(x^2-2)^2-10(x^2-2)+21=0 find one value of x that is a solution to the equation

A oreos says that now it contains 20% more. Originally, it came with 19.5 ounces of oreos . How much oreos does the box come

Zolol [24]

23.4 ounces of Oreos

3 0

3 years ago

Read 2 more answers

Solve and show the steps to the picture attached

lina2011 [118]

Answer:

The image of point (2, 4) after transformation is (-2, 13) ⇒ D

Step-by-step explanation:

Let us revise some transformation

Translation right-left OR up-down

If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h) ⇒ add x-coordinate of every point by h

If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h) ⇒ subtract x-coordinate of every point by h

If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k ⇒ add y-coordinate of every point by k

If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) - k ⇒ subtract y-coordinate of every point by k

A vertical stretching and a vertical compression (or shrinking)

If m > 1, the graph of y = m • f(x) is the graph of f(x) vertically stretched by factor m. ⇒ multiply every y-coordinate by m

If 0 < m < 1 (a fraction), the graph of y = m • f(x) is the graph of f(x) vertically shrunk (or compressed) by factor m ⇒ multiply every y-coordinate by m

Let us use these rules to solve the question.

∵ Point (2, 4) lies on y = x²

∵ The image of y = x² is y = 3(x + 4)²+1

→ The rules of transformation is y = m(x + h)² + k

∵ m is the scale factor of a vertical stretched

∵ m = 3

→ By using the 5th rule above

∴ The y-coordinate of point (2, 4) should multiply by 3

∴ The image of the point is (2, 4 × 3) = (2, 12)

∵ h is the horizontal translation to the left

∵ h = 4

→ By using the 2nd rule above

∴ The x-coordinate of point (2, 12) should subtract by 4

∴ The image of the point is (2 - 4, 12) = (-2, 12)

∵ k is the vertical translation up

∵ k = 1

→ By using the 3rd rule above

∴ The y-coordinate of point (-2, 12) should add by 1

∴ The image of the point is (-2, 12 + 1) = (-2, 13)

∴ The image of point (2, 4) after transformation is (-2, 13)

3 0

3 years ago

Need help with these!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Gelneren [198K]

Answer:

Step-by-step explanation:

8 0

3 years ago

Potassium fluoride is used for frosting glass. calculate the molarity of a solution prepared by dissolving 78.6 g of kf in enoug

melisa1 [442]

<span>There are a number of ways to express concentration of a solution. This includes molarity. Molarity is expressed as the number of moles of solute per volume of the solution. We calculate as follows:

Molarity = 78.6 g KF ( 1 mol / 58.1 g ) / .225 L = 6.013 mol / L KF solution</span>

3 0

3 years ago

A rectangular poster is to contain 578 square inches of print. The margins at the top and bottom of the poster are to be 2 inche

lord [1]

Answer:

19 by 38

Step-by-step explanation:

The area of the poster, A=xy

Margin at both up and bottom is 2inches, at the right and left is 1 inch

Then we can say

(x-4)(y-2)= 578

Let us make y subject of the formula

(y-2)= 578/(x-4)

y=[ 578/(x-4)] + 2

If we substitute into the area A equation we have

A= x { [ 578/(x-4)] + 2}

A= 2x + (578x)/(x - 4)

If we differentiate we have

A'(x)= [2+578(x-4)+578x ]/ (x-4)^2

=[ 2(x-4)^2 + 578(x -4) + 578x ] / (x-4)^2

=[ 2(x^2 - 8x +16) + 578(x-4) + 578x ] /(x-4)^2

If we simplify this we have

=[ 2x^2 -16x +32+578x -578x - 2312]/ (x-4)^2

=( 2x^2 -16x - 2312) / (x-4)^2

At A'(x)= 0

= ( x^2 - 8x - 2312) / (x-4)^ =0

If we divide through by 2 we have

x^2 - 8x - 1156= 0

Solving the quadratic eqn( CHECK THE ATTACHMENT)

X= 38 or -30 then we choose the positive one, then x= 38

Then from area of the poster

A= (x-4)(y-2)= 578

Substitute 38 as value of x

(38-4)(y-2)= 578

34(y-2)=578

34y-68=578

34y=646

y=19

Hence dimensions of the poster is 19 by 38

CHECK THE ATTACHMENT FOR QUADRATIC SOLUTION

7 0

3 years ago