The product of a nonzero rational number and an irrational number is always rational.

True

False

Answer:

-637

Step-by-step explanation:

What number divide by -7 gives you 91

[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

Learn more about functions at:

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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:

Step-by-step explanation:

(-6,8)...x = -6 and y = 8

lets start subbing

5x + 3y = -6

5(-6) + 3(8) = -6

-30 + 24 = -6

-6 = -6

so (-6,8) IS a solution to this equation

2x + y = -4

2(-6) + 8 = -4

-12 + 8 = -4

-4 = -4

so (-6,8) IS a solution to this equation

A. It is the only solution to the system

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:

Multiply the entire expression by the radical denominator. This keeps the expression equal and makes the denominator 3, a whole number.

Step-by-step explanation:

The denominator is irrational because it is a radical number, √3.

To rationalize the denominator, multiply the entire expression by √3. The denominator will become a whole number. This works because you multiply top and bottom by the same value.

[tex]\frac{3 + \sqrt{2} }{\sqrt{3}}[/tex]

[tex]= \frac{(\sqrt{3})(3 + \sqrt{2}) }{(\sqrt{3})(\sqrt{3})}[/tex]

[tex]= \frac{(\sqrt{3})(3 + \sqrt{2}) }{3}[/tex]  

√3 X √3 = 3 because:

√3 X √3 = √3²

Squaring a number and also finding its square root are opposites, or reverse operations. They cancel out

You probably need to simplify the rest of the equation too.

[tex]\frac{(\sqrt{3})(3 + \sqrt{2}) }{3}[/tex]

[tex]= \frac{3(\sqrt{3}) + (\sqrt{2})(\sqrt{3})}{3}[/tex]  Distribute over brackets

[tex]= \frac{3(\sqrt{3}) + \sqrt{2*3}}{3}[/tex]   Simplify

[tex]= \frac{3(\sqrt{3}) + \sqrt{6}}{3}[/tex]

Some people use a more simplified version whether they simplify each term in the numerator:

[tex]\frac{3(\sqrt{3}) + \sqrt{6}}{3}[/tex]    (3√3)÷3 = √3

[tex]\sqrt{3} + \frac{\sqrt{6}}{3}[/tex]

Answer:

a) Hence the Baby Manatee is 4 feet long.

b) Hence the Length of blue whale is 108 feet.

Step-by-step explanation:

Given:

Length of Mother manatee = 12 feet.

Now given that:

A mother  manatee is three  times as long as her baby manatee.

Let the length of baby manatee be 'x'.

So equation can be framed as

[tex]3x=12[/tex]

hence the equation is [tex]3x=12[/tex].

Solving the equation we get;

Dividing both side by 3 using Division property of equality we get;

[tex]\frac{3x}{3}=\frac{12}{3}\\ \\x=4\ feet[/tex]

a) Hence the Baby Manatee is 4 feet long.

Solving for part b we get;

Given:

If a blue whale is 9 times as long as the  mother manatee

Hence equation can be framed as;

Length of blue whale is = [tex]9 \times \textrm{Length of Mother manatee}[/tex]

Length of blue whale is = [tex]9\times 12 =108\ feet[/tex]

b) Hence the Length of blue whale is 108 feet.

Answer:

Step-by-step explanation:

1) Two angles supplementary. So sum of two angles is 180

One angle  = x

Other angle = 2x

x + 2x = 180

3x = 180

x = 180/3 = 60

The angles are 60, 120

2)Two angles complementary. So sum of two angles is 90

one angle  = x

Other angle = x + 20

x +x +20 = 90

2x + 20 = 90

2x = 90- 20

2x = 70

x = 70/2 = 35

The angles are 35,55

3) one angle =x

Other angle = 3x - 20

x + 3x - 20 = 120

4x = 120 + 20

4x = 140

x = 140/4 = 35

The angles are 35,85

5) x + 4x -20 = 180

5x = 180 + 20

5x = 200

x = 200/5 = 40

x = 40

6) This sum is not clear only half is visible

Option B is correct.

Step-by-step explanation:

We need to identify which of the following equations has exactly one solution.

We will solve each equation to find the answer

A. [tex]ax+b=ax+b[/tex]

Solving and finding value of x:

[tex]ax+b=ax+b\\ax-ax=b-b\\0=0[/tex]

This equation has infinite number of solutions because both sides are equal to 0

B. [tex]ax=bx+c[/tex]

Solving and finding value of x:

[tex]ax=bx+c\\ax-bx=c\\x(a-b)=c\\x=\frac{c}{a-b}[/tex]

This equation has exactly one solution

C. [tex]ax+b=ax+c[/tex]

[tex]ax+b=ax+c\\ax-ax=c-b\\0=c-b[/tex]

This equation has no solution because both sides are not equal.

So, Option B is correct.

Keywords: Solving Equations

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The right answer is Option C.

Step-by-step explanation:

Given,

Pizzas made by Paul on first day = 12

Pizzas made each day after that = 6

Let,

p represent the number of pizzas made after first day.

Total pizzas = 6p + 12

Number of days = 8 because first day 12 pizzas are made

Total pizzas = [tex]6(8)+12=60[/tex]

Pizzas made by Cindy on first day = 16

Pizzas made each day after that = 4

Total pizzas = 4p + 16

Total pizzas = [tex]4(8)+16=48[/tex]

Paul has made more pizzas after 9 days. He has made 60 pizzas.

The right answer is Option C.

Keywords: comparison, addition

Learn more about addition at:

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Answer:

C

Step-by-step explanation:

The force of gravity acting on the block(and weight) in the air is 2403.45 newton

Step-by-step explanation:

Density of an object is defined as the ratio of mass to volume

So we can write it as:

[tex]d = \frac{m}{V}[/tex]

And the force is given by:

[tex]F_g = mg[/tex]

We know that

d = 3500 kg/m^2

V = 0.07 m^3

g = 9.81 ms^-2

So we will calculate the mass first

[tex]d = \frac{m}{V}\\3500 = \frac{m}{0.07}\\m = 3500*0.07\\m = 245\ kg[/tex]

Now,

[tex]F_g = 245 * 9.81\\= 2403.45\ N[/tex]

The force of gravity acting on the block(and weight) in the air is 2403.45 newton

Keywords: Force, gravity

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Answer:

Circumcenter of triangle [tex](4,-1)[/tex]

Step-by-step explanation:

Given coordinates are [tex](1,1)(1,-3)(7,-3)[/tex]

We will draw these points on the graph.

Let [tex]A(1,1)[/tex], [tex]B(1,-3)[/tex] and [tex]C(7,-3)[/tex]

We can see it is a right-angle triangle.

Let [tex]O[/tex] be the midpoint of line [tex]AC[/tex]

So, the coordinate of the point [tex]O[/tex] will be

[tex]A(1,1)\ C(7,-3)\\\\Midpoint\ O\ will\ be\\\\O=(\frac{1+7}{2},\frac{1+(-3)}{2})\\ \\O=(\frac{8}{2},\frac{-2}{2})\\\\O=(4,-1)[/tex]

Also, we know the coordinates of circumcenter of a right angle triangle will be midpoint of its hypotenuse.

So, coordinates of circumcenter is [tex](4,-1)[/tex]

Answer:

Step-by-step explanation:

80 minutes.......8 minutes played commercials....that means (80 - 8) = 72 minutes played music

so the ratio of music to commercials is : 72/8 which reduces to 9/1...so the ratio is 9:1 <=== ur answer

** pay attention to the wording, because if it would have asked for the ratio of commercials to music, it would have been 8/72....ratio would be 1:9

Answer:

Slope = - 3, y-intercept is 4 and the equation is y = - 3x + 4.

Step-by-step explanation:

Slope of a straight line passing through two given points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is given by the formula

[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex].

Now, the given graph of the straight line passes through the points (0,4) and (1,1) points.

Hence, the slope of the straight line will be = [tex]\frac{1 - 4}{1 - 0} = - 3[/tex]

Again, the straight line intersects the y-axis at point (0,4) point. hence, its y-intercept is 4.

Therefore, the straight line has equation  

y = - 3x + 4 (Answer)    

Answer:

The mural in David's drawing is 4 cm long.

Step-by-step explanation:

Given:

David made a scale drawing of a mural he is going to paint.

He used a scale of 1 cm=4ft.

If the actual mural will be 16 feet long.

Now, to find how long is the mural in David's drawing.

Let the length of mural in David's drawing be [tex]x\ cm[/tex].

So, as given 1 cm = 4 ft.

1 cm is equivalent to 4 ft.

Thus, [tex]x\ cm[/tex] is equivalent to 16 feet.

Now, to get the length of mural in David's drawing by using the cross multiplication method:

[tex]\frac{1}{4} =\frac{x}{16}[/tex]

By cross multiplication:

[tex]16=4x[/tex]

Dividing both sides by 4 we get:

[tex]4=x[/tex]

[tex]x=4\ cm.[/tex]

Therefore, the mural in David's drawing is 4 cm long.

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.

Answer:

Step-by-step explanation:

The given numbers:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14

Getting the number 28 (using 4 numbers):

If we add the following 4 numbers from 1 to 14, we would get 28.

10 + 9 + 7 + 2 = 28

Getting the number 14 (using 3 numbers):

If we add the following 3 numbers from 1 to 14, we would get 14.

8 + 5 + 1 = 14

Getting the number 30 (using 4 numbers):

If we add the following 4 numbers from 1 to 14, we would get 30.

11 + 12 + 4 + 3 = 30

Getting the number 33 (using 3 numbers):

If we add the following 3 numbers from 1 to 14, we would get 33.

14 + 13 + 6 = 33

Keywords: addition, number

Learn more about addition operation using brainly.com/question/1098659

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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: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:)

Janet has remaining $ 149.16 in her paycheck

Given that Janet's paycheck was $248.60

She put 1/4 of her paycheck into a checking account

Therefore amount put into checking account is given as:

[tex]\text {amount put into checking account }=\frac{1}{4} \times 248.60=62.15[/tex]

So she spent $ 62.15 into checking account

Now the remaining paycheck amount left is:

remaining paycheck amount left = 248.60 - 62.15 = 186.45

Therefore remaining paycheck amount left is $ 186.45

Now she spent 1/5 of what was left to buy dinner for her family

[tex]\text { Amount spend on dinner }= \frac{1}{5} \times 186.45 = 37.29[/tex]

So she spent $ 37.29 on dinner

Now the remaining paycheck amount left is:

remaining paycheck amount left = 186.45 - 37.29 = 149.16

Thus Janet has remaining $ 149.16 in her paycheck

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:

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

Exact form: x= NEGATIVE 6/7

Answer:

t = 51°

Step-by-step explanation:

The total sum of a polygon's exterior angles is always 360°.

Add all of the given angles and equate it to 360°.

40° + 34° + 34° + 46° + (2t - 50°) + (2t - 50°) + 2t = 360°     Collect like terms

154° + 2t - 50° + 2t - 50° + 2t = 360°    Remove brackets and collect like terms

54° + 6t = 360°   Isolate t by doing reverse operations in reverse BEDMAS

6t = 360° - 54°    Subtract 54° from both sides

6t = 306° Divide both sides by 6

t = 51°    Answer

｡☆✼★ ━━━━━━━━━━━━━━  ☾

Form an equation:

14x + 42 = 35

-42

14x = -7

/14

x = -0.5

Have A Nice Day ❤  

Stay Brainly! ヅ  

- Ally ✧  

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Answer:

532

Step-by-step explanation:

14x + 42 = ?

14(35) + 42 = ?

14(35) + 42 =532

Answer:

Larry is about 9 years old

Step-by-step explanation:

Subtract

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.