Answer:
The price after the discount would be $315.
First statement is correct. If Sasha reads her novel for 94 minutes, she meets the minimum reading requirement without reading any of the autobiography.
Given,
The rate of reading of a novel by Sasha = 0.8 pages per minute
The rate of reading of autobiography by Sasha = 0.5 pages per minute
The reading requirement of Sasha's English class = atleast 75 pages per week
The given equation: 0.8n + 0.5a ≥ 75
n is the number of minutes she reads the novel
a is the number of minutes she reads the autobiography
Now, let's check the statements:
Statement 1: If Sasha reads her novel for 94 minutes, she meets the minimum reading requirement without reading any of the autobiography.
That is,
0.8 × 94 + 0.5 × 0 ≥ 75
75.2 ≥ 75
This statement satisfies the equation.
Other 4 statement didn't satisfy the equation.
So, first statement is correct.
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Multiply the first equation by -1
-3x-y=-4
2x+y=5
Add them up
-x=1
So x=-1
And y=7
So the first option is correct
Factor the following:
12 x^4 - 42 x^3 - 90 x^2
Factor 6 x^2 out of 12 x^4 - 42 x^3 - 90 x^2:
6 x^2 (2 x^2 - 7 x - 15)
Factor the quadratic 2 x^2 - 7 x - 15. The coefficient of x^2 is 2 and the constant term is -15. The product of 2 and -15 is -30. The factors of -30 which sum to -7 are 3 and -10. So 2 x^2 - 7 x - 15 = 2 x^2 - 10 x + 3 x - 15 = x (2 x + 3) - 5 (2 x + 3):
6 x^2 x (2 x + 3) - 5 (2 x + 3)
Factor 2 x + 3 from x (2 x + 3) - 5 (2 x + 3):
Answer: 6 x^2 (2 x + 3) (x - 5)
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