Answer:
Step-by-step explanation:
- 10x² - 7ax + (a + 2) (a - 5) =
- 10x² - 7ax + a² - 3a - 10
Factorize by finding the roots
<u>Find the discriminant:</u>
- D = b² - 4ac
- D = (-7a)² - 4*10*(a² - 3a - 10) =
- 49a² - 40a² + 120a + 400 =
- 9a² + 120a + 400 =
- (3a + 20)²
<u>Find the roots:</u>
- x = (- b ± √D)/2a = (7a ± (3a + 20)) / 20
- x₁ = (7a + 3a + 20) / 20 = (10a + 20) / 20 = (a + 2) / 2
- x₂ = (7a - 3a - 20) / 20 = (4a - 20) / 20 = (a - 5) / 5
<u>Factorize the expression:</u>
- 10x² - 7ax + a² - 3a - 10 =
- 10 (x - x₁)(x - x₂) =
- 10[x - (a + 2)/2][[x - (a - 5)/5] =
- (2x - a - 2)(5x - a + 5)
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<u>You would also try a shorter but more difficult way:</u>
- 10x² - 7ax + (a + 2) (a - 5) =
- 2x*5x - 2ax + 10x - 5ax - 10x + (a + 2) (a - 5) =
- 2x*5x - 2x(a - 5) - 5x(a + 2) + (a + 2) (a - 5) =
- 2x(5x - (a - 5)) - (a + 2)(5x - (a - 5)) =
- (5x - a + 5)(2x - a - 2)
Answer:
y=26.67
Step-by-step explanation:
The given equation is 0.75x+1.5y=40.
We need to show the result of substituting x=0 in above equation.
0.75x+1.5y=40
Put x = 0
0.75(0)+1.5y=40
0+1.5y=40
⇒ 1.5y=4
So, the value of y = 26.67 when x = 0.
Answer:
Step-by-step explanation:
Given that Darcie wants to donate minimum 3 blankets to donate to a homeless shelter. No of days left =60
No of days to complete one blanket = 1/(1/15) = 15 days
Hence in 60 days she has to complete ≥3 blankets
No of days she has to utilize for this will be ≥3(15)=45
No of days she can skip crocheting ≤15
Let x be the no of days crocheted and y no of days skipped
Then x+y≤60
See the graph attached as x axis for days crocheted and y for days skipped
No of blankets can be either 3 or 4.
Answer:
Part A: 5x² + 7x - 4
Part B: 5x³ - x² - 8x + 1
Part C: Yes.
Step-by-step explanation:
Part A: The length of two sides of a triangle are given by
Side 1: 3x² - 2x - 1
Side 2: 9x + 2x² - 3
Now, the total length of the two sides, 1 and 2, of the triangle will be
= (3x² - 2x - 1) + (9x + 2x² - 3)
= 5x² + 7x - 4 (Answer)
Part B: If the length of the third side is y and the perimeter of the triangle is (5x³ + 4x² - x - 3), then
y = (5x³ + 4x² - x - 3) - (5x² + 7x - 4) = 5x³ - x² - 8x + 1 (Answer)
Part C: The answers in the part A and part B are closed under addition and subtraction. (Answer)
