If a 40 foot tree cast a 12 foot shadow find the length of the shadow cast by a 27 foot tree

Answer:

15 dollars

Step-by-step explanation:

Postulate SAS can be used to prove triangle [tex]ABC[/tex] is congruent to triangle [tex]AED.[/tex]

" Triangle is defined as the two dimensional closed figure with three vertices, three sides, and three angles enclosed in it."

According to the question,

Given,

In triangle [tex]ABC[/tex] and [tex]AED[/tex]

[tex]\angle ADE = 120\° \ \ \ \ \ \ \ \ \ (1)[/tex]

[tex]\angle ACD = 60\°\\\\\angle ACD + \angle ACB = 180\° (linear \ pair)\\\\\implies \angle ACB = 180\° -60\°\\\\\implies \angle ACB = 120\° \ \ \ \ \ \ \ \ \ \ (2)[/tex]

From [tex](1)[/tex] and [tex](2)[/tex] we get

[tex]\angle ADE \cong \angle ACB[/tex]

[tex]AC \cong AD\\\\BC \cong ED[/tex]

By SAS postulate ,

Triangle ABC is congruent to triangle AED.

Hence, Option 3 is the correct answer.

Learn more about triangle here

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Answer:

Step-by-step explanation:

The formula of a volume of a rectangular prism:

V = lwh

The fomula of a surface area of a rectangular prism:

SA = 2(lw + lh + wh)

l - length

w - width

h - height

We have l = 10cm, w = 6.5cm and h = 8.3cm. Substitute:

V = (10)(6.5)(8.3) = 539.5 cm³

SA = 2[(10)(6.5) + (10)(8.3) + (6.5)(8.3)] = 2(65 + 83 + 53.95)

= 2(201.95) = 403.9 cm²

Answer:

Part 1) The measure of angle C is 90°

Part 2) The measure of angle B is 35°

Part 3) The measure of angle A is 55°

Step-by-step explanation:

we know that

The inscribed angle is half that of the arc it comprises.

step 1

Find the measure of angle C

The diameter divide the circle into two equal parts

so

If AB is a diameter

arc AB=180°

∠C=(1/2)[arc AB]

∠C=(1/2)[180°]=90°

step 2

Find the measure of angle B

arc AC=70°

∠B=(1/2)[arc AC]

∠B=(1/2)[70°]=35°

step 3

Find the measure of angle A

The sum of the internal angles of a triangle must be equal to 180 degrees

so

∠A+∠B+∠C=180°

substitute

∠A+35°+90°=180°

∠A=180°-(35°+90°)

∠A=55°

Answer:

D. 0.43, because 13 of the 30 days were cloudy

Step-by-step explanation:

The fist thing that you should do is divide 100 by 30.  We will do this so taht our percentages add up to 100.  When we do this we get 3.333.  Next we need to multiply this by the nubert of cloudy days 13 to get the answer D.

Answer:

26.78

Step-by-step explanation:

350 * .0765

Answer: it’s definetly C

Step-by-step explanation:

The answer is C.

Hope this helps!

96cm

The area of the rectangle is 72 (6 x 12)

The base of the left triangle is six and the height is six. Base x height is 36. 36/2 is 18.

The base of the right triangle is 2 and the height is 6. 6 x 2 is 12. 12/2 is 6.

6 plus 18 plus 72 is 96, which is the final answer.

ANSWER

[tex]96 {cm}^{2} [/tex]

EXPLANATION

The area of a tra-pezoid is calculated using the formula:

[tex]Area = \frac{1}{2} ( \: sum \: of \: bases )\: \times \: h[/tex]

[tex]Area = \frac{1}{2} ( \: sum \: of \: bases )\: \times \: h[/tex]

From the tra-pezoid

[tex] \tan(45 \degree) = \frac{6}{x} [/tex]

[tex]x = \frac{6}{\tan(45 \degree) } [/tex]

[tex]x = \frac{6}{1} = 6[/tex]

[tex]Area = \frac{1}{2} ( 12 + 20 )\: \times \: 6[/tex]

[tex]Area = \frac{1}{2} ( 32)\: \times \: 6[/tex]

[tex]Area =16 \times 6 = 96 {cm}^{2} [/tex]

ANSWER

D.

[tex]9 {y}^{2} - 4 {x}^{2}- 36y + 16x - 16 = 0[/tex]

EXPLANATION

The standard equation of the hyperbola is

[tex] \frac{ {(y - 2)}^{2} }{4} - \frac{ {(x - 2)}^{2} }{9} = 1[/tex]

We multiply through by 36 to obtain:

[tex]9 {(y - 2)}^{2} - 4( {x - 2)}^{2} = 36[/tex]

We now expand to get,

[tex]9( {y}^{2} - 4y + 4) - 4( {x}^{2} - 4x + 4) = 36[/tex]

Expand :

[tex]9 {y}^{2} - 36y + 36 - 4 {x}^{2} + 16x - 16 = 36[/tex]

To get the general form, we equate everything to zero to get,

[tex]9 {y}^{2} - 4 {x}^{2}- 36y + 16x - 16 = 0[/tex]

The correct choice is D.

Answer:

m = ($55,000 - $40,000)/(9 - 3)

= $15,000/6 = $2,500

A salesperson's salary will increase by about $2,500 per year of employment.

So in a gallon there is 4 quarts, and in 1 quart there are 2 pints and in 1 pint there are 2 cups.

So for the 1 quart of onion that would equal 4 cups. Then for the 4 pints of broth there would be 8 cups and then the 6 cups and 2 cups just stay the same. So if you add those number of cups up you would get 20 cups. Divide that by 4 to see how many bowls she would need.

The answer is she would need 5 bowls

The equation that matches the function shown in the graph is y = 2x + 4

Which equation matches the function shown in the graph?

From the question, we have the following parameters that can be used in our computation:

The graph

A linear equation is represented as

y = mx + c

Where

m = slope

c = y-intercept

From the graph, we have the point (0, 4)

This means that

c = 4

So, we have

y = mx + 4

Using the point (-2, 0) on the graph, we have

-2m + 4 = 0

This gives

2m = 4

m = 2

Recall that

y = mx + 4

So, we have

y = 2x + 4

Hence. the equation is y = 2x + 4

Answer:

Part 1) [tex]42=\frac{1}{2}x(x-5)[/tex]

Part 2) The length of the base is [tex]x=12\ m[/tex]

Step-by-step explanation:

Part 1) Which equation would be help solve the following problem?

Let

x----> the length of the base of a triangle

y----> the height of a triangle

we know that

The area of a triangle is

[tex]A=\frac{1}{2}xy[/tex]

[tex]A=42\ m^{2}[/tex]

so

[tex]42=\frac{1}{2}xy[/tex] ------> equation A

[tex]y=x-5[/tex] -----> equation B

Substitute equation B in equation A  

[tex]42=\frac{1}{2}x(x-5)[/tex]

Part 2) Find the length of the base

we have

[tex]42=\frac{1}{2}x(x-5)[/tex]

solve for x

[tex]84=x^{2}-5x\\x^{2}-5x-84=0[/tex]

Solve the quadratic equation by graphing

The solution is [tex]x=12\ m[/tex]

see the attached figure

Answer:

125.66 in. ³

Step-by-step explanation:

2 × π × r × h  +  2 × π × r²

We only know the length of the diameter, but we have to find the radius. So we divide by 2 because the radius is half the diameter.

4 ÷ 2 = 2

So r = 2.

h = 8

2 × π × r × h

2 × 3.14 × 2 × 8 = 100.48

2 × π × r²

2 × 3.14 × 2²

2 × 3.14 × 4 = 25.12

Now add them up.

100.48 + 25.12 = 125.66

Hope this helps... :)

The formula for volume of a sphere is 4/3 x PI x r^3

Solve for r:

288PI = 4/3 x PI x r^3

Divide both sides by PI:

288 = 4/3 x r^3

Divide both sides by 4/3:

216 = r^3

Take the cubic root of 216 for r:

r = ∛216

r = 6

The radius is 6 cm.

Answer:

The price per pound was $0.88

Step-by-step explanation:

If $1.10--------------> 1.25 Pounds

     x <---------------  1 Pound

x = ($1.10)(1 Pound)/1.25 Pound

x = $0.88

Answer:     2 to 1          and          2;1

Step-by-step explanation:

in general there are 3 ways to write these ratios. A fraction, the one using to, and the ones with semicolans. This is how you will always want to write your ratios on the problems you are solving with your ratios when it asks that.

Answer:

[tex]\frac{2}{1}, 2:1,[/tex]2

Step-by-step explanation:

We can actually use three forms here.

[tex]\frac{x}{y}[/tex]

[tex]x:y[/tex]

x to y.

Use the format for a ratio.

[tex]x:y[/tex]

So

[tex]x=2 \\ y = 1[/tex]

Now we can plug in.

[tex]\frac{2}{1} \\ \\ 2:1 \\ \\[/tex]

2 to 1

Answer:

10

Step-by-step explanation:

Divide 640 by 64 to find 1/64.

640/64=10

Or multiply 1/64*640=10

Answer:

12:15

16:20

Step-by-step explanation:

Note that what you multiply to one side, you multiply to the other (same with dividing) for ratios.

4:5 => 4 * 3: 5 * 3 = 12:15

4:5 => 4 * 4: 5 * 4 = 16:20

~

Answer:

12:5 and 16:20 are equalevent to 4:5

Step-by-step explanation:

12 divided by 3 = 4 (Because 3 x 4 = 12)

15 ÷ 3 =5 (because 5 x 3 = 15, we basicly raised the ration by a scale factor of 3)

12:15 = 4:5

16 ÷ 4 = 4 (because 4 x 4 = 16)

20 ÷ 4 = 5 (4 x 5 = 20 This ratio was raised by a scale factor of 4)

16 : 20 = 4:5

12:5 and 16:20

Hope this helped!

Answer:  Best described as a fixed amount of income that is paid to an someone weekly, every other week, or on a  monthly basis. it could also be described as annual earnings paid out over a year.

Step-by-step explanation:

You can see by the image how did I get the answer

Answer:

78%

Step-by-step explanation:

Answer:Hello there!

2y + 4 = 0

2y = -4

y = -2

My assumption is that you'd graph this as a horizontal line at (0,-2) but PLEASE double check with your teacher/instructor because I'm not sure if I'm right.

Hope this helped!

Step-by-step explanation:

Answer:

Step-by-step explanation:

You'll need to share the graphs mentioned in this problem statement.

One can solve  2y + 4 = 0  for y and thus obtain an equation which is easy to graph:

2y + 4 = 0 becomes

2y = -4, or

 y = -2

The graph of this function is the horizontal line y = -2.  Find (0, -2) on your set of coordinate axes and plot a dark dot there.  Then draw a horizontal line thru it.  This line has a slope of zero (0) and a y-intercept of -2.

Answer:

8

Step-by-step explanation:

7m+8=8m

7m-8m= -8

Whenever you move a number for the opposite side , you change the sign. For example, the number is 6 , then you move it to the other side. The sign becomes negative 6.

-m=-8

The m cannot be a negative sign. So you multiply it by -1 and for -8.

-1(-m)= -1(-8)

m= 8

Double check answer if you want to:

7m+8=8m

Substitute the answer for m.

7(8)+8=8(8)

64=64

So the answer is correct. m=8

Answer:

Step-by-step explanation:

first draw you line down on the equal sign take 2x and devide itso it should be 14/2 you should get 7 2x is no longer there then bring down 9y and add d to 14 thats 23 so its x =23

We need to solve for x.

2x - 9y = 14

Move the 9y to the right side and use inverse operations.

2x = 14 + 9y

Divide both sides of the equation by 2.

x = 7 + 9/2y or x = 7 + 4.5y

I will attach a picture of the graph as well in case that’s what you were looking for.

Answer:

see attached picture

Step-by-step explanation:

I got this by using the free app desmos, you should check it out!

answer for this question is 3.85 units squared

Answer:

[tex]\boxed{\text{38.5 units}^{2}}[/tex]

Step-by-step explanation:

The polygon is a trapezoid on its side.

The formula for the area of a trapezoid is  

A = ½(a + b)h,

where a and b are the lengths of the parallel sides and h is the distance between them.

AD = a = 2 – (-2) = 2 + 2 = 4 units

BC = b = 2 – (-5) = 2 + 5 = 7 units

AB = h = 3 – (-4) = 3 + 4 = 7 units

A = ½(4 + 7) × 7 = ½ × 11 × 7 = 38.5 units²

[tex]\boxed{\text{A = 38.5 units}^{2}}[/tex]

[tex]\text{Hey there!}[/tex]

[tex]\text{Distribute the value of 7 in each of your terms}[/tex]

[tex]\text{(2x}^3+\text{3y}^2)(7)[/tex]

[tex]\text{2x}^3\times7=\text{14x}^3[/tex]

[tex]\text{3y}^2\times7=\text{21y}^2[/tex]

[tex]\text{We cannot combine like terms because they AREN'T any in this equation}[/tex]

[tex]\boxed{\boxed{\bf{Answer:14x^3+21y^2}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

[tex]a=2x^3[/tex] and [tex]b=3y^2[/tex]

Step-by-step explanation:

The given binomial expression is:  [tex](2x^3+3y^2)^7[/tex]

A standard binomial expression is like  [tex](a+b)^n[/tex]

Comparing the given expression with the standard binomial expression.....

[tex](a\ \ +\ \ b)^n \Longleftrightarrow (2x^3\ +\ 3y^2)^7\\ \\ So,\ \ a=2x^3\\ \\ and\ \ b=3y^2[/tex]

Answer:

D.) 1237 spots

Step-by-step explanation:

We have been given the following regression line;

y= 89.5 + 0.409x

It is reasonable to argue that the number of commuters determines the number of parking spots and as such commuters is our explanatory variable (x). On the other hand, the number of parking spots is our response or dependent variable (y).

We are required to predict the number of parking spots at the Metro-North Station of Greenwich which has 2804 commuters. We are simply asked to determine the value of y when x is 2804 using the regression line;

y = 89.5 + 0.409(2804)

y = 1236.336

y = 1237

Equation of line is doubling