Answer:
x=10, y=25
Step-by-step explanation:
First, in a trapezoid, the two angles on the same leg (the legs are the opposite sides that are not parallel) add up to 180 degrees. Therefore, 4y as well as (2y+3x) are supplementary. We can write this out as
4y + (2y+3x) = 180
6y+3x = 180
Next, the angles of a triangle add up to 180 degrees. Therefore, as the angles 2y, 4y, and (5x-20) make up a triangle, they add up to 180 degrees. We can write this as
4y + 2y + (5x-20) = 180
6y + 5x -20 =180
Our two equations are thus
6y + 5x - 20 = 180
6y + 3x = 180
If we subtract 6y from both sides in each equation, we can say
5x - 20 = 180-6y
3x = 180-6y
Therefore, we can write
5x-20 = 180-5y = 3x
5x-20=3x
subtract 3x from both sides to make all x variables on the same side
2x-20 = 0
add 20 to both sides to isolate the x and its coefficient
2x = 20
divide both sides by 2 to isolate x
x = 10
Therefore,
x = 10
6y + 3x = 180
6y + 30 = 180
subtract 30 from both sides to isolate the y and its coefficient
6y = 150
y = 25
Answer:
f(x)^-1=x+12
Step-by-step explanation:
f(x)=x-12
y=x-12
x=y-12
y=x+12
f(x)^-1=x+12
Hope it helps.
Answer:
(x + 3)(x + 7)
Step-by-step explanation:
Find two numbers that when added up to , they ALSO have to multiply up to 21. This is simple because of the fact that there is no leading coefficient greater than 1⃣.
Answer:
a) The slope = 0.144 , means that an increase in dissolved material by 1 mg/cm^2 will lead to an increase in Calcium content by 0.144 g/l
while the coefficient of determination = 0.869 , means that 86% of the variation ( natural ) of calcium content is explainable using the Linear model.
b) 10.878
c) S ≈ 1.99
Step-by-step explanation:
a) The slope = 0.144 , means that an increase in dissolved material by 1 mg/cm^2 will lead to an increase in Calcium content by 0.144 g/l
while the coefficient of determination = 0.869 , means that 86% of the variation ( natural ) of calcium content is explainable using the Linear model.
<u>B) Point estimate of true average calcium content </u>
Given that dissolved material = 50 mg/cm^2
= 3.678 + 0.144 * dissolved material
= 3.678 + 7.2 = 10.878
<u>C) Determine an estimate of error standard deviation </u>
Given that ; sum of squares ( SST ) = 320.398
COD ( r ) = 0.86
first; calculate the value of SSE = SST - SST ( r^2 )
SSE = 320.398 - 320.398 ( 0.86) ^2
= 83.43
Finally ; determine the estimate of error standard deviation
S^2 = SSE / n -2
= 83.43 / 23 - 2
∴ S ≈ 1.99
Answer:
100 in²
Step-by-step explanation:
The area of the banner is equal to the area of the initial rectangle minus the area of the cutout triangle.
The rectangle has a height of 8 inches and width of 14 inches, so its area is:
A = (8 in) (14 in) = 112 in²
The triangle has a base of 8 inches and a height of 3 inches, so its area is:
A = ½ (8 in) (3 in) = 12 in²
So the area of the banner is 112 in² − 12 in² = 100 in².
