Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.) f(x) = x + 3 x2 − 2x − 15

Answers

Answer 1

Answer:

  -3 (removable), +5

Step-by-step explanation:

Maybe you have ...

  [tex]f(x)=\dfrac{x+3}{x^2-2x-15}=\dfrac{x+3}{(x+3)(x-5)}=\dfrac{1}{x-5}\quad x\ne-3[/tex]

This will have discontinuities (points where the function is undefined) at ...

x = -3x = 5

The discontinuity as x = -3 is removable by defining f(-3) = -1/8.

Find The X-values (if Any) At Which F Is Not Continuous. Which Of The Discontinuities Are Removable?

Related Questions

Christina's time for a race was 22.3 seconds. Another​ runner's time was 4.41 seconds faster. Write and evaluate an equation with a variable to find the difference between Christina​'s time and the other​ runner's time.

Answers

Answer:

[tex]Difference = 4.41[/tex]

Step-by-step explanation:

Given

Represent Christina's time with C and the other runner's time with R

C = 22.3

R = 4.41 + C

Required

Determine the difference using an equation

The difference between both runner's time is as follows;

[tex]Difference = R - C[/tex]

Substitute 4.41 + C for R

[tex]Difference = 4.41 + C - C[/tex]

[tex]Difference = 4.41[/tex]

Hence, the difference is 4.41 seconds

Following are the notations for the three sums of squares. State the name of each sum of squares and the source of variation each sum of squares represents.

a. SSE

b. SSTR

c. SST

Answers

Answer:

As in explanation.

Step-by-step explanation:

A) SSE means "Error Sum of Squares". The source of it is the sum of squared deviations within groups.

B) SSTR means "Treatment Sum of Squares". It's source is the weighted sum of squared deviations of group means from grand mean. It's the sum of squares between groups.

C) SST means "Total Sum of Squares''. It's source is total sum of squared deviations from the grand mean. It is a sum of SSE and SSTR.

The source of variation and the naming of each sum of squares is as follows:

A) SSE means "Error Sum of Squares". The source of it is the sum of squared deviations that lies within groups.

B) SSTR means "Treatment Sum of Squares". It's source that represents the weighted sum of squared deviations of group means from the grand mean. It's the sum of squares between groups.

C) SST means "Total Sum of Squares''. It's source that represents total sum of squared deviations from the grand mean. It is a sum of SSE and SSTR.

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A department store offers two promotions. Promotion A says, "Buy one pair of shoes, get the second pair for half the price." Promotion B says, "Buy one pair of shoes, get $10 off the second pair." Jane wants to buy two pairs of shoes that cost $30 each. She can only use one of the promotions, A or B. Jane decides to use the promotion that will save her the most money. How many dollars does Jane save by picking one promotion over the other? (For example, if Jane spends $150 on her purchase by using one promotion and $100 on her purchase by using the other promotion, she saves $150-100=50$ dollars by using the second promotion over the first.)

Answers

Answer:

$5

Step-by-step explanation:

Using Promotion A, Jane would buy the first pair for $30 and the second for 1/2 * 30 = $15 for a total of 30 + 15 = $45. Using Promotion B, she would buy the first pair for $30 and the second for 30 - 10 = $20 for a total of 30 + 20 = $50. Since 45 < 50, Promotion A is the better deal, so Jane would save 50 - 45 = $5.

Which equation can be used to find x, the length of the hypotenuse of the right 18 + 24 = x 18 squared + 24 = x (18 + 24) squared = x squared 18 squared + 24 squared = x squared

Answers

Answer:

18² + 24² = x²

Step-by-step explanation:

Using the Pythagorean theorem, with legs a and b, and hypotenuse c, the equation is:

a² + b² = c²

If the legs measure 18 and 24, and the hypotenuse has length x, then you get:

18² + 24² = x²

Answer:

D

Step-by-step explanation:

Use the set of ordered pairs to determine whether the relation is a one-to-one function. {(−6,21),(−23,21),(−12,9),(−24,−10),(−2,22),(−22,−22)}

Answers

Answer:

the relation is not one-to-one.

Step-by-step explanation:

it can't because every number is in the 4th quadrant.  

The Masim family’s monthly budget is shown in the circle graph provided in the image. The family has a current monthly income of $5,000. How much money do they spend on food each month? A. $250 B. $500 C. $750 D. 1,100 Please show ALL work! <3

Answers

Answer:

C. $750

Step-by-step explanation:

The amount of money to be spent monthly on food = percentage covered by food in the circle ÷ 100% × total monthly income

= [tex] \frac{15}{100}*5000 [/tex]

[tex] = \frac{15}{1}*50 [/tex]

[tex] 15*50 = 750 [/tex]

Amount of money spent each month by the Masims is $750.

PLEASE ANSWER! Which expression is equal to the length of the hypotenuse of a right triangle, formed inside the unit circle, with a radius of 1?
A: sin 0/ cos 0
B: sin^2 0 + tan^2 0
C: sin 0 + cos 0
D: sin^2 0 + cos^2 0​

Answers

Answer:

b

Step-by-step explanation:

b: sin^2 0 + tan^2 0 this is just a gut feelings its been awhile since i done this kind of think i hope i could help

The expression equal to the length of the hypotenuse of a right triangle formed inside the unit circle with a radius of 1 is Option (D) [tex]sin^{2}[/tex]θ+[tex]cos^{2}[/tex]θ

What is Right triangle?

A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees.

What is Hypotenuse?

A hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle.

Here,

The length of the hypotenuse of a right triangle, formed inside the unit circle, with a radius of 1 is 1 unit.

We know that,

[tex]sin^{2}[/tex]θ+[tex]cos^{2}[/tex]θ=1

Hence, The expression equal to the length of the hypotenuse of a right triangle formed inside the unit circle with a radius of 1 is Option (D) [tex]sin^{2}[/tex]θ+[tex]cos^{2}[/tex]θ

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The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with a mean of 1262 chips and a standard deviation of 118 chips.

Required:
a. Determine the 26th percentile for the number of chocolate chips in a bag.
b. Determine the number of chocolate chps in a bag that make up the middle 96% of bags.

Answers

Answer:

(a) The 26th percentile for the number of chocolate chips in a bag is 1185

(b) The number of chocolate chips in a bag that makes up the middle 96% of the bags is between 1020 and 1504

Step-by-step explanation:

From the question, we have the following values:

μ =1262 and σ =118

(a) Let the value of x represents the 26th percentile. So the 26th percentile means 26% data is less than x. We can use the standard normal table to get the particular z-value that corresponds to this percentile.

P( Z<-0.65 )=0.2578 which is approximately 0.26

So for 26th percentile z-score will be -0.65.

Mathematically;

z-score = (x-mean)/SD

-0.65 = (x-1262)/118

-76.7 = x -1262

x = 1262-76.7 = 1185.3

This value is approximately 1,185

(b) Using a graph of standard normal distribution curve, if middle is 96% , then at both tails 2% each.

From z-table, we can find the closest probability;

P(-2.05<z<2.05) = 0.96

So we have two x values to get from the individual z-scores

-2.05 = (x-1262)/118

x = 1020(approximately)

For 2.05, we have

2.05 = (x-1262)/118

x = 1262 + 2.05(118) = 1504 (approximately)

What type of triangle has side lengths 9, 10, and √130? A. obtuse B. not a triangle C. acute D. right

Answers

Answer: Option C.

Step-by-step explanation:

The lengths of our triangle are:

9, 10 and √130.

If the triangle is a triangle rectangle, by the Pitagoream's theorem we have:

A^2 + B^2 = H^2

in this case H is the larger side, this must be √130.

then:

A and B must be 9 and 10.

9^2 + 10^2 = (√130)^2

81 + 100 = 130

This is false, so this is NOT a triangle rectangle, the hypotenuse is shorter than it should be.

Now, we have some kind of rule:

 if A^2 + B^2 = H^2 then we have one angle of 90° and two smaller ones. (triangle rectangle)

 if A^2 + B^2 > H^2 then all the angles are smaller than 90°, this is an acute triangle.

 if A^2 + B^2 < H^2 then we have one angle larger than 90°, this is an obtuse angle.

(H is always the larger side, A and B are the two shorter ones).

In this case:

81 + 100 > 130

Then this must be an acute angle.

Determine the positive integer values of k for which the following polynomia
over the integers given: c^2 – 7c+ k

Answers

Answer: k = 10, 12, 6

Explanation:

c^2 - 7c + 10
= (c -5)(c-2)

c^2 - 7c + 12
= (c - 4)(c -3)

c^2 - 7c + 6
= (c - 1)(c - 6)

A pharmacist needs 16 liters of a 4% saline solution. He has a 1% solution and a 5% solution available. How many liters of the 1% solution and how many liters of the 5% solution should he mix to make the 4% solution?

Answers

x = liters of 1% solution

y = liters of 5% solution

x + y = 16

0.01x + 0.05y = 0.04*16 = 0.64

y = 16 - x

0.01x + 0.05(16 - x) = 0.64

0.01x + 0.8 - 0.05x = 0.64

0.16 = 0.04x

x = 4

y = 12

Convert 6 feet to miles ( round five decimal places

Answers

Answer:

0.00114

Step-by-step explanation:

Divide length value by 5280

Use the model to show to help find the sum 0.34 plus 0.49

Answers

Answer/Step-by-step explanation:

The idea to use in solving this problem using the model, is to express the number of shaded boxes in fraction form.

Thus, the blue red shaded boxes has 34 boxes shaded out of 100 boxes. This represents [tex] \frac{34}{100} [/tex]. This will give us 0.34.

The other shaded boxes represents [tex] \frac{49}{100} = 0.49 [/tex].

Using the model, we can solve 0.34 + 0.49.

Add both fractions together.

[tex] \frac{34}{100} + \frac{49}{100} = \frac{34+49}{100} [/tex]

[tex] \frac{83}{100} = 0.83 [/tex]

9x - 3 -8x = 7 - x what is x Please answer ASAP, is urgent!!

Answers

Solve

Let's solve your equation step-by-step.

9x−3−8x=7−x

Step 1: Simplify both sides of the equation.

9x−3−8x=7−x

9x+−3+−8x=7+−x

(9x+−8x)+(−3)=−x+7(Combine Like Terms)

x+−3=−x+7

x−3=−x+7

Step 2: Add x to both sides.

x−3+x=−x+7+x

2x−3=7

Step 3: Add 3 to both sides.

2x−3+3=7+3

2x=10

Step 4: Divide both sides by 2.

2x

2

=

10

2

x=5

Answer:

x=5

Answer:

Hope this is easier, good luck.

Which point lies on the line with point-slope equation y - 3 = 4(x + 7)?

A.
(7, 3)

B.
(7, -3)

C.
(-7, -3)

D.
(-7, 3)

Answers

Answer:

D. (-7, 3)

Step-by-step explanation:

The equation given is in point-slope form.

Point-slope form is:

y-y1=m(x-x1)

This is where:

y1 is the y-coordinate of a point it goes through

m is the slope of the line

x1 is the x-coordinate of a point that it goes through

That said, in the given equation:

y1=3

m=4

x1=-7

Note that a point is (x-coordinate, y-coordinate)

Therefore, (-7, 3) is the point that lies on the line.

Given the equation 3x+7 which order of operations completely solves for x

Answers

Answer-7/3

Step-by-step explanation:

Gavin goes to the market and buys one rectangle shaped board. The length of the board is 16 cm and width of board is 10 cm. If he wants to add a 2 cm wooden border around the board, what will be the area of the rectangle board?

Answers

Answer:

The answer is 216

Step-by-step explanation:

if there is a 2 cm border, that means that the sides will both become 2 centimeters longer. so (16+2)*(10*2) = 18*12 = 216.

Find the slope of the line that passes through the points (1, 2) and (-4, 2).

Answers

Answer:

0

Step-by-step explanation:

We can find the slope  using the slope formula

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

   = ( 2-2)/(-4 -1)

   = 0/-5

  =0

━━━━━━━☆☆━━━━━━━

▹ Answer

Slope = 0

▹ Step-by-Step Explanation

[tex]Slope = \frac{y2 - y1}{x2 - x1} \\\\Slope = \frac{2 - 2}{-4 - 1} \\\\= \frac{0}{-5} \\\\= 0[/tex]

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

A spring is hanging from a ceiling. The length L(t) (in cm) of the spring as a function of time t (in seconds) can be modeled by a sinusoidal expression of the form a*sin(b*t) +d. At t=0, when the spring is exactly in the middle of its oscillation, its length is 7 cm. After 0.5 seconds the spring reaches its maximum length, which is 12 cm. Find L(t).

Answers

Answer:

  L(t) = 5·sin(πt) +7

Step-by-step explanation:

The middle of the oscillation of the given function occurs when t=0. At that point, ...

  L(0) = d = 7

The next maximum of the oscillation occurs when the argument of the sine function is π/2.

  b·t = π/2

  b = π/(2t) = π/(2·0.5) = π

At that maximum, the length is 12, so we have ...

  L(0.5) = a·sin(0.5π) +7 = 12

  a = 5

The function L(t) is ...

  L(t) = 5·sin(πt) +7

How many vehicles have been driven less than 200 thousand kilometers?

Answers

The number of vehicles that drove less than 200, 000 km is 12 vehicles

How to find the vehicle that drove less than 200 thousand km?

The bar char represents the distance in thousand of km vehicles drove.

3 vehicle drove for 50 thousand kilometres.

4  vehicle drove for 100 thousand kilometres.

5  vehicle drove for 150 thousand kilometres.

Therefore, the total vehicle that drove for less than 200 thousand kilometres is as follows:

total vehicle that drove for less than 200, thousand km = 3 + 4 + 5 = 12 vehicles

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Answer:

2

Step-by-step explanation:

A Ferris wheel has a diameter of 42 feet it rotates 3 times per minute approximately how far will a passenger travel during a 5 minute ride

Answers

Answer:

1978.2 or 630π feet

Step-by-step explanation:

The Ferris wheel will rotate 3 * 5 = 15 times during the 5 minute ride and the radius is 42 / 2 = 21 feet. Since C = 2πr, r = 21 and π ≈ 3.14, C = 2 * 3.14 * 21 = 131.88. However, this only accounts for one rotation so the answer is 131.88 * 15 = 1978.2 or 630π feet.


Aiko is finding the sum (4 + 5i) + (-3 + 7i). She rewrites the sum as (-3 + 7)i + (4 + 5)i. Which statement explains the
error Aiko made by using a mathematical property incorrectly​

Answers

Answer:

Aiko should not have put both of the 'i' out of the brackets.

Step-by-step explanation:

As only one integer has i with it, it is not possible to take the i out of the bracket.

The area of a square is 36cm2. What are the dimensions of the square? You must show your work. Pls tell me what the dimensions of the square are

Answers

Answer:

6 cm by 6 cm

Step-by-step explanation:

We know that the formula for area of a square is A = s² where A = area and s is the length of one side. We know that A = 36 so:

36 = s²

√36 = s

s = ±6

Note that s = -6 is an extraneous solution because you can't have a side length of -6, therefore the answer is s = 6 so the dimensions of the square are 6 cm by 6 cm.

The area of a square is found using the formula area = s^2, where s is the length of a side. ( a square has 4 equal sides).

Given the area you have:

36 = s^2

Find a by taking the square root of both sides:

S = sqrt(36)

S = 6

The square has a side length of 6 cm.

I will be honest I'm having a major brain fart.. What's the line called and what's it do again? it's separating numbers.. Looks like this
29
---
3

I know I'm stupid for this one... I've been up for 30 hours studying and now I can't remember this.. I need sleep but can't till i figure this out now...

Answers

Answer:

fraction bar. separates numerator and denominator in a fraction

Answer:

basically a dividing symbol, but specifically used for fractions

Step-by-step explanation:

Need help with the question below.

Answers

Answer:

A

Step-by-step explanation:

r=10 and the angle bln 5√3 and -5 is 330 or 11π/6


[tex]( \frac{3}{4} - \frac{2}{3} ) \times 1 \frac{1}{5} [/tex]

Answers

Answer: 0.1 or 1/10

Step-by-step explanation:

[tex]\left(\frac{3}{4}-\frac{2}{3}\right)\cdot \:1\frac{1}{5}[/tex]

[tex]1\frac{1}{5}=\frac{6}{5}[/tex]

[tex]\left(\frac{3}{4}-\frac{2}{3}\right)\cdot \frac{6}{5}[/tex]

  [tex]\frac{3}{4}-\frac{2}{3}[/tex]    [tex]=\frac{9}{12}-\frac{8}{12}[/tex]

[tex]=\frac{1}{12}[/tex]

[tex]\frac{6}{5}\cdot \frac{1}{12}[/tex]

Cross, cancel common factor

[tex]\frac{1}{2}\cdot \frac{1}{5}[/tex]

[tex]=\frac{1}{10}[/tex]

Write the quadratic in a verbal sentence. PLEASE HELP I’m super stuck!! If you can explain how to do this as well that would help so much!!

Answers

Answer:

n = 8

Step-by-step explanation:

Follow the question when turning the word equation into an equation

Because we know this is a quadratic equation, the product is a result of n multiplied by itself

[tex]n^{2} -4=60[/tex]

Solve for n

[tex]n^{2} =64[/tex]

[tex]\sqrt{n^{2} } =\sqrt{64}[/tex]

n = 8

Simplify the slope of bd

Answers

Answer:

[tex] \boxed{ - 1}[/tex]

Step-by-step explanation:

The co-ordinates of B = ( 0 , a ) ⇒ ( x₁ , y₁ )

The co-ordinates of D = ( a , 0 )⇒( x₂ , y₂ )

Let's find the slope of BD

Slope = [tex] \mathrm{ = \frac{y2- y1}{x2 - x1} }[/tex]

[tex] \mathrm{ = \frac{0 - a}{a - 0} }[/tex]

[tex] \mathrm{ = \frac{ - a}{a} }[/tex]

[tex] \mathrm{ = - 1}[/tex]

[tex] \mathcal{HOPE \: I \: HELPED !}[/tex]

[tex] \mathcal{BEST \: REGARDS !}[/tex]

In determining your group’s estimate, what mathematical model of a tennis ball did you use? What model of the classroom did you use? Did you make other simplification or assumptions?

Answers

Answer:

bro ur question is not understandable

An opinion poll asked a random sample of adults whether they believe flu shots are ineffective in the United States. A commentator believes less than 35% of all adults believe they are ineffective. Which null and alternative hypotheses should be used to test this claim? H0: p ≠ 0.35, Ha: p 0.35

Answers

Complete Question

The complete question is shown on the first uploaded image

Answer:

The second option is the correct option

Step-by-step explanation:

From  the question we are told that

    The  sample  proportion is  [tex]\r p = 0.35[/tex]

The  Null Hypothesis is  [tex]H_o : \r p = 0.35[/tex]

The reason for this is that the this original claim when represented mathematically does not contain an equality sign ([tex]i.e \ it \ is \ mathematically \ represented \ as \ \r p < 0.35[/tex])  so the null hypothesis is the compliment of it ( i.e  [tex]\r p = 0.35[/tex])

The  Alternative hypothesis is  [tex]H_a : \r p < 0.35[/tex]

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Employ less labor and more capital because a unit of labor costs $100 while a unit of capital costs only $40. )Patrick buys some bananas for 35%. He sells all the bananas for $40.60. Calculate profitpercentage. Show your working. Which element would you expect to have a higher electronegativity than nitrogen (N)?O Fluorine (F)Cesium (Cs)O Boron (B)O Phosphorous (P) A division of a manufacturing company has a return on investment of 24%. The division has an opportunity to accept a project that is expected to earn a return on investment of 22%. The companys hurdle rate is 20% which of the following statements is true? a) A division reports the following figures: Profit margin =20% Investment turnover = 0.5. The division return on investment is b) If a company has $2,000,000 invested in buildings, equipment, and other assets and desires to earn a return on investment of 30%, the company will need to earn a net income of $ . 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