Add the rational expression as indicated be sure to express your answer in simplest form. By inspection, the least common denominator of the given factor is

Add The Rational Expression As Indicated Be Sure To Express Your Answer In Simplest Form. By Inspection,

Answers

Answer 1

Notice that the least common denominator is 9*2=18, therefore:

[tex]\begin{gathered} \frac{x-3}{9}+\frac{x+7}{2}=\frac{2(x-3)}{9\cdot2}+\frac{9(x+7)}{9\cdot2}, \\ \frac{x-3}{9}+\frac{x+7}{2}=\frac{2x-6}{18}+\frac{9x+63}{18}, \\ \frac{x-3}{9}+\frac{x+7}{2}=\frac{2x-6+9x+63}{18}, \\ \frac{x-3}{9}+\frac{x+7}{2}=\frac{11x+57}{18}\text{.} \end{gathered}[/tex]

Answer:

[tex]\frac{x-3}{9}+\frac{x+7}{2}=\frac{11x+57}{18}\text{.}[/tex]


Related Questions

Examine the graph and write a statement about the data. Use specific information from the graph.

Answers

This bar graph represents the percentage of the public's trust in the Federal Government from year 1960 to 2015. The public trust was highest in year 1960 at 74% and it was at its lowest in 2015 at 18%.

A portion of $ 100,000 (x) is invested with a 3% after one year. The rest of the investment (and) obtained a return of 1%. The total return on investment was $ 1,800. 1) What equation shows the return on investment? 2) What equation shows how the $ 100,000 was divided?3) how much money was invested at a 3% rate of return?4) how much money was invested at a rate of return of 1%

Answers

We can write a system of equations that describe our problem.

Since we don't know how the original $100,000 was divided, we call the two parts X and Y

So we know that X + Y = 100000

Then we know the Combined Interest coming from the accounts.

We use the Interest formula for return on investment:

I = P * r * t

were P is the principal, r is the percent rate (in decimal form), and t is the number of years (in our case 1)

Then the interest from the 3% account (let's call it I1) (if X amount of money was deposited there) is:

I1 = X * 0.03 * 1 = 0.03 X

Similarly, the interest I2 coming from the 1% account (if Y amount of money was deposited there) is given by:

I2 = Y * 0.01 * 1 = 0.01 Y

Then, the addition of these two interest is our total return of $1800:

0.03 X + 0.01 Y = 1800

Then our system of equations is:

X + Y = 100000

0.03 X + 0.01 Y = 1800

which we solve by substituting for example for Y in the first equation:

Y = 100000 - X

and replacing the Y by this expression in our second equation:

0.03 X + 0.01 (100000 - X) = 1800

use distributive property to eliminate parenthesis:

0.03 X + 1000 - 0.01 X = 1800

combine like terms

0.02 X + 1000 = 1800

subtract 1000 from both sides

0.02 X = 800

divide both sides by 0.02 to completely isolate X:

X = 800 / 0.02

X = $40000

This is the amount deposited on the 3% account

Then we easily calculate the amount deposited in the other account by replacing x with $40000 in the equation we use for substitution:

Y = $100000 - $40000 = $60000

Then, the amount deposited in the 1% account was $60000

and the amount deposited in the 3% account was $40000.

Consider right triangle PQR what is the value of tan(R)
6/8
8/10
8/6
10/6

Answers

The value of tan(R) in the right triangle PQR where Perpendicular=QP, Base=RQ, Tan R=P/B. The slope of a straight line is the tangent of the angle made by the line with the positive x-axis.

What is perpendicular?

Two geometric objects are perpendicular in simple geometry if they intersect at a right angle. The perpendicular symbol,⟂, can be used to graphically represent the condition of perpendicularity. It can be defined between two planes, two lines, or two planes and another line.

What is base?

The base of a right angle triangle is the side on which it is positioned. The calculation can also be done using any of the two sides other than the hypotenuse as the base. It is the side of the right-angled triangle that is perpendicular to its base.

here,

Perpendicular=QP

Base=RQ

Tan R=P/B

=QP/RQ

Tan R=6/8

The perpendicular QP, base RQ, and tan's (R) values in the right triangle PQR. Tan's (R) = P/B. The tangent of the angle formed by the line with the positive x-axis is what determines a line's slope.

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Gordin has 4.1 GB of data in one 4-week billing cycle on his cell phone. Any unused data will roll over to the next cycle. The table shows how much data Gordon uses each week before his next billing cycle. WEEK. DATA USAGE (IN GB) 1. 0.8 2. 1.3 3. 0.9 4. 1.1How much data does Gordon have left to roll over to the next billing cycle at the end of the four weeks?A. 0 GB of dataB. 0.8 GB of datac. 3 GB of data

Answers

Gordan have left 0 GB to roll over to the next billing cycle at the end of the four weeks.

What is Addition?

The sum of all the numbers are called the Addition of numbers.

Given that;

Gordin has 4.1 GB of data in one 4-week billing cycle on his cell phone.

And, The table shows how much data Gordon uses each week before his next billing cycle as;

WEEK =               1     2    3    4

DATA USAGE = 0.8  1.3  0.9  1.1

Now,

Since, Gordin has 4.1 GB of data in one 4-week billing cycle on his cell phone.

And, The table shows how much data Gordon uses each week before his next billing cycle.

So, We can add all the given data usage in 1 to 4 week as;

Data usage = 0.8 + 1.3 + 0.9 + 1.1

                  = 4.1 GB

Thus, Gordan have left 0 GB to roll over to the next billing cycle at the end of the four weeks.

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Factoring the polynomial 12g + 20h

Answers

[tex]\begin{gathered} 12g+20h \\ 4(3g+5h) \\ the\text{ polymomial after factoring is }4(3g+5h) \end{gathered}[/tex]

[tex] \sqrt{18} (523 \div 8)[/tex]help I need help

Answers

Solution

Given question

11.85 = 2.1n + 4.5

Requirement

To isolate n

Step 1

Using the subtraction property of equality to isolate the variable

11.85 - 4.5 = 2.1n + 4.5 -4.5

7.35 = 2.1n

Step 2

use the division property of equality to isolate the variable

7.35/2.1= 2.1n/2.1

n = 3.5

Answers are 1 first, then 2 next, those are the 2 steps

can I please get answer quickly I just need to confirm I got it right

Answers

SOLUTION

We want to find the magnitude of the vector (-3, 4)

Magnitude of a vector is given as

[tex]\begin{gathered} |v|=\sqrt{x^2+y^2} \\ (x,y)=(-3,4) \\ we\text{ have } \\ =\sqrt{(-3)^2+4^2} \\ =\sqrt{9+16} \\ =\sqrt{25} \\ =5 \end{gathered}[/tex]

Hence the answer is 5 units, the last option

solve the following d. be sure to take into account whether a letter is capitalized or not .3y^3 ×m=5Qd

Answers

Step 1: Write out the equation.

[tex]3g^3+m=5Qd[/tex]

Step 2: Divide both sides of the equation by 5Q, we have

[tex]\frac{3g^3+m}{5Q}=\frac{5Qd}{5Q}[/tex]

this implies that

[tex]d=\frac{3g^3+m}{5Q}[/tex]

4Select the correct equations.Gracie, Mary, and Nancy each have a small collection of seashells. Gracie has 5 more than  times the number of shells Mary has. Nancy has 1 more than  times the number of shells Mary has. Gracie and Nancy have the same number of shells. If x is the number of shells Mary has, identify the equation that represents this situation and identify its solution.

Answers

Given data:

Gracie has 5 more than times mary have G=5+a(x).

Nancy has 1 ore than ties mary have N=1+b(x)

Given that G=N

5+ax=1+bx

4=x(b-a)

can you please help me? I'm having trouble with algebra 2 doing online school

Answers

Brianna, this is the solutiuon:

Part 2: Recalling that the perfect square trinomial has the form:

ax² + bx + c

(x - 1)² = (x - 1) * (x - 1)

x² - x - x + 1

x² - 2x + 1

Thus, b = -2. The correct answer is A.

Part 3: Recalling that the perfect square trinomial has the form:

ax² + bx + c

(x + 25)² = (x + 25) * (x + 25)

x² + 25x + 25x + 625

x² + 50x + 625

Therefore, c = 625. The correct answer is D.

Find an equivalent fraction with the given denominator 7/8 = ?/72

Answers

[tex]\frac{7}{8}=\frac{?}{72}[/tex]

To find the missing numerator si that both fractions are equivalent, you have to multiply both sides of the equal sign by 72:

[tex]\begin{gathered} 72\cdot\frac{7}{8}=72\cdot\frac{?}{72} \\ 63=\text{?} \end{gathered}[/tex]

The missing numerator is 63

The equivalent fractions are:

[tex]\frac{7}{8}=\frac{63}{72}[/tex]

the volume of a sphere is 2304pi in^3 the radius of the sphere is ___ inches.

Answers

Answer:

The radius = 12 inches.​

Explanation:

Given a sphere with radius, r units:

[tex]\text{Volume}=\frac{4}{3}\pi r^3[/tex]

If the volume of a sphere is 2304π in³, then:

[tex]\frac{4}{3}\pi r^3=2304\pi[/tex]

We solve the equation for r:

[tex]\begin{gathered} \frac{4\pi r^3}{3}=2304\pi \\ 4\pi r^3=2304\pi\times3 \\ r^3=\frac{2304\pi\times3}{4\pi} \\ r^3=1728 \end{gathered}[/tex]

Next. take cube roots of both sides.

[tex]\begin{gathered} r=\sqrt[3]{1728} \\ r=12\text{ inches} \end{gathered}[/tex]

The radius of the sphere is 12 inches.​

shows four types of polygons which type of polygon shown has no pairs of parallel sides

Answers

Accoring to the given figures, the pentagon is the one without parallel sides.

Hence, the answer is Pentagon.

I need to know how to 53 evaluate the inverse trigonometric function give answers in both radians and degrees

Answers

GIVEN:

We are given the following trigonometric expression;

[tex]Tan^{-1}(-1)[/tex]

Required;

We are required to evaluate and answer both in radians and in degrees.

Step-by-step solution;

We shall begin by using the trig property;

[tex]tan^{-1}(-x)=-tan^{-1}(x)[/tex]

Therefore, we now have;

[tex]tan^{-1}(-1)=-tan^{-1}(1)[/tex]

We now use the table of common values and we'll have;

[tex]tan^{-1}(1)=\frac{\pi}{4}[/tex]

Therefore;

[tex]-tan^{-1}(1)=-\frac{\pi}{4}[/tex]

We can now convert this to degrees;

[tex]\begin{gathered} Convert\text{ }radians\text{ }to\text{ }degrees: \\ \frac{r}{\pi}=\frac{d}{180} \end{gathered}[/tex]

Substitute for r (radian measure):

[tex]\begin{gathered} \frac{-\frac{\pi}{4}}{\pi}=\frac{d}{180} \\ \\ -\frac{\pi}{4}\div\frac{\pi}{1}=\frac{d}{180} \\ \\ -\frac{\pi}{4}\times\frac{1}{\pi}=\frac{d}{180} \\ \\ -\frac{1}{4}=\frac{d}{180} \end{gathered}[/tex]

Now we can cross multiply;

[tex]\begin{gathered} -\frac{180}{4}=d \\ \\ -45=d \end{gathered}[/tex]

Therefore,

ANSWER:

[tex]\begin{gathered} radians=-\frac{\pi}{4} \\ \\ degrees=-45\degree \end{gathered}[/tex]

12. A high school principal wants to determine if students' mathematical reasoning ability has any impact on their membership in academic clubs at the school. Twenty students were selected and given a mathematical reasoning test, with scores ranging from o to 50 (higher scores indicate more mathematical reasoning ability). Students were motivated to do well on the test with a reward system. These same students' membership in academic clubs was verified. Identify the response variable. A. Mathematical reasoning ability B. The high school C. Mathematical reasoning test D. Membership in academic clubs

Answers

Response variable: The response variable is the subject of an experiment.

In this question:

The experiment is about the mathematical reasoning ability of the students whom are members of academic clubs. So, we are focusing on mathematical reasoning ability, which is the response variable.

The answer is option A

find the unit price of a six pack of water for $6.90 fill in the amount per bottle of water

Answers

Given:

six pack of water = $6.90

To find:

Unit(one) price of water bottle(Price of one water bottle).

[tex]\frac{6.90}{6}=1.15[/tex]

Therefore,

The price of one water bottle is $1.15.

A sole trader operates his business from
a warehouse, which has been damaged
by a fire, which occurred at the end of
the financial year. After the fire, the
remaining inventory that is undamaged
amounts to GHC 2,000 (cost). The
accountant establishes the following
information: I Inventory at the
beginning of the year was GHC 16,000 II
Purchases during the year were GHC
115,000 III Sales during the year were
GHC 140,000 IV The trader sells his
goods at a mark-up of 25% of cost What
is the value of the inventory lost in fire?

Answers

Beginning inventory = 16,000 Purchase = 115,000 Sales = 140,000 Mark up = 25% on cost Undamanged inventory = 2,000

The value of the inventory lost in fire is 2,000

How do you take inventory loss due to fire into account?

The cost of products available for sale is then subtracted from the cost of goods sold. The quantity will reflect how much inventory the fire has actually destroyed. As an illustration, $275,000 minus $80,000 = $195,000, which represents the amount of inventory destroyed in the fire.

Calculate the quantity of inventory destroyed by deducting the cost of sold goods from the cost of goods that are still in stock. In this scenario, the amount of merchandise lost in the fire was $275,000 less $70,000, or $205,000.

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8 Solve: 2 3= 4x + 2 - O- O 1 2 AP 4 ( ) 1 4. O 1 2

Answers

We will have the following:

[tex]3=4x+2\Rightarrow1=4x[/tex][tex]\Rightarrow x=\frac{1}{4}[/tex]

[Third option]

Write an equation that represents a vertical shrink by a factor of 1/4 of the graph of g(x)=|x|.

h(x)=?

Answers

an equation that represents a vertical shrink by a factor of 1/4 of the graph of g(x)=|x| is y = |x|/4

What is vertical stretch/vertical compression ?

• A vertical stretch is derived if the constant is greater than one while the vertical compression is derived if the constant is between 0 and 1.

• Vertical stretch means that the function is taller as a result of it being stretched while vertical compress is shorter due to it being compressed and is therefore the most appropriate answer.

The y-values are multiplied by a value between 0 and 1, which causes them to travel in the direction of the x-axis. This is known as a vertical shrink and tends to flatten the graph. A point (a,b) on the graph of y=f(x) y = f (x) shifts to a point (a,kb) (a, k b) on the graph of y=kf(x) y = k f (x) in both scenarios.

The function g(x) is defined as |x|.

To vertically shrink the graph of g(x) by a factor of 1/4, divide the function by 4.

g(x) = f(x)/3

f(x) is equal to (|x|)/4.

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Find to the nearest degree the measure of the angle of elevation of the sun when a woman 150 cm tall casts a shadow 40 cm long.

Answers

The triangle formed is shown in the diagram below

The angle of elevation of the sun is represented by x. To determine x, we would apply the tangent trigonometric ratio which is expressed as

Tan# = opposite side/adjacent side

opposite side = 150

adjacent side = 40

Tan x = 150/40 = 3.75

x = Tan^-1(3.75)

x = 75.069

To the nearest degree, the measure of the angle of elevation of the sun is 75 degrees

compute the value of the discriminant and give the number of real solutions of the quadratic equation. -2x²+3x+5=0

Answers

Given a quadratic equation in standard form

[tex]y=ax^2+bx+c[/tex]

The discriminant D

[tex]D=b^2-4ac[/tex]

tells the types of roots the equation has.

In this case, we have

[tex]\begin{gathered} -2x^2+3x+5=0 \\ a=-2 \\ b=3 \\ c=5 \end{gathered}[/tex]

Then, the discriminant of this quadratic equation will be

[tex]\begin{gathered} D=b^2-4ac \\ D=(3)^2-4(-2)(5) \\ D=9+40 \\ \mathbf{D=49} \end{gathered}[/tex]

Finally, the value of discriminat is 49 and as he discriminant is greater than zero then this quadratic equation has 2 different real solutions.

Inequality-x less than or equal to 18

Answers

Answer: x[tex]\leq[/tex]18

Hector is thirsty and opens up the refrigerator and finds a half full gallon of milk. Hector drinks 2/5 of the milk Later kevin opens up the refrigerator and finds some milk left in the gallon. He drinks 1/3 of what is left. Draw a picture of the situation above. Include the amount of milk before hector drank any, after hector drank some, and then after kevin drank some. What fraction is the entire gallon did kevin drink What fraction of the entire gallon is left after both hector and kevin drink some milk?

Answers

When Hector opens up the refrigerator he finds the next :

He drinks 2/5 of the milk he found, then he drank:

[tex]\frac{1}{2}\times\frac{2}{5}=\frac{1\times2}{2\times5}=\frac{2}{10}=\frac{1}{5}gallon[/tex]

And he left in the bottle of milk:

[tex]\frac{1}{2}-\frac{1}{5}=\frac{5-2}{2\times5}=\frac{3}{10}gallons\text{ of milk}[/tex]

And after that Kevin open up the refrigerator and finds the next:

Kevin drinks 1/3 of what is left, then he drinks:

[tex]\frac{3}{10}\times\frac{1}{3}=\frac{3\times1}{10\times3}=\frac{3}{30}=\frac{1}{10}\text{gallon of milk}[/tex]

And then he left:

[tex]\frac{3}{10}-\frac{1}{10}=\frac{3-1}{10}=\frac{2}{10}=\frac{1}{5}[/tex]

And the milk he left in the bottle is:

ill take a pic of it

Answers

The line passes through the points given.

Select any two points from the table, (-4,2) and (-3,5).

The slope is given by:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Hence the slope is:

[tex]\begin{gathered} m=\frac{5-2}{-3-(-4)} \\ m=\frac{3}{1} \\ m=3 \end{gathered}[/tex]

The slope is 3.

What is the area of a triangle that has a height of 10 feet and a base of 6 feet?A. 16 feet squaredO B. 30 feet squaredO C.35 feet squaredD. 60 feet squared

Answers

Th formula for the area of the triangle is as follows.

[tex]A=\frac{bh}{2}[/tex]

where b is the base of the triangle and h is its height.

Substitute the given values into the formula and then simplify.

[tex]\begin{gathered} A=\frac{(6)(10)}{2} \\ =\frac{60}{2} \\ =30 \end{gathered}[/tex]

Therefore, the area of the triangle is 30 square feet, which is option B.

Finish the other half of the graph if it was even and odd.

Answers

To solve this problem, first, let's remember the definitions of even and odd functions.

• A function f is ,even, if the graph of f is ,symmetric about the y-axis,.

,

• A function f is ,odd, if the graph of f is ,symmetric about the origin.

a) To make the function even, we must complete the graph such the graph result is symmetric about the y-axis (the vertical axis). Doing that we get:

b) To make the function odd, we must complete the graph such the graph result is symmetric about the origin (the horizontal axis). Doing that we get:

How many different three-digit numbers can be written using digits from the set 5, 6, 7, 8, 9 without any repeating digits?A. 625B. 20C. 120D. 60

Answers

Given:

The given numbers are 5,6,7,8,9.

Required:

Find the way so three-digit numbers can be written using digits from the sets 5, 6, 7, 8, 9 without any repeating digits.

Explanation:

Let n is the total number then the way to write m digits number is given by the formula:

[tex]A(n,m)=\frac{n!}{(n-m)!}[/tex]

So the way to write 3 digits numbers are:

[tex]\begin{gathered} A(5,3)=\frac{5!}{(5-3)!} \\ =\frac{5!}{2!} \\ =5\times4\times3 \\ =60 \end{gathered}[/tex]

Final Answer:

Option D is the correct answer.

Question 17. 4 pts
In 98 years of football, Loudon has averaged 296 points per season and the standard deviation is 14. What percent of the years has Loudon scored between 254 and 338 points per season?​

Answers

Answer:

Over 98 years, London scored 75.14% per season between 254 and 338 points.

Step-by-step explanation:

graph and label each figure and it's image under the given reflection. give the new coordinates. you don't have to graph it for me, could you just helps with the coordinates

Answers

Explanation

Step 1

Let the vertices

[tex]\begin{gathered} C(-4,7) \\ D(-2,4) \\ E(-4,1) \\ F(-6,4) \end{gathered}[/tex]

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite (its sign is changed)

[tex]P(x,y)\rightarrow reflect\text{ across y a }\xi s\rightarrow P^{\prime}(-x,y)[/tex]

then, apply the rule to find the new coordinates

[tex]\begin{gathered} C(-4,7)\rightarrow C^{\prime}(4,7) \\ D(-2,4)\rightarrow D^{\prime}(2,4) \\ E(-4,1)\rightarrow E^{\prime}(4,1) \\ F(-6,4)\rightarrow F^{\prime}(6,4) \end{gathered}[/tex]

I hope this helps you

Find all the powers of four in the range of 4 and 1000

Answers

They are 4, 16, 64 and 256
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the cost of data storage has plummeted recently, making data mining feasible for more firms.a. Trueb. False steven manley buys cake mix for $5, bakes a delicious german chocolate cake, sells it to a market down the street for $22, and then the market sells it for $38. how much value did steven manley add? no dollar sign needed. Companies go through different phases to reach product/market fit. These phases are the:A: idea stage, the prototype stage, the launch stage, the traction stage, the monetization stage, and the growth stage.B: idea stage, the prototype stage, the launch stage, the traction stage, and the growth stage.C: the prototype stage, the launch stage, the traction stage, the monetization stage, and the growth stage.D: idea stage, the traction stage, the monetization stage, and the growth stage. if the population of a city is 158,000 and isdecreasing by 8% every year, what will thepopulation be in 5 years? i need help please help A side of the triangle below has been extended to form an exterior angle of 133. Find the value of x. 133 21 xo Pamela is 8 years older than Jiri. The sum of their ages is 62. What is Jiri's age? solon's reforms in athens select one: a. established democracy in athens. b. established social equality. c. gave citizens a place in the assembly. d. abolished slavery. e. eliminated the position of chief magistrate. Why can the big candy makers produce candy that is less expensive per piece Suppose that you earn $15 Debra earns $12.45 per hour and worked 26 34 hours last week. What is her gross pay? Find the equaton of the line in point-slope form that passes through (-4,6) and (-2,5) the expansion of participatory democracy in the jacksonian era most likely influenced the second great awakening by responses giving rise to individualistic beliefs giving rise to individualistic beliefs transforming gender roles in the family transforming gender roles in the family increasing membership in the national political parties increasing membership in the national political parties generating opposition to the abolitionist movement if a 95% confidence interval for the mean head circumference for adults, based on the results of measuring head circumference for 30 adults, is (21.42, 23.18) inches, what is the margin of error? inches. for every 1-kilometer increase in altitude, the temperature drops 7 degrees Celsius. Find the temperature change from a 5-kilometer altitude increase. ) What is the surface area in square In8 in10 in12 in10 in10 in elaborate the six universal facts about communicationbadly need answer po A car initially traveling at 3.2 m/s accelerated uniformly to a speed of 14.9 m/s over a distance of 60 meters. How much time does it take for the car to reach 9 m/s? Report your answer to 1 decimal place. Do not type in the unit or the computer will mark your answer incorrect. Graph the equation and find the x-coordinate of the x-intercept:1.5x - 3y = 7Round to the nearest hundredth athletes on scholarship at northwestern university in chicago requested the national labor relations board to determine their right to organize a labor union. one of the reasons for this request was that having a union would allow the athletes to: a. challenge the efficiency of existing athlete training programs. b. negotiate extended practice sessions and compensation. c. form an independent team of high performing athletes. d. limit the authority of trainers in team selection processes.