8. The model of a building is 32 inches tall. The actual building is 240 feet tall. What scale is being used?

Answer:

The slopes of parallel lines are the same

The slopes of perpendicular lines are negative reciprocals

Line AB

[tex]\textsf{let}\:(x_1,y_1)=(3,4)[/tex]

[tex]\textsf{let}\:(x_2,y_2)=(7,7)[/tex]

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{7-4}{7-3}=\dfrac{3}{4}[/tex]

Line CD

[tex]\textsf{let}\:(x_1,y_1)=(0,0)[/tex]

[tex]\textsf{let}\:(x_2,y_2)=(-6,8)[/tex]

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{8-0}{-6-0}=-\dfrac{4}{3}[/tex]

As the slopes of AB and CD are negative reciprocals of each other, lines AB and CD are perpendicular.

Answer:

y=2

Step-by-step explanation:

y*3=6

divide both sides by 3

y=2

Answer:

56

Step-by-step explanation:

25 times 4 = 100

14 times 4 = 56

Answer:

y≤2/3x+1/5

or the very first one

Step-by-step explanation:

15x=-42-19y

3x=-54-19y

Subtract both

Put in second

So

Answer:

1, -3

Step-by-step explanation:

Solve the system of linear equations:

-------------------------------------------------------------------------------------

Subtract the equations to eliminate y:

     15x = -42 - 19y

-      3x = -54 - 19y

    ----------------------

    12x = 12

⇒ x = 12 ÷ 12

⇒ x = 1

Now substitute the found value of x into one of the equations and solve for y:

⇒ 15x = -42 - 19y

⇒ 15(1) = -42 - 19y

⇒ 15 = -42 - 19y

⇒ 19y = -42 - 15

⇒ 19y = -57

⇒ y = -57 ÷ 19

⇒ y = -3

Therefore, x = 1 and y = -3

Answer:

2058

Step-by-step explanation:

every 5 years is 0.53 so you times that by 11 to get 7.61 and then half of .53 is .265 and round that up you get three more years so 2058 is the answer.

The true statements are:

From the complete question, we have the dimensions of the parking lot to be: 78 meters by 19 meters

Also, the dimension of the aisle is: 8 meters by 78 meters

The total parking area is the difference between the parking lot area and the aisle area

This gives

Parking Area = 78 * 19 - 8 * 78

Parking Area = 858

The total area available for cars to park is 858 square meters

The number of parking lot is the quotient of the total parking area and the area of each compact

So, we have:

n = 858/12.5

n = 68.64

Remove the decimal

n = 68

Hence, the number of parking space is 68

The number of parking lot is the quotient of the total parking area and the area of each non-compact space

So, we have:

n = 858/(5.5 * 3)

n = 52

Hence, the number of parking space is 52

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Answer:

x would be 48

Step-by-step explanation:

180 (because its a straight line) take away 132 and it gives you 48

Answer:

area:1.9×0.75÷2

perimeter:2+0.75+2.25

Answer:

No solution

Step-by-step explanation:

As the coefficient of x is the same, and the constant terms are different, the lines will lie parallel to each other and never intersect.

Hence, this system of equations has no solution.

Answer:

no solution

Step-by-step explanation:

the equation has no solution

Answer:

15

Step-by-step explanation:

75/5 = 15

This spilts the 75 students into 5 different groups and each one has 15 which is 1/5 of the students

A' = (-6, 2), B' = (-3/2, 4), C' = (9/2, 3),  D' = (3, -2) and E' = (-3, -1). The new figure is similar to the original figure

An equation is an expression that shows the relationship between two or more variables and numbers.

A horizontal stretch by a factor of k uses the rule: (x,y) → (kx, y). Pentagon ABCDE is stretched horizontally by a factor of 3/2, hence:

A' = (-6, 2), B' = (-3/2, 4), C' = (9/2, 3),  D' = (3, -2) and E' = (-3, -1)

The new figure is similar to the original figure

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1 and 2 is 3 (2)

1 and 3 is 4 (3)

1 and 4 is 5 (4)

2 and 1 is 3 (5)

2 and 2 is 4 (6)

2 and 3 is 5 (7)

3 and 1 is 4 (8)

3 and 2 is 5 (9)

4 and 1 is 5 (10)

you have 36 different ways you can role and 10 of them are 5 or less so you have a 26/36 chance of rolling greater than 5

Answer:

x = 30

Step-by-step explanation:

if A||B, then 4x + 2x must equals to 180 (interior angles of 2 parallel lines)

6x = 180

x = 30

Answer:

Figure JK is shown in the drawing.

Step-by-step explanation:

The angle 11π/12 radian after converting it to degree it become 165 degree.

The measurement between the two lines is called an "Angle" when the two lines or rays converge at a common location.

We have given:

An angle 11π/12

Let's denote it with β

[tex]\rm \beta = \dfrac{11\pi}{12}[/tex]

To convert it to degree, replace π with 180°, we get:

[tex]\rm \beta = \dfrac{11\times180}{12}[/tex]

β = 165°

Thus, the angle 11π/12 radian after converting it to degree it become 165 degree.

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Answer:

0.125%

Step-by-step explanation:

area of square

10*10=100

area of triangle

(5*5)/2=12.5

[tex]\frac{12.5}{100}[/tex]=0.125

The dimensions of the rectangular prisms are the side lengths of the rectangular prism

A rectangular prism has the following dimensions

Length, width and height

This means that the dimensions of the rectangular prisms are the length, width and height  of the prism

To determine the dimension, we simply take the value of the above terms i.e. length, width and height

Note that the question is incomplete, so I gave a general explanation

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The two angles are 45 degrees.

Step-by-step explanation:

You are just halfing the 90 degree angle, so all you have to do is divide 90 by two, and you have 45.

Answer: C

Step-by-step explanation:

To determine if a triangle is equilateral, you need to see if all the sides have the same length.

Answer:

C

Step-by-step explanation:

Ben

The value of the expression after rounding to the nearest tens is 600

The expression is given as:

748 - 154

When rounded to the nearest tens, we have:

750 - 150

Evaluate the difference

600

Hence, the value of the expression after rounding to the nearest tens is 600

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The volume of the coffee in each tank will be 1760. in³. The mass of cold coffee and hot coffee will be 6163.29 oz and 10213.45 oz. Then the number of the tank placed on a table is one only.

She is serving hot coffee and cold coffee in two rectangular-shaped tanks, each with dimensions width of 8.75 inches, a length of 8.75 inches, and a height of 23 inches.

The hot coffee has a density of 5.8 oz/in³ and the cold coffee has a density of 3.5 oz/ in³.

Then the volume of the coffee in each tank will be

We know that the dimension of both tanks is equal. Then the volume will remains equal.

Volume = L × B × H

Volume = 8.75 × 8.75 × 23

Volume = 1760.9375 ≅ 1760.94 in³

Then  the mass of the coffee in each the tank will be

The mass of hot coffee will be

Mass = Density × Volume

Mass = 5.8 × 1760.94

Mass = 10213.45 oz

The mass of cold coffee will be

Mass = Density × Volume

Mass = 3.5 × 1760.94

Mass = 6163.29 oz

Then the number of the tank placed on a table is one only.

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Answer:

Step-by-step explanation:

I'm not oversimplifying this answer.

If 1 inch is .25 miles then all you have to do is multiply .25 miles by 5 inches and u get 1.25 miles.

[tex]\begin{array}{ccll} \stackrel{in}{model}&\stackrel{mi}{actual}\\ \cline{1-2} 1 & 0.25\\ 5& x \end{array} \implies \cfrac{1}{5}=\cfrac{0.25}{x}\implies x=(5)(0.25)\implies x=1.25[/tex]

The graph is a quadratic function, and the equation of the function is C(x) = (x + 4)(x - 3)

From the graph the x-intercepts are:

x = -4 and x = 3

Rewrite as:

x + 4 = 0 and x - 3 = 0

Evaluate the product of both equations

(x + 4) * (x - 3) = 0* 0

This gives

(x + 4)(x - 3) = 0

Express as a function

C(x) = (x + 4)(x - 3)

Hence, the equation of the function is C(x) = (x + 4)(x - 3)

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Answer: Translate circle A using the rule (x + 3y - 1), Dilate circle A by a scale factor of 4

Step-by-step explanation:

You need to first map the centers onto each other, then make the radii equal using a dilation.

to get the equation of any straight line, we simply need two points off of it, so let's use the points in the picture below.

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{9}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}}\implies \cfrac{4}{2}\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{2}(x-\stackrel{x_1}{1})[/tex]

now, if we use the last point from the table, namely (x , 17), we can see that x = x and y = 17, so let's plug those in the equation

[tex](17)-5=2(x-1)\implies 12=2x-2\implies 14=2x\implies \cfrac{14}{2}=x\implies 7=x \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (7~~,~~17)~\hfill[/tex]

Step-by-step explanation:

let x=8 for a small triangle

y=10 for a big triangle

Answer:

Diverge

Step-by-step explanation:

Each successive term is larger than the previous one, so the series will diverge.

The given series can be condensed to

[tex]\displaystyle \frac14 + \frac13 + \frac49 + \frac{16}{27} + \frac{64}{81} + \cdots = \frac14 \left(1 + \frac43 + \frac{4^2}{3^2} + \frac{4^3}{3^3} + \cdots\right) = \frac14 \sum_{n=0}^\infty \left(\frac43\right)^n[/tex]

which is a geometric series with ratio 4/3. Since this ratio is larger than 1, the sequence of partial sums of the series diverges, so the infinite series also diverges.

We can also just the n-th term test:

[tex]\displaystyle \lim_{n\to\infty} \frac14 \left(\frac43\right)^n = \frac14 \lim_{n\to\infty} \frac{4^n}{3^n} = \infty[/tex]

since 4ⁿ > 3ⁿ for all n > 0.

To calculate a patient's heart rate, the doctor must take into account a segment of time, such as a minute, and count the number of times the heart beats in that segment.

Heart rate is a term that refers to the number of heart contractions or beats per unit of time.

Heart rate is usually measured at various points, but most commonly it is measured at the wrist, neck, or chest.

According to the above, the most common way for the doctor to establish the patient's heart rate is to count the heart beats in a segment of time such as one minute.

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60 beats per minute

I got it right on the Kahn Academy Unit Test, trust me <3