Courtney walked from her house to the beach at a constant speed of 444 kilometers per hour, and then walked from the beach to the park at a constant speed of 555 kilometers per hour. The entire walk took 222 hours and the total distance Courtney walked was 888 kilometers.

Answers

Answer 1

Answer:

I suppose that each number is repeated 3 times, the actual question is:

Courtney walked from her house to the beach at a constant speed of 4 kilometers per hour, and then walked from the beach to the park at a constant speed of 5 kilometers per hour. The entire walk took 2 hours and the total distance Courtney walked was 8 kilometers.

Now, remember the relation:

Distance = Speed*Time

Let's define:

D1 = distance between Courtney's house and the beach.

D2 = distance between the beach and the park.

T1 = time that it took the first walk.

T2 = time that it took the second walk.

We know that the total distance Courtney walked is 8km, then:

D1 + D2 = 8km.

And we also know that the entire walk took 2 hours, then:

T1 + T2 = 2h.

We also have the equations:

D1 = 4km/h*T1

D2 = 5km/h*T2.

Then we have a system of equations:

D1 + D2 = 8km

T1 + T2 = 2h

D1 = 4km/h*T1

D2 = 5km/h*T2.

To solve this, first let's replace equations 3 and 4 in the first equation:

4km/h*T1 + 5km/h*T2 = 8km

Now we have only two equations left:

4km/h*T1 + 5km/h*T2 = 8km

T1 + T2 = 2h

Now we can isolate one of the variables in the second equation and then replace it in the first equation, i will isolate T1:

T1 = 2h - T2.

Replacing this in the first equation gives:

4km/h*(2h - T2) + 5km/h*T2 = 8km

Now let's solve this for T2.

8km - 4km/h*T2 + 5km/h*T2 =  8km

8km + 1km/h*T2 = 8km

1km/h*T2 = 0

from this, we have T2 = 0

This would mean that T1 = 2h.

Then:

D1 = 4km/h*2h = 8km.

T2 = 0

D2 = 5km/h*0 = 0.

This happens because the numbers in the problem were not well thought.

You can see that when she spends the 2 hours walking at the smaller speed, she already reaches the total distance, then if she walked any amount of time at the larger speed, the total distance would be more than 8km.


Related Questions

Find the slope of the line that passes through the points (-10, 2) and (5, 3).

Answers

Answer:

15

Step-by-step explanation:

If f(x) = x2 + 2x + 3, what is the average rate of change of Rx) over the interval (-4, 6]?

Answers

Answer:

Step-by-step explanation:

The average rate of change of a function over an interval is simply the slope over the interval because:

[tex]let \: g(x)=f'(x)\\\frac{\int\limits^b_a {g(x)} \, dx }{b-a}(the\:average\:value\:of\:g)=\frac{f(b)-f(a)}{b-a}[/tex]

We have to know f(6) and f(-4)

[tex]f(x) = x^2 + 2x + 3\\f(6) = 6^2 + 2(6) + 3\\f(6) = 36 + 12 + 3\\f(6) = 51\\\\f(-4) = (-4)^2 + 2(-4) + 3\\f(-4) = 16 - 8 + 3\\f(-4) = 11\\\\\frac{f(6)-f(-4)}{6-(-4)} = \frac{51-11}{10} = \frac{40}{10} = 4[/tex]

Luis had 4 boxes of party favors. One full box contained 16 bags of favors and each bag had 5 items in it. What is the total number
items that Luis had in his possession?
O A. 360
B. 320
O C. 170
OD. 7.5

Answers

The answer is B. 320. 64 bags times 5 items in each bag.

Suppose that 2000 is placed in an account that pays 13% interest compounded each year. Assume that no withdrawals are made from the account. Do not do any rounding.
A:Find the amount in the account at the end of 1 year.
B: Find the amount in the account at the end of 2 years.

Answers

After one year there will be $2260 and after two years there will be $2553.80

The amount will be $2260 in the account at the end of 1 year. The amount will be $2553.8 in the account at the end of 2 years.

What is Compound interest?

Compound interest is defined as interest paid on the original principal and the interest earned on the interest of the principal.

A = P(1+r/100)ⁿ

Where:

A = the future value of the investment or loan

P = the principal investment or loan amount

r = the interest rate (decimal)

n = the number of compound periods

As per the question, the given data will be:

p = $2000

r = 13%

t = 1 year

To calculate the amount in the account at the end of 1 year.

A = P(1+r/100)ⁿ

Substitute the values of p,r, and t in the formula,

A = 2000(1 + 13/100)¹

A = 2000(1 + 0.13)¹

A = 2000(1.13)

A = $2260

To calculate the amount in the account at the end of 2 years.

A = 2000(1 + 13/100)²

A = 2000(1 + 0.13)²

A = 2000(1.13)²

A = $2553.8

Thus, the amount will be $2260 in the account at the end of 1 year. The amount will be $2553.8 in the account at the end of 2 years.

To learn more about Compound interest click here:

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Here are the first four terms of an arithmetic sequence. 3 10 17 24 Find, in terms of n, an expression for the nth term of this arithmetic sequence.

Answers

Answer:

[tex]a_{n}[/tex] = 7n - 4

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 3 and d = a₂ - a₁ = 10 - 3 = 7 , thus

[tex]a_{n}[/tex] = 3 + 7(n - 1) = 3 + 7n - 7 = 7n - 4

PLEASE HELP PLEASE I NEED IT TODAY

Answers

Answer:

D

:) Hope this helps.

Step-by-step explanation:

Evaluate: 21x: 8 when x = 4*

Answers

Answer:

10.5

Step-by-step explanation:

21(4) / 8

84 / 8

10.5

ABC is congruent to EDC, BC = 5 units and DE = 12 units. What is the length of AE?

Answers

Answer:

AE = 26 units

Step-by-step explanation:

Given that ABC is congruent to EDC, therefore, the corresponding angles and corresponding lengths of ∆ABC and ∆EDC are equal to each other in measure.

AE = 2(AC) = 2(CE) or

AE = AC + CE

Let's find the AC using Pythagorean Theorem, since the ∆s are both right triangles.

BA is congruent to DE.

Since DE = 12 units, therefore, BA = 12 units.

BC = 5 units (given)

Using Pythagorean Theorem:

AC² = BA² + BC²

AC² = 12² + 5² (substitution)

AC² = 144 + 25 = 169

AC = √169

AC = 13 units

Since ∆ABC = ∆EDC, therefore:

AE = 2(AC)

AE = 2(13)

AE = 26 units

Find the product.
(2a^2+b) (3a-3b)
Enter the correct answer.

Answers

Answer:  6a^3-6a^2b+3ab-3b^2

=============================================

Work Shown:

(2a^2+b)(3a-3b)

c(3a-3b)  ..... let c = 2a^2+b

3ac-3bc  .... distribute

3a(c)-3b(c)

3a(2a^2+b)-3b(2a^2+b)  .... plug in c = 2a^2+b

3a(2a^2)+3a(b)-3b(2a^2)-3b(b)  ... distribute

6a^3+3ab-6a^2b-3b^2

6a^3-6a^2b+3ab-3b^2

You could also use the FOIL rule to get the same result. The box method is a visual way to keep track of the terms.

If I accumulate two gallons of SHlT from an undisclosed location and I sell one gallon but in the process get two more gallons how many will I have left

Answers

Answer:

3 gallons

Step-by-step explanation:

2 - 1 + 2 = 3

Please help me out!!!!!

Answers

im a little rusty on this but i believe it is y =-(x+3)-5

What is the volume of a cylinder with a radius of 1.5 inches and a height of 9 inches round your answer to the nearest hundredthWhat is the volume of a cylinder with a radius of 1.5 inches and a height of 9 inches round your answer to the nearest hundredth

Answers

Answer:

V = 63.62

Step-by-step explanation:

Answer: 63.62 cubic inches

Step-by-step explanation:

REMEMBER :: VOLUME OF CYLINDER = πr^2h

r= 1.5 in.

h= 9 in.

V= π (1.5)^2 (9)

V= π (2.25) (9)

V= π (20.25)

V~63.6172512...

nearest hundredth = 63.62 cubic inches

Divide (-3x^2 - 9x) ÷ (x + 3)
please explain/show work! <33

Answers

Step-by-step explanation:

[tex]( - 3 {x}^{2} - 9x) \div (x + 3) [/tex]

This is the original equation so you will open the brackets.

[tex] - 3 {x}^{2} - 9x \div x + 3[/tex]

The x will cross the division sign making it times x.

[tex]3 {x}^{2} - 9x \times x = 3[/tex]

So you will proceed to multiply the 9x by x making it;

[tex]3 {x}^{2} - 9 {x}^{2} = 3 [/tex]

So you will subtract 9x² from 3x² which won't be possible so it will be negative.

[tex] - 6 {x}^{2} = 3 [/tex]

Then you will square root both sides making it;

[tex] - \sqrt{6 {x}^{2} } = \sqrt{3} [/tex]

So the ² will cancel the leaving

-6x=3

-6x=1.73(Divide both sides by -6)

x=0.288

That's the final answer.

At a food festival, 3/8 of the dishes were from china. Another 12.5% of the dishes were from japan. What percent of the dishes were from the other countries?

Answers

Answer: 50%

Step-by-step explanation:

Let x = Total dishes.

Dishes from China = [tex]\dfrac38x[/tex]

Dishes from Japan  = [tex]12.5\% \text{ of }x= 0.125x[/tex]

Total dishes  from China and Japan = [tex]\dfrac38 x+0.125x=0.375x+0.125x=0.5x[/tex]

Dishes from other countries [tex]= x- 0.5x= 0.5x[/tex]

Percent of dishes from other countries= [tex]\dfrac{0.5x}{x}\times100\%= 50\%[/tex]

Hence, dishes from other countries = 50%

riddle
What runs around the whole yard without moving?

Answers

Answer:

a yard stick, maybe I'm right

Answer:

a fence

Step-by-step explanation:

HAHAHA LOL

Help asap
A local hamburger shop sold a combined total of 555 hamburgers and cheeseburgers on Saturday. There were 55 more cheeseburgers sold than hamburgers. How many hamburgers were sold on Saturday?

Answers

Answer:

There were 250 hamburgers sold on Saturday.

Step-by-step explanation:

∵ A local hamburger shop sold a combined total of 555 hamburgers

   and cheeseburgers on Saturday

→ Assume that the shop sold x hamburgers

∵ The shop sold x hamburgers

∵ There were 55 more cheeseburgers sold than hamburgers

→ That means the number of cheeseburgers is greater than the

    number of hamburger by 55

∴ The shop sold x + 55 cheeseburgers

∵ The shop sold 555 burgers

→ Add the two types of burgers and equate the sum by 555

x + x + 55 = 555

∴ 2x + 55 = 555

→ Subtract 55 from both sides

∴ 2x + 55 - 55 = 555 - 55

∴ 2x = 500

→ Divide both sides by 2 to find x

∵ [tex]\frac{2x}{2}[/tex] = [tex]\frac{500}{2}[/tex]

x = 250

∵ x represents the number of hamburgers

There were 250 hamburgers sold on Saturday.

what is 2 over 5 simplafied

Answers

Answer:

2/5 simplified is 1/2.5 or .4

Step-by-step explanation:

You simplify by dividing the numerator by the denominator. Thus 2/5 is

.40.

Hope this helps!

Learn with an example
A triangle has angle measurements of 121°, 35°, and 24°. What kind of triangle is it?
acute
right
obtuse

Answers

Answer:

Obtuse

Step-by-step explanation:

because 121

Question 2
2.5 pts
A firefighter sees a woman trapped in a building 91 feet up from the bottom floor. If the
firetruck is parked 67 feet away from the bottom of the building, at what angle of elevation, to
the nearest degree, should the firefighter extend the ladder to reach the woman?
Previous

Answers

Answer:

The firefighter should extend the ladder at 54° of elevation.

Step-by-step explanation:

Trigonometric Ratios

The ratios of the sides of a right triangle are called trigonometric ratios. There are six trigonometric ratios, sine, cosine, tangent, cosecant, secant, and cotangent.

The longest side of the triangle is called the hypotenuse and the other two sides are the legs.

Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.

Tangent Ratio:

[tex]\displaystyle \tan\theta=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]

The woman is trapped at 91 feet up from the ground, and the firetruck is 67 feet away from the building.

The wall, the ground, and the ladder form a right triangle, where θ is the horizontal angle of the ladder.

Being the height of the woman the opposite leg and the distance where the firetruck is parked, the adjacent leg:

[tex]\displaystyle \tan\theta=\frac{91}{67}=1.3582[/tex]

The angle is calculated as the inverse tangent:

[tex]\theta=arctan(1.3582)\approx 54^\circ[/tex]

The firefighter should extend the ladder at 54° of elevation.

Which of the following mixtures will have a stronger coffee flavor? explain please thank you!!
A) Mixture B
B) Mixture A
C) Both the mixtures are equally strong.

Answers

Mixture B because there’s a higher ratio of coffee to milk than in Mixture A (1:3 vs. 1:2)

Which expression is equivalent to – (4-3)?

A. -2(to the power of 2) + 3
B. -2(to the power of 2)– 3
C. -3 - 2(to the power of 2)
D. -3 +2(to the power of 2)

Answers

Answer:

answer is really hard and small, but I can't help because I don't know,

sorry not sorry

lol

regards,

Rosemary

Given: AB ∩ CD ∩ GF = O, E ∈ interior of ∠GOB, H ∈ interior of ∠AOF. Without changing the picture indicate: Vertical angle to ∠GOB: ____________

Answers

Answer:

The verticle angle to GOB is AOF.

Step-by-step explanation:

Look at the picture, it's pretty clear

HeLp Me pLz

What is the shape of the cross section of the figure that is perpendicular to the triangular bases and passes through a vertex of the triangular bases?

A triangular prism.
a parallelogram that is not a rectangle
a rectangle
a triangle that must have the same dimensions as the bases
a triangle that may not have the same dimensions as the bases

Answers

The answer is a papallelogram that is not a rectangle.

Bernard says “When you halve a whole number that ends in 8, you always
get a number that ends in 4”

Write down an example to show that Bernard is wrong.

is this a trick question?

Answers

Answer:

Bernad is WRONG.

Step-by-step explanation:

Let us take the number '18' (ends with 8)

The half of 18 is '9' (doesn't end with 4)

Let us take the number '38' (ends with 8)

The half of 38 is '19' (doesn't end with 4)

Therefore, Bernard is wrong.

Bernard is wrong because When you halve a whole number that ends in 8, you always cannot get a number that ends in 4

What is an arithmetic operation?

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

It is given that:

Bernard says “When you halve a whole number that ends in 8, you always get a number that ends in 4”

It can be written mathematically:

Let's suppose the number is '18' (ends with 8)

The half of 18 =  9 (doesn't end with 4)

Let's suppose the number is '38' (ends with 8)

The half of 38 = 19 (doesn't end with 4)

Thus, Bernard is wrong because When you halve a whole number that ends in 8, you always cannot get a number that ends in 4

Learn more about the arithmetic operation here:

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80% of the doctors surveyed believe exercising 30 minutes a day help you live a healthier life. If 240 doctors believe in exercising, how many were surveyed.

Answers

Answer:

300 is what I got

Step-by-step explanation:

Find the 39th term of the following sequence. 17,11, 5, -1

Answers

Answer:

-330

Step-by-step explanation:

a39= 17+ (39-1) * -6

17+ 38 = 55

55*-6 = -330

Does this image have a set of inputs to a set of possible outputs where each input is related to exactly one outputs Yes or No?
Explain your answer

Answers

Answer: Yes

This graph passes the vertical line test. This is a test where we try to draw a single vertical line through more than one point on the curve. In this case, such a thing is not possible. Any input x leads to exactly one output y. This graph is a function.

On a coordinate plane, a line goes through points (1, 9) and (4, 3).
What is the slope of a line that contains the points (1, 9) and (4, 3)?

Answers

Answer:

yes

Step-by-step explanation:

l,l,;,;,;,;l,;,;

The slope of the line that contains the point (1,9) and (4,3) would be -2.

Help pls help pls help pls help pls help pls

Answers

Answer:

Domain: -2 < x ≤ 3

General Formulas and Concepts:

Algebra I

Domain is the set of x-values that can be inputted into function f(x)

Step-by-step explanation:

Since domain encompasses x values only, we are looking at the x-values of the graph. We see that our x-values span from -2 to 3. However, since x = -2 is a open dot, it is NOT included in the domain. Since x = 3 is a closed dot, it IS included in the domain:

(-2, 3] or -2 < x ≤ 3

Answer:

ramen is the true answer to lifes problems  

Step-by-step explanation:

3. Solve for a
5(a-2) = 2(10+a)

it’s due by midnight and can you also tell me how you got the answer

Answers

Answer:

a=10

Step-by-step explanation:

distribute on both sides to get

5a-10=20+2a

add/subtract like terms

5a-2a=3a

20+10=30

so the equation is

3a=30

divide 30 by 3 and you get 10

Answer:

a = 10

Step-by-step explanation:

[tex]5(a - 2) = 2(10 + a) \\ \\ 5a - 10= 20 + 2a\\ \\ 5a - 2a= 20 + 10\\ \\ 3a = 30\\ \\ a = \frac{30}{3} \\ \\ \huge \red{ \boxed{a = 10}}[/tex]

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