Consider this scaled figure of a swimming pool. The dimensions of the original pool are 24 feet wide by 36 feet long. A rectangle has a width of 6.4 feet and a width of question mark feet. Use the measurements of the original and of the scaled figure to find the scale factor and the missing length. What is the scale factor? What is the missing length of the scale model?

Answer:

cosine = adjacent / hypotenuse

cosine (62) = x / 12

x = 12 * 0.46947

x = 5.6

Step-by-step explanation:

Answer:

2250m

Step-by-step explanation:

Step 1

Since

Hence,

tan x = 3/4

tan y=5/7

tan x = BA/ CA where BA = height and CA = distance

3/4 = h/ d

4h = 3d

h = 3d/4.......... Equation 1

tan y = BA / DA + 150m

5/7 = h/d + 150

7 × h = 5(d + 150)

7h = 5d + 750............ Equation 2

Since h = 3d/4

7(3d/4) = 5d + 750

21d/4 = 5d + 750

Multiply both sides by 4

21d = 4(5d + 750)

21d = 20d + 3000

21d -20d = 3000

d = 3000

Distance (d) = 3000m

Substitute 3000m for d in equation 1

h = 3d/4

h = 3 × 3000/4

h = 2250m

Answer:

Step-by-step explanation:

[tex]tangent=\dfrac{opposite}{adjacent}[/tex]

We have:

[tex]\tan x^o=\dfrac{3}{4}\\\\\tan y^o=\dfrac{5}{7}[/tex]

By definition of tangent, we have:

[tex]\tan x^o=\dfrac{AB}{AC}\\\\\tan y^o=\dfrac{AB}{AC+150}[/tex]

Therefore we have the system of equations:

[tex]\left\{\begin{array}{ccc}\dfrac{AB}{AC}=\dfrac{3}{4}&(1)\\\\\dfrac{AB}{AC+160}=\dfrac{5}{7}&(2)\end{array}\right[/tex]

From (1)

[tex]\dfrac{AB}{AC}=\dfrac{3}{4}[/tex]             cross multiply

[tex]3AC=4AB[/tex]         divide both sides by 3

[tex]AC=\dfrac{4AB}{3}[/tex]

Substitute it to (2):

[tex]\dfrac{AB}{\frac{4AB}{3}+150}=\dfrac{5}{7}\\\\\dfrac{AB}{\frac{4AB}{3}+\frac{3\cdot150}{3}}=\dfrac{5}{7}\\\\\dfrac{AB}{\frac{4AB}{3}+\frac{450}{3}}=\dfrac{5}{7}\\\\\dfrac{AB}{\frac{4AB+450}{3}}=\dfrac{5}{7}\\\\AB\cdot\dfrac{3}{4AB+450}=\dfrac{5}{7}[/tex]

[tex]\dfrac{3AB}{4AB+450}=\dfrac{5}{7}[/tex]            cross multiply

[tex](3AB)(7)=(5)(4AB+450)\\\\21AB=(5)(4AB)+(5)(450)[/tex]

[tex]21AB=20AB+2250[/tex]         subtract 20AB from both sides

[tex]AB=2250[/tex]

Such a tower height is rather impossible, but this is the solution.

Step-by-step explanation:

tan(37) = x/3

x=tan(37)*3

Answer:

I don't know what general 5' form means, but I'm guessing that means slope-intercept form, the easiest form of a linear equation. So we can use the equation for this is y = mx+b. M being slope, and b is the y-intercept. So that means that we will get an answer of:

y = 1x+5, you spelled 1 wrong so I just correct it.

Answer:

x = -2

y = 3

Step-by-step explanation:

You are given a system of two linear equations:

-2x + 3y = 13

3x + 4y = 6

One of the good ways to solve this system is trying to eliminate one variable (x or y), calculate the remaining variable and substitute the calculated variable back into system to solve for eliminated variable.

Here, we will manipulate the original system, so that we can easily eliminate x.

Let's multiply both sides of the first equation by 3 and the second equation by 2 (this manipulating step does not change the original system of equations).

3*(-2)x + 3*3y = 3*13

2*3(x) + 2*4y = 2*6

<=>

-6x + 9y = 39

6x + 8y = 12

Now, we add up two equations, left side + left side, right side + right side, we obtain:

-6x + 9y + 6x + 8y = 39 + 12

or

17y = 51

We divide both sides of equation by 17, to get y.

=> y = 51/17 = 3

Substitute y = 3 back into the first equation of system (or the second equation, it doesn't matter, here we choose the first one).

=> -2x + 3*3 = 13

=> -2x + 9 = 13

=> -2x = 4

=> x = -2

=> The solution of this system is (x, y) = (-2, 3)

Hope this helps!

:)

Answer:

B

Step-by-step explanation:

The correct answer is CPI. It shows the average price over time paid by consumers.

Hope this helps! (Please consider giving brainliest)

P.S: This is not a mathematics question.

The economic indicator measures inflation among the options given is: C. unemployment rate

CPI (Consumer Price Index) is the appropriate economic indicator for assessing inflation as it monitors price fluctuations of a designated basket of goods and services, giving insights into average price changes.

Conversely, GDP (Gross Domestic Product) quantifies the total value of goods and services produced in an economy, while the unemployment rate measures the percentage of the labor force without jobs.

Therefore, the answer is: C. unemployment rate

Learn more about inflation on:

https://brainly.com/question/21586910

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Answer:

$123.45+$36.55

= $160

Step-by-step explanation:

Answer:

a.114.4kg

b. 486kg

Step-by-step explanation:

Firstly , we want to know the value with which the apples weigh more than the oranges

To calculate this, we simply subtract the weight of the oranges from that of the apple

Mathematically, that would be ;

300.2-185.8 = 114.4kg

The total weight of the things bought is calculated by adding both weights together

That would be 185.8 + 300.2 = 486 kg

Answer:

x = 1.5 when y = 3

Step-by-step explanation:

You can put this in a ratio:

x    :    y

5    :   10

1.5  :    3

x is 1.5 when y is 3.

Answer:

314.16 m

Step-by-step explanation:

The distance across the track is 100 metres. This means that the diameter is 100 m.

The track is circular, so, we need the circumference.

The circumference of a circle is given as:

C = πD

where D = diameter

Therefore, the circumference of the track is:

C = π * 100 = 314.16 m

She walked a distance of 314.16 m

Answer:

A. 6 x + 5

B. 2 x + 6

C. 8 x - 2

D. 5 x - 8

Step-by-step explanation:

Given: division expressions

To find: quotient of each of the division expressions

Solution:

Use formula: [tex]\left ( \frac{x^m}{x^n} \right )=x^{m-n}[/tex]

A.

[tex]\frac{18x^2+15x}{3x}=\frac{18x^2}{3x}+\frac{15x}{3x}=6x^{2-1}+5=6x+5[/tex]

B.

[tex]\frac{16x^2+48x}{8x}=\frac{16x^2}{8x}+\frac{48x}{8x}=2x^{2-1}+6=2x+6[/tex]

C.

[tex]\frac{56x^2-14x}{7x}=\frac{56x^2}{7x}-\frac{14x}{7x}=8x^{2-1}-2=8x-2[/tex]

D.

[tex]\frac{20x^2-32x}{4x}=\frac{20x^2}{4x}-\frac{32x}{4x}=5x^{2-1}-8=5x-8[/tex]

Answer:

A.[tex]\frac{18x^2+15x}{3x}=6x+5[/tex]

B.[tex]\frac{16x^2+48x}{8x}=2x+6[/tex]

C.[tex]\frac{56x^2-14x}{7x}=8x-2[/tex]

D.[tex]\frac{20x^2-32x}{4x}=5x-8[/tex]

Step-by-step explanation:

A.[tex]\frac{18x^2+15x}{3x}[/tex]

[tex]\frac{3x(6x+5)}{3x}[/tex]

=[tex]6x+5[/tex]

[tex]\frac{18x^2+15x}{3x}=6x+5[/tex]

B.[tex]\frac{16x^2+48x}{8x}[/tex]

=[tex]\frac{16x(x+3)}{8x}[/tex]

[tex]=2(x+3)[/tex]

[tex]=2x+6[/tex]

[tex]\frac{16x^2+48x}{8x}=2x+6[/tex]

C.[tex]\frac{56x^2-14x}{7x}[/tex]

[tex]=\frac{14x(4x-1)}{7x}=2(4x-1)=8x-2[/tex]

[tex]\frac{56x^2-14x}{7x}=8x-2[/tex]

D.[tex]\frac{20x^2-32x}{4x}[/tex]

=[tex]\frac{4x(5x-8)}{4x}=5x-8[/tex]

[tex]\frac{20x^2-32x}{4x}=5x-8[/tex]

Answer:

  15% less than its regular price

Step-by-step explanation:

If the toy is marked down 15% in June, its cost during June is 15% less than its regular cost. (It will be 85% of its regular cost.)

Answer:

A =12.92 cm^2

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh where b is the base and h is the height

A = 1/2 ( 7.6) ( 3.4)

A =12.92 cm^2

Answer:

[tex] = 12.92 {cm}^{2} [/tex]

Step-by-step explanation:

[tex]area = \frac{1}{2} \times b \times h \\ = \frac{1}{2} \times 7.6 \times 3.4 \\ = \frac{25.84}{2} \\ = 12.92 {cm}^{2} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

39.0953=39cm2

Step-by-step explanation:

Minor arc =70

Angle of arc=70

Then this sector =70/360=7/36 of the circle

Then area = 7/36x3.14x8x8=39cm2 approximatly

Answer:49882

when I put a number over a number it means I can't put the whole number inside the answer line so I toke out the last number and put it in

5 0 9

× 9 8

45810. this is from multiplying with the nine

+ 4062. this is from multiplying with the right

49882 this is the answer

u had to add the two answer and that's how I got 49882

Answer:

2 ( 2d -3)(2d+3)

Step-by-step explanation:

8d^2 - 18

Factor out the greatest common factor 2

2(4d^2 -9)

Rewriting the terms in parentheses

2 (( 2d)^2 - 3^2)

We recognize that this is the difference of squares ( a^2 - b^2) = (a-b)(a+b)

2 ( 2d -3)(2d+3)

Answer:

[tex]2(2d-3)(2d+3)[/tex]

Step-by-step explanation:

[tex]8 {d}^{2} - 18 \\ 2(4 {d}^{2} - 9)

=2(2d-3)(2d+3) [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

The least possible number of hours you can work at your office job is 20.

Step-by-step explanation:

$12/h ----> office

$10/h ----> babysitting

"o" -----> hours office job

"b" -----> hours babysitting job

[tex]12x + 10y = 440\\x + y \leq 40\\12x + 10y = 440 -----> 6x + 5y = 220 ----> y = \frac{220-6x}{5} \\\\x + y \leq 40\\x + \frac{220-6x}{5} \leq 40\\5x + 220 - 6x \leq 200\\x \geq 20[/tex]

Answer:

-136x

Step-by-step explanation:

Pls brainliest

Answer:

Step-by-step explanation:(2ñ-4)90

(7×2-4)90

=900°

900-(162+125+148+105+98+115)

900-753

=147°

ANSWER:

:2/5 * 560 = D) 224

Answer:

work is shown and pictured

Answer:

I think it's A but I'm not sure

Answer: pretty sure it's this

Step-by-step explanation:

Answer:

1.Corresponding angles theorem

2.Linear postulate

3.By the definition of supplementary angles

Step-by-step explanation:

We are given that  

[tex]w\parallel x \ and \ y[/tex] is a transversal.

We have to prove [tex]\angle 3[/tex] and [tex]\angle 5[/tex] are supplementary

Proof:

1.Given that [tex]w\parallel x \ and \ y[/tex] is a transversal.

We know that [tex]\angle 1\cong \angle 5[/tex]

Reason:Corresponding angles theorem

Therefore, [tex]m\angle 1=m\angle 5[/tex]

by the definition of congruent.We also know that, by definition, angle 3 and angle 1 are a linear pair.

Therefore, they are supplementary by linear pair postulate

By the definition of supplementary angles

[tex]m\angle 3+m\angle 1=180^{\circ}[/tex]

Now, we can substitute [tex]m\angle 5=m\angle 1[/tex]

Then, we get

[tex]\m\angle 3+m\angle 5=180^{\circ}[/tex]

Therefore, by the definition of supplementary angles,angle 3 and angle 5 are supplementary

Answer:

1. Corresponding angles theorem

2. Linear pair postulate

3. Definition of supplementary angles

Answer:

540 degrees

Step-by-step explanation:

Answer:

X=7

Step-by-step explanation: I

63-14=7x

7x=49

x=7

Answer:

C

Step-by-step explanation:

Given

V = πr²h

Isolate h by dividing both sides by πr²

[tex]\frac{V}{\pi r^2}[/tex] = h → C

Answer:

27

Step-by-step explanation:

he started by cutting one log into 3

1×3=3

then cutting each of those into 3

3×3=9

then again

9×3=27

Answer:-5-1 c

Step-by-step explanation:

Answer:

2 imaginary solutions

Step-by-step explanation: