Kelsey solved the following equation:

7x − one over two (8x + 2) = 6


Step Work Justification
1 7x − 4x − 1 = 6
2 3x − 1 = 6
3 3x = 7
4 x = 7 over 3


Which of the following has all of the correct justifications Kelsey used to solve this equation?

Answer:

He have 17 CDs on Monday.

Step-by-step explanation:

Given:

On Tuesday James bought seven CDs. On Wednesday half of all the CDs that he had were destroyed. On Thursday he had 12 left.

Now, to find the CDs he have on Monday.

Let the CDs he have on Monday be [tex]x.[/tex]

So, on Tuesday as James bought 7 CDs:

[tex]x+7.[/tex]

Now, on Wednesday half of all the CDs that he had were destroyed:

[tex]\frac{x+7}{2}[/tex]

As, given on Thursday he had left CDs = 12.

According to question:

[tex]\frac{x+7}{2}[/tex] [tex]=12[/tex]

Multiplying both sides by 2 we get:

[tex]x+7=24[/tex]

Subtracting both sides by 7 we get:

[tex]x=17.[/tex]

Therefore, he have 17 CDs on Monday.

Answer:

The point of intersection gives the solution set(s) of the associated system.

Step-by-step explanation:

If we have a pair of simultaneous equations in 2 variables in x and y, then the point of intersection is the ordered pair (x,y).

This could be a unique intersection, only one point or infinitely many intersection.

This gives us the solution of the simultaneous equations.

Therefore the significance of the point of intersection of a pair of simultaneous equations is that, it gives us the solution set(s) of the associated system.

Answer:

The system has no solution

Step-by-step explanation:

we have

[tex]y=\frac{2}{3}x+7[/tex] ----> equation A

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

Isolate the variable y

Divide by 3 both sides

[tex]y=\frac{2}{3}x-1[/tex] ------> equation B

Compare equation A and equation B

Both lines have the same slope and different y-intercept

so

Line A and Line B are parallel lines

The lines do not intersect

therefore

The system has no solution, because both lines are parallel

see the attached figure to better understand the problem

The solution of the inequality is h > -3 ⇒ 2nd answer

Step-by-step explanation:

Let us revise very important notes about solving inequalities

∵ -4 h - 3 < 9

- Start with adding both sides by 3 to separate the variable

   in one side and the numerical term in the other side of the

   inequality sign

∴ -4 h - 3 + 3 < 9 + 3

∴ -4 h < 12

- Now divide both sides by -4 and use the last note above

∵ -4 ÷ -4 = 1

∵ 12 ÷ -4 = -3

∵ < must change to > (because we divide both sides by (-) number

∴ h > -3

The solution of the inequality is h > -3

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Answer:

h> -3

Step-by-step explanation:

Answer:

Therefore total for her male after the sales tax is added to the subtotal of $8.50 is = $(8.50+0.55) = $9.05

Step-by-step explanation:

Given the sales tax was 6.5%.

The sales tax for Tanya's meal is [tex]=\$ \frac{6.5}{100}\times 8.50[/tex]

                                                      = $0.55

Therefore total for her male after the sales tax is added to the subtotal of $8.50 is = $(8.50+0.55) = $9.05

Answer:

d. 5

Step-by-step explanation:

Answer:

£60000

Step-by-step explanation:

Answer:

Option B

see the attached figure

Step-by-step explanation:

we know that

Opposite number or additive inverse of any number (n) is a number which, if added to n, results in 0

so

In this problem

The opposite of -1/2 is 1/2

so

point M is 1/2 ----> point M is located in the interval (0,1)

The opposite of 5/2 is -5/2

so

point N is -5/2 ----> point M is located in the interval (-3,-2)

therefore

The correct answer is the option B

The larger number is 17

Solution:

Let "x" be the larger number

Let "y" be the smaller number

The difference between of two numbers is 9

Therefore,

larger number - smaller number = 9

x - y = 9 -------- eqn 1

The large number is one more than twice the smaller number

Larger number = 1 + 2(smaller number)

x = 1 + 2y ------ eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 2 in eqn 1

1 + 2y - y = 9

1 + y = 9

y = 9 - 1

y = 8

Substitute y = 8 in eqn 1

x - 8 = 9

x = 8 + 9

x = 17

Thus the larger number is 17

Answer:

C) A small pizza cost $4, and each topping costs and additional $2.

Step-by-step explanation:

Answer:

A small pizza cost $6, and each topping costs an additional $2.

Answer:

[tex]Total\ sales\ should\ be=\$ 300000[/tex]

Step-by-step explanation:

[tex]Let\ her\ total\ sale=x[/tex]

Total Earning:

[tex]The\ offer=\$ 42500\\\\Income\ from\ the\ sales=8\%\ of\ total\ sale\\\\Income\ from\ the\ sales=8\%\ of\ x\\\\Income\ from\ the\ sales=\frac{8}{100}\times x\\\\Income\ from\ the\ sales==0.08x\\\\Total\ earning=Offer+Income\ from\ the\ sales\\\\Total\ earning=42500+0.08x[/tex]

Required Earning=$66500

[tex]To\ move\ that\ city\\\\Total\ earning=required\ earning\\\\42500+0.08x=66500\\\\0.08x=66500-42500\\\\0.08x=24000\\\\x=\frac{24500}{0.08}\\\\x=300000\\\\Total\ sales\ should\ be=\$ 300000[/tex]

Her total sales would need to be at least $300,000 for her to move

Step-by-step explanation:

Briana has been offered a sales job in another city

We need to find what would her total sales need to be for her to move

Assume that her total sales is x

∵ The offer was for $42,500 plus 8% of her total sales

∵ Her total sales = x

- To find her annual salary multiply x by 8% and add the

  product to $42,500

∴ Her annual salary = 8% × x + 42,500

∵ 8% × x = [tex]\frac{8}{100}[/tex] × x = 0.08 x

∴ Her annual salary = 0.08 x + 42,500

∵ Briana needs to have an annual salary of at least $66,500

- At least means ≥

∴ Her annual salary ≥ 66,500

- Substitute her annual salary by the expression above

∴ 0.08 x + 42,500 ≥ 66,500

- Subtract 42,500 from both sides of inequality

∴ 0.08 x ≥ 24,000

- Divide both sides by 0.08

∴ x ≥ 300,000

∴ Her total sales ≥ $300,000

Her total sales would need to be at least $300,000 for her to move

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Answer:

y = 9

Step-by-step explanation:

Substitute the x- coordinate of the point into the equation and solve for y, that is

y = 2(5) - 1 = 10 - 1 = 9

Thus point is (5, 9 )

Natasha can make 6 different combinations by pairing 2 sweaters with 3 skirts. She can pair each of her red and white sweaters with each of her blue, yellow, and black skirts.

Natasha has a red sweater and a white sweater that she wants to pair with a blue skirt, yellow skirt, and a black skirt. To determine the number of different combinations she can make, we use basic combinatorics. Each sweater can be paired with any of the skirts, so we multiply the number of sweaters by the number of skirts.

Here is the calculation:

Thus, Natasha can make 2 sweaters  imes 3 skirts = 6 combinations.

These combinations are:

A fishermen can save gas by implementing the strategies Plan Efficient Routes, Maintain Proper Boat Speed, Reduce Idle Time, Optimize Load and Equipment and Regular Maintenance

Fishermen can save gas by implementing the following strategies:

Plan Efficient Routes: By planning their fishing trips in advance and mapping out efficient routes, fishermen can minimize the distance traveled and save on gas consumption.

Maintain Proper Boat Speed: Operating the boat at an appropriate speed can significantly impact fuel efficiency.

Reduce Idle Time: Minimizing idle time while on the water can help save gas.

Optimize Load and Equipment: Carrying excessive weight on the boat can increase fuel consumption.

Regular Maintenance: Keeping the boat and engine properly maintained is essential for fuel efficiency.

Utilize Wind and Tides: When feasible, fishermen can take advantage of wind and tidal currents to reduce reliance on the engine.

Share Resources: Collaborating with other fishermen or joining fishing cooperatives can help share resources and reduce individual fuel consumption.

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Explanation of how to simplify expressions with exponents by subtracting exponents. The answer shows the equivalence of 5×2/3 and 10×1/3.

The expression [tex]( \frac{5 \times 2}{3} )[/tex] equals [tex]( \frac{10}{3} )[/tex].  Let's break it down:

[tex]\( \frac{5 \times 2}{3} \)[/tex] means you multiply 5 and 2 first, which gives you 10, then you divide by 3, resulting in [tex]\( \frac{10}{3} \)[/tex].

However, if you're asking why [tex]\( \frac{5 \times 2}{3} \)[/tex] and [tex]\( 10 \times \frac{1}{3} \)[/tex] are equal, it's because multiplication is distributive over division.

In other words, [tex]\( a \times \frac{b}{c} = \frac{a \times b}{c} \)[/tex].

So, [tex]\( 10 \times \frac{1}{3} \)[/tex] can be written as [tex]\( \frac{10 \times 1}{3} \)[/tex], which simplifies to [tex]\( \frac{10}{3} \)[/tex], the same as [tex]\( \frac{5 \times 2}{3} \)[/tex].

Answer:

you just have to add or divide

Answer:

144 cubic inches

Step-by-step explanation:

a=lxwxh a=6*6*4

Yo sup??

we should know that the volume of a cuboid is l*b*h

from the given figure we can say that

l=6 inches

b=6 inches

h=4 inches

therefore

V=6*6*4

=144 inches^3

therefore the correct answer is option C

Hope this helps.

Answer:

[tex]0.0749[/tex]

Step-by-step explanation:

[tex]1.498/30[/tex]

To divide the form directly in fraction divide the numerator and denominator by a common number to simplify the values.

Simplifying the value  

    Removing the decimal in the numerator makes 1000 in denominator

                                               [tex]\frac{1498}{30}*\frac{1}{1000}[/tex]

dividing by a common value i.e 2                            

                                         [tex]\frac{749}{10}*\frac{1}{1000}[/tex]

Now, removing the decimals from denominator puts the decimal in the numerator gives   [tex]0.0749[/tex]

Answer:

1.498 divided by 30 equals 749/15000 OR 0.04993

Step-by-step explanation:

Simply divide as you would a whole number, but place the decimal point above in your answer. So, your first step would be to calculate how many times 30 goes into 149. Your answer will go two places AFTER your decimal point. Then you continue to solve, as you would a whole number!

Answer:

[tex]2 \frac{1}{3} [/tex]

Step-by-step explanation:

Assuming the question is

[tex]7 \times \frac{9}{27} [/tex]

reduced to the lowest term.

We proceed as follows:

[tex]7 \times \frac{9}{3 \times 9} [/tex]

We cancel the common factors to get:

[tex]7 \times \frac{1}{3} [/tex]

This simplifies to

[tex] \frac{7}{3} = 2 \frac{1}{3} [/tex]

Answer:

C. Workers to total population.

Unemployment is defined as the condition of people who are able to work but cannot find jobs. The unemployment ratio is most accurately described by option B: 'unemployed workers to total workers'. This does not include people who are not part of the labor force.

Unemployment is defined as the condition in which people who are able and willing to work cannot find jobs. In terms of the provided options, unemployment is best defined by option B: 'unemployed workers to total workers'. This is because the unemployment rate is calculated by dividing the number of unemployed individuals by the total number of individuals in the labor force (which includes both the employed and the unemployed) and then multiplying by 100 to get a percentage.

This measure gives a good representation of the number of people who are jobless compared to the overall amount of people who are either working or actively seeking work. It's important to keep in mind that it doesn't include people who are not part of the labor force, like children, retirees, and others who are not looking for work.

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Answer:

she did not make a mistake

Step-by-step explanation:

Answer:

veronica didn't make a mistake.

Step-by-step explanation:

Answer:

6n

Step-by-step explanation:

Final answer:

The difference of 5 and n cubed is calculated by subtracting n cubed from 5. This involves simple algebraic manipulation.

Explanation:

The difference of 5 and n cubed can be represented as 5 - n³. This means subtracting the cube of the variable n from 5.

To illustrate, if n=2, the calculation would be 5 - 2³ = 5 - 8 = -3.

Therefore, the result of the difference between 5 and n cubed is 5 - n³.

Answer:

42/7 = 6.00

6.00 x 7 = 42

6.00 is fraction for 42.

Step-by-step explanation:

42 divided b 7 is 6.

The solution using laws of exponents is: [tex]y^{\frac{7}{12} } * z^{\frac{1}{2} }[/tex]

How to use laws of exponents?

Some of the laws of exponents are:

- When multiplying by like bases, keep the same bases and add exponents.

- When raising a base to a power of another, keep the same base and multiply by the exponent.

- If dividing by equal bases, keep the same base and subtract the denominator exponent from the numerator exponent.  

The expression we want to solve is given as:

[tex]\frac{(x^{-\frac{3}{2} } y^{\frac{5}{3} } z^{-1})^{-1} }{zx^{\frac{3}{2} } y^{-\frac{1}{4} } * y^{-2} z^{\frac{1}{2} } }[/tex]

Using laws of exponents, we have:

[tex]x^{0} * y^{\frac{7}{12} } * z^{\frac{1}{2} }[/tex]

=[tex]y^{\frac{7}{12} } * z^{\frac{1}{2} }[/tex]

Answer:

she needs 6 ouonces of yellow paint

Step-by-step explanation:

she has 5oz, 3 blue: 2 red, she needs 20oz. which means she needs 15oz more. 15/5=3. 3*2=6

Answer:

To find if something is proportional you want to reduce them to there simplest form, so we want to reduce each fraction down

40/48= 5/6

56/42= 8/7

Therefore; these two fractions are not proportional because they reduce to different numbers

Hope this helps ;)

Answer:

no

Step-by-step explanation:

Cross multiply:

40 * 42 = 48 * 56

Simplifying

40 * 42 = 48 * 56

Multiply 40 * 42

1680 = 48 * 56

Multiply 48 * 56

1680 = 2688

Solving

1680 = 2688

Answer:

$2500

Step-by-step explanation:

25% is one fourth of the total monthly income.

If $625 is = x/4 then multiply both sides of the equation with 4

4 × 625 = x/4 × 4 ➡ 2500 = x

you can plug the x value (9y) into the second equation

5(9y) + 3y = -48

45y + 3y = -48

48y = -48

y = -1

x = 9(-1)

x = -9

Answer:

x = 9

y = -31

Step-by-step explanation:

5x+3y

y = -31

x = 9

plug it in