A student took a system of equations, multiplied the first equation 2 by 3 and the second equation by , then added the results together. Based on this, she concluded that there were no solutions. Which system of equations could she have started with?

A. -2x+4y=4
-3x+6y=6
B. 3x+y=12
-3x+6y=6
C.3x+6y=9
-2x-4y=4
D.2x-4y=6
-3x+6y=9

Answer: sample

Step-by-step explanation:

Answer:

f(x) = 2/3 x +3

Step-by-step explanation:

We know the y intercept ( where it crosses the y axis)  is 3

We can calculate the slope from 2 points (-3,1) and (0,3)

Slope = (y2-y1)/(x2-x1)

         = (3-1)/(0--3)

          = (3-1)/(0+3)

          = (2/3)

The slope is 2/3

Since we know the slope and the y intercept, we can use the slope intercept form

y= mx+b

y = 2/3 x+3

f(x) = 2/3 x +3

Answer:

B. 585

Step-by-step explanation:

A graph of the scatter plot and line of best fit is attached.

The temperature in this problem will be the independent variable, or x.  This is because we are assuming that the number of ice cream cones sold depends on the temperature; this means the number of ice cream cones will be the dependent variable, or y.

This means in our graphing calculator, we will enter temperature in the first list and the number of cones in the second.

After drawing the scatter plot, we run the linear regression; we get the values for a and b in our equation, y = ax+b:

a = 5.08

b = 46.59

This gives us the equation y = 5.08x + 46.59.

Entering our temperature, 106, in for x gives us

y = 5.08(106) + 46.59 = 585.07 ≈ 585

Answer:

B

Step-by-step explanation:

585 Just took the test. Reference above to see explanation.

Answer:

The 9th and 11th students are also boys.

Step-by-step explanation:

Every other student is a boy. Since the 7th student is a boy this means the 8th student is a girl.

You can also think of it with odd numbers. Every odd numbered student is a boy.

Answer:

c. y = 1.25

Step-by-step explanation:

The equation for direct variation is

y = kx,

where k is the constant of proportionality.

We can use the given values of x and y to find k for this case.

y = kx

-10 = k * 40

k = -10/40

k = -0.25

The equation for this case is

y = -0.25x

Now we let x = -5 and solve for y.

y = -0.25x

y = -0.25(-5)

y = 1.25

Answer: c. y = 1.25

Answer:

c    y = 1.25

Step-by-step explanation:

The equation for direct variation is y= kx

If we know y and x we can solve for k

-10 = k*40

Divide each side by 40

-10/40 =k

-1/4 =k

The equation for this direct variation is

y =-1/4 x

Given that x =-5

y = -1/4 *-5

y = 5/4

y = 1.25

Answer:

C

Step-by-step explanation:

to factor x² - x - 2

consider the factors of the constant term which sum to give the coefficient of the x-term.

the factors are - 2 and + 1 since - 2 × 1 = - 2 and - 2 + 1 = - 1

x² - x - 2 = (x - 2)(x + 1), hence (x + 1) is a factor

The relationship between (x + 1) and the polynomial x² - x - 2 is that            ( x + 1) is a factor of x² - x - 2.

A mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a non negative integral power.

The given polynomial is x² - x - 2.

x² - x - 2

= x² - 2x + x - 2

= x( x - 2) + 1( x - 2)

=( x - 2) ( x + 1)

So we can see that, ( x + 1) is a factor of x² - x - 2.

So, option C is correct.

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Answer:

It will crawl 6 yards in 2 hours.  If you can, please mark me the brainliest :)

Step-by-step explanation:

3 yards an hour * 2 hours = 6 yards per hour.

Answer: 2hrs = 120 mins

1km = 100,000cm

120 x 38 = 4560cm

Answer: 6

The equation given to you is in the form (x-h)^2 + (y-k)^2 = r^2

The right hand side 36 is in the place of r^2, so r^2 = 36 leading to r = 6 after you apply the square root to both sides.

Answer:

  [tex]\dfrac{10\sqrt{3}}{3}[/tex]

Step-by-step explanation:

You want the length of the hypotenuse in a 30°-60°-90° right triangle with long leg 5.

The ratios of side lengths in a 30°-60°-90° triangle is ...

  1 : √3 : 2

Multiplying these values by 5/√3 gives ...

  5/√3 : 5 : 10/√3

That is, the length of the side marked X is 10/√3.

The denominator can be rationalized by multiplying the fraction by 1 in the form of (√3)/(√3):

  [tex]X = \dfrac{10}{\sqrt{3}}=\dfrac{10}{\sqrt{3}}\times\dfrac{\sqrt{3}}{\sqrt{3}}\\\\\\\boxed{X=\dfrac{10\sqrt{3}}{3}}[/tex]

Answer:

30.50 = 8p +2d

49= 7p +6d

The price of a bag of popcorn is $2.50

Step-by-step explanation:

p = price of popcorn

d = price of drinks

Luke costs:

30.50 = 8p +2d

Aiden

49= 7p +6d

I will multiply  Lukes equation by -3 so I can use elimination on the d variable

-3 (30.50) =-3( 8p +2d)

-91.50 = -24p -6d

Now add the modified equation to Aidens equation

49       = 7p +6d

-91.50 = -24p -6d

-------------------------

-42.5 = -17p

Divide each side by -17

-42.50/-17 = -17p/-17

2.5 = p

Each popcorn costs 2.5

Answer:

18.75 feet of steel pipe weighs 237 pounds  

explanation:

find out how much 1 feet weighs than u can find out how much 18.75 feet.

by doing it like this  

158÷ 12.5

=12.64

1 feet equals 12.64 pounds

12.64× 18.75

=237 pounds this is the answer

i do apologize if it wrong

Answer:

That new length would weight 237lbs

Step-by-step explanation:

To find this, we first need to find the weight per foot of the pipe. We can do this by taking the total weight and dividing by length.

158lbs/12.5ft = 12.64 pounds per feet.

Now we can multiply the rate by the new length.

12.64 pounds per feet * 18.75ft = 237lbs

Answer:

Ca^(2+) or the charge is 2 plus or just 2

Step-by-step explanation:

Charge on the calcium ion = 20*(+1) + 18*(-1) = 20 - 18 = 2

The charge on the calcium ion is +2

Answer:

I will help you with question number 2.

48:

12*4

Step-by-step explanation:

12*4=48

Answer:

Kentucky Avenue is 575 ft between C street and D street

Step-by-step explanation:

x / (460 ft) = (1000 ft) / (800 ft)

Divide the right side:

x / (460 ft) = 1.25

To solve for "x", multiply both sides by 460 ft:

(460 ft) [x/(460)] = (460) (1.25)

x = 575 ft

Hope this helped :)

Answer:

Step-by-step explanation:

Ratio means division. 36 dm / 6 dm = 6. Cancel out dm.

As a ratio, it would technically be 6:1

They can afford 9. You work it out by dividing 50.40 / 5.60

The math club can buy at most 9 lunch specials from Jimmy John's with the money in its treasury.

To determine how many lunch specials the math club can buy, we need to divide the total amount of money in the treasury by the cost of one lunch special. Let's denote the number of lunch specials the club can buy as \( n \).

The cost of one lunch special is $5.60, which can be written as a fraction of dollars as[tex]\( \frac{560}{100} \)[/tex]to make the calculations easier. The total amount of money in the treasury is $50.40, which can similarly be written as [tex]\( \frac{5040}{100} \).[/tex]

Now, we set up the inequality to find the maximum number of lunch specials \( n \) that can be bought without exceeding the treasury's funds:

[tex]\[ \frac{560}{100}n \leq \frac{5040}{100} \][/tex]

To solve for \( n \), we divide both sides of the inequality by the cost of one lunch special:

[tex]\[ n \leq \frac{\frac{5040}{100}}{\frac{560}{100}} \][/tex]

[tex]\[ n \leq \frac{5040}{560} \][/tex]

[tex]\[ n \leq 9 \][/tex]

 Since \( n \) must be an integer (you can't buy a fraction of a lunch special), the math club can buy 9 lunch specials at most. Any more than that, and they would not have enough money. Thus, the maximum number of lunch specials the club can buy is 9."

Answer:

D.

Step-by-step explanation:

Function does not have duplication of a number.be

The A choice contains duplicates of both 2 and -2.

The B choice contains a duplicate of 4.

Therefor, it must be D.

==============================================

Which of the sets of ordered pairs represents a function?  

A = {(−5, 5), (−2, 2), (2, −2), (5, −5)}

B = {(4, 2), (3, −2), (9, 4), (11, −3)}

Select one:

a. Only A

b. Only B

c. Both A and B

d. Neither A nor B

Answer:

(1) 0.08x + 16

(2) 0.08x + 16=0.12x + 14

Step-by-step explanation:

Checking account A has a monthly fee of $16 and a per-check fee of $0.08

Per check fee is a constant rate that is 0.08

Let x represents the number of checks Cecily writes per month

1 check fee = 0.08

x checks fee = 0.08x

monthly fee is $16 , we add that as well

So total monthly fee charges for account A  is

0.08x + 16

checking account B has monthly fee of $14 and a per-check fee of $0.12.

1 check fee = 0.12

x checks fee = 0.12x

monthly fee is $14 , we add that as well

So total monthly fee charges for account B  is

0.12x + 14

(2) To find number of checks write per month for the accounts to charge the same in fees

WE set both expression , account A = account B

0.08x + 16=0.12x + 14

Subtract 0.12x on both sides

-0.04x + 16 = 14

Now subtract 16 on both sides

-0.04x = -2

Divide by -0.04 on both sides

So x= 50

Hi There!

Step-by-step explanation:

40% = 0.4

124.46 * 0.4 = $49.784 (Discount)

124.46 - 49.784 = $74.676 (Sale Price)

74.676 = 74.68

Answer:

$74.676 or $74.68

Hope This Helps :)

Answer:

The cost would be $74.68

Step-by-step explanation:

To find this amount, multiply the original price by the percentage you would be paying. Since the mark down is 40%, we know that the amount paid is 60%. So multiply that by the original cost.

$124.46 * 60% = $74.68

To find the proportional relationship of 15 mL to 3.75 L, we first convert 3.75 L to milliliters, which is 3,750 mL. Then, we set up a proportion and solve for the unknown liter value. The proportional relationship of 15 mL to 3.75 L is 0.05625 L.

The student is asking about the proportional relationship between two different units of liquid volume: milliliters (mL) and liters (L). To establish this relationship, a conversion is needed, since 1 liter is equivalent to 1,000 milliliters.

First, we need to convert 3.75 liters to milliliters:

Now, let's express the proportion:

The area of Dave's bedroom, which is a rectangle with a length of 60 feet and a width of 50 feet, is calculated to be 3000 square feet.

The subject of this question is Mathematics, specifically geometrical calculations related to rectangles. The question provides the perimeter and one side length of a rectangle (Dave's bedroom) and asks for the area. First, remember that the perimeter of a rectangle is calculated by the formula 2(length + width). In the given problem, the total distance around the room (or the perimeter) is 220 feet and the width of the room is 50 feet. We can use the perimeter formula to find the length: 220 = 2(length + 50), so length = (220/2) - 50, which is 60 feet.

Now, the area of a rectangle is calculated by the formula length x width. In Dave's room, the length is 60 feet and the width is 50 feet. So Area = Length x Width = 60 feet x 50 feet = 3000 square feet. Thus, the area of Dave's bedroom is 3000 square feet.

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To find the area of Dave's rectangular-shaped bedroom, multiply the length by the width which is 6000 sq ft.

To find the area of Dave's bedroom, we need to determine the length of the room.

Since the total distance around the room is 220 feet and the width is 50 feet, we can subtract twice the width from the total distance to find the length.

This gives us a length of 220 - 2(50) = 120 feet.

The area of a rectangle is found by multiplying the length by the width, so the area of Dave's bedroom is 120 * 50 = 6000 square feet.

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Answer:

D) y = -x - 3

Step-by-step explanation:

Step 1. Find the slope (m₁) of the original line

The equation for the original line is

-x + y = 5       Add x to each side

     y = x + 5

slope = m₁ = 1

Step 2. Find the slope (m₂) of the perpendicular line

m₂ = -1/m₁     Substitute the value of m₁

m₂ = -1/1

m₂ = -1

====================

Step 3. Find the equation for the perpendicular line

y = mx + b     Substitute the value of m₂

y = -x + b

The line passes through (2, -5).  

-5 = -2 + b     Add 2 to each side

b = -3  

y = -x - 3

In the image, below  the graph of your original equation is the red line.

The blue line passing through (2, -5) is the perpendicular line.

Answer:

A

Step-by-step explanation:

(2x^2 + 3x - 4) (x + 4)

FOIL.

2x^2 times x = 2x^3

3x times x is 3x^2

-4 times x = -4x

2x^2 times 4 = 8x^2

3x times 4 = 12 x

-4 times 4 = -16

Combine like terms to get 2x^3 + 11x^2 + 8x - 16.

The probability for the spinner landing on the dotted region is 1/2.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lies in the close interval of 0 and 1 [0,1].

The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.

The probability for the given case is evaluated as,

P(Spinner lands on dotted region) = Total space for dotted region/100

                                                         = (25 + 12.5 + 12.5)/100

                                                         = 50/100

                                                         = 1/2

Hence, the probability that the spinner will land on a dotted region is 1/2.

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Hi There!

Answer:

15 to 27

Step-by-step explanation:

Boys: 15

Girls: 12

Total Students: 15 + 12 = 27

Boys to Total Students = 15 to 27

Hope This Helps :)

To find the ratio of boys to total students in a classroom, divide the number of boys by the total number of students. In this case, the ratio is 5/9.

To find the ratio of boys to total students in a classroom, we need to know the total number of students in the classroom. Let's assume that there are 27 students in total.

The ratio of boys to girls is given as 15 to 12. This means that for every 15 boys, there are 12 girls. To find the ratio of boys to total students, we add up the number of boys and divide by the total number of students.

In this case, the number of boys is 15 and the total number of students is 27. So the ratio of boys to total students is 15/27. This can be simplified to 5/9.

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Answer: First, multiply 5 by x-2 to get 5x-10. We now have 5x-10=2x+16. Subtract 2x on both sides: 3x-10=16. Add 10 to both sides: 3x=26. Lastly, divide by 3x to isolate x: x=8.6666667

Answer:

1647.2

Step-by-step explanation:

5.8% times 28,400 = 1647.2

5.8% = 5.8/100 = .058

so .058 times 28,400 = 1647.2

Final answer:

To find the commission, convert the rate to decimal by dividing by 100 then multiply by the sale price. A salesperson earns 5.8% commission, resulting in $1,647.20 for a $28,400 car.

Explanation:

To calculate the commission a car salesperson earns on the sale of a car, you first need to understand that commission is a percentage of the sale price they receive as their payment. In this case, the salesperson earns a 5.8% commission on each car sold. To find out how much commission they would earn on a $28,400 car, the following calculation is performed:

Sale price of car = $28,400
Commission rate = 5.8%

First, convert the commission rate from a percentage to a decimal by dividing by 100:
5.8% / 100 = 0.058

Next, multiply the sale price by the decimal commission rate:
$28,400 x 0.058 = $1,647.20

Therefore, the commission earned on the $28,400 car is $1,647.20.

Answer:

#5: 80mm, #6: 50yd, #7: 36m, #8: 32ft

Step-by-step explanation:

For #5:

The ratio between the two shapes is 24/15 = 8/5, based on the corresponding sides.

So, multiplying 8/5 with the smaller shape's perimeter of 50 would give you 80mm, which is the bigger shape's perimeter.

For #6:

The ratio between the two shapes is 15/9 = 5/3, based on the corresponding sides.

So, multiplying 5/3 with the smaller shape's perimeter of 30 would give you 50yd, which is the bigger shape's perimeter.

For #7:

The ratio between the two shapes is 12/4 = 3, based on the corresponding sides (You can also check this with 15/5).

So, multiplying 3 with the smaller shape's perimeter of 12 would give you 36m, which is the bigger shape's perimeter.

For #8:

The ratio between the two shapes is 12/21 = 4/7, based on the corresponding sides.

So, multiplying 4/7 with the bigger shape's perimeter of 56 would give you 32ft, which is the smaller shape's perimeter.

Hope this helps! Have a nice day!

Answer:

Value of x = 400

Step-by-step explanation:

Joint variation states that describes a situation where a variable depends on two (or more) other variables, and varies directly with some of them.

Given: x varies directly with y and  z.

i.e [tex]x \propto y[/tex] and [tex]x \propto z[/tex]

then we have the joint variation as;

[tex]x = k yz[/tex] ......[1] where k is the constant variation.

Substitute the value of x =1200 when y =20 and z = 30 to solve for k;

[tex]1200 = k (20)(30)[/tex]

Simplify:

[tex]1200 = 600k[/tex]

Divide both sides by 600 we get;

[tex]k = 2[/tex]

Now, substitute k =2 , y =10 and z = 20 to find x;

Using [1] we have;

[tex]x = 2 \times (10)(20) = 2 \times 200[/tex]

Therefore, the value of x is, 400

Answer:

x = 400

Step-by-step explanation:

given that x varies directly with y and z the the equation relating them is

x = kyz ← k is the constant of variation

to find k use the given condition x = 1200 when y = 20 and z = 30

k = [tex]\frac{x}{yz}[/tex] = [tex]\frac{1200}{20(30)}[/tex] = 2, thus

x = 2yz is the direct variation equation

when y = 10 and z = 20, then

x = 2 × 10 × 20 = 400