Answer:
GH = 6.3 units
Step-by-step explanation:
Assuming that 1 box represents 1 unit, the coordinate pair of G = (-2, -3), while H = (0, 3).
Distance between G and H =
Let,
(nearest tenth)
A code is to be made by arranging 7 letters. Three of the letters used will be the letter A, two of the letters used will be the
1 answer:
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Answer:
see explanation
Step-by-step explanation:
(9)
Expand and simplify right side and compare coefficients of like terms on left side.
(x - 2)(x² + ax + b) + c
= x³ + ax² + bx - 2x² - 2ax - 2b + c
= x³ + x²(a - 2) + x(b - 2a) - 2b + c
compare with
x³ + 2x² - 3x + 4
x² terms
a - 2 = 2 ( add 2 to both sides )
a = 4
x terms
b - 2a = - 3 ← substitute a = 4
b - 8 = - 3 ( add 8 to both sides )
b = 5
constant terms
- 2b + c = 4 ← substitute b = 5
- 10 + c = 4 ( add 10 to both sides )
c = 14
Thus a = 4, b = 5 and c = 14
-------------------------------------------------
(10)
Since both functions cross the x- axis at - 2 then (- 2, 0) satisfies both, that is
f(- 2) = + a(- 2)³ + b(- 2)² + 36(- 2) + 144 = 0, that is
- 16 - 8a + 4b - 72 + 144 = 0
- 8a + 4b + 56 = 0
- 8a + 4b = - 56 → (1)
and
g(- 2) = + (a + 3)(- 2)³ - 23(- 2)² + (b + 10)(- 2) + 40 = 0, that is
- 16 - 8(a + 3) - 92 - 2(b + 10) + 40 = 0
- 16 - 8a - 24 - 92 - 2b - 20 + 40 = 0
- 8a - 2b - 112 = 0
- 8a - 2b = 112 → (2)
Subtract (1) from (2) term by term
- 6b = 168 ( divide both sides by - 6 )
b = - 28
Substitute b = - 28 into (2)
- 8a + 56 = 112 ( subtract 56 from both sides )
- 8a = 56 ( divide both sides by - 8 )
a = - 7
Thus a = - 7 and b = - 28
Answer:
m= 1/2.
Step-by-step explanation:
To solve this, we must make the bases equivalent. We can do this by finding the common base which is 5.
We know that 125= 5³ and 25=5², which will help us in this equation. We can rewrite the equation substituting this for the original numbers:
Distribute the exponents to get:
Now, we can simply ignore the '5' and solve for 'm':
6m= 2m+2
4m= 2
m= 1/2.