Answer:
The solutions to equation 1 are x = 3, −1.5, and equation 2 has no solution.
Step-by-step explanation:
Rearranging the two equations, you get ...
- |4x -3| = 9 . . . . . has two solutions
- |2x +3| = -5 . . . . has no solutions (an absolute value cannot be negative)
The above-listed answer is the only one that matches these solution counts.
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Testing the above values of x reveals they are, indeed, solutions to Equation 1.
Answer:
Step-by-step explanation:
1) a² - b² = (a + b)(a- b)
2) a³ + b³ = a³ + 3a²b + 3ab² + b³
3) a³ - b³ = a³ - 3a²b + 3ab² - b³
5) x⁴ - 36 = (x²)² - 6² = (x² + 6) (x² - 6)
6)64c³ + 1 = (4c)³ + 1³ = (4c)³ + 3(4c)²(1) + 3(4c)(1)³ + 1³
= 64c³ + 3(16c²) + 12c +1
= 64c³ + 48c² +12c + 1
7) k³ - 27 = k³- 3³ = (k + 3)(k - 3)
Answer:
g(x)=4x-48
Step-by-step explanation:
f(x)=0.25x + 12
substitute
f(x) with y
y=0.25x + 12
then replace x with y and y with x
x=0.25y + 12
swap equation
0.25y + 12 = x
0.25y = x - 12
divide both sides by 0.25
Y=4x-48
9514 1404 393
Answer:
(a) 75.5
Step-by-step explanation:
There are two ways you can work this.
<u>Pythagorean theorem</u>
Triangle CMP is a right triangle. CM = AC = 55. CP = CB -PB = 55 -15 = 40. Then length PM can be found from ...
PM² +CP² = CM²
PM = √(CM² -CP²) = √(55² -40²) = √1425 ≈ 37.749
The length MN is twice the length of PM, so is ...
MN = 2×PM = 2×37.349 = 75.498
The length of MN is about 75.5.
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<u>Using chord relationships</u>
The products of the different lengths for the same chord are the same for the crossed chords.
AP×PB = MP×PN
We know MP = PN, so ...
MP = √(AP×PB) = √((55+40)(15)) = √1425
As before, MN = 2×MP = 2√1425
MN ≈ 75.5
