−t=9(t−10) pls show work too thank u so much
2 answers:
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Answer:
(- 5, 0 ), (7, 0 )
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (1, - 108 ), thus
y = a(x - 1)² - 108
To find a substitute (0, - 105 ) into the equation
- 105 = a(- 1)² - 108 ( add 108 to both sides )
3 = a
y = 3(x - 1)² - 108 ← equation in vertex form
To find the x- intercepts, let y = 0, that is
3(x - 1)² - 108 = 0 ( add 108 to both sides )
3(x - 1)² = 108 ( divide both sides by 3 )
(x - 1)² = 36 ( take the square root of both sides )
x - 1 = ± = ± 6 ( add 1 to both sides )
x = 1 ± 6, so
x = 1 - 6 = - 5
x = 1 + 6 = 7
x- intercepts are (- 5, 0), (7, 0)
Question # 28
We can use any two points to find the equation of the total cost(y) in terms of number of square feet(x).
I will be using first two points (1800, 630) and (2300, 805)
First we need to find the slope of the line.
Using the slope and a point (1800, 630) we can write the equation as:
y - 630 = 0.35 (x - 1800)
y = 0.35x - 630 + 630
y = 0.35x
So, option G gives the correct equation of the function.
Question # 29
Given function is:
y = 3.54x - 54.68
Increasing the y-intercept by 33.14 will result in following equation:
y = 3.54x - 54.68 + 33.14
y = 3.54x - 21.54
Notice that the slope of the lines are still the same. This suggest the lines are parallel. Addition or subtraction of a number to y-intercept only shifts the graph vertically. So in this case the graph will be shifted up by 33.14 units and will be parallel to the original line. Since graph is shifted up, its y-intercept will also be shifted up i.e. y-intercept will increase.
x-intercept is the point where y is zero. So substituting y=0 in both equations and finding the value of x will result in x-intercepts. The x-intercept decreases on shifting up the y-intercept in this case.
So, the only correct option is option A
We can use any two points to find the equation of the total cost(y) in terms of number of square feet(x).
I will be using first two points (1800, 630) and (2300, 805)
First we need to find the slope of the line.
Using the slope and a point (1800, 630) we can write the equation as:
y - 630 = 0.35 (x - 1800)
y = 0.35x - 630 + 630
y = 0.35x
So, option G gives the correct equation of the function.
Question # 29
Given function is:
y = 3.54x - 54.68
Increasing the y-intercept by 33.14 will result in following equation:
y = 3.54x - 54.68 + 33.14
y = 3.54x - 21.54
Notice that the slope of the lines are still the same. This suggest the lines are parallel. Addition or subtraction of a number to y-intercept only shifts the graph vertically. So in this case the graph will be shifted up by 33.14 units and will be parallel to the original line. Since graph is shifted up, its y-intercept will also be shifted up i.e. y-intercept will increase.
x-intercept is the point where y is zero. So substituting y=0 in both equations and finding the value of x will result in x-intercepts. The x-intercept decreases on shifting up the y-intercept in this case.
So, the only correct option is option A