Which expression is equivalent to the following complex fraction?ХX-3x2-9X-3X+ 31X+ 3ХOХX+3
Answers
To solve the given fraction, we have to multiply the extremes parts and the inner parts between each other.
[tex]\frac{x(x^2-9)}{x^2(x-3)}[/tex]Then, we factor the numerator
[tex]\frac{x(x+3)(x-3)}{x^2(x-3)}[/tex]At last, we simplify
[tex]\frac{x+3}{x}[/tex]Hence, the answer is the third option.Related Questions
Find the equation of the line with the given properties. Sketch the graph of the line. The line passes through (-1.6,4.4) and is parallel to the x-axis. (Simplify)
Answers
Given the point:
(-1.6, 4.4)
Let's find the equation of the line which passes through the given point and is parallel to the x-axis.
Since the line is parallel to the x-axis, the line is a horizontal line located at the y-coordinate of the point.
Therefore, the equation of the line will be:
y = 4.4
To sketch the graph, let's draw a horizontal line that passes through the point: y = 4.
The graph is shown below:
A person stands 5 meters from a building. The angle of elevation to the top of the building is 75°. Find the height of the building to the nearest tenth.
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Using the information given in the exercise, you need to draw the following Right triangle (It is not drawn to scale):
Where "h" is the height of the building in meters.
To find the height, you can use the following Trigonometry Identify:
[tex]\tan \alpha=\frac{opposite}{adjacent}[/tex]In this case:
[tex]\begin{gathered} \alpha=75\degree \\ opposite=h \\ adjacent=5 \end{gathered}[/tex]Then, you can substitute values and solve for "h". This is (rounded to the nearest tenth):
[tex]\begin{gathered} \tan (75\degree)=\frac{h}{5} \\ \\ 5\cdot\tan (75\degree)=h \\ h=18.66 \\ h\approx18.7 \end{gathered}[/tex]The answer is:
[tex]18.7\text{ }meters[/tex]use the given graph of y=-3/2x+3 to solve the following equations. a) solve: 9= -3/2x+3b) solve: -3= -3/2x+3
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The equation of the line is:
[tex]y=-\frac{3}{2}x+3[/tex]This equation is equal to "9" in part (a) and "-3" in part (b).
How do we solve the equation in part(a) and part(b) using graph?
We look at y = 9 and see at which x value it intersects with the graph.
Similarly, we look at y = -3 and see at which x value it intersects with the graph.
a)
We draw a horizontal line at y = 9. The point where it intersects the line drawn, we draw a vertical line to connect to the x-axis. So, it connects at x = -4. This is the solution. Let's check it algebraically as well.
[tex]\begin{gathered} 9=-\frac{3}{2}x+3 \\ \frac{3}{2}x=3-9 \\ \frac{3}{2}x=-6 \\ x=-\frac{6}{\frac{3}{2}} \\ x=-6\times\frac{2}{3} \\ x=-4 \end{gathered}[/tex]b)
We draw a horizontal line at y = -3. The point where it intersects the line drawn, we draw a vertical line to connect to the x-axis. So, it connect at x = 4. Tis is the solution. Let's check algebraically:
[tex]\begin{gathered} -3=-\frac{3}{2}x+3 \\ \frac{3}{2}x=3+3 \\ \frac{3}{2}x=6 \\ x=\frac{6}{\frac{3}{2}} \\ x=6\times\frac{2}{3} \\ x=4 \end{gathered}[/tex]what is the value of 88.25 - 43.5
Answers
Given:
88.25 - 43.5
To find the value:
On solving we get,
[tex]88.25-43.5=44.75[/tex]Thus, the answer is 44.75.
1. Write out a detailed proof of the fact that, given two numbers in scientific notation, a x 10^n and b x 10^n, a < b, if and only if a x 10^n < b x 10^n
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A Gas station A charges $3.50 per gallon of gas plus $8 for a car wash. Gas station B charges $3.25 per gallon of gas plus $10 for a car wash. How many gallons of gas must a customer purchase for the total cost to be the same at both gas stations?
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Gas station A
let number of gallon = x
let number of car = y
A positive B negative C zeroD the parabola opens upE the parabola opens up F the parabola opens down
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Solution
Step 1:
The general parabolic function is given as:
[tex]\text{y = ax}^2+bx+c[/tex]If a is positive, the parabola is upward.
If a is negative, the parabola is downward.
Step 2
The c-value is where the graph intersects the y-axis. In this graph, the c-value is -3. The graph of a parabola that opens up looks like this. The c-value is where the graph intersects the y-axis.
Step 3:
Finally, the c-value can also be called the y-intercept of the parabola. Algebraically, this is where the x-value is zero and graphically, this is where the graph intersects the y-axis.
Final answer
The c value of the function represented in the graph is -3 because the parabola opens up.
2. The movie shop sells posters for $7, DVDs for $15, and CDs for $9. Write 20 points an algebraic expression to represent the total cost for 2 posters, d DVDs, and c CDs.
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According to the information given in the exercise, you know that "d" represents the number DVDs and "c" represents the number of CDs.
Using the information given in the exercise, you know that the cost for "d" DVDs sold can represented as:
[tex]15d[/tex]And the cost of "c" CDs sold can be represented as:
[tex]9c[/tex]You also know that the cost of 2 posters of $7 each, is:
[tex]2(7dollars)=14dollars[/tex]Then, you can identify that the total cost for 2 posters, "d" DVDs and "c" CDs can be found by adding all the costs. Therefore, you can write the following expression to represent this:
[tex]2(7)+15d+9c[/tex]If you simplify it, you get:
[tex]=14+15d+9c[/tex]The answers are: First option and Second option.
A. Input 3, output 0B. Input 4, output 5C. Input -3, output 0D. Input 2, output 3
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The input of a function is the x-value, and the ouput is the corresponding y-value.
From the given options the one that correspond to the function in the graph is:
Input 4, output 5Question Details A car is traveling down a highway at a constant speed, described by the equation d = 65t, where d represents the distance, in miles, that the car travels at this speed in thours. time(t) distance (d) Answer these two questions by FILLING OUT the table provided. 1. How many miles does the car travel in 1.5 hours? 2. How long does it take the car to travel 26 miles at this speed?
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Answer:
(1). 97.5 miles
(2). 0.4 hours
Explanation:
(1).
We are asked what is the value of d when we put in t = 1.5 in the formula.
Putting in t = 1.5 in d = 65t gives
[tex]d=65(1.5)[/tex][tex]d=97.5\text{miles.}[/tex]Hence, the car travels 97.5 miles in 1.5 hours.
(2).
In this case, we are told that d = 26 miles and we are asked to find t.
Putting in d = 26 into the formula gives
[tex]26=65t[/tex]we solve for t by dividing both sides by 65 to get
[tex]t=0.4\text{hours}[/tex]Hence, it takes the car 0.4 hours to travel 26 miles.
Which formula do I use and how do I key it in on my calculator
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Modeling population growth:
Being Po the initial population, K the carrying capacity (or maximum capacity), and r the growth rate, The model for the population at a time t is:
[tex]P(t)=\frac{K}{1+\left(\frac{K-P_o}{P_o}\right)e^{-rt}}[/tex]For the problem, we are given Po = 300, r = 40% = 0.4, K = 3600. Substituting, we get the model:
[tex]P(t)=\frac{3600}{1+\left(\frac{3600-300}{300}\right)e^{-0.4t}}[/tex]Operating:
[tex]P(t)=\frac{3600}{1+11e^{-0.4t}}[/tex]For t = 4 years:
[tex]P(4)=\frac{3600}{1+11e^{-0.4\times4}}[/tex]Calculating:
P(4) = 1118
Answer: 1118 trout
Note: The result above was rounded to the nearest whole number
You spin the spinner twice what is the probability of landing on a number less than 6 and then landing on a 3
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The spinner has a total of 7 numbers, from 3 to 9.
The numbers that are less than 6 are the numbers 3, 4 and 5 (three numbers).
So the probability of the spinner landing on a number less than 6 is P1 = 3/7.
Then, the probability of the spinner landing on a 3 is P2 = 1/7 (just one number three among 7 options).
So the final probability is:
[tex]P=\frac{3}{7}\cdot\frac{1}{7}=\frac{3}{49}[/tex]The equations of 2 lines are shown below. 2x - y = 2 3x + 4y = 25 What is the product of (x.y) of the point of intersection?
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Question:
The equations of 2 lines are shown below. 2x - y = 2 3x + 4y = 25 What is the product of (x.y) of the point of intersection?
Solution:
Consider the following line equations:
Equation 1
[tex]2x-y\text{ = 2}[/tex]Equation 2:
[tex]3x+4y\text{ = 2}5[/tex]Now, solving equation 1 and equation 2 for the variable y, we get:
Equation 3:
[tex]y\text{ = 2x-2}[/tex]and
Equation 4:
[tex]y\text{ = -}\frac{3}{4}\text{x +}\frac{25}{4}[/tex]now, if we relate equations 3 and 4 we obtain:
[tex]2x-2\text{ = -}\frac{3}{4}\text{x +}\frac{25}{4}[/tex]this is equivalent to:
[tex]2x\text{ + }\frac{3}{4}x\text{ = }\frac{25}{4}+2[/tex]this is equivalent to:
[tex]\frac{11}{4}x\text{ = }\frac{33}{4}[/tex]this is equivalent to:
[tex]11x\text{ = 33}[/tex]this is equivalent to:
[tex]x\text{ = }\frac{33}{11}=\text{ 3}[/tex]then:
[tex]x\text{ = 3}[/tex]now, replacing this in equation 3, we get:
[tex]y\text{ = 2(3)-2 = 6-2 = 4}[/tex]thus
[tex]y\text{ = 4}[/tex]Thus the point of the intersection is (x,y) = (3,4) and we can conclude that the product of x = 3 and y = 4 is :
[tex]x\text{ . y = 3 . 4 = 12}[/tex]phil needs to run at least 30miles30miles this weekweek for his training if he has already ran a⋅18milesa⋅18miles as we've been how many milesmiles should you run on each of the 33 remaining dayday this week
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answer: 4 miles per day
find the odds against of randomly selecting a queen from a standard check of cards
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We have to find the odds ofrandomly selecting a queen from a standard check of cards.
We can calculate the odds as the probability that the event will occur divided by the probability that the event will not occur.
In this case, we know we have 4 queens in a total of 52 cards.
Then, we have a probability of 4/52 to select a queen and (52-4)/52= 48/52 of not selecting a queen.
Then, we can calculate the odds as:
[tex]\begin{gathered} odds=\frac{P(queen)}{P(notqueen)} \\ \\ odds=\frac{4/52}{48\/52}=\frac{4}{48}=\frac{1}{12} \end{gathered}[/tex]The odds are then 1:12 or 1 in 12.
Answer: the odds for selecting a queen aoe 1:12.
A person places $13900 in an investment account earning an annual rate of 2.8%, compounded continuously. Using the formula V=PertV=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 18 years.
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The Solution:
Given the formula:
[tex]V=Pe^{rt}[/tex]We are required to find the amount in the account after 18 years.
In this case,
[tex]\begin{gathered} V=\text{ ?} \\ P=\text{ \$13900} \\ r=2.8\text{\%}=0.028 \\ t=18\text{ years} \end{gathered}[/tex]Substituting these values in the above formula, we get
[tex]V=13900e^{0.028\times18}=23009.078\approx\text{ \$23009.08}[/tex]Therefore, the correct answer is $23009.08
A biologist has been observing a tree's height. Thirteen months into the observation, the tree was 21.74 feet tall. Sixteen months into the observation, the tree was 22.58 feet tall. What is the rate at which the tree is growing? In other words, what is the slope if you plotted height versus time? Use ft for feet and mo for months.
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we have two values of time and height
these could serve as our x and y
[tex]\begin{gathered} x_1=13,y_1=21.74_{} \\ x_2=16,y_2=22.58 \end{gathered}[/tex]to find the tree's growth rate, we find the slope.
[tex]=\frac{y_2-y_1}{x_{2-}x_{1_{}}}\text{ =}\frac{22.58\text{ - 21.74}}{16\text{ -13}}=\frac{0.84}{3}=\text{ 0.28 f}t\text{ /mo}[/tex]7) What is the solution of the system of equations? Show your work y = -5x + 7 y = -2x + 1
Answers
ANSWER
x = 2; y = -3
EXPLANATION
We have two equations given:
y = -5x + 7
y = -2x + 1
We can equate both equations because they both yield y.
That is:
-5x + 7 = -2x + 1
Collect like terms:
7 - 1 = -2x + 5x
=> 3x = 6
Divide through by 3:
x = 6/3
x = 2
From the first equation:
y = -5(2) + 7
y = -10 + 7
y = -3
Therefore, the solution to the system of equations is x = 2 and y = -3
(G.12, a points) A circle has a center at (-6.5) and a radius of 8 units. Create the equation of this circle (x + 6² (y + 5) 42 (y - 5) 82 (x - h) (-k) 72
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Information given:
Center at (-6, 5)
Radius= 8 units.
A circle is represented by the following expression:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{where, } \\ (h,k)\text{ is th center} \\ r\text{ is the radius} \end{gathered}[/tex]Then, the equation of this circle would be:
[tex](x+6)+(y-5)=8^2[/tex]What is 2 times 2 equal to
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You have the exercise "2 times 2". The word "times" indicates that it is a Multiplication. Then, you can rewrite this operation in the following form:
[tex]2\cdot2[/tex]That Multiplication indicates that you need to add 2 two times, as follows:
[tex]2+2[/tex]Therefore, based on the explained, you can determine that:
[tex]2\cdot2=2+2=4[/tex]Hence, the answer is:
[tex]4[/tex]Mikey's family is taking a road trip. Their car can travel no more than 260 miles without needing to refill the gas tank. They have traveled 112 miles since they last filled the gas tank.Mikey knows that the inequality representing this situation is 112+x≤260.Select from the drop-down menu to correctly interpret the solution of this inequality.Mikey's family can drive Choose... more miles before they need to refill the gas tank.
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148 more miles before they need to refill the gas tank.
1) Considering that the inequality that represents this situation is:
[tex]112+x\leq260[/tex]Notice that in this equation "x" stands for the number of miles that he needs to finish the trip.
2) So we can solve that to find out the number of miles Mikey's family can make with the gas already in the car:
[tex]\begin{gathered} 112+x\leq260 \\ 112-112+x\leq260-112 \\ x\leq148 \end{gathered}[/tex]Note that we have subtracted 112 from both sides.
3) Hence, the answer is:
Mikey's family can drive up to 148 miles before they need to refill the gas tank
Scott mows 25 lawns. He took a survey to see how many people are satisfied with his services and found that 85% thought he did a good job or better. About how many people were not satisfied with Scott’s work
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Given that Scott mows 25 lawns and 85% thought he did a good job or better.
the percentage of those that are not satisfied with his job is;
[tex]100-85=15\text{\%}[/tex]The number of people that are not satisfied with his job is;
[tex]\begin{gathered} n=15\text{\% of 25}=0.15\times25 \\ n=3.75 \\ n\approx4 \end{gathered}[/tex]Carson wants to use a sheet of fiberboard 29 inches long to create a skateboard ramp with a 19∘angle of elevation from the ground. How high will the ramp rise from the ground at its highest end? Round your answer to the nearest tenth of an inch if necessary.
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The length of the highest point is 9.98 inches.
What is the height?We know that the angle of elevation is the angle that the ramp makes with the ground. Recall that in order to solve thus problem we would have to refer to the geometry of the right angled triangle in this case.
Given that;
tan 19 = opposite/ adjacent
Adjacent = 29 inches long
Opposite = ??
Opposite = 29 tan 19
= 9.98 inches
We can see that the length of the highest part of the ramp from the calculations that we have just made is obtained as 9.98 inches.
Learn more about angle of elevation:https://brainly.com/question/21137209
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write the fractions in order from least to greatest 1/5,2/3,5/8
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The least count of the denominators of the fractions
Prealgebra- Determine whether the lines passing through the pairs of points are parallel, perpendicular, or neither
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It is important to note the following:
• If the slopes of the two lines are equal, they are parallel.
,• If the slopes of the two lines are negative reciprocal of each other, they are perpendicular.
Let's now calculate the slope of each line. Use the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's start with line 1.
[tex]m=\frac{1-13}{-8-1}\Rightarrow m=\frac{-12}{-9}\Rightarrow m=\frac{4}{3}[/tex]The slope of line 1 is 4/3.
Let's move on to line 2.
[tex]m=\frac{\frac{5}{3}-(-1)}{5-3}\Rightarrow m=\frac{\frac{8}{3}}{2}\Rightarrow m=\frac{4}{3}[/tex]The slope of line 2 is also 4/3.
Since the slopes of the two lines are the same, then the two lines are parallel.
The slope indicates how fast y increases or decreases as x increases.TrueFalse
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Slope (m) = rise / run = Δy /Δx
Slope is a measure of the stepness of a line, Change of y as x increases or decreases.
Answer: True
Two pools are being drained. To start, the first pool had 3650 liters of water and the second pool had 4166 liters of water. Water is being drained from the first pool at a rate of 27 liters per minute. Water is being drained from the second pool at a rate of 39 liters per minute.Let x be the number of minutes water has been drained.(Photo includes Questions)
Answers
The first pool has 3650 liters of water.
The second pool has 4166 liters of water.
It is also given that water drained from first pool at a rate of 27 liters per minute.
The water drained from the second pool at a rate of 39 liters per minute.
Explanationa. Let the x be the number of minutes water has been drained.
The amount of water in the first pool in liters
[tex]3650-27x[/tex]The amount of water in the second pool in liters
[tex]4166-39x[/tex]b. To determine the equation when both the pools has same amount of water.
[tex]\begin{gathered} 3650-27x=4166-39x \\ 39x-27x=4166-3650 \\ 12x=516 \\ x=43 \end{gathered}[/tex]Answera. The amount of water in first pool in liters is 3650-27x.
The amount of water in second pool in liters is 4166-39x.
b. The equation when both the pools has same amount of water is x=43.
Tim and Max are going bowling. They need to choosebetween two different bowling alleys. Bowler Worldcharges $3.00 to rent shoes and $3.75 per game.Lucky Spares charges $4.00 to rent shoes and $3.25per game.What would be the total cost of renting shoes andbowling 5 games at Bowler World? Type your answerin the text input box below.
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Answer: $21.75
Bowler World charges $3.00 to rent shoes and $3.75 games
Let the number of games be = x
Total cost = Charges to rent shoes + charges per game x number of games
Total cost = 3 + 3.75 * x
Total cost = 3 + 3.75x
Total cost of renting shoes and bowling 5 games at Bowler world can be calculated as follows
Total cost = 3 + 3.75 x 5
Total cost = 3 + 18.75
Total cost = $21.75
Therefore, the total cost of renting shoes and bowling 5 games at Bowler World is $21.75
The hyperbolic orbit of a comet is represented on a coordinate plane with center at (0, 4). One branch has a vertex at (0, 10) and its respective focus at (0, 14). Which equation represents the comet's orbit?
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Remember that
If the given coordinates of the vertices and foci have the form (0,10) and (0,14)
then
the transverse axis is the y-axis
so
the equation is of the form
(y-k)^2/a^2-(x-h)^2/b^2=1
In this problem
center (h,k) is equal to (0,4)
(0,a-k)) is equal to (0,10)
a=10-4=6
(0,c-k) is equal to (0,14)
c=14-4=10
Find out the value of b
b^2=c^2-a^2
b^2=10^2-6^2
b^2=64
therefore
the equation is equal to
(y-4)^2/36-x^2/64=1the answer is option AAnswer: The final answer
Step-by-step explanation:
The equation representing the hyperbolic orbit of a comet can be determined using the standard form of the equation for a hyperbola with a vertical transverse axis. The center is given as (0, 4), the vertex of one branch is (0, 10), and the focus is (0, 14). By plugging these values into the standard form equation and solving for b^2, we get the equation (y - 4)^2 / 36 - x^2 / (y - 14) = 1. Simplifying this equation gives the final answer, which is x^2 / 64 - (y - 4)^2 / 36 = 1, or the final answer. :)
pls help me and no fake answer i really need help :(Show that the volume of the solid of revolution formed by revolving the region bounded by the graph of f(x) = (3x+5)^3, x =0 and x = 1 about the x-axis is 1/21 (8^7 -5^7) pi unit^3
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Solution
Given the function
[tex]f(x)=(3x+5)^3[/tex]If we graph the equation, we would have.
when x = 0, f(x) = 5^3 = 125
when x = 1, f(x) = 8^3 = 512
Hence, the solid of revolution is given by
[tex]V=\pi\int_0^1(3x+5)^6dx[/tex]Evaluating the integral
[tex]\begin{gathered} V=\frac{\pi}{7\times3}[(3x+5)^7]\text{ from 0 to 1} \\ \\ \end{gathered}[/tex][tex]\Rightarrow V=\frac{\pi}{21}(8^7-5^7)\text{ unit}^3[/tex]