question in photo
!!!!!

Answers

Answer:

Binomial

Step-by-step explanation:

A binomial is a polynomial expression which contains exactly two terms. A binomial can be considered as a sum or difference between two or more monomials.

The box-and-whisker plots show the speed, in miles per hour, for each of 10 fish and 10 mammals. Speed of 10 F 30 50 D 60 Speed of 10 Mammals + 60 70 30 40 50 70 Letecia wants to predict the speeds of one additional fish and one additional mammal. She notices that the box-and-whisker plots show that about 75% of the fish were faster than 40 mph and that about 75% of the mammals were slower than 50 mph. Based upon this information, which prediction about the speeds of the additional fish and the additional mammal is justified? A The speed of the fish will be less than 40 mph, and the speed of the mammal will be greater than 50 mph. The speed of the fish will be greater than 40 mph, and the speed of the mammal will be less than 50 mph. The speed of the fish will be greater than 40 mph, and the speed of the mammal will be greater than 50 mph. The speed of the fish will be less than 40 mph, and the speed of the mammal will be less than 50 mph.​

Answers

Based on the information, the only prediction that is justified is that the speed of the fish will be greater than 40 mph, and the speed of the mammal will be less than 50 mph.

Therefore option B  is  correct.

How do we know this?

Based on the given information above, we were able to deduct that about 75% of the fish were faster than 40 mph and about 75% of the mammals were slower than 50 mph.

We can go ahead and use this information to make predictions about the speeds of one additional fish and one additional mammal.

Note that the median speed is around 50 mph, and the upper quartile (75th percentile) is around 60 mph and  we know that about 75% of the fish were faster than 40 mph, we can predict that the additional fish will have a speed greater than 40 mph. However, since the upper quartile is only at 60 mph, we cannot predict that the additional fish will have a speed greater than 60 mph. Therefore, the only prediction that is justified is that the speed of the fish will be greater than 40 mph, which eliminates options A and D.the only prediction that is justified is that the speed of the fish will be greater than 40 mph, and the speed of the mammal will be less than 50 mph, which is option B

Learn more about speed at:

https://brainly.com/question/4931057

#SPJ1

The quantity y varies directly as x and inversely as z. When x is 10 and z is 4, y is 15. What is y when x is 20 and z is 6?
6
20
27
30

Answers

[tex]\qquad \qquad \textit{combined proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with }\underline{z^5} \end{array} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}x}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{array}{llll} \textit{"y" varies}\\ \textit{directly with "x"}\\ \textit{inversely with "z"} \end{array}\qquad y=\cfrac{kx}{z}\hspace{5em}\textit{we also know that} \begin{cases} x=10\\ z=4\\ y=15 \end{cases} \\\\\\ 15=\cfrac{k(10)}{4}\implies \cfrac{4}{10}\cdot 15=k\implies 6=k\hspace{8em}\boxed{y=\cfrac{6x}{z}} \\\\\\ \textit{when x = 20 and z = 6, what's "y"?}\qquad y=\cfrac{6(20)}{6}\implies y=20[/tex]

Answer:

I think is 500 hope it helps

The two charges q are fixed at the vertices of an equilateral triangle with sides of length



a. If k = 1/4π ε0, the work required to move q from the other vertex to the center of the line joining the fixed charges is:

Answers

The work required to move q from the other vertex to the center of the line joining the fixed charges is (1/4π ε0) x 2 x q 2/a.

To solve this problem, we can use the principle of superposition to calculate the potential at the center of the equilateral triangle due to each of the two fixed charges, and then add them up to get the total potential.

Let's first find the potential due to one of the fixed charges at the center of the triangle. We can use the formula for the electric potential due to a point charge q at a distance r from it, which is given by:

V = k x q/r

In this case, the distance from one of the fixed charges to the center of the triangle is: r = a/2

So the potential due to one fixed charge at the center of the triangle is:

V1 = kq/r = kq/(a/2)

Next, let's find the potential due to the other fixed charge at the center of the triangle. Since the triangle is equilateral, the distance from the other fixed charge to the center of the triangle is also a/2. So the potential due to the other fixed charge at the center of the triangle is:

V2 = k x q/(a/2)

Now, the total potential at the center of the triangle due to the two fixed charges is simply the sum of the individual potentials:

V_total = V1 + V2 = kq/(a/2) + kq/(a/2) = 2kq/a

The work required to move a charge q from infinity to the center of the triangle is equal to the change in potential energy of the charge, which is given by:

W = q x (V_final - V_initial)

In this case, the initial potential is zero (since the charge is at infinity), and the final potential is 2kq/a (which we just calculated). So the work required is:

W = q x (2kq/a - 0) = 2kq 2/a

Substituting the given value of k, we get:

W = (1/4π ε0) x 2 x q2/a

For more such questions on vertex

https://brainly.com/question/13390450

#SPJ11

John has 10 apples he gives Janet 8 how many does he have

Answers

Answer:

2

Step-by-step explanation:

John had 10 and he gave Janet 8, which means that he remained with 2

Sabiendo que sen alpha = 0. 6 y que a es un ángulo agudo, calcula el resto de razones trigonométricas

Answers

Translate: Knowing that sen alpha = 0. 6 and that a is an acute angle, calculates the rest of trigonometric ratios

Rest of the trigonometric ratios for the acute angle alpha are cos(alpha) = 0.8 and tan(alpha) = 0.75.

If we know that sin(alpha) = 0.6, we can use the Pythagorean identity to find cos(alpha) and tan(alpha). Here's how:

Since sin(alpha) = opposite/hypotenuse, we can represent sin(alpha) as the ratio of the length of the side opposite the acute angle alpha to the length of the hypotenuse of the right triangle. Let's assume that the length of the opposite side is a and the length of the hypotenuse is h. Then we have:

sin(alpha) = a/h = 0.6

Solving for a, we get:

a = 0.6h

Using the Pythagorean theorem:

[tex]a^2 + b^2 = h^2[/tex]

Since a and h are related by a = 0.6h, put 0.6h for a to get:

[tex](0.6h)^2 + b^2 = h^2[/tex]

Simplifying:

[tex]0.36h^2 + b^2 = h^2[/tex]

[tex]b^2 = h^2 - 0.36h^2 = 0.64h^2[/tex]

[tex]b = \sqrt{0.64h^2} = 0.8h[/tex]

So now we know that b = 0.8h and a = 0.6h. Using these values, we can find cos(alpha) and tan(alpha) as follows:

[tex]cos(alpha) = adjacent/hypotenuse = b/h = 0.8h/h = 0.8tan(alpha) = opposite/adjacent = a/b = 0.6h/0.8h = 0.75[/tex]

Therefore, the rest of the trigonometric ratios for the acute angle alpha are cos(alpha) = 0.8 and tan(alpha) = 0.75.

Learn more about trigonometric ratios here:

https://brainly.com/question/25122832

#SPJ4

Suppose the solution set of a certain system of linear equations can be described as x_1 = 6 + 3x_3, x_2 = -2 - 5x_3, with x_3 free. Use vectors to describe this set as a line in R^3. Geometrically, the solution set is a line through parallel to

Answers

The solution set of the given system of linear equations can be expressed as a line in R^3 vector as r = (6, -2) + x_3(3, -5).

To express the solution set of the given system of linear equations as a line in R^3, we first need to express the solution set as a vector equation. We can do this by expressing the equations in terms of x_3 as follows:

x_1 = 6 + 3x_3,

x_2 = -2 - 5x_3

Therefore, the solution set of the given system of linear equations can be expressed as a line in R^3 as follows:

r = (6, -2) + x_3(3, -5).

To know more about vectors, refer here:

https://brainly.com/question/29740341#

#SPJ11

Gloria traveled a total of
8
88 miles to get from school to her apartment. Gloria took the bus from school and then walked the remaining
880
880880 yards home

Answers

Gloria traveled a distance of 7.5 miles on the bus.

Why is unit conversion crucial while addressing problems?

The process of translating a measurement from one unit to another is known as unit conversion. Since multiple units are frequently used to measure the same quantity and because unit conversion is required to carry out calculations and solve issues, it is significant in problem solving. Moreover, unit conversion is crucial since it enables us to compare measurements and present them in a uniform manner. For instance, measurements in science and engineering are frequently stated in SI units.

Given that, Gloria traveled a total of 8 miles.

8 x 1760 = 14080 yards.

The distance walked is 880 yards.

So the distance she traveled on the bus is:

14080 - 880 = 13200 yards

13200 / 1760 = 7.5 miles

Hence, Gloria traveled 7.5 miles on the bus.

Learn more about distance here:

https://brainly.com/question/28354920

#SPJ1

The complete question is:

Joe ran 10 kilometers in 5 hours. what is joe’s unit rate

Answers

2 kilometers per hour

Evaluate. (3. 5−2/3)⋅(−2. 8+4 3/5) Enter your answer as a decimal or mixed number in simplest form in the box

Answers

Answer:

5.1, 5 1/10

Step-by-step explanation:

(3.5 − 2/3) ⋅ (−2.8 + 4 3/5) =

= (7/2 - 2/3)(-14/5 + 23/5)

= (21/6 - 4/6)(9/5)

= (17/6)(9/5)

= (17 × 9)/(6 × 5)

= 51/10

= 5.1 = 5 1/10

the position (in thousands of feet) of a car driving along a straight road at time t in minutes is given by the function y

Answers

The position of a car driving along a straight road at time t in minutes is given by the function y = f(t).

The function y represents the position of the car in thousands of feet, while the variable t represents the time in minutes.

To find the position of the car at any given time, you simply need to plug in the value of t into the function and solve for y. For example, if you wanted to find the position of the car at 2 minutes, you would plug in 2 for t and solve for y:

y = f(2)

Once you have solved for y, you will have the position of the car in thousands of feet at 2 minutes. You can repeat this process for any value of t to find the position of the car at any given time.

To know more about Position of a Car, click on the link below:

https://brainly.com/question/30806552#

#SPJ11

I dont know how to do this

pls answer if u know with simple working

Answers

Answer: 11 in the 5th picture

Step-by-step explanation:

or if you add 5 more then it would be 17

add 2

A rope is 4212 meters long. It is cut into 17 pieces of equal lengths. What is the length of each piece?

Answers

Each piece of the rope is 247.76 meters long, approximately.

To find the length of each piece, we need to divide the total length of the rope by the number of pieces it is cut into:

Length of each piece = Total length of the rope / Number of pieces

Length of each piece = 4212 meters / 17

Length of each piece = 247.76 meters (rounded to two decimal places)

The method used to find the length of each piece of rope is division. We divided the total length of the rope by the number of pieces it was cut into, which gives us the length of each piece. This method is based on the fact that the length of each piece is the same, so we can divide the total length equally among the pieces.

learn more about division here:

https://brainly.com/question/12342242

#SPJ4

Other Questions
The sum of the first 18 terms of the series -100 + 122 - 148. 84 + 181. 5848 is1) 1569. 772) -1569. 773) -15840. 454) 15840. 45 What effect did the author most likely intend with charles wentworths Based on this dialogue, what can the reader infer? This is Petrocelli's first time acting as the prosecuting attorney in a court of law. Mr. Harmon knows where he was during the day of the robbery. It is a rule of the court that a lawyer may not argue with someone during questioning. Petrocelli has not been a trial lawyer as long as O'Brien has How is irony used to create meaning and effect in The Laboratory? trey paid 42 dollars for 2/3 ton of concrete. he wants to know the price of 3 tons of concrete. Question 2 (12 marks) A home-printer manufacturer would like to conduct a survey to study their customers' opinion about the photo printer. A new model of photo printer was launched 3 months ago, and 1000 customers have filled in the online warranty cards. Based on the list of these 1000 customers, 20 customers have been selected randomly for the survey. (a) The sample was selected by systematic sampling method. Unique identity numbers were assigned to the customers from00011000. Suppose it is known that customer with identity number 0131 was included in the sample. Write down the identity numbers of the next three selected customers after 0131. Below is the summary statistics of the sample: (b) Find the interquartile range and range of the data. (c) Comment on the skewness of the data. Explain your answer with detailed comparison. (d) Another sample of 10 customers have been collected. The sample mean of this sample is 70 and the minimum and maximum data are 50 and 110 respectively. Combine the two samples, find the mean and range for the combined sample with 30 data. Use point-slope form to write the equation of a line that passes through the point (15,3)(15,3) with slope 37 73 . The light from the Cape Florida Lighthouse in Key Biscayne is visible for a distance of 15 mi. If the beam of light sweeps in an arc of 270, what is the area covered by the beam? Siblings LUkas and Sophie attend the same school. While at home, they get into an argument while playing a video game. Lukas begins talking down to Sophie abOut how bad she is doing and how she will never win. Sophie gets upset and yells at Lukas about how mean and horible of a brother he is. She throws the video game controller and storms out the room. Lukas doesn't speak with his sister for the remainder of the day. At school the next day, Sophie trips and falls down while walking to class. Lukas runs over to help. When Lukas helped his sister, what characteristic of a healthy relationship did the siblings most strongly demonstrate? spending time together solving problems together showing devotion to one another communicating well with each other Noa flies a drone in a circular path around an object that is 210 meters west and 150 meters south of herposition. The drone's path takes it over a point that is 170 meters east and 190 meters north of her.Find an equation for the drone's path. (Assume Noa is located at the origin, with the horizontal axis runningeast-west and the vertical axis running north-south)The drone's path follows the equation________When the drone passes due north of Noa's position, it will be ___________ feet north of her (round your answer to three decimal places). Find the radius of a hemisphere with a volume of 2,712. 3 in3 You have learned about passage tombs. Which one of these statements appears to be TRUE about passage tombs? A. They have a capstone placed over them. B. They are constructed with several upright stone blocks. C. They are also known as menhirs. D. They consist of a stone passageway to a burial chamber, all of which is covered by an earthen mound. sarah attempts to do the popular physics trick of swinging a shallow pail of water around in a vertical circle with uniform circular motion so that the water doesn't spill out when the pail is upside down. if the distance from the bottom of the pail to her shoulder (the center of rotation) is 0.449 meters long, what is the minimum constant tangential speed that the pail bottom must have so that the water does not spill out at the top of the circular path 9. A 1385-kg pickup truck hitched to a 453-kgtrailer accelerates along a level road from astoplight at 0. 75 m/s2 [forward]. Ignore frictionon the trailer and air resistance. Calculate(a) the tension in the hitch a(b) the force of static friction exerted by the roadon the pickup truck to propel it forward a(c) the force the trailer exerts on the pickuptruck a Two practical strategies that you could use to determine whether entrepreneurship would be the best career option for you on each response,indicates how these strategies may assist you in ensuring that entrepreneurship is your best option What's wrong with a message that begins, I am writing this announcement to let everyone know that In this sentence, what type of connection word is "although"? (10 points) find the address of the last location of the on-chip rom for each of the following ds5000-16 ds5000-8 ds5000-32 at89c52 8751 at89c51 ds5000-64 Which of these is located at 20'N,30'ENigeriaKenyaTanzania look at the picture