HELP
Use the definition of continuity and the properties of limits to show that’s the function…

HELPUse The Definition Of Continuity And The Properties Of Limits To Show Thats The Function

Answers

Answer 1

Answer with Step-by-step explanation:

We are given that

[tex]g(x)=(x^2-3x-10)(x^2+2x^2-5x+4)[/tex]

x=-1

Using property of limit

[tex]\lim_{x\rightarrow -1}g(x)=\lim_{x\rightarrow -1}(x^2-3x-10)(3x^2-5x+4)[/tex]

=[tex](1+3-10)(3+5+4)[/tex]

=[tex](-6)(12)[/tex]

=[tex]-72[/tex]

[tex]g(-1)=(1+3-10)(1+2+5+4)[/tex]

[tex]g(-1)=(-6)(12)=-72[/tex]

[tex]\lim_{x\rightarrow -1}g(x)=g(-1)[/tex]

Hence, the function is continuous at x=-1


Related Questions

Someone please do this one

Answers

Answer:

150

Step-by-step explanation:

3x x 5= 15

y=15

5 x 15 = 75

75 x 2 = 150

Answer:

2xy = 150

Step-by-step explanation:

Plug in the values of x and y into 2xy.

You would get 2(5)(3x), which simplifies to 30x.

Plug in the value of x again.

30(5) = 150.

A newsletter publisher believes that 30% of their readers own a Rolls Royce. A testing firm believes this is inaccurate and performs a test to dispute the publisher's claim. After performing a test at the 0.02 level of significance, the testing firm fails to reject the null hypothesis. What is the conclusion regarding the publisher's claim

Answers

Answer:

The evidence is not sufficient at the 0.02 level of significance to reject the claim that the percentage is 30%.

Step-by-step explanation:

Let's first state the null and alternative hypotheses for this research;

H0: p = 0.30

Ha: p ≠ 0.30

Now, since the bull hypothesis is the claim and he fails to reject the null hypothesis from the research, we will conclude that;

The evidence is not sufficient at the 0.02 level of significance to reject the claim that the percentage is 30%.

What value of s makes the equation true?

Answers

Answer:

-17 =s

Step-by-step explanation:

-8s +4 = -7s +21

Add 8s to each side

-8s+8s +4 = -7s+8s +21

4 = s+21

Subtract 21 from each side

4-21 = s+21-21

-17 =s

Answer:

s = -17

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

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

-8s + 4 = -7s + 21

Step 2: Solve for s

[Addition Property of Equality] Add 7s on both sides:                                   -s + 4 = 21[Subtraction Property of Equality] Subtract 4 on both sides:                        -s = 17[Division Property of Equality] Divide -1 on both sides:                                 s = -17

help please asap just the answers​

Answers

[tex]\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]

[tex] \huge\underline{\sf{\red{Problem:}}}[/tex]

7.) Detemine the value of [tex] \sf{ {3a}^{2} -b.}[/tex]

[tex] \huge\underline{\sf{\red{Given:}}}[/tex]

[tex]\quad\quad\quad\quad\sf{a = 2}[/tex]

[tex]\quad\quad\quad\quad\sf{b = - 1}[/tex]

[tex]\quad\quad\quad\quad\sf{c = - 3}[/tex]

[tex] \huge\underline{\sf{\red{Solution:}}}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶{3a}^{2} - b}[/tex]

[tex]\quad \quad \quad \quad \sf{⟶{(3)( 2)}^{2} -( - 1)}[/tex]

[tex]\quad \quad \quad \quad \sf{⟶3(4)-( - 1)}[/tex]

[tex]\quad \quad \quad \quad \sf{⟶12-( - 1)}[/tex]

[tex]\quad \quad \quad \quad \sf{⟶12 + 1 }[/tex]

[tex]\quad \quad \quad \quad ⟶ \boxed{ \sf{ 13}}[/tex]

[tex]\huge\underline{\sf{\red{Answer:}}}[/tex]

[tex]\huge\quad \quad \underline{ \boxed{ \sf{ \red{\:13}}}}[/tex]

8.) Find the value of [tex] \sf{ {a}^{3} {b}^{3} - abc.}[/tex]

[tex] \huge\underline{\sf{\red{Solution:}}}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶ {a}^{3} {b}^{3} - abc}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶{(2)}^{3} {( - 1)}^{3} - (2)( - 1)( - 3)}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶{(8)}{( - 1)} - ( - 2)( - 3)}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶{( - 8)} - ( 6)}[/tex]

[tex]\quad\quad\quad\quad ⟶\boxed{\sf{ - 14}}[/tex]

[tex]\huge\underline{\sf{\red{Answer:}}}[/tex]

[tex]\huge\quad \quad \underline{ \boxed{ \sf{ \red{-14}}}}[/tex]

[tex]\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]

#CarryOnLearning

[tex]\sf{\red{✍︎ C.Rose❀}}[/tex]

Find the value of x. Geometry

Answers

╭⋟───────────────

[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]

Given,

< BAG = 2x°

< BAC = 90° [ < EAF = 90° (vertically opposite angles are equal to each other)]

< CAD = x°

____________________

Value of x = ?

____________________

From the figure we can see that,

< BAG + < BAC + < CAD = 180° (supplementary angles)

____________________

So to solve,

[tex] < BAG + < BAC + < CAD = 180 \\ 2x + 90 + x = 180 \\ 2x + x + 90 = 180 \\ 3x + 90 = 180 \\ 3x = 180 - 90 \\ 3x = 90 \\ x = \frac{90}{3} \\ x = 30[/tex]

The value of x is [tex]\boxed{30}[/tex]

____________________

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

[tex]RainbowSalt2^{2}2^{2}[/tex] ღ

───────────────⋞╯

Fill in the blank with the correct response.

If x:6 as 3:9, then x is equal to .

Answers

Answer:

X is equals to 2

Step-by-step explanation:

I hope it helps you

Mark Brainliest please


Answer: 2

x/6 = 3/9
9x = 18
x = 2

Thank for answer thank you

Answers

Answer:

Volume = 840 cm^3

Step-by-step explanation:

Volume = Area of front x the length

Area of front = 15 x 8 = 120 cm^2

                     = 4 x 5 = 20 cm^2

                     = 120 + 20 = 140 cm^2

Volume = 140 x 6

Volume = 840 cm^3

If this helps you, please mark brainliest!

Answer:

Formula for Volume - L x W x H

Volume = 1080cm^3

360 + 720

1080

Hello! I am simply looking for help, no this is not a test. Once again I am just looking for hints/help.

Answers

Answer:

No problem, here is a tip

Step-by-step explanation:

take each whole number then multiply it by the percent in decimal form. So if its 90% of 136 you do 136 * 0.9

How do I find Y Im still confused on how to solve Y and if you have any tips please lmk asap. Thank you

Answers

Answer:

y = 3

Step-by-step explanation:

Since ABCD is similar to EFGH, therefore, the ratio of their corresponding sides are equal. Thus:

AB/EF = CD/GH

AB = 3

EF = 2

CD = 4.5

GH = y

Substitute

3/2 = 4.5/y

Cross multiply

3*y = 4.5*2

3y = 9

Divide both sides by 3

3y/3 = 9/3

y = 3

i have no clue what i’m doing

Answers

Answer:

c(x) =  16x + 22736

R(x) = -2x^2 + 524x  

[ -2x^2 + 508x  - 22736] = 0

Factored: f(x) = -2(x - 196)(x - 58)

58 to break even

Step-by-step explanation:

Your cost is the amount it cost you to "make" stuff.

You have fixed and variable costs (cost of oven is fixed cost of flower and sugar is variable to make cupcakes)

your cost is c(x) =  16x + 22736

"your oven and building cost $22736 per month and you use $16 worth of sugar butter flour to make one cupcake ( it  must be a huge one) ...

your revenue is the amount of money that "comes into your business"...

the amount of money in the cash register.... Note: this is only money IN you still have to pay for the building, sugar flour etc.

R(x) = -2x^2 + 524x  

Note: the minus and the square basically say that the more you charge the less cupcakes you will sell...

Profit is the money in minus the money out

P - R - E   [ -2x^2 + 524x  ] - [16x + 22736]

the break even point is where the two functions are the same

in other words where C=R or R-C=0

[ -2x^2 + 524x  ] = [16x + 22736]

[ -2x^2 + 508x  - 22736] = 0

Factored: f(x) = -2(x - 196)(x - 58)

Answer:

Step-by-step explanation:

C(x)=16x+22736

R(x)=-2x²+524x

P(x)=R(x)-C(x)

=-2x²+524x-16x-22736

=-2x²+508-22736

when profit is zero then no gain or loss.

so -2x²+508x-22736=0

or x²-254x+11368=0

196+58=254

196×58=11368

x²-54x-196x+11368=0

x(x-54)-196(x-54)=0

(x-54)(x-196)=0

x=54,196

so x=54 is the smallest number of bins to break even.

for which equation x=5 be a solution ?

a. 3 x +6=21
b. 12 - 2 x =13
c. 7+6 x+27
d. 4 x - 7=27

Answers

The correct answer is A. 3x+6=21

Answer:

a) 15+6 =21

Step-by-step explanation:

By rounding to 1 significant figure, estimate
494.37
÷
5.12

please help tyty x

Answers

Answer:

100

Step-by-step explanation:

rounding to 1 sig figure

494.37 ≈ 500

5.12 ≈ 5

Estimating

500 ÷ 5 = 100

Please help, find the slope.

Answers

Answer:

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

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Reading a coordinate planeCoordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Step-by-step explanation:

Step 1: Define

Identify points from graph

Point (0, -1)

Point (-3, 1)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Substitute in points [Slope Formula]:                                                              [tex]\displaystyle m = \frac{1 - -1}{-3 - 0}[/tex][Fraction] Subtract:                                                                                           [tex]\displaystyle m = \frac{2}{-3}[/tex]Rewrite:                                                                                                             [tex]\displaystyle m = \frac{-2}{3}[/tex]

A triangle is shown. What is X?

Answers

it would be 56° since a triangle is a 190° shape

Answer: 44º

Step-by-step explanation:

Hi there! To start out, disregard Y and Z, as they are just there to trip you up.

Use the Triangle Sum Theorem to find out the question! This theory states that all angles in a triangle add up to 180 degrees. So, just set up an equation, like the one down below!

82+54+X=180

Then, add the whole numbers!

136+X=180

Then isolate X by using inverse operations!

136+X-136=180-136

Then your answer is there!

X=44

If you have any follow up questions, please let me know! Have a nice day

14. Which is the first step in solving: X - 1/3 = 1/3 ?*​

Answers

Answer:

Step-by-step explanation:

In this case "solving" involves isolating the variable, x, on the left side of this equation.  

Starting with x - 1/3 = 1/3, we add 1/3 to both sides.  This results in:

x = 1/3 + 1/3, or x = 2/3.

tapes that usually cost $8 each are on sale for 30% off what is the price for a tape on sale?

Answers

Answer:

$5.6

Step-by-step explanation:

Answer:

8*30/100= 2.4

so present cost = 8.0 - 2.4 = $ 5.6

Step-by-step explanation:

Willl




Give





Brainlist




Answer




:))

Answers

Answer:

[tex]x=54^{o}[/tex]

Step-by-step explanation:

Angles of straight line: 126 and x = 180

[tex]x+126=180[/tex]

[tex]x=180-126[/tex]

[tex]x=54^{o}[/tex]

{CHECK: [tex]54+126=180[/tex]}

hope this helps.....

At the beginning of the school year, Liya's goal was to earn an A on
at least 85% of her 60 quizzes for the year. She earned an A on 35 of the first 40
quizzes. If she is to achieve her goal, on at most how many of the remaining
quizzes can she earn a grade lower than an A?

A: 1
B: 2
C: 3
D: 4
E: 5

Answers

Answer:

4

Step-by-step explanation:

If 15% of quizzes don't have to be A's, that means that its 9 quizes that can be lower than an A. She already lost 5 which means she has four left.

Answer:

D; 4

Step-by-step explanation:

Step 1:

Let us figure out exactly how many As Liya has to earn for the year. We must find 85% of 60:

[tex]85 \%\ of\ 60=\\\frac{85}{100}*\frac{60}{1}=\\\frac{85}{5} *\frac{3}{1} =\\17*3=\\51[/tex]

Liya must earn 51 As this year to reach her goal. This also means that she can earn 9 grades lower than an A to still reach her goal ([tex]60-51=9[/tex]).

Step 2:

So far, Liya has earned 35 As out of 40 tests in total. This means that so far, Liya has earned 5 test grade lower than an A:

[tex]40-35=5[/tex]

In total, Liya can only have 9 grades lower than an A. Therefore:

[tex]9-5=\fbox{4}[/tex]

Liya can only earn [tex]\fbox{4}[/tex] grades lower than an A in the remaining quizzes.

I hope this helps! Let me know if you have any questions :)

An article bought for $125 was sold %175. The percentage profit

Answers

Answer:

40% profit

Step-by-step explanation:

There is a profit of $50.

If you were to find the percentage, you would divide 50 by 125. This would give you 0.4

help please, i have absolutely no idea how to do this :(

Answers

Answer:

[tex]m = \frac{1}{2}[/tex]

Step-by-step explanation:

Two points are ( 8, 0 ) and  (0 , - 4)

              [tex]slope \ , \ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 -0}{0-8}=\frac{-4}{-8} = \frac{1}{2}[/tex]


2. A carpenter wants to cut a wood board that is feet long
d on
5
into pieces that are feet long. How many whole pieces
can be cut from the board? How much wood is left over
16

Answers

Answer:

2 whole pieces

5/24 feet left

Step-by-step explanation:

divide 5/6 by 5/16 = 2 2/3 pieces

so there are 2 whole pieces and 2/3 small piece.

The 2/3 small short equals to 5/16 x 2/3 = 5/24 ft

worth 11 points and actually help me instead of taking the points plz

Answers

Answer:

C'(-1,1)

Step-by-step explanation:

The coordinates of C are (-2,4).

The translation is (x+1,y-3), so we take the x value -2 and the y value 4 and plug it in.

(-2+1,4-3)

=(-1,1)

C' has the coordinates (-1,1)

Answer:

Its ([-1],[1])

Step-by-step explanation:

By (x+1, y-3), the trapezoid wll move 1 point to the right, and 3 points down.

A map of an island is shown on a half-centimeter grid,

where A, B, and Care houses.
The actual distance between A and B
is 960 meters.
a) Work out the scale on the map
Give your answer as 1:n

Answers

Answer:

The answer is below

Step-by-step explanation:

A map can either be scaled up or scaled down. If the map is enlarged then it is scaled up and hence represented by n:1, where n > 1. While is the map is reduced, it is scaled down and is represented by 1 : n, where n < 1.

Since one box has a length of 1 cm by 1 cm. The distance between A and B is 4 boxes = 4 cm = 0.04 m

Hence the scale is given as 1:n, where n > 1. n is gotten from:

n = 960 m / 0.04 m = 24000

Therefore the scale is 1 : 24000

Answer:

1:48000

Step-by-step explanation:

960m=96000cm

20% of 2kg ( in g).
Please help

Answers

Answer:

[tex]{ \tt{ = 20\% \times 2}} \\ = 0.4 \: kg \\ { \tt{ = 400 \: grams}}[/tex]

Answer:

400 g

Step-by-step explanation:

0.20 x 2 kg = 0.4 kg

0.4 kg x (1000g / 1kg) = 400 g

Represent -2/11, -5/11, -9/11 on a number line.

Answers

Answer:

-9/ 11 ____-5/11 _____ - 2/11

Step-by-step explanation:

-2/11, -5/11, -9/11

All the numbers are negative ; the fraction which is largest is 9/11 ; then 5 /11 ; then 2 /11 ; however, since they are negative, they largest fraction becomes the least value.

Numbers on a number line are arranged from least to highest. Hence the numbers will be arranged in a number line as follows :

-9/ 11 ____-5/11 _____ - 2/11

The product of b and 5 is greater than or equal to −23.

Answers

Answer:

Step-by-step explanation:

Product of b and 5 = b*5 = 5b

Inequality:

5b ≥ - 23

Solution:

Divide both sides by 5

b ≥ -23/5

b ≥ -4.6

Answer:

5b≥ -23

Step-by-step explanation:

product of b and 5  - this means multiply

5b

is greater than or equal -  ≥

5b≥ -23

Solving

Divide by 5

5b/5≥ -23/5

b≥ -23/5

What is 16/5 inches by 10/4 inches in area

Answers

Answer: 8

Step-by-step explanation:

16/5 x 10/4 = 8

Answer:

Area = 8 inches

Step-by-step explanation:

[tex]\frac{16}{5} *\frac{10}{4} = \frac{160}{20} (Reduce) =8[/tex]

You roll two 6-sided dice.
What is the probability that you would roll an even number on the first dice and a number greater than 4 on the second?

Answers

probability that you will role an even number on the first roll: 3 even / 6 total = 3/6 chance = 1/2 chance

probability that you role a number greater than 4 on the second: only numbers greater than 4 are 5 and 6, so you have 2 numbers / 6 total = 2/6 chance = 1/3 chance

because it says AND, you have to multiply the first role probability by the second role probability

so 1/2 x 1/3 = 1/6

answer: 1/6

if LMNO is a rectangle, and MO=54, what is the length of line NP?
answers
a.) 34
b.) 22
c.) 18
d.) 108
e.) 27
f.) cannot be determined

Answers

Answer:

27 is the correct answer

Answer:

27

Step-by-step explanation:

ILL MARK BRAINLIEST FIRST ANSWER I PROMISE !!!

( if it's absurd i'll report, sorry )


If y represents a student's age, which inequality shows that you must be older than 14 to try out for the basketball team?

a. y>14

b. y≥14

c. y<14

d. 14=y

Answers

I do not see the answer I’m looking for, bc the format is weird. But Y should be greater than the 14. So it should be, Y>14. Just like that with no line underneath the greater than symbol.

Answer:

a) y > 14

Step-by-step explanation:

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