3. Solve the following application of a system of linear equations.
Two students in the same Spanish class, Cindy and Ruben, plan to get together after school to make
vocabulary flashcards. Cindy started on the project yesterday and has already made 14 flashcards.
Ruben hasn't started yet so he has none. Since Cindy makes 9 flashcards per minute and Ruben makes
10 flashcards, Ruben will soon have the same number of flashcards.
Which variables will you use and what do they represent?
Write your system of linear equations below.
Solve the system.
How much time will it take for Cindy and Ruben to have the same number of flashcards?
How many flashcards will each student have at that time?

Answers

Answer 1

Answer:

Equations:

[tex]y = 14 + 9 x[/tex] --- Cindy

[tex]y = 10 x[/tex] --- Ruben

Solution to equation:

Time they have the same amount: 14 minutes

Number of cards they have at that time: 140 flashcards

Step-by-step explanation:

Solving (a): Variables and what they represent

The variables to use are x and y

Where x represent the minutes and y represents the number of flashcards in x minutes

Solving (b): System of linear equation

Cindy:

[tex]Existing\ Flashcards = 14[/tex]

[tex]Additional = 9[/tex] per minute

Total number of flashcards (y) in x minutes is:

[tex]y = Existing\ Flashcards + Additional * x[/tex]

[tex]y = 14 + 9 * x[/tex]

[tex]y = 14 + 9 x[/tex]

Ruben:

[tex]Rate = 10[/tex] per minute

Total number of flashcards (y) in x minutes is:

[tex]y = Rate * x[/tex]

[tex]y = 10 * x[/tex]

[tex]y = 10 x[/tex]

Solution to Equations:

Time they have the same amount.

To do this, we [tex]equate[/tex] [tex]both[/tex] expressions

i.e.

[tex]10x = 14 + 9x[/tex]

Collect Like Terms

[tex]10x - 9x = 14[/tex]

[tex]x = 14[/tex]

Number of cards they have at that time.

Here, we simply substitute 14 for x in any of the equations.

[tex]y = 10 x[/tex]

[tex]y = 10 * 14[/tex]

[tex]y = 140[/tex]

or

[tex]y = 14 + 9 x[/tex]

[tex]y = 14 + 9 * 14[/tex]

[tex]y = 14 + 126[/tex]

[tex]y = 140[/tex]


Related Questions

True or False
1. We find the x-intercepts of a function fby evaluating f(0).

2. The solutions of a function are the first coordinates of the
x-intercepts of the function.

3. We can use completing the square to solve any quadratic equation.

4. The function f(x)=-3(x+4)2-5 has a maximum value.

Answers

1. True
2. True
3. True
4. True

Which expression can be used to find The amount of money for camp leader spends on b books

Answers

Answer:

Part A: A. 7.50 x b

Part B: $90

Step-by-step explanation:

Part A: The cost of a book is $7.50, so the equation that is going to tell you the total cost of however many books purchased is equation A.

Part B: $90. If the cost of a book is $7.50 and the teacher purchases 12 books, you do $7.50 x 12= $90. You can check the equation by adding $7.50 12 times. You will get the same result.




A TV store buys TV's for $250 each, and then increases the price by 120%. What is the sales price of a TV at this store?

Answers

Answer:

$300

Step-by-step explanation:

Answer:

$300

Step-by-step explanation:

250 100

 ?    120

(250x120)/100

Check whether (x – 1) (x +2) = x + 3 is a quadratic equation or not.​

Answers

Answer:

no, it is not

Step-by-step explanation:

STEP 1: Simplify (x−1)(x+2).

[tex]x^2+x-2=x+3[/tex]

STEP 2: Move all terms containing x to the left side of the equation.

[tex]x^2-2=3[/tex]

STEP 3: Move all terms not containing x to the right side of the equation.

[tex]x^2=5[/tex]

STEP 4: Take the square root of both sides of the equation to eliminate the exponent on the left side.

[tex]x=[/tex]±[tex]\sqrt{5}[/tex]

STEP 5: The complete solution is the result of both the positive and negative portions of the solution.

[tex]x=\sqrt{5} ,-\sqrt{5}[/tex]

choose all the polygons

Answers

Answer:

A, B, E, F

Step-by-step explanation:

A polygon is ANY shape formed with only straight lines.

The coordinates of the point P are (−6,−2) and the coordinates of point Q are (−6,9). What is the distance, in units, between the point P and point Q?

Answer____________Units.

Answers

Answer:

The distance in units would be -8, -3.

Step-by-step explanation:

pls help me on this iready question I beg u

Answers

Answer:

We conclude that for 1/2 batch, Faird would require 3/8 cups of sugar.

Step-by-step explanation:

Suger needed for a full batch = 3/4Given that Farid is making 1/2 of batch

We need to determine the expression for the amount of sugar Freed needs to make 1/2 batch.

Let 'x' be the batch and 'y' be the amount of sugar

Suger needed for a full batch = 3/4 cup of a sugar

so

x = 3/4y

But, Farid is making 1/2 of the batch.

Thus, multiply both sides by 1/2

[tex]x\times \frac{1}{2}\:=\:\frac{3}{4}y\times \frac{1}{2}[/tex]

[tex]\frac{x}{2}=\frac{3y}{8}[/tex]

Therefore, we conclude that for 1/2 batch, Faird would require 3/8 cups of sugar.

what is the maximum value of the function? explain what the maximum value of this represents in this situation. make sure to include information about the x-value and y-value in your explanation

Answers

Where’s the picture I need it I order to answer

wowwwww he just roasted youuuuuuuuuu!!!!!

What is the 15th term of the sequence an =
-3n+50
D. 95

Answers

Answer:

= 105

Step-by-step explanation:

Answer:

here ya go

Step-by-step explanation:

a

9

=

105 I think

plz help i have a branliest

Answers

Answer:

Use a calculator lol

Step-by-step explanation:

Answer:

Step-by-step explanation:

s= 2, 2 and 11

I= 2, 5 and 3

u=2, 7 and 5

t= 2, 2, 3 and 3

b= 2, 2, 5 and 5

n= 2, 2, 19

p= 2, 3, 3 and 5

o= 2, 2 and 17

r= 3, 3 and 11

m= 2, 3, 3 and 7

d= 2, 3 and 7

e= 2, 2, 3 and 11

PLEASE EXPLAIN STEPS

Answers

Answer:

C. m<C = m<F

Step-by-step explanation:

this is because in their triangle names, they are in the same spot (third letter of the name)

if they are in the same spot, they have to be congruent

same goes for the other letters, <A has to be congruent to <D and <B has to be congruent to <E

What is the exact distance from (-5,1) to (3,0).

Answers

Answer:

The distance between the two points is [tex]\sqrt{65} \ \text{units}.[/tex]

Step-by-step explanation:

In order to find the distance between two coordinate pairs, we can use the distance formula:

[tex]\displaystyle \bullet \ \ \ d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Our coordinate pairs need to be labeled accordingly, so we can use this naming system:

[tex]\bullet \ \ \ (x_1, y_1), (x_2, y_2)[/tex]

This assigns a name to our points:

[tex]x_1 = -5[/tex][tex]y_1 = 1[/tex][tex]x_2 = 3[/tex][tex]y_2 = 0[/tex]

Therefore, we can plug these into the formula and solve:

[tex]d=\sqrt{(3-(-5))^2+(0-1)^2}\\\\d=\sqrt{(8)^2+(-1)^2}\\\\d=\sqrt{8^2+1^2}\\\\d=\sqrt{64+1}\\\\d=\sqrt{65}[/tex]

Therefore, the distance between the two points is [tex]\sqrt{65} \ \text{units}[/tex].

I REALLY NEED HELp!!!!!!!!

Answers

                                Retail Price      Quantity     Total Price

Twister Pen                   .35          *        2        =     $0.70

Mini Fish Eraser            .50          *        1         =     $0.50

Happy Cap Eraser        .05          *        5        =     $0.25

Erasing Grip                  .35          *        3        =     $1.05

                                                                               ---------

Subtotal                         .7 + .5 + .25 + 1.05    =     $2.50

Sales Tax Amount (unknown because we aren't given a tax value)

Total (also unknown for the same reason)

                                             Retail Price      Quantity     Total Price

Twister Eraser                            .35          *        3        =      $1.05

Astral Wonders Pencils             .20          *        4        =      $0.80

Criss Cross Critters                    .15           *       2        =      $0.30

Traction Mechanical                      

Pencil                                         .35           *       2        =      $0.70

Muchin Mike Sharpener           .50           *       2        =      $1.00

                                                                                            ----------

Subtotal                                 1.05 + .8 + .3 + 0.7 + 1    =     $3.85

Sales Tax Amount (unknown because we aren't given a tax value)

Total (also unknown for the same reason)

Best of Luck!

Find the measures of the exterior angles.

Answers

Answer:

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. (Non-adjacent interior angles may also be referred to as remote interior angles.) FACTS: An exterior ∠ is equal to the addition of the two Δ angles not right next to it.

WA store manager records the number of people who have been in his store compared to the number of hours the store has been open. He graphs the data on the scatterplot below and sketches a trend line.

Store Customers

A graph has hours open on the x-axis, and total customers on the y-axis. A trend line goes through points (1, 25) and (2, 50).

Based on the data collected, if the store has been open 7 hours, which scenario is most likely to be true?
After 1/2 hour, 1 customer had been in the store.
After 6 hours, 129 customers had been in the store.
After 7 hours, 175 customers had been in the store.
After 8.5 hours, 225 customers had been in the store.

Answers

Answer: After 7 hours, 175 customers had been in the store.

Step-by-step explanation:

Did the quiz, Trust me.

Answer:

ccccccccc!

Step-by-step explanation:

8. If a runner’s power is 400 W as she runs, how much chemical energy does she convert into other forms in 10.0 minutes? E = P X t

Answers

Answer:

2400kJ

Step-by-step explanation:

Step one:

given data

power P= 400W

time = 10minutes

to seconds= 60*10 = 600 seconds

Required

the energy

Step two:

we know that Energy= power * time

E=P*t

E=400*600

E=240000

E=2400kJ

She converts 2400kJ into other forms

Steve's bedroom measures 12 feet by 13 feet. Ricardo's bedroom measures 8 feet by 14
feet. Assuming that both bedrooms are rectangular, whose room has the greater area?

Answers

Answer: Steve's bedroom has the greater area.

Step-by-step explanation: The formula for area is Area = Length x Width.

So all you have to do to figure this out is multiply the Width of the rooms by the length.

So Steve's room is 12ft X 13ft = 156ft

Ricardo's room is 8ft X 14ft = 112ft

156ft > 112ft

Steve's room has a greater area.

f(x)=x^2+2x-1
find f(-3)​

Answers

Answer:

2

Step-by-step explanation:

Which two expressions are equivalent?
(F was wrong) H 7(x − 3) and 7x − 7 • 3
g 7(x − 3) and 7x − 4 j 7(x − 3) and 7x + 7 • 3

Answers

Answer:

The correct answer is:

Option H: 7(x − 3) and 7x − 7 • 3

Step-by-step explanation:

Equivalent expressions are those expressions that simplify to the same expression i.e. the result of both expressions is the same. There is no change of sign or variable or any quantity.

Option H:

The two expressions are:

7(x − 3) and 7x − 7 • 3

[tex]7(x-3) = 7x - 21\\7x - 7.3 = 7x-21[/tex]

It can clearly be seen that both the expressions result in same expression

Hence,

The correct answer is:

Option H: 7(x − 3) and 7x − 7 • 3

I need help with this question pleaseeee

Answers

Answer: 639

Step-by-step explanation:

i might be wrong but that's how i was taught! :)

Raise the product of 36 and 9 to the power of the sum of 2 and 4.
Which of the following expressions matches the sentence above?
A.
(36 = 9(2+4)
B.
(36 x
9)(2+4)
O c.
(36 x 9)(2x4)
D.
(36 = 9)2 + 4

Answers

Answer:

B

Step-by-step explanation:

36 x 9 = 324

4+2=6

324^6

=324*324*324*324*324*324

=1156831381426176

What is the value of the expression below?
2 [32 - (4-1) to the power of 3]
Enter your answer in the box.

Answers

Answer:

the answer is 10

Step-by-step explanation:

find the slope of the line please help!

Answers

Answer:

the slope is 2/3

Answer:

Step-by-step explanation: First you determine if the slope if positive (increasing) or negative (decreasing). Second you use two points on the line, calculate the rise and the run and express it as a fraction (rise over run).  Rise is the change in the y-value and Run is the change in the x-value.

What number is equivalent to 15 and 25

Answers

Answer:

yo are you talking about like absolute value?  then it's  | -15 | and | -25 |

Step-by-step explanation:

HEY THS IS WORTH 69 POINTS

The vertices of a rectangle are A(2, 0), B(5, 0), C(5, −2), and D(2, −2). Reflect the rectangle in the y-axis, and then rotate


the rectangle 180° about the origin. What are the coordinates of the image?

Answers

Answer:

A′(-2, 0), B′(-5, 0), C′(-5, 2), and D′(-2, 2)

Step-by-step explanation:

I did FLVS (Online School stuffs)

Answer:

A

Step-by-step explanation:

simplify the fraction 15/20

Answers

15/20

Figure out what number to use for simplify

Which is 5

Divide the numerator and denominator by 5

15/5=3

20/5=4

Answer:3/4

What is 20/19?? absolute value​

Answers

Answer:

1.05263

Step-by-step explanation:

hope it helps !

The price of milk increased from $2 to $2.50. What is the percent of change for the price of milk?

Answers

25.00%

Or

25c

Have a Merry Christmas!


Is there a proportional relationship between x and y? Explain.
8 10 12 14
х
y
5
9
11
A.
Mo
at 2

No; all ratios
are not equivalent.
B.

Yes; each x value and y value increases by 2.
C.
Yes; the difference between each x value and y value is 3.
D

202
No; all ratios
are greater than 1.

Answers

Answer:

The answer is B. Hope it helps :)

need help with this problem it’s math so if you know math come on in

Answers

Answer:

The line is super close to 15 or 20. So one of those for sure

Step-by-step explanation:

Answer: its got to be 15 because the line isn't on 20

Step-by-step explanation:

Other Questions
can sum1, please write an apology letter for throwing a chicken nugget at someone 50 words and ill give u 30pts The club sold shirts and capes to raise money for new stage equipment. The club sold each shirt for $20.00. The club made profit of $4.00 for each shirt. Sold. Part A: The drama club sold a total of $480.00 worth of shirts. How much profit did the club make from the shirt sale? Which function is equivalent to g (k) = -k'+ 6k-9?a g(k) = -(k- 3)g(k) = (-k+ 3)(k+ 3) g(k) =-(k+3)Og(k) = (-k- 3)(k+ 3) Five less than 3 times a number is 25. What is the number? Carbonic acid is a mixture of please help me out Need help ): Due tonightHow did the American government react to all the decolonization movements taking place worldwide? The changing relationship between England and the catholic church Type the correct answer in the box. Spell all words correctly.A freelance graphic designer has received an assignment to design a company logo. What image format is most suitable to display this logo on the company website?The _________ format is most suitable in order to display the logo on the company website. Argue the benefit of chemistry to the field of forensic science, using a specific example. Xander takes a quiz worth 150 points. Each question is worth 30 points. Sketch a graph to show his score if he misses 1,2,3,4 or 5 questions. Who is a sessions judge Explain how organ systems work together to keep organisms alive be sure to include an example Identify the following structure as an atom, molecule, or compound molecule.HydrogenA.atoms B. molecules C.compound molecules Can I actually get help and not people saying random stuff just for points???? What did normal mean in the hive in the b movie write the equation of a parellel to the given line that goes through the given point y=8x+3 (2,4) CAN SOMEONE HELP- I'LL GIVE BRAINLIEST! I need all the questions pls. Cheerios $3.89 for 17 oz. $ [ Select ] per ounce VS. Option 2: Apple Jacks $2.89 for 13 oz. $ [ Select ] per ounce Which is the better deal? 11. Chemist Ernest Rutherford performed the gold foil experiment in which he concluded theatom is mostly empty space, with a small, dense, positively charged center. Rutherford'sdiscovery of the proton did not fully account for the entire mass of the atom. Which is anexample of research that extended Rutherford's findings?a. De Broglie viewed electrons exhibiting wave-like behavior.b. Bohr concluded that electrons orbit the nucleus in set circular paths.c. Chadwick determined the charge of the neutron to be neutral and its mass similar tothat of a proton.d. Thomson determined that the atom consists of negatively-charged particles.