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)
====================================================
<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:
By repeated subtraction.
Step-by-step explanation:
It is pretty much the same thing as division, but in subtraction. Since, Dividing and Subtraction are a like, repeated subtraction is a great example to use for this example
Hope this helps. :)
Area of the three equally sized stripes: A
A=(x+15)(x)(3)
A=3x(x+15)
A=3x^2+45x
One gallon of paint will cover an area of no more than 400 square feet: <=400
She only has half of a gallon of paint left:
1/2(400 square feet)=400/2=200 square feet
Inequality that could be used to find the maximum height, in feet, of each stripe:
A<=200
3x^2+45x<=200
Answer: 3x^2+45x <= 200
Could her stripes be 3' tall?
x=3→A=3(3)^2+45(3)=3(9)+135=27+135→A=162<200 Ok
Yes, her stripes could be 3' tall.
Answer: Yes
Could her stripes be 4' tall?
x=4→A=3(4)^2+45(4)=3(16)+180=48+180→A=228>200 No
No, her stripes couldn't be 4' tall.
Answer: No
We want to find the probability that Berenice gets all the answers correct.
<u>1 question:</u>
Each question has 4 options, each option has the same probability of being the correct option, so she has a 25% of<u> randomly selecting the correct option.</u>
Then the probability here will just be equal to the number of correct options (1) over the total number of options (4)
p = 1/4
2 questions:
We already know the probability for one question, then the probability of getting two questions correct will be equal to the <u>product of the individual probabilities</u> for each question:
p = (1/4)*(1/4 = 1/16
3 questions:
Similar approach as before:
p = (1/4)*(1/4)*(1/4) = 1/64
4 questions:
p = (1/4)*(1/4)*(1/4)*(1/4) = 1/256
If you want to learn more, you can read:
brainly.com/question/23044118
Answer:
Part a) The fraction is 
Part b) The percent is 
Step-by-step explanation:
Part a)
Find the fraction
we know that
To find the fraction of the shaded part in the square divide the number of shaded squares by the total number of squares
so
Let
x-------> the number of shaded squares
y-------> the total number of squares
f-------> the fraction of the shaded part
so
In this problem we have
substitutes
Simplify
Part b) Find the percent
To find the percent multiply the fraction by 100
so
convert to mixed number
