the sum of 4 times a larger integer and 9 times a smaller integer is 3. the difference between 8 times the larger and 3 times the smaller is 27. Find the integers

Answers

Answer 1
Let's break down the problem step by step.

The sum of 4 times a larger integer can be summarized as:

4x


9 times a smaller integer can be summarized as:

9y


We know that we're adding the two expressions because the beginning of the problem has sum. We also know the sum is 3.


So, we get:

4x + 9y = 3


Continuing with the problem, we have the difference between 8 times the larger

8x


We also have 3 times the smaller

3y


This part of the problem mentions the difference between these expressions so we subtract and we know the difference is 27.

8x - 3y = 27


Now, we have both equations so we can solve for either x or y.


4x + 9y = 3
8x - 3y = 27

It's easier to multiply the 4x equation by 2 to have both equations resulting in 8x

(4x + 9y = 3) * 2

We get:

8x +18y = 6


So, we now have:

8x + 18y = 6
8x - 3y = 27

We can subtract the x to get y by itself. We get:

21y = -21

Solve for y and we get:

y = -1

Since we know what y is, we can plug that in and solve for x. It doesn't matter which equation you plug y back in. I'm gonna use the second equation.

8x - 3y = 27
8x - 3 (-1) = 27
8x + 3 = 27
8x = 24
x = 3

So, we now know that

y = -1
x = 3

Hope this helped! If you have any questions then please leave a comment!









Related Questions

select all possible solutions for 2x+7<=3x-5

Answers

Answer:

12, 18, 24, 107

Step-by-step explanation:

Our inequality is

2x+7 ≤ 3x-5

First we will subtract 3x from each side:

2x+7-3x ≤ 3x-5-3x

-1x+7 ≤ -5

Subtract 7 from each side:

-1x+7-7 ≤ -5-7

-1x ≤ -12

Divide both sides by -1:

-1x/-1 ≤ -12/-1

When we multiply or divide an inequality by a negative number, we flip the inequality symbol:

x ≥ 12

We want numbers that are equal to or larger than 12; this leaves us with

12, 18, 24, and 107.

I need to write the number that matches the clues
Hundreds tens ones
Question is
My number has 2 hundreds.
The ten digits is 9 more than the ones digit
What’s the number?

Answers

The answer to this question is 290

The number has 2 hundreds so 200

The tens place is 9 more than the ones place so its 9

The last number is 0

                                                     

Write an expression that represents the amount of hydrochloric acid in x gallons of a 3% hydrochloric acid solution.

Answers

x=3%h I think I'm not to sure hope that helped! Good Luck!!!

Solve for x: 3x - 24 = 81
A-57/3
B-105/3
C-57
D-105
Helpppp please

Answers

[tex]Solution,solve\:for\:x,\:3x-24=81\quad :\quad x=35[/tex]

[tex]Steps: 3x-24=81[/tex]

[tex]\mathrm{Add\:}24\mathrm{\:to\:both\:sides}, 3x-24+24=81+24[/tex]

[tex]\mathrm{Simplify}, 3x=105[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}3, \frac{3x}{3}=\frac{105}{3}[/tex]

[tex]Simplify, x=35[/tex]

The correct answer is B. 105/3

Hope this helps!!!

<3 - austint1414

which describes the behavior of the function f(x)=tan^-1(x)?

Answers

ANSWER

The correct answer is option C


EXPLANATION

The graph of [tex]f(x)=tan^{-1}(x)[/tex] is shown in the attachment.


You can see clearly that as

[tex]x\rightarrow \infty, f(x)\rightarrow \frac{\pi}{2}[/tex]

and as


[tex]x\rightarrow -\infty, f(x)\rightarrow -\frac{\pi}{2}[/tex]

These are are actually the two horizontal asymptotes to the given function.

Answer:

The answer is C I just took the test.

How do you find the domain for 7

Answers

h(x) = -5x² + 15x - 3

It's a quadratic function. The domain of quadratic function is the set of all real numbers.

Therefore

[tex]D=\mathbb{R}[/tex]-all real numbers.

6 4/11 x2 1/12 Estimate the product

Answers

Answer:

The estimated product is 12.

Step-by-step explanation:

When rounding fractions, we can round them to 0, 1/2 or 1. 6 4/11 can be rounded to 6 since 4/11 isn't near the half of 11. 2 1/12 can be rounded to 2 since 1/12 is obviously close to 0. 6 x 2 = 12. The estimated product is 12.

A catering company is setting up for a wedding. They expect 150 people to attend. They can provide small tables that seat 6 people and large tables that seats 10 people. Find a combination of small and large tables that seats exactly 150 people

Answers

Multiply 6 by 10 to get 90.

Multiply 10 by 9 to get 60.

90 plus 60 equals 150.

Therefore, you'd need 10 small sized tables and 9 large sized tables to fit 150 people.

We need 10 small sized tables and 9 large sized tables to fit 150 people.

What is Equation?

Two or more expressions connected with an equal sign is called as Equation.

We have been given that a catering company is expecting 150 people to attend the wedding.

There are two  kinds of tables,

The first kind of tables are small tables in which six people can be fitted.

The second kind of table are big tables in which ten people can be fitted.

Let us form a linear equation by considering  x as the tables which can fit 6 people and y as the tables which can fit 10 people,

The total number of people that can fit on all available tables as:

6x+10y

If there are total 150 people expected in the wedding, then equation can be framed as:

6x+10y=150

Now let us take x as 10.

Then

6(10)+10y=150

60+10y=150

10y=150-60

10y=90

y=9

Therefore, you'd need 10 small sized tables and 9 large sized tables to fit 150 people.

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Simplify.
(4^3)^5
A) 4^-2
B) 4^3
C) 4^8
D) 4^15

Answers

The answer is D because the 4 is the same then you times 5×3 and you get 4^15

8(x-1) - 3x(4-x) + 6 (x+2) - 3. How can I simplify this?

Answers

Use the distributive property. For the first set of parenthesis, multiply everything inside by 8. This gets you to 8x-8.

Next set: Everything inside by 3x: 12x+3x^2.

Next set: Everything inside by 6: 6x+12.

Put it all together: 8x-8-12x+3x^2+6x+12-3.

Combine like terms: 2x+1+3x^2

There are 7 more girls then boys in a club there are 23 members in the club in all how many girls are there in the club? Which expression represents the number of boys

Answers

There would be 16 girls in the club. You should use the expression: 23(total people in the club)-7(total boys in the club)=?,so 23-7=16.

Final answer:

To find the number of girls in a club where there are 7 more girls than boys and 23 members in total, we solve the equation 2b + 7 = 23 to determine that there are 8 boys and thus 15 girls.

Explanation:

If there are 7 more girls than boys in a club and there are 23 members in total, let's call the number of boys b. Then the number of girls would be b + 7. Given that the total number of members is 23, we can set up the equation b + (b + 7) = 23 to find the number of boys. Solving the equation:

Combine like terms: 2b + 7 = 23

Subtract 7 from both sides of the equation: 2b = 16

Divide both sides by 2: b = 8

Therefore, there are 8 boys in the club. To find the number of girls, we add 7 to the number of boys which gives us 8 + 7 = 15 girls.

The expression that represents the number of boys is simply b, which we have determined to be 8 in this context.

Write 0.0123 in dcientific notation


Answers

10x123^-2
----------------------

The scientific notation of the given 0.0123 will be 123 x 10^{-4}.

How does scientific notations work?

The number is written in the form  a x 10^b.

The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10.

We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).

Scientific notations have some of the profits as Better readability due to compact representation.

Its value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.

The scientific notation of the given 0.0123 will be 123 x 10^{-4}.

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Which equation correctly applies the associative property of multiplication

Answers

The second answer is correct since the associative property has the do with how you use parenthesis.

It is the second one, though the equation appears as different, both have the same answer, -56/225

how would numbers -20,0 and 30 appear on a number line

Answers

Number line showing -20,0, 30 in attachment below.

Jill can answer 50 math questions every 20 minutes. How many questions can she answer in 12 minutes? How many math questions can she answer in 36 minutes?

Answers

Answer:

1: 30

2: 90


Step-by-step explanation:


Answer:

In 12 minutes, She can answer 30 math questions.

In 36 minutes, She can answer 90 math questions.

Step-by-step explanation:

Jill can answer 50 math questions every 20 minutes.

1)

How many questions can she answer in 12 minutes

Let (x) represent the number of questions she can answer in 12 minutes:

So, if 50 math question = 20 minutes

   and (x) math question = 12 minutes

To  solve for (x); we have:

(x) × 20 minutes = 50 math question × 12 minutes

(x)  = [tex]\frac{50*12}{20}[/tex]

(x)  = [tex]\frac{600}{20}[/tex]

(x)  = 30 math questions

∴  In 12 minutes, She can answer 30 math questions.

2)

How many math questions can she answer in 36 minutes?

Let (y) represent the number of questions she can answer in 36 minutes:

So, if 50 math question = 20 minutes

   and (y) math question = 36 minutes

To  solve for (y); we have:

(y) × 20 minutes = 50 math question × 36 minutes

(y) = [tex]\frac{50*36}{20}[/tex]

(y) = [tex]\frac{1800}{20}[/tex]

(y) = 90 math questions.

∴  In 36 minutes, She can answer 90 math questions.

pls help will give brainliest

Answers

4= 60
5= about 13
6= 58

Answer:

4.)60

5.)about 13

6.)58

Step-by-step explanation:


What is 119.63 rounded to the nearest whole number ?

Answers

120 is the answer, I may be wrong.

The answer is 120.

If the tenths place is higher than a 5, the number will round up. If the number was lower than a 5, the number would round down.

the base of a parallelogram is 9 1/2 cm and its height is 11 1/2cm. what is the area of the parallelogram.

Answers

The area of the parallelogram is 109 1/4 square centimeters.

To find the area of a parallelogram, we use the formula:

[tex]\[ \text{Area} = \text{Base} \times \text{Height} \][/tex]

Given that the base is [tex]\(9 \frac{1}{2}\)[/tex] cm and the height is [tex]\(11 \frac{1}{2}\)[/tex] cm, we substitute these values into the formula:

[tex]\[ \text{Area} = (9 \frac{1}{2}) \times (11 \frac{1}{2}) \][/tex]

[tex]\[ \text{Area} = \left(\frac{19}{2}\right) \times \left(\frac{23}{2}\right) \][/tex]

[tex]\[ \text{Area} = \frac{19 \times 23}{2 \times 2} \][/tex]

[tex]\[ \text{Area} = \frac{437}{4} \][/tex]

[tex]\[ \text{Area} = 109 \frac{1}{4} \text{ square centimeters} \][/tex]

Divide 3,479 by 9. What is the remainder?

Answers

5/9 is the remainder

Nathan bought a wallet for 5% off its full price. What was the full produce of the wallet if Nathan paid 17.67 before sales tax A.18.60 B.22.67 C. 17.72 D. 19.53

Answers

A. 18.60, because you multiply 18.6 by .05 to get .93, and then subtract .93 from 18.6 to get 17.67.

Answer:

Option A is correct.

Step-by-step explanation:

Let the full price of the wallet be represented by = x

Total amount that Nathan paid for the wallet = $17.67

Discount percentage = 5% or 0.05 = 0.05x (5% of full price)

So, equation becomes: full price - discount price = 17.67

[tex]x-0.05x=17.67[/tex]

[tex]0.95x=17.67[/tex]

x = $18.60

Therefore, the full price of the wallet is $18.60.

We can also check this by taking out 5% of 18.60

[tex]0.05\times18.60=0.93[/tex]

And[tex]18.60-0.93=17.67[/tex]

So, option A is correct.

Help and I'll label you the brainest and a thank you

How many fractions are there between any two numbers on a number line?

A.5
B.20
C.100
D.an infinite number

Answers

The answer would be D: an infinite number, because you can put as far as numbers can go, which is infinite.

Answer:

There are an infinite number of fractions in between numbers on a number line.

Step-by-step explanation:

The reason for this is because we have an infinite number of denominators to use. Therefore, we can not number the amount we use.

3x+5=245

Helpppppppppppp

Answers

Answer:

X = 80

Step-by-step explanation:

Subtract "5" from both sides,

3x + 5 - 5 = 245 - 5

Simplify,

3x = 240

Divide both sides by "3",

3x/3 = 240/3

X = 80


Hope this helps :-)

3x + 5 = 245
Subtract 5 from both sides to get x alone on one side
3x = 246
Now divide by 3 on both sides
x = 82

Sandy has $200 in her bank account if she writes 6 checks for exactly $19.98, what expression describes the change in her bank account ? And also what is her balance after the checks are cashed.

Answers

Answer:

200 - (19.98 * 6) = x

Explanation:

200 - (19.98 * 6) = x

Solve Parentheses

200 - 119.88 = x

Subtract

80.12 = x

Switch so x comes first

x = 80.12

-3a-2b for a=-4 and b=-3

Answers

-3a-2b

-3 times -4= 12

-2 times -3= 6

12+6=18

hope this helps

also can u give brainy

Plug in a=-4 and b=-3 into -3a-2b

-3(-4) -2(-3)

= 12 + 6

= 18

Answer

18

( 2 + 76 ÷ 1 + 9 ) + 4 - 3 x 9

Answers

( 2 + 76 ÷ 1 + 9 ) + 4 - 3 x 9

64

If it is to solve it would be 73

Your supervisor sends you to the truck for 180 special fasteners when you get there you find that the fasteners come in bags of 15 how many bags of fasteners will you need to bring back

Answers

12 bags is the final answer! :)

The number of the bags of the fasteners is 12.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The number of the fastener in each bag will be:-

N   =  180  /  15

N   =  12

The number of bags are 12

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The length of a side of a square is represented by 4x-1 . Express the perimeter of the square in terms of x.

Answers

The perimeter of a shape is the sum of all it sides.

The perimeter of the square is [tex]16x - 4[/tex]

Given that:

[tex]Length = 4x - 1[/tex]

The perimeter (P) of the square is:

[tex]P = 4 \times Length[/tex]

So, we have:

[tex]P = 4 \times (4x -1)[/tex]

Open brackets

[tex]P = 16x - 4[/tex]

Hence, the perimeter of the square is 16x - 4

See attachment for the image of the square

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Walter takes 7/10 of an hour to mow 2/5 of an acre of lawn.at this rate how many acres will he mow in a hour

Answers

Walter can mow 4/7 acres in an hour.

Steps:

Multiply. (7/10 * x = 10/7)

Multiply. (2/5 * 10/7 = 4/7)

Done!

-

Hope this helped! :)

Answer:

u

Step-by-step explanation:

If 250 readers responded, how many chose museums as their favorite attraction?

Answers

This doesn't give any information

Your question is very vague. More info?

2/5(15p-20)= -8p-3(p-6)

Answers

p = [tex]\frac{26}{17}[/tex]

distribute the parenthesis on both sides of the equation.

6p - 8 = - 8p - 3p + 18

6p - 8 = - 11p + 18 ( add 11p to both sides )

17p - 8 = 18 ( add 8 to both sides )

17p = 26 ( divide both sides by 17 )

p = [tex]\frac{26}{17}[/tex]


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