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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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What is the correct solution to this problem? A number divided by 5 is 3 more than –6. What is the number? A. –45 B. –30 C. –15

mihalych1998 [28]

<span>A number divided by 5 is 3 more than –6.
Let the number be "x".

x/5 = -6 + 3
First combine like terms.
x/5 = -3
Now multiply both sides by 5 to get x on one side.
x = -15

The answer is
C. -15
</span>

4 0

3 years ago

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Can anyone help me!

zhenek [66]

Answer:

$\large \text{$ \sf 2^{-64}$}$

Step-by-step explanation:

Given:

$\large \text{$ \sf (256)^{-4^{\frac{3}{2}}}$}$

This reads as: 256 to the power of "-4 to the power of 3/2".

Therefore, we need to deal with the "-4 to the power of 3/2" first.

Rewrite the 4 as 2²:

$\large \text{$ \sf \implies -(2^2)^{\frac{3}{2}}$}$

$\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:$

$\large \text{$ \sf \implies -2^{\left(2 \times \frac{3}{2}\right)}$}$

$\large \text{$ \sf \implies -2^{3}$}$

Therefore:

$\large \text{$ \sf \implies -2^3=(-2)(-2)(-2) = -8$}$

Replace "-4 to the power of 3/2" with -8 :

$\large \text{$ \sf \implies 256^{-8}$}$

Rewrite 256 as 2⁸ :

$\large \text{$ \sf \implies (2^8)^{-8}$}$

$\textsf{Again, apply exponent rule} \quad (a^b)^c=a^{bc}:$

$\large \text{$ \sf \implies 2^{(8 \times -8)}$}$

$\large \text{$ \sf \implies 2^{-64}$}$

In one complete calculation:

$\large\begin{aligned} \sf (256)^{-4^{\frac{3}{2}}} & = \sf (256)^{-(2^2)^{\frac{3}{2}}}\\& = \sf (256)^{-2^{\left(2 \times \frac{3}{2}\right)}}\\& =\sf (256)^{-2^{3}}\\& = \sf (256)^{-8}\\& \sf = (2^8)^{-8}\\& = \sf 2^{(8 \times -8)}\\& =\sf 2^{-64}\end{aligned}$

Learn more about exponent rules here:

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1 year ago

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Math experts ONCE AGAIN :)<br> giving brainly!!

Paladinen [302]

Answer:

A) $49

Step-by-step explanation:

There are two ways to solve this problem. You could either calculate the net change by adding up the values in the table and then adding that to the initial amount, or you could individually add every change in price to the initial amount. I'm going to go with the first way, as I find it to be quicker, but both methods work equally well.

We know that the stock was worth $52 on Monday morning. From the table, the net (or overall) change in the stock over the course of the week is:

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Therefore, the stock's price decreased by $3 over the week, and because the stock's original price was $52, we know it is now worth 52 - 3 = $49. Hope this helps!

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3 years ago

If $1,000 is loaned for 5 months at 6 % annual rate, how much interest is earned?

In-s [12.5K]

Answer:

Interest earned is $25.2

Step-by-step explanation:

The formula to find simple interest is:

I = P₀rt

Where

I = interest rate

P₀ = Principal amount

r = interest rate

t= time

5 months = 5/12 years = 0.42 years

I = 1000* 6/100*0.42

I = 1000*0.06*0.42

I = 60*0.42

I = 25.2

Interest earned is $25.2

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3 years ago

Which of these is a simplified form of the equation 7z + 2 = 8 + 2z + 1z?

WINSTONCH [101]

Simplify it and compare

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3 years ago

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