Christian's furniture store buys a desk and chair at a wholesale price of $320.00 If the markup rate at Christian's store
is 40%, what is the total markup in dollars.

Answer:

Step-by-step explanation:

9x-3y=-10 ...............(1)

3x-4y=1...............(2)

multiplying equation (2) by 3

9x-12y=3...................(3)

Using elimination method, then

9x-3y=-10 ...............(1)

9x-12y=3...................(3

9y= -13

y= -13/9

substituting y= -13/9 in equation (1) then

9x-3(-13/9)= -10

9x+13/3= -10

multiplying throughout by 3

27x+13= -30

27x= -30-13

27x= -43

x= -43/27

since x and y values are known, then

12x-7y = 12(-43/27) - 7(-13/9)

12x-7y = -516/27 + 91/9

12x-7y = -9

The two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

To solve the system of equations, let's assign variables to the two integers. Let the first integer be represented by 'x' and the second integer by 'y'.

According to the given information:

a. Fourteen more than twice the first integer gives the second integer:

This can be expressed as: 2x + 14 = y

b. The second integer increased by one is the square of the first integer:

This can be expressed as: y + 1 = x^2

Now, we have a system of equations:

1) 2x + 14 = y

2) y + 1 = x^2

To solve this system, we can substitute the value of 'y' from equation 1) into equation 2):

2x + 14 + 1 = x^2

2x + 15 = x^2

Rearranging the equation, we have:

\(x^2 - 2x - 15 = 0\)

Factoring the quadratic equation, we get:

(x - 5)(x + 3) = 0

Setting each factor equal to zero:

x - 5 = 0   -->   x = 5

x + 3 = 0   -->   x = -3

Substituting the values of 'x' back into equation 1), we can find the corresponding values of 'y':

For x = 5:

2(5) + 14 = y

10 + 14 = y

y = 24

For x = -3:

2(-3) + 14 = y

-6 + 14 = y

y = 8

Therefore, the two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

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Answer:

x = 2

Step-by-step explanation:

First, subtract 3 from both sides.

2x + 3 = 7

     - 3    -3

2x       = 4

Then, divide both sides by 2.

2x / 2 = 4 / 2

x = 2

Answer:

the solution for x is x = 2

Step-by-step explanation:

To solve for x, we need to get x by itself on one side of the equation. First, we can subtract 3 from both sides to get:

2x + 3 - 3 = 7 - 3

Simplifying the left side gives us:

2x = 4

Then, we can divide both sides by 2 to get:

2x / 2 = 4 / 2

Simplifying the left side gives us:

x = 2

Answer:

Step-by-step explanation:

a) A sheet of paper contains 2 pages. It means that the number of pages in 500 sheets of paper is 500 × 2 = 1000 pages

If 1300 reams were used and 1 ream contains 1000 pages, then the total number of pages that were run off at the copy center is

1300 × 1000 = 1300000 pages

b) Since it charges departments 3¢ per copy, then the amount paid by the college is 3/100 × 1300000 = $39000

c) if the departments are charged 5 cent per copy if they use their own copy machines, then the amount that they would spend is

5/100 × 1300000 = $65000

The amount saved by having a copy center that semester is

65000 - 39000 = $26000

The calculated volume of the cylinder is 424.3 cubic cm

From the question, we have the following parameters that can be used in our computation:

Base diameter = 6 cm

Height = 15 cm

Using the above as a guide, we have the following:

r = 6/2 = 3

h = 15

So, we have

V = πr²h

Substitute the known values in the above equation, so, we have the following representation

V = 22/7 * 3² * 15

Evaluate

V = 424.3

Hence, the volume is 424.3 cubic cm

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Step-by-step explanation:

speed= distance

time

speed= 6.4

4×60

speed= 0.026 m/s

Answer:

35

Step-by-step explanation:

One angle measure provided (27 degrees), to determine the lengths of the sides or the measures of the other Angles.

The triangle, we need more information about the triangle, such as the lengths of the sides or the measures of other angles. The given information, "27 degrees," only specifies one angle of the triangle, but it is not sufficient to solve the triangle completely.

To solve a triangle, we typically need at least three pieces of information, which can include side lengths, angle measures, or a combination of both. With only one angle measure provided (27 degrees), we are unable to determine the lengths of the sides or the measures of the other angles.

To fully solve the triangle, we would need additional information such as the lengths of the sides or measures of at least two more angles. Without this additional information, it is not possible to provide a complete solution or determine the lengths of the sides or the measures of the other angles in the triangle.

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All the values of x, y and z are,

z = 12.99

y = 7.01

x = 28.3 degree

We have to given that;

In a triangle,

Two angles are, 61.7 degree and 90 degree

And, One side is, 14.76.

Now, We can formulate;

sin 61.7° = Perpendicular / Hypotenuse

sin 61.7° = z / 14.76

0.88 = z / 14.76

z = 0.88 x 14.76

z = 12.99

And, By Pythagoras theorem we get;

14.76² = z² + y²

14.76² = 12.99² + y²

217.85 = 168.74 + y²

y² = 217.85 - 168.74

y² = 49.1

y = 7.01

And, By sum of all the angles in triangle, we get;

x + 61.7 + 90 = 180

x + 151.7 = 180

x = 180 - 151.7

x = 28.3 degree

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Answer:

B (2,-3) A (7,-8)

Step-by-step explanation:

they are just the same points but in the negative side of the x-axis

The Operating income is $172,500.

To calculate the margin of safety, contribution margin ratio, and operating income, we need to use the given information.

a. Margin of Safety:

Margin of Safety = Actual Sales - Break-even Sales

Given that the break-even point is at $750,000 in sales revenue and actual sales are $1,100,000, we can calculate the margin of safety:

Margin of Safety = $1,100,000 - $750,000 = $350,000

Therefore, the margin of safety is $350,000.

b. Margin of Safety as a Percentage of Sales:

Margin of Safety Percentage = (Margin of Safety / Actual Sales) * 100

Using the values from the previous calculations:

Margin of Safety Percentage = ($350,000 / $1,100,000) * 100 = 31.82%

Therefore, the margin of safety expressed as a percentage of sales is approximately 31.82%.

c. Contribution Margin Ratio:

Contribution Margin Ratio = (Contribution Margin / Sales) * 100

To calculate the contribution margin, we need to subtract variable costs from sales:

Contribution Margin = Sales - Variable Costs = $1,100,000 - $645,000 = $455,000

Using the values, we can calculate the contribution margin ratio:

Contribution Margin Ratio = ($455,000 / $1,100,000) * 100 = 41.36%

Therefore, the contribution margin ratio is approximately 41.36%.

d. Operating Income:

Operating Income = Sales - Variable Costs - Fixed Costs

Using the values provided:

Operating Income = $1,100,000 - $645,000 - $282,500 = $172,500

Therefore, the operating income is $172,500.

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Answer:

a parallelogram

Step-by-step explanation:

could also be more specific such as a rectangle or even more specific as a square.

the statement "the sum of my two consecutive angles on same side is 180°" is redundant as we are already told we have two pairs of parallel and congruent sides

The values of x, y , and z in the matrix equation is 3, 4, 0 respectively.

The solution of the matrix equation is calculated by applying Cramer's rule as shown below;

[ 1     1     -1 ]  [ 7 ]

[ 2    3     0 ] [ 18 ]

[ -5   -7    -1 ] [ -43 ]

The determinant of the matrix is calculated as follows;

[ 1     1     -1 ]  

[ 2    3     0 ]

[ -5   -7    -1 ]

Δ = 1 (-3 - 0) - 1(-2 - 0 )  - 1(-14 + 15)

Δ = -2

The x determinant of the matrix is calculated as follows;

[ 7     1     -1 ]  

[ 18    3     0 ]

[ -43   -7    -1 ]

Δx = 7 (-3 - 0) - 1 (-18 - 0 )  - 1(-126 + 129)

Δx = -6

The y determinant of the matrix is calculated as follows;

[ 1     7     -1 ]  

[ 2    18     0 ]

[ -5   -43   -1 ]

Δy = 1 (-18 - 0 )   - 7(-2 - 0 )  -1(-86 + 90)

Δy = -8

The z determinant of the matrix is calculated as follows;

[ 1     1     7 ]  

[ 2    3    18 ]

[ -5   -7   -43]

Δz = 1 (-129 + 126) - 1(-86 + 90) + 7(-14 + 15)

Δz = 0

The values of x, y , and z is calculated as;

x = Δx/Δ = -6/-2 = 3

y = Δy/Δ = -8/-2 = 4

z = Δz/Δ = 0/-2 = 0

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By differentiation rules, the expression for the derivative of the function h(x) = u(x)^v(x), where u(x) = x² + 4 and v(x) = 5 · x is h'(x) = [(x² + 4)^(5 · x)] · [[(5 · x) / (x² + 4)] · (2 · x) + ㏑ (x² + 4) · 5].

In this question we find a differentiation rule for a function of the form h(x) = u(x)^v(x). Herein we find a function whose components are u(x) = x² + 4 and v(x) = 5 · x. First, determine the derivatives of u(x) and v(x):

u'(x) = 2 · x, v'(x) = 5

Second, substitute in the expression of the differentiation rule:

h'(x) = [u(x)^v(x)] · [[v(x) / u(x)] · u'(x) + ㏑ [u(x)] · v'(x)]

h'(x) = [(x² + 4)^(5 · x)] · [[(5 · x) / (x² + 4)] · (2 · x) + ㏑ (x² + 4) · 5]

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The solution of the given equation is x = -6/5.

An equation is a mathematical statement that is formed by variables and constant terms. By adding or subtracting the same integer on both sides or by multiplying or dividing by the same integer on both sides we can solve an equation.

Here we have

(2 + 4x)6 = 4(x - 3)      

We can solve the given expression as follows

=> (2 + 4x)6 = 4(x - 3)      

=> 12 + 24x = 4x - 12

Add - 12 on both sides

=> 12 + 24x - 12 = 4x - 12 - 12

=> 24x = 4x - 24

Subtract - 4x from both sides

=> 24x - 4x = 4x - 4x - 24

=> 20x = - 24

Divided by 20 into both sides

=> 20x/20 = -24/20

=> x = - 6/5

Therefore,

The solution of the given equation is x = -6/5.

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Answer:

20%

Step-by-step explanation:

4+3+7=14

14÷7=2

2×10=20

If I am wrong please tell me I haven't had to do this me method in 3 years

Answer:

Factor of GCF(Greatest common factor) of given expression = [2 × 3 × m]

Step-by-step explanation:

Given expression;

24m³ + 54m

Find:

The factor of GCF(Greatest common factor) of the given expression.

Computation:

24m³ + 54m

Step 1 :

Write in factor form;

[2 × 2 × 2 × 3 × m × m × m] + [2 × 3 × 3 × 3 × m]

Step 2 :

By taking [2 × 3 × m as common]

[2 × 3 × m][(2 × 2 × m × m) + (3 × 3)]

Step 3 :

[2 × 3 × m][(4m²) + (9)]

Factor of GCF(Greatest common factor) of given expression = [2 × 3 × m]

Answer:

\(\displaystyle \frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Step-by-step explanation:

This can be solved with either the washer (easier) or the shell method (harder). For the disk/washer method, the slice is perpendicular to the axis of revolution, whereas, for the shell method, the slice is parallel to the axis of revolution.  I'll show how to do it with both:

Shell Method (Horizontal Axis)

\(\displaystyle V=2\pi\int^d_cr(y)h(y)\,dy\)

Radius: \(r(y)=2-y\) (distance from y=2 to x-axis)

Height: \(h(y)=2-(-\ln y)=2+\ln y\) (\(y=e^{-x}\) is the same as \(x=-\ln y\))

Bounds: \([c,d]=[e^{-2},1]\) (plugging x-bounds in gets you this)

Plugging in our integral, we get:

\(\displaystyle V=2\pi\int^1_{e^{-2}}(2-y)(2+\ln y)\,dy=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Washer Method (Parallel to x-axis)

\(\displaystyle V=\pi\int^b_a\biggr(R(x)^2-r(x)^2\biggr)\,dx\)

Outer Radius: \(R(x)=2-e^{-x}\) (distance between \(y=2\) and \(y=e^{-x}\))

Inner Radius: \(r(x)=2-1=1\) (distance between \(y=2\) and \(y=1\))

Bounds: \([a,b]=[0,2]\)

Plugging in our integral, we get:

\(\displaystyle V=\pi\int^2_0\biggr((2-e^{-x})^2-1^2\biggr)\,dx\\\\V=\pi\int^2_0\biggr((4-4e^{-x}+e^{-2x})-1\biggr)\,dx\\\\V=\pi\int^2_0(3-4e^{-x}+e^{-2x})\,dx\\\\V=\pi\biggr(3x+4e^{-x}-\frac{1}{2}e^{-2x}\biggr)\biggr|^2_0\\\\V=\pi\biggr[\biggr(3(2)+4e^{-2}-\frac{1}{2}e^{-2(2)}\biggr)-\biggr(3(0)+4e^{-0}-\frac{1}{2}e^{-2(0)}\biggr)\biggr]\\\\V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\biggr(4-\frac{1}{2}\biggr)\biggr]\)

\(\displaystyle V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\frac{7}{2}\biggr]\\\\V=\pi\biggr(\frac{5}{2}+4e^{-2}-\frac{1}{2}e^{-4}\biggr)\\\\V=\pi\biggr(\frac{5}{2}+\frac{4}{e^2}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4}{2e^4}+\frac{8e^2}{2e^4}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4+8e^2-1}{2e^4}\biggr)\\\\V=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Use your best judgment when deciding on what method you use when visualizing the solid, but I hope this helped!

Answer: no because 13(6+y) is 78+ 13y

Step-by-step explanation:

she saved $162

hope it helps

Answer:

7a-7b

Step-by-step explanation:

we distribute the 7 by multiplying it to each term

7(a)-7(b)

7a-7b

Hopes this helps please mark brainliest

Answer:

7a - 7b

Step-by-step explanation:

Given expression,

→ 7(a - b)

Let's simplify the expression,

→ 7(a - b)

→ (7 × a) - (7 × b)

→ 7a - 7b

Hence, the answer is 7a - 7b.

The table for the number of steps Anne walked in x hours is:

Hours    Steps

1             700

2            1400

3            2100

Anne walked more than Elyse for different numbers of hours.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Anne function:

y = 700x

Now,

The table for the number of steps Anne walked in x hours.

Hours    Steps

1             700

2            1400

3            2100

Now,

Anne has walked more than Elyse for different numbers of hours.

Thus,

The table comparison is given above.

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☁️ Answer ☁️

I got: 7y - 3

Hope it helps.

Have a nice day hyung!~ ￣▽￣❤️

Answer:

7y-3

Step-by-step explanation:

10y-3y= 7y

7-10= -3

7y-3

The blanks that are missing in the sequence are -3 and 11

from the question, we have the following parameters that can be used in our computation:

The blanks in the sequence

When listed out, we have

_, _, 25, 39

Assuming that the sequence, is an arithmetic sequence, then we have

Common difference = 39 - 25

Common difference = 14

This means that

Previous term = 25 - 14 = 11

Firs term = 11 - 14 = -3

So, the missing terms are -3 and 11

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The total weight of Rice that Mark buys is given as follows:

2.5 pounds.

The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.

The weight of each bag is given as follows:

5/8 pounds = 0.625 pounds.

The number of bags is given as follows:

4 bags.

Hence the total weight of Rice that Mark buys is given as follows:

4 x 0.625 = 2.5 pounds.

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Answer:

-2x² - 10xy + 2y²

Step-by-step explanation:

4x² - 9xy - 4y² - 6x² - xy + 6y² =

= 4x² - 6x² - 9xy - xy - 4y² + 6y²

= -2x² - 10xy + 2y²

Answer: whichever graph that goes up 4 and over 5

Step-by-step explanation:

rise over run, 4 up, 5 right

to find it just look at two points on the line and count how many up and how many horizontal units there are between them :)

Answer:

4.5 inches²

Step-by-step explanation:

A of triangle = 1/2 bh

= 1/2×5×5

= 12.5 inches²

A of rectangle = lw

= 4×2

= 8 inches²

A of shape = 12.5 - 8

= 4.5 inches²

Answer:

4.6 inches

Step-by-step explanation:

5 x 5 = 25 = related rectangle

25/2 = triangle = 12.5

12.5 - (2 x 4 ) = 4.5 in.