Find the retail price of a backpack that has a wholesale price of $25 and is marked up 40%. Multiply $25 and 40% in decimal form to find the markup amount. 25(0.40) = $10 Add the wholesale price to the markup amount. What is the selling price? $10 $15 $35 $65

Answers

Answer 1
$35 is your answer, just do 25(0.40) which gives you 10 so add that to your original 25+10=35
Answer 2

Answer:

35   35          35             35

Step-by-step explanation:

it 35


Related Questions

Which foundation drawing matches this orthographic drawing? ( just tell me what picture) 

Answers

The picture with a 3 by 2 square, the middle one uploaded. Orthographic drawings are two-dimensional representations of a three-dimensional figure from different viewing points. This shape would make a two by three by six unit figure.

Check my answers? GIving medal:

7. What is the slope of the line that passes throught the pair of points (1, 7) and (10, 1)?

a. 3/2
b. -2/3
c. -3/2
d. 2/3 <--

8. What is the slope of the line that passes through the points (-5.5, 6.1) and (-2.5, 3.1)?

a. -1
b. 1
c. -3 <--
d. d

9. what is the slope of the line that passes through the pair of points (-7/3, -3) and (-5, 5/2)?

a. 6/22 <--
b. -6/22
c. 22/6
d. -22/6,

Answers

Slope is calculate by dividing the change in y-values by the change in x-values between a pair of points. For 7: (7-1)/(1-10) = 6/-9 = -2/3 For 8: (6.1-3.1)/(-5.5 - -2.5) = 3/-3 = -1 For 9: (5/2 - -3) / (-5 - -7/3) = 11/2 / -8/3 = -33/16. This is not an answer option, so double check the problem.

Number seven  Is B. -2/3

MEDAL!
This Chinese painting is composed small cliffs in the background and a small building with trees in the foreground. This composition reflects what Taoist and Buddhists principle or philosophy?
a) simplicity
b) perseverance
c) harmony
or...
d) balance

btw- I know this is in the wrong section but no one was answering it in the art history section

Answers

This Chinese painting represents the Taoist and Buddhists principle of balance. People who practice Taoism and Buddhism are more attuned to balance and synchronized energy. Social influence and mental distortions are not present. The natural pulse of the universe is all around.

Factor this expression completely, and, then, place the factors in the proper location on the grid. Place the binomial factor first. x 3 + y 3

Answers

  (x-y)(x^2+xy+y^2) 
_______________ 

the first parentheses contain the cubed root of both the terms so x and y respectively. second parentheses follows the formula (a^2 + ab + b^2) 
x corresponds to a and y corresponds to b. The signs are what change depending on what the original equation is. Since the original is a subtraction then the signs are -/+/+. you can remember it using the acronym SOAP. (S = same, O = opposite, AP = always positive) So the first sign is x - y (same as subtraction from original), the second and third are x^2 + xy + y^2 (opposite is a plus, and the last sign is always a positive)

Answer:

[tex]x^{3}+y^{3}=(a+b)(a^{2}-ab+b^{2})[/tex]

Step-by-step explanation:

The given expression is

[tex]x^{3}+y^{3}[/tex]

This expression represents the sum of two perfect cubes, which is factorize as this product

[tex]x^{3}+y^{3}=(a+b)(a^{2}-ab+b^{2})[/tex]

We can demonstrate this factorization by multiplying the product

[tex](a+b)(a^{2}-ab+b^{2})=a^{3}-a^{2}b+ab^{2}+a^{2}b-ab^{2}+b^{3}=a^{3}+b^{3}[/tex]

Therefore, the answer is

[tex]x^{3}+y^{3}=(a+b)(a^{2}-ab+b^{2})[/tex]

How is locating -1.5 on a number line the same as locating 1.5 on a number line? How is it different?

Answers

It’s the same in the sense that 1.5 and -1.5 are the same distance away from 0 - they have he same *absolute value*. It’s different in *where* you look. 1.5 is 1.5 to the *right* of 0, while -1.5 is 1.5 to the *left* of zero.

Locating -1.5 and 1.5 on a number line involves measuring 1.5 units from the origin, but in opposite directions; -1.5 is to the left and 1.5 is to the right.

Locating -1.5 on a number line is similar to locating 1.5 in that you measure the same distance away from the origin (0 point), which is 1.5 units. The main difference is the direction in which you measure from the origin. For -1.5, you would move 1.5 units to the left of the origin since negative numbers are represented to the left on a number line. On the other hand, for 1.5, you would move 1.5 units to the right of the origin because positive numbers are placed to the right.

Another perspective of understanding this concept comes from the coordinate system. If you stand on a straight line and choose a point as the origin, moving to the left will give you the negative coordinates, whereas moving to the right will give you the positive coordinates. Regardless of which side you choose, the absolute value of your position from the origin remains the same; only the sign changes to reflect the direction.

what is the measure of < A? sorry that the pic is backwards. and btw the C aangle is 40 degrees.

Answers

the measurement of A is 50° angle c is 40 and angle b is 90° you add them both and subtract it from 180° and it will give you 50°

WILL MARK BRAINLIEST! - Miguel is calculating the slope of a line of best-fit in the scatterplot below.

(Graph Below)

Which pair of points would be best for Miguel to use?
A. P and W
B. Q and V
C. R and U
D. S and T

Answers

Answer:

I thing its B

Step-by-step explanation:

Just trust

Answer:

"Q and V" should be correct.

Step-by-step explanation:

The data points by themselves create a line formation, all the other choices no good.

In other-words~ "B"

o_o

A car travels 3 times around a traffic circle whose radius is 80 feet. What is the distance the car will travel? Use 3.14 for π . Enter your answer in the box. ft

Answers

Answer : Distance will be 1507.2 feet .

Explanation :

Since we have given that

Radius of circle = 80 feet

So,

Circumference of circle is given by

[tex]2\pi r=2\times 3.14\times 80=502.4 \text{ feet}[/tex]

Since , a car travels 3 times around a traffic circle.

So,

[tex]\text{ Distance covered by the car will travel}= 3\times 502.4= 1507.2 \text{ feet }[/tex]

So, Distance will be 1507.2 feet .

Dominik paid three-quarters of a dollar for a newspaper. Which amount is equivalent to the cost of the newspaper?

Answers

The answer is 75 cents

An equation was created for the line of best fit from actual enrollment data. It was used to predict the dance studio enrollment values shown in the table below:

Enrollment Month
January February March April May June
Actual 12 14 14 13 16 14
Predicted 8 15 15 12 17 15
Residual 4 −1 −1 1 −1 −1


Analyze the data. Determine whether the equation that produced the predicted values represents a good line of best fit.

No, the equation is not a good fit because the sum of the residuals is a large number.
No, the equation is not a good fit because the residuals are all far from zero.
Yes, the equation is a good fit because the residuals are all far from zero.
Yes, the equation is a good fit because the sum of the residuals is a small number.

Answers

Answer: No, the equation is not a good fit because the sum of the residuals is a large number.

Step-by-step explanation:

A residual is the difference on the scatter plot between the actual y-value and the predicted y-value from the regression line equation.

It is the vertical distance from the actual plotted point to the point on the regression line.

The residual is positive then the data point is above the graph.

The sum of the given residual values = [tex]4+(-1)+(-1)+1+(-1)+(-1)=1[/tex]

Since,  the sum of the residuals is greater than 0.

Therefore, The equation is not a good fit .

Answer:

A. No, the equation is not a good fit because the sum of the residuals is a large number.

Step-by-step explanation:

2. Consider this scatter plot.

(a) How would you characterize the relationship between the hours spent on homework and the test scores? Explain.
(b) Paul uses the function y = 8x + 40 to model the situation. What score does the model predict for 3 h of homework?
(c) What does the number 40 in Part (b) mean in the context of the situation?

Answers

(a) How would you characterize the relationship between the hours spent on homework and the test scores? Explain
 For this case what we see is that we have a scatter diagram, which we can model using a linear trend defining the following variables:
 x: number of hours studied.
 y: test scores.
 The linear relationship would be of the form:
 y = mx + b

 (b) Paul uses the function y = 8x + 40 to model the situation. What score does the model predict for 3 h of homework?

 y = 8x + 40
 For three hours of study we have that the note would be approximately:
 y = 8 * (3) + 40
 y = 64

 (c) What does the number 40 in Part (b) mean in the context of the situation?

 The number 40 means that if you do not devote any study time, then you expect the test score to be 40.

(a) The relationship between hours spent on homework and test scores is a positive correlation, where more homework is generally associated with higher test scores.

(b) The model predicts a score of 64 for 3 hours of homework.

(c) The number 40 represents the baseline test score when no homework is done, according to the model.

Analyzing the Scatter Plot and the Model

(a) Characterizing the Relationship

The scatter plot depicts test scores in relation to the hours of homework. Here’s how we can characterize the relationship:

- Positive Correlation: There is a general upward trend, indicating that as the hours of homework increase, the test scores also tend to increase.

- Strength: The points are not perfectly aligned, but there is a noticeable positive correlation, suggesting that more homework hours are associated with higher test scores.

- Outliers: Most points follow the trend, although there are a few variations. For example, there are a couple of points with low homework hours but relatively high test scores.

(b) Predicting the Score for 3 Hours of Homework

Paul uses the function [tex]\( y = 8x + 40 \)[/tex] to model the relationship, where [tex]\( y \)[/tex] represents the test score and [tex]\( x \)[/tex] represents the hours of homework.

To predict the score for 3 hours of homework:

[tex]\[y = 8(3) + 40 = 24 + 40 = 64\][/tex]

So, the model predicts a score of [tex]\( \boxed{64} \)[/tex] for 3 hours of homework.

(c) Meaning of the Number 40 in the Model

In the context of the situation, the number 40 in the equation [tex]\( y = 8x + 40 \)[/tex] represents the y-intercept. This implies:

- Baseline Score: If a student spends 0 hours on homework, the model predicts that they would score 40 on the test. This serves as a baseline score, indicating the minimum test score a student could achieve without any homework.

Summary

(a) The relationship between hours spent on homework and test scores is a positive correlation, where more homework is generally associated with higher test scores.

(b) The model predicts a score of 64 for 3 hours of homework.

(c) The number 40 represents the baseline test score when no homework is done, according to the model.

Write the quadratic equation whose roots are −4 and 3 , and whose leading coefficient is 1 .

Answers

we know that
the roots are
x=-4
x=3
leading coefficient=1 
therefore
(1)*(x+4)*(x-3)=0-----------------> x²-3x+4x-12=0
 x²+x-12=0

the answer is 
 x²+x-12=0

Final answer:

To write a quadratic equation with roots −4 and 3 and a leading coefficient of 1, we start with the factored form (x - root1)(x - root2) = 0, substitute the given roots, and simplify to x² + x - 12 = 0.

Explanation:

The question asks us to write the quadratic equation whose roots are −4 and 3, and whose leading coefficient is 1. To find a quadratic equation given its roots, we can use the factored form of a quadratic equation, which is (x - root1)(x - root2) = 0, where root1 and root2 are the roots of the equation.

Given that the roots are −4 and 3, we substitute these values into the equation to get (x - (−4))(x - 3) = 0. Simplifying this, we first eliminate the double negative to get (x + 4)(x - 3) = 0. Multiplying these two binomials gives us the expanded form, which is x² + x - 12 = 0. This is the quadratic equation with roots −4 and 3, and a leading coefficient of 1.

Whats the number if the prime factorization is 5x7x7x17?

Answers

4165 is the number if you multiply these together.

If the expected adult of a 2 week old puppy is 20 pounds how many grams per day should they gain?

Answers

That will be 20-25 grams

Find the area of the given triangle. Round the answer to the nearest tenth.


A.
7.9 square units
B.
149.4 square units
C.
2,055.6 square units
D.
2,071.8 square units

Answers

Using Heron's formula:
A = √(p(p-a)(p-b)(p-c)) where a,b,c are the sides of the triangle and p is half the perimeter.
The answer is B. 149.4 square units.

Answer:

B) Area of triangle =  149.4 square units.

Step-by-step explanation:

Given : A triangle with sides 16 , 19, 27 .

To find : Area of a triangle.

Solution : We have given that triangle with sides 16 , 19, 27 .

Using heron's formula :

Area of triangle:  [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex].

Where, s = [tex]\frac{a+b+c}{2}[/tex] and a,b,c are sides of triangle.

Then s = [tex]\frac{16+19+27}{2}[/tex].

s = 31 units.

Area of triangle =  [tex]\sqrt{31(31-16)(31-19)(31-27)}[/tex].

Area of triangle =  [tex]\sqrt{31(15)(12)(4)}[/tex].

Area of triangle =  [tex]\sqrt{22320)}[/tex].

Area of triangle =  149.39 square units.

Area of triangle =  149.4 square units. ( nearest tenth)

Therefore, B) Area of triangle =  149.4 square units.

PLEASE HELP NEED ASAP GIVING OUT BRAINLIEST 50 points!!!!

Answers

 The answer is answer number 2! Hope this helped. :-)

Will mark brainiest

According to the chart, from 1996-2006, unintentional drug overdose deaths per 100,000 population rose dramatically. The numbers for each year are, roughly, 3, 3, 3, 4, 4, 5, 6, 6, 7, 9, 9. What is the mean of these statistics?

5.36
59
59.36
5

Answers

3+3+3+4+4+5+6+6+7+9+9=59
59/11=5.36
so your mean is 5.36

The answer to your question is  A) 5.36

Hope this helps :)

Your assigned 32 math exercises for homework you complete 87.5of these before dinner how many do you hav to do after dinner.

Answers

87.5% of 32 questions = 28 questions.

32 - 28 = 4

so there are 4 questions to be done after dinner.

The function graphed approximates the height of an acorn, in meters, x seconds after it falls from a tree.

After about how many seconds is the acorn 5 m above the ground?

Answers

For this case, the first thing to do is observe the vertical axis.
 We look for a height of 5 meters on the vertical axis.
 When finding the height of 5 meters we must observe for what time value this height belongs.
 For this, we observe the horizontal axis.
 The value of time is approximately:
 t = 1.7 seconds
 Answer:
 
t = 1.7 seconds
 
option 3

The equation of the parabola is y = – 5x² + 20. The time when an acorn is 5 m above the ground in 1.7 seconds. Then the correct option is C.

What is the parabola?

It is the locus of a point that moves so that it is always the same distance from a non-movable point and a given line. The non-movable point is called focus and the non-movable line is called the directrix.

The function graphed approximates the height of an acorn, in meters, x seconds after it falls from a tree.

We know that the equation of the parabola will be given as

y = a(x - h)² + k

where (h, k) is the vertex of the parabola and a is the constant.

We have

(h, k) = (0, 20)

Then

y = ax² + 20

The parabola is passing through (2, 0), then we have

0 = 4a + 20

a = -5

Then we have

y = – 5x² + 20

The time in seconds when the acorn is 5 m above the ground.

–5x² + 20 = 5

       –5x² = –15

             x = 1.7

More about the parabola link is given below.

https://brainly.com/question/8495504

***mathtest timed***
Given the data set for the length of time a person has been jogging and the person's speed, hypothesize a relationship between the variables.

A) I would expect the data to be positively correlated.
B)I would expect the data to be negatively correlated.
C) I would expect no correlation.
D) There is not enough information to determine correlation.

Answers

The answer is option A

Abit is planning a birthday party for his grandfather. He bought a cake for $18. He also wants to buy some balloons, which are $4 each. Abit has $35 to spend all together. How much money will Abit have left after he buys the cake and as many balloons as possible?

Answers

Total = $35

After buying the cake,
$35 - $18 = $17

Number of balloons he can buy:
17 ÷ 4 = 4.25
So, he can buy 4 balloons.

4 ballons = 4x4 = $16
So amount left  = $17 - $16 = $1
35 - 18 = 17
The number 4 can fit into the number 17 4 times. 4 x 4 = 16

Therefore, Abit will only have $1 left over. 

In a parking lot of 240 red and blue cars, the ratio of red cars to blue cars is 3 : 5.

How many red cars are in the parking lot?

Answers

3+5 = 8

240/8 = 30

30*3 = 90 red cars


A new car is purchased for 20700 dollars. The value of the car depreciates at 13.75% per year. What will the value of the car be, to the nearest cent, after 12 years?

Answers

Answer:

USD 3,508.16

Step-by-step explanation:

Hello

Let´s see what happens the first year when the car depreciates 13.75% of 20700 USD

[tex]depreciation=20700*\frac{13.75}{100} =2846.25 USD\\[/tex]

at the end of the first year the car will have a price of 20700-2486.25=17853.75 USD,  and this will be the price at the beginning of the second year.

completing the data for the 12 years with the help of excel you get

                                          depreciation           New Value

end of year 1  USD 20,700.00   USD 2,846.25   USD 17,853.75  

end of year 2  USD 17,853.75   USD 2,454.89   USD 15,398.86  

end of year 3  USD 15,398.86   USD 2,117.34   USD 13,281.52  

end of year 4  USD 13,281.52   USD 1,826.21   USD 11,455.31  

end of year 5  USD 11,455.31   USD 1,575.10   USD 9,880.20  

end of year 6  USD 9,880.20   USD 1,358.53   USD 8,521.68  

end of year 7  USD 8,521.68   USD 1,171.73            USD 7,349.94  

end of year 8  USD 7,349.94   USD 1,010.62   USD 6,339.33  

end of year 9  USD 6,339.33   USD 871.66           USD 5,467.67  

end of year 10 USD 5,467.67   USD 751.80       USD 4,715.87  

end of year 11  USD 4,715.87   USD 648.43     USD 4,067.43  

end of year 12 USD 4,067.43   USD 559.27   USD 3,508.16

after 12 years the car will ha a value of USD 3508.16

you can verify this by applying the formula

[tex]v_{2} =v_{1} (1-\frac{depreciatoin}{100} )^{n} \\\\v_{2} =20700 (1-\frac{13.75}{100} )^{12} \\v_{2} = 20700*0.1694\\v_{2} = 3508.16 USD[/tex].

Have a great day.

Final answer:

The value of a new car, originally priced at $20,700 and depreciating at 13.75% per year will be approximately $1446.63 after 12 years. This is calculated using a compound interest formula with a negative rate.

Explanation:

In order to solve this, we are going to use the formula for compound interest. Although we're actually dealing with depreciation, the calculation is the same as for interest, we just use a negative rate. The formula is P(t) = P0 * (1 + r) ^t, where P(t) is the value of the car after time t, P0 is the initial price of the car, r is the rate of depreciation, and t is time.

Here P0 = $20,700, r = -13.75% = -0.1375 (remember to convert rate from percentage to a proportion), and t = 12 years.

Substituting these values into the formula, we get: P(t) = 20700 * (1 - 0.1375)^12. Using a calculator, the value of the car after 12 years, to the nearest cent, is approximately $1446.63.

Learn more about Depreciation here:

https://brainly.com/question/33528280

#SPJ11

Peter is making an "X marks the spot" flag for a treasure hunt. The flag is made of a square white flag with sides of 121212 inches. He will make the "X" by stretching red ribbon diagonally from corner to corner.How many inches of ribbon will Peter need to make the "X"?

Answers

Final answer:

Peter needs approximately 34 inches of ribbon to create an 'X' across his 12-inch square flag, calculated using the Pythagorean theorem to find the length of the diagonals needed for the 'X'.

Explanation:

Peter is making an "X marks the spot" flag, which requires calculating the amount of ribbon needed to create the 'X'. The flag is a square with sides of 12 inches each. For an 'X', two ribbons will be needed, each stretching diagonally across the square. The diagonal length of a square can be determined using the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the square has sides of 12 inches, making the formula for the diagonal:

d = √(12^2 + 12^2) = √(144 + 144) = √288 ≈ 16.97 inches.

Since Peter needs two diagonals to form the 'X', the total ribbon length will be 2 × 16.97 inches, which equals 33.94 inches. Therefore, Peter will need approximately 34 inches of ribbon to create the 'X' on his flag.

A $250,000 home loan is used to purchase a house. The loan is for 30 years and has a 5.4% APR. Use the amortization formula to determine the amount of the monthly payments.

Answers

[tex]\bf ~~~~~~~~~~~~ \textit{Amortized Loan Value} \\\\ pymt=P\left[ \cfrac{\frac{r}{n}}{1-\left( 1+ \frac{r}{n}\right)^{-nt}} \right] \\\\\\ ~~~~~~ \begin{cases} P= \begin{array}{llll} \textit{original amount deposited}\\ \end{array}\to &250000\\ pymt=\textit{periodic payments}\\ r=rate\to 5.4\%\to \frac{5.4}{100}\to &0.054\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{since the payments are}\\ \textit{monthly, then twelve} \end{array}\to &12\\ t=years\to &30 \end{cases} [/tex]

[tex]\bf pymt=250000\left[ \cfrac{\frac{0.054}{12}}{1-\left( 1+ \frac{0.054}{12}\right)^{-12\cdot 30}} \right] \\\\\\ pymt=250000\left[ \cfrac{0.0045}{1-\left( 1.0045\right)^{-360}} \right] \\\\\\ pymt\approx 250000\left[ \cfrac{0.0045}{0.80138080852472389274} \right][/tex]

The legs of a right triangle measure 4 and 6 inches. The area of the triangle is
5 in.²
12 in.²
24 in.²

Answers

Area of a right triangle = .5 * leg1 * leg2
Area = .5* 24
Area = 12 square inches


Answer:

Area of triangle is 12 in.²

Step-by-step explanation:

we are given that:

The legs of a right triangle measure 4 and 6 inches.

(i.e. height and base of right angled triangle)

We have to find the area of this triangle.

area of triangle=[tex]\dfrac{1}{2}\times base\times height[/tex]

                        =[tex]\dfrac{1}{2}\times 4\times 6[/tex]

                       = 12 in.²

Hence, Area of triangle is 12 in.²

Which quotient is equivalent to the mixed number
      2
2----------                  = 
       3 
                                              answer in fractions

Answers

To answer this question you will convert the mixed number into an improper fraction. To do this you have to understand that The two wholes in the mix number each equal 3/3. This would give you 6/3 for the two wholes. Add the 6/3 to the 2/3 that are there in the fraction, and you will have 8/3. the quotient(answer to a division problem) is 8/3 as a fraction.

Final answer:

To convert 2 2/3 to an improper fraction, multiply the whole number by the denominator and add the numerator, resulting in 8/3. The question lacks details to provide another specific quotient to compare this with. In dividing fractions, multiplication by the reciprocal is used to find equivalent quotients.

Explanation:

To find which quotient is equivalent to the mixed number 2 2/3, we must first convert the mixed number to an improper fraction. A mixed number is composed of a whole number and a fraction, which can be converted into an improper fraction by multiplying the denominator by the whole number and then adding the numerator to this product.

For the mixed number 2 2/3, we multiply the whole number 2 by the denominator 3, giving us 6, and then add the numerator 2, resulting in 8. Therefore, 2 2/3 as an improper fraction is 8/3.

However, without context, it's unclear what other quotient we are being asked to compare with the mixed number 2 2/3. Quotients can refer to the result of any division. Nonetheless, in contexts of dividing fractions, we use the multiplication of the inverse to find equivalent quotients. For example, if dividing by 3/1 (which is the same as dividing by 3), we would multiply by its reciprocal, 1/3.

In cases of conversion factors, we could use a factor that equals 1 to convert units without changing the value. For instance, 1 m / 100 cm is a conversion factor that equals 1, allowing us to convert meters to centimeters without changing the quantity.

Remember, multiplication and division in fractions can be seen as interconnected operations, where dividing by a number is the same as multiplying by its reciprocal.

Bill and Greg are walking in opposite directions with speeds of 45 and 75 feet per minute. When they started, the distance between them was 20 feet. What will be the distance between them in 2.5 min?

Answers

Bill moves at 45 feet per minute and Greg 75 per minute and starts with a constant of 20 feet from them.

Let X be the number of minutes

Bill*Minutes +Greg*Minutes +20 = total distnce between

45x + 75x +20 = d

Plug in 2.5 for both values of x

45(2.5) + 75(2.5) + 20 =d

Multiply values by 2.5

112.5 + 165 + 20 = d

add together 

Distance = 297.5 feet apart




Answer:

320 ft

Step-by-step explanation:

I'm not sure how the other person was awarded brainliest answer because that answer is pretty far off. But the work was good just they messed up. Also kinda sad he is a brainly teacher and still has incorrect answers.

WILL GIVE A BRAINLESTTTT

What is the solution of 3x+8/x-4 >= 0

Answers

Solution: (-Infinite, -8/3] U (4, Infinite)

Using that a fraction is greater than or equal to zero when the numerator and denominator have the same sign:
a/b>=0. Then we have two cases:
Case 1) If the numerator is positive, the denominator must be positive too (at the same time):
if a>=0 ∩ b>0

Or (U)

Case 2) If the numerator is negative, the denominator must be negative too (at the same time):
if a<=0 ∩ b<0

In this case a=3x+8 and b=x-4, then:

Case 1):
if 3x+8>=0 ∩ x-4>0
Solving for x:
3x+8-8>=0-8 ∩ x-4+4>0+4
3x>=-8 ∩ x>4
3x/3>=-8/3 ∩ x>4
x>=-8/3 ∩ x>4
Solution Case 1: x>4 = (4, Infinite)

Case 2):
if 3x+8<=0 ∩ x-4<0
Solving for x:
3x+8-8<=0-8 ∩ x-4+4<0+4
3x<=-8 ∩ x<4
3x/3<=-8/3 ∩ x<4
x<=-8/3 ∩ x<4
Solution Case 2: x<=-8/3 = (-Infinite, -8/3]

Solution= Solution Case 1 U Solution Case 2
Solution = (4, Infinite) U (-Infinite, -8/3]
Solution: (-Infinite, -8/3] U (4, Infinite)

Answer:

The inequality is given to be :

[tex]\frac{3x+8}{x-4}\geq 0[/tex]

The inequality will be greater than or equal to 0 if and only if both the numerator and denominator of the left hand side will have same sign either both positive or both negative.

CASE 1 : Both positive

3x + 8 ≥ 0

⇒ 3x ≥ -8

[tex]x\geq \frac{-8}{3}[/tex]

Also, x - 4 ≥ 0

⇒ x ≥ 4

Now, Taking common points of both the values of x

⇒ x ∈ [4, ∞)

CASE 2 :  Both are negative

3x + 8 ≤ 0

⇒ 3x ≤ -8

[tex]x\leq \frac{-8}{3}[/tex]

Also, x - 4 ≤ 0

⇒ x ≤ 4

So, Taking common points of both the values of x we have,

[tex]x=(-\infty,-\frac{8}{3}][/tex]

So, The solution of the equation will be the union of both the two solutions

So, Solution is given by :

[tex]x=(-\infty,-\frac{8}{3}]\:U\:[4,\infty)[/tex]

Ella sold 37 necklaces for $20 each at the craft fair. She is going to donate half of the money she earned to charity. Use the Commutative Property to mentally find how much money she will donate. Explain the steps you used.

Answers

370 because 740 halved is 370

Ella sold 37 necklaces for $20 each at the craft fair. She is going to donate half of the money she earned to charity. Use the Commutative Property to mentally find how much money she will donate. Explain the steps you used.

Solution:

Earning from 1 necklace=$20

Earning from 37 necklaces=$20*37

Half of the earnings= [tex] \frac{20*37}{2} =\frac{20}{2}*37=10*37 [/tex]

Half of the earnings=$10*37

Now, Applying Commutative Propert, a*b=b*a

So, Money she need to donate= Half of the earnings= 10*37 =37*10

So, Money she donates=$370

money she will donate=$370

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