4/7 and 10/17.5
18/8 and 9/4
Proportions
2/3 and 9/12
3/8 and 6/141
7/5 and 27/20
Not a proportion
Answer:
14000
Step-by-step explanation:
Of means multiply
10% * 140000
Change to decimal form
.10 * 140000
14000
Answer: x^2+y^2+2x-18y+18=0 in standard form is (x+1)^2+(y-9)^2=64
Answer:
ΔABC and ΔA'B'C' are congruent, by the SSS rule of congruency
Step-by-step explanation:
The given parameters are;
The transformation undergone by triangle ABC = (x, y) → (x + 7, y + 3) to give triangle A'B'C'
Therefore, the points on triangle ABC are transformed by a translation of 7 units to the right and 3 units up to form triangle A'B'C'
Given that a translation transformation is a form of rigid transformation, we have;
The lengths of triangle ABC are congruent to the lengths of the sides of triangle A'B'C'
Therefore. ΔABC ≅ ΔA'B'C', by the Side-Side-Side (SSS) rule of congruency.
9514 1404 393
Answer:
1) f⁻¹(x) = 6 ± 2√(x -1)
3) y = (x +4)² -2
5) y = (x -4)³ -4
Step-by-step explanation:
In general, swap x and y, then solve for y. Quadratics, as in the first problem, do not have an inverse function: the inverse relation is double-valued, unless the domain is restricted. Here, we're just going to consider these to be "solve for ..." problems, without too much concern for domain or range.
__
1) x = f(y)
x = (1/4)(y -6)² +1
4(x -1) = (y-6)² . . . . . . subtract 1, multiply by 4
±2√(x -1) = y -6 . . . . square root
y = 6 ± 2√(x -1) . . . . inverse relation
f⁻¹(x) = 6 ± 2√(x -1) . . . . in functional form
__
3) x = √(y +2) -4
x +4 = √(y +2) . . . . add 4
(x +4)² = y +2 . . . . square both sides
y = (x +4)² -2 . . . . . subtract 2
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5) x = ∛(y +4) +4
x -4 = ∛(y +4) . . . . . subtract 4
(x -4)³ = y +4 . . . . . cube both sides
y = (x -4)³ -4 . . . . . . subtract 4
