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°
Answer: 8
Step-by-step explanation:
let x = the number
(x + 2)*10 = 8x + 36
10x + 20 = 8x + 36
2x = 16
x = 8
Following expressions will have negative product
Following expressions will have positive product
Further explanation:
We will see at each expression one by one
First expression is:
In the given expression one term is positive and one term is negative. The product of negative and positive terms is negative.
Second Expression is:
Both terms are negative and the product of two negative terms is positive.
Third Expression is:
The expression has one positive and one negative term so the product will be negative
Fourth Expression is:
Both terms are positive so the product will also be positive
Keywords: Product, Expressions
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