Chapter: Simple linear equations Answer in steps

Chapter: Simple Linear Equations Answer In Steps

Answers

Answer 1

Answer:

6x-3=21

6x=24

x=4

........

6x+27=39

6x=39-27

6x=12

x=2

........

8x-10=14

8x=24

x=3

.........

6+6x=22

6x=22-6

x=3

......

12x-2=28

12x=26

x=3

.....

8-4x=16

-4x=8

x=-2

.....

4x-24=3x-3

4x-3x=24-3

x=21

....

9x+6=6x+12

9x-6x=12-6

3x=6

x=2

Answer 2

Answer:

Step-by-step explanation:

1. 3(2x - 1) = 21

 = 6x - 3 = 21

 = 6x = 24

 = x = 24/6 = 4

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

2. 3(2x+9) = 39

   = 6x + 27 = 39

   = 6x = 39 - 27

   = 6x = 12

   = x = 12/6 = 2

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

3. 2(4x - 5) = 14

  = 8x - 10 = 14

  = 8x = 14+10

 = x = 3

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


Related Questions

solve for x: 5x+3+8x-4=90

Answers

Answer:

[tex]x = 7[/tex]

Step-by-step explanation:

We can solve the equation [tex]5x+3+8x-4=90[/tex] by isolating the variable x on one side. To do this, we must simplify the equation.

[tex]5x+3+8x-4=90[/tex]

Combine like terms:

[tex]13x - 1 = 90[/tex]

Add 1 to both sides:

[tex]13x = 91[/tex]

Divide both sides by 13:

[tex]x = 7[/tex]

Hope this helped!

Answer:

x = 7

Step-by-step exxplanation:

5x + 3 + 8x - 4 = 90

5x + 8x = 90 - 3 + 4

13x = 91

x = 91/13

x = 7

probe:

5*7 + 3 + 8*7 - 4 = 90

35 + 3 + 56 - 4 = 90

Suppose you are standing such that a 32-foot tree is directly between you and the sun. If you are standing 140 feet away from the tree and the tree casts a 160-foot shadow, how tall could you be and still be completely in the shadow of the tree? x 160 ft 140 ft 32 ft

Answers

Answer:

Height = 4 feet

Step-by-step explanation:

To determine how tall I can be we take the difference between the shadow cast by the 32-feet tree and the distance away from the tree

But the tree is 32 feet tall but on shadow it's 160

So lemme determine how long I'll be in my shadow first

Distance away from tree= 140 feet

Length of shadow cast by tree

= 160 feet

Length of shadow= 160-140

Length if shadow= 20 feet

My height= x

X/20= 32/160

X= 20*32/260

X = 4 feet

Height = 4 feet

A cardboard box without a lid is to be made with a volume of 4 ft 3 . Find the dimensions of the box that requires the least amount of cardboard.

Answers

Answer:

2ft by 2ft by 1 ft

Step-by-step explanation:

Total surface of the cardboard box is expressed as S = 2LW + 2WH + 2LH where L is the length of the box, W is the width and H is the height of the box. Since the cardboard box is without a lid, then the total surface area will be expressed as;

S  = lw+2wh+2lh ... 1

Given the volume V = lwh = 4ft³ ... 2

From equation 2;

h = 4/lw

Substituting into r[equation 1;

S = lw + 2w(4/lw)+ 2l(4/lw)

S = lw+8/l+8/w

Differentiating the resulting equation with respect to w and l will give;

dS/dw = l + (-8w⁻²)

dS/dw = l - 8/w²

Similarly,

dS/dl = w  + (-8l⁻²)

dS/dw = w - 8/l²

At turning point, ds/dw = 0 and ds/dl = 0

l - 8/w² = 0 and w - 8/l² = 0

l = 8/w²  and w =8/l²

l = 8/(8/l² )²

l = 8/(64/I⁴)

l = 8*l⁴/64

l = l⁴/8

8l = l⁴

l³ = 8

l = ∛8

l = 2

Hence the length of the box is 2 feet

Substituting l = 2 into the function l = 8/w² to get the eidth w

2 = 8/w²

1 = 4/w²

w² = 4

w = 2 ft

width of the cardboard is 2 ft

Since Volume = lwh

4 = 2(2)h

4 = 4h

h = 1 ft

Height of the cardboard is 1 ft

The dimensions of the box that requires the least amount of cardboard is 2ft by 2ft by 1 ft

Can someone explain to me what a “derivative” means? How do you find the derivative of f(x)=x^3+1?

Answers

The derivative is the rate of change of a function, basically represents the slope at different points. To find the derivative of the given function you can use the power rule, which means, if n is a real number, d/dx(x^n)= nx^(n-1). This is a simplification of the chain rule based on the fact that d/dx(x)=1. Anyway, this means that d/dx(x^3 + 1)= 3x^2. Here n is 3 and so it is 3*x^(3-1)= 3x^2. The derivative of x^3+1 is 3x^2.

If you are wondering what happened to the 1, for any constant C, d/dx(C)=0.

12-(3-9) 3*3 help please

Answers

Step-by-step explanation:

42 is your answer according to bodmas

The MCAT is the admission exam that medical schools use as one of the criteria for accepting students. The exam is based on a scale of 0-45. The following data shows the MCAT scores for nine students.

32 36 29 31 30 35 34 26 30

The 35th percentile of this data set is:________

a. 31
b. 32
c. 31.5
d. 30

Answers

Answer:

d. 30

Step-by-step explanation:

The computation of the 35th percentile of this data set is shown below:

Before that first we have to series the number in ascending number

S. No          Numbers

1                       26

2                      29

3                      30

4                      30

5                      31

6                      32

7                      34

8                      35

9                       36

Now use the formula

Here n = 9

Percentile = 100

[tex]= \frac{35(9 + 1)}{100} \\\\[/tex]

= 3.5th

= 3th + 0.5 (4th - 3th)

= 3th + 0.5 (30 - 30)

= 3th + 0

= 30

An evergreen nursery usually sells a certain shrub after 9 years of growth and shaping. The growth rate during those 9 years is approximated by
dh/dt = 1.8t + 3,
where t is the time (in years) and h is the height (in centimeters). The seedlings are 10 centimeters tall when planted (t = 0).
(a) Find the height after t years.
h(t) =
(b) How tall are the shrubs when they are sold?
cm

Answers

Answer:

(a) After t years, the height is

18t² + 3t + 10

(b) The shrubs are847 cm tall when they are sold.

Step-by-step explanation:

Given growth rate

dh/dt = 1.8t + 3

dh = (18t + 3)dt

Integrating this, we have

h = 18t² + 3t + C

When t = 0, h = 10cm

Then

10 = C

So

(a) h = 18t² + 3t + 10

(b) Because they are sold after every 9 years, then at t = 9

h = 18(9)² + 3(9) + 10

= 810 + 27 + 10

= 847 cm

This graph shows the US unemployment rate from August 2010 to November 2011.
Sample Unemployment Rate
Graph
Unemployment Rate
10%
80%
6%
Unemployment Rate
Aug 10
Jan 11
Jun 11
Nov 11
This graph suggests unemployment in the United States
O will continue to fall.
O will continue to rise.
O will remain the same.
O will only change a little.

Answers

Answer: Will continue to rise

Step-by-step explanation:

Looking at the graph one notices that after a slight dip in the unemployment rate from August 2010 to January 2011, the unemployment rate began to rise and by November 2011 was still rising.

The arrow on the graph serves to indicate the direction the unemployment rate is going and as it is pointing upwards, this means that the Unemployment rate will continue to rise.

This was down to the fact that in 2011 the US was still yet to recover from the Great Recession of 2008 - 2009.

Answer:

EDGE 2021

Step-by-step explanation:

1) 4%

2) Increase

6x - 10 = 4(x + 3) x = ? x = 9 x = 10 x = 11 x = 12

Answers

Answer:

x=11

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

6x - 10 = 4(x+3)

6x - 10 = 4*x + 4*3

6x - 10 = 4x + 12

6x - 4x = 12 + 10

2x = 22

x = 22/2

x = 11

check:

6*11 - 10 = 4(11+3)

66 - 10 = 4*14 = 56

What is the first step in mathematical induction?

Answers

Answer:

Show that the statement is true for n=1

Step-by-step explanation:

Hey,

Show that the statement is true for n=1

You can check my other answer there which explains a little bit more the ideas.

https://brainly.com/question/17162256

thank you

can you please help ?

Answers

Answer:

69

Step-by-step explanation:

The order of operations is PEMDAS; parentheses, exponents, multiplication and division, and finally addition and subtraction.

We know that x is the first row, and if there are 30 spots in the first row, then x=30. Using this information, all we have to do now is plug in 30 for x and solve.

[tex]\frac{5(x)}{2} -6[/tex]

[tex]\frac{5(30)}{2}-6[/tex]

[tex]\frac{150}{2}-6[/tex]

[tex]75-6[/tex]

[tex]69[/tex]

what are the comparison symbols for 5/6 and 2/5, 4/10 and 7/8, and 3/12 and 1/4

Answer like this: Example

=
<
>

Answers

Answer:

5/6 > 2/44/10 < 7/83/12 = 1/4

Step-by-step explanation:

The comparison will be the same if you subtract the right side and compare to zero:

  a/b ?? c/d . . . . . . . using ?? for the unknown comparison symbol

  a/b - c/d ?? 0 . . . . subtract the fraction on the right

  (ad -bc)/bd ?? 0 . . . combine the two fractions

  ad - bc ?? 0 . . . . . . multiply by bd to make the job easier

__

5/6 and 2/5

  5(5) -6(2) = 25 -12 > 0   ⇒   5/6 > 2/5

4/10 and 7/8

  4(8) -10(7) = 48 - 70 < 0   ⇒   4/10 < 7/8

3/12 and 1/4

  3(4) -12(1) = 0   ⇒   3/12 = 1/4

_____

Of course, you can use your calculator (or your memory) to change each of these to a decimal equivalent. The comparison should be easy at that point.

  0.833 > 0.400

  0.400 < 0.875

  0.250 = 0.250

find the value of x? please help​

Answers

Answer:

49

Step-by-step explanation:

With these types of problems, you have to subtract the outer and inner values and then divide by 2. So, (125-27)/2 = 49. Hope this helps!

the value of x is 49

Caleb made 6 quarts of trail mix for his camping trip. Each week,he ate 4 pints of the trail mix. How many weeks did Caleb have trail mix?




Sry if this is too much ​

Answers

Answer:

3 weeks

Step-by-step explanation:

6 quarts = 12 pints

12 divided by 3 = 4

Step-by-step explanation:

1 quart = 2 pints

6 quarts = 2 x 6 = 12 pints

12 ÷ 4 = 3

He can have 3 weeks

A researcher wishes to examine the relationship between years of schooling completed and the number of pregnancies in young women. Her research discovers a linear relationship, and the least squares line is: ˆ y = 3 − 5 x y^=3-5x where x is the number of years of schooling completed and y is the number of pregnancies. The slope of the regression line can be interpreted in the following way:
1.) When amount of schooling increases by one year, the number of pregnancies decreases by 4.
2.) When amount of schooling increases by one year, the number of pregnancies increases by 4.
3.) When amount of schooling increases by one year, the number of pregnancies increases by 5.
4.) When amount of schooling increases by one year, the number of pregnancies decreases by 5.

Answers

Answer:

1. When amount of schooling increases by one year, the number of pregnancies will decrease by 4.

Step-by-step explanation:

Regression analysis is a statistical technique which is used for forecasting. It determines the relationship between two variables. It determines the relationship of two or more dependent and independent variables. It is widely used in stats to find trend in the data. It helps to predict the values of dependent and independent variables. In the given question, there is regression equation given. X and Y are considered as dependent variables. When number of schooling increases by 1 year then number of pregnancies will decrease by 4

The force of gravity on an object varies directly with its mass. The constant of variation due to gravity is 32.2 feet per second squared. Which equation represents F, the force on an object due to gravity according to m, the object’s mass? F = 16.1m F = F equals StartFraction 16.1 Over m squared EndFraction. F = 32.2m F = F equals StartFraction 32.2 Over m squared EndFraction.

Answers

Answer:

F = 32.2m

Step-by-step explanation:

According to newton second law, the force of gravity on an object varies directly with its mass and it is expressed mathematically as Fαm i.e

F = mg where;

F is the force of gravity

m is the mass of the body

g is the proportionality constant known as the acceleration due to gravity.

If the constant of variation due to gravity is 32.2ft/s², the equation that represents F, the force on an object due to gravity according to m, the object’s mass can be gotten by substituting g = 32.2 into the formula above according to the law as shown;

F = m*32.2

F =32.2m

Hence the required equation is F = 32.2m

Gina, Sam, and Robby all rented movies from the same video store. They each rented some dramas, comedies, and documentaries. Gina rented 11 movies total. Sam rented twice as many dramas, three times as many comedies, and twice as many documentaries as Gina. He rented 27 movies total. If Robby rented 19 movies total with the same number of dramas, twice as many comedies, and twice as many documentaries as Gina, how many movies of each type did Gina rent?

Answers

Hi there! :)

Answer:

Gina rented 3 dramas, 5 comedies, and 3 documentaries.

Step-by-step explanation:

To solve, we will need to set up a system of equations:

Let x = # of dramas, y = # of comedies, and z = # of documentaries:

Write equations to represent each person:

Gina:

x + y + z = 11

Sam:

2x + 3y + 2z = 27

Robby:

x + 2y + 2z = 19

Write the system:

x + y + z = 11

2x + 3y + 2z = 27

x + 2y + 2z = 19

Begin by subtracting the third equation from the second:

2x + 3y + 2z = 27

x + 2y + 2z = 19

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

x + y = 8

If x + y = 8, plug this into the first equation:

(8) + z = 11

z = 11 - 8

z = 3

We found the # of documentaries Gina rented, now we must solve for the other variables:

Subtract the top equation from the third. Substitute in the value of z we solved for:

x + 2y + 2(3) = 19

x + y + (3) = 11

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

y + 3 = 8

y = 5

Substitute in the values for y and z to solve for x:

x + 5 + 3 = 11

x + 8 = 11

x = 11 - 8

x = 3.

Therefore, Gina rented 3 dramas, 5 comedies, and 3 documentaries.

Answer:

B- x + y + z = 11

2x + 3y + 2z = 27

x + 2y + 2z = 19

Step-by-step explanation:

I took the quiz

16
Select the correct answer.
If function g is defined by the equation Y-3X = -14, which equation represents the function in function notation?
OA. gx) = 3X - 14
OB. gx) = -3X - 14
OC. g(x) = 3X + 14
OD. gx) = -3X + 14
Reset
Next

Answers

Answer:  A)  g(x) = 3x - 14

Step-by-step explanation:

Solve the equation for y and replace y with g(x):

y - 3x = -14

y        = 3x - 14

  g(x) = 3x - 14

nick cut a circular cookie into 5 equal slices. what is the angle measure of each slice?

Answers

Using concepts of circles, it is found that the angle measure of each slice is of 72º.

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

The cookies have circular formats.A complete circle, which is the format of a cookie, has an angular measure of 360º.If it is divided into a number n of equal slices, the angles will be 360 divided by n.

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

5 equal slices, thus:

[tex]\frac{360}{5} = 72[/tex]

The angle measure of each slice is of 72º.

A similar problem is given at https://brainly.com/question/16746988

How many times does 1/4 go into 3/8

Answers

Answer:

3/2

Step-by-step explanation:

3/8 ÷ 1/4

Copy dot flip

3/8 * 4/1

12/8

Divide top and bottom by 4

3/2

Your investment club has only two stocks in its portfolio. $25,000 is invested in a stock with a beta of 0.8, and $40,000 is invested in a stock with a beta of 1.7. What is the portfolio's beta? Do not round intermediate calculations. Round your answer to two decimal places.

Answers

Answer:

The portfolio beta is  [tex]\alpha = 1.354[/tex]

Step-by-step explanation:

From the question we are told that

      The  first investment is [tex]i_1 = \$ 25,000[/tex]

       The  first  beta is  [tex]k = 0.8[/tex]

      The second investment is  [tex]i_2 = \$ 40,000[/tex]

       The  second  beta is  [tex]w = 1.7[/tex]

Generally the portfolio beta is mathematically represented as

           [tex]\alpha = \frac{ i_1 * k + i_2 * w }{ i_1 + i_2}[/tex]

substituting values

          [tex]\alpha = \frac{ (25000 * 0.8) + ( 40000* 1.7 ) }{40000 + 25000}[/tex]

          [tex]\alpha = 1.354[/tex]

As a bowling instructor, you calculate your students' averages during tournaments. In 5 games, one bowler had the following scores: 143, 156, 172, 133, and 167. What was that bowler's average?

Answers

Answer:

154.2

Step-by-step explanation:

143 plus

156 plus

172 plus

133 plus

167 = 771

divide by 5 equals 154.2

Let f(x)=x+8 and g(x)= x2-6x-7 find f(g2)

Answers

Answer:

-7.

Step-by-step explanation:

g(x) = x^2 - 6x - 7

g(2) = 2^2 - 6(2) - 7

= 4 - 12 - 7

= -8 - 7

= -15

f(x) = x + 8

f(-15) = (-15) + 8

= 8 - 15

= -7

Hope this helps!

Variable g is 8 more than variable w. Variable g is also 2 less than w. Which pair of equations best models the relationship between g and w? g = 8w g = w + 2 w = g + 8 w = g − 2 w = 8g w = g + 2 g = w + 8 g = w − 2

Answers

Answer: g = w + 8    g=w-2

Step-by-step explanation:

We could represent the word phrases by the equations.

g = w + 8  

g = w - 2  

Answer:

g = w + 8

g = w - 2

Step-by-step explanation:

Assuming that g and w exists, then we can show the relation as described:

"Variable g is 8 more than variable w."

g = w + 8

"Variable g is also 2 less than w."

g = w - 2

These are the two equations of the described relationship between g and w.

Note that g could not actually exist in the real number system:

g = w + 8

g = w - 2

w + 8 = w - 2

w - w = -2 - 8

0 != -10

This is impossible within the real number system.

Cheers.

The chief business officer of a construction equipment company arranges a loan of $9,300, at 12 1 /8 % interest for 37.5 months. Find the amount of interest. (Round to the nearest cent)

a. $2,761.21


b. $3,583.83


c. $3,523.83


d. $3,722.47

Answers

Answer:

C). $3523.83

Step-by-step explanation:

loan of principles p= $9,300,

at rate R= 12 1 /8 % interest

Rate R = 12.125%

for duration year T = 37.5 months

T= 37.5/12 = 3.125 years

Interest I=PRT/100

Interest I =( 9300*12.125*3.125)/100

Interest I = (352382.8125)/100

Interest I = 3523.83

Interest I= $3523.83

You sell tickets at school for fundraisers. You sold car wash tickets, silly string fight tickets and dance tickets – for a total of 380 tickets sold. The car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each. If you sold twice as many silly string tickets as car wash tickets, and you have $1460 total. Write the matrix in the box below. Write the solution set for this system and include any necessary work.

Answers

Answer:

Matrix :

[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]

Solution Set : { x = 123, y = 246, z = 11 }

Step-by-step explanation:

Let's say that x represents the number of car wash tickets, y represents the number of silly sting fight tickets, and z represents the number of dance tickets. We know that the total tickets = 380, so therefore,

x + y + z = 380,

And the car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each, the total cost being $1460.

5x + 3y + 10z = 1460

The silly string tickets were sold for twice as much as the car wash tickets.

y = 2x

Therefore, if we allign the co - efficients of the following system of equations, we get it's respective matrix.

System of Equations :

[tex]\begin{bmatrix}x+y+z=380\\ 5x+3y+10z=1460\\ y=2x\end{bmatrix}[/tex]

Matrix :

[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]

Let's reduce this matrix to row - echelon form, receiving the number of car wash tickets, silly sting fight tickets, and dance tickets,

[tex]\begin{bmatrix}5&3&10&1460\\ 1&1&1&380\\ -2&1&0&0\end{bmatrix}[/tex] - Swap Matrix Rows

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ -2&1&0&0\end{bmatrix}[/tex] - Cancel leading Co - efficient in second row

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ 0&\frac{11}{5}&4&584\end{bmatrix}[/tex] - Cancel leading Co - efficient in third row

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&\frac{2}{5}&-1&88\end{bmatrix}[/tex] - Swap second and third rows

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&0&-\frac{19}{11}&-\frac{200}{11}\end{bmatrix}[/tex] - Cancel leading co - efficient in row three

And we can continue, canceling the leading co - efficient in each row until this matrix remains,

[tex]\begin{bmatrix}1&0&0&|&\frac{2340}{19}\\ 0&1&0&|&\frac{4680}{19}\\ 0&0&1&|&\frac{200}{19}\end{bmatrix}[/tex]

x = 2340 / 19 = ( About ) 123 car wash tickets sold, y= 4680 / 19 =( About ) 246 silly string fight tickets sold, z = 200 / 19 = ( About ) 11 tickets sold

Find the first term in the sequence when u(subscript)31=197 and d= 10.

Answers

Answer:

197 = 10(31-1) + a

197 = 300 + a

-103 = a

The coffee cups can hold 7/9 of a pint of liquid. If Emily pours 2/3 of a pint of coffee into a cup,how much milk can a customer add? PLZ HELP!​

Answers

Answer:

1/9

Step-by-step explanation:

easy 2/3 is equivalent to 6/9. So there is 1/9 of a pint left

Determine which is the appropriate approach for conducting a hypothesis test. ​Claim: The mean RDA of sodium is 2400mg. Sample​ data: n​150, ​3400, s550. The sample data appear to come from a normally distributed population.

Answers

Answer:

Use the student t distribution

Step-by-step explanation:

Here is the formula

t = (x - u) ÷(s/√N)

From the information we have in the question:

n = 150

s = 550

x = 3400

u = mean = 2400

= 3400 - 2400÷ 500/√150

= 1000/44.9

= 22.27

At 0.05 significance level, df = 149 so t tabulated will be 1.65.

We cannot use normal distribution since we do not have population standard deviationWe cannot use normal distribution since we do not have population standard deviationChisquare cannot be used since we are not testing for population varianceWe cannot use normal distribution since we do not have population standard deviationChisquare cannot be used since we are not testing for population varianceThe parametric or bootstrap method cannot be used either.

The range of values for x?

Answers

Answer:

x = 32

but

I would say anything from 30 to 33

but truly i have no clue about the range

Step-by-step explanation:

3x-9=87 (because 180 -93 =87)

3x = 96

x = 32

Answer:

it is 32

Step-by-step explanation:

Other Questions
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