Which graph best represents the following equation?y + 7 = |x + 5|?(1 point)ResponsesAn absolute value function is graphed on a coordinate plane. Its vertex is 5 comma 7. It passes through the points left-parenthesis 2 comma 10 right-parenthesis and left-parenthesis 8 comma 10.Image with alt text: An absolute value function is graphed on a coordinate plane. Its vertex is 5 comma 7. It passes through the points left-parenthesis 2 comma 10 right-parenthesis and left-parenthesis 8 comma 10.An absolute value function is graphed on a coordinate plane. Its vertex is negative 5 comma negative 7. It passes through the points left-parenthesis negative 2 comma negative 4 right-parenthesis and left-parenthesis negative 8 comma negative 4.Image with alt text: An absolute value function is graphed on a coordinate plane. Its vertex is negative 5 comma negative 7. It passes through the points left-parenthesis negative 2 comma negative 4 right-parenthesis and left-parenthesis negative 8 comma negative 4.An absolute value function is graphed on a coordinate plane. Its vertex is 5 comma negative 7. It passes through the points left-parenthesis 2 comma negative 4 right-parenthesis and left-parenthesis 8 comma negative 4.Image with alt text: An absolute value function is graphed on a coordinate plane. Its vertex is 5 comma negative 7. It passes through the points left-parenthesis 2 comma negative 4 right-parenthesis and left-parenthesis 8 comma negative 4.An absolute value function is graphed on a coordinate plane. Its vertex is negative 5 comma 7. It passes through the points left-parenthesis negative 2 comma 10 right-parenthesis and left-parenthesis negative 8 comma 10.
note: Enter your answer and show all the steps that you use to solve this problem in the space providedxy7118139151017 Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.
To determine if y varies directly with x, we need to check if the ratio between y and x remains constant.
We can find the constant of variation, k, by dividing two sets of corresponding values for y and x.
Looking at the given values:
x: 7, 11, 18, 13, 9, 15, 10, 17
y: 19, 15, 19, 15, 5, 15, 10, 17
Let's calculate the ratios:
19/7 ≈ 2.714
15/11 ≈ 1.364
19/18 ≈ 1.056
15/13 ≈ 1.154
5/9 ≈ 0.556
15/15 = 1
10/10 = 1
17/17 = 1
The ratios are not equal; therefore, y does not vary directly with x. There is no constant of variation, and we cannot write an equation for this relationship.
note: Enter your answer and show all the steps that you use to solve this problem in the space provided.A candle is 17 in. tall after burning for 3 hours. After 5 hours, it is 15 in. tall. Write a linear equation to model the relationship between height h of the candle and time t. Predict how tall the candle will be after burning 8 hours.(2 points)
To write a linear equation to model the relationship between the height h of the candle and time t, we can use the two given data points.
Let's set up a slope-intercept form equation, y = mx + b, where y is the height h of the candle and x is the time t.
Given data points:
(3, 17)
(5, 15)
We can find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (15 - 17) / (5 - 3)
m = (-2) / 2
m = -1
Now we can substitute one of the given points and the slope into the equation y = mx + b to find the y-intercept (b).
Using the point (5, 15):
15 = -1(5) + b
15 = -5 + b
b = 20
So the equation that models the relationship between the height h of the candle and time t is:
h = -t + 20
To predict the height of the candle after burning for 8 hours, we substitute t = 8 into the equation:
h = -(8) + 20
h = 12
Therefore, the candle will be 12 inches tall after burning for 8 hours.
note: Enter your answer and show all the steps that you use to solve this problem in the space provided.The graph of g(x) is f(x) translated to the left 8 units and up 2 units. What is the function rule for g(x) given f(x)=x2 ?%20%20%20%20%20%20(2%20points)
To translate the graph of f(x) = x^2 to the left 8 units and up 2 units, we need to adjust the function rule for g(x) accordingly.
The translation to the left by 8 units is represented by (x + 8), and the translation up by 2 units is represented by +2.
Therefore, the function rule for g(x) is:
g(x) = (x + 8)^2 + 2
This means that g(x) is the result of taking the function f(x) = x^2 and shifting it 8 units to the left and 2 units up.
The graph that best represents the equation y + 7 = |x + 5| is:
An absolute value function is graphed on a coordinate plane. Its vertex is 5 comma -7. It passes through the points (2, -4) and (8, -4).