(x⁴ + 8x³ - 45x + 30) ÷ (x + 7)

Topic is Polynomials. Find the answer using long division. Please, provide detailed steps. ​

Answer:

[tex]f^{-1}[/tex](x) = x - 3

Step-by-step explanation:

let y = f(x) and rearrange making x the subject, that is

y = x + 3 (subtract 3 from both sides )

y - 3 = x

Change y back into terms of x with x = [tex]f^{-1}[/tex](x) , thus

[tex]f^{-1}[/tex](x) = x - 3

Answer:

yeet

Step-by-step explanation:

yeet yeet yeet yeet yeet yeet yeet yeet yeet eet yett yeet yeet yeet yeet yeet yeet yeet yeet yeety

Answer:

its a i did it on egn

Step-by-step explanation:

Answer:

-18x

Step-by-step explanation:

-8 -10 = -18

Answer:

The answer is -0.5 or -1/2

Step-by-step explanation:

You can flip the second fraction over and multiply the two fractions by each other. It would be like this: 2/3 x -3/4, and multiply and you get -6/12 which can be further reduced to -1/2.

Hope this helped! Remember to use the formula Skip, Flip, Multiply in which you skip the first fraction, flip the division sign to multiply and flip the second fraction over!

Answer:

180

Step-by-step explanation:

The 12 th square number is

12² = 12 × 12 = 144

The 6 th square number is

6² = 6 × 6 = 36

Thus

sum = 144 + 36 = 180

Answer:

A: 24

Step-by-step explanation:

The length of Brown's pin is 6, while the width is 2. If Johnson has two more meter in length, that's 8, and 1 more than the the width, that's 3. 8 x 3 is 24.  

Multiply 14 by 0.3

14 x 0.3 = 4.2

The answer is 4.2

Answer:

4.2 is the answer

Step-by-step explanation:

Remember, in math, 'of ' always mean multiplication!!!

Answer:

i think [after solving] that it is option B and C

Step-by-step explanation:

3. Graph the given quadratic function in the factored form as shown below.

4. The quadratic equation in vertex form, given the vertex (-1,3) and passes through (1, -5), is y = -2(x + 1)² + 3.

The given quadratic function in factored form is y = (x - 3)(x + 1).

Graph of the given quadratic function in the factored form as shown below.

Zeros: The zeros of the function occur when y = 0.

So the zeros of the function are x = 3 and x = -1.

Axis of Symmetry:  

The axis of symmetry is x = (3 + (-1)) / 2 = 1.

Vertex:

The vertex is (1, -4).

Y-intercept:

The y-intercept is (0, -3).

Domain: The domain of a quadratic function is all real numbers, so the domain is (-∞, ∞).

Range: Since the coefficient of the x² term is positive, the parabola opens upward. Therefore, the range is y ≥ -4.

Write the quadratic equation of the following in vertex form: vertex (-1,3) and passes through (1, -5)

Using the given information, the vertex form equation can be written as:

[tex]y = a(x - (-1))^2 + 3[/tex]

To find the value of 'a,' we can substitute the coordinates (1, -5) into the equation:

-5 = a(1 - (-1))² + 3

-5 = a(2)² + 3

-5 = 4a + 3

-8 = 4a

a = -2

Plugging the value of 'a' back into the equation, we get the quadratic equation in vertex form:

y = -2(x + 1)² + 3

Therefore, the quadratic equation in vertex form, given the vertex (-1,3) and passes through (1, -5), is y = -2(x + 1)² + 3.

Learn more about quadratic function here:

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Answer:

B.) 12

Step-by-step explanation:

h(x) = 3^x + 3

h(2) = 3^2 + 3

h(2) = 9 + 3

h(2) = 12

Answer:

y = 3/4x -2

Step-by-step explanation:

Rise 3, run 4. Slope 3/4. Y intercept at -2.

Answer:

1) The expected value of the "winnings" is $(-0.97[tex]\overline 2[/tex])

2) The variance for the "winnings" is $0.57966

3) The standard deviation for the "winnings" is$0.761354

4) The game is not a fair game because one is expected to lose $0.97[tex]\overline 2[/tex]

Step-by-step explanation:

1) The probability of having a sum of 2 = 1/6×1/6 = 1/36

The probability of having a sum of 3 = 1/6×1/6 = 1/36

The probability of having a sum of 4 = 1/6×1/6 + 1/6×1/6  = 1/18

The probability of having a sum of 5 = 1/6×1/6 + 1/6×1/6 = 1/18

The probability of having a sum of 6 = 1/6×1/6 + 1/6×1/6 + 1/6×1/6 = 1/12

The probability of having a sum of 7 = 1/6×1/6 + 1/6×1/6 + 1/6×1/6 = 1/12

The probability of having a sum of 8 = 1/6×1/6 + 1/6×1/6 + 1/6×1/6 = 1/12

The probability of having a sum of 9 = 1/6×1/6 + 1/6×1/6  = 1/18

The probability of having a sum of 10 = 1/6×1/6 + 1/6×1/6 = 1/18

The probability of having a sum of 11 = 1/6×1/6  = 1/36

The probability of having a sum of 12 = 1/6×1/6  = 1/36

The values are;

For 2, we have 1/36 × (20 - 5) = 0.41[tex]\overline 6[/tex]

For 3, we have 1/36 × (20 - 5) = 0.41[tex]\overline 6[/tex]

For 4, we have 1/18 × (20 - 5) = 0.8[tex]\overline 3[/tex]

For 5, we have 1/18 ×  (10 - 5) = 0.2[tex]\overline 7[/tex]

For 6, we have 1/12 × (10 - 5) = 0.41[tex]\overline 6[/tex]

For 7, we have 1/12 × (10 - 5) = 0.41[tex]\overline 6[/tex]

For 8, we have 1/12 × (10 - 5) = 0.41[tex]\overline 6[/tex]

For 9, we have 1/18 × (-20 - 5) = -1.3[tex]\overline 8[/tex]

For 10, we have 1/18 × (-20 - 5) = -1.3[tex]\overline 8[/tex]

For 11, we have 1/36 × (-20 - 5) = -0.69[tex]\overline 4[/tex]

For 12, we have 1/36 × (-25 - 5) = -0.69[tex]\overline 4[/tex]

The expected value of the winnings is given as follows;

0.41[tex]\overline 6[/tex] + 0.41[tex]\overline 6[/tex] + 0.8[tex]\overline 3[/tex] + 0.8[tex]\overline 3[/tex] + 0.8[tex]\overline 3[/tex] + 0.41[tex]\overline 6[/tex] + 0.41[tex]\overline 6[/tex] + -1.3[tex]\overline 8[/tex] -1.3 - 0.69[tex]\overline 4[/tex] - 0.69[tex]\overline 4[/tex] = -0.97[tex]\overline 2[/tex]

Therefore, the expected value = $-0.97[tex]\overline 2[/tex], which is one is expected to lose $0.97[tex]\overline 2[/tex]

2) Using Microsoft Excel, we have;

The variance for the "winnings", σ² = $0.57966

3) The standard deviation for the "winnings" = √σ² = √(0.57966) ≈ $0.761354

4) The game is not a fair game because one is expected to lose $0.97[tex]\overline 2[/tex]

Answer:

Step-by-step explanation:

16.) B. y = 3x + 2

17.) y = -2

(show in graph below) - -

                                        |

                                       V

Answer:

step 2

Step-by-step explanation:

he was not supposed to multiply by x

he was supposed to combine like terms

add -2x and 4x and add 6 and 5

Step-by-step explanation:

*Assuming you meant polynomial function of degree 3*

The given zeros are 2, -1, and 3. To get the zeros in the first place, we have a deconstructed polynomial that looks like this:

(x-2)(x+1)(x-3)

Now, we can foil these out. **Quick note: if the degree of your polynomial is greater than 3, simply put a square root on one of the terms: (x-2)^2

After foiling you should get: x^3-4x^2+x+6

Answer:

Graph A

Step-by-step explanation:

The line starts at 1 since that is what he began with. Then it grows by two because every year he gets too more.

Answer:

I am pretty sure the answer would be Option B.

Step-by-step explanation:

If you look on the graph, Option B is the one that makes the most sense because it goes up by a ratio of 1:2 just like in the problem, 1 gift train + 2 trains per year.

Option A would not make sense because it goes up by the ratio of 1:3 and doesn't match up with the problem.

Note:

I hope this helps! :) Please correct me if I am wrong.

Answer:

[tex]5(x - 2) = \frac{15x + 6}{3} - 12 \\ 5(x - 2) = \frac{15x + 6 - 36}{3} \\ 5(x - 2) = \frac{15x - 30}{3} \\ 5(x - 2) = \frac{15(x - 2)}{3} \\ 15(x - 2) = 15(x - 2)[/tex]

Answer:

All real numbers

Step-by-step explanation:

Given

5(x - 2) = [tex]\frac{15x+6}{3}[/tex] - 12

Multiply through by 3 to clear the fraction

15(x - 2) = 15x + 6 - 36 ← distribute left side and simplify

15x - 30 = 15x - 30

Since both sides are equal then any real value of x will be a solution.

Thus the solution is All real numbers

Answer:

f(-12) = -174

Step-by-step explanation:

f(x) = 14x − 6

f(-12) = 14(-12) - 6

f(-12) = -168 - 6

f(-12) = -174

hope this helps, pls mark brainliest :D

Answer:

(x−7,y+5)

A p e x n dat

Answer:

LCM= 154

Step-by-step explanation:

Alternate exterior angles are the pair of angles that lie on the outer side of the two parallel lines but on either side of the transversal line. Illustration: In the diagram above, ∠ a and ∠ d makes a pair of alternate exterior angles and ∠ b and ∠c makes another pair of alternate exterior angles.

Answer: they started at 360 feet

The y-intercept means the height above the canyon floor is 360 feet at

t = 0.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The y-intercept in a graph is the point on the y-axis.

This point is when x = 0.

So,

From the given context it means,

The height above the canyon floor is 360 feet at t = 0.

Thus,

The y-intercept means the height above the canyon floor is 360 feet at

t = 0.

Learn more about coordinates here:

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Answer:

y would be 6

Step-by-step explanation:

Because 5 x 3 would be 15

then you would do 2 x 3 would be 6

Answer:

y=2/3

Step-by-step explanation:

first make the equation to interpret the question

x=k/y

find the value of k, which is a constant

when x=5 and y=2

5=k/2

k=10.

hence, find y when x=15

x=k/y

x=10/y

15=10/y

cross multiply

15y=10

divide both sides by 15

y=10/15

y=2/3

Answer:its 200

Step-by-step explanation:

Answer:

Its 200, that's a funny question though!

Step-by-step explanation:

Have a good day!

Step-by-step explanation:

Rs8,100 / (Rs45 per square meter)

= 180 square meters.

The area of the 4 walls of the room is 180 sq.m.