Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Chase and his little brother made up a game using coins. They flip the coins towards a cup and receive points for every one that makes it in. Chase starts with 19 points, and his little brother starts with 27 points. Chase gets 3 points for every successful shot, and his brother, since he is younger, gets 1 point for each successful shot. Eventually, the brothers will have a tied score in the game. How many points will they both have? How many additional shots will each brother have made? Chase and his brother will both have a score of by making shots.

Answers

Answer 1

Answer:

Chase and his brother will both have a score of 31 points by making 4 successful shots.

Step-by-step explanation:

Given that initially Chase has 19 points and his brother has 27 points.

In one successful flip, Chase get 3 points and in one successful flip, his little brother get 3 points

Assuming that both have the same score after n number successful flip of the coin.

So, points earned by Chase in n successful flip [tex]= 3\times n =3n[/tex]

and points earned by his little brother in n successful flip [tex]= 1\times n=n[/tex].

Total points of Chase [tex]= 19+3n\cdots(i)[/tex]

Total points of his little brother [tex]= 27 + n\cdots(ii)[/tex]

As the brothers have tied scores in the game, that means both have the same score, so from equations (i) and (ii), we have

[tex]19+3n = 27 + n \\\\\Rightarrow 3n-n = 27-19 \\\\\Rightarrow 2n=8 \\\\\Rightarrow n=8/2=4[/tex]

So, after n successful throw, both have the same score.

Hence, each brother made 4 additional successful shots.

Now, put n=4 inequation (i) or (ii) to get the total points, i.e

Total points of each brother [tex]= 19+ 3\times 4 = 31.[/tex]

Hence, each brother has 31 points.


Related Questions

Solve using the box method!

5.3 x 3.5 =

Answers

18.55 is the answer

original price of a pen:$1.50
tax:4%​

Answers

Answer:

$1.56

Step-by-step explanation:

1.50 times 0.04 is 0.06

1.50+0.06

$1.56

Answer:

ANswer is $2.10.

Step-by-step explanation:

The tax is $.60 and you add that to $1.50.

which of these numbers are irrational? A) 4.3 B) -5/9 C) 1.618 D) _/6

Answers

Answer: Its C

Step-by-step explanation:

Well, this irrational, or never-ending, ratio starting with 1.618 has been given many names over the years including the “golden ratio” and the “divine proportion”.

0verall what im trying to say is, its c

Fatima has a car detailing service. She charges $15.00 for a vacuum,
$40.00 for exterior wash and wax, and $60.00 for complete interior clean
including shampooing all upholstery. last week she had a busy week. She
had 7 vacuum jobs, 23 exterior wash and wax jobs, and 15 complete
interior cleans jobs. How much did she make all together for vacuuming
jobs?
A.15
B. 105
C. 50
D. 85​

Answers

Answer:

1

Step-by-step explanation:

Answer is B

B. 105

Hope this helps

Jenna works in an ice cream shop. When she starts her shift the tub of chocolate ice cream is 2/3 full. When she finishes her shift 6 1/2 h later,

there is only 1/6 of the tub left. What was the average hourly change in tub fullness?

13

1

13

5

39

5

39

Answers

Answer:

1/13

Step-by-step explanation:

Ice cream

starting = 2/3 full

After Jenna's shift = 1/6 of the tub

Total Time = 6.5hours

Amount of ice cream consumed = [tex]\frac{2}{3} - \frac{1}{6}[/tex]

                                                  = [tex]\frac{1}{2}[/tex] = 0.5

Rate per hour = amount of ice cream consumed -=/ total time

                      = 0.5/6.5 = 1/13  ice cream consumed per hour

Which equation represents the relationship between the x- values and the y- values in the table?

Answers

Answer:

It would be J

Step-by-step explanation:

Help me look at the picture

Answers

Answer:

it's B

Step-by-step explanation:

lol how do you not know this

Answer:

B

Step-by-step explanation:

Why might you solve this system of equations by adding or subtracting? Explain fully.

2x + 3y = 4
2x - 3y = 8

Answers

The answer is x=3 and y= -2/3
You can either add the equation to find x first or subtract to find y first
Either way it will work

solve the equation:
p-19/6= -15/6

The slash is the fraction bar jsyn :)) pls help

Answers

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

[tex]p - \frac{19}{6} = - \frac{15}{6} \\ [/tex]

Add sides 19 / 6

[tex]p - \frac{19}{6} + \frac{19}{6} = - \frac{15}{6} + \frac{19}{6} \\ [/tex]

[tex]p = \frac{19 - 15}{6} \\ [/tex]

[tex]p = \frac{4}{6} \\ [/tex]

[tex]p = \frac{2 \times 2}{2 \times 3} \\ [/tex]

[tex]p = \frac{2}{3} \\ [/tex]

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

The answer will be

P= 2/3

Here are the steps if you need them : multiply the numbers after divide them after add 19/6 to both sides of the equation after simplify the numbers and after you get your answers :) have a nice day!

Angela is riding a scooter around her neighborhood. The front wheel has a diameter of 10 inches and the back wheel has a diameter of 5 inches. The scooter is moving at a speed of 10 inches per second.

As she is riding her scooter, a spider hops onto the front wheel. Angela looks down and thinks that if the praying mantis has a good grip that he will go all the way around the wheel in just 1 second. Is Angela right or wrong? Why?

If she is wrong find the amount of time it will take to go all the way around

Answers

Answer:

i. Angela is wrong. Because the diameter of the wheel is not the distance covered all the way round.

ii. The time is 3.14 seconds.

Step-by-step explanation:

The font wheel has a diameter of 10 inches. Thus;

radius = [tex]\frac{diameter}{2}[/tex]

           = [tex]\frac{10}{2}[/tex]

           = 5 inches

Circumference of a circle = 2[tex]\pi[/tex]r

⇒ The circumference of the front wheel = 2[tex]\pi[/tex]r

                          = 2 x [tex]\frac{22}{7}[/tex] x 5

                          = 31.4286

The circumference of the front wheel is 31.43 inches.

The total distance to be covered by the mantis = circumference of the front wheel

                                        = 31.43 inches

But,

speed = [tex]\frac{distance}{time}[/tex]

The scooter moves with a speed of 10 inches per second, so that;

10 = [tex]\frac{31.43}{time}[/tex]

⇒ time = [tex]\frac{31.43}{10}[/tex]

            = 3.143 s

The time taken to complete a revolution by the mantis is 3.14 seconds.

Therefore,

i. Angela is wrong. Because the diameter of the wheel is not the distance covered all the way round.

ii. The time is 3.14 seconds.

©
Simplify
2 X X X Y

Answers

Answer:

The question is not clear

if anyone could please help me solve this i’d really appreciate it

Answers

Answer:

D. 26

Step-by-step explanation:

evaluate the fraction first

6+9

---

7-2

15

----

5

3

10 times 3 - 2 to the power of 2 which is 4

30-4 is 26

Hi. I need help with these questions.
See image for question.

Answers

Answer:

(a) P(1) = 3

(b) P(-2) = 15

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Function Notation

Step-by-step explanation:

Step 1: Define

P(x) = x³ + 4x² - 3x + 1

P(1) is x = 1

P(-2) is x = -2

Step 2: Evaluate

P(1)

Substitute:                    P(1) = 1³ + 4(1)² - 3(1) + 1Exponents:                   P(1) = 1 + 4(1) - 3(1) + 1Multiply:                        P(1) = 1 + 4 - 3 + 1Add:                              P(1) = 5 - 3 + 1Subtract:                       P(1) = 2 + 1Add:                              P(1) = 3

P(-2)

Substitute:                    P(-2) = (-2)³ + 4(-2)² - 3(-2) + 1Exponents:                   P(-2) = -8 + 4(4) - 3(-2) + 1Multiply:                        P(-2) = -8 + 16 + 6 + 1Add:                              P(-2) = 8 + 6 + 1Add:                              P(-2) = 14 + 1Add:                              P(-2) = 15

Answer:

a) 3b) 15

Step-by-step explanation:

GivenP(x) = x³ + 4x² - 3x + 1Finda) P( 1 ), b) P( - 2)Solution

Substitute the value of x:

a) P(x) = x³ + 4x² - 3x + 1

P(1) = 1³ + 4(1)² - 3(1) + 1 = 1 + 4 - 3 + 1 = 3P(1) = 3

b) P(x) = x³ + 4x² - 3x + 1

P(-2) = (-2)³ + 4(-2)² - 3(-2) + 1 = -8 + 16 + 6 + 1 = 15P(-2) = 15

What is the solution to this equation? x/-5=15​

Answers

Answer:

x=75

Step-by-step explanation:

Answer:

x=-75

Step-by-step explanation:

Hope this helps.

please help:( i’m not sure....

Answers

Answer:

B. 2 ÷ 11

I hope this helps!

1. What is the solution of the system of equations shown below?
y = 3x + 7
y = x-9

Answers

Answer:

x= -8

y= -17

Step-by-step explanation:

Answer:

If you trying to find x and y is the answer is:

x=-8 and y=-17

or

(-8,-17)

Step-by-step explanation:

First you need to subtract the two equations which becomes 2x+16=0

Now you move the 16 to the other side by subtracting 16 on both sides:

2x=-16

Now divide 2 on both sides to eliminate the 2 on 2x

x=-8

Now that you got -8 as x you can replace x on the two equations any one of them you only need to get one but I am going to use both of them to show you that it is the same:

y= 3(-8)+7

y=-17

y=-8-9

y=-17

Hope this helps!

Hanna is plotting a point in coordinate space. She starts at the origin and moves backward eight units along the x-axis. Then she moves right one unit parallel to the y-axis. Finally, she moves down five units parallel to the z-axis and plots the point. What are the coordinates of the point that she plots?

Answers

Answer:

( -8,0, 0) , ( -8, 1, 0) and  ( -8, 1, -5)

Step-by-step explanation:

We need to visualize the given situation in 3D

Coordinates is in the form of (x, y, z)

Henna starts from origin moves back 8 units Negative x-axis

x = -8   point will be ( -8,0, 0)

turning 1 unit right will be parallel to the y axis in positive y-axis direction

y = 1 point will be ( -8, 1, 0)

Moving down by 5 units, Negative z-axis

Z = -5 point will be ( -8, 1, -5)

Answer:

(-8,1,-5)

Step-by-step explanation:

Dont make it complicated, a whole paragraph for one answer is not needed

what are the solutions to the quadratic equation 6x^2 + 24X = 0?

Answers

Answer: {0, -4}

Step-by-step explanation: Notice that the two terms on the left side

of the equation have a greatest common factor of 6x.

So start by factoring out a 6x to get 6x(x + 4) = 0.

So either 6x = 0 or x + 4 = 0.

Eventually we find that x = 0 or x = -4.

So our solution set is {0, -4}.

factor the expression 6x+18y-54 . Use the GCF to help you factor the expressions

Answers

Answer:

6(x+3y-9)

Step-by-step explanation:

GCF is 6

Answer:

Step-by-step explanation:

6x+18y-54=

6 is the GCF

6(x+3y-9)

Lincoin Glass as a Christmas party for is employees each year. The
cost of food for the party comes to $24.95 a person. How much does
toositor 2175 employees?

Answers

Answer:

54266.25

Step-by-step explanation:

Factor 20w + 70.
i need help!

Answers

Answer:

10(2w+7)

Step-by-step explanation:

hiii, if you do questions 7 and 8, ill mark brainly :) <3

Answers

Answer:

7) nth term a₁₈ is 160

8) nth term a₃₆ is 128

Step-by-step explanation:

7) Find nth term of each arithmetic sequence

[tex]a_1=7, d=9, n=18[/tex]

The formula used to find nth term is: [tex]a_n=a_1+(n-1)d[/tex]

Putting values and finding nth term n=18

[tex]a_n=a_1+(n-1)d\\a_{18}=7+(18-1)9\\a_{18}=7+(17)9\\a_{18}=7+153\\a_{18}=160[/tex]

So, nth term n₁₈ is 160

8) Find nth term of each arithmetic sequence

[tex]a_1=-12, d=4, n=36[/tex]

The formula used to find nth term is: [tex]a_n=a_1+(n-1)d[/tex]

Putting values and finding nth term n=36

[tex]a_n=a_1+(n-1)d\\a_{36}=-12+(36-1)4\\a_{36}=-12+(35)4\\a_{36}=-12+140\\a_{36}=128[/tex]

So, nth term n₃₆ is 128

The cafeteria at Local Middle School offers a choice of either a sandwich or soup every Thursday.
Of 55 students who purchased lunch this Thursday, 30 chose a sandwich.
What is the ratio of the number of students who chose a sandwich to all those who purchased lunch this Thursday?

Answers

Step-by-step explanation:

55-30 = 25

25 out of 55 chose the soup.

Hope that helps

Answer:

30:55

Step-by-step explanation:

30 out of the 55 students that bought lunch, bought sandwiches. So, 30 sandwiches to 55 students. It's a trick question that gives you all the information in the question itself, so it's fairly simple. I hope I'm right tho lol

What is the x-intercept of the equation 4x = 9y + 5
Write your answer in fraction form.

Answers

The correct x intercept is (5/4,0) :)

solve this fast
3.5(2.25 + x) = 14

Answers

Answer:

Step-by-step explanation:

3.5(2.25+x)=14

x=1.75

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

x = 1.75

x to the tenth power divided by x to the seventh power

Answers

Answer:

[tex]x^3[/tex]

Step-by-step explanation:

Division for exponents with the same base is just subtracting the exponents.

10 - 7 = 3

You'll get x to the third power because 10 minus 7 is 3.

How would you write 8 TIMES A NUMBER as an algebraic expression ?

Answers

Answer:

8x

Step-by-step explanation:

8= the times multiply and "x" being the # being multiply

Answer:

8x - y

Step-by-step explanation:

8 times a number (x) is 8 times x = 8x

decreasing by y means take away y...  but u should know that right?

lol hope this helps :)

brainliest?

Which of the following correctly demonstrates a verb tense shift? a. Kurtis is moving to a new city to start the job he was hired for. b. Kurtis moved to a new city and is started the new job he was hired for. c. Kurtis moved to a new city to starting the job he was hired for. d. Kurtis will be moving to a new city to started the job he was hired for. D is wrong

Answers

Answer:  a. Kurtis is moving to a new city to start the job he was hired for.

Step-by-step explanation: "is moving"  is present progressive tense.

"was hired"  is passive past tense.

"to start" is an infinitive.

These are correct verb forms.

b is almost correct. Kurtis "moved" is OK  in the past tense. *is started* should be "has started"

c  is partly correct.  *to starting* is ungrammatical here.

d  is wrong because *to started* is always ungrammatical.

Solve for the unknown side.? Added photo.

Answers

Its 17 because those lines are the same size

Can someone help me please

Answers

Answer:

it should be 9

Step-by-step explanation:

i already did this

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