Solve the expression and find the value of x.
[tex] \frac{x + 1}{10} - \frac{3(x - 1)}{5} = 2 [/tex]

Answers

Answer 1

[tex]\large\underline{\sf{Solution-}}[/tex]

[tex]\sf \dfrac{x + 1}{10} - \dfrac{3(x - 1)}{5} = 2[/tex]

[tex]\sf\longmapsto \dfrac{x + 1}{10} - \dfrac{3x - 3}{5} = 2[/tex]

[tex]\sf\longmapsto \dfrac{(x + 1) - 2(3x - 3)}{10} = 2[/tex]

[tex]\sf\longmapsto \dfrac{x + 1 - (6x - 6)}{10} = 2[/tex]

[tex]\sf\longmapsto \dfrac{x + 1 - 6x + 6}{10} = 2[/tex]

[tex]\sf\longmapsto \dfrac{ - 5x + 7}{10} = 2[/tex]

[tex]\sf\longmapsto - 5x + 7 = 20[/tex]

[tex]\sf\longmapsto - 5x = 20 - 7[/tex]

[tex]\sf\longmapsto - 5x = 13[/tex]

[tex]\sf\therefore x = - \dfrac{13}{5} [/tex]

Hence, the value of x will be -13/5 respectively.

Answer 2

[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]

[tex]\frac{x + 1}{10} - \frac{3(x - 1)}{5} = 2 \\ [/tex]

[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]

[tex]\frac { x + 1 } { 10 } - \frac { 3 ( x - 1 ) } { 5 } = 2 \\ \frac { x + 1 } { 10 } - \frac { 3 ( x - 1 ) } { 5 } = \frac{2}{1} [/tex]

Take a look at the denominators. The denominators are 10, 5 & 1. Their LCM is 10. So, multiply the fractions on both the sides of the equation by 10.

[tex]\frac { x + 1 } { 10 } - \frac { 3 ( x - 1 ) } { 5 } = \frac{2}{1} \\ \frac{x + 1}{10} \times \frac{1}{1} - \frac{3x - 3}{5} \times \frac{2}{2} = \frac{2}{1} \times \frac{10}{10} \\ \frac{x + 1}{10} - \frac{6x - 6}{10} = \frac{20}{10} [/tex]

Now cancel the denominators (as they have the same value) & take the numerators.

[tex]x + 1 - (6x - 6) = 20 \\ [/tex]

Now, simplify it.

[tex]x + 1 - (6x - 6) = 20 \\ x + 1 - 6x + 6 = 20 \\ x - 6x + 1 + 6 = 20 \\ - 5x + 7 = 20 \\ - 5x = 13 \\ x = -\frac{13}{5} \\ \boxed{ \boxed{ \bf x = - \frac{13}{5} =\: - 2 \frac{3}{5} = - 2.6}}[/tex]

__________________

Hope it'll help you!

ℓu¢αzz ッ


Related Questions

Leah is solving the equation below using the properties of exponents.
2^2x-3 = (1/16)^3x+9
Here is Leah's work: (see attached picture)

Which line has Leah's mistake? What is Leah's mistake?

Answers

I think she messed up at the beginning she did solve in the right order but she did i it wrong so what she had to do was do( 2) times the power of the 4 after diving what’s in the Parentheses then she can solve the rest if I’m correct but you might want to fact check it

Answer:

Lea messed up on line one when you flip a fraction the exponents become negative hers haven't changed

Step-by-step explanation:

Part C What conclusion can you draw from this? To determine whether they used the same number of tiles, set the two expressions equal to each other and solve for x. Is there a solution for x? Why or why not? If there is a solution, what is it?

Answers

Answer:

We can conclude that someone used more tiles then the other because both equations are not equal.

Step-by-step explanation:

If you try to solve it both equations will not be shown as equal.

Match each system of equations to its point of intersection.

y = 2x + 1

y = x + 3


y = x + 3

y = -3x - 2


y = -x - 7

y = x + 3


y = -x - 7

y = 2x + 1


y = 2x + 1

y= -3x - 2

Answers

Answer:

1. (2,5)

2. (-1.25, 1.75)

3. (-5,-2)

4.(-2.66, -4.33)

5. (-0.6, -0.2)

Step-by-step explanation:

Solve by substituting the y's and solve for x. Plug in x into one of the equations and find the y value for your point of intersection

Answer:

Ur reatarded

Step-by-step explanation:

graph the function f(x) = 3(4)^x​

Answers

Answer:

That depends on how accurate you are with pen and paper.

You can tell it's a growing exponential, so the form is the traditional one. If you are particularly inclined in crunching numbers and working on a grid I would pick 0, 1 and -1, 1/2 and -1/2, a few positive integers, and that's it.

If not, i would be satisfied saying that when x = 0 (ie, the y intercept) y= 3, and that's all. Then, my drawing is made with paint, don't expect a masterpiece.

help please and thank you​

Answers

Answer:

Function: c = 2(m) + 5

A: Jason will spend $11 because 2(3) + 5 = (6 + 5) =11

B: No, because 2(7) + 5 = (14 + 5) = 19 and he only has 15 dollars.

Step-by-step explanation:

Cost = $2(the rate per mile) x (M)(miles driven) plus $5 (base cost)

For A and B I solved using the function.

The quotient of a number and -4 is -9

Answers

Answer:36

Step-by-step explanation:36÷ -4 = -9

The answer would be 36 which is 36÷ -4 = -9 after applying the arithmetic operation.

What is an arithmetic operation?

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.

It is given that:

The quotient of a number and -4 is -9

Mathematically we can write:

x ÷ -4 = -9

x/(-4) = -9

x = 36

OR

36 ÷ -4 = -9

Thus, the answer would be 36 which is 36÷ -4 = -9 after applying the arithmetic operation.

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What is the probability of picking a number divisible by 4 between (and including) the numbers 12-20?

Answers

Answer:

5/9 or 55.5%

Step-by-step explanation:

there are 5 numbers divisible by 4, 12-20 inclusive:  4, 8, 12, 16, 20

there are 9 numbers from 12-20, inclusive

answer would be 5/9

A rectangular prism is made up of 320 unit cubes. The prism is 8 unit cubes wide.
Which could be the other dimensions of the rectangular prism? Choose all the possible dimensions.
A. 4 unit cubes long
10 unit cubes high
B. 5 unit cubes long
8 unit cubes high
C. 8 unit cubes long
5 unit cubes high
D. 8 unit cubes long
8 unit cubes high
E. 10 unit cubes long
4 unit cubes high
F. 20 unit cubes long
2 unit cubes high
G. 20 unit cubes long
20 unit cubes high
H. 25 unit cubes long
15 unit cubes high

Answers

Answer:

A, B, C, E, F.

Step-by-step explanation:

320 / 8 = 40

So the length times the  height of the prism  will be 40.

So the possible dimensions are

A ( 4 * 10).

B.

C.

E.

F

The option (A), (B), (C), (E), and (F) are correct because the multiplication of the length and height is 40.

What is a rectangular prism?

It is defined as the six-faced shape, a type of hexahedron in geometry.

It is a three-dimensional shape. It is also called a cuboid.

We have volume of rectangular prism = 320 cubic unit

Width of the rectangular prism = 8 unit

320 = l×w×h

320 = 8l×h

l×h = 40

So the multiplication of the length and height should be 40

A. 4 unit cubes long and 10 unit cubes high:

l×h = 4×10 = 40

B. 5 unit cubes long and 8 unit cubes high:

l×h = 5×8 = 40

C. 8 unit cubes long and 5 unit cubes high:

l×h = 8×5 = 40

D. 8 unit cubes long and 8 unit cubes high:

l×h = 8×8 = 64

E. 10 unit cubes long and 4 unit cubes high:

l×h = 10×4 = 40

F. 20 unit cubes long and 2 unit cubes high:

l×h = 20×2 = 40

G. 20 unit cubes long and 20 unit cubes high:

l×h = 20×20 = 400

H. 25 unit cubes long and 15 unit cubes high:

l×h = 25×15 = 375

Thus, the option (A), (B), (C), (E), and (F) are correct because the multiplication of the length and height is 40.

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you are helping your mom cook christmas dinner. you can peel 2 potatoes per minute. you need 60 potatoes to feed the entire group. How long will it take you to finish if you have already peeled 18 potatoes?

Answers

Answer:  21 mins to peel the balanced potatoes

Step-by-step explanation:

If a painter paints 3 rooms in 1/2 day, what would be a reasonable estimate, how many rooms would painter paint in working 5 days? What is painters rate of painting in rooms painted per day? *

Answers

Answer:

Rate per day: 6 rooms

estimate: 6*5 = 30 rooms

Evaluate x + y - 4 when x = 4 and y = 1

Answers

Answer:

1

Step-by-step explanation:

Subsitute x and y:

x + y - 4

= 4 + 1 - 4

= 1

a basketball game that costs 35 was put on sale at a 15 discount what was the sale price of the basketball

Answers

Answer: before the sale, the basketball game was $50.00 .

Step-by-step explanation: you do $35.00 + 15% and you would get $50

How many weeks are there a month?

Answers

Answer:

4 weeks

Step-by-step explanation:

Answer:

About 4 weeks

Step-by-step explanation:

Solve for x: 2/3 = x-1/5

Answers

Answer: x=13/3

Step-by-step explanation:

Describe the domain and range. Graph the function. What do I do with the -3? The graph shows that y and x are at 0 so...?

Answers

Answers:

Domain: all real numbers

Range: [tex]y \le 6[/tex]

Graph is below.

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

Explanation:

This is a piecewise function that is composed of two parts:

The first piece being y = x+6 but only when [tex]x \le 0[/tex]The second piece occurs when x > 0 and that piece is y = -3x

This piecewise function has split identities or multiple aliases so to speak. It all depends on what the x input is.

The graph is shown below.

The domain is the set of all real numbers since any x value will lead to some y output. Even x = 0 itself is allowed. Note the arrows indicate the graph stretches on forever to the left and to the right.

The range on the other hand isn't all real numbers. Instead, it's [tex]y \le 6[/tex] indicating that y = 6 is the largest y can get. Simply locate the highest point on the graph (similar to the concept of the vertex) and you'll spot the highest y value.

Side notes:

The domain in interval notation is [tex](-\infty, \infty)[/tex] which encompasses the entire real number line.The range in interval notation is [tex](-\infty, 6][/tex] where the square bracket includes the endpoint 6.

Solve for x
12x = 22
=
Give your answer as an improper fraction in its
simplest form.
X =

Answers

Answer:  11/6 0r 1 5/6

Step-by-step explanation:

12x = 22

x = 22/12

x = 11/6 or 1 5/6

Asher's sister is eight years older than
Asher. Their combined ages add up to 20.
How old is Asher?

Equation:


Solution:

Answers

You can make the equation by saying x is Asher’s age. Then

x + (x + 8) = 20

This simplifies to

2x = 12

And x = 6

Therefore, Asher is 6 years old

if 2+8=10 then 12+8=20 so Asher is 12 years old while His sister is 20 cus we're adding Ash age to his sister which we don't kno what her age is but at the same time we both know that whatever her age is it adds up to 20

-74 = 4/9x - 2 equation​

Answers

Answer -162

Step-by-step explanation:

Answer:

=−162

Step-by-step explanation:

Select the algebraic definition for the piecewise function graph.

Answers

Answer:

I don't the answer man sorry

Please help me I don’t understand this

Answers

Answer:

14/15

Step-by-step explanation:

9/15+5/15=14/15

3/5+1/3

common denominator is 15 ( just think about the 3 times table and 5 times table )

5*3=15

3*5=15

Multiply the denominator and numerator by 3 for 3/5

Multiply the denominator and numerator by 5 for 1/3

(3)(3)/(5)(3) +(1)(5)/3(5)

9/15+5/15= 14/15

Answer : 14/15

7.21. For a group of 100 people, compute a. the expected number of days of the year that are birthdays of exactly 3 people; b. the expected number of distinct birthdays.

Answers

The expected number of a dataset is the mean of the dataset

The expected number of selection is: [tex]\mathbf{E(x) =365\times ^{100}C_3 \times \frac{1}{365}^3 \times \frac{364}{365}^{97}}[/tex]The expected number of distinct birthdays is: [tex]\mathbf{E(x) = 365\times (1 - (\frac{364}{365})^{100})}[/tex]

The given parameters are:

[tex]\mathbf{n = 100}[/tex] --- sample size

[tex]\mathbf{r = 3}[/tex] --- selection of 3 people

(a) The expected number of birthdays

The probability of a having a birthday on a certain day is:

[tex]\mathbf{p = \frac{1}{365}}[/tex]

The probability of not having a birthday on the day is:

[tex]\mathbf{q = \frac{364}{365}}[/tex]

For a selection of 3 people in 100, the expected number of selection is:

[tex]\mathbf{E(x) =Days \times ^{100}C_3 \times p^3 \times q^{100 - 3}}[/tex]

So, we have:

[tex]\mathbf{E(x) = Days \times ^{100}C_3 \times \frac{1}{365}^3 \times \frac{364}{365}^{100 - 3}}[/tex]

Rewrite as:

[tex]\mathbf{E(x) =Days \times ^{100}C_3 \times \frac{1}{365}^3 \times \frac{364}{365}^{97}}[/tex]

There are 365 days in a year.

So, the expression becomes

[tex]\mathbf{E(x) =365\times ^{100}C_3 \times \frac{1}{365}^3 \times \frac{364}{365}^{97}}[/tex]

(b) Expected number of distinct birthdays

The probability that a person from the has his birthday on a certain day is:

[tex]\mathbf{p = 1 - (\frac{364}{365})^{100}}[/tex]

For 365 days, the expected number of distinct birthdays is:

[tex]\mathbf{E(x) = Days \times (1 - (\frac{364}{365})^{100})}[/tex]

There are 365 days in a year.

So, the expression becomes

[tex]\mathbf{E(x) = 365\times (1 - (\frac{364}{365})^{100})}[/tex]

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I dont understand this question and i keep getting it wrong.

Answers

Answer:

48

11

Step-by-step explanation:

5 glasses  ------  20 sec

12 glasses ------  ?

so 5 * x = 12 * 20

x = 12 * 4

x = 48

12 glasses -------  48 sec

?   glasses -------  44 sec

so 12 * 44 = x * 48

44 = x * 4

x = 44/4 = 11

x = 11

Answer:

12 - 48

11 - 44

Step-by-step explanation:

20 ÷ 5 = 4

12 · 4 = 48

44 ÷ 4 = 11

I hope this helps!

What are the domain and range of each relation?
Drag the answer into the box to match each relation.

Answers

The domain and range of the functions are:

Function (A):

Domain: (-2, -1, 0, 2); Range:  -4

Function (B):

Domain: (-4, -2, 1, 4); Range: -8

What are domain and range?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. The difference between the lowest and highest values in a list or set is known as the range. Put all the numbers in order before determining the range. The lowest number should then be subtracted from the highest.

So, the domain and range of the function:

Function (A):

Domain: (-2, -1, 0, 2)Range: -2 -2 = -4

Function (B):

Domain: (-4, -2, 1, 4)Range: -4 -4 = -8

Therefore, the domain and range of the functions are:

Function (A):

Domain: (-2, -1, 0, 2); Range:  -4

Function (B):

Domain: (-4, -2, 1, 4); Range: -8

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Eliminate the parameter, t, in the parametric equations, x = 3cos(t) and y = -6sin(t).

A) 2 x2 + y2 = 36
B) x2 + y2 = 2
C) 4 x2 + y2 = 36
D) x2 + y2 = 36

Answers

Recall that

cos²(t) + sin²(t) = 1

Then solving for cos(t) and sin(t), we have

x = 3 cos(t)   ===>   cos(t) = x/3

y = -6 sin(t)   ===>   sin(t) = -y/6

so that the above identity gives us

(x/3)² + (-y/6)² = 1

x²/9 + y²/36 = 1

36 (x²/9 + y²/36) = 36

(C) 4x² + y² = 36

The parametric equation in the Cartesian form is 4x² + y² = 36 the correct choice is (C).

What are parametric equations?

A parametric equation in mathematics specifies a set of numbers as functions of one or more independent variables known as parameters.

We have two parametric equations:

x = 3cos(t) and

y = -6sin(t).

As we know, the trigonometric identity:

sin²θ + cos²θ = 1

For checking the option (A):
2x² + y² = 36

= 2(3cos(t))² + (-6sin(t))²

= 18cos²t + 36sin²t ≠ 36

Similarly, for checking the option:

4x² + y² = 36

= 4(3cost)² + (-6sint)²

= 36cos²t + 36sin²t

= 36(cos²t + sin²t)

= 36(1) = 36

Thus, the parametric equation in the Cartesian form is 4x² + y² = 36 the correct choice is (C).

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need the answer noww pls

Answers

Three pounds of apple cost $4.50

A 7-kg bag of apples for $10

Answers

Answer:

finish the question

Step-by-step explanation:

How many ways can you arrange 2 letters from the word S Q U A R E

Answers

Answer:

30

Step-by-step explanation:

WE use permutation for this question:

since the letters in SQUARE are all distinct, so:

[tex]^{6}P_{2} = 6*5=30[/tex]

The number of ways of arranging 2 letters from the word S Q U A R E is given by A = 15 ways

What are Combinations?

The number of ways of selecting r objects from n unlike objects is given by combinations

ⁿCₓ = n! / ( ( n - x )! x! )

where

n = total number of objects

x = number of choosing objects from the set

Given data ,

Let the number of ways of arranging 2 letters from the word S Q U A R E be represented as A

Now , to select 2 letters from the 6 letters in the word SQUARE, without regard to order.

This is a combination problem, since the order in which we select the letters does not matter. Therefore, we can use the formula:

6 C 2 = 6! / 2!(6 - 2)!

= 6 x 5 / (2 x 1) x (4 x 3 / (2 x 1))

= 15

Hence , there are 15 ways to arrange 2 letters from the word SQUARE

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Can you help me in this question ASAP!!!

Answers

What is in the drop down menu????

Answer:

increase

$750

y=750x+1000

Resolver 3 -2x=12 -6x

Answers

Answer:

x = 9/4

Step-by-step explanation:

Solve for x.  Start by adding 6x to both sides, which results in 3 + 4x = 12.

Combine the constants, obtaining 4x = 9.

Dividing both sides by 4, we get x = 9/4.

Answer:

x=

mixed number form: 2 1/4

decimal form: 2.25

exact form: 9/4

the ranch house serves a 24 oz sirloin steak that has a total of 1,800 calories. how many calories per ounce does the steak have

Answers

The amount of calories per ounce does the steak have is 75 calories per ounce.

Using this formula

Calories per ounce=Total calories/Number of oz sirloin steak

Where:

Total calories=1,800 calories

Number of oz sirloin steak=24 oz

Let plug in the formula

Calories per ounce=1800/24 oz

Calories per ounce=75 calories per ounce

Inconclusion the amount of calories per ounce does the steak have is 75 calories per ounce.

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