The sum of three numbers is 14. The largest number is 4 times the smallest number. The sum of the smallest and twice the largest is 18. What are all three numbers?

Answers

Answer 1

Answer:

a = 2, b = 4, c = 8

Step-by-step explanation:

Let:

First (smallest) number = a

Second number = b

Third number(Largest) = c

The sum of three numbers is 14.

a + b + c = 14...... Equation 1

The largest number is 4 times the smallest number.

c = 4a.... Equation 2

The sum of the smallest and twice the largest is 18.

a + 2c = 18........ Equation 3

We substitute Equation 2 in Equation 3

to solve for a

a + 2(4a) = 18

a + 8a = 18

9a = 18

a = 18/9

a = 2

Hence, the smallest number = 2

We find c

c = 4a.... Equation 2

c = 4(2)

c = 8

The largest number is 8

We find b

a + b + c = 14...... Equation 1

2 + b + 8 = 14

b + 10 = 14

b = 14 - 10

b = 4

What are all three numbers?

a = 2, b = 4, c = 8


Related Questions

the product of the sum and the difference of 8x and 4y

Answers

Answer:

4

Step-by-step explanation:

o dont really know. I dont understand the question

You can’t solve this because you can’t add or subtract different variables. However you can multiply different variables and it’ll give you 32xy

Find the slope of the line passing through the points (-4,7) and (2,-8)

Answers

Answer:

[tex]m=\frac{-5}{2}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step-by-step explanation:

Step 1: Define

Point (-4, 7)

Point (2, -8)

Step 2: Find slope m

Substitute:                    [tex]m=\frac{-8-7}{2+4}[/tex]Subtract/Add:               [tex]m=\frac{-15}{6}[/tex]Simplify:                        [tex]m=\frac{-5}{2}[/tex]

On Monday, Deborah ran 3 2− 5miles and on Tuesday she ran 4 1− 5miles. How many miles did she run on these two days together?

Answers

Mixed fraction:

3 2/5 = 17/5

4 4/5 = 24/5

Miles she ran:

17/5 + 24/5

= 41/5 miles or 8.2 miles

find the missing side lengths. leave ur answers as radicals

Answers

Because of the 45 45 90 theorem since the hypotenuse is 9√2 x and y are both 9

Recidivism occurs when a person continues to commit criminal behavior even after having been punished. A prison official wants to estimate the proportion of cases of recidivism. Examining the records of 250 convicts, the official determines that there are 65 cases of recidivism. Construct a 99% confidence interval for the proportion of cases of recidivism.A. (0.331, 0.567)B. (0.188, 0.332)D. (0.289, 0.431)E. (0.069, 0.111)

Answers

Answer:

Option (C)  [0.2574 , 0.2626]

Step-by-step explanation:

Of 250 convicts, there are 65 cases of recidivism.

- Construct a 99% confidence interval for the proportion of cases of recidivism.

This calls for first finding the proportion of cases of recidivism. This will be 65/250  = 0.26

You are 100% confident that the proportion of cases of recidivism is 0.26

You will be 99% confident that the recidivism cases are between:

99% of 0.26  = 0.2574

1% of 0.26  = 0.0026

[0.26 - 0.0026] , [0.26 + 0.0026]  = [0.2574 , 0.2626]

This should be OPTION C, as that option is missing in the list of options.

Find the equation of the line.
The perpendicular bisector to the line segment with endpoints (-8,5) and (4,1).
The equation of the line is
y =

Answers

Answer:

y = 3x + 9

Step-by-step explanation:

The perpendicular bisector to the line segment is passing through the midpoint of the line segment. Coordinates of midpoint are ( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )

Formula of slope is m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

Slopes of perpendicular lines are opposite reciprocals. So, if AB ⊥ CD , then [tex]m_{AB}[/tex] × [tex]m_{CD}[/tex] = - 1

y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] )  

~~~~~~~~~~~

(- 8, 5)

(4, 1)

m = ( 5 - 1) / ( - 8 - 4) = - [tex]\frac{1}{3}[/tex]

Opposite reciprocal to ( - [tex]\frac{1}{3}[/tex] ) is 3

Coordinates of midpoint are ( - 2 , 3 )

y - 3 = 3 ( x + 2 )

y = 3x + 9  

pls help and explain if u can

Answers

Answer:

Step-by-step explanation:

6 - 3(x + 1) = 18 ⇔ 3 - 3x = 18 ⇒ x = 5

y - 6 = 17 ⇒ y = 23

z - 3 = 4z ⇒ z = - 1

18 - 3(0) = 9w ⇒ w = 2

========================

I'm going to solve for you some another question you asked, I did not see the right answer...  :)

There are two scenarios, because the expression under the module can be positive and can be negative: | 3x + 2| - 2 > 3 ⇔  | 3x + 2| > 5

(1). If (3x + 2) is positive then

3x + 2 > 5 ⇒ x > 3

(2). If (3x + 2) is negative then

- (3x + 2) > 5

- 3x - 2 > 5

- 3x > 7 ⇒ x < - [tex]\frac{7}{3}[/tex]

The final answer is x < - 2.3 or x > 1

At Jay Street Middle School, 25%of eighth graders wear glasses. If 100 students wear glasses how many eighth graders are there in total?

Answers

Answer:

400 total

Step-by-step explanation:

so 100 is 25% of 100% and 25%x4=100%

so do 100x4=400=100% of the middle schoolers

Need help please please it due today at 4:50pm really need help please

Answers

Answer:

70

Step-by-step explanation:

PLEASE HELP FAST AND CORRECT! 50 points!

Answers

Answer:

150 cubic centimeters

Step-by-step explanation:

1/6×X+95=4/5×X

Subtract X from both sides of the equation

Multiply/Combine like terms

95=19/30×X

Multiply by 30/19 and simply

30/19*95=X

Solve for X to get 150

1/6×150=25

4/5×150=120

Answer:

150 cubic centimeters

Step-by-step explanation:

1/6*x+95=4/5*x

Move stuff around

95=1/6+4/5*x

Multiply/Combine like terms  

95=19/30*x

Multiply by 30/19 and then simplify

30/19*95=x

Solve for x

1/6*150=25

4/5*150=120

The population of a certain town is growing at a constant rate. Suppose the population is 1900 initially, and after 4 years the population is 2212. Which of these expresses the rate at which the population is increasing?

Answers

Answer:

The rate of change relates the change in population to the change in time.  The population increased by 2212−1900=312 people over the four-years.  To find the rate of change, divide the change in the number of people by the number of years.

2212−19004=3124

3124/4 =78

So the population increased by 78 people per year.

Because we are told that the population increased, we would expect the slope to be positive.  This positive slope we calculated is therefore reasonable.

what are the possible values for the ones digits when a number is a multiple of 5

Answers

Answer:

0, 5

Step-by-step explanation:

5 * 0 = 0

5 * 1 = 5

5 * 2 = 10

5 * 3 = 15

5 * 4 = 20

5 * 5 = 25

etc.

Answer: 0, 5

Volume of 120 grams divided by 480cm3

Answers

Answer:

= 0.25 g/cm3

Step-by-step explanation:

this is called density the grams per volume.

density = mass

               volume

             =   120g

                480cm3

  = 0.25 g/cm3

Opps- THIS IS DUE IN 7 MINS HALPPPPP!!!! I FORGOT TO DO THIS AND NOW I NEED HALPPPP

ps. Giving 30 points if answer is given

Answers

Answer:

I believe the bottom one is true and the rest are false

Step-by-step explanation:

bottom one true

Answer:

it is the last one. it is a smaller distance from Drachten

Step-by-step explanation:

Which of the following could represent the unit side lengths of a right triangle

A 5,8,10

B 3,5,7

C 6,11,13

D 12,16,20

Answers

Answer:

Choice D

Step-by-step explanation:

If you check each one plugging in your info into this you can get [tex]a^{2} +b^{2} =c^{2}[/tex] that 12² + 16² will equal 400 which is the same as 20².

Answer:

Answer: D 12,16,20

Step-by-step explanation:

The Pythagora's Theorem

On a right triangle with side lengths of a,b, and c, being c the hypotenuse, of the longest side, it follows that:

[tex]a^2+b^2=c^2[/tex]

The set {a,b,c} is often called a Pythagorean Triple.

Testing every option:

A

[tex]5^2+8^2=10^2[/tex]

[tex]25+64 = 100[/tex]

89 = 100

Since equality is false, 5,8,10 are not the side lengths of a right triangle.

B

[tex]3^2+5^2=7^2[/tex]

[tex]9+25 = 49[/tex]

34 = 49

Since equality is false, 3,5,7 are not the side lengths of a right triangle.

C

[tex]6^2+11^2=13^2[/tex]

[tex]36+121 = 169[/tex]

157 = 169

Since equality is false, 6,11,13 are not the side lengths of a right triangle.

D

[tex]12^2+16^2=20^2[/tex]

[tex]144+256 = 400[/tex]

400 = 400

Since equality is true, 12,16,20 could be the side lengths of a right triangle.

Answer: D 12,16,20

Snow Dome Ski Resort has 65 inches of snow. It is currently snowing there at a rate of 1 inch per hour. Mt. Winterpark Ski Resort has 74 inches of snow. Currently it is snowing there at a rate of ½ inch per hour.

a) Write equations that show the amount of snow at each resort as a function of the number of hours of snow.

b) If the snow continues at this rate, when will Snow Dome have more snow than Mt. Winterpark? Show your solution process clearly.

Answers

Answer:

a) Equation for Snow Dome Ski Resort:

[tex]I_s = 65+t[/tex]

Equation for Mt. Winterpark Ski Resort:

[tex]I_m = 74+\frac{t}{2}[/tex]

b) After 19 hours, Snow dome will have more snow.

Step-by-step explanation:

Given that:

Initial snow at Snow Dome Ski Resort = 65 inches

Snowing rate at Snow Dome Ski Resort = 1 inch per hour

Initial snow at Mt. Winterpark Ski Resort = 74 inches

Initial snow at Mt. Winterpark Ski Resort = [tex]\frac{1}{2}[/tex] inch per hour

a) To write equations that show amount of snow at each resort.

Let the time in hours be represented by [tex]t[/tex].

Snow increased in [tex]t[/tex] hours by snowing at Snow Dome Ski Resort = [tex]1\times t = t[/tex] inches per hour

Snow increased in [tex]t[/tex] hours by snowing at Mt. Winterpark Ski Resort = [tex]\frac{1}{2}\times t = \frac{t}{2}[/tex] inches per hour

Equation for Snow Dome Ski Resort:

[tex]I_s = 65+t[/tex]

Equation for Mt. Winterpark Ski Resort:

[tex]I_m = 74+\frac{t}{2}[/tex]

b) Time at which Snow Dome has more snow.

Using the above equations, we can write the following inequality:

[tex]65+t>74+\dfrac{t}{2}\\\Rightarrow t-\dfrac{t}{2}>74-65\\\Rightarrow \dfrac{t}{2}>9\\\Rightarrow t>18\ hours[/tex]

After 18 hours have passed, they will have equal amount of snow.

After 19 hours, Snow dome will have more snow.

Please help due in 5 min

Duval went to bat 80 times during a baseball season. In the first half of the season he had 15 hits. In the second half of the season he had 9 hits. Which percent of the time did Duval get a hit during the entire season?

A. 24%
B. 30%
C. 44%
D. 60%

PLEASE show work

Answers

Answer:

B. 30 Percent

15+9=24

24/80=30 Percent

Step-by-step explanation:

What fraction is equivalent to the decimal and percent below? Enter your
answer in simplest form, using the slash (/) as the fraction bar.
Fraction Decimal Percent
? 0.50 50%
Answer here
SUBMIT

Answers

Answer: 1/2

Step-by-step explanation:

Which part of this graph shows a nonlinear relationship?
Distance from home
2.
Time

Answers

Since 2 is not in a line
Answer=2

Answer:

thanks

Step-by-step explanation:

Mitchell walked 5/12 of a mile in 1/2 of an hour. At this rate, how far could Mitchell walk in 1 hour?

Answers

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

[tex]2 \times \frac{1}{2} hour = 1hour \\ [/tex]

Thus ;

[tex]2 \times \frac{5}{12} \: \: miles = \frac{10}{12} \: \: miles = \frac{5}{6} \: \: miles \\ [/tex]

,♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

I think the answer is 5/6

Whoever answers this first gets brainliest
Pls help ASAP

Answers

Answer:

Terminating goes to 3

Repeating goes to 4

Rational goes to 1

Irrational goes to  2

Answer:

1. Rational Number

2. Irrational Number

3. Terminating Decimal

4. Repeating Decimal

Step-by-step explanation:

A Rational Number can be written as a ratio of two integers. For example, as a simple fraction. That leaves us for the answer to the second one as irrational. To terminate means to end, so a terminating decimal is a decimal that does not go on forever. Whereas, a repeating decimal continues repeating forever (or indefinitely).  

I would like to apologize in advance if any of these were incorrect.

please solve this i will give you brainliest​

Answers

Answer:

1

Step-by-step explanation:

gvgbkhbgvbhjbjhbjhbhjnnj

what is the constant of porportionality between 9 and 4.5​

Answers

Answer:

1/2

Step-by-step explanation:

Which equations has a solution of X=1.5

Answers

He hits a little on a number where it will start with a

C(5,-5),D(5,3) what is the distance between the points

Answers

Here is my answer 8.

Please help it would mean alot!
Points and brinliast!

Answers

Answer:

Maybe because what about the other votes that were supposed to be left.

Step-by-step explanation:

What is the length of the line segment with endpoints (11, −4) and (−12, −4) ?

Answers

Answer:

23 units on the x axis

Step-by-step explanation:

HOPEFULLY MY LAST ONE!!!!

What is the slope?

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answers

Answer:

1/3

Step-by-step explanation:

Rise/run

10/30

I hope this is right and that it helps.

Use these points to find out the slope: (10,60) , (40,70)
Slope: 1/3

Look at the long division problem shown on the right. Complete the division to determine what the remainder will be.

What is the remainder?

–10

–7

7

10
x + 4 StartLongDivisionSymbol 4 x Superscript 4 Baseline + 18 x cubed + 3 x squared minus 18 x + 15 EndLongDivisionSymbol. minus 4 x Superscript 4 Baseline + 16 x cubed to get a remainder of 0 x Superscript 4 Baseline + 2 x cubed + 3 x squared. minus 0 x Superscript 4 Baseline + 2 x cubed + 8 x squared to get a remainder of 0 x Superscript 4 Baseline + 0 x cubed minus 5 x squared minus 18 x. minus 0 x Superscript 4 Baseline + 0 x cubed minus 5 x squared minus 20 x to get a remainder of blank and a quotient of 4 x cubed + 2 x squared minus 5 x + c.

Answers

Answer:

The remainder is...

7

Hope this helps!!

Step-by-step explanation:

Answer: it’s c

Step-by-step explanation:

Use the information mZ1 = (3x + 30), m42 = (5x – 10°, and x = 20, and the theorems you have learned to
show that 1 || m.

Answers

Answer:

Step-by-step explanation:

First you have to do 2 + 2=

Other Questions
Which of the following techniques creates the smallest chopped vegetable?SlicingDicingMincingJulienning HELPPPTimmy and Sam ran in a marathon. Timmy ran at a constant speed of 5 miles per hour. Sam ran at aconstant speed of 4 miles per hour and had a head start of 2 miles. Determine where Timmy and Sam willmeet. Jeffrey had both chocolate cake and coconut cake at his birthday party. There were 25 people at the party, and 20 of them picked chocolate cake. What percentage of the people at the party picked chocolate cake? Please help meWhich particle, protons, neutrons, or electrons, has the LEAST mass? Write a paragraph explaining how Lennie from Of Mice and Men and the creature from The Bride of Frankenstein are characterized in similar ways. Think of their physical and psychological selves, as well as actual plot events to compare. Point out the similarity and then explain why. Include at least six complete sentences in your paragraph, or try to fill up the lines provided. Which prisoners were treated the worst early in the history of the concentration camps? This firm is currently operating at 84 percent of capacity. All costs and net working capital vary directly with sales. The tax rate, the profit margin, and the dividend payout ratio will remain constant. How much additional debt is required if no new equity is raised and sales are projected to increase by 12 percent? 9.How is nominal GDP converted into real GDP?O by eliminating the effects of price increases on GDP growthO by adding all incomes earned to total expenditures by consumers, businesses, and governmentO by adding the contributions of American-owned factories in foreign countriesO by adding up all of the real purchases made in the economy A store is having a 20%-off sale on all merchandise. If Mai buys one item and saves $13, what was the original price of her purchase? Explain or show your reasoning. A box that measures 15 inches by 5 inches by 3 inches.What are the units of the volume of the figure?square inchescubic inchessquare centimeterscubic centimeters x reduced by 13 is at least 15 A political leader suggesting that an economic downturn will be cushioned by nondiscretionary fiscal policy is referring to:______. A) Tax policy and spending policy B) A progressive income tax and a welfare state C) Interest rates and the money supply D) Interest rates and tax rates Why are slide presentations universal in business environments?A. Because the software is free and easy to obtainB. Because of their compatibility with media and soundC. Because they are easy to use and can accommodate all varietiesof informationD. Because they are extremely easy to share with your friends andfamily membersSUBMIT why does earth spin eastward on its axis use your own words Describe what the legal ramifications are for having sexual relations with minors. Use the inequality below to find the value of r .150 - 5 r 87.5a. r 12.5b. r 12.5c. r -(12.5)d. r -(12.5) Help megagaagsgsh fdndjfjdd Study the pictures carefully.What visual elements does each picture show?... I want to do someone's IXL'S preferably math What are the answers and explain