Two positive numbers are in the ratio 2 : 3. Find the numbers if ​(a) their sum is 55 and ​(b) their product is 384.

Answers

Answer 1

say the numbers are "a" and "b", we know that they're in the ratio of 2:3, or namely that

[tex]\stackrel{\textit{in the ratio of 2 to 3}}{a~:~b\qquad \qquad 2:3}\qquad \qquad \implies \qquad \cfrac{a}{b}=\cfrac{2}{3}\implies \cfrac{3a}{2}=b \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{their sum is 55}}{a + b = 55}\implies a + \cfrac{3a}{2}=55\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2\left( a + \cfrac{3a}{2} \right)=2(55)} \\\\\\ 2a+3a=110\implies 5a=110\implies a = \cfrac{110}{2}\implies \boxed{a = 22}[/tex]

[tex]\stackrel{\textit{we know that}}{\cfrac{3a}{2}=b}\implies \cfrac{3(22)}{2}=b\implies \boxed{33=b} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{their product is 384}}{ab=384}\implies a\left( \cfrac{3a}{2} \right)=384\implies \cfrac{3a^2}{2}=384\implies 3a^2=768 \\\\\\ a^2=\cfrac{768}{3}\implies a^2=256\implies a=\sqrt{256}\implies \boxed{a=16} \\\\\\ \stackrel{\textit{we know that}}{\cfrac{3a}{2}=b}\implies \cfrac{3(16)}{2}=b\implies \boxed{24=b}[/tex]

Answer 2

The positive numbers for both the parts are obtained as 22,33 and 16,24 respectively.

How to write a linear equation?

A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.

(a) As per the question, the numbers can be considered as 2x and 3x respectively.

Then, the equation for their sum can be written as follows,

3x + 2x = 55

⇒ 5x = 55

⇒ x = 11

The numbers are obtained as 2 × 11 = 22 and 3 × 11 = 33.

(b) Similarly, the equation for the product of numbers can be written as,

3x × 2x = 384

⇒ 6x² = 384

⇒ x² = 64

⇒ x = 8

The numbers are obtained as 2× 8 = 16 and 3 × 8 = 24.

The required number for both the cases are 22,33 and 16,24 respectively.

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Related Questions

The athlete drink 16 ounces of water every two hours starting at 7:30 AM and continuing for the next 14 hours. A) how many quarts did the athlete consume? B) how many pints of water did the athlete consume? ​

Answers

Answer:

16x7 = 112 (16 ounces, 7 hours) 112 ounces to pints = 7 pints of water

Step-by-step explanation:

Helppppppppppppp helppppppppppppp

Answers

Answer:

Should be the first answer, x=5

Step-by-step explanation:

This would flip the graph and the square would land on top of where it currently is.

3. Let Angle ABC be an isosceles triangle with AB = AC. Which of the following describes
LB of the triangle?
A. Exterior Angle
B. Base Angle
C. Vertex Angle
D. Remote Interior Angle

Will mark Brainiest

Answers

Answer:
It’s should be D because
Step by step explanation

is (2×3)×4=2×(3×4) an example of associative property of multiplication?

Answers

Answer:

Yes.

Step-by-step explanation:

Associative property of multiplication is:

(A×B)×C = A×(B×C).

It says that "The way of grouping of terms doesn't change the product."

So, given example (2×3)×4=2×(3×4) is an example of associative property of multiplication.

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

~AH1807

How do u do these percentages questions

Answers

Answer:

Step-by-step explanation:Determine the initial format of the number to be converted to a percentage. ...

Carry out a mathematical process on the number to be converted to a percentage. ...

Multiply the result of the mathematical process by 100. ...

Find the percentage of the original or real number. ...

Multiply the final number by 100.

1. The length of each side of a square increased by 40%. By what percent does the area of the square increase?
2. The length of a rectangle increases by 20%, and the width decreases by 20%. What is the overall percent change in the area of the rectangle?

(they are two separate questions)

Answers

Answer: to number 1 :The area of the square increases by 96% to number 2:  increase in width = 50%

Step-by-step explanation

18/5=t/4 what does t=

Answers

Answer:

72/5

Step-by-step explanation:

18/5 x4 = t/4 x4

(18x4)/5 = t

t = 72/5

What is the diameter of a circular swimming pool with a radius of 9 feet? Enter only the number

Answers

Answer:d=18FT

Step-by-step explanation:

YOUR WELCOM :)

The diameter is double the radius of the circle. So you would do 9*2 = 18 feet.

The question only asks for the number though so you can just enter 18.

Given ABCD, solve for x.
A. 11
B. 13
C. 14
D. 12

Answers

Answer:

Step-by-step explanation:

Because you have a parallelogram, the two angles shown are "same side interior angles" which means they add up to 180°.

We would say that they are supplementary (they add up to 180°)

So add them together and set them equal to 180°

(4x+18) + (8x+30) = 180°

This is all adding, so we dont really need any of these parenthesis.

4x+18+8x+30=180

Add the x terms together and add the constants (plain numbers) together.

12x + 48 = 180

Subtract 48 from both sides of the equation.

12x = 132

Divide both sides by 12

x = 11

I have 100 points
i need some help!!

Answers

Answer:

6c+2(5-7c)=6c+10-14c

=10-8c=-8c+10

A. -8c+10 is correct option.

Thanks :)

Which fractions are equivalent to the fraction below. 20/32

Answers

Answer:

5/8

Step-by-step explanation:

The answer is 5/8 because 4*5 equals 20 and 4*8 equals 32. Therefore, you have to do the same thing you do to the numerator to the denominator. In addition, you I divided 20 by 4 which is 5 and 32 divided by 4 is 8. So, it is 5/8.

Question 1
A number, w, is located to the left of 5 on the number line.
Which inequality represents this situation?
A
W> 5
B
w < 5
с
w > -5
D
w < -5

Answers

The answer is c because left side of number line is negative

A = 1011 + 337 + 337/2 +1011/10 + 337/5 + ... + 1/2021

Answers

The sum of the given series can be found by simplification of the number

of terms in the series.

A is approximately 2020.022

Reasons:

The given sequence is presented as follows;

A = 1011 + 337 + 337/2 + 1011/10 + 337/5 + ... + 1/2021

Therefore;

[tex]\displaystyle A = \mathbf{1011 + \frac{1011}{3} + \frac{1011}{6} + \frac{1011}{10} + \frac{1011}{15} + ...+\frac{1}{2021}}[/tex]

The n + 1 th term of the sequence, 1, 3, 6, 10, 15, ..., 2021 is given as follows;

[tex]\displaystyle a_{n+1} = \mathbf{\frac{n^2 + 3 \cdot n + 2}{2}}[/tex]

Therefore, for the last term we have;

[tex]\displaystyle 2043231= \frac{n^2 + 3 \cdot n + 2}{2}[/tex]

2 × 2043231 = n² + 3·n + 2

Which gives;

n² + 3·n + 2 - 2 × 2043231 = n² + 3·n - 4086460 = 0

Which gives, the number of terms, n = 2020

[tex]\displaystyle \frac{A}{2} = \mathbf{ 1011 \cdot \left(\frac{1}{2} +\frac{1}{6} + \frac{1}{12}+...+\frac{1}{4086460} \right)}[/tex]

[tex]\displaystyle \frac{A}{2} = 1011 \cdot \left(1 - \frac{1}{2} +\frac{1}{2} - \frac{1}{3} + \frac{1}{3}- \frac{1}{4} +...+\frac{1}{2021}-\frac{1}{2022} \right)[/tex]

Which gives;

[tex]\displaystyle \frac{A}{2} = 1011 \cdot \left(1 - \frac{1}{2022} \right)[/tex]

[tex]\displaystyle A = 2 \times 1011 \cdot \left(1 - \frac{1}{2022} \right) = \frac{1032231}{511} \approx \mathbf{2020.022}[/tex]

A ≈ 2020.022

Learn more about the sum of a series here:

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A is equal to 1,685.00049.

Given that A = 1011 + 337 + 337/2 +1011/10 + 337/5 + ... + 1/2021, the following calculation must be performed to determine the result of this operation:

337/2 = 168.5 1011/10 = 101.1 337/5 = 67.4 1/2021 = 0.00049  1011 + 337 + 168.5 + 101.1 + 67.4 + 0.00049 = A 1685.00049 = A

Therefore, A is equal to 1,685.00049.

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what is 70*77 please help

Answers

Answer: 5390
70*7=5390
Here is why: The result of multiplying 70 with 77 is called the product. Thus, the product of 70 and 77 is as follows:

5390

In other words, we find the product of 70 and 77 by simply calculating 70 times 77 which equals 5390. Pretty easy huh?

If someone asks you, "What is the product of 70 and 77?", your answer will be:

70 x 77 = 5390

To find any product in the future on your own, just remember that the product is the answer you get when you multiply numbers together.

using guassion elimination metheed x+2y-3y=11,3x+2y+z=1, 2x+y-5z=11

Answers

3y-2y+2y-y+3x-x+2x+z+5z=1+11+11
2y+4x+6z=23

Find the sum of 1/8 and -3/4 . can you please give an explanation would mean very well please

Answers

First, find the least common denominator. In this case it would be 8. If you are multiplying 4 by 2 to get 8, you must also multiply the numerator by 2.
1/8 + -3(2)/4(2)
1/8 + -6/8
Write all numerators above the common denominator.
1-6/8
Calculate.
-5/8

Hope this helps!

Divide: 1/2÷1/10
SHOW WORK

Answers

Answer:

5

Step-by-step explanation:

1/2÷1/10=

1/2x10/1=

10/2=5

Answer:

the answer is 5

Step-by-step explanation:

keep change flip

1/2 x 10 =5

I need help understanding this

Answers

Step-by-step explanation:

I am sorry but I cannot see your question

given 6x+5y=12 find the equation of the line parallel to it passing through (1,10).

Answers

Answer:

y = -6/5x+56/5

Step-by-step explanation:

given that a/b = 2/3 and b/c = 3/7 find A:B:C

Answers

Answer:

2:3:7

Step-by-step explanation:

a/b = 2/3

That gives us a clue that a=2 and b=3

But to make sure it states b/c = 3/7

So A:B:C is

2:3:7

Hope this helps!

What is 4/5 - 1/4 in the simplest form

Answers

[tex]\cfrac{\underline{4}}{5}-\cfrac{1}{4}\implies \cfrac{(4)(\underline{4})~~ - ~~(5)(1)}{\underset{\textit{using this LCD}}{20}}\implies \cfrac{16-5}{20}\implies \cfrac{11}{20}[/tex]

(dy)/(dx) = (x ^ 2)/(1 + y)

Answers

Answer:
Bye, hope this helps you succeed in school!

ratio
a. L
b. bozo
d. your life is bad
c. ratio again

Answers

Answer:

d

Step-by-step explanation:

The Answer is d for sure

he school that Tony goes to is selling tickets to a play. On the first day of ticket sales the school
sold 9 adult tickets and 8 student tickets for a total of $164. The school took in $73 on the second
day by selling 2 adult tickets and 7 student tickets.

What is the price each of one adult ticket?

What is the price each of one student ticket?

Plz explain how to do this

Answers

Answer:

The price of 1 adult ticket is 12 dollars, and the price of a ticket for one student is 7 dollars

Step-by-step explanation:

Make a system of equations for the two days that the play was shown.

Let x = the price of an adult ticket

Let y = the price of a student ticket

For the first day:

9x+8y=164

For the second day:

2x+7y=73

Now, we can solve using the elimination method. Multiply the first equation by 2 and the second equation by 9. Then swap the order of the equations.

18x+63y= 657-18x+16y= 3280x+ 47y= 329divide both sides by 47y = 7Plug in 7 for y for the 2nd equation2x+7(7)=732x+49=73subtract 49 from both sides2x= 24divide both sides by 2x = 12 Check:2(12)+7(7)=7324+49= 73!

Answer: And I don’t know math

Step-by-step explanation:

Description of a turn for those who have never done math / for a child​

Answers

Answer:

Step-by-step explanation:

1+1=2

2+2=4

3+3=6

4+4=8

5+5=10

A shirt costing $34 is on sale for 30% off. What is the new price of the shirt after the discount?

Answers

Answer:

$23.80

Step-by-step explanation:

30% off means we take 30% off of the original price, or we calculate

(1-30%)=70% of the shirt's price

34*70%=23.8

Find the area and perimeter of a square whose side length is
2x+3

Answers

Answer:

Area = 4x^2 + 12x + 9

Perimeter = 8x + 12

Step-by-step explanation:

11. m2 = 340 Find m 24 and explain how you know. (2 points)
1
X
3
Drawing not to scale.

Answers

Answer:

Angle 4 also has a measurement of 34 degrees because opposite angles of intersecting lines are congruent. In other words, angles 2 and 4 are congruent, so are angles 1 and 3.

50pt Which of the following are maximum and minimum points of the function y=sin(x+ π)?

Answers

Answer:

  none of the above

  Maximum (3π/2, 1); Minimum (π/2, -1)

Step-by-step explanation:

The sine function is shifted left 1/2 cycle by the addition of π to x in the argument. That basically inverts the function, so it is equivalent to ...

  y = -sin(x)

This has a minimum of -1 at π/2, and a maximum of +1 at 3π/2. This does not match any of the offered answer choices.

__

You might want to discuss this question with your teacher.

Answer:

The correct answer is C!

Step-by-step explanation:

The dude that said there’s no answer doesn’t know what he’s talking about.

True or false



Plz help​

Answers

[tex]0 - (-\frac{31}{43})=0+ \frac{31}{43}=\frac{31}{43}[/tex]

ANSWER : true

ok done. Thank to me :>

Answer:

True

Step-by-step explanation:

[tex]0 - ( - \frac{31}{43} ) \\ 0 + \frac{31}{43} \\ = \frac{31}{43} [/tex]

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