The top of a ladder rests at a height of 12 feet against the side of a house. If the base of the ladder is 9 feet from the house, what is the length of the ladder? Round to the nearest foot.
3 ft
11 ft
15 ft
21 ft

The solution to the system of equations is d = 100 and m = 1/4. Multiplying each term in the second equation by 2 helped us to eliminate the variable d and solve for m.

To solve the system of equations, we can use the elimination method, which involves adding or subtracting the two equations to eliminate one of the variables.

In this case, if we add the two equations as they are, we won't be able to eliminate one of the variables.

Multiply each term in the second equation by 2, we will get:

4d + 200m = 450

4d + 800m = 600

Now, we can subtract the first equation from the second equation to eliminate d:

(4d + 800m) - (4d + 200m) = 600 - 450

600m = 150

m = 1/4

Substituting this value of m back into either of the original equations, we can solve for d:

4d + 200(1/4) = 450

4d + 50 = 450

4d = 400

d = 100

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Answer:

First choice, y = -2x+6

Step-by-step explanation:

Convert the original equation to slope-intercept form, where y = mx + b.
We are looking for a parallel line so keep x, y, and the slope. turn the 7 into an intercept variable. Plug in (2,2) for (x,y). Solve for b. b = 6. Rewrite the equation with the same slope and the new y-intercept.

y = -2x + 6

The total number of residents in the project is 17,664.

The total number of residents in the project can be calculated by using the following formula:

Number of residents = Number of apartments x Average number of persons per apartment

In this case, the calculation would be:

Number of residents = 4,416 x 4

Number of residents = 17,664

Therefore, the total number of residents in the project is 17,664.

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The solution of the functions given will be (-3, 2) and (2, 2) as we can see in graph.

What is the definition of a function?

In mathematics, a function is a rule that associates each element in one set, called the domain, with a unique element in another set, called the range. In other words, a function is a relation between two sets such that each element in the domain is paired with exactly one element in the range.

A function can be represented by an equation, a graph, a table, or a verbal description. The notation f(x) is often used to represent a function, where f is the name of the function and x is the input (or independent variable). The output (or dependent variable) is then given by f(x).

Now,

For functions f(x) = x²+x-4

g(x) = -2x²-2x+14

the graph will be made as shown in image

and their intersection points will be the solution of the given functions

Hence,

           The solution of the functions given will be (-3, 2) and (2, 2) as shown in graph.

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The total area, in square centimeters, of the shaded sections of the below would be 33. 93 cm ²

The area of the shaded sections can be found by finding the area of the two triangular sections that are shaded.

Area of first triangle :

= 1 / 2 x base x height

= 1 / 2 x 5. 3 x 5 . 8

= 15. 37 cm ²

The area of the second triangle is :

= 1 / 2 x 6 . 4 x 5 . 8

= 18. 56 cm ²

The total area of the shaded sections is:

= 15. 37 + 18. 56

= 33. 93 cm ²

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well, the total bill doesn't include the tip, so the total bill is the cost plus the tax.

so assuming the total bill means before tax, let's call it "x", now if we apply the tax to "x", hmmm how much is 8% of "x"?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8\% of x}}{\left( \cfrac{8}{100} \right)x}\implies 0.08x[/tex]

so "x" plus the tax will just be x + 0.08x = 1.08x.

The tip was 15% of that 1.08x, and we happen to know that was $1.05.

[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 1.08x & 100\\ 1.05& 15 \end{array} \implies \cfrac{1.08x}{1.05}~~=~~\cfrac{100}{15} \\\\\\ 16.2x=105\implies x=\cfrac{105}{16.2}\implies x\approx 6.48[/tex]

The percentage of observations less than 130 is 97.7%, and the number of observations less than 130 = 879

The question asks about the percentage and number of observations that are less than 130 in a data set that follows a bell-shaped distribution with a mean of 120 and a standard deviation of 5.

a. To find the percentage of observations that are less than 130, we can use the z-score formula:
z = (x - μ) / σ
where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

Plugging in the given values, we get:
z = (130 - 120) / 5
z = 10 / 5
z = 2

Using a standard normal table or calculator, we can find that the probability of a z-score being less than 2 is approximately 0.9772. This means that approximately 97.7% of the observations are less than 130.

b. To find the number of observations that are less than 130, we can multiply the percentage by the total number of observations:
Number of observations = 0.9772 * 900
Number of observations = 879.48

Rounding to the nearest whole number, we get that approximately 879 observations are less than 130.

Therefore, the answers are:
a. Percentage of observations less than 130 = 97.7%
b. Number of observations less than 130 = 879

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Answer:30

Step-by-step explanation:

The cοοrdinates οf the fοurth vertex οf the parallelοgram are (19/2, 19.5).

A spherical οr elliptical cοοrdinate system knοwn as the geοgraphic cοοrdinate system is used tο measure and transmit pοsitiοns οn Earth as latitude and lοngitude.

First, we can find the distance between pοints Y and q, which will be the same as the distance between pοints 5 and B since they are οppοsite sides οf the parallelοgram:

Distance Yq = [tex]\sqrt{[(10-8)^2 + (5-10)^2] }[/tex]

Distance Yq = [tex]\sqrt{8 + 25 }[/tex]

Distance Yq =[tex]\sqrt{ 33}[/tex]

Distance 5B = [tex]\sqrt{[(3-2)^2 + (2-3)^2] }[/tex]

Distance 5B = [tex]\sqrt{2}[/tex]

Since οppοsite sides are cοngruent, √33 = √2x, where x is the length οf the missing side οf the parallelοgram. Sοlving fοr x, we get:

x = (33/2)

Next, we can find the slοpe οf the line passing thrοugh pοints Y and q,

Slοpe Yq = (10-5)/(8-10) = -5/2

Slοpe B-missing vertex = -5/2

write the equatiοn οf the line passing thrοugh B and the missing vertex:

y - 2 = (-5/2)(x - 3)

Simplifying, we get:

y = (-5/2)x + (19/2)

Therefοre, the cοοrdinates οf the missing vertex are (19/2, x), where x = 2 + (33/2) = 19.5.

Sο the cοοrdinates οf the fοurth vertex οf the parallelοgram are (19/2, 19.5).

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Answer:hello

Step-by-step explanation:

Let's use algebra to solve this problem. Let x be the number of 30-minute lessons that the teacher gave last week, and let y be the number of 60-minute lessons. We know that the teacher gave a total of 9 lessons, so we can write:

x + y = 9

We also know that the total time spent on lessons was 7 hours, which we can convert to minutes:

30x + 60y = 420

Now we have two equations with two unknowns, which we can solve using substitution or elimination. Let's use substitution:

x + y = 9 -> y = 9 - x

30x + 60y = 420 -> 30x + 60(9 - x) = 420

Simplifying and solving for x:

30x + 540 - 60x = 420

-30x = -120

x = 4

Therefore, the teacher gave 4 30-minute lessons last week. To find the number of 60-minute lessons, we can substitute x = 4 into either equation:

x + y = 9 -> y = 9 - x -> y = 9 - 4 -> y = 5

So the teacher gave 5 60-minute lessons last week.

Answer:

24.5

Step-by-step explanation:

we know that x=7

so 7x/2 (just a fancy way of saying x multiplied by 7/2)=

7*7/2= 24.5

Hope this helps! :)

Mark and Lynne have 28 years left on their mortgage. To figure out how old their house is right now, we need to divide the remaining years on the mortgage by 5.

This is because when the mortgage is paid off, their house will be 5 times as old. Therefore, 28 divided by 5 is equal to 5.6 years old. This means that the house is currently 5.6 years old. After 28 years, the house will be 33.6 years old.

Mark and Lynne have a mortgage on their house that still has 28 years remaining on it. To figure out the age of the house currently, we need to do a simple calculation. When the mortgage is paid off, their house will be 5 times as old as it is now. Therefore, if we divide the remaining years on the mortgage by 5, we will get the current age of the house. 28 divided by 5 is equal to 5.6 years old. This means that the house is currently 5.6 years old. In 28 years, when the mortgage is paid off, the house will be 33.6 years old. It is important to pay off the mortgage in a timely manner, as this will save Mark and Lynne a lot of money in the long run.

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Answer:

Given as steps.

Step-by-step explanation:

Step 2: Transitive Property of Equality
Step 3: SSS Congruency Therom
Step 5: If alt. Interior angles are congruent when two lines are cut by a transversal then the lines are parallel
Step 6: Quadrilateral with opposite sides parallel and congruent is a parallelogram


hope it helps.

Answer:

x(x - 5)(x + 2)

Step-by-step explanation:

[tex]x^3 - 3x^2 - 10x = x(x^2 - 3x - 10)[/tex]

x² - 3x - 10

Now, we look for two integers which when added give (-3) and when multiplied give (-10). The factors are 2 and (-5).

Sum = -3

Product = -10

Factors = 2 , (-5)       {2*(-5) = -10 and 2 + (-5) = -3}

x² - 3x - 10 = x² - 5x + 2x - 10   {Rewrite the middle term using the factors}

From the first and second term, take out the common factor 'x' & take out the common factor 2 from the third and fourth term.

                 = x(x - 5) + 2(x - 5)

                 = (x -5)(x + 2)

[tex]x^3 - 3x^2 - 10x = x(x -5)(x + 2)[/tex]

Step-by-step explanation:

Find unit rate :

90 miles  in 1.5 hrs

90 /1.5 = 60 miles/hr

    that is one mile per minute     20 miles takes 20 minutes

            120 miles takes 120 minutes = 2 hours

Answer:

[tex]x^{2}[/tex]

Step-by-step explanation:

x*x=[tex]x^{2}[/tex]

Keisha will likely spend any sums over $11 as potential extra money. The response is as follows:

C > 11

One of the four fundamental mathematical operations, along with addition, subtraction, multiplication, and division, in addition. This operator is used to combine two or more objects or numbers. This is essential to our daily living as we engage with many kinds of transactions. Moreover, the fundamental operation introduced to the children at their primary level is added. You will discover the definition of addition, its properties, how to add on a number line, as well as several additional methods and formulae, in this article.

from the question:

Let C represent the extra money Keisha will spend (in dollars).

We are aware that Keisha will purchase gifts for more than $27. This can be written as follows:

16 + C > 27

We can take 16 away from both sides of the inequality to solve for C:

C > 27 - 16

C > 11

Hence, all sums over $11 represent potential extra expenditures by Keisha. The response is as follows:

C > 11

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With the applicatiοn οf Distributive Prοperty οf Multiplicatiοn, the fοllοwing equatiοn 3 (x + 2) + 5 can be written as

3*x + 3*2 + 5

The distributive prοperty οf multiplicatiοn is a mathematical rule that states that the prοduct οf a number and a sum can be οbtained by adding the prοducts οf the number and each term in the sum. In οther wοrds, a(b+c) = ab + ac. This prοperty can be used tο simplify expressiοns by breaking them dοwn intο smaller parts.

It is an impοrtant cοncept in algebra and is οften used tο sοlve equatiοns and simplify expressiοns. The distributive prοperty can alsο be applied tο variables and expοnents, and is a fundamental principle in the study οf algebraic structures such as rings and fields.

With the applicatiοn οf Distributive Prοperty οf Multiplicatiοn, the fοllοwing equatiοn 3 (x + 2) + 5 can be written as

3*x + 3*2 + 5

further simplified will give 3x + 6 + 5 = 3x + 11

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Mr. Golv's total time to complete the jiu-jitsu drill is 7GG + 2KK seconds, where GG is the time taken for guard passes and KK is the time taken for kimura arm locks.

Mr. Golv's total time to complete the jiu-jitsu drill can be calculated as follows:

Guard passes: 5 x GG = 5GG seconds

Kimura arm locks: 2 x KK = 2KK seconds

Total time: 5GG + 2KK = (5 x GG) + (2 x KK) = 7GG + 2KK seconds

Therefore, the total time required by Mr. Golv to complete the jiu-jitsu drill is 7GG + 2KK seconds.

For example, if GG = 10 and KK = 6, then the total time required by Mr. Golv to complete the jiu-jitsu drill is (5 x 10) + (2 x 6) = 50 + 12 = 62 seconds.

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complete question

How much time will Mr. Golv take to complete his jiu-jitsu drill which includes 5 guard passes and 2 kimura arm locks, where a guard pass takes GG seconds and a kimura arm lock takes KK seconds?

The area of the triangle is given as follows:

22.8 ft².

The area of a triangle of base b and height h is given by half the multiplication of these two dimensions, according to the equation presented as follows:

A = 0.5bh.

From the image given at the end of the answer, the dimensions of the triangle are given as follows:

Hence the area of the triangle is given as follows:

A = 0.5 x 8 x 5.7 = 22.8 ft².

The triangle from which we are going to calculate the area is given by the image presented at the end of the answer.

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The correct option is No; Two sides of triangle PQR and angle PQR are not the same measure as the corresponding sides and angle of triangle STU.

What is Side-Angle-Side (SAS) criterion?

The Side-Angle-Side (SAS) criterion is a rule used in geometry to determine whether two triangles are congruent, which means they have the same size and shape. The SAS criterion states that if two sides and the angle between them in one triangle are equal to two corresponding sides and the angle between them in another triangle, then the two triangles are congruent. This means that all corresponding angles and sides of the two triangles are equal in length and measure.

To determine whether the two triangles are congruent, we can use the side-angle-side (SAS) congruence criterion. We can see that triangle PQR has sides PQ, QR, and RP, and angle QPR, while triangle STU has sides ST, TU, and US, and angle TSU. We can compare the corresponding sides and angles:

PQ is of length 4, and ST is of length 4.

QR is of length 1, and TU is of length 4.

RP is of length 2, and US is of length 2.

Angle QPR is a right angle, while angle TSU is an acute angle.

Therefore, the two triangles do not have the same corresponding sides and angles, and we cannot conclude that they are congruent.

The correct option is:

No; Two sides of triangle PQR and angle PQR are not the same measure as the corresponding sides and angle of triangle STU.

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Answer:

x = 6

y = 3√2

Step-by-step explanation:

tan45 = y / (3√2)

y =  (3√2)(tan45) =  3√2

x = (3√2) / cos45  = 6

this is a 45-45-90 isosceles triangle

According to the given information, the measure of the larger acute angle in the 3-4-5 right triangle is approximately 36.87 degrees.

What is 3-4-5 right angle triangle?

A 3-4-5 right triangle is a right triangle where the lengths of the three sides are in the ratio of 3:4:5. In other words, the length of the longest side (the hypotenuse) is 5 times the length of the shortest side, and the length of the remaining side is 4 times the length of the shortest side. This special right triangle has angles of 30 degrees, 60 degrees, and 90 degrees, which are the angles of a 30-60-90 triangle. The sides of a 3-4-5 right triangle can be scaled up or down by any common factor (e.g. 6-8-10, 9-12-15, etc.) and will still form a right triangle with the same angles.

In a 3-4-5 right triangle, the larger acute angle is opposite to the longer leg, which has a length of 4. To find the measure of this angle, we can use the inverse tangent function:

tan(theta) = opposite / adjacent = 3/4

[tex]theta = tan^{-1} (3/4)[/tex]

Using a calculator, we can find that:

theta ≈ 36.87 degrees

Therefore, the measure of the larger acute angle in the 3-4-5 right triangle is approximately 36.87 degrees.

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Answer:347

Step-by-step explanation:=

347 ⇔ 347 R 0

8328 divided by 24

=

347 with a remainder of 0

The required diameter of the actual Ricoffy tin container is approximately 92 mm.

By enclosing units in containers—that is, by circling, boxing, or otherwise enclosing units—container numbers indicate magnitude. The worth of each container's contents is multiplied by the number system's fundamental unit. Typically, the basis is either 2 or 10 (the decimal system) (the binary system).

Let the diameter of the actual Ricoffy tin container be d mm.

Since the volume of the tin container is proportional to the cube of its dimensions, and the tin container is 2.5 times smaller than its actual size, we have:

[tex]$(\frac{d}{2.5})^3 = \frac{1}{2.5} \times d^3 = \frac{3}{4} \times 750\text{ g} = 562.5\text{ g}$$[/tex]

where we have used the fact that the actual weight of the coffee is 750g.

Solving for d, we get:

[tex]$$d = \sqrt[3]{\frac{562.5\text{ g}}{\frac{1}{2.5}}} \approx 91.98\text{ mm}$$[/tex]

Therefore, the diameter of the actual Ricoffy tin container is approximately 92 mm.

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The probability that at least 2 of the people in the class share the same birthday is approximately 0.507 or 50.7%.

The probability that at least two people share the same birthday in a class of 23 people can be calculated using the formula for a complement of an event, which states that the probability of an event happening is 1 minus the probability of it not happening.

Therefore, let’s first calculate the probability that no two people share the same birthday in a class of 23 people.

There are 365 days in a year, and if we assume that all the days are equally likely to be birthdays, then the first person can choose any day, and the probability of the second person not having the same birthday is (364/365), and for the third person, it is (363/365), and so on for the other people.

Therefore, the probability of none of them sharing the same birthday is

(364/365) × (363/365) × … × (343/365) which is approximately 0.493.

The probability of at least two people sharing the same birthday is the complement of the probability that none of them share the same birthday.

Therefore, the probability of at least two people sharing the same birthday in a class of 23 people is

1 − 0.493 ⇒ 0.507.

Hence, there is a 50.7% chance that at least two people share the same birthday in a class of 23 people.

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(a) The probability of a car accident occurring in the two hours is 0.3679.(b) The probability of a car accident occurring between 45 and 75 minutes is 0.3935 (c) The variance of the time until a car accident occurs is 0.0167 d) If a car accident has not happened in 3 hours, the probability it will happen in the next two hours is 0.7385

Since the average rate of car accidents is 1/60 accidents per minute, we can use the Poisson distribution to find the probability:
[tex]P(X = 1) = (e^(-120/60) * (120/60)^1) / 1! = 0.3679[/tex]
So the probability of a car accident occurring in the two hours is 0.3679.

Since the average rate of car accidents is 1/60 accidents per minute, we can use the Poisson distribution to find the probability:
[tex]P(X = 1) = (e^(-30/60) * (30/60)^1) / 1! = 0.3935[/tex], So the probability of a car accident occurring between 45 and 75 minutes is 0.3935.

The variance of a Poisson distribution is equal to the average rate, so the variance of the time until a car accident occurs is: [tex]Var(X) = 1/60 = 0.0167[/tex]Given that no car accident has occurred in the previous 180 minutes. We can use the conditional probability formula to find this probability:

[tex]P(X = 1 | X = 0) = P(X = 1 and X = 0) / P(X = 0) = (e^(-120/60) * (120/60)^1) / (e^(-180/60) * (180/60)^0) = 0.3679 / 0.0498 = 0.7385[/tex]
So the probability of a car accident occurring in the next two hours, given that no car accident has occurred in the previous 3 hours, is 0.7385.

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