Answer:
x = -2 or -9
Step-by-step explanation:
You want the values of x such that the line defined by the two points (2x+3, x+2) and (0, 2) is perpendicular to the line defined by the two points (x+2, -3-3x) and (8, -1).
<h3>Slope</h3>
The slope of a line is given by the slope formula:
m = (y2 -y1)/(x2 -x1)
Using the formula, the slopes of the two lines are ...
m1 = (2 -(x+2))/(0 -(2x+3)) = (-x)/(-2x-3) = x/(2x +3)
and
m2 = (-1 -(-3-3x))/(8 -(x+2)) = (2+3x)/(6 -x)
<h3>Perpendicular lines</h3>
The slopes of perpendicular lines have product of -1:
<h3>Solutions</h3>
The values of x that satisfy this equation are x = -2 and x = -9. The attached graphs show the lines for each of these cases.
Answer:
Step-by-step explanation:
Information given
number of people who rent their home
represent the sample size
represent the proportion of people who rent their home
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by 
and 
. And the critical value would be given by:
The confidence interval for the mean is given by the following formula:
If we replace the values obtained we got:
Subtract the number she completed from what she had left to paint originally.
The fractions have different denominators so first step is to rewrite the fractions with a common denominator.
23/25 can be rewritten as 92/100
Now you have 78 21/100 - 34 92/100
Because 21/100 is smaller than 92/100 subtract 1 whole number from 78 and rewrite 1 as 100/100 and add that to the fraction.
78 21/100 becomes 77 121/100
Now subtract :
77 121/100 - 34 92/100
77-34 = 43
And 121/100 - 92/100 = 29/100
Combine to get 43 and 29/100
Angles are always congruent
I hope this helps you
square root of (4x+41)=x+5
4x+41>=0
x >= -10.25
(square root of4x+41)^2=(x+5)^2
4x+41=x^2+10x+25
x^2+6x-16 =0
x +8
x -2
(x+8)(x-2)=0
x= -8
x= 2 extraneous
