2) f(x)=-3x² + 3x
g(x)=2x+5
Find f(-4) divided by g(-4)

let's firstly convert the mixed fractions to improper fractions and then subtract.

[tex]\stackrel{mixed}{19\frac{1}{5}}\implies \cfrac{19\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{96}{5}} ~\hfill \stackrel{mixed}{11\frac{1}{11}}\implies \cfrac{11\cdot 11+1}{11}\implies \stackrel{improper}{\cfrac{122}{11}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{96}{5}~~ - ~~\cfrac{122}{11}\implies \stackrel{\textit{using the LCD of 55}}{\cfrac{(11)96~~ - ~~(5)122}{55}}\implies \cfrac{1056~~ - ~~610}{55} \\\\\\ \cfrac{446}{55}\implies {\LARGE \begin{array}{llll} 8\frac{6}{55} \end{array}}[/tex]

Answer:

[tex]x = -8[/tex]

Step-by-step explanation:

[tex]\begin{cases}2y = 2x + 12\\2-y = 4\end{cases}[/tex]

It would be easier to start with the second equation.

[tex]2 - y = 4 \text{ // Add y and subtract 4}\\\to 2 - y - 4 = 4 - y - 4\\\to -2 = y[/tex]

From here, we can substitute [tex]y = -2[/tex] into the first equation, to solve for [tex]x[/tex].

[tex]2(-2) = 2x + 12\\\to -4 = 2x + 12 \text{ // Subtract 12 on both sides}\\\to -4 - 12 = 2x + 12 - 12\\\to -16 = 2x \text{ // Divide by 2}\\\to -\frac{16}2 = \frac{2x}2\\\to -8 = x[/tex]

The measure of angle ABD is 20 degrees and this can be determined by using the properties of the angle bisector.

Given :

ABC = 40 and BD is the angle bisector of angle ABC.

The following steps can be used in order to determine the angle ABD:

Step 1 - According to the given data, BD is the angle bisector of angle ABC.

Step 2 - An angle bisector bisects the angle into two equal parts.

Step 3 - So, the measure of angle ABD is calculated as:

So, the measure of angle ABD is 20 degrees.

The volume of Ruth's new lunch box is 1,540 cm³.

The volume is a measure of an object occupied in a three-dimensional space.

Volume is a three-dimensional quantity that measures the capacity of a shape or the amount of three-dimensional space a closed figure can occupy.

The formula for computing a volume is height x length x width.

Height = 5 cm

Length = 22 cm

Width = 14 cm

Volume = 1,540 cm³ (5 x 22 x 14)

Thus, the volume of Ruth's new lunch box, showing the three-dimensional space within, is 1,540 cm³.

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The area of the triangle is 15 square units after using the distance formula.

It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.

The distance formula can be given as:

[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

It is given that:

The triangle is shown on the coordinate plane.

Using the distance formula:

The height of the triangle:

[tex]\rm AC=\sqrt{(-2+2)^2+(-3-3)^2}[/tex]

AC = 6 units

Again using the distance formula:

[tex]\rm BC =\sqrt{(3-(-2))^2+(-3-(-3))^2}[/tex]

BC = 5 units

The area of the triangle = (1/2)6x5

The area of the triangle = 15 square units

Thus, the area of the triangle is 15 square units after using the distance formula.

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The second

The correct answer is N ∈ line MN

The third

The correct answer is P ∉ line MN

The fourth

The correct answer is B ∉ line MN

The symbols are interpreted as follows

Given data

line MN

The first

It is already given that is  M ∈ line MN

point M can be located in line MN

The second

The correct answer is N ∈ line MN

point N can be located in line MN

The third

The correct answer is P ∉ line MN

point P cannot be located in line MN it is off the line

The fourth

The correct answer is B ∉ line MN

point B cannot be located in line MN it is off the line

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When y = 4 and x = 2, the inverse variation equation is y = 8/x

Inverse variation is variation in which the relationship between two variables is an inverse one. That is, while one variable increases, the other decreases.

Given that in an inverse variation, y = 4 when x = 2. Since y and x have an inverse relationship, we have that

y ∝ 1/x, this implies that

⇒ y = k/x where k = constant of proportionality

Now, given that  in an inverse variation, y = 4 when x = 2. Substituting the values of y and x into the equation, we have that

y = k/x

4 = k/2

k = 4 × 2

k = 8

So, susbstituting k = 8 into the equation for y, we have

y = k/x

y = 8/x

So, the inverse variation equation is y = 8/x

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Answer:

hope this helps if this is what you meant

10m6

Step-by-step explanation:

=2*m4*5*m2

=10*m6

=10m6

D. 37.8204

A negative absolute value is always positive.

Answer:

d) 37.8204

Step-by-step explanation:

Given that,

→ |-18.531| + |-19.2894|

Let's solve the problem,

→ |-18.531| + |-19.2894|

→ 18.531 + 19.2894

→ 37.8204

Thus, option (d) is correct.

The inverse of [tex]f[/tex], denoted [tex]f^{-1}[/tex], is such that

[tex]f\left(f^{-1}(x)\right) = x[/tex]

Given [tex]f(x)=\sqrt{x+9}[/tex], we have

[tex]f\left(f^{-1}(x)\right) = \sqrt{f^{-1}(x) + 9} = x[/tex]

Solve for [tex]x[/tex].

[tex]\sqrt{f^{-1}(x) + 9} = x[/tex]

[tex]\left(\sqrt{f^{-1}(x) + 9}\right)^2 = x^2[/tex]

[tex]f^{-1}(x) + 9 = x^2[/tex]

[tex]f^{-1}(x) = x^2 - 9[/tex]

Note that [tex]f(x)\ge0[/tex], so we must also have [tex]f\left(f^{-1}(x)\right) = x \ge 0[/tex]. This makes the third choice the correct one.

The amount of the shed that Jack would have built when Kyle finishes the shed is 8/25.

A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 8/25. 8 is the numerator and 25 is the denominator.

When Kyle finishes building the shed, he would have finished building a fraction of 1/1 of the shed. S

So, the amount of shed, that Kyle still needs to build to complete the shed is 1 ÷ 5/8

= 1 x 8/5 = 8/5

The amount of shed that Jack will have built when Kyle finishes the shed is:

8/5 x 1/5 = 8/25

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Answer:okay

Step-by-step explanation:hm

Answer: 16mph

Step-by-step explanation:

64 miles divided by the 4 hours comes out to 16 per hour

Answer: 16 miles per hour

The contrapositive statement is:

If x ≠ 2, then x^2 ≠ 4

And it is false.

First, we have two propositions:

p = "x^2 = 4"

q = "x = 2"

The contrapositive statement is:

¬q → ¬p

The negation of the propositions are:

¬q  = "x ≠ 2"

¬p = "x^2 ≠ 4"

Then the contrapositive statement with the given propositions is:

If x ≠ 2, then x^2 ≠ 4

Now, is this statement true?

No, because we can have:

x = -2 (which is different than 2, so the hypothesis is true)

and x^2 = (-2)^2 = 4

Then the conclusion is false, so the statement is false.

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Answer:

Step-by-step explanation:

i don't know if this is right but here is how i would do it.

Wins: Losses = 8:3 = 32: 12 = 32 wins + 12 losses = 44 games played.

The number of tiles is mathematically given as

x=2500Tiles

This is further explained below.

Generally, the equation for the Area of the floor is  mathematically given as

A= 20*5

A = 100m^2

Where

20*20=400cm

Therefore no tiles needed is

x=100*10000/400

x=2500Tiles

In conclusion, the number of tiles is

x=2500Tiles

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CQ

\A floor 5m by 20m is covered by square tiles of side 20cm. How many tiles are needed?

Answer:

The customer would have 177 minutes to talk on the phone for their monthly bill to be 84.25

Step-by-step explanation:

Point of correction it's not C=25m +40 but it is

C=0.25m +40

Where,

➟ 84.25 = 0.25m + 40

Let's solve your equation step-by-step.

84.25=0.25m+40

Step 1: Flip the equation.

0.25m+40=84.25

Step 2: Subtract 40 from both sides.

0.25m+40−40=84.25−40

0.25m=44.25

Step 3: Divide both sides by 0.25.

0.25m/0.25 = 44.25/0.25

m=177

∴ The customer would have 177 minutes to talk on the phone for their monthly bill to be 84.25

Answer:r=51

Step-by-step explanation:

Answer:

r = 51

Step-by-step explanation:

r - 17 = [tex]\frac{2}{3}[/tex] r ( multiply through by 3 to clear the fraction )

3r - 51 = 2r ( subtract 2r from both sides )

r - 51 = 0 ( add 51 to both sides )

r = 51

Answer:

9!

Step-by-step explanation:

Because a person who switch with 9 people, then another person switch with 8 people (because the first person was already counted), then another person who switch with 7 people (becsuse the first and the second person was already counted)... and you will get 9!. 9! is 9 factorial which is 9×8×7×6×5×4×3×2×1. :)

The quotient of each of the expressions are:

a. 1⅖ / -1/5 = -7

b. -0.4 ÷ 0.25 = 1.6

c. 7/8 ÷ -3/4 = -7/6

d. 0.7 ÷ -1 1/6 = -0.6

Quotient is the result you get after dividing one quantity by another. For example, the quotient of a and b is a/b.

Find the given quotient as shown below:

a. 1⅖ / -1/5

Convert mixed fraction to improper fraction

7/5 / -1/5

Change the division sign to multiplication and turn the fraction upside down

7/5 × (-5/1)

= -(7 × 5)/(5 × 1)

= -(7 × 1)/(1 × 1)

= -7/1

= -7

b. -0.4 ÷ 0.25

-0.4/0.25

= 1.6

c. 7/8 ÷ -3/4

Change the division sign to multiplication and turn the fraction upside down

7/8 × -4/3

= -(7/8 × 4/3)

= -(7 × 4)/(8 × 3)

= -(7 × 1)/(2 × 3)

= -7/6

d. 0.7 ÷ -1 1/6

0.7 ÷ -7/6

Change the division sign to multiplication and turn the fraction upside down

0.7 × -6/7

0.1 × -6/1

= 0.1 × -6

= -0.6

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Answer:

Step-by-step explanation:

28 + 76=

104

Her elevation is 104 at the peak.

The total amount including the tax rate is found as $34.

For the stated conditions in the question.

The original amount = $31.69.

The tax rate is 6%.

The total mount will be the sum of original amount and tax price.

First calculated the tax price;

6% of 31.69 = 6×31.69/100

6% of 31.69 = 1.9014

Tax price = $1.9014.

Total price = original amount + tax price

Total price = $31.69 + 1.9014

Total price = 33.5914

Total price = $34 (Round to the nearest cent.)

Thus, the total amount is estimated as $34.

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Answer:

x >-2

Step-by-step explanation:

subtract 2x from both sides

-6x - 16 - 2x < 0

subtract 2x from 6x

-8x - 16 < 0

add 16 to both sides

-8x < 16

divide by -8

x> -2

Answer:

1.75 inches deep into the post

Step-by-step explanation:

First, you do 2.5 - 0.75 which is 1.75 in

The answer is 1.75 in

Hope this helps!

Answer:

72

Step-by-step explanation:

this number sentence will be represented as,

72 is 8 times as many as 9

In the given statement is:

You conduct a survey of your small town about having a town wide gargae sale. of those surveyed, 56% are in favor and 44% are opposed. the actual percent could be 5% more or 5% less than the acquired results.

Using the absolute value function, we have that:

A. The least percentage is of 39% and the greatest is of 49%.

B. Since the greatest percentage is below 50%, the statement conflicts with the survey data.

What is the absolute value function?

The absolute function is defined by:

It measures the distance of a point x to the origin.

For this problem, the difference between the percentage of opposed and 44% can be of at most 5%, hence the absolute value equation is:

|x - 44| = 5.

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Answer:

1M

Step-by-step explanation:

HOPE ITS HELP!! PLEASE STAY ALIVE!! :D

Answer:

x=4

Step-by-step explanation:

Based on the number of sheets of construction paper that Cara uses to make 1/6 of her project, the number of sheets for the whole project would be 25 sheets

Cara will use 4¹/₆ sheets of construction paper for 1/6 of her poster board project so to find the sheets needed for the whole project, use direct proportion.

4¹/₆ sheets of construction paper  :  1/6 of project

x sheets of construction paper      : 1

1/6 × x = 4¹/₆

1/6x = 4¹/₆

x = 4¹/₆ ÷ 1/6

x = 25/6 x 6/1

x = 25 sheets

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