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Graph f(x)=|x−2|+3 . Use the ray tool to graph the function.

maks197457 [2]

Answer:

The graph will be 2 units away from the origin on positive $x-axis$ and three units upward from the origin towards $y-axis$ .

Step-by-step explanation:

Here is a graph attached with it.

To graph $\left | x-2 \right |+3$ we know that positive $\left | x \right |$ is a $V$ shaped from the origin.

Key points:

To move rightward there must be a negative inside the parentheses.
And to move upward we must have positive $b = constant$ .

If we have to move towards $x-axis$ then we must have negative inside it.

And if we have to move upward in $y-axis$ positive we must have positive constant value.

So the graph will be three units upward and two units rightward with a V-shaped ray.

4 0

3 years ago

Write the equation of the parabola that has its x-intercepts at (1+<img src="https://tex.z-dn.net/?f=%5Csqrt%7B5%7D" id="TexForm

VladimirAG [237]

Answer:

$y=2x^2-4x-8$

Step-by-step explanation:

Factored form of a parabola

$y=a(x-p)(x-q)$

where:

p and q are the x-intercepts.
a is some constant.

Given x-intercepts:

(1+√5, 0)
(1-√5, 0)

Therefore:

$\implies y=a(x-(1+\sqrt{5}))(x-(1-\sqrt{5}))$

$\implies y=a(x-1-\sqrt{5})(x-1+\sqrt{5})$

To find a, substitute the given point (4, 8) into the equation and solve for a:

$\implies a(4-1-\sqrt{5})(4-1+\sqrt{5})=8$

$\implies a(3-\sqrt{5})(3+\sqrt{5})=8$

$\implies4a=8$

$\implies a=2$

Therefore, the equation of the parabola in factored form is:

$\implies y=2(x-1-\sqrt{5})(x-1+\sqrt{5})$

Expand so that the equation is in standard form:

$\implies y=2(x^2-x+\sqrt{5}x-x+1-\sqrt{5}-\sqrt{5}x+\sqrt{5}-5)$

$\implies y=2(x^2-x-x+\sqrt{5}x-\sqrt{5}x+\sqrt{5}-\sqrt{5}+1-5)$

$\implies y=2(x^2-2x-4)$

$\implies y=2x^2-4x-8$

6 0

1 year ago

5w = 23 - 3f and 4f = 12 - 2w

Kryger [21]

Answer:

f = 1, w = 4

Step-by-step explanation:

Given the 2 equations

5w = 23 - 3f → (1)

4f = 12 - 2w (add 2w to both sides )

2w + 4f = 12 ( subtract 4f from both sides )

2w = 12 - 4f → (2)

Multiplying (1) by 4 and (2) by - 3 and adding the result will eliminate f

20w = 92 - 12f → (3)

- 6w = - 36 + 12f → (4)

Add (3) and (4) term by term to eliminate f

14w = 56 ( divide both sides by 14 )

w = 4

Substitute w = 4 into either of the 2 equations and solve for f

Substituting into (1)

5(4) = 23 - 3f

20 = 23 - 3f ( subtract 23 from both sides )

- 3 = 3f ( divide both sides by - 3 )

1 = f

5 0

2 years ago

Read 2 more answers

Solve. y=x - 7 5+2y=7

lesantik [10]

Answer:

$\huge\boxed{x=8;\ y=1\to(8;\ 1)}$

Step-by-step explanation:

$\left\{\begin{array}{ccc}y=x-7&(1)\\5+2y=7&(2)\end{array}\right\\\\\text{Substitute (1) to (2) and solve for x:}\\\\5+2(x-7)=7\qquad\text{use the distributive property}\\\\5+(2)(x)+(2)(-7)=7\\\\5+2x-14=7\\\\2x+(5-14)=7\\\\2x-9=7\qquad\text{add 9 to both sides}\\\\2x-9+9=7+9\\\\2x=16\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{16}{2}\\\\\boxed{x=8}$

$\text{Substitute it to (1):}\\\\y=8-7\\\\\boxed{y=1}$

8 0

2 years ago

Read 2 more answers

How do you find the surface area of a regular triangular prism

Dmitry [639]

So a triangular prisim is like a triangle stacked on top of x number of identical triangles making a height, like a piece of paper made into a stack

so
basically find the area of each side and add

look at diagram/attachment
find area of triangle
1/2 b times h= area of 1 triangular face

multiply by 2 because 2 sides so 1/2 times 2 b times h=b times h

then 3 other sides
find area of each side and add
areas=(H times B)+(H times c)+(H times a)

so SA=(b times H)+(H times B)+(H times c)+(H times a)

8 0

2 years ago