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?
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]
The graph below shows where the two functions y = f(x) and y = g(x) intersect. Solve the equation f(x) = g(x).
The solutions of the equation f(x) = g(x) are (4, 8) and (-2, 2).
We have a graphical representation of two functions f(x) and g(x) and where they intersect.
We have to solve the equation f(x) = g(x)
Two functions A(x) and B(x) are plotted on the graph such that these these two functions intersect each other at three different coordinates. The total number of solutions possible for - A(x) = B(x) is ?The total number of solutions can be calculated by counting the points at which these curves intersect each other. Hence, the total number of possible solutions are 3.
In the question given - We have a straight line and a parabola -
Now, we just have to look at the points at which these two graphs intersect each other. It can be seen that - both the graphs cut each other at coordinates - (4, 8) and (-2, 2).
Hence, the solutions of the equation f(x) = g(x) are (4, 8) and (-2, 2).
Alternative Method -
The general equation of straight line is : y = mx + c and that of parabola is : y = [tex]\sqrt{4ax}[/tex]
The solution can be calculated by equating both of the above expressions and solving them.
mx + c = [tex]\sqrt{4ax}[/tex]
To solve more questions on solving the equations, visit the link below -
https://brainly.com/question/1386163
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Kenny is on the local swim team for the summer and has swim practice
five days per week. The schedule is the same each day. The team swims in
the morning and then again for 3 hours in the evening. If he swims 30
hours per week, how long does he swim each morning. Write and solve
the equation. You must show the equation and solved solution in order to
receive credit. *
Answer:
She swims for 3 hours each morning.
Step-by-step explanation:
To determine the number of hours that Kenny swims in the morning, it is necessary to perform the following equation, taking into account that he swims 5 days a week for a total of 30 hours a week, and that in the afternoon he swims for 3 hours:
X + 3 x 5 = 30
X + 3 = 30/5
X = 6 - 3
X = 3
Therefore, Kenny swims for 3 hours in the morning.
Helpppppppppppppppppp
Answer:
ik that problem gimmie a sec
Step-by-step explanation:
Step-by-step explanation:
since 1 and 2 are same the lines which create 1(g and p) and 2(h and r)
the lines g h and p r shoul be parallel. we also know that g h is parallel which proves that p and r should be parallel as well
Joe has read 20% of a book. He has 16 more pages to finish. How many pages are there in the book?
There are pages in the book.
(Type a whole number.)
Plz answer ASAP
Answer:
20
Step-by-step explanation:
16 is 80% of 20
24/30 in the simplest form
Answer:
The answer to this question is 4/5.
Answer:
4/5 or 0.8
Step-by-step explanation:
we divide tap and bottom by 6.
Helen borrowed money from her aunt to pay for college expenses. The graph below shows the amount left
on the loan as it is paid off over time. Write a linear equation that describes the amount, A, that Helen owes her
aunt to the number of months, n, since she borrowed the money. Show your work that supports your answer
Answer:
[tex]y = -100x + 13000[/tex]
Step-by-step explanation:
See attachment for graph
First, we need to take any corresponding values of x and y
[tex](x_1,y_1) = (0,13000)[/tex]
[tex](x_2,y_2) = (130,0)[/tex]
Next, we calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{0 - 13000}{130 - 0}[/tex]
[tex]m = \frac{- 13000}{130}[/tex]
[tex]m = -100[/tex]
Next, we calculate the line equation using:
[tex]y - y_1=m(x-x_1)[/tex]
[tex]y - 13000 = -100(x - 0)[/tex]
[tex]y - 13000 = -100x[/tex]
Make y the subject
[tex]y = -100x + 13000[/tex]
Hence, the line equation is:
[tex]y = -100x + 13000[/tex]
help as fast as you can!!!!!! Any living thing is called an organism,no matter if it is one-celled or many-celled. True or False?.
Answer:
true
Step-by-step explanation:
Answer:
TRUE.
Step-by-step explanation:
You have $40 to start a savings account. You plan to put $10 in the account each month.
Write an equation that represents the relationship in the story.
What is the quotient in simplest form? 4/5 ÷ 8 a. 1/10 b. 1/2 c.8 d. 20
Answer:
1/10
Step-by-step explanation:
Answer:
4/5 divided by 8 is 4/40 and 1/10 if simplified.
Step-by-step explanation:
could you please help with this equation:
Simplify the algebraic expression: 4(3x + y) – 2(x – 5y)
Answer: 10x + 14y
Step-by-step explanation: just simplify it
Answer:
10x+14y
Step-by-step explanation:
A business person is desperate to better organize their business. They hire you to act as an efficiency expert. As you review their situation, you notice they file all of their receipts and documents into one overflowing folder. Their workspace is very messy with many piles of papers and useless knick-knacks. They mention difficulty finding important documents and have forgotten important dates and events due to their clutter. Write a formal letter to your client offering tips on ways to make their business more organized and efficient. Make sure your letter has specific examples which can improve the business' organization.
Answer:
Simply have neat and organized ways to save files. You can do this with file cabinets or by having digital copies of all the files to get rid of the clutter. I would recommend the second option.
Step-by-step explanation:
I got it right
The formal letter to the client offering tips on ways to make his business more organized and efficient is;
51, broad street,
Times Square Church,
New York City.
2/12/2021
The General Manager,
Clad financial services Ltd,
Brooklyn, New York city.
Dear Mr. Bill Wilkinson,
Letter of advice on more organized and efficient business.
I am writing with respect to the need to have a more organized and efficient office. Since resumption into this role as an efficiency expert, I have noticed that specific files and documents are very difficult to locate due to unorganization and untidiness.
With respect to the issue of unorganization and untidiness, I have some neat and organized ideas that can be used to save files. This can be can done by making use of file cabinets and also by creating and saving digital copies of all the files in order to get rid of some of the files and documents occupying a lot of space in the office.
Secondly, I will also like to add that unwanted papers or files should be thrown away and the files on the shelf should be properly labeled for easy identification.
Regards.
Frank Johnson,
Efficiency Expert.
Read more at; https://brainly.com/question/9510603
A baker has three banana muffin recipes. Recipe AAA uses 333 bananas to make 121212 muffins. Recipe BBB uses 555 bananas to make 242424 muffins. Recipe CCC uses 111111 bananas to make 484848 muffins.
Order the recipes by number of bananas per muffin from least to greatest.
Answer: Recipe Buses 5 bananas to make 24 muffins. Recipe C uses 11 bananas to make 48 muffins.
Step-by-step explanation:
what is 10:40 plus 7:15 in time?
Answer:
5:55
Step-by-step explanation:
just add it up and you'll get the answer which is 5:55
Answer:5:55
Step-by-step explanation: lol
McDonalds sold 7 boxes of chicken nuggets for $25.90 Burger King sold 3 boxes of chicken fingers for $11.07. Which food item has a higher unit price? (1 Point McDonalds O Burger King.
Answer:
burger king
Step-by-step explanation:
math
It was cloudy 12 out of 30 days in April. Which value is equivalent to the fraction of
days it was cloudy in April?
Answer:
any of the below:
Step-by-step explanation:
12/30
6/15
2/5
Answer:
2/5, or 40%.
Step-by-step explanation:
Write it as a fraction first, then reduce it to simplest form.
12/30
Simplest form is 2/5, or 40%
solve for x.
x/6 =2
A.x=3
B.x=-12
C.x=12
Answer:
C. x=12
Step-by-step explanation:
y-2=1/4(x-3)
how can i graph this?
Answer:
your anwer is x=4y-5
Step-by-step explanation:
40 POINTS Geometry homework
[tex]\angle{DBC }[/tex]=(5x+4)°
[tex]\angle{ A }[/tex]=(2x-2)°
[tex]\angle{C }[/tex]=(4x-6)°
we know that,
[tex]\angle{DBC}[/tex]=[tex]\angle{A}[/tex]+[tex]\angle{C}[/tex]
According to the question,
[tex]\tt{ 5x+4=2x-2+4x-6 }[/tex]
[tex]\tt{ 5x+4=6x-8 }[/tex]
[tex]\tt{ 6x-5x=4+8 }[/tex]
[tex]\blue{x=12 }[/tex]
so,
[tex]\angle{C }[/tex]=(4x-6)°=(4×12-6)°=(48-6)°=42°
A test of a new car results in 300 miles on 10 gallons of gas. How far could you drive on 45 gallons of gas?
Question 5 options:
1350 miles
67 miles
670 miles
135,000 miles
Answer:
1350
Step-by-step explanation:
300x4=1200
300×.5=150
1200+150=1350
1. What is the place value of the 5 in the number 1,589,302? *
hundreds
O hundred thousands
millions
Answer:
Hundred thousand
Step-by-step explanation:
500,000
Mental Math A typical tip in a restaurant is 15% of the total bill. If the bill is $60, what would the
typical tip be?
The typical tip would be $1.
Answer:
It would be $9.
Because 60 * 0.15 = 9
Step-by-step explanation:
plssss it’s due in 5 min answer plsss
PLEASE HELP MEH ON THIS ASAP!!!!
Answer:
b
Step-by-step explanation:
Answer:
option B
Step-by-step explanation:
a is located in the left side of 0 . HENCE IT IS A NEGATIVE NUMBER . b & c are on the right side of 0. HENCE BOTH ARE POSITIVE NUMBER
In option B , it's given that -a > -c . If we'll verify this statement , we'll find that when we put the negative sign in a , the all totla value of a becomes positive BECAUSE 'a' WAS A NEGATIVE NUMBER.
Now if we put a negative sign in c , the all total value becomes negative BECAUSE 'c' WAS A POSITIVE NUMBER.
By comparing -a & -c , we'll get to know that :-
-a > -c
Which of the fractions is equivalent to 2/5 ?
5/2
4/25
12/15
4/10
Answer:
4/10
Step-by-step explanation:
4/10 simplifies to 2/5
4/2 = 2
10/2 = 5
Sunny made 2 pitchers of strawberry smoothies for the science club. If each person got One-fifth of a pitcher, how many science club members are there?
2 area models. Both models are made up of 5 shaded parts.
Which statements are true?Check all that apply.
The correct division problem is One-fifth divided by 2.
The correct division problem is 2 divided by one-fifth.
The quotient isStartFraction 1 Over 10 EndFraction.
The quotient is 10.
There are 10 members in the science club.
There are StartFraction 1 Over 10 EndFraction members in the science club.
Answer:
tell me what grade u are in and I will try my best to help
Answer:WAIT I HAVE IT
Step-by-step explanation:
for algebra 2 please help <3
Answer:
A. 1
Step-by-step explanation:
✔️To find f(g(1)), first find g(1).
From the mapping given for g(x), the corresponding value of x = 1, is 0.
That is,
g(1) = 0
✔️Next is to find f(g(1)) by replacing x with 0 in f(x) = 3√x + 1
Thus:
f(g(1)) = 3√0 + 1
f(g(1)) = 0 + 1
f(g(1)) = 1
Help me pleaseeeeeeeeeeee
Answer:
they first answer or a
Step-by-step explanation:
because if you look at stage direction he is just facing the crowd
Answer:
The stage direction shows how King Frederick looks when he speaks.
Step-by-step explanation:
write the fraction of 7/14in it's simple form
Answer:
1/2
Step-by-step explanation:
Divide both parts by 7
1/2
Hope this helps :)
Need help :) plss will mark brainliest
Answer:
C
Step-by-step explanation: