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).
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.
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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.
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.
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 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.
1 answer