one positive integer is 5 less than another. the product of the two integers is 36. what are the integers?

Answers

Answer 1

let the numbers be x and (x-5)

x(x-5)=36

x^2-5x-36=0

solving the equation we get

x=9 and x= -4

now find out the integers

Answer 2

1st number = x

2nd number = x-5

x*(x-5) = 36

x^2-5x =36

x^2 -5x-36 = 0

factor the polynomial:

(x-9) (x+4)

9-9 = 0, -4 +4 = 0

so x = 9 or -4

the question states a positive number

so x = 9

the 2 numbers are 9 and 4

Related Questions

michael wittry has been investing inhis roth IRA retirement account for 20 years. Two years ago his account was worth $215,658. after losing 1/3 of its origional value, it then gained 1/2 of its new value back, what is the current value of his roth IRA?

Answers

let's say

a = 215,658

ok... so.. he first lost 1/3 of that

[tex]\bf \textit{\underline{lost} }\frac{1}{3}a\qquad \qquad a-\cfrac{1}{3}a\implies a-\cfrac{a}{3}\implies \cfrac{3a-a}{3}\implies \cfrac{2a}{3} \\\\\\ \textit{then he \underline{gained} }\frac{1}{2}\textit{ of }\frac{2a}{3}\qquad \qquad \cfrac{2a}{3}+\cfrac{\frac{2a}{3}}{2}\implies \cfrac{\frac{2a}{3}}{\frac{2}{1}} \\\\\\ \cfrac{2a}{3}+\cfrac{2a}{3}\cdot \cfrac{1}{2}\implies \cfrac{2a}{3}+\cfrac{2a}{6}\implies \cfrac{4a+2a}{6} \\\\\\ \cfrac{6a}{6}\implies \boxed{a}\implies 215,658[/tex]

so, his nickname might just be even steven, because, he ended up with the same original amount after the 1/2 bump.

His current value is 215658 dollars.

How to calculate a fraction of amount of a total amount ?

To calculate a fraction of amount of a total amount just multiply the given fraction to the total amount.

According to the given question

Michael wittry has been investing in his roth IRA retirement account for 20 years.

Two years ago his account was worth $215,658.

1/3rd of it's original value is

= (1/3) × 215658

= 71886 dollars.

∴ Remaining value is

=(215658 - 71886)

=143772 dollars.

After some time it gained half of it's new value back

∴ Half of this new value is

(1/2) × 143772

= 71886 dollars.

So , the current value is

(143772 + 71886)

=215658 dollars.

Actually his currect value of roth IRA is same as it was two years ago.

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At Avery Middle School, 273 students responded to a survey asking whether a Bulldog, a Lion, or a Tiger should be a new school mascot. Four times as many students chose Tiger. Twice as many students chose Lion as chose Tiger. How many students chose Lion?
A) 39 students
B) 78 students
C) 156 students
D) 273 students

Answers

the answer is c 156 students

Answer with Step-by-step explanation:

273 students responded to a survey asking whether a Bulldog, a Lion, or a Tiger should be a new school mascot.

Let t students chose tiger

b students chose bulldog

and l students chose lion

then, t+b+l=273

Four times as many students chose Bulldog as chose Tiger.

i.e. b=4t

Twice as many students chose Lion as chose Tiger.

i.e. l=2t

So, t+4t+2t=273

i.e. 7t=273

Dividing both sides by 7, we get

t=39

Number of students who chose lion=2t

= 2×39

= 78

Hence, Correct option is:

B) 78 students

Ritz can eat 8 apples in 15 minutes. How long does it take to eat 16 apples at same rate?

Answers

Final answer:

To determine how long it takes to eat 16 apples at the same rate as 8 apples in 15 minutes, set up a proportion and solve for the time.

Explanation:

This question demands basic understanding of ratio and proportion in general.

To find out how long it takes to eat 16 apples at the same rate Ritz eats 8 apples in 15 minutes, you can set up a proportion:

8 apples / 15 minutes = 16 apples / x minutes

8/15 × 1/16 = 1/x

1/15 × 1/2 = 1/x

1/x = 1/30

X = 30

y+y+2=18 please help me 8 th grade 45POINTS

Answers

Thanks for the question!

First, we need to combine like terms:

y + y + 2 = 18
2y + 2 = 18

Now, we need to subtract 2 from both sides

2y = 16

Now, we need to divide each side by 2.

y = 8

Hope this helps!

y+y+2=18
2y+2=18
2y=18-2
2y=16
y=8

A book had a length of 5 inches and a width of 8 inches. What is the perimeter of the book

Answers

26 inches hope this helps

the perimeter is 26in

what is the value of each of these digits in 654321

Answers

6 - 600,000
5 - 50,000
4 - 4,000
3 - 300
2 - 20
1 - 1

Hope this helped!

Suppose a line has slope 4 and passes through the point (-2, 5). Which other point must also be on the graph?

A) (2, 6) B) (-1, 9) C) (-1, 1) D) (-6, 4)

Answers

D) -6,4. because if it has a slope of 4 which is positive it has to have an uphill slope which passes through -2,5, in order for that to happen you plot it and make the line and count the rise over run till you have the slope of 4.

[tex]\bf slope = {{ m}}= \cfrac{rise}{run}\implies 4\implies \cfrac{4}{1}[/tex]

so the rise is 4 units and the run is 1 unit, ok.

now, from point -2, 5, if we move 4/1, that is, "1 unit over the x-axis, and 4 units over the y-axis", we'll find another point, now, a fraction can be positive so long both top and bottom are the same sign, so -4/-1 is the same as 4/1 and therefore, if we move +4 and +1 over the axes we get a point, or if we move -4 and -1 we also get another point, and any other subsequent points from there on.

so, hmm let's check [tex]\bf (\stackrel{x+1}{-2}~,~\stackrel{y+4}{5})\implies (-1~,~9)[/tex]

A machine produces 240 bolts in 25 minutes. At the same rate how many bolts would be produced in 45 minutes

Answers

The rate per minute = 240/25 = 9.6 bolts/minute

And in 45 minutes = 45 x 9.6 = 432 bolts

In 1 minute of those 25 minutes 9.6 bolts were produced. 45*9.6=432. So in 45 minutes 432 bolts were made.

Hope that helped. :^)

Nia is three years older than half Jordans age , if Jordan is eight years old , how old is Nia?

Answers

Hello!

If Nia is three years older than half of Jordan's age, we must divide Jordan's age by 2 (to find half of his age).

Jordan is eight years old:
8 divided by 2 equals 4

4 years old is half of Jordan's age. Now, to find Nia's age, we must add 3 to half of Jordan's age (4).

4+3= 7
Nia is 7 years old.

I hope this helps answer your question! Have a great day!

Answer:

Step-by-step explanation:

50 POINTS!!! DO NOT ANSWER JUST FOR THE POINTS!!! IF YOU DO, ALL OF YOUR EARNED POINTS WILL BE TAKEN~~~~~~~~~~~~~~~

Refer to the graph.

The function is increasing on the interval(s):

The function is decreasing on the interval(s):

The function is constant on the interval(s):

Please explain the steps you used.

Answers

A) [-7,-4] U [4,7]; B) [-4,-1]; C) [1,4]

Write forty and eight tenths as a decimal. 48.1 40.8 40.08 40.008

Answers

What we already know is that we have a 40. Eight tenths would look like the following: .8
This is because it says 8 tenths, meaning the 8 is in the tenths place, right after the decimal. So, the answer would be 40.8

The correct representation of forty and eight tenths as a decimal is 40.8.

Here's an explanation for each option:

48.1: This representation is incorrect because it implies forty-eight and one tenth, not forty and eight tenths.

40.8: This is the correct representation. It means forty whole units (40) and eight tenths (0.8).

40.08: This representation is incorrect because it implies forty whole units (40), eight hundredths (0.08), and no tenths.

40.008: This representation is incorrect because it implies forty whole units (40), eight thousandths (0.008), and no tenths.

Therefore, the correct representation of "forty and eight tenths" as a decimal is 40.8.

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Banks pay interest on savings accounts because

A. they can get more customers that way.

B. they want to encourage you to save.

C. they invest your money.

D. they're just very nice.

Answers

I'm gonna go with C or B cause(based on Google)Banks use the money deposited on savings accounts to lend to borrowers, who pay interest on their loans. After paying for various costs, the banks pay money on savings deposits to attract new savers and keep the ones they have.

Hey there!

Banks aren't in the business of being nice and actually get most of their revenue from their relentless overdraft fees. While it may seem like they're doing something nice or encouraging you to save your money, they're really just encouraging you to become a customer. They don't invest your money, since it needs to be present for you if you want to withdraw it.

Interest on your savings is simply a method for getting new customers.

Hope this helped you out! :-)

Jess observed that 60% of the people at the mall on a particular day shopped for clothes 2500 people at the mall did not shop for clothes that day was ? (Only put numeric values, no symbols

Answers

60% of the total people at the mall shopped for clothes....that means 40% of the people didn't shop for clothes. And there were 2500 people who didn't shop for clothes.
so 40% of the total amount of people is 2500
0.40x = 2500
x = 2500/0.40
x = 6250 total people

check...
shop for clothes...60% of 6250 = 0.6(6250) = 3750
did not shop for clothes....40% of 6250 = 0.4(6250) = 2500
total people = 3750 + 2500 = 6250 (correct)

in summary : there were 6250 people at the mall....3750 of them shopped for clothes and 2500 of them didn't shop for clothes <==

Final answer:

To find the total number of people at the mall, we calculate that 2500 represents 40% of the total. Dividing 2500 by 0.40 gives us the total number of people, which is 6250.

Explanation:

Jess observed that 60% of the people at the mall on a particular day shopped for clothes. If 2500 people at the mall did not shop for clothes that day, we can calculate the total number of people who were at the mall. Since 60% is the percentage that shopped for clothes, then 40% represents the percentage that did not shop for clothes. This means that the 2500 people constitute 40% of the total number of people at the mall.

To find the total number of people, we can set up the equation: 40% of total people = 2500. Translating percentages into decimals (40% = 0.40), the equation becomes 0.40 × total people = 2500. To solve for the total number of people, we divide 2500 by 0.40:

Total people = 2500 ÷ 0.40

Total people = 6250

Therefore, the total number of people at the mall that day was 6250.

Order pairs (x,y) that is the solution to the equation.
5x-y=4
(x,y) =

Answers

Given: 5x-y=4. Create a couple of ordered pairs by choosing x and calculating y from this equation:

x=1 results in y=1. Thus, (1,1) is a solution.
x=-3 results in -15-y=4, or -y=19, or y=-19. Thus, (-3,-19) is a solution.

x=0 results in -y=4, so that y=-4. Thus, (0,-4) is a solution.

386-123= estimate then find the difference

Answers

390-125= 265
Round 386 to 390 and 123 to 125

you estimate 386 to 400 and 123 to 100 so you will get
400-100=300

The sum of three numbers is 99. The first number is 9 more than the third. The second number is 4 times the third. What are the numbers?

Answers

first number=x+9
second number=4x
third number=x
4x+x+x+9=99
6x=90
x=15
first number=24
second number=60
third number=15

Final answer:

The first number is 24, the second number is 60, and the third number is 15.

Explanation:

Let's assign variables to represent the three numbers. Let x represent the third number. Since the first number is 9 more than the third, we can write the equation:

First number = x + 9

Since the second number is 4 times the third, we can write the equation:

Second number = 4x

Now, we can add the three numbers together, according to the given information:

(x + 9) + 4x + x = 99

Simplifying this equation, we get:

6x + 9 = 99

Subtracting 9 from both sides, we have:

6x = 90

Dividing both sides by 6, we find:

x = 15

So the third number is 15. Plugging this value back into the two other equations, we find that the first number is 24 and the second number is 60. Therefore, the three numbers are 24, 60, and 15.

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The arctic lion's Mane Jellyfish is one of the largest known animals. Its tentacles can be as long as 120 feet. Find how this length compares to your height. Round your height to the nearest foot. 120 feet is time as long as feet.

Answers

To solve this problem, we must first know your height. So assuming that your height is 5 feet. Therefore we can divide:

120 feet / 5 feet = 24

So that the answers in the blanks are:

120 feet is 24 times as long as 5 feet

How long will it take you to ski a distance of 36 miles at a speed of 3 miles per 30 minutes?

Answers

So first, divide 36 by 3 to find how many chunks of 30 minutes you need.

12.

Multiply that by 30 minutes to find the total time, and you'll get 6 hours.

Math please help!!!!

Answers

Separate the numbers out into
50 x 5
7 x 5

That gets you 250 and 35
Add the numbers and you get 285, the same as 57 x 5

What are the input variable and the output variable?

number of rowers in a rowboat and the speed of the rowboat

input: number of rowers in the rowboat; output: speed of the rowboat

input: speed of the rowboat; output: number of rowers in the rowboat

input: number of rowboats; output: speed of the rowboat

input: number of rowers in the rowboat; output: the number of rowboats

Answers

The input variable is the number of rowers in a rowboat and the output variable is the speed of the rowboat. When you input the number of rowers into an equation, you should be able to find out how fast the rowboat is going. The speed of the rowboat is directly proportional to the number of rowers.

Answer:

input: number of rowers in the rowboat; output: speed of the rowboat

Step-by-step explanation:

took the test and this was correct

Using place value how to increase 2384598 by six million

Answers

6 million = 6,000,000

2,384,598 + 6,000,000 = 8,384,598

your answer is 8,384,598

hope this helps

Which of the following statements is true? 0.74 < 0.80 0.61 > 0.93 0.83 < 0.94 1.548 < 0.698

Answers

0.74 < 0.80
0.83 < 0.94

Among the given statements, the only true statements are

0.74 < 0.80 and 0.83 < 0.94.

How is this so?

In both cases, the number on the left is less than the one on the right. Which makes the expression and or use of the less than symbol correct.

The greater than symbol (>) and the less than symbol (<) are used to compare two numbers or expressions to determine their relationship.

The greater than symbol (>) represents "greater than" and indicates that the number on the left side is larger than the number on the right side.

The less than symbol (<) represents "less than" and indicates that the number on the left side is smaller than the number on the right side.

For example, 5 > 3 means "5 is greater than 3," and 2 < 7 means "2 is less than 7."

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12 tenths plus 9 tenths =21 tenths = ____ ones _____ tenths

Answers

2100 ones if I am thinking about this right. hope it helps

Is m=1/2 a solution of the equation 6m-8= -5

Answers

Yes correct it is a solution and here is why. :D

Add 8 to both sides

(6m = -5 + 8)

Simplify -5 + 8 to 3

(6m = 3)

divide both sides by 6

(m = 3/6)

simplify 3/6 to 1/2

Answer: m = 1/2

A 30-gallon tank initially contains 15 gallons of salt water containing 6 pounds of salt. suppose salt water containing 1 pound of salt per gallon is pumped into the top of the tank at the rate of 2 gallons per minute, while a well-mixed solution leaves the bottom of the tank at a rate of 1 gallon per minute. how much salt is in the tank when the tank is full

Answers

suppose you wanted the tank to hold 100 gallons of water and it was 50 gallons per cubic feet. How many cubic feet would you need? Obviously, 2 cubic feet. How did you get that?? Well, you divided 100 by 50 to get 2.

O.K., now, let's try YOUR problem. 225000 gallons and 7.5 gallons per cubic feet. How many cubic feet do you need? Must be 225,000/7.5 = 30,000 cubic feet

O.K., now we're half way there. we (should) know that the volume of a prism is

l x w x h. We now know the volume must also be 30,000

so l x w x h = 30000
100 x 20 x h = 30000

you should be able to take it from there.

Problem #2

We approach it the exact same way.

It's too hard as stated. Let's make up an easier problem.

suppose 1 gallon took up 5 cubic feet. If you had 10 cubic feet, how many gallons would you have?
well, clearly, you would have 2 gallons. How did you get it?

Now, how many cubic feet in the cylinder? Well you (should) know that the volume of a cylinder is:

Pi r^2h = 3.14 x 25^2 h = 1962.5 h

Now we have a bit of a problem. You didn't tell me how high the tank is. Let us say it is 10 feet.

So, the tank had 19,625 cubic feet.

Go back to the start of this problem and you will know what to do next.

Final answer:

Calculate the amount of salt in a tank given rates of inflow and outflow, and determine the final salt quantity when the tank is full.

Explanation:

A 30-gallon tank initially contains 15 gallons of salt water containing 6 pounds of salt.

Find the initial amount of salt per gallon in the tank: 6 pounds / 15 gallons = 0.4 pounds per gallon.

Calculate the rate of salt being added and leaving the tank: In: 1 pound per gallon × 2 gallons per minute = 2 pounds per minute; Out: 0.4 pounds per gallon × 1 gallon per minute = 0.4 pounds per minute.

Subtract the rate of salt leaving from the rate of salt coming in to find the net rate of salt accumulation: 2 pounds per minute - 0.4 pounds per minute = 1.6 pounds per minute.

How much salt is in the tank when it is full?

Using the net rate of salt accumulation, calculate the time needed to fill the tank: 30 gallons / 2 gallons per minute = 15 minutes.

Finally, calculate the total amount of salt in the tank when full: 15 minutes × 1.6 pounds per minute = 24 pounds of salt.

A rectangular plot of land has an area of 1/8 square mile. Its width is 3/20 mile.What is the length of the plot of land?

Answers

A = L * W
A = 1/8
W = 3/20

1/8 = 3/20L
(1/8) / (3/20) = L
1/8 * 20/3 = L
20/24 reduces to 5/6 miles = L <===

Is y=2x-8 and 2x-y=8 a dependent independent or inconsistent

Answers

Note that 2x-y=8 can be solved for y: y=2x-8. This is identical to the first equation. The graph of one is exactly the same as the graph of the other. Thus, the two equations are dependent.

Answer:

dependent

Step-by-step explanation:

[tex]y=2x-8[/tex] and [tex]2x-y=8[/tex]

First equation is already solve for y

LEts solve the second equation for y

[tex]2x-y=8[/tex]

Subtract 2x on both sides

[tex]-y=-2x+8[/tex]

Divide the whole equation by -1

[tex]y=2x-8[/tex]

After solving for y, both equation are same

When both the system of equation are same then it has infinite solutions.

They are said to be dependent.

What is 10000 times 20000000

Answers

the answer to you problem given is, 200000000000

The answer is 200,000,000,000
Hope this helps you!
Have a nice day!

kim has 3/4 pound servings of grapes. how many 1/8 pound servings can Kim make from his grapes

Answers

he can make 6 servings

(3/4) / (1/8) =
3/4 * 8/1 =
24/4 =
6 <=== there are 6 one-eighth pound servings

solve for x −1/2(x+2)+11/2x=3

Answers

The answer to this problem is 4/5 Hope I helped!

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