Find the domain for the rational function f of x equals quantity x plus 1 end quantity divided by quantity x minus 2 end quantity.

(−[infinity], 2) (2, [infinity])

(−[infinity], −2) (−2, [infinity])

(−[infinity], 1) (1, [infinity])

(−[infinity], −1) (−1, [infinity])

Answers

Answer 1

Answer:

[tex](- \infty, 2), (2, \infty)[/tex]

Step-by-step explanation:

Given the function:

[tex]f(x) = \dfrac{x+1}{x-2}[/tex]

To find:

Domain of the function.

Solution:

First of all, let us learn about definition of  domain of a function.

Domain of a function is the valid input values that can be provided to the function for which output is defined.

OR

Domain of a function [tex]f(x)[/tex] are the values of [tex]x[/tex] for which the output [tex]f(x)[/tex] is a valid value.

i.e. The function does not tend to [tex]\infty[/tex] or does not have [tex]\frac{0}0[/tex] form.

So, we will check for the values of [tex]x[/tex] for which [tex]f(x)[/tex] is not defined.

For value to tend to [tex]\infty[/tex], denominator will be 0.

[tex]x-2\neq 0 \\\Rightarrow x \neq 2[/tex]

So, the domain can not have x = 2

Any other value of x does not have any undefined value for the function [tex]f(x)[/tex].

Hence, the answer is:

[tex]\bold{(- \infty, 2), (2, \infty)}[/tex]     [2 is not included in the domain].


Related Questions

2x.tg60= 10+csc30 plis

Answers

Answer:

[tex]2\sqrt{3}[/tex]

Step-by-step explanation:

I'm assuming the angles are in degrees.

[tex]2x \tan(60\º)=10+\csc(30\º)[/tex]

[tex]$2x\cdot \sqrt{3}=10+\frac{1}{\sin(30\º)} $[/tex]

[tex]$2x\cdot \sqrt{3}=10+\frac{1}{\frac{1}{2} } $[/tex]

[tex]$2x\cdot \sqrt{3}=10+2} $[/tex]

[tex]$x=\frac{12}{2\sqrt{3}} $[/tex]

[tex]$x=\frac{6}{\sqrt{3}} =\frac{6\sqrt{3}} {3} }=2\sqrt{3} $[/tex]

I got this wrong please help me get the right answer in the first little box marked in red. thx

Answers

Answer:

The inverse is 1/2x +2

Step-by-step explanation:

f(x) = 2x-4

y= 2x-4

To find the inverse

Exchange x and y

x = 2y-4

Solve for y

Add 4 to each side

x+4 = 2y

Divide by 2

x/2 + 4/2 = 2y/2

1/2x +2 = y

The inverse is 1/2x +2

solve 3(11)× =3,993 for x​

Answers

Hi there! :)

Answer:

[tex]\huge\boxed{x = 3}[/tex]

Given the equation:

[tex]3(11)^{x} = 3993[/tex]

Divide both sides by 3:

[tex](11)^{x} = 1331[/tex]

Rewrite both sides of the equation with a base of 11.

[tex]1331 = 11^{3}[/tex], therefore:

[tex](11)^{x} = 11^{3}[/tex]

x = 3.

Answer:

121

Step-by-step explanation:

121 x 33 = 3993

Someone pls help & at least try to show a little work . I will be marking someone brainliest ! & thank you sm i appreciate you !

Answers

Answer:

4+7x=32

7x=32-4

7x=28

x=4

Step-by-step explanation:

Answer:

This is how I calculated it.

If the total is $912

And the equipment costs $612.

I did $912- 612= $300 (There's only $300 remaining after purchasing the equipment)

Each uniform costs $25

So I did $300:25= 12

The School purchased 12 uniforms.

Have a nice day.

If an octagon is 24, how many is a pentagon?

Answers

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Hi my lil bunny!

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If an octagon is 24, how many is a pentagon?

Ans : Pentagon has 5 sides.

( A five-sided shape is called a pentagon. A six-sided shape is a hexagon, a seven-sided shape a heptagon, while an octagon has eight sides. The names of polygons are derived from the prefixes of ancient Greek numbers. )

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Have a great day/night!

❀*May*❀

The pentagon is 15, when octagon is 24.

What is Polygon?

A polygon is a figure made up of line segments (not curves) in a two-dimensional plane. Polygon is the combination of two words, i.e. poly (means many) and gon (means sides).

Polygon with 8 sides known as Octagon and polygon with 5 sides known as Pentagon.

Here, given that, Octagon = 8 sides = 24

So, 1 side= 3

Then, we get, pentagon = 5 sides = (5×3) = 15

Hence, the pentagon is 15.

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Ссппер
What is the image of (7, -2) after a reflection over the line y = -x?

Answers

Answer:

(2, -7)

Step-by-step explanation:

Pls answer this urgently

Answers

Answer:

The pic there has a step by step explanation

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        Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

[tex]\frac{(3^-2)^2 * (5^2)^-3 * ( t ^-3)^2 }{( 3^-2) ^5 ( 5^3) ^-2 ( t ^-4)^3}[/tex]

[tex]= \frac{\frac{1}{1265625^t12} }{1}[/tex]

[tex]= \frac{\frac{1}{992640625^t6} }{1}[/tex]

[tex]= \frac{992640625^t6}{1265625}[/tex]

[tex]= \frac{922640625tttttt}{1265625}[/tex]

[tex]= 729t^6[/tex]

Answer : [tex]729t^6[/tex]

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If this helped you, could you maybe give brainliest..?

❀*May*❀

Please help me answer I need an answer asap:3

Answers

Answer:

please mark my answer brainliest

Step-by-step explanation:

it's 115

Answer:

115 degrees.

Step-by-step explanation:

< DBC = (180 - 40) / 2 = 70    ( as it is a base angle of an isosceles Δ)

< EBD = 45 degrees ( as the diagonal of a square bisects 90 degree <).

So < EBC = 70 + 45 = 115 degrees.

Can someone tell me if this is correct? I said neither is correct.

Answers

Answer:

Neither is correct

Answer:

You are right.

Step-by-step explanation:

Neither transformation gives the triangle FGE.

Pablo graphs a system of equations. One equation is quadratic and the other equation is linear. What is the greatest
number of possible solutions to this system?

Answers

Answer:

greatest number of solutions is 2

Step-by-step explanation:

one is a parabola, the other is a line

so it can intersect in 0, 1, 2 points

What is the missing reason in the proof?
Statements
Reasons
1. AB / CD; BC // DA 1. given
2. Quadrilateral ABCD 2. definition of parallelogram
is a
3. AB CD; BC = DA 3. opposite sides of a
parallelogram are >
4. AC AC
4. reflexive property
5. AABC 2 ACDA 5. ?
perpendicular bisector theorem
Pythagorean theorem
HL theorem
SSS congruence theorem

Answers

Answer:

The correct option is;

SSS congruency theorem

Step-by-step explanation:

Given that opposite sides of a parallelogram are equal, whereby side AB is congruent to side CD and  side BC is congruent to side DA and also that side AC is congruent to side CA, we have;

Triangle ABC with sides AB, BC, and AC is congruent to triangle CDA with corresponding sides CD, DA, and CA, by the Side-Side-Side (SSS) rule of congruency (two or more triangles that have all three sides of one triangle congruent to the three sides of the other triangle are congruent).

The missing reason in the proof is: SSS Congruence Theorem.

What is the SSS Congruence Theorem?SSS means side-side-side, meaning two triangles have three pairs of congruent sides.According to the SSS Congruence Theorem, two triangles with three pairs of congruent sides must be congruent to each other.

Thus, ΔABC and ΔCDA has been shown to have three pairs of congruent sides, therefore, the missing reason in the proof is: SSS Congruence Theorem.

Learn more about SSS Congruence Theorem on:

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Can guys please help me, please solve E

Answers

Answer:

Step-by-step explanation:

h(x)=12/x

h(a)= 12/a  ( a is a variable number just replace x with a)

A newborn blue whale weighs 3^7 an adult blue whale weighs 81 times a new way of the newborn how many kilograms does the dog blue away write your answer as a power of three

Answers

Answer:

3^11 kilogram

Step-by-step explanation:

We were told a newborn blue whale weighs 3^7

But an adult blue whale weighs 81 times a new way of the newborn this can be expressed below as

=81×3^7

This can be expressed in standard form as

3^4 × 3^7

Then we need to determine number of kilograms the adult blue whale weigh.

81=3^4

=3^11

Therefore, number of kilograms the adult blue whale weigh 3^11kg

Point F lies on line EG and point M lies on line EN. If F, E, and M are collinear, what must be true of these rays?

Answers

Answer:

Step-by-step explanation:

Some options would have definitely helped in answering this question. i am answering this question based on my knowledge. If F,E, and M are collinear, then EG and EN will form a line. Some options would have definitely helped in answering this question. i am answering this question based on my knowledge. If F,E, and M are collinear, then EG and EN will form a line.

PLZ HELP!!!! ASAP !!!!

Answers

Answer:

(A)

Sin á = a/c

Cos ∅ = a/c

Tan á = a/b

(B)

Sin á = a/c

Cos á = b/c

Tan á = a/b

Therefore á=

(inverse sin) a/c

Or

(Inverse cos) b/c

Or

(Inverse tan) a/b

(C)

If b = 12 and c = 13

then a =√(c²-b²)

= 5

Hence 5/13 = a/c

Therefore sin á = cos ∅ = a/c = 5/13

A graph has Quantity Demanded on the x-axis, from 0 to 60 in increments of 10, and Price on the y-axis, from 0 to 20 dollars in increments of 2 dollars and 50 cents. 2 lines with identical negatives slopes are shown. Line D is slightly lower than line D 1. This graph shows the quantity of t-shirts demanded at D and D1. The change in quantity demanded caused by a change in the price of t‐shirts is shown as a shift to the right of the demand curve. a shift to the left of the demand curve. movement along the demand curve.

Answers

Answer:

Movement along the demand curve

Step-by-step explanation:

edge 2021.

The change in price as shown in the graph is shown as movement along the demand curve.

What is demand and supply?

The terms demand and supply are common themes in economics. They show the relationship between the amount that a seller wants to sell and the amount that a buyer wants to buy. A number of factors affect the demand curve.

The change in price as shown in the graph is shown as movement along the demand curve.

Learn more about demand and supply: https://brainly.com/question/13353440

A hiker starts walking due west from Sasquatch Point and gets to the Chupacabra Trailhead before she realizes that she hasn't reset her pedometer. From the Chupacabra Trailhead she hikes for 8 miles along a bearing of N27°W which brings her to the Muffin Ridge Observatory. From there, she knows a bearing of S38°E will take her straight back to Sasquatch Point. How far will she have to walk to get from the Muffin Ridge Observatory to Sasquach Point, to the nearest tenth of a mile?

Answers

Answer:

9.05 mile

Step-by-step explanation:

From the information given :

Let represent S for Sasquatch Point

Let C represent Chupacabra Trailhead

Let M represent Muffin Ridge Observatory

The diagram for the bearing of the information given can be seen in the attached file below.

At angel C = 90° -27° =  63°

The Alternate angles are shown in the second diagram below.

In order to determine the distance she will have to walk from the Muffin Ridge Observatory to Sasquatch Point, we use the sine formula:

[tex]\mathtt{\dfrac{sin \ C }{c} = \dfrac{sin \ S}{s}}[/tex]

[tex]\mathtt{\dfrac{sin \ 63 }{c} = \dfrac{sin \ 52}{8}}[/tex]

By cross multiply

8 × sIn 63  = c× sin 52

[tex]\mathtt{c = \dfrac{8 \times Sin 63}{Sin \ 52}}[/tex]

[tex]\mathtt{c = \dfrac{7.1281}{0.7880}}[/tex]

c = 9.0458 mile

c [tex]\simeq[/tex] 9.05 mile to  the nearest tenth

Question 5 of 5
Select the correct answer.
Which of these tables represents a function?

Answers

Answer:

the answer is w

Step-by-step explanation:

the answer to that question is w

Answer: y

Step-by-step explanation:

there can not be two of the same number in the x row

help help help me plZZZZZ ill give you brainly ;DDD

Answers

Answer:

the answer is 60.7

Step-by-step explanation:

60 to has a between numbers like given in the picture

so as number line it's

60.1 . 60.2 60.3 60.4 60.5 60.6 60.7 60.8 and continue

if u get any 3 digit number like 600 to 650 in number line

u do it like it the same 600.1 600.2.... and go on

Answer:

63½ or 63.5

Step-by-step explanation:

65-60=5

10points=5

1point=?

1×5/10= ½

that means the sequence continues after adding ½ i.e

60..60½...61...61½...62...62½...63...63½...64..64½...65

you have been asked the 8th number which is 63½

A piece of aluminum occupies a volume of 12.7 milliliters and weighs 87.3 grams. What is its density of the aluminum rounded to the nearest hundredth? Only enter numerical values, which can include a decimal point.

Answers

Answer:

6.87 g/mL

Step-by-step explanation:

The density of an object can be found by dividing the mass by the volume.

[tex]density=\frac{mass}{volume}\\\\ d=\frac{m}{ v}[/tex]

We know that the aluminum occupies a volume of 12.7 milliliters and weighs 87.3 grams. Therefore, the mass is 87.3 g and the volume is 12.7 mL.

[tex]m= 87.3 g\\\\v=12.7 mL[/tex]

Substitute the values into the formula.

[tex]d= \frac{87.3 g}{12.7 mL}[/tex]

Divide 87.3 g by 12.7 mL

[tex]d=6.87401575 g/mL[/tex]

Round to the nearest hundredth. The 4 in the thousandth place tells us to leave the 7 in the hundredth place.

[tex]d= 6.87 g/mL[/tex]

The density of the aluminum is about 6.87 grams per milliliter.

A local high school held a two-day fundraiser selling lunches. The equations shown represent the amount of money the school collected during the two days. {12x + 4y = 15232x + 12y = 420 In the equations, x represents the cost of a chicken lunch and y represents the cost of a vegetarian lunch. Which is the cost of the vegetarian lunch?

Answers

Answer:

  11

Step-by-step explanation:

The two equations appear to be ...

12x +4y = 15232x +12y = 420

These can be solved for y using Cramer's rule:

  y = (152(32) -420(12))/(4(32) -12(12)) = -176/-16 = 11

The cost of the vegetarian lunch is 11.

_____

Comment on Cramer's Rule

For equations ...

  ax +by =c

  dx +ey = f

The solutions are ...

  x = (bf -ey)/(bd -ea)

  y = (cd -fa)/(bd -ea) . . . . note the denominators are the same expression

Once you memorize the pattern of products, this can be the simplest way to solve a pair of equations--especially if you only need one of the variable values.

Answer:

11

Step-by-step explanation:

quick mafs

Graphically, a point is a solution to a system of two inequalities if and only if the point lies in the shaded region of the top inequality, but not in the shaded region of the bottom inequality. lies in the shaded region of the bottom inequality, but not in the shaded region of the top inequality. lies in the shaded regions of both the top and bottom inequalities. does not lie in the shaded region of the top or bottom inequalities.

Answers

Answer:

  lies in the shaded regions of both the top and bottom inequalities

Step-by-step explanation:

For a point to be a solution of two inequalities, it must lie in both solution sets. It ...

  lies in the shaded regions of both the top and bottom inequalities

We want to define when a point is a solution of a system of inequalities, we will see that the correct option is: "lies in the shaded regions of both the top and bottom inequalities."

Just like in a system of equations, a solution of the system is must be a solution of both equations.

Here, a solution ot the system of inequalities must be at the same time a solution of each inequality.

Remember that the solutions of the inequalities are represented by shaded regions, so the point must belong to the intersection of the two shaded regions.

So the correct option is:

"lies in the shaded regions of both the top and bottom inequalities."

If you want to learn more, you can read:

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Mr Lim, Mr Tan and Mr Chan have $8650 altogether. Mr Lim has $450 more than Mr Tan. Mr Chan has twice as much money as Mr Tan. How much money does Mr Lim have?​

Answers

Answer:

Mr. Lim will have $2500

Step-by-step explanation:

Given:

The total amount of money which Mr. Lim, Mr. Tan and Mr. Chan is $8650;

Mr. Lim has $450 more than what Mr. Tan has;

Mr. Chan has double the amount of money than what Mr. Tan has.

Therefore, if we assume that the amount of money Mr. Tan has as x, then...

Total money = Mr. Tan + Mr. Lim + Mr. Chan

therefore,

8650 = x + (x + 450) + 2x

8650 = x + 2x + x + 450

8650 = 4x + 450

8650 - 450 = 4x

8200 = 4x

8200/4 = x

2050 = x

As we assumed earlier, x will be equal to the amount of money Mr. Tan has and the question is asking us how much money Mr. Lim has. To find this out, you have to add $450 to the amount of money Mr. Tan has which is $2050. This is because the question also gives us that Mr. Lim has $450 more that Mr. Tan.

I hope this helped you :)

Select the correct answer. For what purpose are goods and services produced in a socialist economy? A. profits B. their usefulness C. to create demand D. to meet all consumer needs

Answers

Answer: B. their usefulness

Step-by-step explanation: A socialist economy may be described as a system whereby factors of production including goods and services are generally explored and processes in other to serve and benefit the people. In socialism, resources are deemed to be owned by all members of the public and as such total control resides with the government who makes decision on production, processing and sales of the resources to serve useful benefit for the people. The socialist econmoy opposes the capitalist form of government whereby goods and services are generated in other to yield profit.

Puzzle corner
Look Before You Leap!
See how long it takes you to work out the
following:
(1 x2)×(3 x 4)×(586)×(7 x 8) x (
9×0)

Answers

Answer:

0

Step-by-step explanation:

Notice that the last factor is null (9×0)

So the result will be null since any number that is multiplied by 0 equals 0.

A travel agent is booking trips for tourists who travel from New York to Chicago. Tourists have three choices for how to travel from New York to Chicago. They can take an airplane for $350, a bus for $150, or a train for $225. Once they arrive in Chicago, they can travel by van to their hotel for $60 or take a cab for $40. If each option is equally likely to occur, what is the probability that a tourist will spend more than $300 on these 2 legs of the trip?

Answers

List all the different combinations with total cost:

Airplane  + van = 350 + 60 = $410

Airplane  + cab = 350 + 40 = $390

Bus + van = 150 + 60 = $210

Bus + cab = 150 + 40 = $190

Train + van = 225 + 60 = $285

Train + cab = 225 + 40 = $265

There are 6 different combinations.

There are 2 that are more than $300

The probability would be quantity higher than 300 / total combinations.

Probability = 2/6 = 1/3

What is the measure of angle B?​

Answers

Answer:

b = 60

Step-by-step explanation:

The sum of the angles of a triangle are 180

80+40+b = 180

Combine like terms

120+b =180

Subtract 120 from each side

b = 180-120

b = 60

Answer:

60°

Step-by-step explanation:

Recall that all triangles have an interior angle sum of 180. In other words:

[tex]\angle A+\angle B +\angle C = 180[/tex]

Plug in the angle values we know:

[tex](80)+(40)+\angle B = 180\\120+\angle B =180\\\angle B = 60\textdegree[/tex]

Select the correct answer. Frank created a scatter plot and drew a line of best fit, as shown. What is the equation of the line of best fit that Frank drew?

Answers

The equation of the line of best fit that Frank drew will be y = -(1/3) x + 16. Then the correct option is D.

What is the equation of a line passing through two points?

Suppose the given points are (x₁, y₁) and (x₂, y₂), then the equation of the straight line joining both two points is given by

[tex]\rm (y - y_1) = \left [ \dfrac{y_2 - y_1}{x_2 - x_1} \right ] (x -x_1)[/tex]

Frank created a scatter plot and drew a line of best fit, as shown.

From the graph, the two points are taken that are (0, 16) and (3, 15).

(x₁, y₁) → (0, 16)

(x₂, y₂) → (3, 15)

Then the equation of line will be

y – 16 = -1/3(x – 0)

       y = -(1/3) x + 16

Then the correct option is D.

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Use slope-intercept form to graph each system of equations and solve each system.

Answers

Answer:

(0,3), graph is attached.

Step-by-step explanation:

We know that the first equation will increase 2 points in y for every 1 x, since the constant next to x is 2. We also know it's y-intercept will be 3.

As for the second equation, we know it will have no y and instead run through the y=3 line, crossing every value of x.

Graphing this, we see that these lines intersect at (0,3) so that's the solution to this system.

Hope this helped!

If you invest $600 at 5% interest compounded continuously, how much would you make after 6 years?

Answers

Answer:

809.915$

Step-by-step explanation:

Amount of money = Principal x e^(rate x year)

                              = 600 x e^(0.05 x 6)

                              = 809.915$

Answer:

$809.92

Step-by-step explanation:

(see attached for reference)

Recall that the formula for compound interest (compounded continuously) is

A = P e^(rt)

where,

A = final amount (we are asked to find this)

P = principal = given as $600

r = interest rate = 5% = 0.05

t = time = 6 years

e = 2.71828 (mathematical constant)

Substituting the known values into the equation:

A = P e^(rt)

= 600 e^(0.05 x 6)

= 600 (2.71828)^(0.30)

= $809.92

Other Questions
HELP ME ILL GIV ROBUX Identify the property shown by the equation. 14 6 = 6 14 A. Commutative Property B. Associative Property C. Identity Property D. Distributive Property PLEASE HELP ME 3. How many meters above sea level is the base of your landform?How many meters above sea level is the top of your platform? I WILL GIVE BRAINLIEST!80 patients gave information about how long they waited to see the doctor. 1. Work out an estimate of the mean time that the patients waited. 2. The doctor says, 70% of our patients wait less than 30 minutes to be seen. Is she correct? 3.What were the major effects of the Cultural Revolution? You consider undertaking the research project. It will increase sales by $100K per year starting next year and its life is 10 years. The maintenance cost is $50K and the depreciation of the equipment is 20K per year. The tax rate is 40% and there are no changes in net operating working capital. What is the annual operating cash flow from the project? A. $10,000 B. $18,000 C. $38,000 D. $30.000 Was is a macroeconomics Jordan says that he wants to make as much money as he can after college so that he can retire at age 45. He plans to "save every dime" that is not needed for his basic living expenses. David says that he wants to earn a decent salary but that he is more interested in using some of his earnings to travel and meet interesting people. Jordan and David have different:___________a) ideas about how to spend their time.b) goals for their lives.c) values about money.d) none of these choices are correct. The braking distance, D, of a car is directly proportional to the square of its speed, v. When d=5, v=10Find d when v=70 went to the lake.is that a sentence or a fragment Jeremiah is on a school trip to a forest preserve. According to the urban heat island effect, as Jeremiah leaves the city and heads toward the nature preserve, the temperature should (first drop-down) . That's because large cities (second drop-down) more heat than rural areas. When Jeremiah arrives at the preserve, he immediately notices the effects of solar radiation. The blacktop in the parking lot feels (third drop-down) the green grass where his class will eat their picnic lunch. First drop -down options 1. Remain the same 2. decrease 3. increase Second drop-down options 1. absorb 2. transmit 3. reflect third drop-down options 1. hotter than 2. cooler than 3. same temperature as You bought one of Great White Shark Repellant Co.s 6.6 percent coupon bonds one year ago for $1,056. These bonds make annual payments and mature 11 years from now. Suppose you decide to sell your bonds today, when the required return on the bonds is 4.5 percent. The bonds have a par value of $1,000. If the inflation rate was 3.2 percent over the past year, what was your total real return on investment? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Which are entrepreneurial jobs in the nutrition and wellness field? A. catering B. universities C. government agencies D. national grocery store chain E. sports trainer for the Olympics Solve for x: 3(x + 1) = -2(x - 1) + 6. (1 point) Need help ASAP!!!! THX Someone explain to me if this is correct? In a competitive market, a furniture company decides to use cheaper materials to decrease production costs and pass on the savings. This is an example of In an explanatory/informative article write about summer activities for teenagers which of these concepts would be used to inform the readerA. the importance of staying active B. the best new summer movies C. the locations of summer campsD. the amount of money earned in part time jobs what is the best defintion of efficency HHHHEEEEELLLLLPPPPPPP PLEASEEE ANSWER #1 AND #2 Hi i need help on this im not that smart sorry, what is the x-intercept of the graph that is shown below