The sum of two numbers is 13. Two times the first number minus three times the second number is 1. If you let x stand for the first number and y for the second number what are the two numbers

Answers

Answer 1
Steps:

So for this, we will be setting up a system of equations with the information we have:

[tex]x+y=13\ \textsf{"The sum of two numbers is 13."}\\2x-3y=1\ \textsf{"Two times the first number minus three times the second number is 1."}[/tex]

Now we have our system of equations set up. Next, I will be using the substitution method to solve this system. So firstly, subtract y on both sides of the first equation:

[tex]x=13-y\\2x-3y=1[/tex]

Now, substitute x for (13 - y) in the second equation and solve for y as such:

[tex]2(13-y)-3y=1\\26-2y-3y=1\\26-5y=1\\-5y=-25\\y=5[/tex]

Now that we have the value of y, substitute it into either equation to solve for x:

[tex]x+5=13\\x=8\\\\2x-3(5)=1\\2x-15=1\\2x=16\\x=8[/tex]

Answer:

In short, the first number (x) is 8 and the second number (y) is 5.


Related Questions

Can some please help and how to do it with the work shown.

Answers

10 + 6 + 6 = 22 cubes.

Lina bought 22 boxes of crayons for $28.16 how much did she pay for each box of crayons

Answers

She payed $1.28 for each box of crayons

Cost per box = $1.28
The cost of each box of crayons can be calculated by dividing the total cost by the number of boxes purchased.

Total cost: $28.16

Number of boxes: 22

Cost per box = Total cost / Number of boxes

Cost per box = $28.16 / 22
=$1.28

Quadrilateral ABCD is a parallelogram if its diagonals bisect each other. Prove that Quadrilateral ABCD is a parallelogram by finding the value of x.
A) x = 2
B) x = 3
C) x =- 9|2
D) x = -3|4

Information that goes with the picture:
AO = 5x + 2
BO = x − 1
CO = 3x − 7
DO = 3x + 8

Answers

Because this is a parallelogram, we know that the diagonals bisect. This means that AO = DO, and CO = BO

It doesn't matter which two segments we use, but I'm going to use CO = BO for this one.

3x - 7 = x - 1

2x = 6

x = 3

Option B. is the answer.

Answer: d

Step-by-step explanation:

Alissa would like to make a deposit into her savings account. She filled out a deposit ticket and handed it to the teller at her bank. The teller apologizes to Alissa and explains that she cannot accept the deposit ticket in its current form. Determine what, if anything, Alissa will have to change in order for her deposit ticket to be accepted. a. The sub total is calculated incorrectly b. Alissa forgot to sign the deposit ticket for less cash back c. The total is calculated incorrectly d. Alissa forgot to date the deposit ticket

Answers

I would think b, but if u don’t agree then I would go with d

The correct option is c. The total is calculated incorrectly.

When making a deposit, it is crucial that the total amount being deposited is calculated correctly on the deposit ticket. This total amount should match the sum of the cash and checks being deposited. If there is a discrepancy between the subtotal of the individual amounts and the total, the deposit ticket will not be accepted because it does not accurately reflect the amount of money being handled.

Here's the logic behind why the other options are not the primary issue:

a. The sub total is calculated incorrectly: While this is a potential error, the primary concern for the teller would be the total amount being deposited. The subtotal informs the depositor and the bank of the breakdown of the deposit, but the total is what ultimately needs to be correct for the deposit to be processed accurately.

b. Alissa forgot to sign the deposit ticket for less cash back: While a signature is important for verification purposes, especially if cash back is requested, the absence of a signature would typically result in the teller asking for a signature rather than outright rejection of the deposit ticket. The calculation of the total deposit amount is a more fundamental error that must be corrected before the deposit can be accepted.

d. Alissa forgot to date the deposit ticket: The date on a deposit ticket is important for record-keeping purposes. However, forgetting to date the deposit ticket is usually a minor issue that can be resolved quickly at the teller's window. It would not typically prevent the deposit from being accepted, assuming the total deposit amount is correct.

In summary, the teller's refusal to accept the deposit ticket in its current form most likely stems from an incorrect total calculation, as this directly affects the accuracy of the deposit transaction. Alissa will need to ensure that the total on the deposit ticket correctly reflects the sum of the cash and checks she is depositing. Once the total is corrected, the deposit ticket should be accepted by the teller.

Which of the following equations represents a degenerate ellipse?

Answers

Answer:  [tex]\frac{x^2}{10} = -\frac{y^2}{18}[/tex]

Step-by-step explanation:

Since, The degenerate form of an ellipse is always a point.

Thus, the equation that shows only a point will be our answer.

Since [tex]9x^2 + 4y^2 = 1[/tex] is the equation of an ellipse,

Thus, It can not be a point.

[tex]\frac{x^2}{14} + \frac{y^2}{19} =2[/tex] is not a point ( because it is an equation of ellipse)

But, when we plot [tex]\frac{x^2}{10} = -\frac{y^2}{18}[/tex]

We get only a point (0,0).

Thus, equation, [tex]\frac{x^2}{10} = -\frac{y^2}{18}[/tex] shows only one point.

Therefore, it is a generated form of ellipse.



Final answer:

The equation representing a degenerate ellipse would have the sum of the distances from the foci to any point on the curve as a constant.

Explanation:

An ellipse is a closed curve such that the sum of the distances from a point on the curve to the two foci is constant. So, the equation representing a degenerate ellipse would have the sum of the distances from the foci to any point on the curve as a constant. The correct equation is (b).

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What does x <-20 mean

Answers

x<-20 means that x has a greater value than -20.

X is greater than negative 20     (-20)

Solve for k:

k + 6 > -20




Answers

Answer:

k > -26

Step-by-step explanation:

To isolate the k, you subtract 6 from both sides to get k < -26.

The correct answer is k > -26

Explanation:

To solve our equation first we need to set out our equation, k + 6 > -20. Next, we have to subtract 6 from both sides of the equation, k + 6 - 6 > -20 - 6 =      k > -26. Finally, we have our answer of k > -26.

Hope This Helps!!!

-AnimeDabGirl

how do you solve this?

Answers

Answer: To solve these types of questions what I always do is get a protractor if you have one and put it up against to where the dot is in the middle of the empty hole and then get a ruler or a pencil and make the line keep going to see what angle. In this case your answer is 65% I think.

Calculate a5 for the geometric sequence in which a1=1600 and the common ratio is 3/4.

Answers

Answer:

a₅ = 506.25                   option a

Step-by-step explanation:

Given that,

first term a₁ = 1600

common ratio (r) = [tex]\frac{3}{4}[/tex]

We need to find the fifth term of the geometric progression

We know that the nth term formula

aₙ = a₁rⁿ-¹

where a₁ is first term and r is the common ratio

n is the number of terms

So, n = 5

a₅ = 1600 [tex](\frac{3}{4})^{5-1}[/tex]

a₅ = 1600*[tex](\frac{3}{4}) ^{4}[/tex]

a₅ = 1600*81/256

a₅ = [tex]\frac{2025}{4}[/tex]

a₅ = 506.25                   option a

That's the final answer

Answer:

A. 506.25    

Step-by-step explanation:

1.) (7.RP.3) Tracy started a savings account that is set up so that the simple interest earned on the investment is moved into a separate account at the end of each year. Tracy invests $5,000 at 4.5%, what is the total simple interest accumulated in the checking account after 2 years? (1 pt) *
a) $4.50
b) $45
c) $450
d) $4,500
e) $45,000
BACKNEXT


2. 2. (7.RP.3) Sylvia bought a 6-month $1900 certificate of deposit. At the end of 6 months, she received a $209 simple interest. What rate of interest did the certificate pay? Show all of your work.

Answers

Answer:

1. c. $450.

2.  22%

Step-by-step explanation:  

1. We will use simple interest formula to find the amount of interest after 2 years on $5,000. As interest is not compounded, so it will not matter if she moves the simple interest earned in separate account or not.

[tex]I=P*r*t[/tex], where,  

I= Amount of interest.

P= Principal amount.

r= Interest rate in decimal form.  

t= Time in years.

[tex]4.5\text{ percent}=\frac{4.5}{100}=0.045[/tex]

Upon substituting our given values in above formula we will get,

[tex]I=5000*0.045*2[/tex]

[tex]I=5000*0.09[/tex]

[tex]I=450[/tex]

Therefore, Tracy will get an amount of $450 as simple interest after 2 years and option c is the correct choice.

2. Sylvia bought a 6-month $1900 certificate of deposit. At the end of 6 months, she received a $209 simple interest.

6 months is same as 1/2 year.

[tex]I=P*r*t[/tex]

Upon substituting our given values in above formula we will get,

[tex]209=1900*r*\frac{1}{2}[/tex]

[tex]209=950*r[/tex]

[tex]r=\frac{209}{950}[/tex]

[tex]r=0.22[/tex]

Since interest rate is in decimal form, let us convert it in percent.

[tex]\text{Interest rate}=0.22\times 100=22\text{ percent}[/tex]

Therefore, interest rate of certificate of deposit was 22%.

PLEASE SHOW WORK
Solve using substitution
y=x+1
3x-y=9

Answers

y = x + 1   (*)

3x - y = 9   (**)

Substitute (*) to (**):

3x - (x + 1) = 9

3x - x - 1 = 9      add 1 to both sides

2x = 10     divide both sides by 2i

x = 5

Put the value of x to (*):

y = 5 + 1

y = 6Answer: x = 5 and y= 6 → (5, 6).

using the order of operations. select true or false for 81 ÷ 9 + 2 = 11

Answers

Answer: true


Step-by-step explanation: Using the order of operations, 81 / 9 would be first, which is equal to 9. Then, add 2. 2+9 = 11, so the answer is true.


Since division goes before addition we first divide 81:9 and get 9 and to that we add 2 addition goes after division. 9+2 is equal to 11 so the answer is True.

A good way to remember it is:

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

Hope this helps! <3


(3x+7x-20) ÷ (x+4) can someone solve this?

Answers

Answer:

Alright well solve by dividing using polynomial division

10 - 60/x + 4 Hope this helps have a nice day :)

Step-by-step explanation:


Irene bought six pounds of fish for $12.90. Based on that cost, how much would 3.4 pounds of the same fish cost?
A) $2.15
B. $6.45
C) $7.31
D. $22.76
Please help.

Answers

Answer:

B. 6.45

Step-by-step explanation:

So we know that you bought six pounds for $12.90, and you need to know how much it would cost for three pounds. You need to find out what one pound would cost, then multiply that by three.

You would do:

12.90 ÷ 6

Which equals : 2.15

Then take that and multiply it by 3:

2.15 × 3

Giving you 6.45.

Thus leading to, this fish would cost $6.45 for three pounds.


Answer the following questions showing all your work. You are trying to save up money by working in the summer. You have been able to secure two part time jobs. a. Your first job is to babysit a couple of times a week. You charge a flat fee of $10 for transportation back and forth to the house plus $5.50 per hour. Let t be the time in hours that you babysit. Write an algebraic expression to define the amount of money you will make for t hours of work. b. You also work at a local coffee shop in the mornings. You are paid $10 per hour. Write an algebraic expression to define the amount of money you will make for t hours of work. c. Write an algebraic expression for how much money will you will make for both jobs together.

Answers

Let’s use the variable p for the total amount of money you make.
First off, p= 5.5t + 10 for the babysitting job. Technically, that is all the work you can possibly have.
Secondly, p= 10h for the coffee shop job, with h being a separate amount of time than the variable t due to the fact that the are attributed to different jobs.
Lastly, p= 5.5t + 10h + 10 for both jobs during the entire day, with the hours worked being applied separately from each job.
Your welcome

Perform the specified operations on the polynomials: Subtract 5a−6b+7c from 13a−4b+8c

Answers

Answer:

8a + 2b + c

Step-by-step explanation:

For subtracting polynomials we just need to operate subtracting the terms with same unknown. In our case we sum/subtract the terms that include a between them, the terms that have b between them and the therms with c between them. So we have:

(13a−4b+8c) - (5a−6b+7c) =?

13a−4b+8c - 5a+6b-7c = ?

Lets operate putting together terms with same unknown:

(13a - 5a) + (-4b +6b) + (8c-7c) =

8a + 2b + c

So, if we subtract 5a−6b+7c from 13a−4b+8c we get 8a + 2b + c

I hope it is clear!

Andy has 9 math books and 6 reading books. If he wants to distribute them evenly among some bookshelves so that each has the same combination of books, with none left over, what is the greatest number of bookshelves Andy can use?

Answers

Answer:

3 is the greatest number of book shelves Andy can use.

Step-by-step explanation:

You can solve this by finding the greatest common factor of 9 and 6, which turned out to be 3.

6/3 = 2 (reading books per shelf)

9/3 =3 (math books per shelf)

Every shelf there are 2 reading books and 3 math books.

Help with trig homework
A 6 m ladder is leaning against a wall. The base of the ladder is 1.5 m from the wall. Calculate how high up the wall the ladder reaches.

Answers

Answer:

height = 5.809

Step-by-step explanation:

l=6m

b=1.5m

l^2=b^2+h^2

36=2.25 +h^2

h^2 = 36 - 2.25

h=[tex]\sqrt{33.75}[/tex]

h = 5.809

What is the value of y ?

Answers

Answer:the value of y is 44


Step-by-step explanation:


the answer to the question is b

Total blood cholesterol level was measured for each of
8 adults. Here are the 8
measurements (in mg/dL):
264, 191, 160, 148, 262, 212, 268, 246

Answers

Answer: Mean = 218.9.Median = 229Mode = Zero mode.

Step-by-step explanation:

Given blood cholesterol level was measured for each of 8 adults (in mg/dL) are:

264, 191, 160, 148, 262, 212, 268, 246

In order to find the mean, we need to add all those 8 numbers and divide by 8.

Therefore, mean = [tex]\frac{264+191+160+148+262+212+268+246}{8} =\frac{1751}{8} =218.9.[/tex]

Mean = 218.9.

In order to find the median, we need to arrange them in ascending order:

148, 160, 191, 212, 246, 262, 264, 268.

The middle most two values are 212 and  246.

Therefore, median = [tex]\frac{212+246}{2} =\frac{458}{2} = 229.[/tex]

Median = 229.

[tex]\mathrm{The\:mode\:is\:the\:term\:in\:the\:data\:set\:that\:appears\:the\:most.}[/tex]

[tex]\mathrm{If\:there\:is\:more\:than\:one\:term\:that\:appears\:the\:most,\:then\:there\:is\:no\:mode.}[/tex]

[tex]\mathrm{Count\:the\:number\:of\:times\:each\:element\:appears\:in\:the\:list}[/tex]

[tex]\begin{pmatrix}148&160&191&212&246&262&264&268\\ 1&1&1&1&1&1&1&1\end{pmatrix}[/tex]

[tex]\mathrm{The\:most\:common\:element\:is\:not\:unique,\:so\:there\:is\:no\:mode}[/tex]

Therefore, Mode = Zero mode.

use the following table to find the value of h'(3) if h(x)=g[f(x)]

Answers

Since

h(x) = g(f(x)), h'(x) = g'(f(x))×f'(x) (Chain rule).

Setting x=3 we get

h'(3) = g'(f(3))×f'(3)

Plugging in values we get

h'(3) = g'(4)×7

h'(3) = 2×7

h'(3) = 14

A differential equation is an equation that contains one or more functions with its derivatives. The value of h'(3) iss 14.

What is Differential equation?

A differential equation is an equation that contains one or more functions with its derivatives.

Given

h(x) = g(f(x))

Let us differentiate with respect to x by using chain rule we get

h'(x) = g'(f(x))f'(x)

plug the value x =3 in the above equation

h'(3) = g'(f(3))f'(3)

The value of f(3)=4, f'(3)=7 by table given

Plugging in values we get

h'(3) = g'(4)×7

We have g'(4)=2

so h'(3) = 2×7

h'(3) = 14

Hence the value of h'(3) is 14.

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What is the area of a parallelogram ABCD

Answers

Answer:

Area of a parallelogram would be 13.46

Step-by-step explanation:

Since area of a parallelogram is represented by the formula

Area = [tex]\frac{1}{2}[/tex] ([tex](D_{1}*D_{2})[/tex]

Where [tex]D_{1}[/tex] and [tex]D_{2}[/tex] are two diagonals of the given parallelograms.

In the given figure [tex]D_{1}=AC[/tex] and [tex]D_{2}[/tex] = BD

We will find the length of [tex]D_{1}[/tex] and [tex]D_{2}[/tex] first

Since points A and C are (3,6) and (5,1)

So distance AC = [tex]\sqrt{(6-1)^{2}+(3-5)^{2}  }[/tex]

= [tex]\sqrt{5^{2}+(-2)^{2}}[/tex]

= [tex]\sqrt{25+4}=\sqrt{29}[/tex]

Since B and D are the points (6, 5) and (2, 2)

So length of BD = [tex]\sqrt{(6-2)^{2}+(5-2)^{2}}[/tex]

BD = [tex]\sqrt{4^{2}+3^{2}}=\sqrt{25}=5[/tex]

Now we will put these values in the formula

Area of parallelogram = [tex]\frac{1}{2}(\sqrt{29})(5)[/tex]

= [tex]\frac{5}{2}[/tex] × [tex]\sqrt{29}[/tex]

= (2.5) (5.385)

= 13.46

Jim drove 605 miles in 11 hours. At the same rate, how many miles would he drive in 13 hours?

Answers

Answer: 715 Miles


Step-by-step explanation:

Divide 605 miles by 11 hours, which would give you how far he travels in 1 hour. (605/11=55)  Since they give you 13 hours, multiply 13 hours by 55 miles which gets you 715 miles :)

Identify the explicit function for the sequence in the table.

(PLEASE HELP NEED ANSWERS ASAP)

Answers

14 - 9 = 5
19 - 14 = 5
24 - 19 = 5
29 - 24 = 5

It is an arithmetic sequence with differences, b = 5 and a = 9
a(n) = a + b(n - 1)
a(n) = 9 + 5(n - 1)

The answer is B

Answer: B(APEX)

Step-by-step explanation:

A large beetle can be 2x2x2x2x2x2x2 millimeters long. One of the smallest beetles can be 2(-2 (power)) millimeter long. How many times as great is the length of the large beetle than the length of the small beetle?

Answers

Answer:

I think the answer is 2^8 millimeters longer than the small beetle

Step-by-step explanation:


What is the value of (4x^2-10)/y when x=5 and y=6

Answers

4(5)^2-10/6

4(25)-10/6

100-10/6

90/6

=15

write an equation of the line containing the specified point and perpendicular to indicated line. (-5,6) 4x-y=3

Answers

Greetings!

Answer:

y = [tex]\frac{1}{2}x + \frac{29}{4}[/tex]

Step-by-step explanation:

First, we need to rearrange the equation to make it y = mx + c

4x - y = 3

y + 3 = 4x

y = 4x -3

So the slope of the line is 4.

The slope of a line perpendicular to an equation is:

[tex]\frac{-1}{gradient}[/tex]

So the slope of the perpendicular line is:

[tex]\frac{-1}{4}[/tex] = -0.25

Now to find the equation of a line you can use the following equation:

y - y₁ = m(x - x₁)

Where y₁ is the y-coordinate, x₁ is the x-coordinate and m is the gradient. Plug the values in:

y₁ = 6

x₁ = -5

m = [tex]\frac{-1}{4}[/tex]

y - 6 = [tex]\frac{-1}{4}[/tex](x - - 5)

To get rid of the fraction we need to multiply the whole equation by 4:

4y - 24 = -1(x - - 5)

The two negatives cancel out:

4y - 24 = -1(x + 5)

Multiply the brackets out:

4y - 24 = -x + 5

Now, to rearrange the formula back into y = mx + c

Move the -24 over to the other side making it a +24:

4y = 2x + 5 + 24

4y = 2x + 29

Divide everything by 4:

y = [tex]\frac{2}{4}x + \frac{29}{4}[/tex]

y = [tex]\frac{1}{2}x + \frac{29}{4}[/tex]


Hope this helps!

What number is 30% of 20?

Answers

Answer:

6

Step-by-step explanation:

20 times .3 equals 6

the answer is 6 because (30 ÷ 100) × 20


Will award brainiest to whoever answers and helps, I really need this ;;

Mathematics of personal finance:

Assume that the probability of a driver getting into an accident is 7.1%, the average cost of an accident is $14,886.05, and the overhead cost for an insurance company per insured driver is $110. What should the driver's insurance premium be?

A)$1156.43
B)$1242.93
C)$1276.27
D)$1165.49

Answers

Multiply the probability by the cost of the accident:


14,886.05 x 0.071 = 1056.91

Now add the overhead cost:

1056.91 + 110 = 1166.91

The closest answer to this is number D.

Answer:

D. $1165.49

Step-by-step explanation:

We have that the probability of a driver getting into an accident = 7.1% i.e. 0.071.

Now, the average cost of an accident = $14,886.05

Then, the expected cost of an accident =  $14,886.05 × 0.071 = $1056.91

As, the overhead cost for insurance = $110

Therefore, the driver's insurance premium = $1056.91 + $110 = $1166.91

Since, the closest option to $1166.91 is option D.

Hence, the driver's insurance premium will be $1165.49.

factor each expression 45x + 63y

Answers

Answer:

9(5x+7y)

Step-by-step explanation:


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