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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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Please help me. -1/2x+3=-x+7

Ber [7]

Answer:

x=8

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

-1/2*x+3-(-x+7)=0

simplify 1/2

((0 - (1/2• x)) + 3) - (7 - x) = 0

Adding a whole to a fraction

Rewrite the whole as a fraction using 2 as the denominator :

3 3 • 2

3 = — = —————

1 2

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

-x + 3 • 2 6 - x

—————————— = —————

2 2

(6 - x)

——————— - (7 - x) = 0

ubtracting a whole from a fraction

Rewrite the whole as a fraction using 2 as the denominator :

7 - x (7 - x) • 2

7 - x = ————— = ———————————

1 2

Adding up the two equivalent fractions

(6-x) - ((7-x) • 2) x - 8

——————————————————— = —————

2 2

x - 8

————— = 0

When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

x-8

——— • 2 = 0 • 2

Now, on the left hand side, the 2 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

x-8 = 0

Solve : x-8 = 0

Add 8 to both sides of the equation :

x = 8

Hope this helps :)

5 0

3 years ago

Read 2 more answers

Use elimination to solve.<br> 3y-6x=7<br> -4y-3x=9

shtirl [24]

Answer:

x = -5/3, y = -1 or $(-\frac{5}{3}, -1)$

Step-by-step explanation:

Solving systems of linear equations using process of elimination involves eliminating one of the variables (and its coefficient) in order to solve the other variable either through addition or subtraction. However, there may be other mathematical operations necessary before one of the variables can be eliminated.

Equation 1: 3y - 6x = 7

Equation 2: -4y - 3x = 9

<h3>Step 1: Multiply Equation 2 by -2:</h3>

(-2)(-4y - 3x) = 9 (-2)

8y + 6x = -18

<h3>Step 2: Add "8y + 6x = -18" to Equation 1:</h3>

8y + 6x = -18

+ 3y - 6x = 7

11y = -11

<h3>Step 3: Divide both sides by 11 to solve for y:</h3>

$\frac{11y}{11} = \frac{-11}{11}$

y = -1

<h3>Step 4: Substitute y = -1 into Equation 2 to solve for x: </h3>

-4(-1) - 3x = 9

4 - 3x = 9

<h3>Step 5: Subtract 4 from both sides:</h3>

4 - 4 - 3x = 9 - 4

- 3x = 5

<h3>Step 6: Divide both sides by -3 to solve for x:</h3>

$\frac{-3x}{-3} = \frac{5}{-3}$

$x = - \frac{5}{3}$

Verify whether the values for x and y are correct by substituting their values into both equations:

x = -5/3, y = -1

Equation 1: 3y - 6x = 7

$3(-1) - 6(-\frac{5}{3}) = 7$

-3 + 10 = 7

7 = 7 (True statement).

Equation 2: -4y - 3x = 9

-4(-1) - 3 (-5/3) = 9

$-4(-1) - 3(-\frac{5}{3}) = 9$

4 + 5 = 9

9 = 9 (True statement).

Therefore, x = -5/3 and y = -1 are the solutions to the given systems of linear equations.

8 0

3 years ago

The length of the base of a square pyramid is 15 inches. The slant height is 10 inches. What is the surface area of the pyramid?

Dimas [21]

Answer: 150

Step-by-step explanation:

15x10= 150

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4 years ago

What is exact area of circle with radius=7.

Illusion [34]

153.94 is the area of a circle

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3 years ago

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The ratio of boys to girls in a class is 5:3. There are 32 students

Bezzdna [24]

Answer:

8more boys

Step-by-step explanation:

girls: 32*3/8= 12

boys: 32-12=20

20-12=8

7 0

3 years ago