Need Help ASAP! Timed Assignment!
Mike and his friends bought cheese wafers for $2 per packet and chocolate wafers for $1 per packet at a carnival. They spent a total of $25 to buy a total of 20 packets of wafers of the two varieties.

Part A: Write a system of equations that can be solved to find the number of packets of cheese wafers and the number of packets of chocolate wafers that Mike and his friends bought at the carnival. Define the variables used in the equations. (5 points)

Part B: How many packets of chocolate wafers and cheese wafers did they buy? Explain how you got the answer and why you selected a particular method to get the answer. (5 points)

Answers

Answer 1

Answer:

Part A)

Our system of equation is:

[tex]\displaystyle \begin{aligned} 2x+y&=25\\x+y&=20\end{aligned}[/tex]

Where x represent the amount of cheese wafers bought and y represent the amount of chocolate wafers bought.

Part B)

Mike and his friends bought five cheese wafers and 15 chocolate wafers.

Step-by-step explanation:

Let cheese wafers be represented by x and let chocolate wafers be represented by y.

Part A)

They spent a total of $25. Since each cheese wafer cost $2 and each chocolate wafer cost $1, we can write that:

[tex]2x+1y=25[/tex]

Or, simply:

[tex]2x+y=25[/tex]

They also purchased a total of 20 packets of wafers. Hence:

[tex]x+y=20[/tex]

Our system of equation is:

[tex]\displaystyle \begin{aligned} 2x+y&=25\\x+y&=20\end{aligned}[/tex]

Where x represent the amount of cheese wafers bought and y represent the amount of chocolate wafers bought.

Part B)

Since both equations have the same coefficient for y, we can use elimination. First, multiply the second equation by negative one:

[tex]-x-y=-20[/tex]

Add it to the first equation:

[tex](2x+y)+(-x-y)=(25)+(-20)[/tex]

Simplify:

[tex]x=5[/tex]

So, five cheese wafers were bought.

Using the second equation again, we can see that:

[tex](5)+y=20\Rightarrow y=15[/tex]

So, 15 chocolate wafers were bought.

Notes:

If we wanted to solve this using substitution, we can subtract x (or y, doesn't really matter) from both sides from either equation. Using the second equation, this yields:

[tex]y=20-x[/tex]

Substitute this into the first:

[tex]2x+(20-x)=25[/tex]

Simplify:

[tex]x=5[/tex]

And we will acquire the same answer:

[tex]y=20-(5)=15[/tex]


Related Questions

I need help solving both of these 2 I’ve tried asking but nobody knows

Answers

Answer:

Step-by-step explanation:

x/7 - 13 ≥ -11

x/7 ≥ 2

x ≥ 14

m/-6 + 16 ≥ 19

m/-6 ≥ 3

m/6 ≤ -3

m ≤ -18

Answer: -18

Step by step explanation

What is the point of intersection to the system below?
2x - 3y = 5
3x +3y = 5

Answers

Answer:

Solution: {x = 2, y = -1/3}

Step-by-step explanation:

On observation, we see that the y-terms are equal and opposite in sign, therefore to solve the system, we add the two equations.

2x-3y = 5 ..........(1)

3x+3y = 5............(2)

(1) + (2)

2x - 3y + 3x + 3y = 5+5

5x = 10

x = 2 .......(3)

Substitute (3) in (2) and solve for x

3x+3y = 5 .....(2)

3(2) + 3y = 5

3y = 5-6 = -1

y = -1/3  .......(4)

assemble (3) and (4) to give the answer

Solution: {x = 2, y = -1/3}

Help please giving brainly and points! :)​

Answers

Answer:

(8,5):

8 is x-axis

5 is y-axis

(8,5) yeeeeeettttttttttr

Stationary points. Help ASAP please. Thanks

Answers

You can use the power rule for derivatives for each problem (though you could also use the product rule for the fourth curve).

y = x ² + 6x - 1   ==>   dy/dx = 2x + 6

y = x ² - 5x + 1   ==>   dy/dx = 2x - 5

y = 2 - 4x - x ²   ==>   dy/dx = -4 - 2x

y = (1 + x) (7 - x) = 7 + 6x - x ²   ==>   dy/dx = 6 - 2x

--

or, using the product rule,

dy/dx = (1 + x) (-1) + 1 (7 - x) = -1 - x + 7 - x = 6 - 2x

--

Now, stationary points occur where the derivative is zero. We have

2x + 6 = 0   ==>   x = -3

2x - 5 = 0   ==>   x = 5/2

-4 - 2x = 0   ==>   x = -2

6 - 2x = 0   ==>   x = 3

Please help. Will give 15 points!!!!

Answers

I believe it’s false I’m not too sure I haven’t done that in a while

it should be false but its been a while since i did that but the expressions should be multiplied together  

Question is in photo.
Thanks

Answers

Answer:

what do you mean for this question. What do you need help on?

Three sides of a triangle measure 25 inches, 24 inches, and 7 inches. Which statement about the side lengths is correct?

Answers

Answer:

Well this needs more of a discription. I would say that 25 inch is the hypotenuse and the lenght is 24 inches. 7 inches is the width

A real estate agent earns about a 6% commission on each house sold. How
much commission would an agent earn on a house that sold for $125,000?

Answers

Answer:

132'500

Step-by-step explanation:

It is like doing tax, you just needed to multiply your number by 0.6

Answer:

$ 7,500

Step-by-step explanation:

commission=6%

House price= $125,000

Commission=6/100 ×125,000

Commission= $ 7,500

Which of the pairs of functions and their inverses will always have a domain and range of all real numbers?

Answers

Answer:

A pair of linear functions

Step-by-step explanation:

Given

See comment for options

Required

Which has real numbers as its range and domain

The answer to this is, the linear functions

Take for instance

[tex]f(x) = mx + b[/tex]

The above function is real for all values of x

The inverse is calculated as thus:

[tex]f(x) = mx + b[/tex]

Replace f(x) with y

[tex]y = mx + b[/tex]

Swap y and x

[tex]x = my + b[/tex]

Make y the subject

[tex]my = x - b[/tex]

Divide by m

[tex]y = \frac{x - b}{m}[/tex]

Replace y with the inverse function

[tex]f^{-1}(x) = \frac{x - b}{m}[/tex]

The above function (i.e. the inverse function) is real for all values of x

This is not true for other options

A can of soup is 8 centimeters in diameter and 10 centimeters high. What is the volume of the can in terms of ?

Answers

Answer:

volume= 502.4cm

Step-by-step explanation:

see attachment for detailed solution

Answer:

Step-by-step explanation:

Formulae for Volume = Pi x r2 x h

Pi = 3.14 or 314/100 because the radius is not a product of 7

Radius = 4 cm

Height = 10 cm

314/100 x 4 x 4 x 10 = 512.4 cm2

= 512.4 cm2

i need help like asap!!!!

Answers

Answer:

to do this lets first solve this so

5*5*5*5=625

5^-3=0.008

0.008^2=0.000064

0.000064*625=0.4

so all equations that are equal to 0.4 are right which is C

39.63+0.30=24.45+0.80

Answers

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\large\textsf{39.63 + 0.30 = 24.45 + 0.80}[/tex]

[tex]\large\textsf{39.63 + 0.30}[/tex]

[tex]= \boxed{\large\textsf{\bf 39.93}}\large\checkmark[/tex]

[tex]\large\textsf{24.45 + 0.80}[/tex]

[tex]=\boxed{\large\textsf{\bf 25.25}}[/tex]

[tex]\large\textsf{\bf 39.93 } \mathsf{\bf \neq }\large\textsf{ \bf 25.25}[/tex]

[tex]\boxed{\boxed{\large\textsf{Answer: \bf FALSE or NOT TRUE because 39.93 }\mathsf{\neq }\large\textsf{ \bf 25.25}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

31/24 menos 5/8 cuanto es?

Answers

Answer:

31/24 menos 5/8 cuanto es 2/3

Step-by-step explanation:

=31/24- 5/8

=31-15/24

= 16/24

=2/3

Hence the final answer is 2/3

BD is the angle bisector of ABC. Find m ABC and m DBC. (Picture attached!) Thank you!!!

Answers

Answer:

60 Degree,30 degree

Step-by-step explanation:

BD is bisector of ∠ABC

=> ∠ABD = ∠DBC

=> 3x = x + 20

=> 3x - x = 20

=> 2x = 20

=> x = 20/2  

=> x = 10

Now,

∠ABD = ∠DBC = x + 20 = 10 + 20 = 30 Degree

∠ABC = ∠ABD+∠DBC = 30+30 = 60 Degree

What is the slope of the line formed by (7,1) and (-3,3)?

Answers

Answer:

JMK

Step-by-step explanation:

Answer:

[tex]-\frac{1}{5}[/tex] is the slope of the line.

Step-by-step explanation:

(7 , 1) = (x1 , y1)

(-3 , 3) = (x2 , y2)

slope = y2 - y1/x2 - x1

=3 - 1/-3 - 7

=2/-10

=1/-5

=[tex]-\frac{1}{5}[/tex]

how do do this plz help

Answers

Answer:

okay for graphing first one start at zero go up five. then rise over run. so go up one and right four.

second one go down one. then down one right one

out of 75 student 3 were a scent what percentage was present​

Answers

Answer:

To find a percentage, divide the number present by the total number of students, then multiply that number by 100.

Answer:

96% were present.

Step-by-step explanation:

75/100 , 72/? Find percent (?)

(72*100 / )75

96%

Think of 5 positive integers that have a mode of 4, a median of 6, a mean of 7 and a range of 10.

Answers

Answer:

6 6 6 6 11

Step-by-step explanation:

The median is the middle number

the mode is the number of items, usually the number that are the same.

the mean is the average

the range is the number between the smallest and the largest.

So the information you have makes 4 of the 5 numbers the same.

The middle number is 6. This is an interesting fact because it means that 4 of the five numbers are 6

x 6 6 6 6  or  6 6 6 6 x  is what you know so far.

The range is a bit of a devil. And so is the mean. We need the mean to be related to  5*7 = 35. So the sum of the five numbers equals 35. The range would have to be 5, I think. (35 - 4*6) = 11

The difference between 11 and 6 = 5

So 11 works for everything but the range.

If the range must be ten, then x = 16 but then the mean = 8 and 7  is incorrect

So I can get 3 out of 4, but not them all.

What measure is represented by 17 feet in the figure below?

A cylinder with diameter 17 feet.
the radius of the base
the diameter of the base
the area of the base
the height of the cylinder

Answers

Answer: The answer is the diameter.

Step-by-step explanation:

Answer:

diameter

Step-by-step explanation:

the diameter goes straight through the center of the circle

The area of a wall that needs to be papered is 84sqft. The wallpaper that needs to be papered is 18in wide and 33ft long. Rolls of solid color wallpaper will be used, so patterns do not have to match up.

Answers

Answer:

The answer is below

Step-by-step explanation:

The area of the wall is 84 ft².

The width of the wallpaper is 18 in.

1 ft. = 12 in

Hence; 18 in = 18 in * 1 ft. per 12 in = 1.5 ft

The length of the wallpaper is 33 ft.

Therefore, the area of the wallpaper = length * width = 1.5 ft. * 33 ft. = 49.5 ft². This means that each roll of wallpaper has an area of 49.5 ft²

Therefore, the minimum amount of rolls of wallpaper needed = area of wall / area of wallpaper

Amount of wallpaper = 84 ft² / 49.5 ft² = 1.7 rolls

Find the area of the figure




Will





Give






Brainlist

Answers

Answer: 52x+4

Step-by-step explanation: Do 16(2x-1)+4(5x+5) and get 52x+4.

If using the method of completing the square to solve the quadratic equation
22 + 2x + 16 = 0, which number would have to be added to "complete the
square"?

Answers

Answer:

complete the square 2 x + 38 = 0

Step-by-step explanation:

A cyclist travels 7 km from home to the park.
She leaves home at 17:40 and arrives at the park at 17:55.
What is her average speed in km/h?

Answers

Answer:

28 km per hour

Step-by-step explanation:

First determine the amount of time that the trip took

17:55 - 17:40 = :15 or 15 minutes

We need the time in hours

15 minutes * 1 hour/ 60 minutes = 15/60 hours = 1/4 hours

To determine speed, take distance and divide by time

7 km ÷( 1/4 hours)

Copy dot flip

7 * 4/1

28 km per hour

The scores from Dr. Wilhelm's students science fair project are shown below .
Dr wilhelm made a histogram for the data.

answer choices :
50
65
70
71

plsss help I appreciate it thank you so much

Answers

Answer:

See Explanation

Step-by-step explanation:

You posted an incomplete question with little and unclear details.

I will answer this question with a more complete version (see attachment)

Given that:

[tex]Scores: 100\ 95\ 88\ 62\ 76\ 90\ 100\ 58\ 72\ 60\ 85\ 90\ 70\ 72\ 54\ 100\ 60\ 80\ 75\ 51[/tex]

Required

The fraction that passed the test

Rearrange the score in ascending order:

[tex]Scores: 51\ 54\ 58\ 60\ 60\ 62\ 70\ 72\ 72\ 75\ 76\ 80\ 85\ 88\ 90\ 90\ 95\ 100\ 100\ 100[/tex]

The total number of students is:

[tex]n =20[/tex]

Extract the students that passed (scored 70 and above)

[tex]Passed: 70\ 72\ 72\ 75\ 76\ 80\ 85\ 88\ 90\ 90\ 95\ 100\ 100\ 100[/tex]

Their numbers are:

[tex]Passed: 14[/tex]

So, the fraction of those that passed is:

[tex]Fraction = \frac{Passed}{n}[/tex]

[tex]Fraction = \frac{14}{20}[/tex]

Reduce fraction

[tex]Fraction = \frac{7}{10}[/tex]

Carol wants to tile her utility room. Each tile is 1 square foot. She draws the shape of her room on a grid. Each square unit on the grid represents 1 square foot. How many tiles will she need?

Answers

Answer:

1

Step-by-step explanation:

that's a very vague question

**PLEASE HELP**The frequency table below represents the 30 best battling averages for a semi pro baseball league. Which ranges of battling averages were least common among the players

Answers

The lower the frequency the least common the average.

There are two frequencies that are 1, which would be the least common.

The answer is C. 0.320-0.329 and 0.360 -0.369

Answer:

option C

Step-by-step explanation:

option c is contains the two batting averages which have a frequency of 1, this means that they both only occurred once which is the least amount of times any of the batting averages has occurred.

Use the diagram right above
AB=?
m

Answers

I am pretty sure is 70 degrees but I don’t know for sure

help me..........
only 23...​

Answers

Question 23

Recall that a kite in geometry is any four sided figure where we have two different pairs of adjacent sides that are the same length.

We're told that PS = 4.5 and RS = 6. So this isn't an adjacent pair of congruent sides. But we can say that PS and PQ are one pair of adjacent congruent sides. That makes PQ to be 4.5 cm long.

Similarly, RS = RQ = 6 is the other pair of adjacent congruent sides. Notice that triangle PQR reflects over line PR to get triangle PSR.

See the diagram below.

A cube of sides 10cm was cut across to obtain a prism. Calculate the surface area of the prism and the volume of the prism
[tex] \frac{1}{2} bh \times h[/tex]

Answers

Answer:

Part A

The volume of the triangular prism is 500 cm³

Part B

The total surface area of the prism is approximately 441.42 cm²

Step-by-step explanation:

The given details are;

The dimensions of the side length of the cube, s = 10 cm

The shape the cube was cut across to obtain = A prism

Part A

Whereby the prism obtained is a triangular prism, we have;

The cube can be cut in half to form a triangular prism

The volume of each triangular prism obtained = (1/2) × The volume of the cube

∴ The volume of the triangular prism = (1/2) × (10 cm)³ = 500 cm³

Part B

The height of the prism, h = 10 cm × sin(45°) = 5·√2 cm = (1/2) × The base width of the prism

The triangular cross sectional area of the prism, A₁ = 5·√2 × 5·√2 = 50

The square cross sectional area, A₂  = 10 × 10 = 100

The cross sectional area of the base, A₃ = 10·√2 × 10 = 100·√2

The total surface area of the prism, A = 2·A₁ + 2·A₂ + A₃

∴ A = 2×50 + 2×100 + 100·√2 = 300 + 100·√2 ≈ 441.42

The total surface area of the prism, A ≈ 441.42 cm²

Write the equation of the line that passes through the point (4,−1) that is parallel to the line 2x−3y=9

Answers

First we find the slope of the line 2x−3y+8=0 by placing it into slope intercept form:

2x−3y+8=0

⇒−3y=−2x−8

⇒3y=2x+8

⇒y=  

3

2

x+  

3

8

 

Therefore, the slope of the line is m=  

3

2

.

Now since the equation of the line with slope m passing through a point (x  

1

,y  

1

) is

y−y  

1

=m(x−x  

1

)

Here the point is (2,3) and slope is m=  

3

2

, therefore, the equation of the line is:

y−3=  

3

2

(x−2)

⇒3(y−3)=2(x−2)

⇒3y−9=2x−4

⇒2x−3y=−9+4

⇒2x−3y=−5

Hence, the equation of the line is 2x−3y=−5.

Answer:

y=2/3x-11/3

Step-by-step explanation:

Hi there!

We are given the equation 2x-3y=9 and we want to write an equation that is parallel to it and that passes through (4,-1)

Parallel lines have the same slopes

So we need to first find the slope of 2x-3y=9

We can do this by converting the equation of the line from standard form (ax+by=c where a, b, and c are integers) to slope-intercept form (y=mx+b, where m is the slope and b is the y intercept)

To do this, we need to isolate y on one side

2x-3y=9

subtract 2x from both sides

-3y=-2x+9

divide both sides by -3

y=2/3x-3

as 2/3 is in the place where m is, 2/3 is the slope of the line

It's also the slope of the line parallel to it that passes through (4,-1).

Here's the equation of that line so far:

y=2/3x+b

now we need to find b

as the line will pass through the point (4,-1), we can  4 as x and -1 as y in order to solve for b

-1=2/3(4)+b

multiply

-1=8/3+b

subtract 8/3 to both sides

-11/3=b

Substitute -11/3 as b into the equation

y=2/3x-11/3

There's the equation

Hope this helps!

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