The Simplification of the following expression is;
- m = -30/7
- v = -8.8
- x = 3
- u = -2.49
- a = -3/70
<h3>Simplification</h3>
7/8m - 4/7 - 5/6m = - 3/4
7/8m - 5/6m = -3/4 + 4/7
21m-20m/24 = -21+16/28
1/24m = -5/28
m = -5/28 ÷ 1/24
= -5/28 × 24/1
= -120/28
m = -30/7
4.3v + 10.75 - 4v = 8.11
0.3v = 8.11 - 10.75
0.3v = -2.64
v = -2.64/0.3
v = -8.8
9/7 + 9/7x - 6/7x =0
9/7x - 6/7x = - 9/7
(9-6)x /7 = 9/7
3/7x = 9/7
x = 9/7 ÷ 3/7
= 9/7 × 7/3
= 9/3
x = 3
6.9u - 2 - 3.2u - 10 = 2.8
3.7u = 2.8 - 12
3.7u = -9.2
u = -9.2/3.7
u = -2.49
8/5 = - 4a + 7/5 - 2/3a
8/5 - 7/5 = -4a - 2/3a
8-7/5 = -12a-2a/3
1/5 = -14/3a
a = 1/5 ÷ -14/3
= 1/5 × -3/14
a = -3/70
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Answer:
q = -8, k = 2.
r = -6.
Step-by-step explanation:
f(x) = (x - p)^2 + q
This is the vertex form of a quadratic where the vertex is at the point (p, q).
Now the x intercepts are at -6 and 2 and the curve is symmetrical about the line x = p.
The value of p is the midpoint of -6 and 2 which is (-6+2) / 2 = -2.
So we have:
f(x) = 1/2(x - -2)^2 + q
f(x) = 1/2(x + 2)^2 + q
Now the graph passes through the point (2, 0) , where it intersects the x axis, therefore, substituting x = 2 and f(x) = 0:
0 = 1/2(2 + 2)^2 + q
0 = 1/2*16 + q
0 = 8 + q
q = -8.
Now convert this to standard form to find k:
f(x) = 1/2(x + 2)^2 - 8
f(x) = 1/2(x^2 + 4x + 4) - 8
f(x) = 1/2x^2 + 2x + 2 - 8
f(x) = 1/2x^2 + 2x - 6
So k = 2.
The r is the y coordinate when x = 0.
so r = 1/2(0+2)^2 - 8
= -6.
<span>The correct answer is option B. i.e. (1,-10) two equations are y = -x^2 - 5x - 4 and y = -x^2 + 9x - 18. Now, equating both the equations we get, -x^2 - 5x - 4 = -x^2 + 9x - 18 or 14 x= 14 or x = 1. Now, y = -1 -5 -4 = -10.</span>
