simplify: 1/(x-2)(x+3) +3/x+3


You must show your work and enter your answer below

Answer:

B, C, G

Step-by-step explanation:

If we look at the graph, it shows that if an employee works for 5 hours, then they will earn $36.25.

We can take 36.25 and divide that by 5 to get the hourly wage.

36.25 ÷ 5 = 7.25

We now know that employees get $7.25 every hour.

Using this we can look back to the graph.

'A' says that if an employee does not work, they will earn $7.25.

We know that this is wrong because if you do not work, then you do not earn money.

Let's look at 'B'.

If employees work for one hour, they will earn $7.25

We know this is correct because we now know the hourly wage.

Let's look at 'C'

If employees work for 4 hours, then they will get a revenue of $29.

We can figure this out by using this equation.

number of hours × hourly wage = total payment

4 × 7.25 = 29

Then this means that this is correct.

Let's look at 'D'

It says that if employees work for 10 hours, they will earn $73

Let's use that same equation again.

10 × 7.25 = 72.5

Employees earn $72.5 for working 10 hours, not $73.

So, this is obviously incorrect.

Let's look at 'E'

It says that if employees work for 3.5 hours, they will get a revenue of $21.75.

3.5 × 7.25 = 25.375

Therefore, this is incorrect.

Now let's take a look at 'F'.

It says that if employees work for 7.25 hours, then they earn $1.

This is incorrect.

And lastly, 'G'.

We know that if you do not work, then you do not earn money.

Therefore, A, B and G are the correct answers.

The nth term of the sequence is a(n) = 3 + Σ(2k - 1) from k = 1 to k = n - 1.

We have,

To find the nth term of the quadratic sequence 4, 9, 16, 25, 36, we need to find the rule that generates the sequence.

We can observe that the sequence is generated by adding consecutive odd numbers to 3, starting with the odd number 1:

4 = 3 + 1

9 = 4 + 3

16 = 9 + 7

25 = 16 + 9

36 = 25 + 11

So the rule for the sequence is:

a(n) = a(n - 1) + (2n - 1)

where a(n) is the nth term of the sequence, a(n-1) is the previous term, and (2n - 1) is the nth odd number.

Using this rule,

We can find the nth term of the sequence by substituting the value of n into the formula.

For example, to find the 6th term of the sequence, we can use:

a(6) = a(5) + (2*6 - 1)

a(6) = 36 + 11

a(6) = 47

The 6th term of the quadratic sequence is 47.

In general,

The nth term of the sequence can be found using the formula:

a(n) = 3 + Σ(2k - 1) from k = 1 to k = n - 1

where Σ(2k - 1) means the sum of the first n-1 odd numbers

(1, 3, 5, 7, ..., 2n-3).

Thus,

The nth term of the sequence is a(n) = 3 + Σ(2k - 1) from k = 1 to k = n - 1.

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Answer:

The standard form of the equation of a circle with center at (h, k) and radius r is:

(x - h)^2 + (y - k)^2 = r^2

We are given that the center of the circle is (4, -1), so h = 4 and k = -1. We also know that the circle passes through the point (-4, 1), which means that the distance from the center of the circle to (-4, 1) is the radius of the circle.

The distance between two points (x1, y1) and (x2, y2) is given by the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

So the radius of the circle is:

r = sqrt((-4 - 4)^2 + (1 - (-1))^2) = sqrt(100) = 10

Now we can substitute the values of h, k, and r into the standard form equation of a circle:

(x - 4)^2 + (y + 1)^2 = 10^2

Expanding the equation gives:

x^2 - 8x + 16 + y^2 + 2y + 1 = 100

Simplifying and putting the equation in standard form, we get:

x^2 + y^2 - 8x + 2y - 83 = 0

Therefore, the equation in standard form of the circle with center at (4, −1) and that passes through the point (−4, 1) is:

x^2 + y^2 - 8x + 2y - 83 = 0

Answer:

the sum of 1.25+(0.75)=2.00

Answer:

14, 28, 42, 56, 70, 84

20, 40, 60, 80, 100, 120

Step-by-step explanation:

Answer:

this might be wrong but i believe its 23

Let:

x = numbers of hours you can work housecleaning

y = numbers of hours you can work at your sales work

You can work a total of no more than 41 hours each week, so:

You need to earn at least $254 each week to pay your bills. and besides, Housecleaning pays $5 per hour and your sales job pays $8 per hour, therefore:

Step-by-step explanation:

The amplitude is 2. Amplitude means height from the x-axis to the crest/trough.

The period is 2pi. It is from crest to crest (next crest) or trough to trough (next trough).

Note that crest are the highest points of a wave, and that troughs are the lowest points of a wave. (we are talking about transverse waves, but this is more of a physics thing).

Function of graph:
By playing around in a graphing calculator, I got the equation to be

2 (cos (x + pi/2)).

the 2 changes the amplitude, and the + pi/2 shifts the graph by pi/2 to the left.

Answer:

(9,16)

Step-by-step explanation:

We Know

The equation y = 3x - 2

Find the y coordinate (9, ?)

We just simply put 9 in for x and solve for y

y = 3(9) - 2

y = 18 - 2

y = 16

So, the coordinate are (9,16)

Answer:

15 us the answer I knowwww

Answer:

Step-by-step explanation:

a) Find the gradient

\(\nabla f(x,y) =f_x(x,y)\bold{i} +f_y (x,y)\bold{j}\)

\(Also, sin(4x+3y)= sin(4x)cos(3y)+sin(3y)cos (4x)\)

\(f_x(x,y) = 4cos(4x)cos(3y)-4sin(3y)sin(4x) = 4 cos(4x-3y)\)

\(f_y(x,y) = -3sin(4x)sin(3y)+3cos(3y)cos(4x)=3cos(4x-3y)\)

Hence

\(\nabla f(x,y) = 4cos(4x-3y)\bold{i}+3cos(4x-3y)\bold{j}\)

b) At point (-6, 8) just replace the values in gradient to find it out. You can do it.

c) directional derivative in the direction u.

\(D_uf(x,y)=\nabla f(x,y). u\)

I stuck with your 1 2 3 i -j . What does 1 2 3 mean? is it not 123 or 1 2/3 or else?

The zeros of the function defined by

h(x) = x³ – 4x² – 5x are x = 0, x = 5 and x = -1

The zeros of a function, also referred to as roots or x-intercepts, occur at x-values where the value of the function is 0. It is simply the values of x when f(x) is equal to 0.

For x = 0, we substitute 0 for x in the function h(x);

h(0) = (0)³ - 4(0)² - 5(0)

h(0) = 0

For x = 1, we substitute 1 for x in the function h(x);

h(1) = (1)³ - 4(1)² - 5(1)

h(1) = 1 - 4 - 5

h(1) = -8

For x = -5, we substitute -5 for x in the function h(x);

h(-5) = (-5)³ - 4(-5)² - 5(-5)

h(-5) = -125 - 100 +25

h(-5) = -200

For x = 5, we substitute 5 for x in the function h(x);

h(5) = (5)³ - 4(5)² - 5(5)

h(5) = 125 - 100 - 25

h(5) = 0

For x = -1, we substitute -1 for x in the function h(x);

h(-1) = (-1)³ - 4(-1)² - 5(-1)

h(-1) = -1 - 4 + 5

h(-1) = 0

Therefore, the values of x that makes the function h(x) = x³ – 4x² – 5x equal to zero are; 0, 5, and -1, they are the zeros of the function h(x).

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\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$8.75\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &\frac{1}{4} \end{cases} \\\\\\ 8.75 = (1000)(\frac{r}{100})(\frac{1}{4})\implies 8.75=\cfrac{10r}{4} \\\\\\ 8.75=\cfrac{5r}{2}\implies 17.5=5r\implies \cfrac{17.5}{5}=r\implies \stackrel{\%}{3.5}=r\)

Answer: Area = l × w

= 3.5 × 2.8

= 9.8 meters2

Step-by-step explanation:

Answer:

6n+30

Step-by-step explanation:

Step 1:

Multiply 6 and n

Step 2:

Multiply 6 and 5

Step 3:

Put together!

have a great day and thx for your inquiry :)

Answer:

the answer is A

Step-by-step explanation:

distributive property states

a(b+c)=ab+ac

therefore

6(n+5)=6n+30

Answer:

x= -6

Step-by-step explanation:

5.(x+3) = 2x-3

5x+15=2x-3

5x-2x+15=-3

5x-2x=-3-15

3x=-3-15

3x=-18

x=-6

Step-by-step explanation:

5(X+3) =2X_3

Expand the brackets

5X + 15 = 2X _ 3

CLT(Collect like terms)

5X_2X= _3 _ 15

3X = _ 18

DBS( Divide both sides) by 3

3X/ 3 = _18 / 3

X = _9

Given the equation;

to solve for x;

add 33 to both sides to collect the like terms, we have;

then let's divide both sides by 2;

then to get the value of x, we will square root both sides;

from the following equation, we can see that all the steps in the initial solution is right.

to confirm; let us substitute x=6 into the initial equation to see if we will get the corresponding answer;

This confirms that x=6 is the correct answer.

He made no error.

The standard error is of 0.2246, which means that the mean scores for samples of 30 vary around 0.2246 from the mean.

The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.

The confidence interval formula is \(\bar x\pm t\frac{s}{\sqrt{n}}\).

Where, \(\bar x\) is the sample mean, t is the critical value, n is the sample size and s is the standard deviation for the sample.

Here,

\(\bar x\) =1.267, s=1.23, n=30

The standard error is Se= 1.23/√30

= 0.2246

Item a:

The standard error is of 0.2246, which means that the mean scores for samples of 30 vary around 0.2246 from the mean.

Item b:

Using a t-distribution calculator, considering a confidence level of 0.99 with 30 - 1 = 29 df, the critical value is t = 2.7564.

\(\bar x\pm tS_c\)

\(\bar x+ tS_c\) =1.267-2.7564(0.2246) =0.6479

\(\bar x- tS_c\) =1.267+2.7564(0.2246) =1.8861

Therefore, the 99% confidence interval to estimate the true mean score on this question is (0.6479, 1.8861). It means that we are 99% that the true mean score of all students in this question is between 0.6479 and 1.8861.

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The missing angle is <B= 40 degree and missing side length is AB = 12.25 and AC = 19.068.

To find the missing angle and side measures of ΔABC, we can use the properties of a triangle.

Given:

∠A = 50°

∠C = 90°

CB = 16

We can start by finding the measure of ∠B:

∠A + ∠B + ∠C = 180° (Sum of angles in a triangle)

50° + ∠B + 90° = 180°

∠B + 140° = 180°

∠B = 180° - 140°

∠B = 40°

Now, using Sine law

CB/ sin A = AB / sin C

16 / sin 50 = AB / sin 90

16 / 0.766044 = AB

AB = 12.25

Again 12.25 = AC/ sin B

12.25 = AC / sin 40

AC = 19.068

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Answer:

There is no difference in the number of sales between The Florida salespeople and Washington salespeople

Sp^2 = 39

Step-by-step explanation:

Given data :

Florida: 39, 44, 42, 50, 55, 48, 51, 38, 54

Washington: 42, 43, 56, 50, 49, 52, 53, 56

number of sales persons in Florida = 9

number of sales persons in Washington = 8

variance = constant

a)Determine if there is difference between the Florida salespeople and Washington salespeople

we will carry out a two tailed test based on the given data

H0 : u1 = u2  

H1 : u1 ≠ u2

x ( mean ) = 46.77,  y ( mean ) = 50.13 ,

s1^2 = 39.69,  s2^2 = 28.41,   n1 = 9 ,   n2 = 8

therefore :

Sp^2 = \(\frac{n1s1^2 + n2s2^2}{n1 + n2-2}\) =  38.96  ≈ 39

performing test statistic

t = \(\frac{x- y }{sp\sqrt{\frac{1}{n1} +\frac{1}{n2} } }\)    = \(\frac{-3.36}{3.0330}\) = -1.1078

critical value is at t = 0.05 and for a two tailed test it is at 2.13  therefore e accept H0 at 5% .    This shows that there is no difference in sales

Answer:

9.286

Step-by-step explanation:

I'm not guaranteeing this answer. If this is correctly written without any indication of how to deal with x, then here is as much as you can do.

850-53x m= 720-39x m                         Subtract 720 from both sides.

850 - 720 - 53x = 720 - 720 - 39xm      Combine

- 53xm + 130 = - 39xm                             Add 53x

-53x+53xm + 130 = -39x + 53xm            Combine

                      130 = 14xm                         Divide by 14

xm = 130/14

xm = 9.28

===============================

You can use the same steps above. I'm abbreviating the steps because they are the same.

I'm sure there is more to the problem, but I can't imagine what it is. If you have additional directions, put it under this answer. I will get it as a comment.

850-53m= 720-39m

850 - 720 - 53m = - 39m

130 - 53m = - 39m

130 = -39m + 53m

130 = 14m

130/14 = m

m =9.286

Answer:

1. 50 = 5x+15

2. 50 = 3x+20

3. 7

4. 10

5. Skating Rink

Step-by-step explanation:

1. As the maximum amount of money is 50 dollars, you are given that there is a 5 dollar entry *per* person, alongside the 15 room rental fee added on. That is where the equation 5x+15 = 50 comes from

2. The same can be said with the skating rink, with different numbers. 3 *per* person plus the extra 20 room rental fee.

3. 50 = 5x+15 can be solved by subtracting 15 by both sides. This gives us 35=5x and dividing by 5 will give us 7 = x

4. 50 = 3x+20 can be solved by subtracting 20 by both sides. This gives us 30=3x and dividing by 3 will give us 10 = x

5. As 10>7, it's apparent that you can bring more people to the Skating Rink

For the party, at the skating rink, more people can be invited than at the bowling alley.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

here,
1.
According to the question,
Expression ⇒ 5x + 15 = 50

2.
According to the question,
Expression ⇒ 3x + 20= 50

3

For bowling alleys,
5x + 15 = 50

x = 7 people

4.
For the skating rink,
3x + 20 = 50
x = 10 people

5.
At the skating rink, more people can be invited.

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Here's the solution :

perimeter of equilateral triangle = 3 × x = 3x

perimeter of square = 4 × (x + 10)

now, according to above statement :

permission (square) = 3 × perimeter (triangle)

that is :

therefore, side of triangle = 8 cm

Answer:

Let the side of the equilateral triangle = x

so the side of the square =  x+10

The perimeter of the triangle = 3x

and the perimeter of the square = 4(x+10)

condition : the perimeter of the square is 3 times the perimeter of the triangle.

so, 4(x+10) =  3*(3x)

Step-by-step explanation:

Answer

50

Step-by-step explanation:

60 is supplementary to 120 so 60+70=130

and a triangle adds up to 180 so 180-130 would be 50

Answer:

Step-by-step explanation:

Given

\(x=1-sin(a)\\y=1+cos(a)\)

Solve for \(a\) in the second equation.

\(y=1+cos(a)\)

\(y-1=cos(a)\)

\(a=cos^{-1}( y-1)\)

Insert our answer for \(a\) into the first equation.

\(x=1-sin(a)\)

\(x=1-sin(cos^{-1}( y-1))\)

\(cos^{-1}=arccos\)

\(x=1-sin(arccos( y-1))\)

Lets simplify \(1-sin(arccos( y-1))\)

A piece of graph paper would be helpful in my opinion.

Here is how I would go about doing so

Draw a triangle in the plane with vertices \((y-1,\sqrt{1^2-(y-1)^2}),(y-1,0)\) and the origin.

\(arccos(y-1)\) is is the angle between the positive x-axis and the ray beginning at the origin and passing through \((y-1,\sqrt{1^2-(y-1)^2})\). Therefore \(sin(arccos(y-1))\) is \(\sqrt{1-(y-1)^2}\)

Now we have

\(x-1-\sqrt{1-(y-1)^2}\\a=arccos(y-1)\)

We can write \(1\) as \(1^2\). Since both terms are now perfect squares, we can factor using the difference of squares formula.

\(a^2-b^2=(a+b)(a-b)\) where \(a=1\) and \(b=y-1\)

\(x=1-\sqrt{(1+y-1)(1-(y-1))}\)

After simplifying we get

\(x=-\sqrt{y(-y+2)}+1\)

\(x=-\sqrt{y(-y+2)}+1\)

\(a=arccos(y-1)\)

I think this is what your question was. If not let me know.

Answer: 6.5, 6.25, 6.05, 6.007

Step-by-step explanation:

We need to look at each place value to see which one is the biggest. Since the units place is the same for all the numbers, let's look at the tenths place.

6.5, 6.25, 6.05, 6.007

Since 5 is the biggest number out of all that are underlined, 6.5 is the biggest one, and goes first.

2 is the second biggest number out of all that are underlined, so 6.25 goes second.

However, there are 2 numbers that have 0 in their tenths place, so we need to go one place value further: the hundredths place.

6.05, 6.007

Since 5 is bigger than 0, 6.05 goes third. 6.007 is the only number left, so it goes last.

Hence, the order is 6.5, 6.25, 6.05, 6.007

The area of the parallelogram is 475.2 square units.

A parallelogram is a polygon with four sides whose each pair of opposite sides are equal and parallel.

The properties of parallelogram are:

Given base b of the parallelogram a 36 units and height h of the parallelogram as 13.2 units.

Therefore we know from the properties of the parallelogram that area is given by the product of base and height.

∴area = b × h

or, area = 36 × 13.2

or, area = 475.2 square units

Hence the area of the parallelogram is 475.2 square units .

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