Answer: The height of the palm tree is 21 feet.
Step-by-step explanation:
We can use a ratio to solve this:
Actual height to shadow for both objects. The fraction equivalents must be equal.
6/8 = x/28 . Cross multiply
6(28) = 8x
168 = 8x Divide both sides by 8 (8's "cancel" on the right)
168/8 =8x/8
21 = x . This gives us the tree's height as 21 feet.
<em>Another way to solve this is to use the ratios, but simplify the first fraction</em>
<em>6/8 = 3/4</em>
<em>Then multiply the length of the shadow by 3/4</em>
<em>3/4 × 28 = height</em>
<em>28÷4 = 7 7 × 3 = 21</em>
<em>21 feet= the height of the palm tree.</em>
Answer:
(-16a)-72b+56
Step-by-step explanation:
Multiply 8 to each number
Hope this helped :)
Answer:
(x + 1)² = 7
Step-by-step explanation:
Given:
-2x = x² - 6
We'll start by rearranging it to solve for zero:
x² + 2x - 6 = 0
The first term is already a perfect square so that's fine. Normally, if that term had a non-square coefficient, you would need to multiply all terms a value that would change that constant to a perfect square.
Because it's already square (1), we can simply move to the next step, separating the -6 into a value that can be doubled to give us the 2, the coefficient of the second term. That value will of course be 1, giving us:
x² + 2x + 1 - 1 - 6 = 0
Now can group our perfect square on the left and our constants on the right:
x² + 2x + 1 - 7= 0
x² + 2x + 1 = 7
(x + 1)² = 7
To check our answer, we can solve for x:
x + 1 = ± √7
x = -1 ± √7
x ≈ 1.65, -3.65
Let's try one of those in the original equation:
-2x = x² - 6
-2(1.65) = 1.65² - 6
- 3.3 = 2.72 - 6
-3.3 = -3.28
Good. Given our rounding that difference of 2/100 is acceptable, so the answer is correct.
Multiply to remove the variable from the denominator.
