a telephone booth 7 ft tall casts a shadow 20 ft long. At the same time, a nearby fire hydrant casts a shadow 8 ft long. Find the height of the fire hydrant

Answer:

Step-by-step explanation:

Exact Form:

[tex]-\frac{21}{8}[/tex]

Decimal Form:

−2.625

Mixed Number Form:

[tex]-2\frac{5}{8}[/tex]

Answer:

(a) 3:4

(b) 3:4

(c) 9:16

Step-by-step explanation:

(a) The ratio of the sides would be 15:20 but after you simplify them (divide by 5), you'd get 3:4

(b) The ratio of the perimeter would be 60:80 because you're multiplying each side length by 4. When you simplify this again (divide by 20), however, it becomes 3:4 again

(c) To find the area, you would multiply the width times height, the ratio would be 225:400. You would get the greatest common factor which is 25 and divide it on both sides to get 9:16

Answer:

4.3

Step-by-step explanation:

Add the numbers and divide by 2 , finding the average, that is

middle number = [tex]\frac{1.5+7.1}{2}[/tex] = [tex]\frac{8.6}{2}[/tex] = 4.3

Answer:

4.3 is the answer

Step-by-step explanation:

(1.5 + 7.1 ) ÷ 2 = 4.3

Answer:

1: height is 28/3 (9 1/3)

2: Base is 25/2 (12 1/2)

3: Height is 59/4 (14 3/4)

Step-by-step explanation:

Since the formula to find the area of a pallelogram is A=base × height

I divided the area by either the Base or the height (depending which one the problem had gave me)

Therefore 147 will be divided by 15 3/4.

Then 140 5/8 will be divided by 11 1/4.

Finally 151 3/16 would be divided by 10 1/4.

Feel free to double check the math btw.

Answer:

Step-by-step explanation:

Factoring the given expression:

Answer:

−5x(3x+2)^2

Step-by-step explanation:

-45x^3-60x^2-20x

Factor out 5.

5(−9x^3-12x^2-4x)

Consider −9x^3-12x^2-4x. Factor out x.

x(−9x^2−12x−4)

Consider −9x^2−12x−4 Factor the expression by grouping. First, the expression needs to be rewritten as −9x^2+ax+bx−4. To find a and b, set up a system to be solved.

a+b=−12

ab=−9(−4)=36

Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 36.

−1,−36

−2,−18

−3,−12

−4,−9

−6,−6

Calculate the sum for each pair.

−1−36=−37

−2−18=−20

−3−12=−15

−4−9=−13

−6−6=−12

The solution is the pair that gives sum −12.

a=−6

b=−6

Rewrite −9x^2−12x−4 as (−9x^2−6x)+(−6x−4).

(−9x^2−6x)+(−6x−4)

Factor out −3x in the first and −2 in the second group.

−3x(3x+2)−2(3x+2)

Factor out the common term 3x+2 by using distributive property.

(3x+2)(−3x−2)

Rewrite the complete factored expression.

5x(3x+2)(−3x−2)

Problem 1

There's not much to say about these. You'll just have to memorize the terms. Note with standard form that the exponents decrease as you move from left to right (2,1,0).

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

Problem 2

Other names for zeros are:

The term "root" is also applicable here.

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

Problem 3

We set each piece equal to 0 and solve for x. This is the zero product property

f(x) = (x-2)(x+4)

0 = (x-2)(x+4)

(x-2)(x+4) = 0

x-2 = 0 or x+4 = 0

x = 2 or x = -4

The two x intercepts are located at (2,0) and (-4,0)

Answer: Choice C

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

Problem 4

In the last problem, we found the two roots were x = 2 and x = -4

I'll let p = 2 and q = -4.

Average the roots to get (p+q)/2 = (2+(-4))/2 = -2/2 = -1

This is the x coordinate of the vertex. So h = -1

Plug this into the function to find k, which is the y coordinate of the vertex.

k = f(h)

k = f(-1)

k = (-1-2)(-1+4)

k = (-3)(3)

k = -9

The vertex is located at (h,k) = (-1, -9)

This is another way of saying the vertex is when x = -1 and y = -9

Answer: Choice C

9514 1404 393

Answer:

  7.5 m

Step-by-step explanation:

The cosine relation applies.

  Cos = Adjacent/Hypotenuse

  cos(60°) = (distance to wall)/(15 m)

  distance to wall = (15 m)cos(60°) = (15 m)(1/2) = 7.5 m

The foot of the ladder is 7.5 m from the wall.

Answer:

[tex]\tt{}10x[/tex]

Step-by-step explanation:

[tex]\tt{}2x + 3x + 5x[/tex]

[tex]\tt{}(2 + 3 + 5)x[/tex]

[tex]\tt{}10x[/tex]

Answer:

Step-by-step explanation:

An improper fraction is a fraction that the numerator is greater than the denominator. As for a mixed fraction, that is a whole number with a fraction next to it.

Answer:

y = 2327.49 ---> 25 hrs

starting plot points (0,640) and ending (25, 2327.49)

Step-by-step explanation:

b = 640

r = 5.3% = 0.053

t = 25

y = 640 ( 1 + 0.053)^25

y = 640 ( 1.053)^25

y = 2327.49 ---> 25 hrs

starting plot points (0,640) and ending (25, 2327.49)

Answer:

1. 70

2. 54

3. 54

4. 40

Step-by-step explanation:

Answer:

210:28

Step-by-step explanation:

Answer:

18 More Minutes

Step-by-step explanation:

Hi,

I think I can help.

What I would first do here is try to find the value of 10% relative to the 12 minutes. If we find what 10% is we can multiply that to get 100% to find the total amount of minutes he wants to study. We can then subtract the time already studied to find our answer.

To do this we want to take the 40% we have and find 10. We can do 40/4 to find this since 40 divided by 4 is actually 10.

But if we do this we also have to do with to the number it is relating to / representing. Which is 12. (12 minutes = 40%)

So we can do :

40 / 4

=

10%

Also

12 / 4

=

3

So with this we can conclude that 10% of his total time is 3 minutes.

Now lets multiply this by 10 to get the 100% we are looking for so we can get the total amount of time he spent studying.

So :

10% x 10

=

100%

3 x 10

=

30 minutes

So his total time is 30 minutes of studying, but we have to find how many more minutes after his 12.

We can now simply take the total time and take off the time spent already to find this answer :

30 - 12

=

18 minutes

That is your answer, he needs to study 18 more minutes.

I hope this helps!

If you have any questions or concerns please comment or message me! :)

Answer:

122 times

Step-by-step explanation:

20+102=122

(what is this question lol)

Answer:

Well. Depending on Sam's age, she could've been kissed many times. Not just boy her bf or bestie, anyone could kiss her throughout her life time. Your question is very vague and can have many answers. But I'll take a guess and say she was kissed more than 122 times.

Step-by-step explanation:

life.

9514 1404 393

Answer:

  629 kilopascals

Step-by-step explanation:

The tire pressure is given by the exponential function ...

  p(t) = 900·0.95^t

where t is in minutes and p is in kilopascals.

  p(7) = 900·0.95^7 ≈ 629 . . . . kilopascals

Answer:

The answer is 1080°

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

Delta math

The measure of the angle G will be equal to 27.50°.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry. The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that in ΔFGH, f = 880 inches, g = 450 inches, and h=890 inches.

The value of the angle G will be calculated as,

g² = h² + f² -2hfcosG

450² = (890)² + (880)² - 2(890)(880)cosG

202500 = 792100 + 774400 + 1566400cosG

cosG = ( 1364000) / ( 12 x 890 x 880 )

cosG = 0.87

G = cos⁻¹(0.87)

G = 27.50°

Therefore, the measure of the angle G will be equal to 27.50°.

To know more about Trigonometry follow

https://brainly.com/question/24349828

#SPJ5

Answer:

a) 1/25

b) 4/25

Step-by-step explanation:

Answer:

Each cube with side lengths of 1/4 have a volume of (1/4)3 which means each cube's volume is 0.015625 cubic units. To find how many cubes are needed to fill the prism, divide 3 cubic units by 0.015625 cubic units. Your answer will be 192 cubes.

Step-by-step explanation: Furthermore, how many 1/4 unit cubes does it take to fill the prism? Each cube with side lengths of 1/4 have a volume of (1/4)3 which means each cube's volume is 0.015625 cubic units. To find how many cubes are needed to fill the prism, divide 3 cubic units by 0.015625 cubic units. Your answer will be 192 cubes. you welcome

Answer:

r=0

Step-by-step explanation:

1) Place point (2, 3) on graph.

2) Use the slope of -1 to go left -1 and go down -1

3) Until you get to x value of -1

Answer:

Abdullah is correct.

Step-by-step explanation:

The bottle contained originally 12 fl oz, so 12 fl oz is 100%.

The box now contains 20% more, so now it contains 120% of 12 fl oz.

120% * 12 fl oz = 1.2 * 12 fl oz = 14.4 fl oz

Also, 20% is 1/5. Abdullah divided 12 oz into 5 equal parts, and then he added one more 1/5. He interpreted the problem correctly. The amount in the new bottle is the amount of the old bottle plus 20% of that old amount.

Kanna considers the original amount to be 80%. When he adds another 20%, he is adding 1/4 of 12 which is too much. That is why he gets an incorrect answer that is to high. He interpreted the problem incorrectly. For him, the old bottle has 20% less than the new bottle. That is incorrect.

Abdullah is correct.

Answer:

This is some ton of work LOL

Step-by-step explanation:

A. 4/7×5/5=20/35  We multiply by 5 for A because 35÷5=7 and you need to multiply top and bottom. You can NOT forget that. We do not need to simplify something this time? 3/5X7/7=21/35. Why are we muliplying something new? figure out. no need to simplify. oBVIOUSLY 3/5 IF BIGGER

B. As usual etc...

Answer:

x = no. of quarters

3x = no. of dimes

3x + 11 = no. of nickels

2(3x + 11) = no. of pennies

340 quarters

1020 dimes

1031 nickels

2062 pennies

Step-by-step explanation:

x = no. of quarters

3x = no. of dimes

3x + 11 = no. of nickels

2(3x + 11) = no. of pennies

x + 3x + 3x + 11 + 2(3x + 11) = 4453

x + 3x + 3x + 11 + 6x + 22 = 4453

13x + 33 = 4453

13x = 4420

x = 340 quarters

3x = 1020 dimes

3x + 11 = 1031 nickels

2(3x + 11) = 2062 pennies

Check:  340 + 1020 + 1031 + 2062  = 4453

Answer:

x>7

Step-by-step explanation:

7x +5 > 2x +35

-2x -5  -2x

5x>35

x>7

Answer:

Using trigonometric identities: A trigonometric identity is a relationship between trigonometric functions that we can use to find an exact value of a trigonmetric function.Using the unit circle: The unit circle is a circle with its center at the origin and a radius of 1 unit. If we place an angle, θ, with its initial side along the positive x-axis, then the point where the angle's terminal side intersects the unit circle is (cos(θ), sin(θ)).Using reference angles: Reference angles are the smallest angle that the terminal side of an angle makes with the x-axis. As it turns out, trigonometric functions of an angle and its reference angle have the same value, except that they may have different signs.

For example, suppose we want to find the exact value of tan(405°). First, we take a look at the angle 405° on a graph with the unit circle:

in this that the reference angle of 405° is 45°. We can use the fact that tangent is positive in the first quadrant and the rule for reference angles to deduce that tan(405°) = tan(45°). Then we can use the well-known fact that tan(45°) = 1 to get that tan(405°) = 1.

Step-by-step explanation:

Answer:

hope this helps :)

Step-by-step explanation:

Commutative property of addition: Changing the order of addends does not change the sum. For example, 4 + 2 = 2 + 4 4 + 2 = 2 + 4 4+2=2+44, plus, 2, equals, 2, plus, 4.

Answer: Commutative property of addition: Changing the order of addends does not change the sum. For example, 4 + 2 = 2 + 4 4 + 2 = 2 + 4 4+2=2+44, plus, 2, equals, 2, plus, 4.

if this makes sense

Answer:

2

Step-by-step explanation:

Vertex means point where three edges meet . Two middle figures have vertices