Two expressions are below.

M = 4(2x + 6)
N = 8x + 10

Part A:
Apply the distributive property to write an expression that is equivalent to expression M.

Part B:
Explain whether or not expressions M and N are equivalent for any value of x.

Label your answers to both parts of the problem in the response box.

Answer:

one solution (1,5)

Step-by-step explanation:

if you graph the equations on a graph the line would intersect.

intersect = one solution

overlap = infinite solutions

parallel = no solution

Answer:

The solution is 36/35

Step-by-step explanation:

5 2/3 - 1 1/6

———————-

8 5/8 - 4 1/4

17/3 - 7/6

= ———————-

69/8 - 17/4

17/3×2 - 7/6

= ———————-

69/8 - 17/4 × 2

34/6 - 7/6

= ———————-

69/8 - 34/8

9/2

= ———————-

35/8

= 9/2 ÷ 35/8

= 9/2 × 8/35

= 9(8)/2(35)

= 9(4)/35

= 36/35

Final answer:

Betty needs 13 jars to can 104 pears and 21 jars to can 126 apples, making a total of 34 jars.

Explanation:

To determine how many jars Betty needs to can 104 pears and 126 apples, we must consider the capacity of the jars. Each jar holds 8 pears or 6 apples. Therefore, we need to calculate how many jars are required for each fruit separately.

For pears:

For apples:

The total jars needed equals the sum of the jars needed for pears and the jars needed for apples, which is 13 jars for pears plus 21 jars for apples, totaling to 34 jars.

The total purchase price is $ 357.75

Solution:

Joanna buys a table and 2 chairs

Cost of table = $ 250

Cost of 1 chair = $ 100

Therefore, cost of a table and 2 chairs = 250 + 2(100) = 450

Thus, cost price = $ 450

She receives a 25% discount for being a preferred customer

Therefore, discount = 25 % of cost price

[tex]discount = 25 \% \times 450\\\\discount = \frac{25}{100} \times 450\\\\discount = 0.25 \times 450 = 112.5[/tex]

Thus, amount after discount = cost price - discount

amount after discount = 450 - 112.5 = 337.5

Thus, amount after discount is $ 337.5

Then pays 6% sales tax on the discounted purchase price

Sales tax = 6 % of 337.5

[tex]sales\ tax = 6 \% \times 337.5\\\\sales\ tax = \frac{6}{100} \times 337.5\\\\sales\ tax = 20.25[/tex]

Thus, total purchase price is given as:

total purchase price = Amount after discount + sales tax

total purchase price = 337.5 + 20.25 = 357.75

Thus total purchase price is $ 357.75

Answer:

b = -6

Step-by-step explanation:

Given:

y=6x+b ----- (eq 1)

and

-3x+1/2y=-3    (Rearrange this equation to look likes eq (1) , add -3x to both sides)

(1/2) y = 3x - 3   (multiply both sides by 2)

y = 2(3x -3)   (distribute the 2 into parentheses)

y = 6x - 6 -----(eq 2)

Recall that a system of equations will have an infinite number of solutions if both equations are the same line.  (i.e they have the same slope and y intercept)

In our case, if you compare eq 1 and eq 2, the way to make both equations the same line is if b = -6. (this is the answer)

Answer:

Step-by-step explanation:

3.38times3=10.14

5times.79=3.95

1times2.30=2.30

10.14+3.95+2.30=18.04

Answer:

3.38times3=10.14

5times.79=3.95

1times2.30=2.30

10.14+3.95+2.30=18.04

Step-by-step explanation:

Answer:

3/5

Step-by-step explanation:

there are 20 people altogether in the class (12 plus 8)

since 12 of them are girls the probability it 12/20

but to simplify it we divide both sides of the fraction by 4 (as that's the largest whole number they will both divide by) and we get 3/5

Answer:

[ 4 2 ] x [ -2 5 7 -1 ]​ = [- 10,836]

Step-by-step explanation:

Here, the given expression is:

[ 4 2 ] x [ -2 5 7 -1 ]​

Now solving :  [ -2 5 7 -1 ]​ , we get

[ -2 5 7 -1 ]​ =  [-258]

Now simplifying

[-258] x [ 4 2 ] =  - 10,836

⇒  [ 4 2 ] x [ -2 5 7 -1 ]​ = [- 10,836]

Hence the solution is:   [- 10,836]

Answer:

D. [6 18]

Step-by-step explanation:

Edge2020

Have a great day y'all :)

The sum of two numbers:

x + y = 108

The difference of the same two numbers:

x - y = 78

We can use substitution to figure out x and y:

x - y = 78 can be changed to x = 78 + y

We can plug this into the first equation:

78 + y + y = 108

78 + 2y = 108

2y = 30

y = 15

Now solve for x using any of the two equations. I'll use the first equation since it's easier:

x + 15 = 108

x = 93

Answer:

g(x) = -x^2 - 4

Step-by-step explanation:

f(x) = x^2

To flip the graph, you need the negative of the right side,

y = -x^2

This is a parabola that opens downward, but the vertex is at (0, 0).

Now you need to translate the graph 4 units down, so subtract 4 from -x^2.

g(x) = -x^2 - 4

The area of the triangle is 16 square feet.

The formula for finding the area of a triangle is given by:

Area = 1/2 * base * height

Given that the base of the triangle measures 6.4 feet and the height measures 5 feet, we can substitute these values into the formula:

Area = 1/2 * 6.4 * 5 = 16 square feet

Therefore, the area of the triangle is 16 square feet.

Option A

The simple interest earned is $ 105

Solution:

Given that, $300 at 5% annual interest for 7 years

Therefore,

Principal = $ 300

Rate of interest = 5 %

Number of years = 7

The simple interest is given by formula:

[tex]Simple\ Interest = \frac{p \times n \times r }{100}[/tex]

Where,

p is the principal

r is the rate of interest

n is the number of years

Substituting the values in formula,

[tex]Simple\ Interest = \frac{300 \times 7 \times 5 }{100}\\\\Simple\ Interest = 3 \times 7 \times 5\\\\Simple\ Interest = 105[/tex]

Thus simple interest earned is $ 105

Answer:

None of the above graph gives the function.

Step-by-step explanation:

The function is given by

f(x) = - x + 1 for, x ≤ 0  .......... (1) and

f(x) = x + 1 for, x > 0 ............. (2)

Now, from this definition we can write for x = 0, the value of f(x) will be governed by the equation (1) and f(0) = - 0 + 1 = 1

So, (0,1) is a point on the graph and for x < 0 the f(x) will have negative slope and for x > 0, the f(x) will have  positive slope.

So, none of the above graphs gives the function. (Answer)  

Answer:

the 4 graph

Step-by-step explanation:

Answer:

The graph is shown below.

Step-by-step explanation:

Given:

The inequalities to solve by graphing are given as:

[tex]y>2x\\\\y<3[/tex]

Now, in order to graph them, we first replace inequality sign by equal to sign.

So, the two equations are given as:

[tex]y=2x\\\\y=3[/tex]

Now, the first equation is a straight line of the form [tex]y=mx[/tex]. This is a line that passes through origin with slope equal to 'm'.

So, the slope of the first line is 2.

In order to plot the line,we take a random value of 'x'. Let [tex]x=1[/tex]

So, [tex]y=2\times 1=2[/tex]

So, the point on the line is (1, 2)

Now, we draw a line passing through the points (0, 0) and (1, 2). This is the line for the first equation.

Now, the second equation is a straight line parallel to the x-axis.

So, the equation [tex]y=3[/tex] is a straight line parallel to x-axis passing through the point (0, 3) as shown below.

Now, since the first inequality has 'y' greater than '2x'. So, the solution region is left of the line excluding the line.

Also, the second inequality has 'y' less than 3. So, the solution region is below the line excluding the line.

The common region for both the line inequalities is the solution.

The solution region is shown below.

Answer:

o, the solution region is left of the line excluding the line.

Also, the second inequality has 'y' less than 3. So, the solution region is below the line excluding the line.

Step-by-step explanation:

Answer:

WHERE IS IT

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The answer is A because it says -4 and not -1/4.

Final answer:

Option C, adding 1 to both sides, is not an appropriate first step in solving the equation -1/4(x-1)=2/3x+2. Claire should instead focus on simplifying the equation, such as using distributive property or eliminating fractions.

Explanation:

To solve the equation -1/4(x-1)=2/3x+2, there are several steps that Claire can take. However, answer option C, which suggests adding 1 to both sides, is not an appropriate first step for solving for x. Instead, Claire might consider other steps like using the distributive property or getting rid of the fractions by multiplying both sides of the equation by a common denominator.

When solving linear equations, it is generally more logical to start by simplifying each side of the equation by using distribution or by eliminating fractions. This makes further manipulation of the equation simpler and more straightforward. The inappropriate step of adding 1 would create an extra unnecessary step, not simplifying the equation in a beneficial way.

Answer:

  24

Step-by-step explanation:

  [tex]\dfrac{3}{7}\times 56=3\times\dfrac{56}{7}=3\times 8=24[/tex]

Even if you don't know your times tables or how to multiply fractions, you can use a calculator to compute the value.

Kevin gave 24 stamps to his friends.

Final answer:

The egg will take approximately 3.35 seconds to reach the ground.

Explanation:

To solve this problem, we can use the equation [tex]y = yo + vot + 0.5at^2[/tex] position, yo is the initial position, vo is the initial velocity, a is the acceleration, and t is the time.

In this case, yo = 90 ft, vo = 0 ft/s, a = -16 [tex]ft/s^2[/tex]y = 0 ft (since the egg reaches the ground). Plugging these values into the equation, we get 0 = 90 + (0)(t) + 0.5(-16)t^2.

Simplifying the equation, we have [tex]0 = 90 - 8t^2[/tex], we get[tex]8t^2 = 90[/tex] both sides by 8, we get [tex]t^2 = 11.25[/tex]e square root of both sides, we find that t ≈ 3.35 seconds.

Answer:

The answer is B

Step-by-step explanation:

just did

Answer:

[tex]tan(\theta)=-\frac{5}{\sqrt{119}}[/tex]

Step-by-step explanation:

The correct question is

Suppose that ∅ Is an angle with csc(∅)=-12/5 and ∅ Is not in the third quadrant. Compute the exact value of Tan(∅).

∅ Is not in the third quadrant

If csc(∅) is negative the angle lie in the III Quadrant or in the IV Quadrant

∅ Is not in the third quadrant ----> given problem

so

That means ----> ∅ Is in the fourth quadrant

step 1

Find the value of [tex]sin(\theta)[/tex]

we have

[tex]csc(\theta)=-\frac{12}{5}[/tex]

we know that

[tex]csc(\theta)=\frac{1}{sin(\theta)}[/tex]

therefore

[tex]sin(\theta)=-\frac{5}{12}[/tex]

step 2

Find the value of [tex]cos(\theta)[/tex]

we know that

[tex]sin^2(\theta)+cos^2(\theta)=1[/tex]

we have

[tex]sin(\theta)=-\frac{5}{12}[/tex]

substitute

[tex](-\frac{5}{12})^2+cos^2(\theta)=1[/tex]

[tex]\frac{25}{144}+cos^2(\theta)=1[/tex]

[tex]cos^2(\theta)=1-\frac{25}{144}[/tex]

[tex]cos^2(\theta)=\frac{119}{144}[/tex]

[tex]cos(\theta)=\frac{\sqrt{119}}{12}[/tex] ---> is positive (IV Quadrant)

step 3

Find the value of [tex]tan(\theta)[/tex]

we know that

[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]

substitute the values

[tex]tan(\theta)=-\frac{5}{12} : \frac{\sqrt{119}}{12}=-\frac{5}{\sqrt{119}}[/tex]

Answer:

C

Step-by-step explanation:

[tex] \frac{2}{3} \times 18 = \frac{2}{5} \times x[/tex]

[tex] \frac{36}{3} = \frac{2x}{5} [/tex]

[tex]180 = 6x[/tex]

[tex]30 = x[/tex]

Two third of 18 is equal to 2/5 of 30, Option C is the correct answer.

An equation in math is an equality relationship between two expressions written on both sides of the equal to sign.

It is given in the question

two third of 18 is equal to 2/5 of what number

Let the number be x

then the expression that can be formed = (2/5)x

and (2/3)*18

These two expression are equal

Equating the expression will give

(2/5)x = (2/3)*18

(2/5)x = 12

x = 12*5/2

x = 30

Therefore the number = 30.

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Answer:

3.1415926535

I can't explain why but I tried my best, I hope it helped.

Answer:

B. Heading, Body, Closing and Signature line

Step-by-step explanation:

Quiz Verified

The three main parts of a professional cover letter are:

- Introduction

- Body

- Conclusion

Option D is the correct answer.

A professional cover letter is a formal document that accompanies a job application.

It introduces the applicant to the potential employer and highlights their qualifications, skills, and experience that make them a suitable candidates for the job.

We have,

The three main parts of a professional cover letter are:

-Introduction

-Body

- Conclusion

The introduction typically includes a greeting, a brief overview of the position being applied for, and a statement of interest in the position.

The body of the cover letter is where the applicant can expand on their qualifications, skills, and experience, highlighting relevant achievements and providing examples that demonstrate their fit for the position.

The conclusion usually summarizes the applicant's interest and qualifications, and thanks the employer for considering the application.

It may also include a call to action, such as a request for an interview or an invitation for further discussion.

Thus,

The three main parts of a professional cover letter are:

-Introduction

-Body

- Conclusion

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Answer:

10.8 cm

Step-by-step explanation:

we know that

1) A square picture with side length 30 cm is scaled by 60% on a photocopier

Remember that

[tex]60\%=60/100=0.60[/tex]

so

The length of the first copy of the picture is

[tex]30(0.60)=18\ cm[/tex]

2) The copy is then scaled by 60% again

so

The length of the second copy of the picture is

[tex]18(0.60)=10.8\ cm[/tex]

Based on the information given, the side length of the second copy of the picture is 10.8cm.

Therefore, the side length will be:

= 30 × 60% × 60%

= 10.8cm

In conclusion, the correct option is 10.8cm.

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Final answer:

The two numbers that add up to 29, where one number is one more than the other, are 14 and 15. The equation 2x + 1 = 29 helped determine that the smaller number is 14, and adding one gives us the larger number, 15.

Explanation:

The two numbers in question are those that sum up to 29, and one number is one more than the other. Let's denote the smaller number as x, which makes the larger number x + 1 because it's one more than the smaller one. Setting up the equation based on the information given, we have:
x + (x + 1) = 29
Combining like terms gives us:
2x + 1 = 29
To find the value of x, we subtract 1 from both sides:
2x = 28
And then divide by 2:
x = 14
Therefore, the smaller number is 14, and the larger number, being one more than 14, is 15.

Ima edit this-Step-by-step explanation:

Answer:

20

Step-by-step explanation:120÷6=20

Answer:

Discounted percent = 42.5% and price of the discounted product compared to original is 57.5%

Step-by-step explanation:

$46 = Discount of some decimal of $80

46 = x(80)

46/80 = 0.575

Change it to percent

57.5% discount

The discount expressed as a percent of the regular price is approximately 42.5%.

Here, we have,

To calculate the discount as a percent of the regular price, we can use the following formula:

Discount Percentage = (Discount Amount / Regular Price) × 100%

Given that

the regular price is $80 and the sale price is $46, we can calculate the discount amount by subtracting the sale price from the regular price:

Discount Amount = Regular Price - Sale Price

Discount Amount = $80 - $46

Discount Amount = $34

Now we can calculate the discount percentage:

Discount Percentage = (Discount Amount / Regular Price) × 100%

Discount Percentage = ($34 / $80) × 100%

Discount Percentage ≈ 42.5%

Therefore, the discount expressed as a percent of the regular price is approximately 42.5%.

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Answer:

36/5 = 7 1/5

Step-by-step explanation: hope this help!