In each pair, tell if the fractions are equal by using cross multiplication.
a. 5/30 and 1/6
b.4/12 and 21/60
c. 17/34 and 41/82
d. 6/9 and 25/36​

Answers

Answer 1

Answer:

a. 5/30 and 1/6 ---> are equal

b.4/12 and 21/60 ---> are not equal

c. 17/34 and 41/82 ---> are equal

d. 6/9 and 25/36​ ---> are not equal

Step-by-step explanation:

case a) we have  5/30 and 1/6

equate the fractions

[tex]\frac{5}{30}=\frac{1}{6}[/tex]

using cross multiplication

[tex](5)(6)=(30)(1)[/tex]

[tex]30=30[/tex] ----> is true

therefore

The fractions are equal

case b) we have  4/12 and 21/60

equate the fractions

[tex]\frac{4}{12}=\frac{21}{60}[/tex]

using cross multiplication

[tex](4)(60)=(21)(12)[/tex]

[tex]240=252[/tex] ----> is not true

therefore

The fractions are not equal

case c) we have  17/34 and 41/82

equate the fractions

[tex]\frac{17}{34}=\frac{41}{82}[/tex]

using cross multiplication

[tex](17)(82)=(41)(34)[/tex]

[tex]1,394=1,394[/tex] ----> is true

therefore

The fractions are equal

case d) we have  6/9 and 25/36​

equate the fractions

[tex]\frac{6}{9}=\frac{25}{36}[/tex]

using cross multiplication

[tex](6)(36)=(25)(9)[/tex]

[tex]216=225[/tex] ----> is not true

therefore

The fractions are not equal

Answer 2

Answer:

a. The fractions are equal.

b. The fractions are not equal

c. The fractions are equal.

d. The fractions are not equal

Step-by-step explanation:

By definition, equivalent fractions have the same value, but they look different.

In order to verify if two fractions are equivalent, you can use Cross multiplication.

The procedure is: multiply the numerator of the first fraction by the denominator of the second fraction, and the numerator of the second fraction by the denominator of the first fraction.

Then:

[tex]a.\ \frac{5}{30}=\frac{1}{6}\\\\5*6=1*30\\\\30=30\ (The\ fractions\ are\ equal)[/tex]

[tex]b.\ \frac{4}{12}=\frac{21}{60}\\\\4*60=21*12\\\\240=252\ (FALSE.\ The\ fractions\ are\ not\ equal)[/tex]

[tex]c.\ \frac{17}{34}=\frac{41}{82}\\\\17*82=41*34\\\\1394=1394\ (The\ fractions\ are\ equal)[/tex]

[tex]d.\ \frac{6}{9}=\frac{25}{36}\\\\6*36=25*9\\\\216=225\ (FALSE.\ The\ fractions\ are\ not\ equal)[/tex]


Related Questions

what is the slope of the line x=2

Answers

Answer:

infinite

Step-by-step explanation:

The slope is the amount the line moves in y direction when you go move unit in the x direction. For a vertical line that is infinite...

PLEASE HELP!!
identify the cross section shown.
a. octagon
b. rectangle
c. trapezoid
d. triangle

Answers

Answer:

c

Step-by-step explanation:

The figure is a triangular prism

It is like  you take an iron sheet with the shape of a trapezoid  to cut the figure

The bottom part of the "sheet match the triangular base of the prism

The top part of the"sheet match the middle point of the triangular top of the prism

Help meeeeeee need by 12:50 for me it’s 12:30 nowwwwwwww WILL MARK BRAINLIEST!!

Answers

Answer:

Step-by-step explanation:

XW II Yz and XY is transversal

∠XYZ +∠ZYX =  180°           {sum of co-interior angle is 180}

2x + 90 + 3x - 5 = 180

5x = 180 - 90 + 5

5x = 95

x = 95 / 5

x = 19

the world population in 2013 was about 7.125 billion. in 2003,it was about 6.357 billion. which number represents the increase in the world population between 2003 and 2013?

Answers

there was a 768million person increase in that decade

Answer:

768million

Step-by-step explanation:

Which of the following values would complete the ordered pair if the point is on the graph of ƒ(x) = -2x - 1? (-2, ___)

A. 3

B. 4

C. 5

Answers

Option A: 3 is the right answer

Step-by-step explanation:

Given

[tex]f(x) = -2x-1[/tex]

In an ordered pair, the x-coordinate is the input to the function and y-coordinate is the output of the function on specified input.

In the given ordered pair,

x-coordinate is -2 so we will put it into the function to get the y-coordinate

So,

[tex]f(-2) = -2(-2)-1\\= 4-1\\=3[/tex]

3 will complete the ordered pair of the point on the graph

Hence,

Option A: 3 is the right answer

Keywords: functions, variables

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Answer:

A

Step-by-step explanation:

(x coodinate, y coodinate) = (x, f(x))

(-2, ___) is saying us x=-2, and question is asking y =?

f(x) = -2x -1

f(-2) = -2.-2 -1

f(-2)= 4 -1

f(-2) = 3

so, y= f(-2) = 2

(x, f(x)) = (-2, f(-2)) = (-2,3)

Hope this helps ^-^

Solve 6x - 2 = 4x + 13 for x.
15/2
112
3/12

Answers

Answer:

[tex]\large \boxed{x = \dfrac{15}{2}}[/tex]

Step-by-step explanation:

[tex]\begin{array}{rcll}6x - 2& = & 4x + 13 & \\6x & = & 4x + 15 & \text{Added 2 to each side}\\2x & = & 15 & \text{Subtracted 4x from each side}\\x & = & \mathbf{\dfrac{15}{2}}& \text{Divided each side by 2}\\\\\end{array}\\\large \boxed{\mathbf{x = \dfrac{15}{2}}}[/tex]

Circle A and circle B are congruent. CD is a cord of both circles. if AB = 24 inches in the radius is 13 inches how long is CD A.10in B.26in C.12in D.9in

Answers

Option A

Length of CD is 10 inches

Solution:

The diagram is attached below

Given that, Circle A and circle B are congruent

CD is a cord of both circles

AB = 24 inches

Radius = 13 inches

To find: length of CD

Draw a straight line connecting A and C

AC represents the radius of circle. Also given that radius is 13 inches, So AC = 13 inches

Given in question that AB = 24 inches

Therefore from figure, AO = AB/2 = 24/2 = 12

AO = 12

Let "b" be the length of CO

Therefore, CD = CO + OD = b + b

AOC forms a triangle, so we can use pythogoras theorem

Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

By above definition for triangle AOC

[tex]AC^2 = AO^2 + OC^2[/tex]

Substituting AC = 13 and AO = 12 and OC = b

[tex]13^2 = 12^2 + b^2\\\\b^2 = 169 - 144\\\\b^2 = 25\\\\b = 5[/tex]

Thus length of CD is:

CD = b + b = 5 + 5 = 10

Thus length of CD is 10 inches

What makes a trapezoid an isosceles trapezoid?

Answers

Answer:

A: Its legs are congruent

Step-by-step explanation:

A trapezoid is a quadrilateral with exactly one pair of parallel sides. In a trapezoid the parallel sides are called bases. A pair of angles that share a base as a common side are called a pair of base angles. A trapezoid with the two non-parallel sides the same length is called an isosceles trapezoid.

Final answer:

An isosceles trapezoid is a trapezoid with two congruent sides and congruent base angles.

Explanation:

An isosceles trapezoid is a trapezoid that has two congruent sides. In other words, the two non-parallel sides of an isosceles trapezoid are equal in length. The base angles of an isosceles trapezoid are also congruent. The parallel sides of an isosceles trapezoid are not equal in length.

For example, if a trapezoid has sides AB = 6 cm, BC = 5 cm, CD = 4 cm, and DA = 5 cm, then it is an isosceles trapezoid because sides BC and DA are congruent.

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the sum of 3x and 14 equals the difference of 20 and 2x

Answers

Answer. 17<18

The sum of 3x + 14 equals 17x.

The difference between 20 - 2x equals 18x.

Therefore the equation is not equal to each other.

Amaya used these steps to solve the equation 8x+4=9+4(2x−1). Which choice describes the meaning of her result, 4=5?

Answers

Answer:

No value of x makes the equation true.

Step-by-step explanation:

Here are the choices which are missing in the question:

a) Amaya made a mistake because 4 is not equal to 5

b) No value of x make the equation true.

c) All value of x make the equation true.

d) The solution is x= 4 or 5

Given equation is [tex]8x+4=9+4(2x-1)[/tex]

Now, solving the equation:

[tex]8x+4=9+4(2x-1)[/tex]

distributing 4 with both 2x and -1

⇒[tex]8x+4= 9+8x-4[/tex]

⇒[tex]8x+4= 5+8x[/tex]

Subtracting both side by 8x

∴ 4=5

The result indicate that equation has the same result and x has no value.

Answer:

No values of x make the equation true.

Benson played 12 games of trivia. He had
a perfect score on every game and received
35 bonus points per game. He earned a
total of 1,260 points. How many points did
he earn per game not including the
bonus points?

Answers

Benson earned 70 points per game not including the bonus points.

Step-by-step explanation:

Given,

Games of trivia played = 12

Bonus points received per game = 35 points

Bonus points for 12 games = 35*12 = 420 points

Total points earned = 1260 points

Points earned in games = Total points - bonus points

Points earned in games = 1260 - 420 = 840 points

As he scored 840 points in 12 games, therefore,

12 games = 840 points

1 game = [tex]\frac{840}{12} = 70\ points[/tex]

Benson earned 70 points per game not including the bonus points.

Keywords: subtraction, division

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Find the greatest common factor of 10, 30,10,30,10, comma, 30, comma and 454545.

Answers

Answer:

GCF = 5

Step-by-step explanation:

Given:

The numbers are given as:

10, 30 and 45

A factor of a number is a number by which the given number is evenly divisible.

Example: 2 is a factor of 4 as [tex]4\div 2 =2[/tex]. So, 4 is evenly divisible by 2 and hence 2 is a factor of 4.

Now, factors of 10 = 1, 2, 5, 10.

Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30.

Factors of 45 = 1, 3, 5, 9, 15, 45.

So, the greatest common factor in all the three numbers is 5.

Hence, the greatest common factor of 10, 30 and 45 is 5.

A factory runs nonstop for three 14 - hour shifts. The first shift starts at 9.00 AM. At what times does their third shift end?

Answers

Answer:

Step-by-step explanation:

3 fourteen hr shifts.....that (14 * 3) = 42 hrs....thats 1 day and 18 hrs

first shift starts at 9 AM......

one day later will make it 9 AM the next day....now we have the 18 hrs.....so from 9 AM to 9 PM is 12 hrs.....so we are at 9 PM and have 6 hrs left.....making the last shift end at 3 AM <==

3:00 pm is the  time where  does their third shift end.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Given that A factory runs nonstop for three 14 - hour shifts.

The first shift starts at 9.00 AM.

We need to find the times does their third shift end.

First shift:

9:00Am to 11:00Pm (14 hours)

second shift:

11:00pm to 1:00 am (14 hours)

Third shift

1:00 am to 3:00 pm (14 hours)

Hence, 3:00 pm is the  times where  does their third shift end.

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Solve for y in terms of x: 3y-2x=7

Answers

Answer will be: y=7/3+2x/3

Answer:

y =  2/3x + 7 / 3

Step-by-step explanation:

Step 1: Add 2x to both sides.

−2x+3y+2x=7+2x

3y=2x+7

Step 2: Divide both sides by 3.

3y  / 3 = 2x+7 / 3

y=  2 / 3x  + 7 / 3

an airport shuttle company owns cars that have a maximum capacity of 3 passengers and vans that have a maximum capacity of 8 passengers . their 12 vehicles have a combination maximum capacity of 61 passengers. write and solve a system of equations to determine how many vans the company owns

Answers

Answer:

The Total number of car is 7 and The Total number of van is 5 .

Step-by-step explanation:

Given as :

The maximum capacity of car = 3 passengers

The maximum capacity of van = 8 passengers

Total number of vehicles = c + v = 12 vehicles

The maximum capacity of vehicles combination = 61 passengers

Let The Total number of car = c

Let The Total number of van = v

Now, According to question

c + v = 12            .........A

3 c + 8 v = 61            ............B

Now, Solving eq A and B

I.e (3 c + 8 v) - 3 × (c + v) = 61 - (3 × 12)

Or, (3 c - 3 c) + (8 v - 3 v) = 61 - 36

Or, 0 + 5 v = 25

∴ v = [tex]\dfrac{25}{5}[/tex]

i.e v = 5

So,The Total number of van = v = 5

Now Put the value of v into eq A

∵ c + v = 12    

So, c + 5 = 12

∴ c = 12 - 5

i.e c = 7

So,The Total number of car = c = 7

Hence,The Total number of car is 7 and The Total number of van is 5 . Answer

Final answer:

The student's question is about determining the number of vans owned by a company using a system of linear equations. By setting up two equations and using the elimination method, we find that the company owns 5 vans and 7 cars.

Explanation:

The question involves solving a system of linear equations to determine how many vans a company owns. We know that the company has a total of 12 vehicles, which are either cars with a capacity of 3 passengers or vans with a capacity of 8 passengers. The total capacity of all 12 vehicles combined is 61 passengers. To solve this problem, we will create two equations based on this information:

Let c represent the number of cars and v represent the number of vans.The first equation is based on the number of vehicles: c + v = 12.The second equation represents the total capacity: 3c + 8v = 61.We can solve this system using substitution or elimination methods.

Using elimination to solve the equations:

Multiply the first equation by -3 to align the passenger capacity of the cars: -3c - 3v = -36.Add this result to the second equation: (-3c - 3v) + (3c + 8v) = -36 + 61.Simplify the equation: 5v = 25.Divide both sides by 5 to find v: v = 5.Substitute v back into the first equation: c + 5 = 12.Solve for c: c = 7.

Therefore, the company owns 7 cars and 5 vans.

A garden is rectangular with an area of 6/7 square miles. If the length of the garden is 3/5 miles, what is its width?

Answers

Answer:

Step-by-step explanation:

Area= length x width

area=6/7, length=3/5, width=?

6/7=3/5 x width

6/7 divided by 3/5= 6/7 x 5/3 (you have to multiply by the recipricol, or flip the fraction.)

6/7 x 5/3=30/21= 1 3/7=width

The area of a 2D form is the amount of space within its perimeter. The width of the rectangle is 10/7 miles.

What is an area?

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The area of a rectangle is the product of its length and its width, therefore, the width of the rectangle can be written as,

Area = Length × Width

Width = Area / Length

Given the area of the rectangle is 6/7 square miles, while the length of the rectangle is 3/5 miles, therefore, the width of the rectangle is,

Width = (6/7)/(3/5)

Width = (6×5)/(7×3) = 10/7

Hence, the width of the rectangle is 10/7 miles.

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mr.james runs a petting zoo. he records the number of visitors each week,v, t weeks, after opening the petting zoo. according to the table what is the average rate of change over the interval [2,5]
a.57 visitors per month
b. 28 visitors per month
c. 36 visitors per month
d 19 visitors per month ​

Answers

Answer:

[tex]\large \boxed{\text{19 visitors/mo}}[/tex]

Step-by-step explanation:

The average rate of change is the change in the number of visitors divided by the change in the number of months.

1. Change in number of  visitors  

Change in visitors = 182 -125 = 57 visitors

2. Change in number of weeks

Change in time = 5 - 2 = 3 months

3. Average rate of change

[tex]\begin{array}{rcl}\text{Average rate of change} &= &\dfrac{\text{change in visitors}}{\text{change in months}}\\\\&= &\dfrac{\text{57 visitors}}{\text{3 mo}}\\\\& = & \textbf{19 visitors/mo}\\\end{array}\\\text{The average rate of change is $\large \boxed{\textbf{19 visitors/mo}}$}[/tex]

Mike is making a scale model of his favorite car. The actual car is 8 feet long and four feet wide. Mike wants his model to be 12 inches in length. Which of the following proportions could be used to find the width, w, of his model?

A:8/4=12/w B:8/4=w/12 C: 8/12=w/4 D:12/8=4/w

Answers

Answer:

A. 8/4=12/w

Step-by-step explanation:

8/4=12/x

8feet long           12 inches

----------------   =    ----------------

4feet wide            X because we dont know exact width

Answer:

A. 8/4=12/w

Step-by-step explanation:

About 4/5 of the weight of a pineapple is water. About how much water would you expect to find in 2 1/2 pounds of pineapple?

Answers

Answer:

2 pounds

Step-by-step explanation:

all you have to do is 2 1/2 x 4/5 because 4/5 is equal to 1. So if you multiply that by 2 1/2 you will get the answer




The quadrilateral shown is a rhombus. What is m∠4?

Answers

Answer:

m∠4= 360-(m∠A+m∠1+m∠3+m∠C+m∠2)

Step-by-step explanation:

In the diagram. check attach image

m∠A + m∠B + m∠C + m∠D = 360º.

Every quadrilateral can be decomposed (cut apart) into two triangles, each of whose angles' measures sum to 180º.

m∠A + m∠1 + m∠ 3 = 180º

m∠C + m∠2 + m∠4 = 180º

m∠A+m∠1+m∠3+m∠C+m∠2+m∠4 = 360º

therefore :

m∠4= 360-(m∠A+m∠1+m∠3+m∠C+m∠2)

Help me find 7x+6=41

Answers

Answer:

x=5

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

what i did was..

41-6 = 30

30/7 = 5

x=5

Read through the scenarios below and calculate the predicted change in kinetic energy of the object compared to a 100 kg ball traveling at 5 m/s.
A 1,000 kg ball traveling at 5 m/s would have ____ Kinetic energy
A 10 kg ball traveling at 5 m/s would have ____ kinetic energy
A 100 kg person falling at 5 m/s would have ____ Kinetic energy

Answers

10 times

tenth

the same

Step-by-step explanation:

K.E is directly proportional to mass thus if the mass increases or decreses "k" times, then so does the K.E

Answer:

1). 10 times more 2). 10 times less 3). the same

Step-by-step explanation:

Solve. 5x−3/2=3x+8   
–26

–19

13

19

Answers

Good morning,

Answer:

-19

Step-by-step explanation:

(5x−3)/2=3x+8 ⇌ 5x−3 = 2×(3x+8)  ⇌  5x−3 = 6x+16  ⇌ 6x-5x = -3-16

⇌ x=-19.

:)

Answer:

x = - 19

Step-by-step explanation:

Given

[tex]\frac{5x-3}{2}[/tex] = 3x + 8

Multiply both sides by 2 to clear the fraction

5x - 3 = 6x + 16 ( subtract 6x from both sides )

- x - 3 = 16 ( add 3 to both sides )

- x = 19 ( multiply both sides by - 1 )

x = - 19

5(2r+6)-12r ; Simplify

Answers

First, use distributive property:

5(2r+6)-12r  The original expression; multiply 5 by 2r, and 5 by 6.

10r+30-12r  Keep the -12r, just add it on to the end of the number(s) you found

Next, use communitive property:

10r+30-12r  What we found in the previous step

-2r+30        Combine the like terms; 10r-12r=-2r, then place the 30 at the end

Done! Your answer is -2r+30.

Hope that helps!

Can someone EXPLAIN how I find cf on 10. Thx

Answers

Answer:

Step-by-step explanation:

parent function is the main function the start function and transformations are the new function so parent function is y = x^2 and the transformations is down for (due to the -) and left 3 (due to the +)

HOPE THIS HELPED ;3

Answer:

so....wya

Step-by-step explanation:

To be labeled as a jumbo egg, the egg is supposed to weight 2.5 oz. However, when Desmond buys a carton of jumbo eggs, the weight of one is 2.4 oz. What is the percent error?

(Explain in a detailed way on how you got your answer)

Answers

The percent error is 4.17 %

Solution:

To be labeled as a jumbo egg, the egg is supposed to weight 2.5 oz

When Desmond buys a carton of jumbo eggs, the weight of one is 2.4 oz

To find: percent error

Percent error is the difference between a measured and known value, divided by the known value, multiplied by 100%

[tex]\% \text { error }=\frac{\text {approximate value}-\text {exact value}}{\text {exact value}} \times 100[/tex]

Here approximate value = 2.5 oz and exact value = 2.4 oz

[tex]\% \text { error }=\frac{2.5-2.4}{2.4} \times 100\\\\\% \text { error }= \frac{0.1}{2.4} \times 100 = 4.17[/tex]

Therefore percent error is 4.17 %

Find the other endpoint given one endpoint (-1,6) and the midpoint is (4,2)

Answers

Answer:

The required points of the given line segment  are ( 9, - 2 ).

Step-by-step explanation:

Given that the line segment AB whose midpoint M is ( 4, 2 ) and point A is ( - 1, 6), then we have to find point B of the line segment AB -

As we know that-

If a line segment AB is with endpoints ( [tex]x_{1}, y_{1}[/tex] ) and  ( [tex]x_{2}, y_{2}[/tex] )then the mid points M are-  

M = ( [tex]\frac{ x_{1} + x_{2} }{2}[/tex] , [tex]\frac{ y_{1}  + y_{2}}{2}[/tex]   )

Here,

Let A ( - 1, 6 ), B ( x, y ) with midpoint M ( 4, 2 ) -

then by the midpoint formula M are-

( 4, 2 )  = ( [tex]\frac{ - 1 + x}{ 2}[/tex] ,  [tex]\frac{ 6 + y}{2}[/tex] )

On comparing x coordinate and y coordinate -

We get,

( [tex]\frac{ -1 + x}{2}[/tex] = 4 , [tex]\frac{ 6 + y}{2}[/tex]  =  2)

( - 1 + x = 8,  6 + y = 4)

( x = 8 + 1, y = 4 - 6 )

( x = 9, y = -2 )

Hence the required points  A are ( 9, - 2 ).

We can also verify by putting these points into Midpoint formula.

There are 30 chairs in the band room mr avery wants to have the same number of chairs in each row there must be more than 1 row and the number of chairs in each row must also be greater than the number of rows explain how mr avery could arrange the chairs

Answers

Final answer:

Mr. Avery can arrange the 30 chairs in 5 rows of 6 chairs each or 3 rows of 10 chairs each to satisfy the conditions of having more than one row and the chairs per row being greater than the number of rows.

Explanation:

Mr. Avery can arrange the 30 chairs in the band room in multiple configurations but must satisfy two conditions: there must be more than one row and the number of chairs in each row must be greater than the number of rows. To find such arrangements, we can look for factors of 30 that adhere to these conditions. One possible arrangement is 5 rows with 6 chairs in each row. This satisfies the conditions because there are more than one row, and the number of chairs per row (6) is greater than the number of rows (5).

Another possible arrangement could be 3 rows with 10 chairs each. Here, the condition is also met since there are more than one row and the number of chairs per row (10) is greater than the number of rows (3). Mr. Avery must ensure there's enough space to move around, so he may need to rearrange the chairs to provide adequate pathways between rows.

Which of the following rational numbers represents a repeating decimal 11 / 40 ,3/25, 25/48,or 7/32

Answers

[tex]\frac{25}{48}[/tex] represents repeating decimal

Solution:

We are asked to find the rational number that represents repeating decimal

A repeating decimal, also called a recurring decimal, is a number whose decimal representation eventually becomes periodic (i.e., the same sequence of digits repeats indefinitely)

Option 1

[tex]\frac{11}{40} = 0.275[/tex]

So here the decimal part is not repeating. So [tex]\frac{11}{40}[/tex] does not represent repeating decimal

Option 2

[tex]\frac{3}{25} =0.12[/tex]

So here the decimal part is not repeating. So [tex]\frac{3}{25}[/tex] does not represent repeating decimal

Option 3

[tex]\frac{25}{48} = 0.52083333333[/tex]

So here in decimal part "3" is repeating and goes on forever

So [tex]\frac{25}{48}[/tex] represents repeating decimal

Option 4

[tex]\frac{7}{32} = 0.21875[/tex]

So here the decimal part is not repeating. So [tex]\frac{7}{32}[/tex] does not represent repeating decimal

Jerry needs to buy nails and screws for the construction site. Nails cost $2.75 per pound and screws cost $3.25 per pound. If he
only has $500 to spend on nails and screws, which inequality represents the situation where he buys x pounds of nails and y
pounds of screws?
A)
3.25x +2.75y s 500
B)
3.25x + 2.75y 2 500
2.75x + 3.25y s 500
D)
2.75x + 3.25y 2 500

Answers

Answer:

C) 2.75x+3.25y ≤ 500

Step-by-step explanation:

Here are the correct options given:

A) 3.25x +2.75y ≤ 500

B)  3.25x + 2.75y ≥ 500

C) 2.75x + 3.25y ≤ 500

D)  2.75x + 3.25y ≥ 500

Given: Nails cost is $2.75 per pound

           Screw cost is $3.25 per pound

           Jerry has only $500 to spend on nails and screws.

           x represent quantity of nail bought and y represent quantity of screw    bought.

As given we know that Jerry has only $500 to spend, so the total cost has to be less than or equal to $500. It cannot go more than $500.

Remember, Total cost= [tex]\textrm{cost of goods per pound}\times quantity[/tex]

Now, Inequality to represent the cost of buying nails and screw.

[tex]\$2.75\times x\ pounds+ \$3.25\times y\ pounds\leq \$ 500[/tex]

∴ [tex]2.75x+3.25y\leq 500[/tex]

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