The produce market is having a sale on grapes and oranges. A customer found the following two receipts in her cart as she was walking into the store. Use the information from the receipts to write a system of linear equations that can be used to determine the price per pound of grapes and the price per pound of oranges. Then, use the system to test the following solutions to determine which solution is viable. A. Given these constraints, grapes cost $3.25 per pound, and oranges cost $1.05 per pound. B. Given these constraints, grapes cost $1.60 per pound, and oranges cost $2.15 per pound. C. Given these constraints, grapes cost $1.05 per pound, and oranges cost $3.25 per pound. D. Give these constraints, grapes cost $2.15 per pound, and oranges cost $1.60 per pound.

Answer:

x = -2, y = 3

Step-by-step explanation:

Given equations are,

4x + 5y = 7 ---------(1)

3x - 2y = -12 ----------(2)

Multiply equation (1) by 3

12x + 15y = 21 ------(3)

Multiply equation (2) by (-4)

-12x + 8y = 48 --------(4)

Now add equations (3) and (4),

(12x + 15y) + (-12x + 8y) = 21 + 48

(12x - 12x) + (15y + 8y) = 69

23y = 69

y = 3

From equation (2),

3x - 2(3) = -12

3x - 6 = -12

3x = 6 - 12

x = -2

Therefore, x = -2 and y = 3 will be the answer.

Answer:

What is the solution to this system of equations?

[tex]4x +5y = 7[/tex]

[tex]3x-2y=-12[/tex]

The solution is ✔ [tex](-2,3)[/tex] .

Answer:

200

Step-by-step explanation:

55 / 5x = 20

5x=1100

x=200

Answer:

A

Step-by-step explanation:

Reflected across the x-axis => but then moved up 4 units

this makes it in a way "flipped"

We see a's coordinates = (-3, 3)

b's coordinates = (-1, 1)

c's coordinates = (-2, 3)

Hope this helps!

Answer:

Choice A

Step-by-step explanation:

Step 1 - reflection across x-axis, affects y-coordinate only

Step 2- 4 units up, affects y-coordinate only

So for the given points we have:

Choice A is correct

Answer:

75.36

Step-by-step explanation:

3.14 (a2 + ab)

Substitute a = 4 and b = 2 into the equation:

3.14 (4^2 + 4*2)

= 3.14 (16 + 8)

= 3.14 (24)

= 75.36

Answer:

75.36

Step-by-step explanation:

=> (3.14)(a²+ab)

Putting a = 4, b = 2

=> [tex](3.14)[(4)^2+(4)(2)][/tex]

=> [tex](3.14)(16+8)[/tex]

=> [tex](3.14)(24)[/tex]

=> 75.36

Answer:

No . Natural numbers are a subset of whole number. Negative numbers are entire numbers but not natural. And any set that contains it. For example, the set {1, 2.3, 2.236067977} or {-79000, pi, 2.236067977, sin(47)} or all real numbers, etc

Step-by-step explanation:

Answer:

11, 13, 17, 31, 37, 71, 73, 79, 97 are the two digit numbers which remain prime even on interchanging the digits.

Step-by-step explanation:

Answer : The area of given rectangle is p² - 7p

Step-by-step explanation :

Formula used to calculate the area of rectangle is:

Area of rectangle = length × breadth

Given:

Length = (p-7)

Breadth = p

Area of rectangle = length × breadth

Area of rectangle = (p-7) × p

Area of rectangle = p² - 7p

Therefore, the area of given rectangle is p² - 7p

Answer:

6 boys and 11 girls

Step-by-step explanation:

hello,

let 's note x the number of boys and y the number of girls, we can write two equations

"there are a total of 17 kids"

(1)  x + y  = 17

"There are 5 more girls than boys"

(2) y = x + 5

We can replace (2) in (1) it comes

x + x + 5 = 17

<=> 2x = 17-5 = 12

<=> x = 6

and then y = 11

So, there are 6 boys and 11 girls

graphs below

hope this helps

The number of girls in the club is 6

An equation is a mathematical statement formed from two algebraic expression when equated by an equal sign.

It is given that

Total Kids = 17

Let the number of boys be x

There are 5 more girls than boys

Let number of girls be y

y = x+5

The number of girls = x +5

x +y = 17

The graph is plotted  and is attached with the answer.

The intersection of the graph gives us the total number of girls and boys

(6,11) is the point of intersection and therefore

Number of boys = 6

No. of girls = 11

To know more about Equation

https://brainly.com/question/10413253

#SPJ2

Answer:

6.78 me too I have to work at the same place and time to go home and see you soon I have to go home to sleep now but I'm

Answer:

a) 10.7 cm

b) 11.6 cm

c) 29.9 cm²

Step-by-step explanation:

a) sin(α)/a = sin(β)/b

sin(∠BCD)/BD = sin(DBC)/DC

sin(41°)/BD = sin(55°)/13.4

BD = 13.4*sin(41°)/sin(55°) = 10.73 cm ≈ 10.7 cm

b) From ΔBCD , ∠BDC = 180-(41+55) = 84°

∠ABD and ∠BDC are alternate interior angles, so they are congruent, and

∠ABD = ∠BDC  = 84°

AD²= AB² + BD² - 2*AB*BD*cos (∠ABD) =

= 5.6² + 10.73² - 2*5.6*10.73*cos(84°) = 133.93 cm²

AD =√(133.93) ≈11.6 cm

c) Area(ADB) = (1/2)*AB*BD*sin(∠ABD)=(1/2)*5.6*10.73*sin(84°) ≈ 29.9 cm²

Answer:

f^-1(x) = (x-8)/4

Step-by-step explanation:

To find an inverse function, simply flip the x and y variables in a equation and then solve in terms of y.

x = 4y + 8

x - 8 = 4y

y = (x-8)/4

And we have our final answer!

Answer:

180

Step-by-step explanation:

20×9=180

Answer:

x>15

Step-by-step explanation:

subtract 4x from both sides and add 7 to both sides

Step-by-step explanation:

-2.21z + 1.82a - 3.38

I think this is the answer

Answer:

if it is a rectangular prism then it is a rectangle.

Step-by-step explanation:

Answer:

Rectangle

Step-by-step explanation:

Answer:

3/8

Step-by-step explanation:

for the number 1 on spinner a there are 4 possibilites.

same goes for 2,3 and 4. all in all, there is 32 posibilities total.

for number 1 on spinner a, there are 3 poss. for number 2, there are 2 poss.

in total there are 6 possibilities on spinner A and 6 on spinner B. 6 plus 6 is 12.

12/32=3/8

Answer:

Its 3/8

Step-by-step explanation:

Corrected Question

Which equation can be solved by using this system of equations?

[tex]y= 3x^5 - 5x^3 + 2x^2 - 10x+4$ and y= 4x^4 + 6x^3 - 11[/tex]

Options

[tex](A)3x^5 -5x^3 + 2x^2 - 10x +4=0\\(B)3x^5 - 5x^3 + 2x^2 - 10x+4-4x^4 + 6x^3 - 11=0\\(C)3x^5 +4x^4 + x + 2x^2 - 10x-7=0\\(D)3x^5 - 5x^3 + 2x^2 - 10x+4-4x^4 - 6x^3 + 11=0[/tex]

Answer:

(D) [tex]3x^5 - 5x^3 + 2x^2 - 10x+4-4x^4 - 6x^3 + 11=0[/tex]

Step-by-step explanation:

[tex]y= 3x^5 - 5x^3 + 2x^2 - 10x+4\\y= 4x^4 + 6x^3 - 11\\$Therefore:\\3x^5 - 5x^3 + 2x^2 - 10x+4=4x^4 + 6x^3 - 11\\$Bring the terms on the right to the left\\3x^5 - 5x^3 + 2x^2 - 10x+4-4x^4 - 6x^3 + 11=0[/tex]

Answer:

Option A

Step-by-step explanation:

[tex]-14m-7m+1=-7m+1\\\\-14-7m+1-(-7m+1)=-7m+1-(-7m+1)\\\\-14m=0\\\\-14m/-14=0/-14\\\\\boxed{m=0}[/tex]

Answer:A

Step-by-step explanation:

-14m-7m+1=-7m+1

then

-14m-7m+7m=1-1

-14m=0

m=0

Answer:

A) 0

B) 1

C) 36

D) 101

Question:

Given the strings, identify which PA are and their reason (r): Remember: to be a PA the difference between two consecutive terms is always the same and is called the (r) ratio. A) (1, 1, 1, 1, ...) B) (-1, 0, 1, 2, ...) C) (12, 48, 84, 120, ...) D) (101 , 202, 303, 404, ...)

Step-by-step explanation:

PA is said to be the difference between two consecutive terms. The PA is always the same for these terms. It is also called the (r) ratio.

A) (1, 1, 1, 1, ...)

PA = 2nd term - 1st term = 3rd term - 2nd term

Using the 1st and second term

1st term = 1

2nd term = 1

PA = 1-1

PA = 0

B) (-1, 0, 1, 2, ...)

PA = 2nd term - 1st term = 3rd term - 2nd term

Using the 1st and second term

1st term = -1

2nd term = 0

PA = 0- (-1) = 0+1

PA = 1

C) (12, 48, 84, 120, ...)

PA = 2nd term - 1st term = 3rd term - 2nd term

Using the 1st and second term

1st term = 12

2nd term = 48

PA = 48 - 12

PA = 36

D) (101 , 202, 303, 404, ...)

PA = 2nd term - 1st term = 3rd term - 2nd term

Using the 1st and second term

1st term = 101

2nd term = 202

PA = 202 -101

PA = 101

Answer:

Since these angles are vertical their angle measures are equal so the equation is 7x - 9 = 110.

Answer:

x=17

Step-by-step explanation:

7x-9=110

7x=119

x=17

Answer:

2/5

Step-by-step explanation:

subtract 130,35,and 74 from 400 you will have 160/400 left then you find the greatest common and divide! and get 2/5

Answer: 2/5

Step-by-step explanation:

Ben gives 35 to Sonia, 130 to Phill, 75 to Lance, in total he gives away 240 counters. the fraction of the counters left in his bag would be 400-240 which is 160 and so his fraction would be 160/400 and this in simplest form would be 8/20 if you divide by 20 and then to simplify that you can divide by 4 to get 2/5

Answer:

B

Step-by-step explanation:

4.5 x 6 = 27

4.5 x 8 = 36

27 x 2 = 54

36 x 2 = 72

54 + 72 = 126cm Perimeter/

27 x 36 = 972 cm2 Area/

Answer:

7.10a.m.

Step-by-step explanation:

Thats it , byeee

Answer:

7.10am

Step-by-step explanation:

....................

Answer:

f(50) = 31928.24 thousands

Therefore, it means that the US population in year 1850 is 31928.24 thousands

Step-by-step explanation:

Given the function;

f(x)=165.6x^1.345

Where;

f(x) is in thousand and

x is the number of year after 1800

To determine f(50), we will substitute x = 50 into the function of f(x);

f(50)=165.6(50)^1.345

f(50) = 31928.24 thousands

Since f(50) is the US population in year 1800+50 = 1850

Therefore, the US population in year 1850 is 31928.24 thousands

Area: 68

Perimeter: 50

Answer:

(a)

[tex]r\geq 5[/tex]

[tex]r+y\leq 15[/tex]

[tex]8r+12y\geq 120[/tex]

[tex]y\geq 0[/tex]

(c)Maximum number of hours Lia can work at the restaurant and still meet her earnings goal = 15 hours

(d)Maximum Earning = $160

Step-by-step explanation:

Let r be the number of hours worked at the restaurant.

Let y be the number of hours of yard work,

Lia must work at least 5 hours per week in her family’s restaurant for $8 per hour.

[tex]r\geq 5[/tex]

Since she does yard work, [tex]y\geq 0[/tex]

Lia’s parents allow her to work a maximum of 15 hours per week overall.

[tex]r+y\leq 15[/tex]

Lia’s goal is to earn at least $120 per week.

The restaurant, r pays $8 per hour

Yard work, y pays $12 per hour.

Therefore:

[tex]8r+12y\geq 120[/tex]

The system of inequalities that represent this problem is therefore:

[tex]r\geq 5[/tex]

[tex]r+y\leq 15[/tex]

[tex]8r+12y\geq 120[/tex]

[tex]y\geq 0[/tex]

(b)The graph of the inequality is attached below

(c)When the graph is plotted, the vertices of the feasible region are:

Where the first term is for the number of hours worked in the restaurant.

The maximum value of r possible is 15 from the three points.

Therefore, she can work at the restaurant for 15 hours and still meet her earning goal.

(d)Maximum Amount Lia can earn in 1 Week

Since she has to work at least 5 hours at the restaurant, the maximum amount possible is $160.

Answer:

1 / (x + 1)(x - 3).

Step-by-step explanation:

x^3-3x^2-x+3

= x^2(x - 3) - 1(x - 3

= (x^2 - 1)(x - 3)

= (x - 1)(x + 1)(x - 3)

So x - 1 divided by  x^3 - 3x^2 - x + 3

= (x - 1) /  (x - 1)(x + 1)(x - 3)

= 1 / (x + 1)(x - 3).

Answer:

20

Step-by-step explanation:

1,2,5 have the same ratio as 4,8,20 and add up to 32

Answer:

First problem: 2sqrt(5)

Second problem: 20 ft

Step-by-step explanation:

First problem:

The geometric mean, x, of a and b is

a/x = x/b

Here you have 4 and 5, so the geometric mean, x, of 4 and 5 is

4/x = x/5

Cross multiply.

x^2 = 4 * 5

x = sqrt(4 * 5)

x = 2sqrt(5)

Second problem:

Ratio of lengths of sides is

1 : 2 : 5

Add all numbers, 1 + 2 + 5 = 8

The ratio of the longest side to the perimeter is

5 : 8

Let the longest side have length x.

5/8 = x/32

8x = 5 * 32

8x = 160

x = 20

Answer: 20 ft

Answer:

Step-by-step explanation:

Distance traveled = speed*time taken

The total distance traveled around the tires is the circumference.

If the tire of a go-kart with circumference of 1m revolves 15 times per second, the speed of the go-kart will be 1*15 = 15m/s

Given the time taken by the go-kart to travel round to be 40 seconds;

Distance traveled by the go-kart = 15*40 = 600m

Answer:

x+8/x^2 * 2x^2/2x+16

Step-by-step explanation: