Solve the |4X -5|= |-X +5|

Answers

Answer 1

Recall the definition of absolute value:

[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]

Then we have a few cases to consider:

• If [tex]4x-5\ge0[/tex] and [tex]-x+5\ge0[/tex], the equation simplifies to

[tex]4x-5 = -x+5 \implies 5x=10 \implies \boxed{x=2}[/tex]

• If [tex]4x-5<0[/tex] and [tex]-x+5\ge0[/tex], we get

[tex]-(4x-5) = -x + 5 \implies -3x = 0 \implies \boxed{x=0}[/tex]

• If [tex]4x-5\ge0[/tex] and [tex]-x+5<0[/tex], then

[tex]4x-5 = -(-x+5) \implies 3x=0 \implies x=0[/tex]

but we already have this solution.

• If [tex]4x-5<0[/tex] and [tex]-x+5<0[/tex], then

[tex]-(4x-5) = -(-x+5) \implies -5x = -10 \implies x=2[/tex]

which we also already found.


Related Questions

(07.03 LC)
Identify the factors of x2 - 8x - 20. (1 point)
O (x + 4Nx - 5)
O (x + 5)(x - 4)
O (x - 10)(x + 2)
O (x-2)(x + 10)

Answers

Answer:

(x - 10)(x + 2)

Step-by-step explanation:

We are looking for two things that multiply together to give us

x^2 - 10x - 20

These things are binomials, such as (x+2) or (x-7) or (x+8) or (x-5)

We know the first term in the binomial has to be x, because x times x is x^2.

And then we are looking for two numbers that multiply to -20 but also add up to -8.

-10 and 2 multiply to make -20 and add up to -8 so we pick the answer (x-10)(x+2)

Answer:

Option C

Step-by-step explanation:

x² - 8x - 20

x² - (10x - 2x) - 20

x² - 10x + 2x - 20

x(x - 10) + 2(x - 10)

(x - 10)(x + 2)

Hence

Option C is correct

#3
Determine whether the ratios are equivalent.
5:2 and 30: 12
o equivalent
not equivalent

Answers

Answer:

yes

Step-by-step explanation:

Ratios are equivalent if they are multiples or divisors of each other.

5 : 2 ( multiply both sides by 6 )

= 30 : 12

or

30 : 12 ( divide both sides by 6 )

= 5 : 2

Thus 5 : 2 and 30 : 12 are equivalent ratios

Answer:

equivalent

Step-by-step explanation: 5 x 6 = 30      2 x 6 = 12

Professor Lee Xiao teaches an online class. She is paid $2,409 for up to 25 students,
plus an extra of $136 for every student beyond 25.
Professor Xiao is paid $3,262 for the class. How many students did she have? (Round
to the nearest integer).
acha

Answers

Answer:

25 + 6 = 31

Step-by-step explanation:

Her actual pay is 3262

Her base rate is   2409               Subtract to get the amount over the base

Amount of + 25      853

So how many student more does that amount to?

853 / 136 = 6.27

If you have to round to the nearest integer, the answer is 6.

a plane flies 5.0km due north from a point O and then 6.0km on a bearing of 060° the pilot then changes course on a bearing of 120° for 4.0km. find how far and in what direction the plane is from the starting point?​

Answers

The plane flies a distance of approximately 10.536 kilometers in straight line and with a bearing of approximately 035°.

A plane that travels a distance [tex]r[/tex], in kilometers, with a bearing of [tex]\theta[/tex] sexagesimal degrees can be represented in standard position by means of the following expression:

[tex]\vec r = r\cdot (\sin\theta, \cos \theta)[/tex] (1)

We can obtain the resulting vector ([tex]\vec R[/tex]) by the principle of superposition:

[tex]\vec R = \Sigma_{i=1}^{n} [r_{i}\cdot (\sin \theta_{i}, \cos \theta_{i})][/tex] (2)

If we know that [tex]r_{1} = 5\,km[/tex], [tex]\theta_{1} = 0^{\circ}[/tex], [tex]r_{2} = 6\,km[/tex], [tex]\theta_{2} = 60^{\circ}[/tex], [tex]r_{3} = 4\,km[/tex] and [tex]\theta_{3} = 120^{\circ}[/tex], then the resulting vector is:

[tex]\vec R = 5\cdot (\sin 0^{\circ}, \cos 0^{\circ}) + 6\cdot (\sin 60^{\circ}, \cos 60^{\circ}) + 4\cdot (\sin 120^{\circ}, \cos 120^{\circ})[/tex]

[tex]\vec R = (5\sqrt{3}, 6) \,[km][/tex]

The magnitude of the resultant is found by Pythagorean theorem:

[tex]\|\vec R\| = \sqrt{R_{x}^{2}+R_{y}^{2}}[/tex]

And the bearing is determined by the following inverse trigonometric relationship:

[tex]\theta_{R} = \tan^{-1} \left(\frac{R_{y}}{R_{x}}\right)[/tex] (3)

If we know that [tex]R_{x} = 5\sqrt{3}\,km[/tex] and [tex]R_{y} = 6\,km[/tex], then the magnitude and the bearing of the resultant is:

[tex]\|\vec R\| = \sqrt{(5\sqrt{3})^{2}+6^{2}}[/tex]

[tex]\|\vec R\| \approx 10.536\,km[/tex]

[tex]\theta_{R} = \tan^{-1} \left(\frac{6}{5\sqrt{3}} \right)[/tex]

[tex]\theta_{R} \approx 34.715^{\circ}[/tex]

The plane flies a distance of approximately 10.536 kilometers in straight line and with a bearing of approximately 035°.

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A pencil at a stationery store costs $1, and a pen costs $1.50. Shawn spent $12 at the store. He bought a total of 9 items. Which system of equations can be used to find the number of pencils (x) and pens (y) he bought? (5 points)

1.5x + y = 12
x = 9y

x + 1.5y = 12
x + y = 9

x + 9y = 12
x = 1.5y

9x + y = 12
x = 1.5y

Answers

Answer:

9 = x + y

1x + 1.5y = 12

Step-by-step explanation:

9 (number of items) = x (number of pencils) + y (number of pens)

1x (cost of x number of pencils) + 1.5y (cost of y number of pen s)= 12 (total cost)

simplify.
|−6 + (−3)| (−3) + 8 ÷ 2

Answers

Convert
6
3
8
6
3
8
to an improper fraction.
Tap for more steps...
51
8

2
1
4
51
8
-
2
1
4
Convert
2
1
4
2
1
4
to an improper fraction.
Tap for more steps...
51
8

9
4
51
8
-
9
4
To write

9
4
-
9
4
as a fraction with a common denominator, multiply by
2
2
2
2
.
51
8

9
4

2
2
51
8
-
9
4

2
2
Write each expression with a common denominator of
8
8
, by multiplying each by an appropriate factor of
1
1
.
Tap for more steps...
51
8

9

2
8
51
8
-
9

2
8
Combine the numerators over the common denominator.
51

9

2
8
51
-
9

2
8
Simplify the numerator.
Tap for more steps...
33
8
33
8
The result can be shown in multiple forms.
Exact Form:
33
8
33
8
Decimal Form:
4.125
4.125
Mixed Number Form:
4
1
8

If the expression inside the absolute value bars which is -6 .Simplifying the expression |−6 + (−3)| (−3) + 8 ÷ 2 is: 9.

What is the expression?

Let simplify the given expression step by step:

|-6 + (-3)| = |-9| = 9

First calculate the expression inside the absolute value bars which is -6 + (-3) = -9. Then  take the absolute value of -9, which is 9.

(-3) + 8 ÷ 2 = (-3) + 4 = 1

We follow the order of operations (PEMDAS/BODMAS).

First perform the division:

8 ÷ 2 = 4

Add -3 to 4 which gives us 1.

Simplified expression :

9 * 1 = 9

Therefore the expression is 9.

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Name each polynomial by degree and number of terms .
1) -10x
2) -10r4- 8r2
3) 7
4)9a6 + 3a5 - 4a4 - 3a2 + 9
5)-3n3 + n2 - 10n + 9
6) 7x2 - 9x - 10
7) -4b
8) -9 + 7n3 - n2

Answers

Answer:

Polynomials are classified according to their number of terms. 4x3 +3y + 3x2 has three terms, -12zy has 1 term, and 15 - x2 has two terms. As already mentioned, a polynomial with 1 term is a monomial. A polynomial with two terms is a binomial, and a polynomial with three terms is a trinomial.

How do I solve this

Answers

Answer:

Step-by-step explanation:

well, I'd just multiply each option out using FOIL

First, Outside, Inside, Last

A) (x + 2√3i)(x - 2√3i)

First                x(x) = x²

Outside          x(- 2√3i) =  - 2x√3i

Inside             x(2√3i)   =    2x√3i

last            (- 2√3i)(2√3i) = -(2²)(√3²)(i²) = -4(3)(-1) = 12

add them all up  x² + 12      looks like it works for me

B) = x² + 36

C) = x² + 4√3 + 12

D) = x² - 12

Sean has three dollars more than twice as much money as Peter if Sean has $10 how much money does Peter have

Answers

Answer:

peter has $3.50

Step-by-step explanation:

3.50 times 2 is 7 plus 3 is 10

NEED HELP RELATIONSHIP IN TRIANGLES

Answers

Answer:

Step-by-step explanation:

10x-13=17x-41

DO YOUR WORK

Answer: 10x-13=17x-41
here is a picture

Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 5 hours. Together they charged a total of $2750.
What was the rate charged per hour by each mechanic if the sum of the two rates was $205 per hour?

-Whats the First mechanic: $ -----per hour

-Whats the Second mechanic: $ ---- per hour ​

Answers

I answer this question before this is the solution just change the total of $2750:

Two mechanics worked on a car, The first mechanic worked for 20 hours and the second mechanic worked for 5 hours together they charged a total of $1150.

Let's make,
mechanic #1's rate = x
mechanic #2's rate = y

* Their rate is dollars per hour ($/hr)

mechanic #1 worked for 20 hours (hr × $/hr = $)
20x = money earned by mech#1

and mechanic #2 worked for 5 hours
5y = money earned by mech#2

together they charged a total of $1150. So the amount of money earned by both mechanics.

20x + 5y = 1150

the sum of the two rates was $95 per hour.

x + y = 95

which means
x = 95 - y

plug (95 - y) in for "x" in the other equation to get everything in terms of one variable.

20(95 - y) + 5y = 1150

solve for y

1900 - 20y + 5y = 1150
1900 - 15y = 1150
-15y = 1150 - 1900
-15y = -750
y = -750/-15
y = 50 $/hr

Now use this to solve for x

x + y = 95
x + 50 = 95
x = 95 - 50
x = 45 $/hr

mech#1 charged 45$/hr
mech #2 charged 50$/hr

Twice the difference of a number and 4 is equal to three times the sum of the number and 10.

Answers

Answer:

2(x-4)=3(x+10)

Step-by-step explanation:

What is the gradient of the graph shown?
Give your answer in its simplest form.

Answers

Answer:

Step-by-step explanation:

When it's clear, the easiest way to do the problem is to used the x and y  intercepts.

This question is one of the clear one.

The x intercept is 2,0

The y intercept is 0,1

You want the slope.

m = (y2 - y1)/(x2 - x1)

y2 = 1

y1 = 0

x2 = 0

x1 = 2

m = (1 - 0)/(0 - 2)

m = 1 / -2

m = -1/2

In this case the slope and gradient have the same value --   - 1/2 or - 0.5


88, 89, 86, 90, 83, 81, 89
What is the median number
A 88
B. 89
C 90
D. 86

Please answer this I really need help

Answers

Answer:

The answer is 90.

Step-by-step explanation:

90 is in the middle

Answer:

d

Step-by-step explanation:

cause i said so

Solve -2/3x > 8 or -2/3x < 4.

{x | x > -12 or x < -6}
{x | -12 < x < -6}
{x | x < -12 or x > -6}

Answers

Answer: Choice C

{x | x < -12 or x > -6}

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

Explanation:

Let's solve the first inequality for x.

(-2/3)x > 8

-2x > 8*3

-2x > 24

x < 24/(-2)

x < -12

The inequality sign flips when we divide both sides by a negative value.

Let's do the same for the second inequality.

(-2/3)x < 4

-2x < 4*3

-2x < 12

x > 12/(-2)

x > -6

The conclusion of each section is that x < -12 or x > -6 which points us to choice C as the final answer.

Side note: The intervals x < -12 and x > -6 do not overlap in any way. There's a gap between the two pieces. We consider these intervals to be disjoint. The number line graph is below.

HELP
Lyndie is making reduced copies of a photo that measures 25 centimeters in height. She sets the copy machine to an 80% size
reduction.

PART A
Write a percent equation that represents
the relationship of the height of the first
copy to the height of the original photo.

PART B
Lyndie wants to make another copy that
will have a height of 17 cm. The copy
machine settings increase or decrease in
increments of 5%. Which photo should she
make her copy from, the original or her
first copy? Explain.

Answers

Answer: 5+ba*7= 88

Step-by-step explanation:

The square below represents one whole.
What percent is represented by the shaded area?

Answers

40%
——————————————-

The manager of a grocery store in Decatur currently provides special service to people who still use checks to pay for food. They have a separate pay/bag line for people who insist on waiting for a dollar total to pull out their checkbook and start writing. On average, 30 customers per hour arrive at the checking pay/bag line and they can be modeled with a Poisson distribution. The clerk at this line can handle an average rate of 35 customers per hour and their service can be modeled with exponential distribution.

a. 67%.

b. 75%.

c. 33%.

d. 25%.

Utilization Average time a customer spends in the system

rho = λ/μ w = 1/μ - λ = L/λ

Average # of customers in the system Average time a customer spends in the queue

Ls = λ/μ - λ Wq = λ/μ(μ - λ) = Ls/λ

Average # of customers in queue Probability of n units in the syst

Answers

75% I think I don’t know

The correct option is: c. 33%. (The probability of having 36 customers in the system is approximately 0.00183%, which is approximately 0.033%, or 33%).

To find the utilization (ρ) of the clerk at the check/pay line, we can use the formula:

ρ = λ / μ

where:

ρ = Utilization

λ = Arrival rate (rate at which customers arrive at the line)

μ = Service rate (rate at which the clerk can handle customers)

Given in the problem:

Arrival rate (λ) = 30 customers per hour

Service rate (μ) = 35 customers per hour

Now, let's calculate the utilization (ρ):

ρ = 30 / 35 ≈ 0.8571

To convert this to a percentage, we multiply by 100:

ρ ≈ 0.8571 * 100 ≈ 85.71%

Since the utilization represents the percentage of time the clerk is busy, we need to find the percentage of time the clerk is idle (not busy). This can be calculated by subtracting the utilization from 100%:

Idle time = 100% - Utilization

Idle time ≈ 100% - 85.71% ≈ 14.29%

Now, let's find the average time a customer spends in the system (W) using Little's Law:

W = L / λ

where:

W = Average time a customer spends in the system

L = Average number of customers in the system (both in the queue and being served)

λ = Arrival rate (rate at which customers arrive at the line)

Given in the problem:

Arrival rate (λ) = 30 customers per hour

Now, we need to find the average number of customers in the system (L) to calculate the average time.

L = Ls + λ

where:

Ls = Average number of customers in the queue

Ls = λ / (μ - λ)

Given in the problem:

Service rate (μ) = 35 customers per hour

Ls = 30 / (35 - 30) = 30 / 5 = 6 customers

Now, calculate the average number of customers in the system (L):

L = Ls + λ

L = 6 + 30 = 36 customers

Now, calculate the average time a customer spends in the system (W):

W = L / λ

W = 36 / 30 = 1.2 hours per customer

Finally, let's find the probability of having n units in the system (both in the queue and being served). In this case, n would be the number of customers in the system (L):

Probability of having n units in the system = (ρ^n) * (1 - ρ)

Probability of having 36 units in the system (L):

Probability of L customers in the system = (0.8571^36) * (1 - 0.8571) ≈ 0.0000183

The question asks for the percentage, so we multiply by 100 to convert to percentage:

Probability ≈ 0.0000183 * 100 ≈ 0.00183%

Thus, the correct option is: c. 33%. (The probability of having 36 customers in the system is approximately 0.00183%, which is approximately 0.00183% * 18 ≈ 0.033%, or 33%).

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(−3, −1), (−1, 5) Find the slope of the line that passes through the pair of points.

Answers

[tex]slope = \frac{ 5 - ( - 1)}{ - 1 - ( - 3)} \\ [/tex]

[tex]slope = \frac{5 + 1}{ - 1 + 3} \\ [/tex]

[tex]slope = \frac{6}{2} \\ [/tex]

[tex]slope = 3[/tex]

WHOEVER EXPLAINS FIRST GETS BRAINLIEST!!


Enter your answer and show all the steps that you use to solve this problem in the space provided. Solve.


-2/5x-9<9/10

Answers

It is 9 7/5 I did this question in school lol

Jack’s school bag contains 8 books each of weight 3/8 pounds, and 6 folders of weight 1/2 pound. b) What fraction of the total weight is folders?

Answers

Answer:

6 pounds

Step-by-step explanation:

3/8×8/1=24/8=3

6/1×1/2=6/2=3

3+3=6

12 tenths+ 9 tenths = tenths = ones = tenths

Answers

Explain: it’s equals to 20

Izzo's Pizza sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what she found.
Type of Crust Number Sold
Thin crust
344
Thick crust
391
Stuffed crust 155
Pan style
185
Based on this information, or the next 3500 pizzas she sells, how many should she expect to be thin crust? Round your answer to the nearest whole number. Do
not round any intermediate calculations.

Answers

Total number of Pizzas sampled = 344+391+155+185 = 1075

No. of Thick crust Pizzas in sample = 391

Proportion of Thick crust Pizzas in sample = 391/1075

Expected number of Thick crust in next 3500 pizzas = 3500*(391/1075)

Expected number of Thick crust in next 3500 pizzas = 1273

Out of 3500, he may expect 1273 pizzas to be thick crust

Which of the following sets is equal to {1, 2, 3, ...)?
{x| xER, x>1}
{x|xER, x> or equal to 1}
{x|xEN, x> or equal to 1}

Answers

Answer:

[tex]\{x~ | ~x\in \mathbb{N}, x \geq 1\}[/tex]

Step-by-step explanation:

HELP PLZ PLZ ITS DUE IN 30 MINUTES

Answers

Answer:

wouldn't that be...24x²?

graph the relation y=2x

Answers

This is the graph for y= 2x

6. Expand the brackets: a) 3(x - y) )​

Answers

Answer:

3x-3y

Step-by-step explanation:

3(x-y)

open the brackets:

(3×x)-(3×y)

= 3x-3y

what is 5y² if y= -1​

Answers

Answer:

5

Step-by-step explanation:

Input all of the numbers and solve:

5×-1×-1

Start by solving -1*-1=1

5*1=5

Answer:

the answer for this question is 5

I NEED HELP PLSSS GEOMETRY

Answers

Answer:

Its the first one (top left option)

Step-by-step explanation:

ur in a rush so i wont explain, pls give me brainliest

Determine whether each graph shows a positive correlation, a negative
correlation, or no correlation. If there is a positive or negative correlation,
describe its meaning in the situation.

Answers

Answer:

Positive correlation.

Step-by-step explanation:

From the graph we can see overall increasing trend.

It means there is a positive correlation.

The meaning of this is the more time you spend on study the better test score you get.

Answer:

Negative correlation

Step-by-step explanation:

As TV hours increase, exercise

hours decrease.

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He preferred to make things of beauty.Leonardo made the decision that he could tolerate making weapons if the resources the duke could provide would also allow him to create things he loved. He sent a letter to the duke detailing his skills in designing and building weapons. I will assemble catapults, mangonels, trebuchets and other instruments of wonderful efficiencyI will make an infinite number of items for attack and defense, he wrote.Leonardos letter convinced the duke of his talents, and he got the job. He set about designing the weapons that the duke desired. But Leonardo was infinitely creative, always thinking of new things, new ideashe could not be limited to weapons alone. One idea that he had not mentioned in his application was the ornithopter. It was not a weapon of war, and it was not something that the duke had asked for, but Leonardo went ahead and designed it anyway.Leonardo was fascinated by the idea of flight. The word ornithopter comes from two words meaning bird and wings. And on first inspection, his plans resembled a birds wings attached to a human beings arms. He concluded that a human beings arms were neither strong enough nor light enough to stay in the air for long. So, his design included sets of foot pedals and levers that were operated with the hands. He created detailed plans and presented them to the duke, uncertain of how the duke would react to a design for which he didnt ask.As it turned out, the duke was very impressed with the ornithopter, but it wasnt Leonardos innovation that excited him. He immediately thought of the ways this machine could be used in war. If a spy could fly over the enemys camp, imagine what information he could gather! This was not what Leonardo had intended for his beautiful flying machine.But how Leonardo felt about war turned out not to matter in the end. His ornithopter was never builtalong with his designs for tanks, parachutes, diving suits, machine guns, and even robots that he created for the duke. The ideas of Leonardo da Vinci were centuries ahead of the technology needed to make them.Read the excerpt from "The Ornithopter."He created detailed plans and presented them to the duke, uncertain of how the duke would react to a design for which he didn't ask.Which type of conflict is expressed in this excerpt?individual vs. natureindividual vs. individualindividual vs. societyindividual vs. self What was the main difference between how Japan and China reacted to Western interest in their nations in the late 1800s?1. Japan closed all of its ports to trade, while China opened.2. Japan modernized and adopted western ways, while China believed in building on its historic strengths.3. Japan believed in the strength of its feudal past while China modernized and adopted western traditions.4. There was no difference QuestionRefer to attachment nonsense answer will get report A physician orders Fragmin 1,600 international units subcutaneously stat. There are 9-mL vials of Fragmin (dalteparin) 10,000 international units/mL available in stock. What volume of medication should be administered? a) 16 mL O b) 1.6 mL c) 0.16 mL d) 0.016 mL