For the equation y - x < 0,
y < x
The shaded portion will be under the dashed line joining points (-2, -2) and (3, 3).
for the equation x - 1 > 0,
x > 1
The shaded portion will be to the right of the dashed line joining points (1, 5) and (1, -3).
The portion affected by the two shadings will be the portion common to the right of the dashed line joining points (1, 5) and (1, -3) and under the dashed line joining points (-2, -2) and (3, 3).
Therefore the correct answer is option c.
Here you have a system of 2 equations and 2 unknowns. An easy way to solve this type is to isolate one of the variables.
12a + 2b = 8
2b = 8 - 12a
b =
b = 4 - 6a
Now plug 4 - 6a into equation 1 to solve for a.
a + 5(4 - 6a) = 19
a + 20 - 30a = 19
-29a = -1
a = 1/29 (answer)
Now plug a into the equation for b
b= 4 - 6(1/29)
b= 110/29 (answer)
Answer:
50 miles
Step-by-step explanation:
if a car travels 100 miles in two hours, divide 100 by 2 and you get 50 miles.
Answer:
9. m(YZ) = 102°
10. m(JKL) = 192°
11. m<GHF = 75°
Step-by-step explanation:
9. First, find the value of x
4x + 3 = 3x + 15 (inscribed angle that are subtended by the same arc are equal based on the inscribed angle theorem)
Collect like terms
4x - 3x = -3 + 15
x = 12
4x + 3 = ½(m(YZ)) (inscribed angle of a circle = ½ the measure of the intercepted arc)
Plug in the value of x
4(12) + 3 = ½(m(YZ))
48 + 3 = ½(m(YZ))
51 = ½(m(YZ))
Multiply both sides by 2
51*2 = m(YZ)
102 = m(YZ)
m(YZ) = 102°
10. First, find the value of x.
7x + 5 + 6x + 6 = 180° (opposite angles in an inscribed quadrilateral are supplementary)
Add like terms
13x + 11 = 180
13x = 180 - 11
13x = 169
x = 169/13
x = 13
7x + 5 = ½(m(JKL)) (inscribed angle of a circle = ½ the measure of the intercepted arc)
Plug in the value of x
7(13) + 5 = ½(m(JKL))
96 = ½(m(JKL))
Multiply both sides by 2
2*96 = m(JKL)
m(JKL) = 192°
11. First, find x.
5x + 15 = ½(11x + 18) (inscribed angle of a circle = ½ the measure of the intercepted arc)
Multiply both sides by 2
2(5x + 15) = 11x + 18
10x + 30 = 11x + 18
Collect like terms
10x - 11x = -30 + 18
-x = -12
Divide both sides by -1
x = 12
m<GHF = 5x + 15
Plug in the value of x
m<GHF = 5(12) + 15
m<GHF = 60 + 15
m<GHF = 75°
