Answer:
B
Step-by-step explanation:
The red graph is a horizontal translation of 5 units left, followed by a reflection in the x- axis, of the black graph.
Given f(x) then f(x + a) is a horizontal translation of f(x)
• If a > 0 then shift to the left of a units
• If a < 0 then shift to the right of a units
Here the graph is shifted 5 units to the left, thus
f(x) → f(x + 5)
Under a reflection in the x- axis
a point (x, y ) → (x, - y )
Note the y- coordinate of the image is the negative of the original
Note that 
= - y, thus
The equation of the red graph is
= f(x + 5) → B
Answer:
x = 12
y = 9
z = 11
Step-by-step explanation:
so, let's just do all the calculations in there :
(3×5)⁴ = 3⁴×5⁴
(2×3)⁵ = 2⁵×3⁵
(2×5)⁷ = 2⁷×5⁷
multiplying all 3 terms is then
3⁴×5⁴×2⁵×3⁵×2⁷×5⁷
more let's "group" and combine these terms based on the bases of the power operations, as we need to get an expression showing 2, 3 and 5 with their powers.
so, for the base of 2 we have
2⁵×2⁷ = 2¹²
for the base of 3 we have
3⁴×3⁵ = 3⁹
fire the base of 5 we have
5⁴×5⁷ = 5¹¹
so we get
2¹² × 3⁹ × 5¹¹
=>
x=12
y=9
z=11
The answer to the question is 1.032
STEP-BY-STEP SOLUTION:
( x + 4 )^2 + y^2 = 22
x^2 + 2 × x × 4 + 4^2 + y^2 = 22
x^2 + 8x + 16 + y^2 = 22
y^2 = 22 - x^2 - 8x - 16
y^2 = - x^2 - 8x + 6
FINAL ANSWER:
Therefore, the answer is:
D. y^2 = - x^2 - 8x + 6
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