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:
3/4 gallons of juice
Step-by-step explanation:
Katie bought 2 one-gallon bottles for a party.
2 one-gallon bottles = 2-gallon bottles of juice
We are told that:
Her guest drank 5/4 gallons of juice.
The fraction of juice leftover is calculated as:
2 gallons of juice - 5/4 gallons of juice
2 - 5/4
Lowest Common Denominator = 4
2/1 - 5/4
= 8 - 5/4
= 3/4 gallons of juice
Therefore, the fraction of juice leftover is 3/4 gallons of juice
Answer:
1. no. 2.no
Step-by-step explanation:
1.
= (5\3) × (1/1-x)
but 8-8x = 8(1-x)
2. 2(6-3x) = 12-6x =6(2-x)
2(3x) + x= 6x +x = 7x
We assume all money is spent on new lighting. Since they currently have $160 and need $400 we can subtract what they currently have from what they need.
$400-$160 = $240
Since we know the price of the ticket and now know they need $240 we can divide our $240 with the price of each ticket ($3)
$240/$3 = 80
So the drama club has to sell 80 more tickets in order to afford new lighting
