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3 years ago

A 10 foot pole casts a 15 ft shadow. At the same time, a tree casts a 24 foot shadow. How tall is the tree

Mathematics

2 answers:

Ludmilka [50]3 years ago

7 0

1. Set up a ratio for the pole comparing height to shadow length:

10 feet tall / 15 feet shadow

2. Set this ratio equal to a similar ratio for the tree:

$\dfrac{10 \text{ feet tall}}{15 \text{ feet shadow}} =\dfrac{x \text{ feet tall}}{24 \text{ feet shadow}}$

3. Solve the equation by multiplying by 24 on both sides of the equation:

$24 \cdot \dfrac{10}{15} = x$

x = 16 feet

hichkok12 [17]3 years ago

4 0

Answer:

Step-by-step explanation:

10=15

24=x

cross multiply

24×15=410

410÷10=41

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(x+16)²=12 plz help me and show work

Readme [11.4K]

Answer:

The answer is $x=-16$ ± $2\sqrt{3}$ in exact form or $x=-12.535898$ , $x=-19.464102$ in decimal form.

Step-by-step explanation:

To solve this problem, start by moving all terms to the left side of the equation and simplify. Simplify the equation by subtracting 12 from both sides of the equation and squaring $x+16$ , which will look like $x^{2} +32x+256-12=0$ . Next, simplify the equation again, which will look like $x^{2} +32x+244=0$ .

Then, use the quadratic formula to find the solutions. The quadratic formula looks like $\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}$ .

For this problem, the quadratic variables are as follows:

$a=1$

$b=32$

$c=244$

The next step is to substitute the values $a=1$ , $b=32$ , and $c=244$ into the quadratic formula and solve. The quadratic formula will look like $\frac{-32(+-)\sqrt{32^2-4(1*244)} }{2*1}$ . To simplify the equation, start by simplifying the numerator, which will look like $x=\frac{-32(+-)4\sqrt{3} }{2*1}$ . Then, multiply 2 by 1 and simplify the equation, which will look like $x=-16(+-)2\sqrt{3}$ . The final answer is $x=-16$ ± $2\sqrt{3}$ in exact form. In decimal form, the final answer is $x=-12.535898$ , $x=-19.464102$ .

6 0

3 years ago

5. What is the volume of the right triangular prism?

kompoz [17]

5. C

V = 0.5 • 12 • 8 • 4 = 192

6. G

V = (1/3) 6x^2 • 6 • 8 = 96x^2

3 0

3 years ago

Troy’s canoe is 18 feet long. Ariel’s canoe is the length of Troy’s canoe.

tankabanditka [31]

Well the answer i think is going to be 18

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4 years ago

Read 2 more answers

Eli and Angela are saving money to buy their grandparents an anniversary gift. Eli has saved 8 more than 1/3 of Angela's savings

Trava [24]

Answer:

$10

Step-by-step explanation:

Let a = the amount Angela has saved.

Let e = the amount Eli has saved.

"Eli has saved $8 more than 1/3 of Angela's savings."

e = a/3 + 8

"If they each save $10 more." then

Eli will have: e + 10

Angela will have a + 10

"Eli will have saved $4 more than Angela's savings."

e + 10 = a + 10 + 4

This equation simplifies to: e = a + 4

We have a system of two equations in two variables.

e = a/3 + 8

e = a + 4

Since both equations are solved for e, we just equate the right sides.

a/3 + 8 = a + 4

Subtract a/3 from both sides. Subtract 4 from both sides.

a/3 - a/3 + 8 - 4 = a - a/3 + 4 - 4

4 = (2/3)a

Multiply both sides by 3/2

(3/2)4 = (3/2)(2/3)a

6 = a

a = 6

Angela has $6.

e = a + 4 = 6 + 4 = 10

Eli has $10.

4 0

3 years ago

The function h(t) = −5t2 + 25t shown in the graph models an architectural arch:

alukav5142 [94]

Answer:

the answer is actually 0 ≤ x ≤ 5

Step-by-step explanation:

i got it right

6 0

4 years ago