Answer:
The roots of the given equation are x = 0 and x = -8.
General Formulas and Concepts:
<u>Algebra I</u>
Terms/Coefficients
Quadratic Equations
- Solving quadratic equations
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify.</em>
y = x² + 8x
<u>Step 2: Find Roots</u>
- [Quadratic] Factor: y = x(x + 8)
- [Quadratic] Set up [Solve]: 0 = x(x + 8)
- [Quadratic] Define: x = 0, -8
∴ the roots of the quadratic equation y = x² + 8x is equal to 0 and -8.
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Topic: Algebra I
Answer:
175 cm
7 years
Step-by-step explanation:
Here is the complete question
When Vlad moved to his new home a few years ago, there was a young oak tree in his backyard.
He measured it once a year and found that it grew by 26 centimeters each year. 4.5 years after he moved into the house, the tree was 292 centimeters tall.
1. How tall was the tree when Vlad moved into the house?
2. How many years passed from the time Vlad moved in until the tree was 357 centimeters tall?
The formula for calculating future value:
FV = P + (r x n)
FV = Future height of the tree
P = Present height of the tree
R = growth rate
N = number of years
292 = p + (26 x 4.5)
292 = p + 117
p = 292 - 117
p = 175 cm
b. 357 = 175 + (26 x n)
375 - 175 = 26n
182 = 26n
n = 182 / 26 = 7 years
Answer:
length: 13 cm
width: 5 cm
Step-by-step explanation:
You may be aware that 65 = 5×13. We note that 13 is 3 more than twice 5, so these are the dimensions of the rectangle:
5 cm wide; 13 cm long
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If you want so solve this algebraically, you can let w represent the width. Then the length is 2w+3 and the area is ...
A = LW
65 = (2w+3)(w)
In standard form, this equation is ...
2w^2 +3w -65 = 0
To factor this, you look for factors of 2×(-65) = -130 that have a sum of 3. Those would be ...
-130 = (-10)(13)
Then the factored equation is ...
2w^2 +13w -10w -65 = 0
w(2w+13) -5(2w+13) = 0
(w -5)(2w +13) = 0 ⇒ w = 5, -13/2
The positive solution makes sense in this problem, so ...
width = 5 cm
length = 2(5) +3 = 13 cm
Answer:
125 degree
Step-by-step explanation:
As m // n, so angle 2 and angle 6 is the same so angle 2 = 55 degree, then angle 1 + angle 2 = 180 degree, so angle 1 = 180 - 55 = 125 degree.
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Answer:
$3/book
Step-by-step explanation:
cost per book means divide the price of all the books by the number of books
$15/(5 books) = $3/book
