Answer:
36
Step-by-step explanation:
when solving for two variables, we need to find one variable in terms of the other.
so, we can turn:
x - y = 5
into
x - y = 5
+ y + y
x = y + 5
Then, we can substitute "x" in the given equation with "y + 5"
x² - y² = 30
(y+5)² - y² = 30
(y + 5)(y + 5)
F: y² O: +5y I: +5y L: 25 {foil}
y² + 10y + 25 - y² = 30 {cancel y² - y²}
10y + 25 = 30
-25 -25
10y = 5
÷10 ÷10
y = 0.5
x = y + 5
x = 0.5 + 5
x = 5.5
check:
(5.5)² - (0.5)²
30.25 - 0.25 = 30
30 = 30
(TRUE)
now, we must find the value of:
(5.5 + 0.5)²
= (6)²
= 36
So, the value of (x + y)² is found to be 36
hope this helps!!
Answer:
The sample mean is 3.48 and the margin of error is 0.44.
Step-by-step explanation:
We know that the confidence interval is written in the form "x − E to x + E", meaning x: sample mean or estimator, and E: margin of error.
To calculate the mean, we can calculate the average of both bounds of the confidence interval:
![X=(UL-LL)/2=(3.92+3.05)/2=6.97/2=3.48](https://tex.z-dn.net/?f=X%3D%28UL-LL%29%2F2%3D%283.92%2B3.05%29%2F2%3D6.97%2F2%3D3.48)
With one of the bounds, we can calculate the margin of error E
![UL=X+E\\\\E=UL-X=3.92-3.48=0.44](https://tex.z-dn.net/?f=UL%3DX%2BE%5C%5C%5C%5CE%3DUL-X%3D3.92-3.48%3D0.44)
The solution for the inequality (x − 1)(x + 2) < 0 if x-1 < 0 and x+2 > 0 and x ∈ (-2, 1)
<h3>What is inequality?</h3>
It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have:
(x -1)(x + 2) < 0
The product of (x-1) and (x+2) is less than zero it means:
x-1 < 0 and x+2 > 0 or
x-1 > 0 and x+2 < 0
Solve for first case:
x-1 < 0 and x+2 > 0
x < 1 and x > -2
x ∈ (-2, 1)
Solve for the second case:
x > 1 and x < -2
There will be no intersection region, so no solution in this case.
Thus, the solution for the inequality (x − 1)(x + 2) < 0 if x-1 < 0 and x+2 > 0 and x ∈ (-2, 1)
Learn more about the inequality here:
brainly.com/question/19491153
#SPJ1
divide 400 by 24
400 / 24 = 16.666
so they would need to buy 17 crates