The difference of two integers is 1. The product of the integers is 30. What
are the integers?

Answers

Answer 1

[tex]\large\underline{\bf \red{Step \:by\: Step \:Explanation:}}[/tex]

Let us take ,

First integer be x .Second integer be y .

Also let us consider x > y .

According to first Condition :-

⇒ x - y = 1.

⇒ x = y + 1. .............(i)

According to second Condition :-

⇒ x × y = 30 .

⇒ ( y + 1 )y = 30 . [ From (i) ]

⇒ y² + y = 30.

⇒ y² + y - 30 = 0 .

⇒ y² + 6y - 5y -30 = 0.

⇒ y ( y + 6 ) -5 ( y + 6 ) = 0 .

⇒ ( y + 6 ) ( y - 5 ) = 0 .

[tex]\red{\bf \longmapsto y = 5 , (-6)}[/tex]

Here y can sustain both values 5 and minus 6 as y is an integer.

So , x = -6 , 5 .

Hence possible answers are ,

[tex]\boxed{\purple{\bf x = -6 , y = -5 }}[/tex]

[tex]\qquad\qquad\qquad \bf Or [/tex]

[tex]\boxed{\purple{\bf x = 6 , y = 5 }}[/tex]

.


Related Questions

Between which pair of numbers is the of exact product
379 and 8

Answers

Answer:

3032

Step-by-step explanation:

379 x 8 = 3032

use math, also box method

escribe el número igaul a 5 decenas y 13 unidades​

Answers

Answer:

63

Step-by-step explanation:

The graph below shows the amount of money Janet earned at her new job.
Janet's Earnings
у
80
70
60
50
Money Earned ($)
40
30
20
10
0
2 4 6 8 10 12 14 16
Hours Worked
How much does Janet earn per hour?

Answers

Answer:

b

Step-by-step explanation:

The amount of money Janet earns per hour is given by the slope of the line m = $ 7.50

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 4 , 30 )

Let the second point be Q ( 8 , 60 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = amount of money Janet earns per hour

So , slope m = ( 60 - 30 ) / ( 8 - 4 )

On simplifying , we get

The amount of money Janet earns per hour = 30/4

The amount of money Janet earns per hour = $ 7.50

Hence , the amount of money Janet earns = slope = $ 7.50

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Use the figure to decide the type of angle pair that describes 4 and 5

Answers

Answer:

Alternate interior angles

Step-by-step explanation:

Angles 4 and 5 are alternate interior angles

10
-25 please answer​

Answers

Answer:

(-15)

Step-by-step explanation:

10-25 = (-15)

Please follow me and mark as brainliest

Eloise practiced piano for 25 of an hour. Sarah practiced piano for 34 of an hour.

How much longer did Sarah practice than Eloise?

Answers

Answer:

34 - 25 = 9

Step-by-step explanation:

I’m not sure what it’s asking for, do you mean 25 minutes of an hour and 34 minutes of an hour? If so then Sarah practiced 9 minutes more.
I’m sorry if this isn’t very helpful, I don’t really understand the question :)

What is the sum of (2x2 + 5x -3) and (-3x2 -10 + x2)​

Answers

Answer:5x-13

Step-by-step explanation:

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[tex](2 {x}^{2} + 5x - 3) + ( - 3 {x}^{2} + {x}^{2} - 10) = \\ [/tex]

[tex]2 {x}^{2} - 2 {x}^{2} + 5x - 3 - 10 = [/tex]

[tex]5x - 13[/tex]

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Water flows through a pipe at a rate of 8 pints per hour. Express this rate of flow in cups per week.

Answers

Answer:

2,688 cups per week

Step-by-step explanation:

Lets begin by figuring out the pints per week/pints per day. Multiplying 8 times 24, we get our daily total of 192 pints per day. Multiply this by 7 and we get a total of 1344 pints per week. We now must convert these pints into cups, which can be done by multiplying the total amount of pints by 2. 1344 times 2 = 2,688 cups

What is the z-score for Paula If she got 1400 on the SAT, the mean was 1100 and the
standard deviation was 275?

Answers

Yea it is 275 with standard subtract
1400-deviation=275

The fastest doughnut machine can fry 9600 doughnuts per hour. Which is closest to the number
of doughnuts this machine can fry every second?

Answers

Answer:

9600/60 minutes = 9600/ 360 seconds = 26

Keep practicing :)

Step-by-step explanation:

Answer:

9.6

Step-by-step explanation:

The reason is because you divide this number by 1,000 which gives you 9.6

9600 divided by 1,000= 9.6

Calculate the area of the trapezoid.
12 mm
5 mm
9 mm
________square millimeters

Answers

Answer:

52.5 square millimeters.

Step-by-step explanation:

Area of a Trapezoid = (a+b/2)h

= (9+12/2)•5

=(21/2) • 5

= 10.5 • 5

= 52.5 square millimeters

hope this helps!

Answer:

52.5 mm^2 (square millimeters)

Step-by-step explanation:

Just split the figure into two sections to make a rectangle, and a right triangle (This whole figure can be thought of as a composite figure)

Once that is done, you will notice that the length and width of the rectangle is 9mm by 5mm, and the triangle is 3mm by 5mm (because 12mm - 9mm is 3 mm, and the height of the triangle is shared with the width of the rectangle).

The area of a triangle is 1/2(base×height) [just as a triangle is half of a rectangle], so the area of the rectangle is (length × width).

Therefore the 9mm by 5mm rectangle has an area of 9×5 mm = 45 mm^2, and the 3mm by 5mm triangle has an area of 1/2(5×3) = 15/2 = 7.5 mm^2.

Add both areas to find the total area:

45mm^2 + 7.5mm^2 = 52.5 mm^2.

____________________________

Or using the formula for the area of a trapezoid: A = h (b1 + b2) / 2

Where A is the area, b1 is the first base, b2 is the second base, and h is the height of the figure.

Given that our first base is 9, second base is 12, and our height is 5.

A = h ( b1 + b2 ) / 2 → A = 5 ( 9 + 12 ) / 2 → 5 ( 21 ) / 2 → 105 / 2 → 52.5

Then just put this quantity in mm^2 because it is the area of the figure in that unit.

→ 52.5 mm^2

_____________________________

6m + 4n + 3m - 6

What are the terms? Separate them with a comma.

Answers

6m, +4n, +3m, -6

(I also added a picture)

The quadratic function modeling the height of a ball over time is symmetric about the line , where t is time in seconds. Which statement is true about this situation?


A.

The height of the ball is the same after 1 second and 3 seconds.

B.

The height of the ball is the same after 0 seconds and 4 seconds.

C.

The height of the ball is the same after 0.5 second and 5.5 seconds.

D.

The height of the ball is the same after 1.5 seconds and 3.5 seconds.

Answers

Answer:

A. The height of the ball is the same after 1 second and 3 seconds.

Step-by-step explanation:

The quadratic equation function modeling is used to analyze the relationship between variables in the equation. If the ball is at height and t is time then the ball is on symmetric line which will move for initial 1 second then stabilizes at 3 seconds.

If paper clips are 7/8 of an inch long and cost $0.02 to make, how much would it cost to produce enough paper clips to make a line, end to end, that stretches 56 inches?

Answers

Answer:

$1.12

Step-by-step explanation:

When you multiply 8/7 of 56, you get 64.

This shows that you will need 64 paperclips to make 56 inches worth of paper clips. If each paper clip costs two cents, you need to multiply 56 paperclips by 2 cents. 56x0.02=1.12 so it will cost you 1 dollar and twelve cents

An automatic teller machine gives you $150 in five and ten-dollar bills.  There are two more than twice as many five-dollar bills as there are ten-dollar bills.  How many of each denomination are there?​

Answers

Answer:

There are 7 ten-dollar bills and 16 five-dollar bills.

Step-by-step explanation:

Let's call:

T: Number of ten-dollar bills

F: Number of five-dollar bills

The amount of money withdrawn from the ATM is $150:

10T+5F=150

Dividing by 5:

[tex]2T+F=30\qquad\qquad [1][/tex]

We also know there are two more than twice as many five-dollar bills as there are ten-dollar bills:

[tex]F=2+2T\qquad\qquad [2][/tex]

Substituting [2] into [1]:

2T+2T+2=30

Rearranging:

2T+2T=30-2

Simplifying:

4T=28

Solving:

T=28/4=7

From [2]:

F=2+2*7=2+14=16

There are 7 ten-dollar bills and 16 five-dollar bills.

the martin family‘s truck gets an average of 25 miles per gallon. Predict how many miles they can drive using 7 gallons of gas.

Answers

Answer:

175

Step-by-step explanation:

7 times 25=175

Dominique has $13.75 in her piggy bank. All of the money are quarters. How many quarters are in the piggy bank?

Answers

Answer: I think its 0.55

Step-by-step explanation: if you do 25 times 0.55 because quarter's are 25 cents it equals 13.75

The number of quarters in the piggy bag will be 55.

What is unit conversion?

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure. Unit conversion is the process of changing a quantity's measurement between different units, frequently using multiplicative conversion factors.

Given that Dominique has $13.75 in her piggy bank. All of the money is quarters.

The number of the quarters will be calculated as:-

1 dollar ⇒ 4 quarters

13.75 dollars ⇒ 13.75 x 4 quarters

13.75 dollars ⇒ 55 Quarters

Therefore, the number of quarters in the piggy bag will be 55.

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Find the value of x. 4^3 = x

Answers

Answer:

x=64

Step-by-step explanation:

Is 4.95 a terminating decimal

Answers

Answer:

Definitely

since the definition of a terminating decimal is one that has an ending, and a Repeating decimal is one that never ends.

Step-by-step explanation:

When multiplying the factors 2/3 and 4/7 what is the product of the denominators

Answers

Answer:

21

Step-by-step explanation:

When multipling fractions you go straight across so, all you have to do in the furture is multiply the demonators, anyways all i had to was 3x7 which is 21. Hope this helps and have a wonderful day!

Answer:

21

Step-by-step explanation:

2/3+4/7= 8/21

the top number is the numerator and the bottom number is the denominator.

What is the value to the expression -2.1(4.7+(-7.4))

Answers

The correct answer is 5.67
Someone said 5.67 so

Can you help me identify where I went wrong? I'm having trouble understanding this concept and I need to in order to understand what I will be learning next, thank you!

Answers

Step-by-step explanation:

Your work is correct.  First, you graphed the region.  The minimum or maximum is always at the corner, which you found to be (3.08, 3.64).

The value of C at this point is C = 14.

An experiment consists of determining the speed of automobiles on a highway using a radar equipment. The random variable in this experiment is a:

Answers

Answer:

the speed value that the radar equipment outputs.

Step-by-step explanation:

A random variable in an experiment is also (and most times the case) called a dependent variable. In this scenario, the random variable would be the speed value that the radar equipment outputs. This is because this value depends on the actual velocity of the cars that pass by the equipment. The faster the car is moving when it passes the radar the higher value will be displayed on the equipment. Therefore, depending completely on the vehicles.

you just purchased a new hooded sweatshirt for $24. the total cleaning cost is $2 total because it will be washed with other sweatshirts. you will wear the sweatshirt 18 times this winter. calculate the cost per wearing.

Answers

Answer:

Step-by-step explanation:

espera y termino y te ayudo vale que me falta poco vale

what are the slopes of the two lines?

Answers

Step-by-step explanation:

The slopes of two lines are equal

Find the remainder when f(x) is divided by g(x) given that f(x) = 4x3 − 5x2 − 3x + 2 and g(x) = x − 3.

Answers

Given:

[tex]f(x)=4x^3-5x^2-3x+2[/tex]

[tex]g(x)=x-3[/tex]

To find:

The remainder when f(x) is divided by g(x).

Solution:

According to remainder theorem, if f(x) is divides by (x-c), then remainder is f(c).

Using remainder theorem, if [tex]f(x)=4x^3-5x^2-3x+2[/tex] is divides by [tex]g(x)=x-3[/tex], then remainder is f(3).

Substitute x=3 in f(x).

[tex]f(3)=4(3)^3-5(3)^2-3(3)+2[/tex]

[tex]f(3)=4(27)-5(9)-9+2[/tex]

[tex]f(3)=108-45-7[/tex]

[tex]f(3)=56[/tex]

Therefore, the required remainder is 56.

Use technology to solve the following problem: The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean μ = 38 and standard deviation σ = 7. What proportion of tires have lifetimes between 36 and 46 thousand miles?

Answers

Answer:

0.4859

Step-by-step explanation:

The formula for calculating a z-score is is z = (x-μ)/σ,

where x is the raw score,

μ is the population mean, and

σ is the population standard deviation.

From the question:

mean μ = 38,000

standard deviation σ = 7,000

For.

36 ( thousand miles) = 36,000

z = (x-μ)/σ

z = 36,000 - 38,000/7000

z = -0.28571

Probability value from Z-Table:

P(x = 36000) = 0.38755

For 46 thousand miles = 46,000

z = (x-μ)/σ

z = 46,000 - 38,000/7000

z =1.14286

Probability value from Z-Table:

P(x = 46000) = 0.87345

The proportion of tires that have lifetimes between 36 and 46 thousand miles is calculated as:

P(x = 46000) - P(x = 36000)

0.87345 - 0.38755

= 0.4859

A grocery store sells cheese for $0.48 a pound. What would be the price for 6 pounds of cheese?

Answers

Answer:

$2.88

Step-by-step explanation:

0.48×6=2.88

os the right answer

$0.48 x 6 pounds = $2.88

grrrrrr please help i’ll give u a cookie :)

Answers

im only in 6th grade

Step-by-step explanation:

Express 610.47 in unit form.

Answers

Answer:

6 hundreds

1 tens

0 ones

4 tenths

7 hundredths

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