The larger of two numbers is one more than four times the smaller number. If the sum of the numbers is 106, find the numbers.

a
32,56
b
32,74
c
21,85
d
52,54

Answers

Answer 1

Answer:

c.  21, 85

Step-by-step explanation:

Define the variables:

Let the two numbers be x and y, where x > y.

Given information:

The larger of two numbers is one more than four times the smaller number.The sum of the number is 106.

Create two equations from the given information and defined variables:

[tex]\begin{cases}x = 4y + 1\\x + y = 106\end{cases}[/tex]

Substitute Equation 1 into Equation 2 and solve for y:

[tex]\implies (4y+1)+y=106[/tex]

[tex]\implies 4y+1+y=106[/tex]

[tex]\implies 5y+1=106[/tex]

[tex]\implies 5y+1-1=106-1[/tex]

[tex]\implies 5y=105[/tex]

[tex]\implies \dfrac{5y}{5}=\dfrac{105}{5}[/tex]

[tex]\implies y=21[/tex]

Substitute the found value of y into the second equation and solve for x:

[tex]\implies x+21=106[/tex]

[tex]\implies x+21-21=106-21[/tex]

[tex]\implies x=85[/tex]

Therefore, the two numbers are 21 and 85.

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Related Questions

What does g =
g-16
------
2

Answers

Answer:

8?

Step-by-step explanation:

Answer:

g = -8

Step-by-step explanation:

g-16

------ = -8

2

g = -8

A panel of judges was rating the taste of different brands of potato chips

Answers

Two expressions with equal sign is called as Equation. The rating of a brand that costs $3.00 per bag is 7.

What is equation?

Two expressions with equal sign is called as Equation.

A simple linear regression equation is used to estimate the value of the dependent variable based upon the independent variable.

The general form of a simple linear regression equation is:

y=a+bx

Here,

y = dependent variable

x = independent variable

a = intercept

b = slope

The output of the least squares regression analysis for predicting rating from price is provided.

So, the dependent variable is the ratings and the independent variable is the price.

The regression equation for predicting rating from price is:

y=0.39+2.52x

Predict the rating of a brand that costs $3.00 per bag as follows:

y=0.39+(2.52*$3.00)

=0.39+7.56

=7.17

=7 approximately.

Thus, the rating of a brand that costs $3.00 per bag is 7.

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What is the slope of the line that passes through the points (-4, 2) and (-5, 0)? Write your answer in simplest form.

Answers

The slope of the line that passes through (-4, 2) and (-5, 0), in simplest form is calculated as: 2.

How to Find the Slope of a Line that Passes through two Points?

The slope of a line (m) = change in y/change in x = y2 - y1/x2 - x1 or rise/run of the line.

Given the following points on the line:

(-4, 2) = (x1, y1)

(-5, 0) = (x2, y2)

Substitute the values into m = y2 - y1/x2 - x1:

Slope (m) of the line = (0 - 2) / (-5 - (-4))

Slope (m) of the line = (-2) / (-5 + 4)

Slope (m) of the line = -2/-1

Slope (m) of the line = 2

Thus, the slope of the line that passes through (-4, 2) and (-5, 0), in simplest form is calculated as: 2.

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Which of these strategies would eliminate a variable in the system of equations? \begin{cases} -7x + 2y = 5 \\\\ 3x - 5y = -5 \end{cases} ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ ​ −7x+2y=5 3x−5y=−5 ​

Answers

One strategy to eliminate a variable is by multiplying the first equation by 5 and the second equation by 2 and then adding the resulting equations or by multiplying the first equation by 3 and the second equation by 7 and then adding the resulting equations

Solving system of Equations

From the question, we are to determine the strategies that would eliminate a variable in the given system of equations

The given system of equations is

-7x + 2y = 5

3x - 5y = -5

We can eliminate the variable y multiplying the first equation by 5 and the second equation by 2

That is,

5 × [-7x + 2y = 5

2 × [3x - 5y = -5

--------------------------

-35x + 10y = 25

6x - 10y = -10

------------------------

-29x = 15

Also,

We can eliminate the variable x by multiplying the first equation by 3 and the second equation by 7

That is,

3 × [-7x + 2y = 5

7 × [3x - 5y = -5

-------------------------

-21x + 6y = 15

21x - 35y = -35

---------------------

-29y = -20

Hence, one strategy is by multiplying the first equation by 5 and the second equation by 2 and then simplify by adding

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what has no length, no width, and no height

Answers

Answer:

line

Step-by-step explanation:

It would be a line right?

[(12-18)/3-5] multipied by(-4)

Answers

12-18=-6
3-5=-2
-6/-2=3
3x-4=-12
X=-12

Question 4 of 5

Meredith is trying to estimate √51 She uses this table of values:

7. 4² 7. 5²

Square 7. 02 07. 12 7. 22 7. 3²

Value 49. 0 50. 41 51. 84 53. 29 54. 76 56. 25

Square 7. 62 7. 72 7. 82 7. 92 8. 02

Value 57. 76 59. 29 60. 84 62. 41 64. 0

4

What should she do next to find √51 to the nearest hundredth?

OA. She should find the average of 7. 1 and 7. 2.

B. She should find the squares of numbers between 7. 2 and 7. 3.

OC. She should find the squares of numbers between 7. 1 and 7. 2.

O D. She should estimate that √51 is 7. 20.

SUBMIT

Answers

She needs to locate the squares of the integers between 7.1 and 7.2 in order to estimate √51.

What is the square root of a number?

Finding an integer's square root is the inverse of squaring an integer. A number's square value is obtained by multiplying it by itself, whereas the square root of a number can be discovered by looking for a number that, when squared, produces the original value. It follows that a× a = b if "a" is the square root of "b." Every number has two square roots, one of a positive value and one of a negative value because the square of any number is always a positive number.

In the question given to us,

look at the table, we know

(7.1)² = 50.41 and (7.2)² = 51.84

So, (7.1) < √51 < 7.2 { estimate }

They should therefore determine the squares of the numbers between 7.1 and 7.2.

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The complete question is :

Meredith is trying to estimate √51 She uses this table of values:

What should she do next to find √51 to the nearest hundredth?

A. She should find the average of 7. 1 and 7. 2.

B. She should find the squares of numbers between 7. 2 and 7. 3.

C. She should find the squares of numbers between 7. 1 and 7. 2.

D. She should estimate that √51 is 7. 20.

6x+5y=39

3x+5y=27
grade 8

Answers

Answer:

y = 3 and x = 4

Step-by-step explanation:

Let's solve your system by substitution.

6x+5y=39;3x+5y=27

Step: Solve6x+5y=39for x:

6x+5y=39

6x+5y+−5y=39+−5y(Add -5y to both sides)

6x=−5y+39

6x/6=−5y+39/6

(Divide both sides by 6)

x=−5/6y+13/2

Step: Substitute −5/6y+13/2 for x in 3x+5y=27:

3x+5y=27

3(−5/6y+13/2)+5y=27

5/2y+39/2=27(Simplify both sides of the equation)

5/2y+39/2+−39/2=27+−39/2

(Add (-39)/2 to both sides)

5/2y=15/2

5/2y/5/2=15/2/5/2

(Divide both sides by 5/2)

y=3

Step: Substitute 3 for y in x=−5/6y+13/2:

x=−5/6y+13/2

x=−5/6(3)+13/2

x=4(Simplify both sides of the equation)

can someone help? Work out the missing numbers in the identity

__ (p²-2) - p(2p³- __) =p(p²-2) + 3 p​

Answers

Step-by-step explanation:

I hope you wrote the equation correctly.

there could be parts missing. and exponents be wrong.

I am concerned, because the missing parts are not just numbers. they are full terms in the variable p.

so, well, the right side is

p³ - 2p + 3p = p³ + p

on the left side we have

a(p² -2) - p(2p³ - b)

ap² - 2a - 2p⁴ - pb

so, the first thing we see : we need to eliminate the p⁴ terms, because there are none on the right side.

so,

a = 2p²

that gives us

2p⁴ - 4p² - 2p⁴ - pb = -4p² - pb

let's see, if we can create the missing items just by "b" (and we have to get rid of -4p²) when we bring left and right sides together again :

-4p² - pb = p³ + p

p³ + p + 4p² = -pb

b = (p³ + p + 4p²)/-p = -p² - 1 - 4p

so,

the equation would look like

2p²(p² - 2) - p(2p³ - (-p² - 1 - 4p)) = p(p² - 2) + 3p

which could be also written as

2p²(p² - 2) - p(2p³ + p² + 1 + 4p) = p(p² - 2) + 3p

what is the solution to this system of equations?

y = x - 2
y = - 0.5x + 4

Answers

Answer:

(4, 2 )

Step-by-step explanation:

y = x - 2 → (1)

y = - 0.5x + 4 → (2)

substitute y = x - 2 into (2)

x - 2 = - 0.5x + 4 ( add 0.5x to both sides )

1.5x - 2 = 4 ( add 2 to both sides )

1.5x = 6 ( divide both sides by 1.5 )

x = 4

substitute x = 4 into (1)

y = 4 - 2 = 2

solution is (4, 2 )

6x-6+x-6 pls he help thank you very mid ce

Answers

Answer:

7x-12

Step-by-step explanation:

Answer:The answer is 7x-12

Step-by-step explanation:You would do 6x+x which would equal 7x then you would do -6-6 which would equal -12.So the answer would be 7x-12.

1-39. Estimate the areas of Montana and California using the grid below. Which state has the greatest
area? Compare the area of Montana to the area of California. Explain how you estimated the area of
each state.

Answers

California   has the greatest area of each state.

What does a math area mean?

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.

So, we know that

         Montana  =    5 * 9 =  45 grids

California  = 15 + 16 + 14 + 6 = 51 grids

                          45 < 51

California   has the greatest area .

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Question 1
She just knew she would die if she didn't get a job.
Is it a hyperbole or idiom?

Answers

Answer:

Hyperbole

Hope this helps :)

Step-by-step explanation:

This is because she is exaggerating, and hyperoble is when someone exaggerates. She will not really die if she didn't get a job.

Mrs. Saunders can clean the windows of her house in 3 hours. Her daughter can clean the windows in 6 hours. How long will it take them to clean the windows if they work together?

Answers

Answer:4.5 hours, 4 hours and 30 minutes, 4 and a half hours

Step-by-step explanation: you are averaging, so you add all of the numbers together and divide that by the number of numbers.

3+6=9, 9 divided by 2=4.5

Answer:

2hours

Step-by-step explanation:

let windows = x

Mrs. Saunders can clean one-third of the windows in an hour = x/3

daughter can clean one-sixth of the windows in an hour = x/6

so,

x/3+x/6 = 1

thus, x = 2

mother and daughter together can clean the windows in 2 hours

a)find the value of 2x+y when x=4 and y=3

Answers

Answer:

11

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Plug in x and y values into the equation

2(4) + (3)

Multiply

8 + 3

Add

11

Cam earns $400/week plus 2. 5% commission. He has been offered another job that pays $700/week but no commission.


a) Describe three strategies that you could use to compare Cam’s

earnings for the two jobs

Answers

Two jobs a 800 to 1000 each jobs

what is the answer to this ? 5b+3.79

Answers

Answer:

5

Step-by-step explanation:

5b+3.79

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^n is nax^n−1 .

5b^1-1

Subtract 1 from 1.

5b^0

For any term t except 0, t^0 = 1

5×1

For any term t, t×1=t and 1t=t.

5

How do you message ppl?

20 points!!!

Answers

Answer:

You can't. You must be a trusted helper.

Answer:

just message them by messaging them

I NEED HELP ASAP!!!
Which of the following expressions represents “the difference between a number and eleven”?

11 – n
-11 n
n + 11
n – 11


All of the following represent the same concept except _____.

a number minus five
five more than a number
the sum of a number and five
a number increased by five
thank you!!

Answers

The expressions represents “the difference between a number and eleven” is (n - 11) while, for the second case, the one statement which does not represent the same concept, among the four options provided is "a number minus five".

As per question statement, we are provided with two separate questions, first one requiring us to determine the expressions represents “the difference between a number and eleven”, while the second one requiring us to determine the one statement which does not represent the same concept, among the four options provided.

Considering the first case, the statement “the difference between a number and eleven”, considering the number to be "n" can be mathematically expressed as [tex](n - 11)\\[/tex]. Hence, the correct answer is [tex](n - 11)\\\\[/tex].

Coming to the second case, considering the number to be "n",

Option (A) is "a number minus five" which when mathematically stated becomes [tex](n-5)[/tex]

Option (B) is "five more than a number" which when mathematically stated becomes [tex](n+5)[/tex]

Option (C) is "the sum of a number and five" which when mathematically stated becomes [tex](n+5)[/tex]

And, option (D) is "a number increased by five" which when mathematically stated becomes [tex](n+5)[/tex].

That is, Option (B), (C) and (D) all belong to the same concept. Hence, the one statement which does not represent the same concept, among the four options provided is "a number minus five".

Expressions: Expressions in mathematics, are mathematical statements that have two or more terms, consisting of numbers or variables, or both, and being connected by operators in between.

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I was to tired today and I have homework and don’t know what to do

Answers

Step-by-step explanation:

Just do it and it will pay off

Your trip started near mile marker 42 on I-10 in El Paso. Now you're at mile marker 837 near Winnie. How many miles have you traveled?

Answers

Answer:

Step-by-step explanation:

Your trip started near mile marker 42 on I-10 in El Paso. Now you're at mile marker 837 near Winnie. How many miles have you traveled?

A 2-gallon container of laundry detergent costs $14.64. What is the price per quart?

Answers

Answer:

Step-by-step explanation:

$1.20 dollars


Write a rational function with the given characteristics.
A vertical asymptote at x=-4 and a horizontal asymptote at y=3

Answers

The rational function with the given characteristics is [tex]f(x) = \frac{3x + 1}{x - 4} [/tex].

How to find a rational function with the given characteristics?

Any function that can be expressed mathematically as a rational fraction—an algebraic fraction in which both the numerator and the denominator are polynomials—is referred to as a rational function. The polynomials' coefficients don't have to be rational numbers,they can be found in any field K.

given that a vertical asymptote at x=-4.

A horizontal asymptote at y=3.

The denominator of the function cancels for this value and the numerator does not cancel at this value if the rational function has a vertical asymptote at x=4.

[tex]f(x) = \frac{p(x)}{(x - 4)} [/tex]

The degree of the numbered variable is equal to the degree of the denominator if the rational function has a horizontal asymptote at y=3, and the coefficient of the higher degree variable is three times larger.

Hence,

[tex]f(x) = \frac{3x + 1}{x - 4} [/tex]

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a jogger begins her workout by jogging to a park, a distance of 12 miles. she then jogs home at the same speed, but along a different route. this return trip is 18 miles, and her time is one hour longer. find her jogging speed.

Answers

The jogging speed of the jogger is 6 miles/hour.

Given that:-

Distance from home to park = 12 miles

Distance from park tp home from a different route = 18 miles

It is also given that the time taken to reach home from park is 1 hour longer than the number of hours taken to reach park from home.

We have to find the speed of the jogger.

Let the time taken by jogger to reach park from home be t hours.

Hence, according to the data given in the question,

Time taken by jogger to reach home from park is (t+2) hours.

We know that,

Speed = distance/time

We know that the speed of jogger in each route is same.

Hence, we can write,

12/t = 18/(t+1)

2/t = 3/(t+1)

2(t+1) = 3t

2t+2 = 3t

t = 2 hours.

Hence, speed of the jogger = 12/2 = 6 = 18/(2+1) = 18/3.

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What is the perimeter of this rectangle in simplest form.

Answers

The perimeter of the rectangle in it simplest form is 8x - 10.

How to find the perimeter of a rectangle?

The perimeter of a rectangle can be found as follows:

perimeter of a rectangle = 2(l + w)

where

l  = lengthw = width

Therefore,

length = 3x - 7

width = x + 2

perimeter of a rectangle = 2(3x - 7 + x + 2)

perimeter of a rectangle = 2(3x + x - 7 + 2)

perimeter of a rectangle = 2(4x - 5)

perimeter of a rectangle = 8x - 10

Therefore, the perimeter of the rectangle in it simplest form is 8x - 10.

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i need help on this i don’t understand it really

Answers

Answer:

Point G

Step-by-step explanation:

It is point G because since you mirrored it and flipped it, you need to flip figure one and if you move it to where figure two is, in the same place, the new point R is where point G is, so G corresponds to R

The answer is point g I believe


Let g(x)=5 x-2 and h(x)=x²+1 . Find the value of each expression. (g ⁰ h)(a)

Answers

For the functions g (x) = 5 x - 2 and h (x) = x² + 1, the value of the composite function g o h (a) will be 5 a² + 3.

We are given the functions:

g (x) = 5 x - 2

h (x) = x² + 1

We first need to find the composite function g o h (x).

So, we get that:

g o h (x) = g ( h (x) )

g o h (x) = 5 ( x² + 1 ) - 2

g o h (x) = 5 x ² + 5 - 2

g o h (x) = 5 x² + 3

Now, we need to find the value of the composite function for x = a. So, we get that:

g o h (x = a) = 5 (a)² + 3

g o h (a) = 5 a² + 3

Therefore, for the functions g (x) = 5 x - 2 and h (x) = x² + 1, the value of the composite function g o h (a) will be 5 a² + 3.

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A/an is calculated by dividing the difference between a data value and the mean by the standard deviation.

Answers

Answer: Z-score

Step-by-step explanation:


For each direct variation, find the constant of variation. Then find the value of y when x=-3 .
y=1 when x=-1.5

Answers

After direct variation y = 2 when x = -3.

What do we mean when we say "direct variation"?To give the reader a hint, direct variation equations use the same phrase.The phrase could be "directly proportional" or "directly varies."For example, the area of a square is proportional to the square of its side.The variational constant is k = 3 if y varies directly as x and y = 6 when x = 2.As a result, y = 3x is the direct variation equation.

So,

The initial statement is y = kx

Then to find y when x = -3.

K constant will be y/x ⇒ 1/-1.5That is y = kx ⇒ y = 1/-1.5 × x

When x = -3:

1/-1.5 × -3 ⇒ y = 2

Therefore, y = 2 when x = -3.

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y = - x + 1 + 4
t
2 3
X
|
0
- |
-21
-3
y

Answers

Answer:

1+4=5 23×21=44 44-3=41

Step-by-step explanation:

ANSWER= LOL

Other Questions
Consider the graph given above. Add a new edge so the resulting graph has an Euler path (without repeating an existing edge). ______Use Fleury's Algorithm to find an Euler path through the graph using this new edge by listing the vertices in the order visited. _______ Center = (6,15)Radius = 2 Which statement is true about a person who is in good social health? a. She spends a lot of time alone. b. She has few friends at school. c. She may not be in good physical health. d. She gets along with others. A problem that can be solved through technological design has been identified. A brief has been written. What is the next step in the design process? Which situation is represented by the inequality?7x + 50 > 4x + 100ResponsesA Molly has $50 and Mary has $100. Molly saves $7 per week and Mary saves $4 per week. How long will it be before Molly has more money than Mary?Molly has $50 and Mary has $100. Molly saves $7 per week and Mary saves $4 per week. How long will it be before Molly has more money than Mary?B Molly has $50 and Mary has $100. Molly saves $4 per week and Mary saves $7 per week. How long will it be before Molly has more money than Mary?Molly has $50 and Mary has $100. Molly saves $4 per week and Mary saves $7 per week. How long will it be before Molly has more money than Mary?C Molly has $50 and Mary has $100. Molly saves $4 per week and Mary saves $7 per week. How long will it be before Molly and Mary have the same amount of money?Molly has $50 and Mary has $100. Molly saves $4 per week and Mary saves $7 per week. How long will it be before Molly and Mary have the same amount of money?D Molly has $50 and Mary has $100. Molly saves $7 per week and Mary saves $4 per week. How long will it be before Molly and Mary have the same amount of money?Molly has $50 and Mary has $100. Molly saves $7 per week and Mary saves $4 per week. How long will it be before Molly and Mary have the same amount of money? solve the equation 5(2x+1)=25 comparing and contrasting which two philosophies in the chart would you say had the most similar ideas? explain This stage in relational escalation is defined by potential partners or friends observing each other and talking with other people about each other without having any direct interaction. Zalaria5. For each pair of shapes, decide whether or not Shape A is congruent to Shape B.Explain your reasoning.a. First pair: Which categories does 3.7 belong to? Solve each equation. 3=243 sum of the roots lf 4x2+8x+3=0 A contractor purchases 6 dozen pairs of padded work gloves for $89.28 . He incorrectly calculates the unit price at $14.88 per pair for the expense report. What is the correct unit price? Why is the contractor's unit price incorrect? What similarities, if any, do you find between the care required for manufactured fibersand natural fibers? What current goes through a 2070 W kettle connected to a 230 V mains supply? Find the correct answer for the following question.Welche der vier Krankheiten ist ansteckend?O die DiabetesOder HerzinfarktO das AsthmaO die Grippe What do studies of isolated children teach us about the importance of social experience? 1) In a reaction, 0.486 g of magnesium was added to oxygen to produce magnesium oxide. Mg(s) + O2(g) 2MgO(s) a) Calculate the amount, in moles, of magnesium that reacted SOMEONE HELP MEEEEEE 2. When does an ionic bond form?When electrons are shared by two or more atoms equally.When two positive ions combine to form a polyatomic ion.When electrons are lost by one atom and gained by another atom.When two negative ions combine to form a polyatomic ion.