calculate the absolute value
| 4 - 3x | = 5x + 4 ​

Answers

Answer 1

Recall the definition of absolute value:

• |x| = x if x ≥ 0

• |x| = -x if x < 0

So we have 2 cases to consider:

• If 4 - 3x ≥ 0, then |4 - 3x| = 4 - 3x, and we have

4 - 3x = 5x + 4

8x = 0

x = 0

• If 4 - 3x < 0, then |4 - 3x| = -(4 - 3x) = 3x - 4, which gives

3x - 4 = 5x + 4

2x = -8

x = -4

However, keep in mind that |x| is always non-negative. If x = -4, then the right side of the equation becomes

5(-4) + 4 = -20 + 4 = -16 < 0

so the solution in this case is extraneous.


Related Questions

Which one of the following is an example of algebraic expression?
a. 22+7÷4
b. 12=7−1
c. x,y,z
d. x2+y−2

Answers

Answer:

Option D. +y-2

Step-by-step explanation:

Algebraic expressions include at least one variable and at least one operation (addition, subtraction, multiplication, division). For example, 2(x + 8y) is an algebraic expression.

Answer:

The correct option is choice D.  x^2+y−2

Algebraic expression means that equation needs to have one variable, meaning any alphabet and one kind of operation. Operations are + - / and*

If you look at your answer choices, option d is the only that has an expression as well as the operation, so both things in one equation.

A salesman's salary is $18,500 per year. In addition, the salesman earns 5% commission on the year's sales. Last year the salesman earned $25,400. How much was sold that year?

Answers

Answer:

138000

Step-by-step explanation:

25,400 - 18,500

6900

5% = 6900

100% = ?

cross multiplication

5x6900 / 100

yearly sale = 138000

Please help me I nned help

Answers

Answer:

length*breadth*height

Can someone plz solve the math problem i attached as a screenshot. Thx

Answers

Answer:

[tex]radius \: of \: first \: circle \: = \frac{3}{2} = 1.5cm \\ radius \: of \: \: second = \frac{4}{2} = 2cm \\ radius \: of \: third = \frac{6}{2} = 3cm \\ then \: ab \: length \\ = radius \: of \: first + diameter \: of \: second \: +r adius \: of \: third \\ = 1.5 + 4 + 3 \\ = 1.5 + 7 \\ = 8.5 cm\\ thank \: you[/tex]

One bolt of cloth will make shirts for 47 people. How many bolts are needed for 376 people?

Answers

Answer:

8

Step-by-step explanation:

the relationship of one "unit" (bolt) of cloth to 47 people makes this number (47 people) also an unit.

to answer the question we need to find out, how many units fit into the target.

how do we do that ? by division.

when we divide a/b, then we are actually asking, how many times does b fit into a.

so, how many bolts are needed for 376 people ?

well, how often does 47 fit into 376 ? how often can we build groups of 47 people out of the 376 ?

the answer

376 / 47 = 8

so, 8 bolts are needed.

Answer:

1 bolts = 47 people

so, 47+47+47+47+47+47+47+47= 376 people

The answer is 8 bolts

Find the value of x (give in steps)

Answers

Answer:

[tex]sum \: of \: exterior \: angle \: for \: a \: quadrilateral= 360 \\ x + 5x - 5 + 4x + 20 + 4x - 5 = 360 \\ x \: terms \: togather \\ x + 5x + 4x + 4x - 5 - 5 + 20 = 360 \\ 14x + 10 = 360 \\ 14x = 350 \\ x = 25 \\ thank \: you[/tex]

Which property of equality can be used to justify this step?

15 - 10x = 6x
+ 10x + 10x
————————
15 = 16x


A. Substitution Property of Equality
B. Summation Property of Equality
C. Addition Property of Equality
D. Subtraction Property of Equality

Answers

C. Addition property of Equality
C. Addition Property of Equality
because you are adding 10x to both sides

PLEASE HELP NOW

write and solve an equation to find the value of X. please explain in details and show your work!

Answers

Answer:

Solution=96°+x+35°

=x+96°+35°

=x=96°-35°

=x=61°

Solve |3n +6| = 21

Answers:
n= -5 and n = 5
n= -9 and n = 9
n= -9 and n = 5
no solution

Answers

Answer:

a

Step-by-step explanation:

Sasha places an online order. In addition to the price of the item she orders, she pays 5% tax and a flat shipping fee of $15. The total cost of her order is $141. What is the price of the item she orders?

Answers

Answer:

$120

Step-by-step explanation:

Let the price is x.

Set the equation and solve for x:

(x + 5%) + 15 = 1411.05x + 15 = 1411.05x = 126x = 126/1.05x = 120

Answer:

$119.7

Step-by-step explanation:

Shipping is typically taken after tax so we can subtract shipping and find the tax.

141 - 15 = 126

126 * 0.05 = 6.3

Now we can subtract to find what she spent on items.

126 - 6.3 = 119.7

Best of Luck!

What is the best description of the relationship in the scatterplot below?

Answers

Step-by-step explanation:

As x increases. f(x) increases so their is a positive linear association.

Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.

Answers

Answer:

slope=2/2 or 1

Step-by-step explanation:

From (-2,0) rise up by 2 and then run to the right and land on 2. So the slope will be 2/2. To simplify it's 1.

Remember this Rise goes⬆/Run to the right➡ or the other way around depends on how the graph is but you get my drift, right? ☺

solve x+5y=11 and -x+4y=7 using elimination​

Answers

Answer: (1, 2)

Concept:

There are three general ways to solve systems of equations:

EliminationSubstitutionGraphing

Since the question has specific requirements, we are going to use elimination

Solve:

Given expressions

x + 5y = 11

-x + 4y = 7

Add both equations together to elimination [x] variable

(x + 5y) + (-x + 4y) = 11 + 7

x - x + 5y + 4y = 18

9y = 18

Divide 9 on both sides

9y / 9 = 18 / 9

[tex]\boxed{y=2}[/tex]

Find the x value

x + 5y = 11 ⇔ Given equation

x + 5(2) = 11 ⇔ Substitute values of y

x + 10 = 11 ⇔ Simplify by multiplication

x + 10 - 10 = 11 - 10 ⇔ Subtract 10 on both sides

[tex]\boxed{x=1}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Stack the two equations and add them together as if they were multi-digit numbers. That will eliminate the x and then you can solve for the y. Knowing y you can then go back and solve for x.

Step-by-step explanation:

x + 5y = 11

-x + 4y = 7

---------------- "Add" the equations above to get the equation below.

9y = 18

Now you can divide both sides by 9 to see that y is equal to 2.

Now that you know that y = 2 you can substitute y in either of the two original equations. I'll use the first.

x + 5(2)= 11

x + 10 = 11

x = 1

How far below the surface of the water is the top of a submerged mountain if the ocean floor depth is 12,500 feet and the mountain has a height of 10,190 feet?

Answers

Answer:

12500 - 10190 = 2310 ft.

Step-by-step explanation:

Complete the slope-intercept form of this line.
y=-4x +

Answers

Answer:

It is y = -4x + 9

Step-by-step explanation:

General equation of a line:

[tex]y = mx + c[/tex]

For a y-intercept, c :

consider point (2, 1):

y is 1, x is 2 and m is -4

[tex]y = mx + c \\ 1 = (2 \times - 4) + c \\ 1 = - 8 + c \\ c = 1 + 8 \\ c = 9[/tex]

therefore, equation is:

[tex]y = - 4x + 9[/tex]

The complete form of the equation is y = - 4x + 9

The slope intercept form of the line is given as:

y = - 4x + c

Where c = intercept , we need to calculate, c

Take any given value of y and x and substitute into the equation, the solve for c

Take x = 1, y = 5

5 = - 4(1) + c

5 = - 4 + c

Add 4 to both sides

5 + 4 = - 4 + c + 4

9 = c

Hence, the complete form of the equation is y = - 4x + 9

Learn more : https://brainly.com/question/20976827?referrer=searchResults

Is square root of 49/5 a rational number?

Answers

It depends on how that’s written mathematically.

If it’s sqrt(49) / 5, then yes, since that’s 7/5 and 7/5 is a fraction of two integers.

If it was sqrt( 49/5 ), where the /5 is inside the square root, then the answer is no.

SOMEONE HELP ME WITH THIS QUESTION PLEASE!!!!

Answers

Answer:

E(-2, -1.5)

Step-by-step explanation:

Coordinates of the points C and D:

C(1, 6), D(-3, -4)

The point E has coordinates of (x, y).

The point E is at 3/4 of CD from C and 1/4 of CD from the point D.

Find coordinates of E:

x = -3 + 1/4(1 + 3) = -3 + 1 = -2y = -4 + 1/4(6 + 4) = -4 + 2.5 = -1.5

You have 2 cups of ketchup. You need 2 Tbspoons to make barbecue sauce. How many servings can you make?

Answers

Answer:

1 cup equals 16 tablespoons you have 2 cups so that is 32 tablespoons so you can make 16 servings. I think :)

hope this helps

find the y-intercept and x-intercept of the line. 2x+3y= -14

Answers

Answer:

X-intercept: (-7, 0)

Y-intercept: (0, -14/4)

Step-by-step explanation:

To find the intercepts plugin 0 for one variable and solve

2x+3(0)=-14

x=-7

2(0)+3y=-14

y=-14/3

Help Please!!!
Find lim h → 0 f(x+h)-f(x)/h for the given function and value of x.

f(x) = -4x -1, x = 5

Answers

Step-by-step explanation:

[tex]\displaystyle \lim_{h \to 0} \dfrac{[-4(x + h) - 1] - (-4x - 1)}{h}[/tex]

[tex]\displaystyle \:\:\:\:\:\:\:\:\:=\lim_{h \to 0}\dfrac{-4h}{h}[/tex]

[tex]\:\:\:\:\:\:\:\:\:=-4[/tex]

suppose the functions u and w are defined as follows u(x)=x+9 w(x)=the square root of x+8 find the following (wou)(8)= (uow)(8)=

Answers

Answer:

5 and 13

Step-by-step explanation:

To evaluate (w ○ u)(8) , evaluate u(8) then substitute the value obtained into w(x) , that is

u(8) = = 8 + 9 = 17 , then

w(17) = [tex]\sqrt{17+8}[/tex] = [tex]\sqrt{25}[/tex] = 5

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

To evaluate (u ○ w )(8) , evaluate w(8) then substitute the value obtained into u(x) , that is

w(8) = [tex]\sqrt{8+8}[/tex] = [tex]\sqrt{16}[/tex] = 4 , then

u(4) = 4 + 9 = 13

Answer:

Step-by-step explanation:

[tex]u(x)=x+9\\\\w(x)=\sqrt{x+8} \\\\(wou)(x)=u(w(x))=u(\sqrt{x+8} )=\sqrt{x+8}+9\\(wou)(8)= \sqrt{8+8}+9=4+9=13\\\\\\(uow)(x)=w(u(x))=w(x+9)=\sqrt{x+9+8}=\sqrt{x+17}\\(wou)(8)= \sqrt{8+17}=\sqrt{25}=5\\\\[/tex]

How do you add 1.7 plus 2 and 2/3

Answers

Answer:

4.37 (repeated)

Step-by-step explanation:

Answer:

[tex]\frac{131}{30}[/tex]

Step-by-step explanation:

1. Convert the decimal into a fraction by writing our number above a fraction line without the decimal sign.

2. Count the decimal places. Below the fraction lines write the multiple of 10 with that many zeros so that would be [tex]\frac{17}{10}[/tex]

3. Now write all numerators above the lcd (least common denominator) 30. So that would be [tex]\frac{51 + 60 + 20}{30}[/tex]

4. Calculate the sum of the positive numbers. The result is [tex]\frac{131}{30}[/tex]

5. Answer is [tex]\frac{131}{30}[/tex]

Which expression is equivalent to 10° ?
o 10 - 10 - 10 - 10 - 10 - 10
O 6.6.6.6.6.6.6.6.6.6
0 10. 10. 10. 10.10
o I don't know.
Hi

Answers

Answer:

The first one: 10*10*10*10*10*10

Step-by-step explanation:

This is because the power of a number is how many times you multiply it by itself (example: [tex]2^{4}[/tex] = 2*2*2*2 because the power is 4 which means you multiply the base by itself 4 times, in this case the base is 2)

Answer:

A. 10 · 10 · 10 · 10 · 10 · 10

Step-by-step explanation:

[tex]10^6[/tex] is just 10 times itself, 6 times.

100,000 less than five hundred sixty thousand,three hundred thirteen is __________.​

Answers

Answer:

100,000>56,313 56, 56,313<100,000

Find the LCM of 17, 120 and 240.​

Answers

17 = 17
120 = 2 × 2 × 2 × 3 × 5
240 = 2 × 2 × 2 × 2 × 3 × 5

LCM(17, 120, 240)
= 2 × 2 × 2 × 2 × 3 × 5 × 17
= 4080

LCM = 4080

does this table represent a function

Answers

Answer:

yes

Step-by-step explanation:

Each input has one corresponding output.

A cell phone company $500 for a new phone and $60 for a monthly plan. If C(t) is a rational function that represents the average monthly cost of owning the cell phone, what is the range of the function?
A. R: (0,500)
B. R: (60,560)
C. R: R
C: R: (-infinity, infinity)

HOW DO I SOLVE THIS?!

Answers

The range of a function is the set of possible values that can be obtained from the dependent variable. The range of the function is: [tex]R: (500, \infty)[/tex]

Given that:

[tex]Phone = \$500[/tex]

[tex]Monthly\ Plan = \$60[/tex]

Let the number of months be t. So, the function C(t) is calculated as follows:

[tex]C(t) = Phone + Monthly\ Plan \times t[/tex]

[tex]C(t) = 500 + 60 \times t[/tex]

[tex]C(t) = 500 + 60t[/tex]

The range is calculated as follows:

The smallest possible value of t is 0 i.e. when no monthly subscription is done.

So, we have:

[tex]C(0) = 500 + 60\times 0= 500 + 0 = 500[/tex]

And the highest is [tex]\infty[/tex] i.e. for a large value of t

So, we have:

[tex]C(\infty) = 500 + 60\times \infty= 500 + \infty = \infty[/tex]

Hence, the range of the function is:

[tex]R: (500, \infty)[/tex]

Read more about range of functions at:

https://brainly.com/question/13824428

Which ratio expresses the scale used to create this drawing? The post office has dimensions of 24 meters by 60 meters

Answers

Answer: 2:5

Step-by-step explanation:

To find the ratio, we need to find the greatest common factor and divide both of the dimensions by the greatest common factor. In this case 12 is the greatest common factor.

24/12=2

60/12=5

Therefore, the ration that expresses the scale used to create this dimension is 2:5.

Answer the question with explanation;​

Answers

Answer:

The statement in the question is wrong. The series actually diverges.

Step-by-step explanation:

We compute

[tex]\lim_{n\to\infty}\frac{n^2}{(n+1)^2}=\lim_{n\to\infty}\left(\frac{n^2}{n^2+2n+1}\cdot\frac{1/n^2}{1/n^2}\right)=\lim_{n\to\infty}\frac1{1+2/n+1/n^2}=\frac1{1+0+0}=1\ne0[/tex]

Therefore, by the series divergence test, the series [tex]\sum_{n=1}^\infty\frac{n^2}{(n+1)^2}[/tex] diverges.

EDIT: To VectorFundament120, if [tex](x_n)_{n\in\mathbb N}[/tex] is a sequence, both [tex]\lim x_n[/tex] and [tex]\lim_{n\to\infty}x_n[/tex] are common notation for its limit. The former is not wrong but I have switched to the latter if that helps.

Answer:

[tex]\displaystyle \sum^{\infty}_{n = 1} \frac{n^2}{(n + 1)^2} = \text{div}[/tex]

General Formulas and Concepts:

Calculus

Limits

Special Limit Rule [Coefficient Power Method]:                                         [tex]\displaystyle \lim_{x \to \pm \infty} \frac{ax^n}{bx^n} = \frac{a}{b}[/tex]

Series Convergence Tests

nth Term Test:                                                                                               [tex]\displaystyle \sum^{\infty}_{n = 1} a_n \rightarrow \lim_{n \to \infty} a_n[/tex]Integral Test:                                                                                                 [tex]\displaystyle \sum^{\infty}_{n = a} f(n) \rightarrow \int\limits^{\infty}_a {f(x)} \, dx[/tex]P-Series:                                                                                                         [tex]\displaystyle \sum^{\infty}_{n = 1} \frac{1}{n^p}[/tex]Direct Comparison Test (DCT)Limit Comparison Test (LCT)Alternating Series Test (AST)Ratio Test:                                                                                                     [tex]\displaystyle \sum^{\infty}_{n = 0} a_n \rightarrow \lim_{n \to \infty} \bigg| \frac{a_{n + 1}}{a_n} \bigg|[/tex]

Step-by-step explanation:

*Note:

Always apply the nth Term Test as the first test to use for convergence.

Rules:

If  [tex]\displaystyle \lim_{n \to \infty} S_n = 0[/tex], then the nth Term Test is inconclusive.If  [tex]\displaystyle \lim_{n \to \infty} S_n = l[/tex]  (some number l), then the series is divergent by the nth Term Test.

Step 1: Define

Identify

[tex]\displaystyle \sum^{\infty}_{n = 1} \frac{n^2}{(n + 1)^2}[/tex]

Step 2: Find Convergence

Substitute in variables [nth Term Test]:                                                       [tex]\displaystyle \sum^{\infty}_{n = 1} \frac{n^2}{(n + 1)^2} \rightarrow \lim_{n \to \infty} \frac{n^2}{(n + 1)^2}[/tex]Expand:                                                                                                         [tex]\displaystyle \lim_{n \to \infty} \frac{n^2}{(n + 1)^2}= \lim_{n \to \infty} \frac{n^2}{n^2 + 2n + 1}[/tex]Evaluate limit [Special Limit Rule - Coefficient Power Method]:                 [tex]\displaystyle \lim_{n \to \infty} \frac{n^2}{(n + 1)^2} = 1[/tex]Compute [nth Term Test]:                                                                             [tex]\displaystyle \sum^{\infty}_{n = 1} \frac{n^2}{(n + 1)^2} = \text{div}[/tex]

∴ by the nth Term Test, the series diverges.

Topic: AP Calculus BC (Calculus I + II)

Unit: Convergence Tests

If R = {(1,2) ,(2,3) ,(3,4) ,(4,5) } is subset of A x B , Find domain (A) and Range (B) ​

Answers

Answer:

hey

here is the attachment of your question

Answer:

[tex]thank \: you[/tex]

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