i shall brainliest you. Use the distributive property to expand the following expression.
-4(3.2x + 5y - 2.1)

[tex]h(x) =8x^3-19x^2+14x-3[/tex]

Step-by-step explanation:

Given functions are:

[tex]f(x) = 8x-3\\g(x) = (x-1)^2[/tex]

h(x)  is the product of g(x) and f(x)

[tex]h(x) = f(x) * g(x)\\= (8x-3)(x-1)^2\\= (8x-3)(x^2-2x+1)\\= 8x(x^2-2x+1)-3(x^2-2x+1)\\= 8x^3-16x^2+8x-3x^2+6x-3[/tex]

Combining like terms

[tex]=8x^3-16x^2-3x^2+8x+6x-3\\=8x^3-19x^2+14x-3[/tex]

Hence,

[tex]h(x) =8x^3-19x^2+14x-3[/tex]

Keywords: Functions, product

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Answer:

Anil would take 10 days and Sunil would take 15 days to complete the work.

Step-by-step Explanation:

To Determine:

How many days they took to complete the work?​

Information Fetching and Solution steps:

Let is consider,

The number of days taken by Anil to complete the required work = d.

The number of days taken by Sunil to complete the required work = d + 5

Work done by Anil in one day = 1÷d

Work done by Sunil in one day = 1÷ (d+5)

Work done together by Anil and Sunil for one day = 1/d + 1/(d+5)

                                                                                    = (d+5+d)/d(d+5)

                                                                                    = (2d+5)/d(d+5)  

Work done together by Anil and Sunil for 4 days = 4×(2d+5)/d(d+5) ....[A]

Work done by Sunil in 5 days = 5÷ (d+5)  ....[B]

By adding equation [A] and [B], we can determine the complete work

[A] + [B] = 1

((4×(2d+5)/d(d+5))) + (5÷ (d+5)) = 1

8d+20+5d=1d(d+5)

13d+20=d²+5d

−d²+8x+20=0

(−d−2)(d−10)=0

d=−2 or d=10

As number of days can not be negative. So, d = 10. Therefore,

The number of days taken by Anil to complete

the required work = 10 days

The number of days taken by Sunil to complete

the required work = d+5 = 15 days

Hence, Anil would take 10 days and Sunil would take 15 days to complete the work.

Keywords: days, work

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Answer:

(-18, 2)

Step-by-step explanation:

To rotate a point by 90°:

R₉₀ (x, y) = (-y, x)

R₉₀ (1, 9) = (-9, 1)

To dilate by 2:

D₂ (x, y) = (2x, 2y)

D₂ (-9, 1) = (-18, 2)

Answer:

The value remains the same.

Step-by-step explanation:

using the expression: [tex](x + 1)^{2}[/tex],

where x = 2

substitute for x in the expression;

[tex](2 + 1)^{2}[/tex]

= [tex](3)^{2}[/tex]

=9          

The value of the expression before expansion = 9

Lets expand the expression:  [tex](x + 1)^{2}[/tex]

= (x + 1) (x + 1)

= [tex]x^{2}[/tex] + 2x + 1

substitute for x in the expression

= [tex]2^{2}[/tex] + 2(2) + 1

= 4 + 4 + 1              = 9

The value of the expansion after expansion = 9

The value remains the same before and after expansion.

The value of an expression, before and when it is expanded will be always same.

Let us consider that an expression,

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

Substitute x = 2 in above relation.

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

Now expand,

                        [tex]f(x)=(x-1)^{2}=x^{2} -2x+1\\\\f(2)=2^{2}-2*2+1\\\\f(2)=4-4+1\\\\f(2)=1[/tex]

Hence, the value of an expression, before and when it is expanded will be always same.

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Exact form: x= NEGATIVE 6/7

Answer:

The profit = $(3x - 75) where x = number of t-shirts sold

Step-by-step explanation:

School spirit club wants to raise money by selling t-shirts. one local company charges a fixed fee of $75 for creating the design and $5 for each shirt that they print.

We have to find the club's income if they sell each t-shirt for $8.

Let the number of t-shirts that the club sell be equal to x.

So the cost of making x t-shirts = 75 + 5x

If the club sells x t-shirts , then the money they earn = 8x

Profit = selling price - cost price

          = 8x - (75 + 5x)

          = $(3x - 75)

The club also needs to sell at least 25 t-shirts to make a profit and from then on makes a profit of $3 on each t-shirt they sell.

Answer:

I think D.

Step-by-step explanation

Answer:

Part(B) is the correct answer

Step-by-step explanation:

Given functions are

f(x) = [tex]4x^3+5[/tex]   and g(x) = [tex]\sqrt[3]{x-5/4}[/tex]

So both are inverse of each other

Since Definition of inverse function is

If a function f(x) is  mapping from x to y , then the inverse function  of f(x) maps

y back to x.

Solution

suppose

y = f(x)

y = [tex]4x^3+5[/tex]

in order to find inverse of f(x)

interchange the variables x and y

x = [tex]4y^3+5[/tex]

Now solve for y

Subtract 5 from both sides we get

[tex]4y^3[/tex] = x-5

Divide both sides by 4 we get

[tex]y^3[/tex] = (x-5)/4

[tex]y = \sqrt[3]{x-5/4}[/tex]

so this is the inverse of the f(x) and also from this we see that  is [tex]g(x) = \sqrt[3]{x-5/4}[/tex]

This is Answer.

Subtract the length of the tail from the whole length.

3/5 - 1/5 = 2/5

The answer is 2/5

3/5  -  1/5  = 2/5

so your answer is 2/5

Answer:

21.04

Step-by-step explanation:

Start by adding the hundredths category.  0.09 + 0.05 = 0.14,  this means that your hundredths column will be a 4,  and you will carry the 1 over to the tenths.

Now add your tenths.  0.0 + 0.9 + 0.1 = 1.0,  which means that your tenths column is a 0.  Carry the 1 over to the whole numbers.

Now add your whole numbers.  7 + 13 + 1 = 21.  Combine your terms and you get 21.04

Final answer:

21.04

Explanation:

To find the sum of 7.09 and 13.95, we simply add the two numbers together, aligning the decimal points vertically.

Putting it all together, we get 21.04 as the final sum.

Answer:

$280

Step-by-step explanation:

Interest = Interest Rate x Principal x time

Interest = 0.04 x $3,500 x 2

Interest = $280

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Form an equation:

14x + 42 = 35

-42

14x = -7

/14

x = -0.5

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Answer:

532

Step-by-step explanation:

14x + 42 = ?

14(35) + 42 = ?

14(35) + 42 =532

Answer: 1.0

Step-by-step explanation: Since a percent is a ratio that compares a number to 100, think of 100% as the ratio 100/100 or 100 divided by 100.

Now, dividing a number by 100 moves the decimal point two places to the left so 100 divided by 100 will move the decimal point two places to the left which will gives us 1.0 or simply just 1.

So 100% can be written as the decimal 1.0.

Answer:

1

Step-by-step explanation:

Byeeee, get a hundred!

Answer:

AOC

Step-by-step explanation:

Angle COX is formed at vertex O with two rays OC and OX.

Angle AOX is formed at vertex O with two rays OA and OX.

Ray OA lies between rays OC and OX.

All three rays have the common vertex O.

The angle addition postulate describes that putting two angles side by side with their vertices together creates a new angle whose measure equals the sum of the measures of the two original angles.

So,

[tex]m\angle AOX+m\angle AOC=m\angle COX[/tex]

Answer:

1 quart blue + 1 1/2 quart red

Step-by-step explanation:

Given:

Ratio of blue paint : red paint = 1/3 : 1/2

simplifying this ratio into whole numbers by multiplying both sides by 2 and 3, we get:

(1/3) x (3x2) : (1/2) x (3x2)

2 : 3

From this we can determine the fractions of red and blue paint used in any total purple mix

fraction of blue paint = 2/(2+3) = 2/5 of purple mix

fraction of red paint = 3/(2+3) = 3/5 of purple mix

we are given that we want to make 2 1/2  (= 5/2) quarts of purple paint

hence

amount of blue paint

= fraction of blue paint in purple mix x total amount of purple paint

= (2/5) x (5/2) = 1 quart

amount of red paint

= fraction of redpaint in purple mix x total amount of purple paint

= (3 /5) x (5/2) = 3/2 quart = 1 1/2 quart

Answer:

[tex]\displaystyle y = 4x - 1[/tex]

Step-by-step explanation:

7 = 4[2] + b

8

[tex]\displaystyle -1 = b \\ \\ y = 4x - 1[/tex]

* Parallel Lines have SIMILAR RATE OF CHANGES [SLOPES], so 4 remains the way it is.

I am joyous to assist you anytime.

Answer:

3.375 miles

Step-by-step explanation:

3/4 can be changes to 0.75. SO multiply 4.5 times 0.75 to get your answer

Answer:

-637

Step-by-step explanation:

What number divide by -7 gives you 91

Answer:

Part 1) [tex]x=1.25\ units[/tex]

Part 2) [tex]y=1.75\ units[/tex]

Step-by-step explanation:

In this problem

the triangles of the figure are similar by AA Similarity Theorem

Remember that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

so

Applying proportion

Find the value of x

[tex]\frac{5}{5+x}=\frac{8}{10}[/tex]

solve for x

[tex]5(10)=8(5+x)\\50=40+8x\\8x=50-40\\8x=10[/tex]

[tex]x=\frac{10}{8}=1.25\ units[/tex]

Find the value of y

[tex]\frac{7}{7+y}=\frac{8}{10}[/tex]

solve for y

[tex]7(10)=8(7+y)\\70=56+8y\\8y=70-56\\8y=14[/tex]

[tex]y=\frac{14}{8}=1.75\ units[/tex]

Answer:

40x-24y

Step-by-step explanation:

Answer:

Part a) [tex]3x+5y=30[/tex]

Part b) see the explanation

Part c) see the explanation

Step-by-step explanation:

Part a) Construct a liner equation

Let

x ----> the number of bags of  tootsie rolls

y ----> the number of bags of lolly-pops

we know that

The number of bags of tootsie rolls bought multiplied by their price ($3) plus the number of bags of lolly-pops bought multiplied by their price ($5) must equal $30

so

The linear equation that represent this problem is

[tex]3x+5y=30[/tex]

Part b) Find the intercepts

Find the y-intercept

The y-intercept is the value of y when the value of x s equal to zero

In this context, the y-intercept is the number of bags of lolly-pops that i can buy when the number of bags of tootsie rolls is equal to zero

For x=0

[tex]3(0)+5y=30[/tex]

[tex]y=6[/tex]

The y-intercept is the point (0,6)

so

I can buy 6 bags of lolly-pops and 0 bags of tootsie rolls

Find the x-intercept

The x-intercept is the value of x when the value of y s equal to zero

In this context, the x-intercept is the number of bags of tootsie rolls that i can buy when the number of bags of lolly-pops is equal to zero

For y=0

[tex]3x+5(0)=30[/tex]

[tex]x=10[/tex]

The x-intercept is the point (10,0)

so

I can buy 10 bags of  tootsie rolls and 0 bags of lolly-pops

Part c) Find the slope

we have

[tex]3x+5y=30[/tex]

isolate the variable y

[tex]5y=-3x+30[/tex]

[tex]y=-\frac{3}{5}x+6[/tex]

The slope is m=-3/5  ---> is negative because is a decreasing function        

That means ---> For every three less lollipops you get, you can have 5 more tootsie rolls

Answer:

Step-by-step explanation:

Blueberries cost $4.00 for 1 pound. The number of blueberries that can be bought $1.00 = (1×1)/4 pounds

= 1/4 pounds

Answer:

4(6x) + 4(12)

Distributive property

4(6x + 12) =  4(6x) + 4(12)

To see if the answer is correct, we can solve the equations

24x + 12 = 24x + 12

The expressions are equal, so the equivalent expression provided is correct

Hope this helps :)

Answer:

By applying the Distributive Property, I can generate these equivalent expressions: 24x + 48, 24(x + 2), and 12(2x + 4).

Answer:

19 coach seats

Step-by-step explanation:

let the number of coach seats be C and number of first class seats be F

given that the total number of seats is 29,

C + F = 29 ---------(eq 1)

also given that each coach seat = $600, each 1st class seat is $1050 and a total of $21900 was collected,

600C + 1,050F = 21,900 -------(eq 2)

we have 2 equations and 2 unknowns, we can solve the system of equations by elimination

(eq 1) x 1,050 gives us:

1,050 (C + F) = 1,050(29)

1,050C + 1,050F = 30,450 ----- (eq 3)

by elimination, subtract eq 2 from eq 3

(1,050C + 1,050F) - (600C + 1,050F) = 30,450 - 21,900

1,050C - 600C = 8,550  

450C = 8550

C = 855 /450

C = 19

Answer:

Step-by-step explanation:

Each Television earns $72 and each Computer earns $90.

The manager’s target is to make at least $360.00 a day.

It is not clarified the exact number of Televisions and Computers.

Hence, as per the given condition, [tex]72x + 90y \geq  360\\8x + 10y \geq  40\\4x + 5y \geq  20[/tex].

Now we just need to check the given options, whether they satisfy the above equation, or not.

Except the option B, each inequality indicates a value greater than 360.

Hence, option B can not be the possible solution.

To meet the profit target of 72x + 90y ≥ 360, the correct points are listed in Option A: (5, 2), (3, 3), and (1, 4). These points meet the required profit condition.

To solve this problem, we need to find the inequality that represents the manager's profit target and identify the solutions that meet this condition. Given:

The manager’s goal is to make at least $360. This can be represented by the equation: 72x + 90y ≥ 360.

We need to check which option lists points that satisfy this inequality. Let's test the points:

Option A: 72x + 90y > 360 (5, 2), (3, 3), and (1, 4)

Option B: 72x + 90y < 360 (4, 0), (2, 2), and (1, 1)

Option C: 72x + 90y > 360 (3, 1), (2, 2), and (1, 0)

Option D: 72x + 90y > 360 (4, 0), (3, 3), and (1, 4)

Only Option A lists points that all satisfy the inequality 72x + 90y ≥ 360. Therefore, Option A is the correct answer.

Answer:

[tex]1 \dfrac{5}{7}\ mph[/tex]

Step-by-step explanation:

Let x mph be the current's rate.

Upstream:

Distance = 18 miles

Rate = 12 - x mph

Time [tex]=\dfrac{18}{12-x}[/tex] hours

Downstream:

Distance = 24 miles

Rate = 12 + x mph

Time [tex]=\dfrac{24}{12+x}[/tex] hours

Time is the same, so

[tex]\dfrac{18}{12-x}=\dfrac{24}{12+x}\\ \\18(12+x)=24(12-x)\\ \\216+18x=288-24x\\ \\18x+24x=288-216\\ \\42x=72\\ \\x=\dfrac{12}{7}=1 \dfrac{5}{7}\ mph[/tex]

Step-by-step explanationF(t)= 24 + 36*t

G(t) = 22 + 38*t

They are the same when 24 + 36t = 22 + 38t

Everything to right side: 0 = 22 + 38t - 24 - 36t

0 = 2t - 2

2 = 2t

t=1

THey are the same at one hour.

Longer than 1 hour, the first one is cheaper.

Here's the table to compare them side by side

t 24 + 36 t 22 + 38t

1/2 42 41

1 60 60

2 96 98

3 132 136

The fashion show needs to be 1 hour long for the cost of hiring either makeup artist Austin or Brad to be the same.

To determine how long the fashion show would need to be for the costs of hiring makeup artists Austin and Brad to be the same, we can set up an equation based on their respective fees. Austin charges a booking fee of $54 plus $80 per hour, while Brad charges a $65 booking fee plus $69 per hour.

Let's let 'h' be the number of hours for which the fashion show will run. For Austin, the total cost will be $54 + $80h. For Brad, the cost will be $65 + $69h. To find the number of hours where the costs are equal, we set the two expressions equal to each other:

54 + 80h = 65 + 69h

Now we solve for 'h':

Subtract 69h from both sides: 54 + 11h = 65

Subtract 54 from both sides: 11h = 11

Divide both sides by 11: h = 1

So, the fashion show needs to be 1 hour long for the cost of hiring either makeup artist to be the same, which would be $134.

Answer:

Total cost to paint the room = £73.51

Step-by-step explanation:

Given:

Dimensions of the room = 6.8 m [tex]\times[/tex] 9.2 m

Cost of tin of paint = £11.75

A tin of paint covers an area = 20 [tex]m^2[/tex]

To find the cost of painting the room with two coats of paint.

Solution:

Area of the room = [tex]length\times width=6.8\ m\times 9.2\ m= 62.56\ m^2[/tex]

We will use unitary method to find the amount of paint required for the room.

If [tex]20\ m^2[/tex] of area is covered by 1 tin of paint.

For [tex]1\ m^2[/tex] of area, amount of paint required = [tex]\frac{1}{20}[/tex] of a tin

Then, for [tex]62.56\ m^2[/tex] amount of paint required = [tex]\frac{62.56}{20}=3.128[/tex] tins of paint.

For double coats twice paint must be required.

So, total amount of paint required for painting the room with two coats of paint = [tex]3.128\times 2=6.256[/tex] tins of paints.

Using unitary method to find total cost.

If 1 tin of paint costs = £11.75

6.256 tins of paint will cost = [tex]6.256\times \£11.75=\£73.508\approx\£73.51[/tex]

Total cost to paint the room = £73.51

Answer:8-oz jar

First, we have to find out what is the unit rate of the 2-oz jar. $1.50÷2 is $.75.

Second, we have to find the unit rate of the 4-oz jar. $2.92÷4=$73.

Third, we have to find the unit rate of the 8-oz jar. $5.68=$.71.

Fourth, we have to find the unit rate of the 16-oz jar. The division for this one may be tricky. From dividing $11.62 by 16, is stopped at the 3rd number I got from dividing. I got $.726. This is not a value of cents and the value can't go in the thousandths place. So, I rounded .726. I got $.73. So $11.62÷16=$.73.

Lastly, you have to compare the amounts.

The lowest amount or better buy, is $.71 or 8-oz jar.

Answer:

8-oz

Step-by-step explanation:

had the same question on the same assignment:)

Answer:make a graph

Step-by-step explanation: