A magician asks a volunteer to think of two different positive integers without telling her what they are. She then asks him to calculate x, the sum of the larger number with the square of the smaller, and y, the difference between the numbers. The volunteer tells her that x = 9 and y = 3. Find the original numbers.

Answers

Answer 1

Answer: 2 and 5.

Step-by-step explanation: We can use algebra to solve for the original numbers. Let's call the smaller number "a" and the larger number "b". From the information given, we know that:

x = b + a^2

y = b - a

The volunteer tells the magician that x = 9 and y = 3. So we can use these values to create a system of equations:

b + a^2 = 9

b - a = 3

To solve for the original numbers, we can first add the two equations together to eliminate b:

a^2 + 2a + 2 = 12

a^2 + 2a = 10

a^2 + 2a - 10 = 0

(a + 5)(a - 2) = 0

This tells us that the two solutions for a are -5 and 2. But since a is a positive integer, we know that it must be 2.

We can now substitute this value of "a" back into the original equations to find "b":

b + a^2 = 9

b + 2^2 = 9

b + 4 = 9

b = 5

So the original numbers are 2 and 5.

Related Questions

Szklanka ma pojemnóść 250ml czyli 250cm³. Ile szklanek można napełnić wodą z litrowej butelkki

Answers

Answer:

75cm

Step-by-step explanation:

Solve the system of linear equations by elimination. Check your solution. 3x + 2y = 7 -3x + 4y = 5

Answers

Answer:

(3x+2y=7-3x+4y)=5

3x+3x+2y-4y-7=5

6x-2y-7=5

6x-2y=5+7

=12

2(3x-y)=12

3x-y=12/2

= 6

Mrs. Dyson is making trail mix for Christmas gifts. She needs 4 cups of nuts, 6 ups of raisins, and 5 cups of chocolate chips. What percent of the trail mix are
raisins
HINT: Use Part to Whole and Reduce

A.60%
B.40%
C.6%
D.15%

Answers

Answer:

Step-by-step explanation:

15/6=2.5

100/2.5=40

A human heart beats an average of 80 beats per minute. How many beats is this in an hour?

Answers

Answer:

4800 beats an hour

Step-by-step explanation:

there are 60 minutes in and hour

the heart beats 80 times per minute( that is actually a very high heart rate)

80*60=4800 per hour

I believe the answer is an average of 4800 beats per hour.
We know that the heart beats an average of 80 beats per minute and there are 60 minutes in an hour. We can use this information and multiply 80x60 to find the average amount of heartbeats in an an hour.

Help me plz., ,, ,, ,, ,,,

Answers

Answer:

1. 100000

2. 16777216

3. x7

4.64

5.1/64 (Decimal: 0.015625)

Step-by-step explanation:

Ava pours 3 gallons of paint equally into 5 cans. How many gallons of paint will there be in each can?

Answers

Answer:

0.6

Step-by-step explanation:

first you well have a 3 and then dived it by 5 and after you dived them to you well get the answer 0.6

Kelly works at her own nail
salon. Today, she did 11
manicures and received $52.25
overall in tips. If x represents the
cost of each manicure, which of
the following equations can be
used to find the total amount of
money she earned, including
tips, for her nail salon today?
A. y = 11(x + 52.25)
B. y = 52.25x + 11
c. y = 52.25(x + 11)
D. y = 11x + 52.25

Answers

Answer:

(x×11)÷52.25

Step-by-step explanation:

if 11=52.25 and y=x then x11÷52.25 i think that is the answer

Michael needs to gain weight. He weighs 120 pounds and thinks he can gain 2 pounds a week. He wants to weigh at least 165 pounds. How long will it take him to reach this goal? inequality: solution:

Answers

Answer:

The answer is B

Step-by-step explanation:

3 times the length of a field increased by 4 times the width gives 24 units. Two times the length decreased by 3 times the width is -1 unit. Find the dimensions

Answers

Answer:

width = 3

length = 4

Step-by-step explanation:

Ok so you can form a system of equations where w is the width and l is the length:

3l + 4w = 24

2l - 3w = -1

you want to eliminate one of the variables and then solve, so you can first take the top equation and multiply both sides by 2:

6l + 8w = 48

next, multiply the second equation by 3:

6l - 9w = -3

now that both include 6l, you can subtract the two equations

6l + 8w = 48

- (6l - 9w = -3)

17w = 51

divide both sides by 17

w = 3

Plug w = 3 into the equation 3l + 4w = 24:

3l + 4 * 3 = 24

3l + 12 = 24

subtract 12 from both sides

3l = 12

divide both sides by 3

l = 4

please help me on this will give you brainliest

Answers

Answer:

2,010,000

Step-by-step explanation:

3 x 10^5

10^5= 100000

3 x 100000 = 300000

300000 x 6.7 = 2,010,000

Hope this helps

Answer:

Im not 100% sure but i think its 44,776.1194

Step-by-step explanation: What you do is multiply 3 x 100,000 because 10 to the 5th power is 100,000. Then you divide 300,000 by 6.7 and get your answer of 44,776.1194. Sorry if its incorrect

Hi! PLS HELP!!! 20 POINTS!

A children's pool contains 17,500 milliliters. How many liters are in the pool?

1.75 liters
17.5 liters
175 liters
1,750 liters

pls help!
If u put something of the topic imma report u
Have a great day! :)
(its not a I did it and got it wrong!!)

Answers

Answer:

17.5 liters

Step-by-step explanation:

hope its the answer your looking for

17.5 liters hope this helps

Finding a percentage of o total amount without a calculator...
An item is regularly priced at $35. It is on sale for 40% off the regular price. How much (In dollars) Is discounted from the regular price?
Amount discounted: si
х
5
?

Answers

9514 1404 393

Answer:

$14

Step-by-step explanation:

Computing 40% can be done a couple of ways.

40% = 40/100 = 4/10 = 2/5

40% of 35 = (2/5)(35) = 2(35/5) = 2(7) = 14

40% = 4/10 = 2(2(1/10))

40% of 36 = 2(2(1/10)(35)) = 2(2(3.5)) = 2(7) = 14

The amount discounted is $14.

Item 4 Find the distance between the two points. (4, −5), (−1, 7)

Answers

Answer:

yes , the distance between the two points is 13 units

Is -50 greater than 2

True or false

Answers

FALSE

because negative (-) numbers are always smaller than positive (+) numbers

How do you list all of the rational zeros of g(x)=x^4-3x^3-53x^2-9x?

I only know how to list them for when the last number doesn’t have the variable x.

Answers

Answer:

No lo se

Step-by-step explanation:

is a rectangle a plane shape

Answers

Answer:

A plane shape with four straight sides and four right angles for corners is called a rectangle.

Step-by-step explanation:

please answer this question

Answers

Answer:

activity2

1. ( 14.4) adn

2.(0.616) adn

3.( 5-36) adn

Please help! Complete answers please.

Answers

Answer:

m3 = 103 degrees

m4 = 77 degrees

Step-by-step explanation:

comment if you want me to explain please :)

The interior angles of ∆AUL (or any triangle for that matter) sum to 180°, so

∠3 + 20° + 57° = 180°

===> ∠3 = 103°

Angles ∠3 and ∠4 occur on the same ray LP, so they are supplementary to one another. In other words,

∠3 + ∠4 = 180°

so that

∠4 = 180° - 103° = 77°

john makes $400 per week. What does it mean for him to get a 150% salary raise? Explain in words and then give an example showing a calculation.
plzzzzzzzzzzzzzzzzzzzzzz help me

Answers

Answer:

1200

Step-by-step explanation:

400 x 300 because double

A quantity with an initial value of 720 decays continuously at a rate of 9% per hour. What is the value of the quantity after 69 hours, to the nearest hundredth?

Answers

Answer:

1.45

Step-by-step explanation:

f(t)=720e^rt

f(t)=720e

Continuously uses Pe^(rt)

r\text{: decays }9\% \

r: decays 9%→−0.09

per hour

f(t)=720e^{-0.09t}

f(t)=720e

−0.09t

(where t is in hours)

69\text{ hours: no time conversion necessary}

69 hours: no time conversion necessary

hours are the only units in the problem.

\text{Plug in }t=69

Plug in t=69

f(69)=720e^{-0.09(69)}

f(69)=720e

−0.09(69)

1.44665097413

\approx 1.45

≈1.45

Round to the nearest hundredth

Please work out -80 ÷ -8

Answers

Answer:

Step-by-step explanation:

-80 / -8 = 10

the negatives cancel each other out

-80÷-8=10

.....................

A student was given the following instructions:
"Given f(x) = 6x + 4, find f(4)."

Answers

Answer: 28
X=4
You plug in ‘4’ to the equation
6(4)+4= 28

Help pls!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

9x6=54 ur welcome:)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The perimeter of a rectangle formula is P = 2*Length + 2*Width

The length is the largest side, so it's 9.

The width is the smallest side, so it's 6.

So, our formula would be like this: P = 2*9 + 2*6.

solve using quadratic equation

Answers

Answer:

±5 is your answer

Step-by-step explanation:

x²-25=0

comparing above equation with ax²+bx+c

we get

a=1

b=0

c=-25

by using quadratic equation

x=(-b±√(b²-4ac))/2a=(-0±√(0²-4×1×-25))/2×1

=±{√(100)}/2=±(√10²)/2=±10/2=±5

Answer:

5, - 5

Step-by-step explanation:

x^2 = 25

x = ± √25

= ± 5

x = 5, - 5

If you know that a denominator in your ratio table is 12 and one of
the other ratios is 1/3, what numerator should you apply to your
12 denominator to make that ratio have the same value?

Answers

Answer:

the numerator is 4

Step-by-step explanation:

1/3 = ?/12

How did the values of the denominator change from 3 in the fraction 1/3 to 12 in the fraction ?/12? 3 was multiplied by 4 to get 12.

Then, since 12 is 4 times 3, then the missing numerator must be 4 times 1.

1/3 = 4/12

Answer: the numerator is 4

What’s the radius of a circle with the circumference of 37.68 feet

Answers

Answer:

r≈6ft

Step-by-step explanation:

Using the formula

C=2πr

Solving forr

r=C

2π=37.68

2·π≈5.99696ft

pls mark as brainliest

Nita needs at least $85 to buy a skateboard. She already has $61. Which graph best represents all the possible dollar amounts that Nita can save to buy a skateboard? (5 points)

Number line graph with open circle on 24 and shading to the right.
Number line graph with closed circle on 24 and shading to the right.
Number line graph with open circles on 0 and 24 and shading in between.
Number line graph with closed circles on 0 and 24 and shading in between.

Answers

Answer:

Number line graph with closed circle on 24 and shading to the right.

Step-by-step explanation:

First, the graph has to have a closed circle on only 24.

Since she has $61 and needs at least $85 to buy a skateboard, she needs to have at least $24 saved to buy one.

This means the last 2 answer choices are wrong, because there cannot be shading in between.

The first answer choice is also wrong because it puts a open circle, instead of a closed one, on 24.

So, the correct answer is Number line graph with closed circle on 24 and shading to the right.

give the other brainliest

Find the radius of a circle in which an inscribed square has a side of 8 inches.

Answers

Answer:

r = 4

Step-by-step explanation:

side of square is the same as the diameter of the circle

if diameter is 8 then radius is 4

You deposit $500 in an account that earns 6.5% annual interest compounded yearly. Write a function that represents the balance y (in dollars) after x years.

Answers

Answer:

f(x)=.65+y

Step-by-step explanation:

The function for compound interest is A = 500 ( 1.065 )ˣ

What is Compound Interest?

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

Let the compound interest amount be represented as A

Now , the interest rate r = 6.5 %

The number of times the interest is applied = yearly

The principal amount P = $ 500

n = 1 ( compounded yearly )

t = x ( number of years )

So, the function that represents the balance y (in dollars) after x years is:

y ( x ) = 500 ( 1 + 0.065/1 )ˣ

On simplifying , we get

y ( x ) = 500 ( 1.065 )ˣ

Hence , the function is A = 500 ( 1.065 )ˣ

To learn more about compound interest click :

https://brainly.com/question/21270833

#SPJ2

Please I need formula and faces

Answers

Answer:

+3[36 hahahahhh Sana all mag hanap ka nlg sa iba

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