Answer:
k(x) = -|x + 2| + 3
Step-by-step explanation:
Parent function of the absolute function given in the graph,
f(x) = |x|
1). Function 'g' is reflected across the x-axis, then the image will be,
h(x) = -f(x) = -|x|
2). Function 'h' the shifted 2 units left and 3 units upwards, image function will be,
k(x) = h(x + 2) + 3
k(x) = -|x + 2| + 3
Therefore, the transformed function is k(x) = -|x + 2| + 3.
Those two angles are alternate interior angles, so they must be congruent.
3x = 2x + 20
x = 20
The length of the segment HI in the figure is 32.9
<h3>How to determine the length HI?</h3>
To do this, we make use of the following secant-tangent equation:
HI² = KI * JI
From the figure, we have:
KI = 21 + 24 = 45
JI = 24
So, we have:
HI² = 45 * 24
Evaluate the product
HI² = 1080
Take the square root of both sides
HI = 32.9
Hence, the length of the segment HI is 32.9
Read more about secant and tangent lines at:
brainly.com/question/14962681
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Answer: There were 78 red apples at the party.
Step-by-step explanation:
This situation can be represented by the equation
x + 3x + 2(3x) = 130 where x is the number of green apples, 3x is the number of yellow apples and 2(3x) is the number of red apples.
Now solve for x
x +3x +2(3x) =130
4x + 6x = 130
10x = 130
x = 13
Now we know that x is 13 so put it into the expression for red apples and solve for the actual number of red apples.
2 * (3*13) = ?
2 * 39 = 78