The midpoint is exactly in the middle
meaning
VW = WX
3x+7 = x + 25
solve from x
3x + 7 = x + 25
subtract 7 from both sides
3x = x + 18
subtract x from both sides
2x = 18
divide both sides by 2
x = 9
Now we have x = 9 but we aren't done.
plug what we found into the expressions
3x + 7
3(9) + 7
27 + 7
34
x + 25
9 + 25
34
34 + 34
68
The length of VX is 68.
Or option D.) 68
Hope this helps
The value of the expression when g = -2 is -1
<h3>How to simplify the expression</h3>
Given the expression;
(5+2g)exp5
(5+2g)^5
For g = -2
Let's substitute the value of g in the expression
= ( 5 + 2 ( -2) ) ^5
Expand the bracket
= ( 5 - 4) ^ 5
Find the difference
= (-1) ^5
= -1
Thus, the value of the expression when g = -2 is -1
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Answer: 10, 11, & 12
<u>Step-by-step explanation:</u>
Let x represent the age of the youngest child.
Their ages are consecutive so,
Youngest: x
Middle: x + 1
Oldest: x + 2
The age of the Youngest squared (x²) equals 8 times the Oldest [8(x + 2)] plus 4.
x² = 8(x + 2) + 4
x² = 8x + 16 + 4
x² = 8x + 20
x² - 8x - 20 = 0
(x - 10)(x + 2) = 0
x - 10 = 0 or x + 2 = 0
x = 10 or x = -2
Since age cannot be negative, x = -2 is not valid
So, the Youngest (x) is 10
the Middle (x + 1) is 11
and the Oldest (x + 2) is 12
The interpretation of 0 = -12 is (a) There are no solutions to the system because the equations represent parallel lines.
<h3>How to interpret the result?</h3>
The result is given as:
0 = -12
By comparison 0 and -12 do not have the same value
i.e. 0 ≠ - 12
This means that the system of equation has no solution
Hence, the interpretation of 0 = -12 is (a)
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Answer:
a). m∠AED = 70°
b). x = 10°
Step-by-step explanation:
a). Quadrilateral ABDE is a cyclic quadrilateral.
Therefore, by the theorem of cyclic quadrilateral,
Sum of either pair of opposite angle is 180°
m(∠AED) + m(∠ABD) = 180°
m(∠AED) = 180° - 110°
m(∠AED) = 70°
Since, ∠AED ≅ ∠EAD
Therefore, m∠AED = m∠EAD = 70°
b). By triangle sum theorem in ΔABD,
m∠ABD + m∠BDA + m∠DAB = 180°
110° + 40° + m∠DAB = 180°
m∠DAB = 180° - 150°
m∠DAB = 30°
m∠BAE = m∠EAD + m∠BAD
= 70° + 30° = 100°
By angle sum theorem in ΔACE,
m∠EAC + m∠AEC + m∠ACE = 180°
100° + 70° + x° = 180°
x = 180° - 170°
x = 10°
