please help!!!!
simplify the rational expression. state any restrictions on the variable.
t^2+2t-24/t^2-36

Answers

Answer 1

Answer: hope this helps! :)

t - 4

—————

t - 6

Step-by-step explanation:

          t2 + 2t - 24

Simplify   ————————————

            t2 - 36    

Trying to factor by splitting the middle term

  Factoring  t2 + 2t - 24  

The first term is,  t2  its coefficient is  1 .

The middle term is,  +2t  its coefficient is  2 .

The last term, "the constant", is  -24  

Multiply the coefficient of the first term by the constant   1 • -24 = -24  

Find two factors of  -24  whose sum equals the coefficient of the middle term, which is   2 .

    -24    +    1    =    -23  

    -12    +    2    =    -10  

    -8    +    3    =    -5  

    -6    +    4    =    -2  

    -4    +    6    =    2    That's it

Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  6  

                   t2 - 4t + 6t - 24

 Add up the first 2 terms, pulling out like factors :

                  t • (t-4)

            Add up the last 2 terms, pulling out common factors :

                  6 • (t-4)

Step-5 : Add up the four terms of step 4 :

                  (t+6)  •  (t-4)

           Which is the desired factorization

Trying to factor as a Difference of Squares :

1.2      Factoring:  t2-36  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

       A2 - AB + BA - B2 =

       A2 - AB + AB - B2 =

       A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 36 is the square of 6

Check :  t2  is the square of  t1  

Factorization is :       (t + 6)  •  (t - 6)  

Canceling Out :

  Cancel out  (t + 6)  which appears on both sides of the fraction line.

Answer 2

Answer:

t⁴ + t³ - 36t - 24

Step-by-step explanation:

Given :

t² + 2t - 24/t² - 36

Solving :

Multiply throughout with t² so the polynomial is easier to simplifyt² (t² + 2t - 24/t² - 36)t⁴ + t³ - 24 - 36t²t⁴ + t³ - 36t - 24

Related Questions

which question is a statistical question

1. who is your teacher?
2. what is your favorite movie?
3. What is the age of each child currently at the zoo?
4. How many pages are in the book you are reading?
5.How many pairs of shoes do students in your school have?

please answer asap

Answers

Answer:

5

Step-by-step explanation:

Cause you can actually get multiple different answeres which you can make a statistical question on

Answer the question below

Answers

Answer:

v=k+5

Kora is 13 yrs old when Venla is 18 yrs old

how to find area of triangle

Answers

Answer:

[tex]\displaystyle A =\frac{B*H}{2}[/tex]

Step-by-step explanation:

    To find the area of a triangle, we can use the formula of:

[tex]\displaystyle A =\frac{B*H}{2}[/tex]

    This formula comes from the area of a rectangle, because a triangle is half a rectangle.

❒ Question -:

How to find the area of a triangle?

❒ Explanation -:

Triangle :

A polygon which has three sides is called a triangle.

Formula :

Assume a rectangle ABCD and let the height be h and base be b.

If we draw a diagonal from one vertex, it will break the rectangle into two congruent or equal triangles. The area of each triangle is half the area of the rectangle.

The area of the triangle ABC is [tex]\dfrac{1}{2}[/tex] × base × height.

[tex] \star \small\boxed{ \rm{ Area \: of \: a \: triangle = \dfrac{1}{2} × Base × Height}} [/tex]

This formula comes from the area of a rectangle. A triangle is half as big as the rectangle that surrounds it, that is why the area of a triangle is one-half base times height.

A factory makes circular rugs with a radius of 3.5 feet. How much braid do they need to go all the way around the outside of the rug? Use 3.14 for pi

Answers

I believe that the answer is 21.48

The factory would need approximately a circumference of 21.98 feet of the braid to go all the way around the outside of the circular rug.

We have,

The formula for the circumference (C) of a circle is:

C = 2πr

where r is the radius of the circle and π is a mathematical constant approximately equal to 3.14.

In this case, the radius of the rug is 3.5 feet, so we can calculate the circumference as:

C = 2 × 3.14 × 3.5 = 21.98 feet

Therefore,

The factory would need approximately a circumference of 21.98 feet of the braid to go all the way around the outside of the circular rug.

Learn more about circumference of a circle here:

https://brainly.com/question/26605972

#SPJ2

The length of a rectangle is 2 centimeters less than five times the width of a rectangle. The area of the rectangle is 16 square centimeters. Find the length and width of the rectangle.

Answers

Answer:

Length: 8 cm

Width: 2 cm

Step-by-step explanation:

Check the attachment.

Please help! Will mark brainlyest.

Answers

Answer:

D

Step-by-step explanation:

there is a curve

Is the following a statistical question?
How many letters are in the English alphabet?
yes
no

Answers

There are 26 letters in the English alphabet and no it’s not a statistical question

Geometry math work help pls

Answers

Answer:

Step-by-step explanation:

Remark

If you sweep all the way around the circle starting at 13,0, you go through 360 degrees.  

The formula for that event: Circumference = 2*pi * r

If you stop after sweeping out 135 degrees, then you need to multiply by a fraction.

Formula and givens

Arc RST = (135/360) * 2 * pi * r

pi = 3.14

r = 13

Solution

Arc RST = .375 * 2 * 3.14 * 13

Answer = 30.615

(question in image)

i need the equation and it solved

Answers

Answer:

Option ASpeed of plane is 240 km/h, speed of wind is 50 km/h

Step-by-step explanation:

With the tail wind the total speed is the sum of the speeds of plane and wind.

When into wind the total speed is the difference of speeds of plane and wind.

The first equation is

(r + w)*6 = 1740

The second equation is

(r - w)*3 = 570

Simplify both equations and solve the system

r + w = 1740/6 ⇒ r + w = 290r - w = 570/3 ⇒ r - w = 190

Solve by elimination, add up the equations

r + w + r - w = 290 + 1902r = 480r = 240

Find the value of w

240 + w = 290w = 290 - 240w = 50

A valuable watch has an original price of $x. It is sold for $5304 after its original price has been increased by 2% and then by 4%. Find x.
SHOW YOUR WORKING. ​

Answers

Answer:

$5416.67

Step-by-step explanation:

If A valuable watch has an original price. It is sold for $5304 after its original price has been increased by 2% and then by 4%. The original price of watch is 5096.

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part

let the original price be x.

The selling price of watch is $5304 .

2% of $5304  is 2/100×5304=0.02×5304

=106.08

Now let us remove the 2% from the selling price of the watch.

$5304 - 106.8 =5197.2

4% of $5197.2 is 4/100×5197.2=0.04×5197.2

=207.888

So Selling price of watch minus percentage in increase is the original price

5304-207.888=5096.1

Hence if a valuable watch has an original price. It is sold for $5304 after its original price has been increased by 2% and then by 4%. The original price of watch is 5096.

To learn more on Percentage click:

https://brainly.com/question/28269290

#SPJ2

If the last 2 months of the year each have the most common amount of rainfall, how much more rain will fall for the year?

Answers

Answer:

Step-by-step explanation:

The table shows the amount of rainfall recorded over the first 10 months of a year. Draw a line plot, if needed.

Amount of Rainfall (inches)

Part A

What is the difference between the greatest and least amounts of rainfall in a month?

Let x = the unknown.

Greatest amount= 3 1/4

Least amount = 3/4

x= 3 1/4 - 3/4 = 2 1/2 inches.

Part B

If the last 2 months of the year each have the most common amount of rainfall, how much more rain will fall for the year?

The number with the most common amount is  2 3/4.

2 3/4 + 2 3/4 = 5 1/2 inches.

(Will give brainliest help asap pls)

A membership at a classic film center cost $75 per year.tickets to film cost members $5.50 . Which of the following statements is true of the annual cost of membership at the film center? Let y= total cost and x= number of films seen.

A. The annual cost is shown by the linear function y=x+5.50. The rate of change is 1, and the initial value is 5.50

B. The annual cost is shown by the linear function y=75x+5.60. The rate of change is 75, and the initial value is 5.50.

C. The annual cost is shown by the linear function y=80.50x. The rate of change is 80.50, and the initial value is 0.

D. The annual cost is shown by the linear function y=5.50x+75. The rate of change is 5.59, and the initial value is 75

Answers

D because 5.50 is x and your y so boom D

A well-known chewing gum maker wants to determine if any of its four flavors of gum are more popular than the others. A random sample of 80 people who say they chew gum regularly is asked to identify their favorite flavor of gum. Here are the results:

Answers

The appropriate null hypothesis is (b) Flavor preferences are evenly distributed across all flavors

How to determine the appropriate null hypothesis?

The distribution of the gum flavors is given as:

Peppermint = 25Cinnamon = 19Wintergreen = 22Spearmint = 14

The sample size is given as:

Sample = 80

From the distribution of the gum flavor, we can see that the count of each flavor are not equal i.e. uneven

This means that we can use the following statement as the null hypothesis:

Flavor preferences are evenly distributed across all flavors

Hence, the appropriate null hypothesis is (b)

Read more about test of hypothesis at:

https://brainly.com/question/15980493

#SPJ1

Which graph shows the effect of changing the slope of the line
y = 1/2x - 3 to 2?

Picture linked below if you want

Answers

Answer:

A

Step-by-step explanation:

Y intercept is -3

Rise 2 run 1

Please help.
Solve for a

Answers

Answer:

a = [tex]\sqrt{68}[/tex] = 8.2

Step-by-step explanation:

Look at picture ↓

[tex]Hope[/tex] [tex]this[/tex] [tex]helps![/tex] [tex]:)[/tex]

Answer:

60

Step-by-step explanation:

You have the proper formula. You just need to swap some things around so we aren't solving for C. C is always the hypotenuse, the diagonal line opposite the right triangle. A and B can be either side unless specified.

1. The side we're solving for can either be called a or b. Let's call it A.

2. Now, switch around the theorem to solve for a: [tex]C^2-B^2=A^2\\[/tex]

3. Plug in what we know: [tex]8^2-2^2=a^2[/tex]

4. It simplifies down to [tex]60=a^2[/tex]

5. The  "[tex]a^2[/tex] " means to square the a. We need to undo that to get a by itself. The opposite of squared is the square root

6. This leaves us to take the square root of both sides, which isolates a.

7. [tex]\sqrt{60}[/tex] is the answer. It's asking for it in the square root so we don't need to simplify it.

Which model best represents the data set? exponential, because there is a relatively consistent multiplicative rate of change exponential, because there is a relatively consistent additive rate of change linear, because there is a relatively consistent multiplicative rate of change linear, because there is a relatively consistent additive rate of change

Answers

The first choice, is exponential, because there is a relatively consistent multiplicative rate of change.

What is exponential?

An exponential function is a function whose value is a constant raised to the power of an argument

1) I have attached the figure with the data table that represents the temperature of a cup of coffee over time.

These are the data:

Time (min) ------ Temperature (°F)

0 ----------------------- 200

10 ---------------------- 180

20 --------------------- 163

30 --------------------- 146

40 ---------------------131

50 -------------------- 118

60 -------------------- 107

2) Since, the increase in time is constant, while the decrease in temperaute is not, you know that it is not linear.

3) The other two options involve exponential models.

The exponential models have a constant multiplicative rate of change, not additive. Therefore, the only feasible choice is the first one: temperature of a cup of coffee over time.

4) You can prove it:

i) Exponential models have the general form y = A [r]ˣ, where B is r is the multiplicative rate of change: any value is equal to the prior value multiplied by r:

y₁ = A [r]¹

y₂ = A[r]²

y₂ / y1 = r ← as you see this is the constant multiplicative rate of change.

ii) Test some data:

180 / 200 = 0.9

163 / 180 ≈ 0.906 ≈ 0.9

146 / 163 ≈ 0.896 ≈ 0.9

131 / 146 ≈ 0.897 ≈ 0.9

118 / 131 ≈ 0.901 ≈ 0.9

107 / 118 ≈ 0.907 ≈ 0.9

As you see all the data of the table have a relatively consistent multiplicative rate of change, which proves that the temperature follows an exponential decay; so the right choice is the first one.

To know more about exponential follow

https://brainly.com/question/2456547

Answer:

first choice, exponential, because there is a relatively consistent multiplicative rate of change.

explanation:

because it is <3

Look at this diagram:
a)
What fraction is shaded?
b)
What percentage is shaded?

Answers

⊱─━━━━━━━━━⊱༻●༺⊰━━━━━━━━━─⊰

⚘✨ HI BRAINLY USER!! ✨

JUST CLICK THE ATTACHMENT PHOTO

⊱─━━━━━━━━━⊱༻●༺⊰━━━━━━━━━─⊰

#CARRY ON LEARNING #ulzanggirlth

Given h(x)=-x+2h(x)=−x+2, find h(4)h(4).

Answers

Answer:

(-4 + 2 • h(4))^2

Step-by-step explanation:

h(4)h(4)

h(4) • h(4) = (-4 +2 • h(4)) • (-4 +2 • h(4))


Calculate

(-4+2× h(4)) × (-4+2× h(4))

Simplify using exponent rule with same base

a^n • a^m = a^n+m

(-4+2× h(4))^2

I hope this helps out.

PLSSS HELP IF YOU TURLY KNOW THISS

Answers

Answer:

the answer to your question is 9 miles

the answer in its simplest from is 9 miles

Describe how to translate the graph of y=√x to obtain the graph of y=√x+2
A.shift right 2 units

B.shift left 2 units

C.shift up 2 units

D.shift down 2 units

Answers

Answer:

D

Step-by-step explanation:

Shift down 2 units, you want to make the graph only move in the y direction and take it back to the origin

4 1/6 add 2 3/4 PLEASE

Answers

Answer: 6.91666666667, or 6 11/12

TEN POINTS
Select the correct answer.
Solve the following quadratic equation.
(x+4)^2=25

A. x=9 and x=-1

B. x=-9 and x=-1

C. x=-9 and x=1

D. x=9 and x=1

Answers

Answer:

hi I need actually a lot of help with Matt since I'm not the best?

Write the equation of the graph in y=ab^x form.

Answers

Answer:

Step-by-step explanation:

i really need some help on this question

Answers

Answer:

What is the car's rate in kilometers per minute?

[tex]0.9\frac{km}{min}[/tex]

How many kilometers will the car travel in 5 minutes?

[tex]4.5\ km[/tex]

Step-by-step explanation:

If we know:

[tex]\frac{54\ km}{1\ hour}[/tex]

And there are 60 minutes in an hour:

[tex]\frac{1\ hour}{60\ minutes}[/tex]

We can do:

[tex]\frac{54\ km}{1\ hour} * \frac{1\ hour}{60\ minutes} = \frac{54\ km}{60\ minutes} = 0.9 \frac{km}{min}[/tex]

From here, we figure out the distance from minutes:

[tex]0.9\frac{km}{min} * 5 = 4.5\ km[/tex]

The foci and the vertices of the hyperbola are labeled.

Which equation represents the hyperbola shown in the graph?


Answer is B

Answers

The answer is B and pls mark me brainiest

The equation of the hyperbola is:

(x - 3)² / 9 - (y - 2)² / 16 = 1.

To find the equation of the hyperbola with the given foci and vertices, we need to determine the center, semi-major axis (a), and semi-minor axis (b) of the hyperbola.

The center of the hyperbola is the midpoint between the two vertices:

Center = ((3 + 3) / 2, (5 + (-1)) / 2) = (3, 2).

The distance between the center and one of the vertices gives us the semi-major axis (a):

a = distance between center and vertex = 5 - 2 = 3.

The distance between the center and one of the foci gives us the distance c (the distance from the center to the focus):

c = distance between center and focus = 7 - 2 = 5.

Now, we can find the value of b (the semi-minor axis) using the relationship between a, b, and c in a hyperbola:

c² = a² + b²

5² = 3² + b²

25 = 9 + b²

b² = 25 - 9

b² = 16

b = 4.

Now that we have the center (h, k) = (3, 2), the semi-major axis (a) = 3, and the semi-minor axis (b) = 4, we can write the equation of the hyperbola in standard form:

For a hyperbola (center at (h, k)), the equation is:

(x - h)² / a² - (y - k)² / b² = 1.

Plugging in the values:

(x - 3)² / 3² - (y - 2)² / 4² = 1.

The equation of the hyperbola is:

(x - 3)² / 9 - (y - 2)² / 16 = 1.

Learn more about hyperbola here

https://brainly.com/question/16457232

#SPJ2

Can anyone help me? me please

Answers

Answer:

approx 8.5 cm

Step-by-step explanation:

Given:

Volume= 225 cm^2

Diameter= 10cm

∴Radius= 10/2= 5cm

Volume of cone= 1/3 pi r^2 h

(now substitute the values we know),

225 = 1/3 * pi * (5)^2 *h

225*3= 25*pi*h

675= 25*pi*h

675/25= pi*h

27= 22/7*h

h= 27* 7/22

h= 8.5 cm approx.

I have mentioned every minor step. Hope it helps!!

In a different plan for area​ codes, the first digit could be any number from 4 through​ 8, the second digit was either 0, 1, or 2​, and the third digit could be any number 4 except With this​ plan, how many different area codes are​ possible?

Answers

Answer:

135 choices

Step-by-step explanation:

5 choices for 1st dig

3 choices for 2nd dig

9 choices for third digit

5 x 3 x 9 = 135

Answer:

135

Step-by-step explanation:

But, for the last digit that is go from 0-9 except the 4

So it also depends on the range for the last digit

Hope this helped! :)

If p → q is true, then ~ p → ~ q is __________ true.

Sometimes
Always
Never

Answers

Answer:

1. If p is true and q is false, the p -> q is never true.

2. When p is false and q is true, then p or q is always true.

3. If p is true and ~ q is false, then p -> ~ q

N

is never false.

4. If p is true and q is true, then ~ p -> ~ q is always true.

5. If p->q is true and q is true, then p is

always true.

Further Explanation:

The logic gates are used here.

Here, the symbol -> is for implication. Implication p-> q means that if p is true then q must be true.

So let us look at all the questions one by one.

1. p is true and q is false, the p -> q is always, sometimes, never true.

p-> q

true -> false

The true should imply true so the given statement will never be true.

2. When p is false and q is true, then p or q is always, sometimes, never true.

false or true

We know that in or gate even if one input is true, the whole output is true. So this statement will be always true given p is false and q is true.

3. If p is true and~q is false, then P q is always, sometimes, never false.

This translates to:

true -> true

So it will never be false.

4. If p is true and q is true, then ^p -> ~q is always, sometimes, never true.

This translates to:

false false

This will always be true.

5. If p->q is true and q is true, then p is always, sometimes, never true.

If p->q is true and q is true then will always be true. "Implies to" states that in p->q, in order for q to be true p has to be true. So p will always be true.

Which word describes 5 in the number sentence shown?

5x−2=18
Term
Coefficient
Variable
Equation

Answers

Answer:

Coefficient

Step-by-step explanation:

5 is the Coefficient for x

∠1 and ∠2 are linear pair. If m∠1 = 3x + 4 and m∠2 = 2x – 9, find x.

Answers

Answer:

37

Step-by-step explanation:

Linear pairs are supplementary (adds up to 180)

m∠1 + m∠2 = 180

3x + 4 + 2x - 9 = 180

5x - 5 = 180

5x = 185

x = 37

Hope this helps :)

Have a nice day!

Other Questions
Basic properties are characteristic of all alkaline earth metal oxides except one. The formula of this exception is? BeO, MgO, SO2, B2O3, CaO 1 mile south 1 mile west 1 mile north where are you. Powwows were, and still are a part of Native American life. TRUEFALSE The use of displays, coupons, product samples, and other brand communications to influence shopping behavior in a store is termed Blank______. Rosa Parks was an African American woman and seamstress who lived in Alabama. One evening during the 1950s, while returning home on a bus, she defied segregation laws and refused to give up her seat for a White man. This incident, and the events that followed it, essentially birthed the: 4) Reflection: why is it important to understand radius and circumference to solve problems in the real world? Find the perimeter of the rectanglebelow in inches. Find the measure of angle CED in the figure below. Enter only the number. Mr. Walter recorded the heights of the students in his class. The dot plot below shows the recorded data.Which of the following is the best measure of center for the data? A. interquartile range B. mean C. range D. median Whats the answer????#13 Summarize the features of several stand-alone operating systems __________ is the most common cause of dementia, usually affecting patients over the age of 65. a. parkinsons disease b. huntingtons disease c. alzheimers disease d. aids Find the 66th term of the arithmetic sequence 3, 13, 23, ... Vikram drinks 6/10 of a liter of water after gym class and 33/100 hours of a liter of juice withhis lunch. Vikram says he drank a total of 39/100 of a liter.Use the drop-down menus to explain why Vikram is not correct. The NCAA arose in response to: Group of answer choices The desire to act like a monopsonist. The desire to act like a monopolist. Point-shaving scandals in college basketball. Increasing violence in college football. A line passes through point (-8,-2) and has a slope of -3/2. Write an equation in Ax+By=C form for this line. Use integers for A, B, and C. Read the sentences and then answer the question that follows:There are many things that people must do to become physically fit. Yoga offers stretches that can help build strength and flexibility.Which transition should go between these sentences?O Therefore, However,One example,Finally, Which equation is correct according to ohms law? r = vi v = i over r. r = i over v. v = ir The rule for the dilation of quadrilateral QRST to the image Q'R'S'T' is DO,0.5(x, y) (0.5x, 0.5y).What are the coordinates of Q', if Q(0, 2)?(, ) Select the star life cycle that is accurate.A. Nebula, star of two stellar mass, supernova, black holeB. Star of three stellar masses, red supergiant, supernova, neutronstarC. Supernova, star of three stellar masses, black hole, nebulaD. Nebula, white dwarf, red giant, black hole