8x - (2x - 13) = 42
solve and check the equation​

Answers

Answer 1

Answer:

x = 29/6

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Distributive Property

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify

8x - (2x - 13) = 42

Step 2: Solve for x

[Distributive Property] Distribute negative:                                                     8x - 2x + 13 = 42[Subtraction] Combine like terms:                                                                    6x + 13 = 42[Subtraction Property of Equality] Subtract 13 on both sides:                        6x = 29[Division Property of Equality] Divide 6 on both sides:                                 x = 29/6

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Substitute in x:                                                                                                  8(29/6) - [2(29/6) - 13] = 42Multiply:                                                                                                             116/3 - [29/3 - 13] = 42[Brackets] Subtract:                                                                                           116/3 - -10/3 = 42Subtract:                                                                                                            42 = 42

Here we see 42 does indeed equal 42.

∴ x = 29/6 is the solution.

Answer 2

Answer:

x = 29/6

Step-by-step explanation:

solve for x.

8x - ( 2x - 13 ) = 42

distribute minus sign

8x - 2x + 13 = 42

combine like terms

6x + 13 = 42

subtract 13 from both sides

6x + 13 - 13 = 42 - 13

6x = 29

Divide each side by 6

6x / 6 = 29 / 6

x = 29 / 6

Check the equation :

8x - ( 2x - 13 ) = 42

substitute the value of x in equation

8 ( 29/6) - ( 2(29/6) - 13) = 42

reduce the number with the greatest common factor 2

4 × 29 /3 - ( (29/3) - 13) = 42

calculate the product

116/3 - ( 29/3 - 13 )= 42

calculate the difference

116/3 -( -10/3 )= 42

change the sign

116/3 + 10/3 = 42

add the fractions to get 42.

42 = 42

Hence, verified.


Related Questions

Find the value of x for which WXYZ must be a parallelogram.

Answers

Answer:

[tex](5x - 4) \degree = (2x + 14)\degree \\ 3x = 18\\ x = 6[/tex]

choose the appropriate postulate of the following pair lf triangles are congruent.

Answers

it would be ASA since we know 2 angles are congruent and we can use the reflexive property on the side in between the 2 angles

Answer:

ASA

Step-by-step explanation:

they share the side in the middle (reflexive property) and have two congruent angles

I needddd helpppp
Which point is a representation of -(-3)???

Answers

Answer:

Point a

negative means on a number line to the left side

Step-by-step explanation:

A medical researcher is studying the spread of a virus in a population of 1000 laboratory mice. During any week, there is a 70% probability that an infected mouse will overcome the virus, and during the same week there is a 40% probability that a noninfected mouse will become infected. Four hundred mice are currently infected with the virus. How many will be infected next week and in 3 weeks?
(a) next week mice rilex
(b) in 3 weeks mice

Answers

Answer:

a) 360 mice

b) 364 mice

Step-by-step explanation:

Assume :

A = number of infected mice , B = number of non-infected mice

P( infected mice overcoming infection ) = 70% = 0.7

P ( Infected mice not overcoming infection ) = 1 - 0.7 = 0.3

P( mice becoming infected ) = 40% = 0.4

P ( mice not becoming infected ) = 1 - 0.4 = 0.6

Number of infected mice = 400

Number of non-infected mice = 1000 - 400 = 600

step 1 ; express the probabilities in matrix form

[tex]P = \left[\begin{array}{ccc}0.3&0.4&\\0.7&0.6&\\\end{array}\right][/tex]

[tex]X = \left[\begin{array}{ccc}400\\600\\\end{array}\right][/tex]

step 2 : multiply the matrix above to determine the number of mice that will be infected

a) For next week

PX = [tex]\left[\begin{array}{ccc}360\\640\\\end{array}\right][/tex]

i.e. 360 mice will get infected next week

next 2 week = P ( PX )

= [tex]\left[\begin{array}{ccc}0.3&0.4&\\0.7&0.6&\\\end{array}\right][/tex]  * [tex]\left[\begin{array}{ccc}360\\640\\\end{array}\right][/tex]  = [tex]\left[\begin{array}{ccc}364\\636\\\end{array}\right][/tex]

b) In 3 weeks time

P ( P(PX) = [tex]\left[\begin{array}{ccc}0.3&0.4&\\0.7&0.6&\\\end{array}\right][/tex]  * [tex]\left[\begin{array}{ccc}364\\636\\\end{array}\right][/tex]  

               = [tex]\left[\begin{array}{ccc}363.6\\636.4\\\end{array}\right][/tex]

i.e.  364 mice will get infected in 3 weeks time

Select the statement that represents all the solutions of the inequality. d < 7 all rational numbers equal to 7 all integers less than 7 all rational numbers greater than 7 all rational numbers less than 7


the answer is :
all rational numbers less than 7
have a good day <3

Answers

Aspongebob at the bottom of the sea

Step-by-step explanation:

In a plain, robust, conversational style, the author known as “Elena Ferrante” has captivated readers worldwide with her chronicle of a complicated friendship between two women.

Answer:

Step-by-step explanation:

anything  1-6

Write the equation of the line parallel to y=1/2x−6 that passes through (−10,4).

Answers

Answer:

y = 1/2 x + 9

Step-by-step explanation:

y = 1/2 x + b

4 = (1/2)(-10) + b

4 = -5 + b

b = 9

Please help due today

Answers

Answer:

55

Step-by-step explanation:

all of the angles in a triangle ALWAYS add up to 180 degrees.

do the math.

X=55.
The sum of a triangle is always 180. You find the given angles and subtract them from 180 to find your third angle! hope this helps

A line through the point (2,5) forms a right triangle with the x-axis
and y-axis in the 1st quadrant. Determine the equation of the line that
will minimize the area of this triangle.

Answers

9514 1404 393

Answer:

  5x +2y = 20

Step-by-step explanation:

Suppose 'a' is the x-intercept of the line.

Then the slope is given by the slope formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (0 -5)/(a -2)

And the y-intercept is ...

  b = y -mx = 5 -(-5/(a-2))(2) = 5 +10/(a -2)

The area of the triangle is half the product of 'a' and 'b', so is ...

  A = 1/2ab

  A = 1/2(a)(5 +10/(a -2)) = 2.5a +5a/(a-2)

The area is minimized when the derivative of this is zero.

  A' = 2.5 -10/(a -2)^2 = 0

Solving for 'a' gives ...

  (a -2)^2 = 10/2.5 = 4

  a = 2 + 2 = 4 . . . . . . . . . . . x-intercept

  b = 5 +10/(4 -2) = 10 . . . . . y-intercept

  m = -5/(4 -2) = -5/2 . . . . . . slope

An equation of the line is ...

  y = -5/2x +10 . . . . . slope-intercept form

  5x +2y = 20 . . . . . standard form

__

You may have noticed that the x-and y-intercepts are double the x- and y-values of the given point. That is, the given point is the midpoint of the hypotenuse of the triangle with minimum area. That is the general solution of this sort of problem.

What is the common ratio for the geometric sequence below, written as a fraction?

768, 480, 300, 187.5, …


/

Answers

Answer:

5/8

Step-by-step explanation:

Find the common ratio by dividing one of the numbers in the sequence by the previous one:

480/768

= 0.625

Convert this to a fraction:

0.625

= 5/8

So, the common ratio is 5/8

how do i solve this problem

Answers

Answer:

[tex]A\approx 159.6[/tex]

Step-by-step explanation:

1. Approach

To solve this problem, divide the given figure up into two smaller figures, a rectangle and a semi-circle. Find the area of each figure and add up the values to find the total area. Remember the formula to find the area of a rectangle is as follows ([tex]A=(length)(width)[/tex]). The formula to find the area of a circle is the following, ([tex]A=(\pi)(r^2)[/tex]).

2. Find the area of the rectangle

The radius is the measurement in a circle from the center of a circle to any point on the circle's circumference (outer edge). The diameter is a line going through a circle connecting two opposite edges on a circle and passing through the center of a circle. By its definition, the diameter is always twice the radius of a circle.

As one can see in the rectangle, the side of the rectangle is made of the diameter of the circle. Since the diameter of a circle is twice the radius, one must multiply the radius by (2), then multiply that value by the length of the rectangle to find the area of the rectangle,

[tex]A=(length)(width)\\[/tex]

Substitute,

[tex]A_r=(length)(2(radius))\\A_r=(14)(2(5))[/tex]

Simplify,

[tex]A_r=(14)(2(5))\\A_r=(14)(10)\\A_r=140[/tex]

3. Find the area of the semi-cricle

Now one has to find the area of the semi-circle. Since a semi-circle is half of a circle, one must divide the formula to find the area of a circle by (2) in order to find the area of a semi-circle. Remember parameter (r) represents the radius, and ([tex]\pi[/tex]) represents the numerical value (3.1415...)

[tex]A=\frac{(\pi)(r^2)}{2}[/tex]

Substitute,

[tex]A_s=\frac{(\pi)(5^2)}{2}[/tex]

Simplify,

[tex]A_s=\frac{(\pi)(5^2)}{2}\\A_s=\frac{(\pi)(25)}{2}\\A_s=12.5\frac{(\pi)}{2}\\A_s\approx19.635[/tex]

4. Find the total area

To find the total area of the figure, one must add up the two components, add the area of the rectangle to the area of the semi-circle,

[tex]A=A_r+A_s\\[/tex]

Substitute,

[tex]A=140+19.635[/tex]

Simplify,

[tex]A=159.635[/tex]

[tex]A\approx 159.6[/tex]

A dancing competition has 13 competitors, of whom four are American, two are Mexicans, four are Russians and three are Italians. If the contest result lists only the nationality of the competitors, how many outcomes are possible?

Answers

Answer:

900,900 outcomes are possible.

Step-by-step explanation:

Arrangements with repetition:

The number of possible arrangements of n elements, considered that they are divided in classes of [tex]n_1,n_2,...,n_n[/tex] elements, is given by:

[tex]A = \frac{n!}{n_1!n_2!...n_n!}[/tex]

A dancing competition has 13 competitors

This means that [tex]n = 13[/tex]

Four are American, two are Mexicans, four are Russians and three are Italians.

This means that [tex]n_1 = 4, n_2 = 2, n_3 = 4, n_4 = 3[/tex]

How many outcomes are possible?

[tex]A = \frac{13!}{4!2!4!3!} = 900900[/tex]

900,900 outcomes are possible.

helppp please i need this answered fast please :⊂

Answers

Answer:

dang good luck

Step-by-step explanation:

PLEASE HELP FOR 10 POINTS what is the length of PM
A.) 3 units
B.) 4 units
C.) 5 units
D.) 6 units

Answers

Answer:

D

Step-by-step explanation:

The figures are the same just flipped. We can tell AD=NM ON=AB, BC=OP. Thus DC =MP

DC has the length of 6 and because MP is congruent to DC it also has 6.

Can someone please help me? thank you

Answers

Answer:

c = (ef-ab)/d

Step-by-step explanation:

ab+cd = ef

Subtract ab from each side

ab+cd -ab = ef-ab

cd = ef-ab

Divide by d

cd /d =(ef-ab)/d

c = (ef-ab)/d

50 POINTS!!!!!!!!!!!!!!!
28,45,12,34,36,45,19,20

Find the mean absolute deviation of this set of data. PLEASE PUT STEPS

Answers

Answer:

10.125

Step-by-step explanation:

Given the data :

28,45,12,34,36,45,19,20

The mean absolute deviation of the data is :

Σ|x - mean| / n

n = number of values = 8

Mean = Σx / n = 239 / 8

Mean = 29.875

Take the sum of the absolute value if the difference between each data value and the mean, then divide by the data size

Using a mean absolute deviation calculator ;

Mean absolute deviation = Σ|x - mean| / n = 10.125

4x+9=41 x is equal to

Answers

Answer and Step-by-step explanation:

Simply solve for x (very easy to do).

4x + 9 = 41

Subtract 9 from both sides of the equation.

4x = 32

Divide both sides of the equation by 4.

x = 8

x is equal to 8.

#teamtrees #PAW (Plant And Water)

What is an equivalent expression to 4( x + 2) + 6x

Answers

Answer:  10x+8

Work Shown:

4(x+2) + 6x

4x+8 + 6x

(4x+6x) + 8

10x+8

Answer: 10x+8

Step 1: Rewrite equation

4(x+2)+6x

Step 2: Distribute

To distribute, multiply the number on by outside of the parentheses with the values on the inside of the parentheses. 4 times x is 4x, and 4 times 2 is 8. Substitute this into the equation.

4x+8+6x

Step 3: Combine like terms for final product

Like terms will be valued that share the same variable, or lack of. In this case, it is 4x and 6x. Add these terms to combine them.

10x+8

Hope this helps!

Cho tam giác ABC vuông cân tại A
Cạnh đáy BC 5cm, AB 7cm. Tính diện tích

Answers

Answer:

7 × 5 :2 it is the answer ,i love you

Please help me with this as quickly as possible

Answers

3 hour 30 minutes : 36 minutes

1 hour = 60 minutes

3 hour = 3×60 minutes = 180 minutes

3hour 30 minutes = 180 minutes + 30 minutes

                               = 210 minutes

210 minutes : 60 minutes

3 hours 30 minutes : 60 minutes = 6:2

can someone help asap

Answers

Answer:

C

Step-by-step explanation:

8×26×6=1200 cubic centimeters

hence, C is the closest

If the function f(2x + 3) = 3x- 8, find f -¹(x)​

Answers

Answer:

(2x + 35)/3

Step-by-step explanation:

f(2x + 3) = 3x - 8

= 3(2x)/2 - 8

= 3(2x + 3 - 3)/2 - 8

= 3(2x + 3)/2 - 3(3)/2 - 8

= ( 3(2x + 3) - 25)/2

Therefore, f(x) = (3x - 25)/2

Let f(x) = (3x - 25)/2 = y

Therefore,

x = (2y + 35)/3 = f(y)

Hence,

f-¹(x) = f(y) = (2y + 35)/3

Just by merely replacing y,

f-¹(x) = (2x + 35)/3

Answer:

Step-by-step explanation:

[tex]let~g(x)=2x+3,~ then~f\circ g(x)=f(g(x)=3x-8\\\\[/tex]

lets assume that f(x) is a line, so f(x)=mx+b

[tex]f(g(x))=m(2x+3)+b=2mx+3m+b=3x-8[/tex]

the follow equation system results:

[tex]2m=3 \\ 3m+b=-8[/tex]

[tex]m=\frac{3}{2}\\\\b=-\frac{25}{2}[/tex]

finally:

[tex]y=f(x)=\frac{3}{2}x-\frac{25}{2}[/tex]

now is time to calculate the inverse function:

[tex]y=\frac{3}{2}x-\frac{25}{2}=>2y+25=3x=>x=\frac{2}{3}y+\frac{25}{3}[/tex]

so

[tex]f^{-1}(x)=\frac{2}{3}x+\frac{25}{3}[/tex]

Which one hurry
A.2 unit sides
B.3 unit sides
C.4 unit sides
D.5 unit sides

Answers

Answer:

4 units

Step-by-step explanation:

P of a square is P =4s

A of a square is A = s^2

4s = s^2

Divide each side by s

4s/s = s^2/s

4 =s

Translate and solve: twenty-three greater than b is at least −276.

Answers

Answer:

b+23≥-276

b≥-276-23

b≥-299

Step-by-step explanation:

hope this is helpful

Please help me with this I need it bad

Answers

Answer:

1

Step-by-step explanation:

The average rate of change is the gradient _

Gradient = Rise / Run = (y2 - y1) / (x2 - x1)

From the table ;

x2 = 4 ; x1 = - 1 ; y2 = 5 ; y1 = 0

Gradient = (y2 - y1) / (x2 - x1) = (5-0) / (4 - - 1) = 5/5 = 1

A quick quiz consists of a multiple-choice question with 5 possible answers followed by a multiple-choice question with 5 possible answers. If both questions are answered with random guesses, find the probability that both responses are correct.

Answers

Answer:

1/25

Step-by-step explanation:

P of both answers are correct =

P first question is answered correct and P second question is answered correct

in probability,  and = multiplication

P first question is answered correct =1 correct answer/5 possible answers =1/5

P second question is answered correct = 1/5

P of both answers are correct = (1/5) · (1/5) = 1/25

Pls helpi neeed the answer

Answers

Answer:

I believe that the answer is 80X (or C)

Step-by-step explanation:

it looks like it is just under a right angle so i believe that it would be 80X

Answer:

y=6x

Step-by-step explanation:

Solve. Four times the sum of 2 and some number is - 8. What is the number?​

Answers

Answer:

-4

Step-by-step explanation:

Let say other number is 'x'

Equation:-

4(2 + x) = -8

8 + 4x = -8

4x = - 16

x = - 16/4

x = - 4

Help me wit this rq…………..

Answers

I’m pretty sure it’s C

Which value is in the domain of f(x)? PLS help :)

Answers

Answer:

(c) 4

Step-by-step explanation:

Given

The piecewise function

Required

The value in f(x) domain

The domain of f(x) is:

[tex]-6 < x \le 0[/tex] and [tex]0 < x \le 4[/tex]

Combine both inequalities:

[tex]-6 < x \le 4[/tex]

List the values of the inequality

[tex]-6 < x \le 4 = \{-5,-4,-3,-2,-1,0,1,2,3,4\}[/tex]

From the list of given options

Only 4 is among the domain

Others are not

Will mark Brainlest help please (find the value of x or theta) step by step​

Answers

Answer:

Step-by-step explanation:

BC=[tex]\sqrt{5^2+5^2}[/tex]

x   =[tex]\sqrt{50}[/tex]

x   = 5[tex]\sqrt{2}[/tex]

tan theta= 5/5

      theta= tan^-1 (5/5)        

                =45°

Step-by-step explanation:

BC=\sqrt{5^2+5^2}52+52

x   =\sqrt{50}50

x   = 5\sqrt{2}2

tan theta= 5/5

      theta= tan^-1 (5/5)        

                =45°

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