The positive difference of two integers is 13. The sum of the larger number and the square of the smaller is 103. Give your solution(s) as ordered pair (larger, smaller).

Answers

Answer 1

Answer:

(22, 9)

Step-by-step explanation:

The positive difference of two integers is 13. The sum of the larger number and the square of the smaller is 103. Give your solution(s) as ordered pair (larger, smaller).    I'll call the two integers a and b.

a - b  =  13        a + b² = 103

  +b     +b

a   =  13 + b    plug this into the second equation

a + b² = 103

(13+b) + b²  = 103    subtract 103 from both sides to get one side equal to zero

-103              -103

b² + b - 90 = 0      what factors (two numbers multiply) to -90 that also add up

                             to 1? The only two that work are -9 and 10.  

(b-9)(b+10) = 0      so  b-9 = 0     or    b+10 = 0

                                     +9  +9    or       -10   -10

                                     b = 9      or    b = -10 but both numbers must be positive

b = 9  and a = 13 + b so   a = 13 + 9 = 22

(22, 9)


Related Questions

A farmer sells 9.6 kilograms of apples and pears at the farmer's market. 3/4 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market (i need it expressed in fraction and decimal form please!! im almost out of time to answer :<) please answer asap!!

Answers

Answer:

Decimal form = 2.4 / Fraction form = 1/4

Step-by-step explanation:

We know that the farmer sold 9.6 kilograms of apples and pears where 3/4 of that weight was apples. That means that 1/4 of the 9.6 kilograms were pears. Lets divide 9.6 by 1/4 to get our answer.

9.6 / 1/4 = 2.4

Decimal form = 2.4

Fraction form = 1/4

Expand.
If necessary, combine like terms.
(3+4.)(3 - 4x) =

Answers

Answer:

-16x^2 +9

Step-by-step explanation:

To start this problem I would rearrange so that the terms with the x's come first. Making it look like this

(4x+3)(-4x+3)

Now you take the 4x and distribute it to the -4x and the 3.  

-16x^2+12x  This is the first part

Take the 3 and distribute it to the -4x and the 3 as well.

-12x+9

All you do now is combine the twoso you'd have

-16x^2 +12x -12x +9  Notice there are two terms that have a regular x with no exponent. This means you can combine them to simplify further.

-12x+12x=0  So you no longer have to include this term in your answer.

-16x^2+9 Would then be your final answer.


How many solutions does this equation have?

4x − 10
2
= 2x − 5

A) no solution
B) exactly one solution
C) exactly two solutions
D) infinitely many solutions

Answers

Answer:

d

Step-by-step explanation:

x=3 then the equation has one soultion like 3=3

The equation is a linear equation with one variable then the solution will be exactly one. Then the correct option is B.

What is the linear system?

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

The linear equation is given.

4x − 10² = 2x − 5

In the equation above equation, the number of variables is one.

And the equation is a linear equation which means the degree of the x is one then the solution will be unique.

More about the linear system link is given below.

https://brainly.com/question/20379472

Which equation represents the line
5x - y = 3 in slope-intercept form?

Answers

Answer:

y=5x-3

Step-by-step explanation:

if 5^x = 1/125, find the value of x

Answers

The answer is the following:

X = -3

Answer:

Step-by-step explanation:

hello :

5^x = 1/125

5^x = (1/5)^5      but : 1/5 = 5^-1

so : x= -1

A bag contains 12 marbles: 5 red, 3 blue and 4 green. If two marbles are pulled from the bag consecutively and no replacement occurs, what is the probability of pulling a blue marble followed by another blue marble?

Answers

Answer:

3/12

Step-by-step explanation:

sorry if this is wrong I'm not an expert at math


Tyrone's age is 2 years less than 4 times his younger sister's age. If his younger sister's age is b years, which of the following expressions best shows Tyrone's age?
4b b − 2 2b − 4 4b − 2

Answers

Answer:

Four times his sister's age would be 4b.   his age is two years less, so we need to subtract 2.

put together, this is 4b - 2.

Answer:

Your answer will be  4b - 2

Step-by-step explanation:

Hope this helps!!

You might need:
Calculator
The following dot plot summarizes the distance Roger ran in each of his tennis matches last month. Each dot
represents one game.
Number of kilometers
BI83
Based on this data, what is a reasonable estimate of the probability that Roger runs less than 5 km in his next
tennis match?
Choose the best answer.
Choose 1 answer:
©
22%

Answers

Answer: 33%

Step-by-step explanation:

The measure of arc XZ is 32°.

What is the measure of XYZ?
A. 32°
B. 64°
C. 148°
D. 16°

Answers

Given:

Measure of arc XZ = 32°

To find:

The measure of XYZ

Solution:

The measure of inscribed angle is half of the measure of the intercepted arc.

[tex]$\Rightarrow m\angle XYZ = \frac{1}{2}m(ar XZ)[/tex]

[tex]$\Rightarrow 32^\circ = \frac{1}{2}m(ar XZ)[/tex]

Multiply by 2 on both sides.

[tex]$\Rightarrow 2\times 32^\circ =2\times \frac{1}{2}m(ar XZ)[/tex]

[tex]$\Rightarrow 64^\circ =m(ar XZ)[/tex]

The measure of angle XYZ is 64°.

I need 5 mins!!! pls help!!
60 ÷ 10 × 3 to make it equivalent to 2??

Where should we put the Parentheses?

Answers

Answer:

60÷(10x3)

Step-by-step explanation:

After you do the parenthesis it would be 60÷30=2

Answer:

The answer is you put the parentheses in between 10*3

Step-by-step explanation:

99 POINTS!!! PLEASE HELP ME! I'M FAILING MATH AAAAAAA!!

Answers

Answer:

False

Step-by-step explanation:

Thats the only one i know to amswer sorry but it is false

I couldn’t tell whether or not you wanted it to be solved so I just did it based on the number line.

Write three equations whose solution is x=3.5

Answers

Final answer:

To write three equations whose solution is x=3.5, you can use different algebraic expressions. Three examples are x + 2 = 5.5, (2x - 5) / 3 = 1.8333, and x^2 - 12x + 42 = 0.

Explanation:

To write three equations whose solution is x=3.5, we can use different algebraic expressions to represent the same value. Here are three examples:

x + 2 = 5.5 - In this equation, if we substitute x with 3.5, we get 3.5 + 2 = 5.5, which is true.(2x - 5) / 3 = 1.8333 - If we plug in x=3.5, we get (2(3.5) - 5) / 3 = 1.8333, which is true.x^2 - 12x + 42 = 0 - If we solve this quadratic equation, we find x=3.5 as one of the solutions.

Learn more about Equations with a specified solution here:

https://brainly.com/question/34695214

#SPJ3


Q4. The dimensions of a rectangular sheet of metal are 9.96m by 5.08 m. Find
a. the perimeter of the metal, correct to 1 significant figure
b. the area of the metal, correct to the nearest 0.1 m2

Answers

Answer:

a) 30m

b) 50.6m²

Step-by-step explanation:

Perimeter = 2(length + width)

= 2(9.96 + 5.08)

= 30.08 m

Area = length × width

9.96 × 5.08

50.5968 m²

The Smiths spend 6% of their budget on entertainment. Their total budget this year is $3,000 more than last year, and this year they plan to spend $2,580 on entertainment. What was their total budget last year?

Answers

Answer: Their total budget last year was $40,000.

Step-by-step explanation:

Given : The Smiths spend 6% of their budget on entertainment.

i.e. , The money they spend on entertainment = 0.06 x ( Total budget)

{ 6% is converted to 0.06 , when we divide it by 100 to remove percentage)

Since , this year they plan to spend $2,580 on entertainment.

i.e. 0.06 x ( Total budget )  = $2,580

On dividing both sides by 0.06 , we get

( Total budget )  = $2,580 ÷ 0.06

=  $43,000

Thus , their total budget for this year = $43,000

Also, Their total budget this year is $3,000 more than last year.

Therefore , their last year total budget = ( Total budget this year ) - $3000

= $43,000 - $3000

= $40,000

Hence, their total budget last year was $40,000.


Estimate the size of a crowd at an airshow that occupies a rectangular space with dimensions of 500 feet by 750 feet (to the nearest whole number).

Assume that each person occupies 9 square feet.
A) 10,417 people
B) 20,833 people
C) 41,667 people
D) 83,333 people

Answers

Answer:

C. 41667 people

Step-by-step explanation:

750 * 500 =  375000 / 9 = 41666.666 = 41667

the answer is c.) 41,667 people

ΔA'B'C' was constructed using ΔABC and line segment EH.

2 triangles are shown. Line E H is the line of reflection. Line segment B B prime has a midpoint at point D. Line segment A A prime has a midpoint at point F. Line segment C C prime has a midpoint at point G.

For to be the line of reflection between and , which statements must be true? Select three options.

BD = DB'
DF = FG
m∠EFA = 90°
The line of reflection, EH, is the perpendicular bisector of BB', AA', and CC'.
ΔABC is not congruent to ΔA'B'C'.

Answers

Answer:1,3,4

Step-by-step explanation:

please help me
Find the volume of the cylinder.
Either enter an exact answer in terms of \piπpi or use 3.143.14 for PI

Radius 2
Height 5

Answers

Answer:

The answer is 62.83

Step-by-step explanation: Just do 3.14 times 2 squared or 4 they are the same thing in this context then multiply 5 because that's your height.

what does 3 +3 equal?

Answers

Answer:

6

Step-by-step explanation:

3 + 3 = 6

What is the equivalent measure of 78 centiliters in milliliters?

Answers

170 milliliters is the answer

Answer:

780 milliliters

Step-by-step explanation:

Recall,

1 centiliter = 10 milliliters

So, 78 centiliters = 78 * 10 milliliters

= 780 milliliters

mike made a fruit basket of the total fruit 5 were apples 5/8 were bananas and 1/4 were oranges,how many pieces of fruit did mike use?​

Answers

Answer: 5 7/8

Step-by-step explanation: 5 + 5/8 + 1/4= 5 7/8

The total number of pieces of fruit Mike used is [tex]40.[/tex]

Based on the information given.

1. Let [tex]\( T \)[/tex] be the total number of pieces of fruit.

2. Mike has [tex]5[/tex] apples.

3. [tex]\(\frac{5}{8}T\)[/tex] are bananas.

4. [tex]\(\frac{1}{4}T\)[/tex] are oranges.

Since these fractions represent parts of the total fruit, the sum of the apples, bananas, and oranges should equal the total number of pieces of fruit:

[tex]\[5 + \frac{5}{8}T + \frac{1}{4}T = T\][/tex]

Rewrite the equation with all terms having the same denominator:

[tex]\[5 + \frac{5}{8}T + \frac{2}{8}T = T\][/tex]

Combine the fractions on the left side:

[tex]\[5 + \frac{7}{8}T = T\][/tex]

Subtract [tex]\(\frac{7}{8}T\)[/tex] from both sides to isolate the constant term:

[tex]\[5 = T - \frac{7}{8}T\][/tex]

[tex]\[5 = \frac{1}{8}T\][/tex]

Multiply both sides by [tex]8[/tex] to solve for [tex]\( T \)[/tex]

[tex]\[5 \times 8 = T\][/tex]

[tex]\[T = 40\][/tex]

It has been announced that 64% of all teenagers say they have a television in their bedroom. These findings came from a simple random sample of 1,000 teens. The standard error estimated from this sample was 1.5%

1. Which of the following is the best estimate of the 85% confidence interval for the proportion of teenagers who say that they have a TV set in their bedroom ?
A. 59.5% to 68.5%. C. 62.5% to 65.5%
B. 61% to 67% D. 64% to 100%

Answers

Answer:

D

Step-by-step explanation:

Started at 0 degrees and rose 2 degrees each minute

Answers

if you want to put it into slope intercept form, it would be y=2x
The slope intercept form is y=2x

Abraham just accepted a new job at consulting firm that pays $47,500 during the first year, with an annual increase of 7% per year beginning in the second year. What can Abraham expect to earn in his fifth anniversary with the consulting firm? Round your answer to the nearest dollar

Answers

Answer:

64,125 I think

Step-by-step explanation:

7%x 5 years =35%

35% of 47, 500 is 16625

16625 + 47,500=64,125

Answer:

about $66,621

Step-by-step explanation:

Since its an increase in salary, we want 0.07+1 = 1.07 (if he was losing his salary, it instead would be 0.07-1, but that's not the case here)

Then we plug it in as 47,500(1.07)^x

he's expecting what would he get in his fifth year at the firm. So let's set x = 5.

47,500(1.07)^5 = $66,621.20721 or ≈ $66,621 to the nearest dollar.

Note: This is how I'm doing it in High School. So if this is incorrect, I'm sorry.

Brian tied a 136-foot rope around the perimeter of his rectangular house. He knows that the length of the house is 10 feet less than twice the width. Find the dimensions of Brian’s house.

Answers

Answer:

length 42 cm and width 26 cm

Step-by-step explanation:

Given

Since Brian tied 136 foot rope around the perimeter , hence perimeter of house is 136 foot.

Given that shape of house is rectangular.

formula to calculate perimeter of rectangle can be used which is 2*(L+B)

where L is length of rectangle and B width of rectangle

Let the L and B be length of rectangular side of house

According to question

length of house is 10 feet less than twice the width of house

mathematically it can be represented as

L = 2*B - 10  --->eq. 1

Perimeter of house = 136 feet

using formula of Perimeter of rectangle

136 = 2*(L+B)

substituting the value of length in terms of width from eq. 1 in formula of perimeter

=> 136/2 = 2*B - 10 + B  (2*B+ B = 3B)

=> 68 = 3*B - 10

=> 78 = 3*B

B = 78/3 = 26

Therefore B which is width = 26 CM

length = 2*B - 10= 26*2 - 10 = 52-10=42

length of house = 42  cm

Hence dimension of Brian's house is length 42 cm and width 26 cm

Newton’s Law of Cooling expresses the relationship between the temperature of a cooling object y and the time t elapsed since cooling began, in minutes. This relationship is given by y=ae where c is the temperature of the medium surrounding the cooling object, a is the difference between the initial temperature of the object and the surrounding temperature, and k is a constant related to the cooling object. -The initial temperature of a liquid is When it is removed from the heat, the temperature in the room is . For this object, Use Newton’s Law of Cooling to find the temperature of the liquid after 15 minutes.

Answers

Answer:

79 °F

Step-by-step explanation:

Newton’s Law of Cooling:

[tex]y = ae^{-kt} + c[/tex]

Data

The initial temperature of a liquid is 160 °F The temperature in the room (c) is 76 °FThen a = 160 - 76 = 84 °Fk = 0.23t = 15 minutes

Replacing into the equation:

[tex]y = 84e^{-0.23 \times 15} + 76[/tex]

y = 79 °F

Answer:

The correct answer is 78.7°F

Step-by-step explanation:

Got it right on Edge 2020

What is the solution to the equation 2 (x-3) ^2 =13 help help ASAP !

Answers

Answer:

3+sqrt(13/2)

3-sqrt(13/2)

Step-by-step explanation:

2 (x-3) ^2 =13

Divide each side by 2

2/2 (x-3) ^2 =13/2

(x-3) ^2 =13/2

Take the square root of each side

sqrt((x-3) ^2) =±sqrt(13/2)

x-3 = ±sqrt(13/2)

Add 3 to each side

x-3+3 = 3±sqrt(13/2)

x = 3±sqrt(13/2)

Step-by-step explanation:

x=√3+3,−√1          

                                                        I tried...

1. 5x + 2 = 27
how to work backwards on this type of problem​

Answers

Substrate 2 from 2 and 27 then divide by 5 on both and get 5.

7. What is the area of this figure?

Answers

Answer:

20 m.

Step-by-step explanation:

Formula for rhombus: base x height.

Base: 8

Height: 2.5

2.5 x 8 = 20.

Tip: Usually when finding the area of a rhombus there is another length (in this scenario, 4) to try to fool or trick you. It's the length of the slanted side to the right. A rhombus is a square or rectangle when you take the triangle and piece it into the slanted area, so even though it looks like a complicated parallelogram it really isn't.

Hope this helped ^^

The box-and-whisker plot below shows the age distribution of people at a family reunion.
16
24
32
40
48
56
64
Ages
The stem-and-leaf plot below shows the same data.
089
10 1 4 5
3 3 5 6 6
1 6 6 8 9 9 9
0 1 2 4 6
To 236
01

Answers

Answer: CCCCCC

Step-by-step explanation:

Stephanie works at a store that sells clothing accessories. The supply
function for scarves is P = Q-12, where Pis the price and Q is the quantity of
scarves. If Stephanie sells the scarves for $11 apiece, how many scarves can
the store make?
O
A. 34 scarves
O B. 12 scarves
O c. 23 scarves
O D. 11 marves

Answers

Answer:

23 scarves

Step-by-step explanation:

To solve this you need to plug the price Stephanie sells the scarves for, $11, in for P in the equation and solve for Q.

11 = Q - 12Add 12 to both sides: 23 = Q

The quantity she can make is 23 scarves.

Other Questions
Find the slope of the line through the points (4, -1) and (-2, -1). Find the sum of a geometric series. 20 - 5 + 5/4 - 5/16 + ...A) 220/7B) 16 C) 286/13D) 66 How have earthquakes affected Japan? Type this number in decimal form. (61000)+(2100)+(110)+(71)+(8110)+(51100) How was trade able to flourish before Rome fell? Which of the following was one effect of European colonization in Mesoamerica?A. New cultures were created as the colonists intermarried with native populations.OB. Native populations increased because the colonists improved their quality of life.C. Native populations had to adopt new job skills because slavery was forbidden.D. New governments were created as native populations assumed political power. You wish to lift a 12,000 lb stone by a vertical distance of 15 ft. Unfortunately, you can only generate a maximum pushing force of 2,000 lb.a. What is the amount of work you must input in order to move the stone?b. What is the actual mechanical advantage (AMA) required by a machine to complete the work above?c. You build a ramp to create the ideal mechanical advantage. What is the length of the ramp in feet? Imagine that you have just moved into a house with four other people. One of your housemates, Tony, doesn't seem to like you all that much. If you were to make use of the Ben Franklin effect, what can you do to increase Tony's liking for you? A wildlife biologist catches and releases 20 fish from two different lakes at random locations. He catches 10 fish at Lake Palmer and 10 fish at Lake Dalton. He measures the length of each fish to the nearest quarter of an inch. Palmer Dalton First Quartile 6.75 5.5 Second Quartile (Median) 10.25 6.75 Third Quartile 13 7.5 Based on the samples, what generalization can be made? A. Not enough information is provided to draw any of these conclusions. B. The first quartile value at Lake Palmer is 1.25 inches longer than the first quartile value at Lake Dalton. C. The interquartile range for Lake Dalton is 2 inches greater than the interquartile range for Lake Palmer. D. At least 25 percent of the fish in both lakes are no longer than 6 inchesPlease put the correct answer, if it's correct i will mark with the crown and give a good ratingThanks! What is a consequence of ending a performance appraisal interview on a negative note? Both the supervisor and employee may develop deflated egos. The supervisor who conducted the interview may develop a deflated ego. The employee whose performance was appraised may develop a deflated ego. None of these A well-known Hollywood actress owns a home in Beverly Hills and another one on the French Riviera. She owns her own movie production company along with a large portfolio of stocks. The total value of the different things she owns, minus her debts, is considered her In what way is the desert bloom even more impressive when viewed with an awareness of the underlying science? With a partner, discuss the complex ways desert plants ensure their survival. Cite specific textual evidence to support your ideas. An odd-looking waggon laden with odd-looking packages rolled into Hobbiton one evening and toiled up the Hill to Bag End. The startled hobbits peered out of lamplit doors to gape at it.The Fellowship of the Ring,J. R. R. TolkienWhat does the reader learn about Bag End, Bilbos house, from the passage? Check all that apply.Bag End is at the top of a hill.Bag End has a beautiful garden.Bag End is a very large house.Bag End looks strange and unusual. Bag End is close to other hobbit homes. will give brainiest if answered plz helpp!!!!! A cylinder has a diameter of 10 inches and a height of 8 inches. What is the volume of the cylinder? The cross section of a water bin is shaped like a trapezoid. The bases of the trapezoid are 21 feet and 5 feet long. It has an area of 26 square feet. What is the height of the cross section? Inherited traits are traits that children get from their parents throughA.imitating their parents.B.genesC.InfectionsD.sharing their parents' environment.Correct answer is: B. Genes Explain one way in which geospatial data that iscollected by individuals can assist governmenttransportation departments. A dog is leashed to the corner of a house. How much running area does the dog have? Round your answer to the nearest square foot, If necessary. What is the length of the line segment?