Multiply. Stars and restrictions on the variable. Simplify the rational expression.
Answers
Given,
The expression is:
[tex]\frac{x^2+2x-8}{x^2+4x-12}\times\frac{5x+30}{x+5}[/tex]Required:
The simplified rational expression.
Simplifying the expression,
[tex]\begin{gathered} \frac{x^2+2x-8}{x^2+4x-12}\times\frac{5x+30}{x+5}=\frac{x^2+4x-2x-8}{x^2+6x-2x-12}\times\frac{5x+30}{x+5} \\ =\frac{x(x+4)-2(x+4)}{x(x+6)-2(x+6)}\times\frac{5(x+6)}{x+5} \\ =\frac{(x+4)(x-2)}{(x+6)(x-2)}\times\frac{5(x+6)}{x+5} \\ =\frac{(x+4)}{1}\times\frac{5}{x+5} \\ =\frac{5(x+4)}{x+5} \\ =\frac{5x+20}{x+5} \end{gathered}[/tex]Hence, the simplified rational expression is (5x+20)/(x+5).
The restriction of the expression is:
[tex]x\ne-5,\text{ 2,-6}[/tex]
Related Questions
help meeeeeeeeeeeeeeeeeee please
Answers
Answer:c
Step-by-step explanation:
Determine whether the variable is qualitative or quantitative.Favorite basketball playerIs the variable qualitative or quantitative?A. The variable is quantitative because it is an attribute characteristic.B. The variable is qualitative because it is a numerical measure.C. The variable is quantitative because it is a numerical measure.D. The variable is qualitative because it is an attribute characteristic.
Answers
We have that favorite is a characteristic. It is a qualitative data. We cannot measure it at the weight, length, and other similar variables.
Therefore, the correct option is D:
If you buy a car for $24,686 and it depreciates linearly at a rate of 8% per year, what will be its value after 6 months?
Answers
The value of a car after 6 months will be $23,698.56.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
Cost of a car = $24,686
And, The cost of a car is depreciates linearly at a rate of 8% per year.
Now,
The depreciated cost of a car in 1 year = 8% of $24,686
= 8/100 x $24,686
= $1,974.88
So, The depreciated cost of a car in 1 year will be $1,974.88
Since, In 1 year there is 12 month.
Hence, The depreciated cost of a car in 6 month = $1,974.88 ÷ 2
= $987.44
Therefore, The value of a car after 6 month = $24,686 - $987.44
= $23,698.56
Hence, The value of a car after 6 months will be $23,698.56.
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GI = 6, HI = 8, DT = 12, what is IE?a.12b.16c.8d.4
Answers
Since both chords passes through the point I the should be equal.
Now we know that GI=6 and HI=8, then GH=14; hence DE have to be equal to 14 too.
From this we conclude that IE should be 4.
Select the correct answer.Consider these three numbers expressed in scientific notation: 2.4 x 104,6.3 105, and 9.6 x 10”. Which number is the greatest, and by howmany times Is It greater than the smallest number?OA. The greatest number is 9.6 % 10%. It is 400 times greater than the smallest number.ОВ.The greatest number is 6.3 x 105. It is 40 times greater than the smallest number.OCThe greatest number is 6.3 x 109. It is 400 times greater than the smallest numberODThe greatest number is 9.6 x 10'. It is 4,000 times greater than the smallest number.
Answers
We have the next numbers
[tex]\begin{gathered} 2.4\cdot10^4 \\ 6.3^{}\cdot10^5 \\ 9.6\cdot10^7 \end{gathered}[/tex]In this case, the greatest number will be the number that is multiplied by 10 a greater number of times.
So, the greatest number is 9.6 x 10^7,
Then, the smallest number will be the number that us multiplied by 10 a smaller number of times.
So, the smallest number is 2.4 x 10^4,
Now, to know the number of times that the greatest number is greater than the smallest number we must divide it
[tex]\frac{9.6\cdot10^7}{2.4\cdot10^4}=4\cdot10^3=4000[/tex]Finally, The greatest number is 9.6 × 10^7. It is 4,000 times greater than the smallest number. (Letter D).
Find the value of x in the figure below. (7x + 17) (8.x + 2)(please be kind)
Answers
The angles shown are vertically opposite, then they are equal:
[tex]7x+17=8x+2[/tex]Solving for x, we have:
[tex]\begin{gathered} 7x+17=8x+2 \\ 7x-8x=2-17 \\ -x=-15 \\ x=15 \end{gathered}[/tex]Therefore, x=15.
Shannon's bicycle travels 50 feet for every 3 pedal turn. How many pedal turns are needed to travel one mile (1 mile=5280 feet)?
Answers
Shannon's bicycle travels 50 feet for 3 pedal turn
He travels
[tex]50ft=3\text{ pedal turn}[/tex]Converting 1 mile to feet
[tex]1\text{mile}=5280ft[/tex]The number of pedal turns needed to travel a mile is
[tex]\begin{gathered} 50ft=3\text{ pedal turn} \\ For\text{ 1mile (5280ft)=}\frac{5280\times3}{50}=3168\text{ pedal turns} \end{gathered}[/tex]Hence, the answer is 3168 pedal turns
Find the slope of the line that passes through the following points . Simplify your answer .
(-10, 10) and (-9, -10)
Answers
Answer:
-20 is the slope
Step-by-step explanation:
Using the slope formula y1-y2/x2-x1,
you get the slope of -20
Answer: -20/1
Step-by-step explanation:
1) Use the slope formula
y1-y
--------
x1-x
2) Substitute the numbers
-10-10
------
-9-(-10)
3) Solve
-20
------
1
-20/1
What is the equation for the translation of x2 + y² = 64 three units to the left and two units down
(x - 3)² + (y-2)² = 64
(x+3)2 + (y + 2)2 = 64
(x-3)² + (y + 2)² = 64
(x+3)² + (y-2)² = 64
Answers
The equation for the translation of [tex]x^{2} +y^{2}=64[/tex], three units to the left and two units down is option (b) [tex](x+3)^2+(y+2)^2=25[/tex]
The equation is [tex]x^{2} +y^{2}=64[/tex]
The standard form of the circle
[tex](x-h)^2+(y-k)^2=r^{2}[/tex]
Where r is the radius of the circle
(h,k) are the coordinates of the center of the circle.
The equation is [tex]x^{2} +y^{2}=64[/tex]
The center is (0,0)
Here the circle translated three units to the left
Therefore h = -3
The circle is translated two units down
k = -2
Substitute the values in the standard form of the circle
[tex](x--3)^{2}+(y--2)^{2}=25[/tex]
[tex](x+3)^2+(y+2)^2=25[/tex]
Hence, the equation for the translation of [tex]x^{2} +y^{2}=64[/tex], three units to the left and two units down is option (b) [tex](x+3)^2+(y+2)^2=25[/tex]
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. Erin deposited $1,300 into a savings account that earns6% simple interest for 3 years.
Answers
The simple interest formula is:
A = P(1 + rt)
where A is the final amount, P is the principal, r is the annual interest rate (as a decimal) and t is time in years.
Substituting with P = 1,300, r = 0.06 and t = 3, we get:
A = 1,300(1 + 0.06*3)
A = 1,300*1.18
A = 1,534
The final amount will be $1,534
Suppose that there are two types of tickets to a show: Advanced and same day. Advanced tickets cost $40 and same-day tickets cost $25. For one performance there are 65 tickets sold in all, and the total amount paid for them was $2225. How many tickets of each type were sold?
Answers
Solution:
Given:
Two types of tickets; advanced and same-day tickets.
Let a represent advanced tickets
Let s represent same-day tickets.
Developing the word problem (statements) into mathematical expressions, we have;
[tex]\begin{gathered} \text{Advanced tickets cost \$40. This means;} \\ a=\text{ \$40} \\ \\ \text{Same}-\text{day tickets cost \$25. This means;} \\ s=\text{ \$25} \end{gathered}[/tex][tex]\begin{gathered} \text{Total tickets sold in all is 65. This means;} \\ a+s=65\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}\mathrm{}(1) \\ \\ \text{Total amount paid for advanced tickets = \$40a} \\ \text{Total amount paid for same-day tickets = \$25s} \\ \\ \text{Total amount paid for all tickets = \$2225.} \\ \text{Hence,} \\ 40a+25s=2225\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(2) \end{gathered}[/tex]Solving equations (1) and (2) simultaneously to get the values of a and s;
[tex]\begin{gathered} \text{From equation (1)},\text{ } \\ a+s=65 \\ a=65-s\ldots\ldots\ldots\ldots\ldots\ldots\ldots\text{.}(3) \\ \\ \text{Substituting equation (3) in equation (2),} \\ 40a+25s=2225 \\ 40(65-s)+25s=2225 \\ 2600-40s+25s=2225 \\ 2600-15s=2225 \\ \text{Collecting the like terms;} \\ 2600-2225=15s \\ 375=15s \\ 15s=375 \\ \text{Dividing both sides by 15 to get s,} \\ s=\frac{375}{15} \\ s=25 \\ \text{Thus, same-day tickets sold were 25 tickets} \end{gathered}[/tex]Substituting the value of s in equation (3) to get the value of a.
[tex]\begin{gathered} a=65-s \\ a=65-25 \\ a=40 \\ \text{Thus, advanced tickets sold were 40 tickets} \end{gathered}[/tex]Therefore, advanced tickets sold were 40 tickets and same-day tickets sold were 25 tickets.
I will send u a picture of the topic it is hard to explain in words. it job is to find the measure of each labeled angle so 5x and 4x
Answers
According to the given image, we have a parallelogram whose two consecutive angles are 5x and 4x.
Remember that two consecutive interior angles in a parallelogram sum 180°, so we can express the following equation.
[tex]5x+4x=180[/tex]Now, we solve for x.
[tex]\begin{gathered} 9x=180 \\ x=\frac{180}{9} \\ x=20 \end{gathered}[/tex]We use this value to find each angle.
[tex]\begin{gathered} 5x=5(20)=100 \\ 4x=4(20)=80 \end{gathered}[/tex]Therefore, the angles are 100° and 80°.a sample of 49 customers was taken at a computer store. each customers was asked the price of the computer she brought. find the mean price sampleround to the nearest dollar
Answers
The mean is computed as follows:
[tex]\operatorname{mean}=\frac{\text{ sum of the terms}}{\text{ number of terms}}[/tex]In this case, the number of terms is the number of computers.
To find the sum of the terms, we need to multiply the number of computers by each price and add them, that is,
[tex]\begin{gathered} \operatorname{mean}=\frac{17\cdot2050+18\cdot1050+14\cdot1000}{17+18+14} \\ \operatorname{mean}=\frac{34850+18900+14000}{49} \\ \operatorname{mean}=\frac{67750}{49} \\ \operatorname{mean}=1383\text{ \$} \end{gathered}[/tex]What is the ratio of the areas of ΔABC to ΔA'B'C' ?
Answers
The first step is to find the scale factor relating ABC to A'B'C'. Since they are dilated, ABC is similar to A'B'C'. This means that the ratios of their corresponding sides are equal. Thus,
AB/A'B' = BC/B'C' = AC/A'C'
From the information given,
AB = 7
A'B' = 28
Thus,
ratio of ABC to A'B'C' = 7/28 = 1/4
Ratio of area of ABC to A'B'C' = (1/4)^2
Ratio of area of ABC to A'B'C' = 1/16
Find the y-intercepts of the graph of the following quadratic function. If there is more than one intercept, separate them with commas. If there are no x-intercepts type DNE.
f(y) = 5y^2 - 240
y-intercept(s): __________
Answers
The y-intercepts are the values of y such that f(y) = 0, solving that we will get:
y-intercepts: -6.93, 6.93.
How to find the y-intercepts of the function?
Here we have a function that depends of y, and we want to find the y-intercepts.
The function is:
f(y) = 5*y^2 - 240
The y-intercepts are the values of y such that the function becomes zero, so we need to solve:
0 = 5*y^2 - 240
240 = 5*y^2
240/5 = y^2
48 = y^2
Now we apply the square root in both sides to get:
±√48 = y
±6.93 = y
So the two y-intercepts are:
y = 6.93
y = -6.93
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create a non linear function that has a solution at (-2,6). Include a calculation that shows why this is a solution to your function.
Answers
In order to find a nonlinear function that has a solution at (-2,6) we need to choose first a parent function that is no linear in this case, we will use
[tex]y=x^2[/tex]in order to know that the solution is (-2, 6) so if I introduce the value of x coordinate which is -2 in the function we need to have as result 6
In this case, taken the parent function above and in order to have the desired result we have the next calculations
[tex]\begin{gathered} 6=(-2)^2+2 \\ 6=4+2 \\ 6=6 \end{gathered}[/tex]so the function that has a solution (-2,6) and is no linear is
[tex]y=x^2+2[/tex]If the same number is added to the nunerator of 12/13 and subtract from the denominator, the new fraction is equal to 3/2. What is the number?
Answers
Answer:
x = 3
Step-by-step explanation:
If the same number is added to the numerator of 12/13 and subtract from the denominator, the new fraction is equal to 3/2. What is the number?
[tex]\frac{12+x}{13-x} =\frac{3}{2}[/tex]
multiply both sides by 13-x:
[tex](13-x)\frac{12+x}{13-x} =\frac{3}{2}(13-x)\\\\12+x = \frac{3(13-x)}{2} \\\\12+x = \frac{39-3x}{2} \\[/tex]
multiply both sides by 2:
[tex]2(12+x) = (\frac{39-3x}{2})\\\\24+2x = 39-3x[/tex]
subtract 24 from both sides:
24 + 2x - 24 = 39 - 3x - 24
2x = 15 - 3x
add 3 x to both sides:
2x + 3x = 15 - 3x + 3x
5x = 15
divide both sides by 5:
5x/5 = 15/5
x = 3
check:
[tex]\frac{12+x}{13-x} =\frac{3}{2}\\\\\frac{12+3}{13-3} =\frac{3}{2}\\\\\frac{15}{10} =\frac{3}{2}\\\\\frac{3}{2} =\frac{3}{2}[/tex]
P(x) = x3 + 3x2 − 16x − 48, c = −3 Show that the given value of c is a zero of P(x)
Answers
The value of c is a true zero of the polynomial function P(x)
How to show that c is a zero of the polynomial?The polynomial function is given as
P(x) = x³ + 3x² - 16x - 48
Also, we have the value of c to be
c = -3
If truly, the variable c is a zero of the polynomial, then the following must be true
P(c) = 0
Start by substituting -3 for c in the equation P(x) = x³ + 3x² - 16x - 48
So, we have
P(-3) = (-3)³ + 3(-3)² - 16(-3) - 48
Evaluate the exponents
P(-3) = -27 + 3(9) - 16(-3) - 48
Evaluate the products
P(-3) = -27 + 27 + 48 - 48
Evaluate the sum and the difference
P(-3) = 0
Recall that
c = -3
So, we have
P(c) = 0
Hence, c is a zero of the polynomial because P(c) = 0
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Use equation below to find v, if u = 18, a=6, and t = 4. v=utat
Answers
The given equation is
[tex]v=u\cdot t\cdot a\cdot t[/tex]Where, u=18, a=6, and t=4. Replacing these values, we have
[tex]v=18\cdot4\cdot6\cdot4=1,728[/tex]Therefore, the answer is 1,728.A consumer group buys identical radios at 14 different stores. if the mean(average)price per radio is $23.50, how much did the consumer group spend for all the radios?
Answers
If the consumer group bougth 14 different radios it means they bought 14 units and to calculate how much did they spend.
[tex]14\cdot(23.50)=329[/tex]they spend about $329 in the 14 radios.
8) Type your answers in the boxes.
A sequence is given by the equation an= 1/4n where a1 = 512 and n > 1 and is a
whole number.
What are the first 4 terms of the series?
Series:
Answers
The first 4 terms of the sequence are 512 , 128 , 32 and 8 .
In mathematics, a sequence is a named collection of elements where repeats are allowed and order matters.
It has pieces, much like a set (also called elements, or terms). The number of items determines how long the series is (potentially infinite). The same elements could appear in a sequence more than once at different places in contrast to a set, where the order is crucial. Formally, a sequence can be defined as a relationship between the items at each of the positions in the sequence and natural numbers (the positions of the sequence's constituents). It is possible to think of an indexed family, which is a function from any index set, as a generalization of the concept of a sequence.The formula for the sequence is given by aₙ = 1/4 aₙ₋₁
It is given that a₁ = 512
Hence a₂ = 1/4 a₁ = 1/4 × 512 = 128
a₃ = 1/4 a₂ = 32
a₄ = 1/4 a₃ = 8
Therefore the first 4 terms of the sequence are 512 , 128 , 32 and 8 .
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Golfer Tiger Woods drives a golf ball with a vertical speed of 144 ft/sec at the time when he hits the ball with his club. The height function of one of his drives is H=-161 +1441, where t is the time in seconds and H is the height in feet. Find the maximum height of a drive. (hint: where does the maximum occur on a parabola?)
Answers
The given quadratic function
[tex]H=-16t^2+144t[/tex]Describes the height, in feet, of one of Tiger Woods's drives with respect to the time, t, measure in seconds.
The function is a parabola, to determine its maximum point, the first step is to determine if the parabola opens up or down, to do so you have to look at the sign of the coefficient of the quadratic term (a).
-If a>0, the parabola opens up, and its vertex will indicate the minimum value of the funtion.
-Id
For this function, the coefficient is a= -16, the coefficient "a" is negative, which
write the rule for the quadratic function in the form you would use to graph it. then graph the function
Answers
The quadratic function is already written in a recognizable way:
[tex]f(x)=x^2-6x+11[/tex]Evaluate the function at some values to find points on the graph of f:
[tex]\begin{gathered} \\ f(-1)=(-1)^2-6(-1)+11=18 \\ f(0)=(0)^2-6(0)+11=11 \\ f(1)=(1)^2-6(1)+11=6 \\ f(2)=(2)^2-6(2)+11=3 \\ f(3)=(3)^2-6(3)+11=2 \\ f(4)=(4)^2-6(4)+11=3 \\ f(5)=(5)^2-6(5)+11=6 \\ f(6)=(6)^2-6(6)+11=11 \\ f(7)=(7)^2-6(7)+11=18 \end{gathered}[/tex]Plot the points (x,f(x)) on a coordinate plane:
Draw a smooth line through those points:
I do not know how to find the information from a word question and would love some help
Answers
Explanation
Given
From the question, we can see that the bottom of the ferris wheel is 30 feet about the ground and also while rotating, it can move to a height of 550 feet off the ground. In essence the actual height the ferris wheel can attain is
[tex]h=550-30=520[/tex]The amplitude then becomes half of the height which is
[tex]A=\frac{h}{2}=\frac{520}{2}=260[/tex]The vertical shift the Ferris wheel undergoes becomes the sum of the amplitude and its distance above the ground.
[tex]D=260+30=290[/tex]Since it takes the Ferris wheel 15 minutes to move from bottom to top, it will take it twice that to complete one revolution which will be its period.
[tex]T=2\times15mins=30[/tex]Therefore, the frequency B, becomes;
[tex]B=\frac{2\pi}{T}=\frac{2\pi}{30}=\frac{\pi}{15}[/tex]We can then place in the above parameters to form the equation.
[tex]y=Acos(B(t+C))+D\Rightarrow260cos(\frac{\pi}{15}(t+C)+290[/tex]The last missing parameter is the phase shift C. At time t =0, the function (y) has a position at 30. Therefore,
[tex]\begin{gathered} 30=260cos(\frac{\pi}{15}C)+290 \\ 260cos(\frac{\pi}{15}C)=-290+30 \\ 260cos(\frac{\pi}{15}C)=-260 \\ divide\text{ both sides by 260} \\ \frac{\begin{equation*}260cos(\frac{\pi}{15}C)\end{equation*}}{260}=\frac{-260}{260} \\ cos(\frac{\pi}{15}C)=-1 \\ \frac{\pi}{15}C=cos^{-1}(-1) \\ \frac{\pi}{15}C=\pi \\ C=\frac{15\pi}{\pi} \\ C=15 \end{gathered}[/tex]Therefore, the function y becomes
Answer:
[tex]y=260cos(\frac{\pi}{15}(t+15)+290[/tex]For a card trick, Barry is using 14 cards from a deck if each suit he uses had 5 numbered cards and c face cards, which expression shows how many suits he is using.
A. 14 x 5 + c
B 14 divided by (5+c)
C 14 divided by 5+ C
D 14 x (5+c)
Answers
Answer:
b
Step-by-step explanation:
Translate each sentence into a formula. The area of a parallelogram is the product of the base of the parallelogram and the height of the parallelogram. a. A=h-bb. b=h/A c. A=b/hd. A=bh
Answers
Question: Translate each sentence into a formula. The area of a parallelogram is the product of the base of the parallelogram and the height of the parallelogram.
Solution: The product between two objects means the multiplication between these two objects, then the correct solution would be:
d. A=bh
Mark and Nina own different flower shops, which both open at the same time in the morning.
Function m models the number of roses Mark has at his flower shop, and function n models the number of roses in Nina's flower shop, x hours after
the shops open.
m(x)=616-24x
n(x)=552-36x
Which function correctly represents how many more roses Mark has at his flower shop than Nina has at hers, x hours after the shops open?
A. (m-n)(x)=64 + 12x
B. (m-n)(x)=64-16x
C. (m-n)(x)=64-12x
D. (m-n)(x) = 64-60x
Answers
Correct option is A. The equation representing the how many more roses Mark has at his flower shop than Nina has at hers is (m-n)(x)=64 + 12x
What constitutes a function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Four main categories can be used to classify different sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.
From the given equations,
Subtracting both of the functions,
m(x) - n(x) = (616-24x) - (552-36x)
⇒ (m - n) (x) = 64 - 12x
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Lacey’s bank account shows a balance of –$45.10. The next day, she deposits $65.00 and uses her debit card for a purchase of $23.75. What is her new balance?
Answers
Lacey's new balance in the account is -$3.85.
What is account balance?
The amount of funds held in a financial institution, for example, a savings or checks account, at any particular time is known as the account balance. The net amount, which includes all debits and credits, is always the account balance.In order for a company's accounts to balance, debits and credits must be employed in the bookkeeping process. Credits raise liability, revenue, or equity accounts while decreasing asset or expenditure accounts. Credits operate in reverse.Lacey’s bank account balance = –$45.10
she deposits = $65.00
Debit card for a purchase = $23.75
Updated balance = –$45.10+$65.00-$23.75= -$3.85
Lacey's new balance in the account is -$3.85.
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In a company, %90 of the workers are men . If 500 people work for the company who aren't , how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.
Answers
90%=500x9=4500
4500+500=5000
or
90:10
9:1
4500:500=5000
5000 people
I NEED HELP ASP!! Which expression is equivalent to −2(5x + 3y)?
Answers
Answer:
-10x - 6y
Step-by-step explanation:
simplify - 2(5x + 3y): - 10x - 6y
-2(5x + 3y)
Apply the distributive law: a(b + c) = ab + ac
-2(5x + 3y) = -2 · 5x - 2· 3y
simplify -2 · 5x - 2· 3y : - 10x - 6y
therefore the answer is: = -10x - 6y
