System of Equations : Money

Damian has been saving coins he finds on the ground for several months. So far he has found 37 coins that are either pennies or nickels. The combined value of his found pennies and nickels currently is $1.09. What is the system of linear equations, written using standard form, represents the situation if Damian found p pennies and n nickels.​

Answers

Answer 1

Answer:

18 nickles 19 pennies

Step-by-step explanation:

value of 1 penny=$0.01

value of 1 nickle=$0.05

0.01p+0.05n=1.09

p+n=37

there are two methods for this system

I.substitution

p+n=37

p=37-n

we replace p in the first relation

0.01(37-n)+0.05n=1.09

0.37-0.01n+0.05n=1.09

0.04n=0.72

n=18 nickels

p+18=37

p=37-18=19 pennies

II.reduction

0.01p+0.05n=1.09

p+n=37

we multiply the second equation by 100

p+5n=109

p+n=37

we calculate the difference between the two relations

p-p+5n-n=109-37

4n=72

n=18

p+18=37

p=19


Related Questions

There are a total of 168 hockey games in the season and 7 are played at night. The season is played for 14 months. How many games were played each month if each month has the same number of games?

Answers

Answer: 8

Step-by-step explanation: I added 7+14 then whatever i got i divied that by 168 so 168 by 21 which equals 8 but don’t hate if it’s wrong i’m only in the grade 5

Julio says,”If you subtract 15 from my number and multiply the difference by -7,the results is -175.” What is Julio number

Answers

Answer:

Julio's number is 40.

Step-by-step explanation:

We need to reverse the operations Julio performed on his number. First, we divide -175 by -7, and we get 25. Then, we add 15 to that, giving us Julio's number of 40.

Hope this helps!

Write the equation x2 + 6x + y2 – 8y = 19 in standard form.

Question 11 options:


1)
(x + 3)2 + (y – 4)2 = 44


2)
(x + 3)2 + (y – 4)2 =


3)
(x – 3)2 + (y – 4)2 =


4)
(x + 3)2 + (y + 4)2 = 44

Answers

Answer:

i think its 2

Step-by-step explanation:

The equation of  x² + 6x + y² - 8y = 19 in standard form is (x + 3)² + ( y - 4)² = 44. Hence, Option A is the correct answer.

What is a system of equations?

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

We have been given the equation as;

x² + 6x + y² - 8y = 19

We need to find the standard form of the equation.

Thus, we have,

(x²  + 6x )+(y²- 8y) = 19

We shall complete the square for the term;

(x²  + 6x + 9 - 9 ) + (y² +  4y + 16 - 16) = 19

Simplifying, we get,

(x²  + 6x + 9) - 9 + (y²- 8y + 16) - 16 = 19

(x²  + 6x + 9) - 9 + (y²- 8y + 16) - 16 = 19 + 9 + 16

Formula used :

x²+2xy+y² = (x+y)²

x²-2xy+y² = (x-y)²

Simplifying, we get,

(x + 3)² + ( y - 4)² = 44

Thus, the equation of  x² + 6x + y² - 8y = 19 in standard form is (x + 3)² + ( y - 4)² = 44.

Hence, Option A is the correct answer.

Learn more about equations here;

https://brainly.com/question/10413253

#SPJ2

Solve for x.
13(x-3) = 39
X=1
X=4
x=6
x=10

Answers

13 factored out is 13x - 39 add 39 to both sides it equals 13x=78 and 78 divided by 13 is 6 the anwser is x=6

A line passes through the point (-8,-5) and has a slope of 3/4. Write an equation in slope intercept form for this line.

Answers

Answer:

y = ¾x + 1

Step-by-step explanation:

Point-slope equation for line of slope ¾ that passes through (-8,-5):

y+5 = ¾(x+8)

Put into slope-intercept form:

y = ¾(x+8) - 5 = ¾x + 6 - 5 = ¾x + 1

Determine whether the points on the line rise, fall, are horizontal, or vertical.
(2, -4) and (4, -1)

Answers

Answer:

The points rise.

Step-by-step explanation:

Points on a line have the following format: (x,y)

They rise if: As x increases, so does y.

They fall if: As x increases, y decreases.

They are horizontal if: As x increases, y remains constant.

They are vertical if: x is constant as y changes.

In this question:

Points (2,-4) and (4,-1).

x increases from 2 to 4.

y increases from -4 to -1.

That is, both increase, so the points rise.

Find the missing values in the equation below.
Line 1: 2/3 - 1/2 = 4/?-?/6
Line 2: / - / = ?/6

Answers

Answer:

[tex]\frac{2}{3} - \frac{1}{2} = \frac{4}{6} - \frac{3}{6}[/tex]

[tex]\frac{2}{3} - \frac{1}{2} = \frac{1}{6}[/tex]

Step-by-step explanation:

Given

[tex]\frac{2}{3} - \frac{1}{2} = \frac{4}{?} - \frac{?}{6}[/tex]

[tex]/ - / = \frac{?}{6}[/tex]

Required

Fill in the gaps

For Line 1, convert both fraction to a denominator of 6.

This is shown below:

[tex]\frac{2}{3} - \frac{1}{2} = \frac{4}{?} - \frac{?}{6}[/tex]

[tex]\frac{2}{2}*\frac{2}{3} - \frac{1}{2} *\frac{3}{3}[/tex]

[tex]\frac{2*2}{2*3} - \frac{1*3}{2*3}[/tex]

[tex]\frac{4}{6} - \frac{3}{6}[/tex]

Hence:

[tex]\frac{2}{3} - \frac{1}{2} = \frac{4}{6} - \frac{3}{6}[/tex]

For Line 2;

We have:

[tex]\frac{2}{3} - \frac{1}{2} = \frac{4}{6} - \frac{3}{6}[/tex]

[tex]\frac{2}{3} - \frac{1}{2} = \frac{4-3}{6}[/tex]

[tex]\frac{2}{3} - \frac{1}{2} = \frac{1}{6}[/tex]

What is the area of the region bounded by the lines x= 1 and y= 0 and the curve y=xe^x^2?

Answers

Answer:

A = 0.859

Step-by-step explanation:

We want to find the area of the region bounded by the lines x = 1 and y = 0 and the curve y = xe^(x²).

At y = 0, let's find x;

0 = xe^(x²)

Solving this leads to no solution because x is infinity. Thus we can say lower bound is x = 0.

So our upper band is x = 1

Thus,lets find the area;

A = ∫xe(x²) dx between 1 and 0

A = (e^(x²))/2 between 1 and 0

A = ((e¹)/2) - (e^(0))/2)

A = 1.359 - 0.5

A = 0.859

simplify:
[tex] \frac{ \sqrt{4} }{ \sqrt[3]{4} } [/tex]
choices:
[tex]4 \frac{5}{6} [/tex]
[tex]4 \frac{1}{6} [/tex]
[tex]4 \frac{3}{2} [/tex]
[tex]4 \frac{1}{3} [/tex]

Answers

Step-by-step explanation:

= 4^1/2 /4^1/3

=4^1/2-1/3

=4^1/6

A bag of marbles contains 2 white, 3 black, 1 red and 4 blue marbles. Cate draws one marble from the bag, looks at it and then replaces it. What is the probability that she will draw a black marble and then a black marble?

A) 9/10
B) 9/100
C) 3/5
D) 1/25​

Answers

Step-by-step explanation:

Number of black marbles = 3

Total number of marbles = 2 + 3 + 1 + 4 = 10

P(Drawing a black marble) = 3/10

Since the drawing is replaced,

they are considered independent events.

=> P(Black marble, following by black)

= [P(Drawing a black marble)]²

= (3/10)²

= 9/100. (B)

Solve the inequality

Answers

The answer is A. P>9

Answer:

P > 9

Step-by-step explanation:

22 x 9 would equal 198 also, but if you want it to be like in the equation where 22p is more than 198 it has to be more than 9. So if you were to substitute any number over 9 it would work.

Simplify or solve the problems
1) 14a+2a=
2) 4x - 7 - 3 =0
3) 6x + 6 - =o

Answers

1. add like terms so 14a + 2a = 16a

2. put variables on side and constants on the other so
4x = 10
x = 5/2

3. I’m confused on this one? Is there supposed to be another number after the subtraction sign ?

What is the missing number in this pattern?
2.704 * 10 = 27,04
2.704 * 100 = 270,4
2.704 * 1,000 = ???

Answers

Answer:

Step-by-step explain:

2.704 * 10 = 27,04

2.704 * 100 = 270,4

2.704 * 1,000 = 2,704

A person draws a card from a hat. Each card is one color, with the following probabilities of being drawn: 1/15 for blue, 1/25 for green, 1/5 for pink, and 1/20 for black. What is the probability of pulling a black or pink card, written as a reduced fraction?

Answers

Answer:

Step-by-step explanation:

DAM I JUST STARTED LEARNING ABOut that

below is the graph of f'(x) the derivative of f(x) and has x intercepts at x = -3 x = 1 x = 2 and a relative maximum at x = -1.5 and a relative minimum at x = 1.5. Which of the following statement is true?

Answers

Answer:

A

Step-by-step explanation:

Answer: A

Step-by-step explanation:

it makes the most sense anyways heres a bernie sanders meme cause its giving me life

In equation form. What goes through the points (0, 4) and (2, 7)?

Answers

Answer:y=1.5x+4

Step-by-step explanation:

i got 90.50. does that seem right?

Answers

there is no context to this question. what would you like help with?

Step-by-step explanation:

90.50. as money if it is it would be $90.50

if as a number 9,050

help please. Find the measure of each angle

Answers

1.  139

2.  41

3.  139

4.  139

5.  41

6.  139

7.  41

Do anybody know which one is it thank you.

Answers

Answer:

Its 2/8

Step-by-step explanation:

2/8 simplified is 1/4

Answer:

The answer will be 2/8 because if you think about it 4/8 is 1/2 and 1/2 of 4/8 is 2/8 and since 1/2 4/8 is 2/4 which is actually 1/2 of 1/2 so that makes it 1/4 hope this helps!!

(to make it clear the answer is 2/8)

Two siblings are racing. The older sibling can run at a constant speed of 11 feet per second. The younger sibling can run at a constant speed of 7 feet per second. If the younger sibling is given a 32-foot head start in the race, how long will it take the older sibling to catch the younger sibling, and how far will the older sibling have run at that moment?(1 point)

The older sibling will catch the younger sibling after ___ second(s) and running___feet.

Answers

Answer:

8 seconds after running 88 feet

Step-by-step explanation: this is what it told me the answer was

Answer:

The older sibling will catch the younger sibling after 8 second(s) and running 88 feet.

Step-by-step explanation:

Older Sibling:  11ft  22ft  33ft  44ft  55ft  66ft  77ft  88ft

Younger Sibling: 32ft  39ft  46ft  53ft  60ft  67ft  74ft  81ft

The younger sibling started at 32ft because of the headstart.  Each number was after 1 second. So this means it took 8 seconds for the older sibling to get to 88ft, and it took 8 seconds to get the younger sibling to 81ft.

I hope you can understand. :)

60 is it rocking horse has a weight limit of 60 pounds what percentage of the weight limit is 114 pounds

Answers

144 pounds long heyyy

Answer:

86.4

Step-by-step explanation:

find the sum.

Please please please help me!!



Answers

Answer/ explanation:

3a + 4

a + b

Given that R= 6x + 5y
Find y when x = 8 and R =20
Give your answer as an improper fraction in its simplest form​

Answers

Answer:

-28/5=y

Step-by-step explanation:

20=6(8)+5y

20=48+5y

-28=5y

-28/5=y

-4x + 12 = -6x
Step 1: Add 4x to both sides:
12 = -6x + 4x
Step 2: Combine like terms:
12 = -2x

Answers

uh- this is the correct way to answer the problem....

−4x+12=−6x

Step 1: Add 6x to both sides.

−4x+12+6x=−6x+6x

2x+12=0

Step 2: Subtract 12 from both sides.

2x+12−12=0−12

2x=−12

Step 3: Divide both sides by 2.

[tex]\frac{2x}{2}[/tex] = [tex]\frac{-12}{2}[/tex]

x=−6

ANSWER THIS QUESTION RIGHT WHAT YOU NEED TO FIND THE ANSWER IS ON THE PHOTO The Figure below shows the graph of the function f(x) In the coordinate plane. Identify the following key features of the graph

Answers

Answer:

vertex: (0,3)

Axis of symmetry: x=0

y-intercept: (0,3)

x-intercept: n/a

min

A would be positive since the parabola opens at the top

Step-by-step explanation:

what linear equation in slope intercept from does this graph represent?​

Answers

Answer:

[tex]y = 16\frac{2}{3} x + 100[/tex] or [tex]y = \frac{50}{3} + 100[/tex]

Step-by-step explanation:

The equation of a line is [tex]y = mx + b[/tex], with [tex]m[/tex] being the slope and [tex]b[/tex] being the y-intercept.

We can see on the graph that the y-intercept, where the line crosses or touches the y-axis, is 100. So, our new equation is [tex]y = mx + 100[/tex].

Now we have to find the slope. Let's pick a point that's clearly on the graph. Perhaps (3, 150). And then we'll take the y-intercept point for convenience, (0, 100).

Then, we'll use [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1} }[/tex] to find the slope.

Let's substitute in our points.

[tex]\frac{150-100}{3-0}[/tex]

Simplify.

[tex]\frac{50}{3}[/tex]

Now, we can leave the slope like that or turn it into a mixed number. As a mixed number, your slope is [tex]16\frac{2}{3}[/tex].

We'll put that in our equation for a line and...bam!

[tex]y = 16\frac{2}{3} x + 100[/tex] or [tex]y = \frac{50}{3} + 100[/tex]

A basketball player makes 145 out of 180 free throws. We would estimate the probability that the player makes the next throw to be

Answers

They made 80% of those the probability is 29/36

Solve 3a – 8= 5a + 12

Show your work. (please)

Answers

Answer:

a = - 10

Step-by-step explanation:

3a – 8 = 5a + 12

3a – 8 + 8 = 5a + 12 + 8

3a = 5a + 20

3a - 5a = 5a + 20 - 5a

- 2a = 20

[tex]\dfrac{-2a}{-2}=\dfrac{20}{-2}[/tex]

a = - 10

Choose all equations for which x=2 is a solution.

A:x+3=5
B:x+2=8
C:x+1=1
D:x-2=4
Ex-7=5-

Answers

A and D that’s the answer

Which linear equation is represented by the table?

x −2 1 3 6
y 7 4 2 −1

Answers

Answer:

help calll me daddy

Step-by-step explanation:

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