(x + 4) (x + 2)
=x^2 +2x + 4x + 8
=x^2 + 6x + 8
the other factor is (x + 2)
Answer:
Step-by-step explanation:
<u>Given system:</u>
<u>Multiply the first equation by 7 and add up the equations:</u>
- -7x + 7y + 7x + 3y = 7*8 - 16
- 10y = 40
- y = 4
<u>Find y:</u>
Answer:
31.5 units^2
Step-by-step explanation:
Rectangle area (RA) = l × w
Triangle area (TA) = (bh)/2
RA = 3 × 7
RA = 21
TA = (7 × 3)/2
TA = 21/2
TA = 10.5
(Triangles are congruent as shown by the lines on each side of the triangle so I can calculate area of both of them together as I just did)
Add areas together
21 + 10.5 = 31.5
Answer:
The minimum value of f(x) is 2
Step-by-step explanation:
- To find the minimum value of the function f(x), you should find the value of x which has the minimum value of y, so we will use the differentiation to find it
- Differentiate f(x) with respect to x and equate it by 0 to find x, then substitute the value of x in f(x) to find the minimum value of f(x)
∵ f(x) = 2x² - 4x + 4
→ Find f'(x)
∵ f'(x) = 2(2)
- 4(1)
+ 0
∴ f'(x) = 4x - 4
→ Equate f'(x) by 0
∵ f'(x) = 0
∴ 4x - 4 = 0
→ Add 4 to both sides
∵ 4x - 4 + 4 = 0 + 4
∴ 4x = 4
→ Divide both sides by 4
∴ x = 1
→ The minimum value is f(1)
∵ f(1) = 2(1)² - 4(1) + 4
∴ f(1) = 2 - 4 + 4
∴ f(1) = 2
∴ The minimum value of f(x) is 2
Answer:
3/4 of a batch
Step-by-step explanation:
9 out of the total 12 cups is what she has. So this converts into the fraction of 3/4 when simplified so she can make 3/4 of a batch.