Answer:
4(x) + 4(2)
Step-by-step explanation:
4(x+2) = 4(x) + 4(2)
Distribution property
Answer:
g(x) = - x² - 4 ⇒ A
Step-by-step explanation:
Let us revise the reflection and translation of a function
- If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)
- If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)
- If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)
- If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)
- If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k
- If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) – k
f(x) = x² is the blue curve
g(x) is its image is the red curve
∵ g(x) is the image of f(x)
∵ f(x) is opened upward
∵ g(x) is opened downward
→ That means the sign of y-coordinates of all points on the blue
graph are opposite
∴ f(x) is reflected about the x-axis
∴ Its image is - f(x)
∵ The vertex of f(x) is (0, 0)
∵ The vertex of g(x) = (0, -4)
→ That means the function translated 4 units down
∴ - f(x) is translated 4 units down
∴ Its image is - f(x) - 4
∴ g(x) = - f(x) - 4
∵ f(x) = x²
∴ g(x) = - x² - 4
Answer:
<h2>
62.832 mi.²</h2><h2>
</h2>
Step-by-step explanation:
surface area = 2πrh + 2πr²
where r = 2 miles radius
h = 3 miles
<u>plugin values into the formula</u>
surface area = 2πrh + 2πr²
= 2π (2) 3 + 2π (2)²
= 37.699 + 25.133
= 62.832 mi.²
the graph of 13y + kx = 4 and the line containing the points (5, -8) and (2, 4) are parallel.
We find the slope of parallel line using two given points
(5, -8) and (2, 4)
Slope formula is



so slope = -4
Slope of any two parallel lines are always equal
Lets find the slope of the equation 13y + kx = 4
Subtract kx on both sides
13 y = -kx + 4
Divide both sides by 13

Now slope = -k/13
We know slope of parallel lines are same
So the slope of 13y + kx = 4 is also -4
Hence we equation the slope and find out k

Multiply by 13 on both sides and divide by -1
k = 52
the value of k = 52
Answer:
x = 4
Step-by-step explanation:
1.5(x + 4) – 3 = 4.5(x – 2)
Distributive property
1.5x + 6 - 3 = 4.5x - 9
1.5x + 3 = 4.5x - 9
1.5x - 4.5x = -9 -3
-3x = -12
x = 4