!!!!!!!!!!!!!!!!!!!!​

!!!!!!!!!!!!!!!!!!!!

Answers

Answer 1

Option 3

The solution for given expression is [tex]\frac{(x - 4)(x - 4)}{(x + 3)(x + 1)}[/tex]

Solution:

Given that we have to divide,

[tex]\frac{x^2 -16}{x^2 + 5x + 6} \div \frac{x^2 + 5x + 4}{x^2 -2x - 8}[/tex]   ---- (A)

Let us first factorize each term and then solve the sum

Using [tex]a^2 - b^2 = (a + b)(a - b)[/tex]

[tex]x^2 -16 = x^2 - 4^2 = (x + 4)(x -4)[/tex]  ----- (1)

[tex]x^2 + 5x + 6 = (x + 2)(x + 3)[/tex]   ----- (2)

[tex]x^2 + 5x + 4 = (x+1)(x + 4)[/tex]   ---- (3)

[tex]x^2 -2x - 8 = (x-4)(x + 2)[/tex]   ---- (4)

Now substituting (1), (2), (3), (4) in (A) we get,

[tex]\frac{(x + 4)(x -4)}{(x +2)(x +3)} \div \frac{(x+1)(x+4)}{(x-4)(x +2)}[/tex]

To do division with fractions, we turn the second fraction upside down and change the division symbol to a multiplication symbol at the same time. Then we treat this as a multiplication problem, by multiplying the numerators and the denominators separately.

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

On cancelling terms we get,

[tex]= \frac{(x -4)(x-4)}{(x + 3)(x + 1)}[/tex]

Thus option 3 is correct


Related Questions

Karen bought a coat for 20% more than the price she wanted to pay. If she paid $150, how much was she looking to pay?

The first one to get both correct will be brainiest!!!!!!!

Answers

120% = $150

divide both sides by 6

20% = $25

We want the regular price, so 100%.

multiply both sides by 5

100% = $125

Answer:125

Step-by-step explanation:

150/1.20

=125

In 12 weeks Jim earns $4500 Doing yardwork he earns the same amount each week let M stand for the amount and each week how much does Jim make in one week

Answers

Answer:

375

Step-by-step explanation:

Jim earns a total of $4500 over 12 weeks. To find out how much he makes weekly, divide the total earnings by the number of weeks, which is $4500 divided by 12, resulting in Jim earning $375 per week.

To calculate how much Jim makes in one week, we can divide his total earnings over the 12-week period by the number of weeks. Jim earns a total of $4500 over 12 weeks, so we can use the following equation where M stands for the amount Jim earns each week:

M = Total Earnings÷ Number of Weeks

M = $4500÷ 12

By performing the division, we find that Jim earns $375 per week. This is done by dividing 4500 by 12:

M = $375

Therefore, Jim makes $375 each week doing yardwork.

❤❤Solve for the unknown by using the additive inverse. Type the FULL answer in the box, without using any spaces (ex., X=5).

–X + 4 = –2X – 6

Answer:

Answers

Answer: x=−10

Explanation:
1.regroup terms:4−x=−2x−6
2.add 2x to both sides: 4−x+2x=−6
3. Simplify 4−x+2x to 4+x.:: 4+x=−6
4. Subtract 4 from both sides: x=−6−4
5. Simplify —6−4 to −10: x=−10

please help me first thinks​

Answers

Answer:

3 minutes

5 minutes.

Step-by-step explanation:

It is given that, Amelia can wash 8 plates in 24 minutes.

So, if this rate remains constant then 1 plate will be washed in [tex] \frac{24}{8} = 3[/tex] minutes.

Again, it is given that, Amelia bakes 12 cookies in 60 minutes.

So, if this rate also remains constant then she will bake 1 cookie in [tex] \frac{60}{12} = 5[/tex] minutes. ( Answer )

over what interval will the immediate value theorem apply

Answers

Answer:

Any [a,b] that does NOT include the x-value 3 in it.

Either an [a,b] entirely to the left of 3, or

an  [a,b] entirely to the right of 3

Step-by-step explanation:

The intermediate value theorem requires for the function for which the intermediate value is calculated, to be continuous in a closed interval [a,b]. Therefore, for the graph of the function shown in your problem, the intermediate value theorem will apply as long as the interval [a,b] does NOT contain "3", which is the x-value where the function shows a discontinuity.

Then any [a,b] entirely to the left of 3 (that is any [a,b] where b < 3; or on the other hand any [a,b] completely to the right of 3 (that is any [a,b} where a > 3, will be fine for the intermediate value theorem to apply.

35 is 51% of what number?​

Answers

Answer:

68.627

Step-by-step explanation:

51%=0.51

35/0.51=68.627

Answer:

68.627 is the answer!

Step-by-step explanation: I just took a test on it like 5 minutes ago!PLEASE MARK BRAINLIEST!!!! PLEASE!!! HAVE A NICE DAY!!!!

What is the product?

(negative 3 s + 2 t)(4 s minus t)

negative 12 s squared minus 2 t squared
negative 12 s squared + 2 t squared
negative 12 s squared + 8 s t minus 2 t squared
negative 12 s squared + 11 s t minus 2 t squared

Answers

Answer:

(d) negative 12 s squared + 11 s t minus 2 t squared    is the PRODUCT.

Step-by-step explanation:

Here, the given expression is:

(negative 3 s + 2 t)(4 s minus t)   =  (- 3s + 2t) (4s - t)

Now, by DISTRIBUTIVE PROPERTY:

   A(B-C) = AB - AC

Simplifying the given expression ,we get:

[tex](- 3s + 2t) (4s - t)  = -3s(4s-t) + 2t(4s -t)\\= -3s(4s) -3s(-t) + 2t(4s) + 2t(-t)  = -12s^2 + 3st + 8 st - 2t^2\\= -12s^2 + 11st - 2t^2\\\implies (- 3s + 2t) (4s - t)  =   -12s^2 + 11st - 2t^2[/tex]

Now, the resultant expression can also be written as

[tex]-12s^2 + 11st - 2t^2[/tex]  =  negative 12 s squared + 11 s t minus 2 t squared.

Hence, the option (4) is the correct option.

Answer:

option 4 is the answer

Step-by-step explanation:

Complete this statement:
45x^3a + 27xa^2= 9xa
Enter the correct answer.
0000
DO
Clear all
DOO

Answers

Answer:

[tex]45x^3a+27xa^2= 9xa(5x^2+3a)[/tex]

Step-by-step explanation:

Given:

[tex]45x^3a+27xa^2= 9xa[/tex]

We need to complete this Statement.

By Solving the above equation we get;

We will take some common factor out so we will get;

[tex]45x^3a+27xa^2= 9xa(5x^2+3a)[/tex]

Hence the Complete statement is [tex]45x^3a+27xa^2= 9xa(5x^2+3a)[/tex]

Write in vertex form y=x^2+16x-71

Answers

Good evening ,

Answer:

x^2+16x-71 = (x+8)²-135

Step-by-step explanation:

x^2+16x-71 = (x+8)²-8²-71

                 = (x+8)²-(64+71)

                 = (x+8)²-135.

:)

Find the midpoint between A and C.


A. (1, 1)


B. (5, -7)


C. (-5, 7)


D. (0.5, 0.5)

Answers

Answer:

D. [tex]\displaystyle (0,5, 0,5)[/tex]

Step-by-step explanation:

C(3, −3) and A(−2, 4)

Just by looking at the graph, we can CLEARLY see that answer choice D is EXACTLY halfway in between the two given endpoints.

I am joyous to assist you anytime.

Find the y intersept of

y=logbase (b)(a-k) based on the constants b and k ?

Answers

Answer:

[tex](0, log_{b}(-k)), k < 0[/tex]

Step-by-step explanation:

[tex]y = \log_{b}(a - k)[/tex]

To find the y-intercept, set a = 0 and solve for y.

[tex]y = \log_{b}(0 - k)\\y = \log_{b}(-k)[/tex]

This equation is undefined for k ≥ 0.

There is a y-intercept only if k < 0. Only then can the argument of the log function be positive.

The y-intercept is at

[tex]\mathbf{(0, log_{b}(-k)), k < 0}[/tex]

For example, if b = 2 and k = -3, log₂(3) = 1.585

The intercept is at (0, 1.585).

Gabrielle has 3 gallons of paint. She uses 9 quarts to paint her bedroom. How much paint does she have left?

Answers

Answer:

3 quarts

Step-by-step explanation:

There are 4 quarts in a gallon

3×4=12

12-9= 3

What is the value of the expression if m=3 and n=2?

2(m3) + (6-n)n

Be sure to explain all of the steps you used in solving this problem.

Answers

Step-by-step explanation:

So fill it in

2(3 times 3)+(6-2)2

so

2(9)+(4)2

then

18+8=26

Answer: 26

hope that is right

Answer:

First plug in for m and n

2(3)(3) +(6-2)(2)

Next solve

18 + 8

Answer= 10

Step-by-step explanation:

solve the inequality and enter your solution as an inequality comparing the variable to the solution

-19>x-26​

Answers

Answer:

x < 7

Step-by-step explanation:

We are given an equation of inequality and we have to solve the equation as an inequality.

The given equation is - 19 > x - 26

⇒ - 19 + 26 > x

⇒ 7 > x

x < 7 {Since, if a > b then we can write b < a, as they are equivalent}

Hence,the solution of the equation of the inequality is x < 7. (Answer)

Five tenths in standard and expanded form

Answers

Answer:

Standard form: 5 x 10^-1

Expanded form: 0.5

Step-by-step explanation:

hope this helps

Simultaneous equations !
Who can help

Answers

The cost of glass is:  £4

The cost of mug =  £2

Step-by-step explanation:

Let g be the number of glasses and

m be the number of mugs

[tex]3g+3m = 18\ \ \ \ \ Eqn\ 1\\6g+4m=32\ \ \ \ \ Eqn\ 2[/tex]

Multiplying equation 1 by 2

[tex]6g+6m=36\ \ \ \ Eqn\ 3[/tex]

Subtracting Eqn 2 from Eqn 3

[tex]6g+6m - (6g+4m) = 36-32\\6g+6m-6g-4m=4\\2m=4[/tex]

Dividing both sides by 2

[tex]\frac{2m}{2} = \frac{4}{2}\\m = 2[/tex]

Putting m=2 in eqn 1

[tex]3g+3(2) = 18\\3g+6 = 18\\3g = 18-6\\3g = 12[/tex]

Dividing both sides by 3

[tex]\frac{3g}{3} = \frac{12}{3}\\g = 4[/tex]

Hence,

The cost of glass is:  £4

The cost of mug =  £2

Keywords: Linear Equation, simultaneous equations

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A textbook costs $65.49 before tax. The tax on the textbook is 6.5%.

What is the total cost of the textbook?

Round your answer to the nearest cent.

Enter your answer in the box.

Answers

Answer:

$69.75

Step-by-step explanation:

Given: Cost of textbook before tax=$65.49

The tax on the textbook = 6.5%

The tax amount = 6.5% of $65.49

=\frac{65}{1000}\times65.49=4.25685\approx4.26

⇒The tax amount = $4.26

The total cost of the textbook=Cost of textbook before tax+tax amount

=$65.49+$4.26

=$69.75

The total cost of the textbook is $69.75.

Credit goes to @JeanaShupp

Answer:

Answer is69.75

Step-by-step explanation:

Three fifths of the members of a hiking club went
on the last hiking trip. It 39 people went on the
trip, how many are in the club?

Answers

There are 65 people in the club.

Step-by-step explanation:

Given,

Fraction of people went on hiking = [tex]\frac{3}{5}[/tex]

No. of people went on hiking = 39

Let,

x be the number of people at club.

According to given statement;

[tex]\frac{3}{5}\ of\ x = 39\\\\\frac{3}{5}x=39\\0.6x=39\\[/tex]

Dividing both sides by 0.6

[tex]\frac{0.6x}{0.6}=\frac{39}{0.6}\\x=65[/tex]

There are 65 people in the club.

Keywords: fractions, division

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Help me please with question 4 b​

Answers

Answer:

see explanation

Step-by-step explanation:

The second term of sequence P is 2a + b

The third term of sequence Q is 3b + a

Equating gives

2a + b = 3b + a ( subtract a from both sides )

a + b = 3b ( subtract b from both sides )

a = 2b ← as required

Good evening ,

Step-by-step explanation:

4 (b)

The 2nd term of sequence P is 2a+b

The 3rd term of sequence Q is 3b+a

2a+b=3b+a ⇌ (2a-a) = (3b-b) ⇌ a=2b.

:)

The graphs below have the same shape. What is the equation of the blue graph?

Answers

Answer:

Option C. [tex]g(x)=(x+5)^{2}[/tex]

Step-by-step explanation:

we know that

The equation of the parent function f(x) (red graph) is

[tex]f(x)=x^{2}[/tex]

This is a vertical parabola open upward

The vertex is the point (0,0) (the origin)

The function g(x) (blue graph) is a vertical parabola open upward

The vertex is the point (-5,0)

The transformation of f(x) to g(x) has the following rule

f(x) -----> g(x)

(0,0) ----> (-5,0)

(x,y) ----> (x-5,y)

That means----> The transformation is a translation of 5 units at left

therefore

The equation of g(x) is

[tex]g(x)=(x+5)^{2}[/tex]

There's 5 trees fill with apples. Alex wants 2 off each tree. How much apples do she have? ​

Answers

Answer:

10

Step-by-step explanation:

5 trees * 2 from each = 10 apples

Answer:

10

Step-by-step explanation:

5*2=10

The equation S = -16t2 + 34t + 184 models the height of a ball that is thrown upward from the roof of a 184 foot building and falls to the street below. In this equation S is the height in feet of the ball above the ground and t is the time in seconds the ball has traveled. According to this model, how many seconds did it take the ball to reach a height of 91 feet? (round to 1 decimal place)

Answers

Answer:

t=1.6

Step-by-step explanation:

If the equation [tex]S=-16t^2+34t+184[/tex] models the height of a ball above the ground, where t is time the ball travelled.If the height of the ball above the ground is S=91 instead of 184, then the time the ball should take to get to the ground comes from the expression above: [tex]S=-16t^2+34t+91[/tex] (because now we want to know how much time does it takes to reach the ground if it is thrown from 91 foot, not 184). Then, to know when the ball reaches the floor, we must equal the equation to zero [tex]-16t^2+34t+91=0[/tex] (because when the equation is zero, the height of the ball is zero, which means it is in the ground).To obtain the value of t in the expression [tex]-16t^2+34t+91=0[/tex] , we can apply the well known formula [tex]t=\frac{-b(+-)\sqrt{b^2-4ac} }{2a}[/tex], where a is the coefficient that accompanies the quadratic term (in this case a=16), b is the coefficient that accompanies the linear term (b=34 in this case), and c is the constant coefficient (c=91).Because time is always possitive, we only retain the possitive value for t that solves the equation:[tex]\frac{-34(+-)\sqrt{34^2-4\times(-16)\times93} }{2\times16}[/tex]. [tex]t=1.55\simeq1.6[/tex]

Benjamin drove a distance of 301.5 miles in
4.5 h. If Benjamin drove at a constant rate, how
many miles per h did he drive?​

Answers

Answer: 67 miles per hour

Step-by-step explanation: [tex]v = \frac{s}{t}[/tex] where v is velocity, s is space and t is time;

[tex]\frac{301.5 miles}{4.5 h}[/tex] = 67

Which three comparisons are true?

1/2 = 2/4

6/8 = 1/4

3/6 = 2/4

2/4 = 4/6

4/8 = 2/4

Answers

Answer:

The answer is 4/8=2/4 because 4/8 simplifying is 2/4 or 1/2

The true fraction comparisons are 1/2 = 2/4 and 4/8 = 2/4. The other comparisons are false. Simplifying fractions helps determine their equality.

Comparing Fractions:

Let's determine which of the given fraction comparisons are true:

1/2 = 2/4: To check this, we can simplify 2/4. Dividing both the numerator and the denominator by 2, we get 1/2. Thus, 1/2 equals 2/4. This is a true statement.6/8 = 1/4: We simplify 6/8 by dividing both the numerator and the denominator by 2, which gives us 3/4. This does not equal 1/4. This is a false statement.3/6 = 2/4: Simplifying 3/6 by dividing both the numerator and the denominator by 3, we get 1/2. Simplifying 2/4 gives us 1/2 as well. Therefore, 3/6 equals 2/4. This is a true statement.2/4 = 4/6: Simplifying 2/4 to 1/2 and simplifying 4/6 to 2/3 shows that 2/4 does not equal 4/6. This is a false statement.4/8 = 2/4: Simplifying 4/8 by dividing both the numerator and the denominator by 4, we get 1/2. Simplifying 2/4 also gives us 1/2. Thus, 4/8 equals 2/4. This is a true statement.

The three true comparisons are: 1/2 = 2/4, 3/6 = 2/4, 4/8 = 2/4, and none from the rest.

using the z table, find the critical value for a=0.024 in a left tailed test

Answers

Answer:

Critical value is -1.98.

Step-by-step explanation:

Given:

The value of alpha is, [tex]\alpha=0.024[/tex]

Now, in order to find the critical value, we need to subtract alpha from 1 and then look at the z-score table to find the respective 'z' value for the above result.

The probability of critical value is given as:

[tex]P(critical)=1-\alpha=1-0.024=0.976[/tex]

So, from the z-score table, the value of z-score for probability 0.976 is 1.98.

Now, in a left tailed test, we multiply the z value by negative 1 to arrive at the final answer. We do so because the area to the left of mean in a normal distribution curve is negative.

So, the z-score for critical value 0.024 in a left tailed test is -1.98.

The critical value for α = 0.024 in a left-tailed test is -1.98.

To find this value, we locate α = 0.024 in the z-table. The z-table is a table that shows the probability of obtaining a z-score less than or equal to a certain value.

The z-score is a measure of how many standard deviations a particular data point is away from the mean of the population.

Here is the critical value for α = 0.024 in a left-tailed test: -1.98

In this case, we are looking for the z-score that corresponds to a probability of 0.024. This z-score is -1.98. Therefore, if our test statistic is less than or equal to -1.98, we will reject the null hypothesis.

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A drawer contains 60 coins consisting of dimes and quarters. If the total value of the coins is $12.30, how many dimes and how many quarters are in the drawer?

Answers

Answer:

my mistake sorry

Step-by-step explanation:

At a music festival, T-shirts are sold for $15 and sweatshirts are sold for $20. The festival organizers pay x dollars for each T-shirt and y dollars for each sweatshirt. The festival sells 53 T-shirts and 39 sweatshirts.
Write and simplify an expression that represents the profit.

Answers

Answer:

38.0

Step-by-step explanation:

you have to you's the part and whole number ≤

Answer:

53(15) + 39(20) = x

795 + 780

=1,575

Step-by-step explanation:

there are 53 t-shirts 15$ each. Then 39 sweatshirts each 20$. so 53*15 + 39*20 will be your final solution.

On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 0) and (0, 2). Everything to the right of the line is shaded. Which linear inequality is represented by the graph? y ≤ One-halfx + 2 y ≥ One-halfx + 2 y ≤ One-thirdx + 2 y ≥ One-thirdx + 2

Answers

Answer:

[tex]y\le\dfrac{1}{2}x+2[/tex]

Step-by-step explanation:

On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, 0) and (0, 2). This line has the equation

[tex]y-0=\dfrac{2-0}{0-(-4)}(x-(-4))\\ \\y=\dfrac{1}{2}(x+4)\\ \\y=\dfrac{1}{2}x+2[/tex]

The origin belongs to the shaded region, so its coordinates must satisfy the inequality. Since

[tex]\dfrac{1}{2}\cdot 0+2=2\ge 0,[/tex]

then the correct inequality is

[tex]y\le\dfrac{1}{2}x+2[/tex]

Answer:

A

y ≤ [tex]\frac{1}{2}[/tex]x + 2

Step-by-step explanation:

plz help me plz I will mark brainlest for the person who answer first​

Answers

Answer:

[tex] \frac{16}{20} [/tex]

Step-by-step explanation:

he sold 16 and he was supposed to sell 20. therefore it's 16/20. not relevant, but he sold 80% of the tickets

Answer:

I don't know why but I personally think its 1/4 I'm probably wrong but I'm trying my best well I hope dis helps and stay safe :3

Find the value of 9y-9 given that 5y-2=3.

Answers

Answer:

0

Step-by-step explanation:

5y-2=3

5y=3+2

5y=5

y=5/5=1

9y-9=9(1)-9=9-9=0

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