John, Cindy, and Isaiah went to the store to buy school supplies. John bought 2 pens, 3 folders, and 4 notebooks for a total of $20. Cindy bought 5 folders and 5 notebooks for a total of $25. Isaiah bought 3 pens, 1 folder, and 2 notebooks for a total of $11

Answers

Answer 1

Using a system of equations, it is found that:

Each pen costs $0.6.Each folder costs $0.4.Each notebook costs $4.4.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Variable x: The cost of a pen.Variable y: The cost of a folder.Variable z: The cost of a notebook

John bought 2 pens, 3 folders, and 4 notebooks for a total of $20, hence:

2x + 3y + 4z = 20.

Cindy bought 5 folders and 5 notebooks for a total of $25, hence:

5y + 5z = 25.

x + z = 5.

x = 5 - z.

Isaiah bought 3 pens, 1 folder, and 2 notebooks for a total of $11, hence:

3x + y + 2z = 11.

y = 11 - 3x - 2z

Replacing the second and the third equation on the first, we have that:

2x + 3y + 4z = 20.

2(5 - z) + 3(11 - 3x - 2z) + 4z = 20.

10 - 2z + 3[11 - 3(5 - z) - 2z] + 4z = 20.

2z + 3(11 - 15 + 3z - 2z) = 10

2z + 3(z - 4) = 10

5z = 22.

z = 4.4

x = 5 - z = 5 - 4.4 = 0.6

y = 11 - 3x - 2z = 11 - 3(0.6) - 2(4.4) = 0.4.

Hence:

Each pen costs $0.6.Each folder costs $0.4.Each notebook costs $4.4.

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Related Questions

Solve and show the answer in simplest terms 2 over 5 + 1 over 3

Answers

Answer:  

11/15

Step-by-step explanation:

2/5+1/3

Find a common denominator-15. The fractions with the common denominator are 6/15 and 5/15. They make 11/15. 11/15 is in its simplest form.

Bbh. Pls help i am stuck and need it i give 25 pts thanks

Answers

Answer:

  8 cm

Step-by-step explanation:

You want the base of a triangle, given its height is 3 cm. From the base of 12 cm, the same triangle has a height of 2 cm.

Area

The area of a triangle is given by the formula ...

  A = 1/2bh

The area will be the same for any (base, height) pair of dimensions. The height is always measured perpendicular to the base. The base is generally one side of the triangle.

Application

Here, the longest side is labeled 12 cm, and the perpendicular distance to the opposite vertex (height) is labeled 2 cm. This means the triangle area is ...

  A = (1/2)(12 cm)(2 cm) = 12 cm²

The distance perpendicular to the unknown side is shown as 3 cm. This gives you a clue that using the area of the triangle to find the unknown side is probably useful.

  A = 1/2bh

  12 cm² = 1/2(b)(3 cm)

  8 cm = b . . . . . . . . . . . . multiply by 2/(3 cm)

The value that goes in the box is 8.

__

Additional comment

The attachment is drawn to scale.

<95141404393>

help please

What is the surface area of a cube with an edge of 5 cm?​

Answers

Answer:

150 cm^2

Step-by-step explanation:

A cube has 6 surfaces

Each surface square = 5 by 5

So.....

5 x 5 (or 25) times 6

25 x 6 = 150

Hope this helps!

Can somebody please help me? I have dyscaluca and don't understand this

Answers

Answer:

man

Step-by-step explanation:

im sorry...you'll get it soon i swear

What is the average rate of change for the table and graph below over the interval [0,3]?

Answers

Answer:

-2

Step-by-step explanation:

The average rate of change is the slope using the points (0, 10) and (3, 4).  The slope is found using the formula [tex]\frac{y2-y1}{x2-x1}[/tex]

[tex]\frac{4-10}{3-0}= \frac{-6}{3}=-2[/tex]

help me please i need help

Answers

Yes they intersect at one point

Decrease £19064.67 by 9.5%

Answers

Answer:

£17,253.53

Step-by-step explanation:

9.5% of 19,064.67 is 1,811.14 (rounded to the nearest hundredth.)

Subtract 1,811.14 from 19,064.67, and this will give you 17,253.53. This is a 9.5% decrease.

A spinner is divided into 8 identical sectors and labeled 1 through 8.

How many spins are expected for a multiple of 3 to be spun 6 times?

Select from the drop-down menu to correctly complete the sentence.

The spinner is expected to have to spin approximately
Choose...
times for a multiple of 3 to be spun 6 times.


12
16
24
48

Answers

Answer:

The answer is 12

Step-by-step explanation:

1-8(6)

The multiples of 3 would be 3 and 6.

3 and 6 are found 12 times within those 6 spins

Option 12 is the correct answer.

What is permutation?

The permutation refers to the various ways in which objects from a set may be selected, generally without replacement, to form subsets.

For the given situation,

The spinner has 8 identical sectors {1,2,3,4,5,6,7,8}.

The multiples of three from the given sectors are 3 and 6.

Multiples of 3 in the sector = 2

The spinner is expected to have to spin the multiples of 3 to be spun 6 times = [tex]2[/tex] × [tex]6[/tex]

⇒ [tex]12[/tex]

Hence we can conclude that option 12 is the correct answer.

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please help!!!! what is the equation for this graph

Answers

Answer:

[tex]f(x)=\sqrt[3]{x-2} +1[/tex]

Step-by-step explanation:

Given function for graph:  [tex]f(x)=1\sqrt[3]{x-h} +k[/tex]

where (h, k) is the midpoint of the curve.

Therefore, the parent function is [tex]f(x)=\sqrt[3]{x}[/tex]

[tex]f(x)=1\sqrt[3]{x-h} +k[/tex] can be obtained by translating [tex]f(x)=\sqrt[3]{x}[/tex] to [tex]h[/tex] units to the right and [tex]k[/tex] units up

The x and y intercept of [tex]f(x)=\sqrt[3]{x}[/tex] is the origin

Therefore, this graph has been translated 2 units to the right and 1 unit up.

Therefore, [tex]h=2[/tex] and [tex]k=1[/tex]

Substituting these values into the given function:

[tex]\implies f(x)=\sqrt[3]{x-2} +1[/tex]

the figure shows a solid cube with dimensions 24 cm by 15 CM by 16 cm. A cylinder with a base radius of 4 cm and height of 7 cm is removed from the cuboid. find the area that will be covered in paint? (surface area)

Answers

Answer:

=2,133 3/7cm^2

Step-by-step explanation:

sides

15x16=240

240x2

=480cm^2

24×16=384

384×2= 768cm^2

768+480

a=1248cm^2

24x15=360cm^2

22/7x4x4

=50 2/7cm^2

360- 50 2/7

=354 5/7cm^2

(354 5/7)2

b=709 3/7cm^2

22/7x8x7

=22x8

c=176cm^2

a+b+c

1248+709 3/7+ 176

=2,133 3/7cm^2

The table shows the speeds of the four fastest drivers in a car race.
Driver
Speed (miles per hour)
Marco
224.362
Finn
224.136
Will
224.48
Liz
224.392
Did Marco win this week's race? Use words and numbers to justify your answer.
Answer:
14

Answers

Marco only got 2nd place

Step-by-step explanation:

A little confused can I get some help?

Answers

Answer:

Step-by-step explanation:

4+(7-5)2= 8 I guess

a rectangle has a perimeter of 36 feet. The length of the mat is twice the width. Write and solve an equation to determine the length, in feet, of the mat.
Then find the area, in square feet, of the mat.

Answers

Concept :-

We have been provided with some information regarding a rectangular shaped mat. And on the basis of that information, we will create some assumptions and create and equation and equate it to get our required answer.

Given Information :-

A rectangular mat with,

Perimeter = 36 ft. Length = twice the width

To Find :-

The dimensions of the matArea of the mat

Formula Used :-

[tex] \diamond \: \underline{ \boxed{\begin{array}{cc} \sf1. \: Perimeter_{Rectangle} = 2(l+b) \\ \\ \sf 2. ~Area_{Rectangle} = l\times b \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{array}}} \: \star \\ [/tex]

Solution :-

Let the breadth of the mat be x, therefore,

Length = 2x

Now, according to the question,

[tex] \sf \hookrightarrow 36 \: = 2(2x + x) \\ \\ \\ \sf \hookrightarrow 6x = 36 \: ft. \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow x = \cancel\frac{36}{6} = 6 \: ft. \: \: \\ [/tex]

Thus,

Length = 2x = 2 x 6 = 12 ft. Breadth = x = 6 ft.

Now, we have to find out the area of the mat, thus,

[tex] \sf \hookrightarrow Area=6 \times 12 \\ \\ \\\sf \hookrightarrow Area=72 \: sq. ~ft. \\ \\ [/tex]

Thus, the area of the mat is 72 sq. ft.

[tex]\underline {\rule{221pt}{2.5pt}} \\ \\ [/tex]

Answer:

72 sq. feet

Step-by-step explanation

Since the perimeter is 36 feet and the length is 2w, you have to do the guess and check method.

I already did the guess and check method. So, here's how it became:

length =12

width=6

because 6x2=12 or 12 divide 2=6.

12 + 6 + 12 + 6.

12+6= 18. 12+6=18. 18+18=36 feet.

To find the area of a rectangle, you have to do L times W.

Which means 12x6.

12x6=72 sq. feet.

I hope this helps!!!

pls help ill give a hundred points. select the correct answer from the drop down menu A(1,3),B(5,3),and D(1,-2) are three vertices of rectangle ABCD the coordinates of vertex C are select from the drop down menu (5,2),(-5,1),(5,-2),(2, -5)

Answers

Question ↷

A(1,3),B(5,3),and D(1,-2) are three vertices of rectangle ABCD the coordinates of vertex C are select from the drop down menu (5,2),(-5,1),(5,-2),(2, -5)

Answer↷

(5,-2)

Solution ↷

we know that,

the midpoint of the diagonals of a rectangle bisect each other,

so,

MP of AC = MP of BD

[tex] \huge \rightarrow \frac{x + 1}{2},\frac{y+ 3}{2} = \frac{5 + 1}{2},\frac{3 - 2}{2} \\ [/tex]

[tex] \huge \rightarrow \: x = 5 \: \\ \huge \rightarrow \: y = - 2[/tex]

Answer:

(5,-2)

Step-by-step explanation:

Cause me smart

Graph the image of the figure using the transformation given

Answers

Answer:

See the explanation

Step-by-step explanation:

Please see the photo

If i have 36 assignments how many should i do a week to have it all done in 6 weeks
25 points

Answers

Answer: 6

Step-by-step explanation: 36/6 = 6

Answer:

6

Step-by-step explanation:

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

6x6=36

What is origin? Write down the coordinates of origin. ​

Answers

Answer:

(0, 0)

Step-by-step explanation:

Origin is the center of the coordinate plane which is located where the x-axis and y-axis meet

Explain the advantages and disadvantages of a non-linear rate structure.
Please, help!​

Answers

Answer:

advantage: it uses memory very efficiently than linear data structures

disadvantages: Non - linear data structures are quite hard to understand and implement than linear data structures

Planes Q and R are parallel planes. Plane Q contains line a. Plane R contains line b.

Planes Q and R are parallel. Plane Q contains line a and plane R contains line b. Both lines are going the same direction.
If a third plane could be drawn which contains both lines a and b, then

lines a and b must be parallel.
lines a and b cannot be parallel.
lines a and b must be skew.
lines a and b must be perpendicular.

Answers

Answer:

lines a and b must be parallel

Step-by-step explanation:

if lines a and b are parallel in plane r and q, then the lines must always be parallel.

Answer:

A

Step-by-step explanation:

on e2020

Question is in the picture:

Answers

Answer:

its a cause you divide 6 on both sides and 48 divided by 6 is 8 and since its a greater than symbol and the numbers werent negative its gonna be a

Step-by-step explanation:

Answer:

A ) the Value of t is greater than 8

Step-by-step explanation:

6t>48

t>48/6

t>8

A ball is placed in a machine that throws the ball up in the air. The table represents some points on a graph of a function that models the ball’s distance from the ground with respect to the time since the ball was thrown. What is the range for this situation?

Answers

By analyzing the table we conclude that the range is the set R : [0, 7.66] so the correct option is the last one.

What is the range in the situation?

For a relation y = f(x), we define the range as the possible values of y.

In this case, y represents the height that the ball takes, in the table, we can see that it starts at 0, then in reaches a maximum value of 7.66, and then it decreases again until it reaches the zero again when the ball returns to the ground.

Then y can take all the values between 0 and 7.66, meaning that the range is:

R : [0, 7.66]

Then the correct option is the last one.

If you want to learn more about range, you can read:

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Name a value for x that will make the statement true.

x<-4

Answers

Answer:

-5

Step-by-step explanation:

-5 is less than -4, and -4 is greater than -5.

Negative numbers become smaller to the left on the number scale.

There are infinite possible answers to this. :)

Answer:

-5

Step-by-step explanation:

-5 is less than -4 and -4 is bigger than -5

Is (-7, -3) a solution to this system of equations?

x = -7
y = -x - 10

Yes or no

Answers

Answer:   Yes

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

Explanation:

The point (-7,-3) means x = -7 and x = -3

Right off the bat, the first equation x = -7 is proven true based on the first coordinate.

Let's now plug the coordinates into the second equation.

y = -x-10

-3 = -(-7)-10

-3 = 7-10

-3 = -3

Which is a true statement.

Both equations are true when (x,y) = (-7,-3)

This is why it is a solution to the system. It turns out it's the only solution to this system. This system is consistent and independent.

You can use a graphing tool like Desmos to plot the two equations, and you should see them crossing at the point (-7,-3)

Answer:

The answer is yes

*View the attached graph to check your answer graphically.*

Step-by-step explanation:

x = -7

y = -x - 10

For this problem, I will be using substitution, since the second equation is already in the slope-intercept form.

First, I will substitute the first equation, for x, into the first equation:

x = -7

y = -x - 10

y = -(-7) - 10 <== multiplying two negatives, makes a positive

y = 7 - 10

y = - 3 <== the value of y

Now, we find the value of x by substituting - 3 for y:

y = -x - 10

- 3 = -x - 10

+10     +10

7 = -x <== you can't have a negative variable

/-1    /-1

-7 = x <== the value of x

(x, y) ==> (-7, -3)

Therefore, yes (-7,-3) is a solution to this system of equations.

*View the attached graph to check your answer graphically.*

Hope this helps!

Find the first three terms the described arithmetic series:

n=8

an= 36

a1=-6

Sn=120

Answers

Answer should be 1,3,5

i kinda need help! No links No files :)

Answers

Answer:

14 sq. units

Step-by-step explanation:

We know that :

Area (Δ) = 1/2 x Base x Height

Base

Take the difference between the lowest x-value and highest x-value-4 + 8 = 4 units

Height

Take the difference between the lowest y-value and highest y-value9 - 2 = 7 units

Area

1/2 x 4 x 728/214 sq. units

What is the solution to the system
x + 4y = -8
x - 4y = -8

Answers

Answer:

x = -8

y = 0

Step-by-step explanation:

Chloe has a part-time job at an ice skating rink selling hot cocoa. She decided to plot
the number of hot cocoas she sold relative to the day's high temperature and then
draw the line of best fit. What does the line's y-intercept represent?

Answers

Answer: a prediction of the number of hot cocoas sold when the temperature is 0F

Step-by-step explanation: i did it on delta math

The line's y-intercept represent ''Number of hot cocoas sold''.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Chloe has a part-time job at an ice skating rink selling hot cocoa.

She decided to plot the number of hot cocoas she sold relative to the day's high temperature and then draw the line of best fit.

Now,

Since, She decided to plot the number of hot cocoas she sold relative to the day's high temperature and then draw the line of best fit.

Hence, By the graph we have;

The line's x - intercept represent ''Temperature''.

And, The line's y-intercept represent ''Number of hot cocoas sold''.

Thus, The line's y-intercept represent ''Number of hot cocoas sold''.

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what is 43-3y=16 find the unknown?

Answers

Answer:

9

Step-by-step explanation:

We have to move -3y to by itself so we move 43 to the other side, when we do this 43  becomes negitive.

-3y = 16 - 43

-3y = -27

Now we divide -27 by -3

y = -27/-3

y = 9

Answer:-

[tex]\rightarrow\sf{y \:=\: 9}[/tex]

Solution:-

[tex]\rightarrow\sf{43 - 3y\: = \:16}[/tex]

[tex]\rightarrow\sf{-3y\: = \:16-43}[/tex]

[tex]\rightarrow\sf{-3y\: = \:-27}[/tex]

[tex]\rightarrow\sf{3y \:= \:27}[/tex]

[tex]\rightarrow\sf{y\: = \:\frac{27}{3}}[/tex]

[tex]\rightarrow\sf{y \:= \:9}[/tex]

Therefore, value of unknown y = 9.

_________________________________

Hope it helps you:)

What is the slope of the line that passes through the points (−2,−4) and)(3,−9)? Write your answer in simplest form.

Answers

Answer:

The slope is -1

Step-by-step explanation:

Formula for finding slope: [tex]\frac{rise}{run} = \frac{y2 - y1}{x2-x1}[/tex]

we got the points:

(−2,−4) and)(3,−9)

let's plug them in.

[-9-(-4)] / [3-(-2)] =

-5 / 5 = -1

The graph of g is a translation 2 units left of the graph of f(x) = x−−√x. What is the domain of g? A. all real numbers B. x ≥ −2 C. x ≥ 0 D. x ≥ 2

Answers

y=x√x

4 units left means change in x

y=x√x+2

So

Solve for domain

x+2≥0x≥-2

Domain=[-2,oo)

Option A

The domain of g is x ≥ -2, which is option B.

What is Translation?

Translation is a type of transformation of geometrical figures. After translation, the original figure is shifted from a place to another place without affecting it's size.

Given that,

the graph of g is a translation 2 units left of the graph of f(x) = x√x.

When f(x) is translated k units to the left, the new function will be f(x + k).

So the new function g is,

g(x) = (x + 2) √(x + 2)

In order for the function to be defined, the part inside the square root must be greater than or equal to 0.

x + 2 ≥ 0

x ≥ -2

Hence the domain is x ≥ -2.

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