Using the definition of vertical angles, the value of z is: 15.
<h3>Vertical Angles Pair</h3>
The two pairs of opposite angles formed when two straight lines intersect are called vertical angles, and are therefore congruent to each other.
Thus:
2z + 10 = 40
2z = 40 - 10
2z = 30
z = 30/2
z = 15
Therefore, using the definition of vertical angles, the value of z is: 15.
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The answer would be the first option :
4/3r (3x)^3.
Hope this helps !
Photon
Answer:
A) A = X^2 + 11X + 24
B) X = 18 ft
C) 414 ft^2
D) 132 ft^2
Step-by-step explanation:
A) Width W of yard and path = X + 3
Lenght L of path = X + 5 + 3 = X + 8 ft, therefore,
Area of yard and path = L x W = (X +3) x (X +8)
A = X^2 + 11X + 24
B) if area of the yard and path is 546 ft^2,
546 = X^2 + 11X + 24
X^2 +115X - 522 = 0 (quadratic equation)
Solving the quadratic equation gives
X = 18 and X = -29
Our answer can only be positive so we choose X = 18 ft
C) lenght of yard = 5 + 18 = 23 ft
Width = 18 ft
Therefore area = L x W = 23 x 18 = 414 ft^2
D) area of path = area of path and yard minus area of yard
= 546 - 414 = 132 ft^2
Answer:
a / b = 1/7
b = a x 7
a / c = 4 /1
a = c x 4
b = a x 7
= c x 4 x 7
= c x 28
b is 28 times bigger than c
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