The value of h is h = -1.5
Step-by-step explanation:
The quadratic equation is represented by a parabola, the vertex form of the equation is y = a(x - h)² + k, where
- (h , k) are the coordinates of its vertex point
- a is the coefficient of x²
∵ The graph is a parabola opens up
∵ It has a vertex at (-1.5, 0)
∵ The vertex of the parabola is (h , k)
∴ h = -1.5 and k = 0
∵ The graph shows f(x) = (x - h)²
∵ The coordinates of the vertex are (h , k)
∵ h = -1.5 and k = 0
∴ h = -1.5
The value of h is h = -1.5
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Answer:
y =
x - ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = ![\frac{y_{2}-y_{1} }{x_{2}-x_{1} }](https://tex.z-dn.net/?f=%5Cfrac%7By_%7B2%7D-y_%7B1%7D%20%20%7D%7Bx_%7B2%7D-x_%7B1%7D%20%20%7D)
with (x₁, y₁ ) = (- 6, - 5) and (x₂, y₂ ) = (2, 1) ← 2 points on the line
m =
=
=
=
, then
y =
x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (2, 1 ) , then
1 =
+ c ⇒ c = 1 -
=
-
= - ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
y =
x -
← equation of line
<h3>
Solution (Line 2): <u>(Refer to graph 1)</u></h3>
<u>Note that:</u>
- Given points: (0, -2) and (1, -4)
- Slope formula: Rise/Run
- Point slope form formula: y - y₁ = m(x - x₁)
To create the equation of the line, find the slope. Then, use point slope form to find the equation of the line.
<u>Use the slope formula to find the slope.</u>
- Rise/Run = Slope
- => Rise = -2; Run = 1
- => Rise/Run = -2/1 = -2
<u>Use the point slope form formula.</u>
- y - y₁ = m(x - x₁) = Equation of line.
- => y - (-4) = -2(x - 1) = Equation of line.
- => y + 4 = -2x + 2
- => y = -2x + 2 - 4
- => y = -2x - 2
<h3>
Solution (Line 3): <u>(Refer to graph 2)</u></h3>
<u>Note that:</u>
- Given points: (0, -2) and (-4, 3)
- Slope formula: Rise/Run
- Point slope form formula: y - y₁ = m(x - x₁)
To create the equation of the line, find the slope. Then, use point slope form to find the equation of the line.
<u>Use the slope formula to find the slope.</u>
- Rise/Run = Slope
- => Rise = -5; Run = 4
- => Rise/Run = -5/4
<u>Use the point slope form formula.</u>
- y - y₁ = m(x - x₁) = Equation of line.
- => y - 3 = -5/4{x - (-4)} = Equation of line.
- => y - 3 = -5/4{x + 4}
- => y - 3 = -5x/4 - 5
- => y = -5x/4 - 2
<h3>
Solution (Line 4): <u>(Refer to graph 3)</u></h3>
<u>Note that:</u>
- Given points: (0, -2) and (-3, -5)
- Slope formula: Rise/Run
- Point slope form formula: y - y₁ = m(x - x₁)
To create the equation of the line, find the slope. Then, use point slope form to find the equation of the line.
<u>Use the slope formula to find the slope.</u>
- Rise/Run = Slope
- => Rise = 3; Run = 3
- => Rise/Run = 3/3 = 1
<u>Use the point slope form formula.</u>
- y - y₁ = m(x - x₁) = Equation of line.
- => y - (-5) = 1{x - (-3)} = Equation of line.
- => y - (-5) = 1{x + 3}
- => y + 5 = x + 3
- => y = x - 2
Hoped this helped!
The answer would be 59 miliseconds
Using it's formula, the surface area of the figure is:
A. S=2332 m²
<h3>What is the surface area of a rectangular prism?</h3>
The surface area of a rectangular prism of dimensions l, w and h is given by:
S = 2(lw + lh + wh)
In this problem, the dimensions are:
35m, 9m, 16m
Hence the surface area of the rectangular prism is:
S = 2(35 x 9 + 35 x 16 + 16 x 9) = 2038 m².
<h3>What is the surface area of a cube?</h3>
The surface area of a cube of side length l is given by:
S = 6l².
In this problem, we have that l = 7 m, hence the surface area is:
S = 6 x 7² = 294 m².
<h3>What is the total surface area?</h3>
The total surface area is the sum of the surface areas, hence:
T = 2038 m² + 294 m² = 2332 m².
Which means that option A is correct.
More can be learned about surface area at brainly.com/question/13030328
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