The line equation in slope-intercept form is y=mx+b
You have one line with a y-intercept at 1 and a slope of -3 -> y=-3x+1
and another with a y-intercept at -1 and a slope of
-> ![y=\frac{1}{2}x-1](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7Dx-1)
The area marked is below the first line and above the second one -> replace = with < and >:
y<-3x+1
![y>\frac{1}{2}x-1](https://tex.z-dn.net/?f=y%3E%5Cfrac%7B1%7D%7B2%7Dx-1)
Which is the system of linear inequalities shown in the graph
Answer:
D x = 18
Step-by-step explanation:
Given equation:
−2x = −36
Divide both sides by -2 to find x
−2x / -2 = −36 / -2
x = −36 / -2
x = 18
x = 18 makes the equation −2x = −36 true
Answer:
310
Step-by-step explanation:
9 + 100 = 109
109 + 1 = 110
110 + 200 = 310
Since she has 125 cats and 5 of them are both old and her favorite, we’ll just take that away and get 120. Out of the 7 that are old, 5 were her favorite, so only 2 of them were just old and we now have 118. Out of the 9 that were her favorite, 5 were old, so only 4 if them were just her favorite and now we have 114. A total of 11 cats were either old, her favorite, or both, so we’re left with 114 that are neither.
Answer:
Part a) The measure of the sides of triangle DEF are
![d_D_E=\sqrt{90}\ units](https://tex.z-dn.net/?f=d_D_E%3D%5Csqrt%7B90%7D%5C%20units)
![d_E_F=\sqrt{65}\ units](https://tex.z-dn.net/?f=d_E_F%3D%5Csqrt%7B65%7D%5C%20units)
![d_D_F=\sqrt{221}\ units](https://tex.z-dn.net/?f=d_D_F%3D%5Csqrt%7B221%7D%5C%20units)
Part b) Is a scalene triangle
Step-by-step explanation:
we know that
the formula to calculate the distance between two points is equal to
![d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28y2-y1%29%5E%7B2%7D%2B%28x2-x1%29%5E%7B2%7D%7D)
we have the coordinates
D(8,-6) E(-1,-3) F(-2,5)
step 1
Find the length side DE
D(8,-6) E(-1,-3)
substitute in the formula
![d=\sqrt{(-3+6)^{2}+(-1-8)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-3%2B6%29%5E%7B2%7D%2B%28-1-8%29%5E%7B2%7D%7D)
![d=\sqrt{(3)^{2}+(9)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%283%29%5E%7B2%7D%2B%289%29%5E%7B2%7D%7D)
![d_D_E=\sqrt{90}\ units](https://tex.z-dn.net/?f=d_D_E%3D%5Csqrt%7B90%7D%5C%20units)
step 2
Find the length side EF
E(-1,-3) F(-2,5)
substitute in the formula
![d=\sqrt{(5+3)^{2}+(-2+1)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%285%2B3%29%5E%7B2%7D%2B%28-2%2B1%29%5E%7B2%7D%7D)
![d=\sqrt{(8)^{2}+(-1)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%288%29%5E%7B2%7D%2B%28-1%29%5E%7B2%7D%7D)
![d_E_F=\sqrt{65}\ units](https://tex.z-dn.net/?f=d_E_F%3D%5Csqrt%7B65%7D%5C%20units)
step 3
Find the length side DF
D(8,-6) F(-2,5)
substitute in the formula
![d=\sqrt{(5+6)^{2}+(-2-8)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%285%2B6%29%5E%7B2%7D%2B%28-2-8%29%5E%7B2%7D%7D)
![d=\sqrt{(11)^{2}+(-10)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%2811%29%5E%7B2%7D%2B%28-10%29%5E%7B2%7D%7D)
![d_D_F=\sqrt{221}\ units](https://tex.z-dn.net/?f=d_D_F%3D%5Csqrt%7B221%7D%5C%20units)
step 4
Classify the triangle by the measure of its sides
we have
![d_D_E=\sqrt{90}\ units](https://tex.z-dn.net/?f=d_D_E%3D%5Csqrt%7B90%7D%5C%20units)
![d_E_F=\sqrt{65}\ units](https://tex.z-dn.net/?f=d_E_F%3D%5Csqrt%7B65%7D%5C%20units)
![d_D_F=\sqrt{221}\ units](https://tex.z-dn.net/?f=d_D_F%3D%5Csqrt%7B221%7D%5C%20units)
so
Is a scalene triangle, because is a triangle in which all three sides have different lengths.