Answer:
20. AB = 42
21. BC = 28
22. AC = 70
23. BC = 20.4
24. FH = 48
25. DE = 10, EF = 10, DF = 20
Step-by-step explanation:
✍️Given:
AB = 2x + 7
BC = 28
AC = 4x,
20. Assuming B is between A and C, thus:
AB + BC = AC (Segment Addition Postulate)
2x + 7 + 28 = 4x (substitution)
Collect like terms
2x + 35 = 4x
35 = 4x - 2x
35 = 2x
Divide both side by 2
17.5 = x
AB = 2x + 7
Plug in the value of x
AB = 2(17.5) + 7 = 42
21. BC = 28 (given)
22. AC = 4x
Plug in the value of x
AC = 4(17.5) = 70
✍️Given:
AC = 35 and AB = 14.6.
Assuming B is between A and C, thus:
23. AB + BC = AC (Segment Addition Postulate)
14.6 + BC = 35 (Substitution)
Subtract 14.6 from each side
BC = 35 - 14.6
BC = 20.4
24. FH = 7x + 6
FG = 4x
GH = 24
FG + GH = FH (Segment Addition Postulate)
(substitution)
Collect like terms


Divide both sides by -3

FH = 7x + 6
Plug in the value of x
FH = 7(6) + 6 = 48
25. DE = 5x, EF = 3x + 4
Given that E bisects DF, therefore,
DE = EF
5x = 3x + 4 (substitution)
Subtract 3x from each side
5x - 3x = 4
2x = 4
Divide both sides by 2
x = 2
DE = 5x
Plug in the value of x
DE = 5(2) = 10
EF = 3x + 4
Plug in the value of x
EF = 3(2) + 4 = 10
DF = DE + EF
DE = 10 + 10 (substitution)
DE = 20
Answer:
Step-by-step explanation:
1) Tangent makes 90 degrees with the radius. Hence
a) Angle ABD = 90-angle BDC = 90-61.3 = 28.7
b) Triangle BCD is isosceles since tangents have equal length.
Hence angle BCD = 180-(61.3+61.3) = 57.4
c) Angle BDC = 57.4 (since triangle BCD is isosceles)
d) Angle BAC and Angle BCD are supplementary. Hence angle BAC = 122,6
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2) Arc length of minor arc BC = 
b) ARc length of minor arc = circumference -minor arc
= 18.713
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3) circumference = pi d =
Million, Billion, Trillion, and Quadrillion
Percentage by which the gas tank of the car is full = 40%
Amount of gas in the gas tank = 8 gallons
Let us assume the capacity of the gas tank = x gallons
Then
40% * x = 8
(40/100) * x = 8
4x/10 = 8
4x = 8 * 10
4x = 80
x = 80/4
= 20 gallons
So the total capacity of the gas tank of the car is 20 gallons. I hope the procedure is clear to you.
Answer:
28 and 30
Step-by-step explanation:
'x' = 1st consecutive #
'x+2' = 2nd consecutive #
x + x+2 = 58
2x + 2 = 58
2x = 56
x = 28
x+2 = 30