simplify this problem$ \frac{9x}{4x - 4} + \frac{ {x}^{2} + 6x }{ {x}^{2} + 5x - 6} $

Answers

Answer 1

$\frac{9x}{4x-4}+\frac{x^2-6x}{x^2+5x-6}$

1. Factor the denominators as follow:

$\begin{gathered} 4x-4=4(x-1) \\ \\ \\ x^2+5x-6 \\ =x^2+6x-x-6 \\ =x(x+6)-(x+6) \\ =(x-1)(x+6) \\ \\ \\ \\ \\ \frac{9x}{4(x-1)}+\frac{x^2-6x}{(x-1)(x+6)} \end{gathered}$

2. Write the expresion with the less common denominator:

Multiply the first fraction by (x+6) (both parts, numerator and denominator):

$\frac{9x}{4(x-1)}\cdot\frac{x+6}{x+6}=\frac{9x(x+6)}{4(x-1)(x+6)}$

Multiply the second fraction by 4 (both parts, numerator and denominator):

$\frac{x^2-6x}{(x-1)(x+6)}\cdot\frac{4}{4}=\frac{4(x^2-6x)}{4(x-1)(x+6)}$

Rewrite the expression with the less common denominator:

$\begin{gathered} \frac{9x(x+6)}{4(x-1)(x+6)}+\frac{4(x^2-6x)}{4(x-1)(x+6)} \\ \\ =\frac{9x(x+6)+4(x^2-6x)}{4(x-1)(x+6)} \end{gathered}$

3. Remove parentheses and simplify:

$\begin{gathered} \frac{9x^2^{}+54x+4x^2-24x}{(4x-4)(x+6)} \\ \\ =\frac{13x^2+30x}{4x^2+24x-4x-24} \\ \\ =\frac{13x^2+30x}{4x^2+20x-24} \end{gathered}$

Then, the given expression simplified is:$\frac{9x}{4x-4}+\frac{x^2-6x}{x^2+5x-6}=\frac{13x^2+30x}{4x^2+20x-24}$

$Simplify This Problem[tex] \frac{9x}{4x - 4} + \frac{ {x}^{2} + 6x }{ {x}^{2} + 5x - 6} [/tex]$

Related Questions

what is the scale factor of 10 inches = 5 meters?

Answers

Answer:

2:1

Step-by-step explanation:

I'm not completely sure if this is correct, but I'm like 90% sure it is.

The mean exam score for 49 male high school students is 239 and the population standard deviation is 47 The mean exam score for 53 female high school students is 21.1 and the population standard deviation is 4.3. At α=001, can you reject the claim that male and female high school students ha equal exam scores? Complete parts (a) through (e). Click here to view page 1 of the standard normal distribution table. Click here to view. page 2 of the standard normal distribution table. A. Male high school students have lower exam scores than female students B. Male and temale high school students have different exam scores. C. Male and female high school students have equal exam scores D. Male high school students have greater exam scores than female students

Answers

Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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Need Help ASAP

Morgan arrived at her destination at 5:45 pm. If she left at 4:48 pm on the same day, how long did the journey take?

I'm not too good at these at all :(

Answers

It would be 57 minutes. Also love the Kenma profile picture!!

EXPLANATION: so 4:48 is almost an hr to 5:45. Just subtract 3minutes from an hr and you have your answer!

Answer and explanation please

Answers

3u^5

because the cube root of 27 is 3 and 15/3 is 5

f limit as x approaches zero of f of x equals three and limit as x approaches zero of g of x equals one, then find limit as x approaches zero of the quantity f of x plus g of x squared. (True or False)

Answers

The limit as x approaches zero of the quantity f(x) + $g(x)^2$ can be determined based on the given information about the limits of f(x) and g(x). The statement is true

Since the limit as x approaches zero of f(x) is equal to three and the limit as x approaches zero of g(x) is equal to one, we can apply the properties of limits to find the limit of the given expression.

Using the limit properties, we know that the limit of a sum is equal to the sum of the limits. Therefore, the limit as x approaches zero of f(x) + g(x)^2 is equal to the sum of the limits of f(x) and g(x)^2 individually.

The limit as x approaches zero of f(x) is three, and the limit as x approaches zero of g(x)^2 is equal to one squared, which is also one. Thus, the sum of three and one is four.

Therefore, the limit as x approaches zero of the quantity f(x) + g(x)^2 is four. This confirms that the given statement is true.

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please answer. will give brainliest

Answers

Answer:

Step-by-step explanation:

thats the answer pls give brainliest.

Answer: OPTION B

Step-by-step explanation:

Angle 25° is in the interior of two lines so we are actually finding the alternative interior angles.

Alternate angles are angles that on opposite sides that locate on opposite relative sides of the other lines.

The only three labeled angle that are interior. Angle 25°, Angle 2, and Angle 3.

Angle 25° and Angle 3 are on opposite sides, but they are on the same relative side of the other lines, which does not fit the alternate angle definition.

Angle 25° and Angle 2 are on opposite sides and on the opposite relative side of the other lines, so Angle 2 is the alternate to Angle 25°

Hope this helps!! :)

Please let me know if you have any question

True/False based on the t-test assuming equal variances on the t-testequal worksheet, it is reasonable to assume that the variances are equal?

Answers

Based on the t-test assuming equal variances a. Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal."

It is vital to establish whether or not the variances of the two groups being compared are indeed identical before performing a t-test under the assumption of equal variances. This is significant since the t-calculation statistic depends on the assumption that variances are equal.

One can look at the ratio of the variances between the two groups to evaluate the assumption of equal variances. Typically, it is acceptable to infer that the variances are not equal if the ratio of the variances is more than two or lower than half. One can presume that the variances are equal in the absence of such proof. Since the variances are not equal, it is not logical to infer that they are.

Complete and correct Question:

Based on the t-test assuming equal variances on the T-Test Equal worksheet, is it reasonable to assume that the variances are equal?
a. Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal.
b. Whether the variances are equal or not is not relevant for this situation.
c. Examining the ratio of the variances, it is reasonable to conclude that the variances are equal.
d. It is impossible to determine if the variances are equal given the data we have.

Answers

x=2x+48
x-2x=48
-x=48
x= -48

Please brainliest

Sprinkler heads come in all different sizes depending on the angle of rotation desired. If a sprinkler head rotates 90 ° and has enough pressure to keep a constant 25-foot spray, what is the area of the sector of the lawn that gets watered? Round to the nearest square foot.

Answers

Answer:

491 ft²

Step-by-step explanation:

We know the area of a sector, A = Ф/360° × πr² where Ф = angle subtended by sector = angle of rotation of sprinkler = 90° and r = radius of sector = length of spray = 25 feet.

Substituting the values of the variables into the equation, we have

A = Ф/360° × πr²

A = 90°/360° × π(25 ft)²

A = 1/4 × 625π ft²

A = 1/4 × 1963.5 ft²

A = 490.9 ft²

A ≅ 491 ft² to the nearest square foot

Find the value of x.

Answers

Answer:

x = 4

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

(19x + 3)° is an exterior angle of the triangle, then

11x - 2 + 9x + 1 = 19x + 3

20x - 1 = 19x + 3 ( subtract 19x from both sides )

x - 1 = 3 ( add 1 to both sides )

x = 4

The time required to drive a fixed distance varies inversely as the speed. It takes 2 hr at a speed of 200 km/h to drive a fixed distance. How long will it take to drive the same distance at a speed of 80 km/h?

Answers

Answer:

5 hours

Step-by-step explanation:

From the question, we are told that:

Time required to drive a fixed distance varies inversely as the Speed

T ∝ 1/S

k = proportionality constant hence,

T =k × 1/S

T = k/S

Step 1

Find k

It takes 2 hr at a speed of 200 km/h to drive a fixed distance

T = 2 hours, S = 200km/h

T = k/S

2 = k / 200

k = 2 × 200

k = 400

Step 2

How long will it take to drive the same distance at a speed of 80 km/h?

S = 80km/h

T = k/S

k = 400

T = 400/80

T = 5

Therefore, it takes 5 hours to drive the same distance at a speed of 80km/hr

n a simple linear regression model, y = ß 0 ß 1 x ε the parameter ß 1 represents the _____. a. intercept b. error term c. slope of the true regression line d. mean value of x

Answers

The simple linear regression line is found to be y = a + bx.

In a simple linear regression model, y = ß0 + ß1x + ε, the parameter ß1 represents the slope of the true regression line.

ß1 is used in simple linear regression to represent the change in y for each unit increase in x.

When x changes by 1 unit, ß1 represents how much y will change.

The slope is positive when y and x are both increasing and negative when y decreases as x increases.

This is why the slope is negative.

When the slope is zero, there is no correlation between y and x.

This would be demonstrated by a scatter plot in which the points are dispersed randomly around the horizontal axis without following any discernible trend.

When the slope is positive, the data points are rising from left to right. This may be seen as a line sloping upward. If the slope is negative, the points are descending from left to right and form a line sloping downward.

Therefore, we may correctly infer that ß1 represents the slope of the true regression line.

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By using compatible numbers, the estimate is
Use a calculator to multiply 92 × 12. What do you get?
Circle whether the estimates were all less than or greater than
the actual product.

Answers

Answer:

92*12=1104

Step-by-step explanation:

help pleaseeeeeeeeee

Answers

Answer:

Step-by-step explanation:

Find the area of the shaded portion if we know the outer circle has a diameter of 4 m and the inner circle has a diameter of 1. 5 m. A Circle

Answers

The area of the shaded portion is given by the difference between the area of the outer circle and the area of the inner circle.

First, let's find the areas of the circles:

Outer Circle: Area = πr^2 = π (2)^2 = 4π square meters

Inner Circle: Area = πr^2 = π (0.75)^2 = 0.5625π square meters

Area of shaded portion = Area of outer circle - Area of inner circle = 4π - 0.5625π = 3.4375π square meters

So the area of the shaded portion is approximately 10.8 square meters.

two red balls and two green balls are placed in a bag. if you take two of the balls out of the bag without replacement, what is the probability that both balls are red? (enter your probability as a fraction.)

Answers

Answer:

1/6

Step-by-step explanation:

2 red + 2 green = 4 balls

P(1st red) = 2/4

now there's one less red in there and one less ball in total

P(2nd red) = 1/3

P(both red) = 2/4 X 1/3 = 2/12 = 1/6

Practice another write the function in terms of unit step functions. find the laplace transform of the given function. f(t) = t, 0 ≤ t < 4 0, t ≥ 4

Answers

Using the Laplace transform to solve the given integral equation f(t) = t, 0 ≤ t < 4 0, t ≥ 4 is $\frac{4(1-2e^-5s)/}{s}$

explanation is given in the image below:

Laplace remodel is an crucial remodel approach that's particularly beneficial in fixing linear regular equations. It unearths very wide programs in var- areas of physics, electrical engineering, manipulate, optics, mathematics and sign processing.

The Laplace transform technique, the function inside the time domain is transformed to a Laplace feature within the frequency area. This Laplace function could be inside the shape of an algebraic equation and it may be solved without difficulty.

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Practice another write the function in terms of unit step functions. find the laplace transform of the

There are 36 coins consist of nickels, dimes, and quarters. There are three fewer quarters than nickels and six more dimes than quarters. How many of each kind of coin is there?

Answers

Answer:

Number of Nickels is 12

Number of Dimes is 9

Number of Quarters is 15

Step-by-step explanation:

Given that there are a total of 36 coins, which consists of nickels, dimes, and quarters.

That is, when we sum the numbers of nickels, dimes, and quarters, we have 36.

Let number of nickels be N

Let number of dimes be D

Let number of quarters be Q

Then

N + D + Q = 36 .................................(1)

- There are three fewer quarters than nickels.

This implies that

N = Q - 3 ..............................................(2)

Q = N + 3 .............................................(3)

- There are six more dimes than quarters.

This implies that

Q = D + 6 .............................................(4)

Comparing (3) with (4), we see that

N + 3 = D + 6

N - D = 6 - 3

N - D = 3 ................................................(5)

Using (3) in (1)

N + D + (N + 3) = 36

2N + D = 36 - 3

2N + D = 33 ..........................................(6)

Solving (5) and (6) simultaneously

From (5): D = N - 3

From (6): D = 33 - 2N

=> N - 3 = 33 - 2N

N + 2N = 33 + 3

3N = 36

N = 36/3 = 12..........................................(7)

Using (7) in (6)

2(12) + D = 33

24 + D = 33

D = 33 - 24

D = 9 ........................................................(8)

Using (7) and (8) in (1)

12 + 9 + Q = 36

21 + Q = 36

Q = 36 - 21 = 15.......................................(9)

Therefore,

Number of Nickels, N = 12

Number of Dimes, D = 9

Number of Quarters, Q = 15

(6m^2-3m+15)(4m-7) simplify

Answers

2 4$m^{3}$ − 5 4$m^{2}$ + 8 1 − 1 0 5

Answer:

24m^3−54m^2+81m−105

Step-by-step explanation:

The sum of one-fifth of a number and three is equal to half of the number. What is the number?

Answers

Answer:

Step-by-step explanation:

(1/5)(x)+3=(1/2)(x)

3=(1/2)x-(1/5)x

3=(5/10)x-(2/10)x

3=(3/10)x

3=0.3x

30=3x

x=30/3

x=10

what is the y intercept of the points (2,72) and (5,162)

Answers

Answer:

Step-by-step explanation:

Type Into Calculator:

SAT-EDIT-TYPE IN X VALUES AND Y VALUES (FROM ORDERED PAIR)-STAT-CALC-4-ENTER

what is the y intercept of the points (2,72) and (5,162)

A runner covers a distance of 1200m with an average speed of 4m/s. How long does it take to run this distance? Then calculate the time in min.

Be the first answer for Brainliest, please I need help.

Answers

Answer:

5mins

Step-by-step explanation:

well i did 1200 divided y 4 then divided that answer by 60

use headlights between sunset and sunrise and at any time when visibility is less than 500 feet to 1000 feet.

Answers

Use headlights between sunset and sunrise and at any time when visibility is less than 500 feet to 1000 feet: TRUE

What are headlights?A headlamp is a lamp connected to the front of a vehicle to illuminate the road ahead. Headlamps are also commonly referred to as headlights, but in the most precise usage, the flashlight is the term for the device itself, and the headlight is the term for the beam of light produced and sold by the device. If you are driving with your high-beam lights on, you must dim them at least 500 feet from any oncoming vehicle to avoid blinding the oncoming driver. If you are within 200-300 feet of the vehicle you are following, you must use low-beam lights. When visibility is less than 500 feet and there is insufficient light/adverse weather, headlights must be turned on for 1/2 hour after sunset to 1/2 hour before sunrise.

Therefore, the statement "use headlights between sunset and sunrise and at any time when visibility is less than 500 feet to 1000 feet" is TRUE.

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The correct question is given below:
Use headlights between sunset and sunrise and at any time when visibility is less than 500 feet to 1000 feet. TRUE or FALSE

Find the area of the triangle described below. Round to the nearest hundredth.b = 20, a = 29, c = 21

Answers

Solution

We want to find the area of the triangle given te sides

b = 20

a = 29

c = 21

Note: Hero formula for calculating the Area of a Triangle

We will first find S

$\begin{gathered} S=\frac{a+b+c}{2} \\ S=\frac{29+20+21}{2} \\ S=35 \end{gathered}$

To find the Area

$\begin{gathered} Area=\sqrt[]{S(S-a)(S-b)(S-c)} \\ Area=\sqrt[]{35(35-29)(35-20)(35-21)} \\ Area=\sqrt[]{35\times6\times15\times14} \\ Area=\sqrt[]{44100} \\ Area=210 \end{gathered}$

Therefore, the area is

$Area=210$

¿¡ Cuanto es "(8 x 7 + 5 x (-8)) : (-4)" ??

Answers

Answer:

-4

Step-by-step explanation:

So like ur last problem do it in order left to right.

[8x7]+5x(-8)/(-4)

56+[5x(-8)/-4

56+(-40)/-4

16/-4=(-4)

Sorry if i did in wrong order.

Answer: 4(14x-11) hop that can help you

Please help me with this question,it's really simple.

What is the probability of landing on heads on the coin, and a number less than 7 on the spinner?

Answer choices:
A.)3/8
B.)1/4
C.)1/16
D.)2/3

The picture will help you out

Answers

Answer:The correct answer is A) 3/8Step-by-step explanation:

The probability of landing on heads on the coin is 1/2. The probability of landing on a number less than 7 on the spinner is 6/8 or 3/4. Since these two events are independent, the probability of both events happening is the product of their individual probabilities:

$(1/2) \times (3/4) = 3/8$

Note:- I'm sorry to bother you but can you please mark me BRAINLEIST if this ans is helpfull

Please help me I really need this done

Answers

Answer:

the one on the top right

Step-by-step explanation:

it multiplies by 6 and shows 3/4 of the all the columns shaded in

I was wondering if someone could help with this question

Answers

Answer:

A rational number

Step-by-step explanation:

If "a" and "b" are integers, then a/b must be rational since it can be written as a fraction.

Automobiles arrive at a vehicle equipment inspection station according to a Poisson process with rate α = 10 per hour. Suppose that with probability .5 an arriving vehicle will have no equipment violations. a. What is the probability that exactly ten arrive during the hour and all ten have no violations?
b. For any fixed y ≥ 10, what is the probability that y arrive during the hour, of which ten have no violations?
c. What is the probability that ten "no-violation" cars arrive during the next hour? [Hint: Sum the probabilities in part (b) from y =10 to [infinity].]

Answers

a. The probability that exactly ten arrive during the hour and all ten have no violations is given by the Poisson distribution, P(X=10) = (e-α*(α10)/(10!) = 0.024

b. The probability that y arrive during the hour, of which ten have no violations is given by the Binomial distribution, P(Y=y) = (y!/(10!*(y-10)!))*(0.510)*(0.5y-10)

c. The probability that ten "no-violation" cars arrive during the next hour is given by summing the probabilities in part (b) from y=10 to [infinity]. This is given by P(Y≥10) = Σy=10 to ∞P(Y=y) = 1 - Σy=0 to 9P(Y=y).

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Create an explicit equation for the function
X f(x)
0 8
1 12
2 18
3 27

Answers

The explicit equation for the function is: f(x) = 8(1.5)^(x - 1)

Creating an explicit equation for the function

Given that we have the table of values

x f(x)

0 8

1 12

2 18

3 27

We can see that the function is a geometric function

So, the common ratio is

r = 12/8

r = 1.5

The explicit equation for the function is then calculated as

f(x) = ar^(x - 1)

So, we have

f(x) = 8(1.5)^(x - 1)

Hence, the explicit function is f(x) = 8(1.5)^(x - 1)

simplify this problem\( \frac{9x}{4x - 4} + \frac{ {x}^{2} + 6x }{ {x}^{2} + 5x - 6} \)

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