Use a given information to create the equation for the rational function. The function is written in factored form to help you see how the given information shapes our equation. Enter the values for factor from smallest to largest.
Answers
we have that
the numerator is
a(x-1)(x-5)
where a is the leading coefficient of the numerator
the denominator is
(x+4)(x+1)
so
[tex]f(x)=\frac{a\mleft(x-1\mright)\mleft(x-5\mright)}{\mleft(x+4\mright)\mleft(x+1\mright)}[/tex]Find out the value of a
the y-intercept is (0,7)
substitute
[tex]7=\frac{a(0-1)(0-5)}{(0+4)(0+1)}[/tex][tex]7=\frac{a(-1)(-5)}{(4)(1)}[/tex][tex]\begin{gathered} 7=\frac{5a}{4} \\ a=\frac{28}{5} \end{gathered}[/tex]therefore
the numerator is (28/5)(x-1)(x-5)
and
the denominator is (x+4)(x+1)
Related Questions
What is the distance between (4,2) and (8,5)?Choose 1 answer:OT7C12V28
Answers
We need to use the Pythagorean theorem to solve this problem.
The points we have are:
(4,2) and (8,5)
Step 1. Label the coordinates as follows:
[tex]undefined[/tex]What is the approximate probability that a person will be a female and prefer suspense movies? MaleFemale Horror Movies 8294Suspense Movies1846Comedy Movies4891
Answers
Probability that a person will be a female and prefer suspense movies = 0.12
Explanation:Total number of males = 82 + 18 + 48 = 148
Total number of females = 94 + 46 + 91 = 231
Total population = 148 + 231 = 379
Number of females that prefer suspense movies = 46
Probability that a person will be a female and prefer suspense movies = 46/379
Probability that a person will be a female and prefer suspense movies = 0.12
The formula, F = 9/5C ×+ 32, converts temperatures between Celsius and fahrenheit degrees. What is the temperature in degrees Celsius that is equivalent to 50 degrees Fahrenheit?A) 9B) 10C) 11D) 12
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we have the formula
[tex]F=\frac{9}{5}C+32[/tex]in this problem we have
F=50
substitute
[tex]50=\frac{9}{5}C+32[/tex]Solve for C
[tex]\begin{gathered} \frac{9}{5}C=50-32 \\ \\ \frac{9}{5}C=18 \end{gathered}[/tex]C=(18*5)/9
C=10 degrees
the answer is option BSolve: - ( 2/3 a - 1/3) + 5/3a = -4.Solve the equation.
3
4
(2a − 6) + 1
2
= 2
5
(3a + 20)
a =
Answers
To solve the equation for a, we first apply the distributive property to the left side:
[tex]\begin{gathered} -\mleft(\frac{2}{3}a-\frac{1}{3}\mright)+\frac{5}{3}a=-4 \\ -\frac{2}{3}a+\frac{1}{3}+\frac{5}{3}a=-4 \end{gathered}[/tex]Now, we add similar terms on the left side of the equation:
[tex]\begin{gathered} \text{ Reorder} \\ -\frac{2}{3}a+\frac{5}{3}a+\frac{1}{3}=-4 \\ \mleft(-\frac{2}{3}+\frac{5}{3}\mright)a+\frac{1}{3}=-4 \\ \mleft(\frac{-2+5}{3}\mright)a+\frac{1}{3}=-4 \\ \frac{3}{3}a+\frac{1}{3}=-4 \\ 1\cdot a+\frac{1}{3}=-4 \\ a+\frac{1}{3}=-4 \end{gathered}[/tex]Now, we subtract 1/3 from both sides of the equation:
[tex]\begin{gathered} a+\frac{1}{3}-\frac{1}{3}=-4-\frac{1}{3} \\ a=-\frac{4}{1}-\frac{1}{3} \\ a=-\frac{4\cdot3}{1\cdot3}-\frac{1}{3} \\ a=-\frac{12}{3}-\frac{1}{3} \\ a=\frac{-12-1}{3} \\ \boldsymbol{a=-\frac{13}{3}} \end{gathered}[/tex]Therefore, the value of a that satisfies the equation is -13/3.
Answer:
a = 40
Step-by-step explanation:
Solve the formula Ax + By = C for x.A. X= C+ByAB. X= C-C. x = CFR+C-ByD. X=+ By
Answers
Step 1:
Write the equation
[tex]Ax\text{ + By = C}[/tex]Step 2:
To make x subject of the relation, you will need to solve for x.
[tex]\begin{gathered} Ax\text{ + By = C} \\ Ax\text{ = C - By} \\ \text{Divide through by A} \\ \frac{Ax}{A}\text{ = }\frac{\text{C - By}}{A} \\ \text{x = }\frac{\text{C - By}}{A} \end{gathered}[/tex]Final answer
[tex]\begin{gathered} \text{x = }\frac{\text{C - By}}{A} \\ \text{Option C} \end{gathered}[/tex]Simpson Office Furniture pays Donald Hughes a $720 monthly salary plus a 10% commission on merchandise he sells each month. Assume Donald's sales were S28,800 for last month.
Answers
Since the office pays 720 dollars monthly
Since the office gives a 10% commission on the amount of selling
Then Donald will earn = 720 + 10% of x
Where x is the amount of selling
Since the amount of selling is 28800 dollars for the last month, then
Then x = 28800
[tex]S=720+\frac{10}{100}(28800)[/tex]Then
[tex]\begin{gathered} S=720+2880 \\ S=3600 \end{gathered}[/tex]Then Donald earned last month 3600 dollars
sal is mixing plant food for his garden the plant food requires 5 and 1/2 gallons of water but sal's measuring container has marks for only pints how many pints of water should he use
Answers
Given:
the plant food requires 5 and 1/2 gallons of water
The measuring container has marks for only pints
So, we need to convert from gallon to pints
1 gallon = 8 pints
So, 5 1/2 gallons =
[tex]5\frac{1}{2}\cdot8=\frac{11}{2}\cdot8=44\text{ pints}[/tex]so, She will use 44 pints of water.
what is least amount of green ooze any one contestant carried? 0 1/8 1/4 3/8 1/2 5/8 3/4 7/8 1
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Given the information on the number line, the least amount of green ooze would be 1/4
What is the system of equations, and a example of them?
Answers
x = 2
y = 2
see explanation below
Explanation:Using an example of system of equations:
x + y = 4
2x + y = 6
The equations are above are two systems of equations having two unknown x and y. There are different methods to solve the two equations. We can use elimination method or substitution method.
In elimination method, we eliminate one of the variables in order to get the other variable.
In substitution variable, we substitute for one of the variables in any of the equations.
Using elimination method to solve the two equations, the variable we want to eliminate must have the same coefficient.
Let's eliminate y. This is because the coefficient of y is the same in both equation.
The coefficient of y is 1.
Note: if we want to eliminate x, we will need the coefficent of both to be the same. One coefficent is 1, the order is 2.
This means we would multiply equation 1 by 2 and multiply equation 2 by 1. This will ensure they have same coefficient of 2.
x + y = 4 ...equation 1
2x + y = 6 ...equation 2
subtract equation 1 from 2:
2x - x + y - (+y) = 6 - 4
2x - x + y - y = 6 -4
x + 0 = 2
x = 2
We replace 2 with x in any of the equations in order to get y.
using equation 1: x + y = 4
2 + y = 4
y = 4 - 2
y = 2
Find the missing number of each unit rate.48/3 = ?/1
Answers
ANSWER
16
EXPLANATION
We want to find the missing number in the unit rate.
Let the missing number be x.
We have that:
[tex]\frac{48}{3}=\text{ }\frac{x}{1}[/tex]We can find x, by simply dividing 48 by 3.
That is:
[tex]x\text{ = 16}[/tex]Therefore, the missing number is 16.
What is the solution to this system of equations? 10 y=x-4 y = -0.5x + 8 2 2 8 10 O A. (4,8) O B. (4,2) O C. (2,4) O D. (8,4) HELPPPPP
Answers
the given system of equations :
[tex]\begin{gathered} 10y\text{ = x -4} \\ y\text{ =-0.5x+8} \end{gathered}[/tex]we can solve this equations by using substitution method :
Simplify the equation (2) for y and substitute the value of y in equation (1)
[tex]\begin{gathered} y\text{ =-0.5x +8} \\ \text{The equation already shows the solution for the y} \\ \text{Substitute it to the first equation} \\ y=x-4 \\ (-0.5x+8)=x-4 \\ -0.5x+8=x-4 \\ \text{ x+0.5x=8+4} \\ 1.5x=12 \\ x=8 \end{gathered}[/tex]x = 8
now, put x = 8 in the second equation and solve for y
[tex]\begin{gathered} y=-0.5x+8 \\ y=-0.5(8)+8 \\ y=-4+8 \\ y=4 \end{gathered}[/tex]y = 4
Answer : D (x,y) = (8, 4)
I need help with this. There are 3 other options. 2 only. 1 only. Or none of the above.
Answers
Given: An expression-
[tex]\sqrt{36}+\sqrt{49}-\sqrt{16}[/tex]Required: To simplify the expression and determine the correct solution.
Explanation: The square root of a number can be simplified by factorizing the term inside the square root into the product of its factors as follows-
[tex]\sqrt{6\times6}+\sqrt{7\times7}-\sqrt{4\times4}[/tex]Now, we take out a number outside the square root from the pairs of numbers to give the following-
[tex]6+7-4=9[/tex]Also, we know that the square of 9 is 81. Hence,
[tex]\sqrt{81}=9[/tex]Hence, the given expression is equal to 9 and the square root of 81.
Final Answer: Option A (1 and 4) is correct.
Mr. Powers' chickens eat their food at a rapid pace. He calculated that theyeat 5 pounds of food each day. There is currently 128 pounds of chickenfood in their trough. When will the chickens run out of food? Round youranswer to the nearest day.*
Answers
Ok,
We have that they eat 5 punds of food per day, and there are currently 128 punds of food.
So, if they eat 5 pounds of foor a day, how many days will it take them to eat 128 punds of food:
[tex]5-->1\text{ \& 128}-->x[/tex]In order to solve for x, we multiply the total ammount of food (128 pounds) times the ammount of time it takes to eat five pounds (1 day) and divide by the ammount of pound they eat per day (5 pounds):
[tex]x=\frac{128Lb\cdot1D}{5Lb}\Rightarrow x=25.6D\Rightarrow x\approx26[/tex]So the food is going to be running out at about the 26th day.
Given y = -3 + 9 sin 7x , the amplitude is ___
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Solution
Step 1:
Amplitudedefinition}.
[tex]\mathrm{For\:f\left(x\right)=A\cdot \sin \left(Bx-C\right)+D\:the\:amplitude\:is\:|A|}[/tex]Step 2:
[tex]\begin{gathered} f\left(x\right)=-3+9\sin \left(7x\right),\:A=9 \\ \mathrm{Therefore,\:\:the\:amplitude\:|A|\:is\:}9 \\ 9 \end{gathered}[/tex]Final answer
Amplitude is 9
Solve the equation. Check your solution. x/6+x/3=3/4-2/3-3/2-5/6-6/5-2/23-23/2
Answers
Solution:
This is a fractional algebraic equation.
To solve it, we simplify the left-hand side of the equation as a single fraction and then equate to the right-hand side to get the solution.
[tex]\begin{gathered} \frac{x}{6}+\frac{x}{3}=\frac{3}{4} \\ \\ U\sin g\text{ the Lowest Common Multiple (LCM) of the left-hand side,} \\ \text{The }LCM\text{ is 6} \\ \frac{x+2x}{6}=\frac{3}{4} \\ \frac{3x}{6}=\frac{3}{4} \\ \text{Cross multiplying the equation;} \\ 4\times3x=3\times6 \\ 12x=18 \\ \text{Dividing both sides by 12;} \\ x=\frac{18}{12} \\ x=\frac{3}{2} \end{gathered}[/tex]Therefore, the solution to the equation is;
[tex]x=\frac{3}{2}[/tex]Picture Perfect a photo company sells prints in venous sizes. The cost of 4Y6 prinis can be represented by y= 25X-2 where is the number of prints oroered. Max is going to order between 15 and 20 4x6 prints The domain for this stuaron is
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y = 25x - 2
the above equation represent the cost of 4Y6 prints
he wants to order between 15 and 20 of 4Y6 prints
the minimum is 15 and maximum is 20
x could be 15 or 20
Y = 25(15) - 2
y = 375 - 2
y = 373
for x = 20
y = 25(20) -2
y = 500 - 2
y = 498
I need help with this practiceI am brand new to this type of math, please explain and tutor me step-by-step (with words as well)*I’m also trying to find the most efficient way to solve this Thank you in advance. I’ll be taking notes with a pencil and paper as you work, so please take your time no need in rushing
Answers
If 5x=55, x+y=23 and y-z=2 we need to find the value of (2x+y)/z
To get the last value, we need to know the value for each variable, it means we need to know the value for x, the value for y and the value for z.
You have three equations and from these equations, you need to get the values for the variables.
We have the following
[tex]5x=55[/tex][tex]x+y=23[/tex]and
[tex]y-z=2[/tex]We can notice that almost all the equations have two variables, with exception of the first one. For example, the second one has the variables x and y, and the last equation has the variables y and z. So, the first thing that we are going to do, is to choose the equation which has less variables than the other equations. So we'll work with 5x=55.
To get x apart from the numbers we can divide in both sides by 5, as follows
[tex]5x=55\leftrightarrow\frac{5x}{5}=\frac{55}{5}[/tex]Then
[tex]\frac{5x}{5}=x[/tex]and on the other hand
[tex]\frac{55}{5}=11[/tex]Then
[tex]x=\frac{5x}{5}=\frac{55}{5}=11,\text{ }\leftrightarrow x=11[/tex]Now, we've got that x=11.As we have one value, we need to look for the other equations and try to change the x by its numerical value. We notice that now we only have two equations, the second one and the third one.
[tex]x+y=23[/tex]and
[tex]y-z=2[/tex]Since the third equation doesn't have an x, we need to use the second one, i.e. x+y=23 and put the numerical value for x. Then
[tex]x+y=23\leftrightarrow11+y=23[/tex]Now, once again we get an equation with only one variable, it means that we can solve it.
[tex]11+y=23[/tex]To apart the y from the numbers, we can substract 11 from both sides to get
[tex]11+y-11=23-11[/tex]On the left hand side we get
[tex]11+y-11=y[/tex]and from the right hand side we have
[tex]23-11=12[/tex]Then,
[tex]y=11+y-11=23-11=12\leftrightarrow y=12[/tex]Now, we got that y=12.Now, we only have to solve the last equation,
[tex]y-z=2[/tex]As we found the value for y=12, we can use it to get a new equation and get the value for z.
[tex]y-z=2\leftrightarrow12-z=2[/tex]So, after changing the value of y, we get
[tex]12-z=2[/tex]Once more time, we have gotten an equation with one variable. In this case we are going to apart the z, from the numbers.
The first thing to do is substract 12 from both sides. Then
[tex]12-z-12=2-12[/tex]For the Left hand side we will get
[tex]12-z-12=-z[/tex]and for the right hand side we get
[tex]2-12=-10[/tex]Then
[tex]-z=12-z-12=2-12=-10\leftrightarrow-z=-10[/tex]We've gotten that -z=-10, but we need to get the value for z, so we need to do one step more. In this case, you need to multiply in both sides by -1
[tex](-1)(-z)=(-1)(-10)[/tex]Then
it means that the value for z is 10. z=10To get the answer for the expression
[tex]\frac{2x+y}{z}[/tex]we need to replace the values x=11, y=12, z=10
[tex]\frac{2x+y}{z}=\frac{2(11)+12}{10}=\frac{22+12}{10}=\frac{34}{10}[/tex]and by simplifying we get that
[tex]\frac{2x+y}{z}=\frac{34}{10}=\frac{17}{5}[/tex]So your answer is 17/5Use the simple interest formula to determine the missing value.p = $960.95, r=4.5%, t= ?, i = $302.70t = years(Do not round until the final answer. Then round to the nearest whole number as needed.)
Answers
simple interest formular
S.I = p x r x t/100
where p is the principal
r is the rate
t is the time
so,
p = 960.95
r = 4.5
t = not given
I = 302.70
so making t subject of formula from the main formula
t = I x 100/p x r
t = 302.70 x 100/960.95 x 4.5
t = 30270/4324.275
t = 6.99
t = 7years to the nearest whole number
Question 131 f(x) = x2 and g(x) = 2x + 3, what is f(g(x))?x2 + 2.0 + 3AB20c2 +3С4.2 +9D4.2 + 12x + 9
Answers
We need to know what is the composition function
[tex]\begin{gathered} f(g(x))=(g(x))^2=(2x+3)^2 \\ =4x^2+12x+9 \end{gathered}[/tex]One liter is approximately 34 ounces. A 2-liter soda bottle can hold how many 12-ounce cans of soda?A Between 1 and 2B Between 3 and 4C Between 5 and 6D Between 6 and 7
Answers
1 liter is approximately 34 ounces according to your question. The amount of 12 ounce cans of soda a 2 liter soda bottle can hold can be calculated below
[tex]\begin{gathered} 1\text{ liter = 34 ounces} \\ 2\text{ liters = ?} \\ \text{cross multiply} \\ \text{amount in ounces = 34}\times2=68\text{ ounces} \\ \frac{68}{12}=5.6667 \\ it\text{ can betw}een\text{ 3 to 4 } \end{gathered}[/tex]if you have a 30 60 90 triangle and the hypothesis is a what are the lengths of the triangle of the other two sides
Answers
The triangle is given with angles, 30, 60 and 90 degrees. Since only one side is given, we shall find the other two sides one after the other by applying the Trigonometry ratios.
Using the angle30 as the reference angle,
Sin 30 = Opposite/ Hypotenuse
Note that the hypotenuse (longest side) has been provided as 8, and the opposite is the side facing the reference angle. Since we have chosen 30 as the reference angle, the side facing angle 30 shall be the opposite.
Sin 30 = Opposite/8
By cross multiplying you now have,
Sin 30 * 8 = Opposite
By use of calculator, Sin 30 equals 0.5
0.5 * 8 = Opposite
4 = Opposite
Now that two of the sides have been calculated, we can further calculate the third side by either use of Pythagoras theorem or the Trigonometry ratios
The Triangle now has three angles named and two sides named as follows;
Sin 60 = Opposite/Hypotenuse
Sin 60 = Opposite/8
Sin 60 in the calculator is given as 0.8660
0.8660 * 8 = Opposite
6.928 = Opposite
Opposite is approximately 7 units
The triangle below is an equilateral triangle. Find yy = 10y = 180y = 7y = 13
Answers
Solution
For this case we have the following
y+3 = x = 10
Then x= 10
So we can set up this equation:
y+3 = 10
y= 7
Then the answer is:
y=7
Which category best fits this group of shapes what do you think the answer is
Answers
-Parallelograms are quadrilaterals with two pairs of parallel sides.
-Rectangles are quadrilaterals with two pairs of parallel sides, and the opposite sides are equal.
-Rhombus are quadrilaterals with four congruent sides, and 4 acute angles.
-Trapezoids are quadrilaterals with only one pair of parallel sides.
Considering the shapes given, two of them the green and the orange shapes, are trapeziums, and the third shape is a rectangle.
The group that best fits this group of shapes, considering that the three have at least one pair of parallel sides, is the "trapezoids" group
To become a member at a local nature preserve, applicants must pay an initiation fee of $100 plus their yearly membership dues , as shown in the graph . What is the slope of the line joining these points, and what does the slope represent?
Answers
The points are (2,150), (4,200).
The slope of the line joining the points is,
[tex]\begin{gathered} m=\frac{200-150}{4-2} \\ =25 \end{gathered}[/tex]Thus, the slope represents the increse in cost per year of membership.
According to the authors of a certain book, in a global village of 200 people, 28 suffer frommalnutrition. How many people of the world's 6.9 billion people (2010 population) sufferfrom malnutrition?
Answers
Let the number be x
Then
[tex]\begin{gathered} x=\frac{28}{200}\times6.9\times10^9 \\ =966000000 \end{gathered}[/tex]Hence 0.966 billion people suffered malnutrition
Which is 1 billion people
If you don't have a fraction calculator, what can you do to change a fraction to its decimal form?
Answers
EXPLANATION
If we do not have a fraction calculator, we can aaply the following relationship in order to get the decimal form:
If the number is for instance 7/100, then:
Consider the numerator
Then mark the decimal point after one place or two places or three places from right towards left if the given fraction's denominator is 10, 100 or 1000, respectively.
So, in this case 7/100 should be represented as follows:
7/100 = 0.07 [The denominator has two zeros]
But if we have 77/100
The decimal number is 77/100 = 0.77 [because the numerator has two numbers]
If we have the number 999/1000 the decimal number is 0.999
let the graph GPA horizontal shrink by a factor of four, followed by a translation two units up of the graph of f(x)=x^3-6x-1
Answers
By the rules of transformation of functions, you know that
*f(bx), where b>1, the function shrinks the curve horizontally by a factor of b.
*f(x)+k moves the function k units up
So, in this case, you have
*b=4 and
*k=2
[tex]\begin{gathered} g(x)=f(bx)+k \\ g(x)=f(4x)+2 \\ f(x)=x^3-6x-1 \\ g(x)=(4x)^3-6(4x)-1+2 \\ g(x)=64x^3-24x+1 \end{gathered}[/tex]To verify you can graph the functions f(x) and g(x), like this
Therefore, the function g(x) is
[tex]g(x)=64x^3-24x+1[/tex]The dimensions of a rectangle are 5x+3 and 4x - 6. Write an expression that represents the perimeter the rectangle.
Answers
The perimeter of a Rectangle.
[tex]\begin{gathered} Perimeter\text{ of a rectangle = 2(L+}B) \\ \text{ P = 2\lbrack(5x+3)}+(4x-6)\rbrack \\ P=2(5x+3+4x-6) \\ P=\text{ 2(5x+4x+3-6)} \\ P=2(9x-3) \\ P=18x-6 \end{gathered}[/tex]The correct expression for the required perimeter is 18x - 6
i need help solving this equation for x(5^x/6) (5^x/2) = 5^16
Answers
Given equation:
[tex]\begin{gathered} (5^{\frac{x}{6}})(5^{\frac{x}{2}})\text{ = 5}^{16} \\ 5^{\frac{2x}{3}}\text{ = 5}^{16} \\ \frac{2x}{3}=16 \\ x\text{ = 24} \end{gathered}[/tex]During the summer months, Kaleb consumes large quantities of sports drinks. In terms of cost per ounce,which of the following is the best way for him to purchase his drinks?8 oz. bottles for $0.4912 oz. bottles for $0.6920 oz. bottles for $0.9932 oz. bottles for $ 1.59
Answers
Given:
8 oz. bottles for $0.49
12 oz. bottles for $0.69
20 oz. bottles for $0.99
32 oz. bottles for $ 1.59
Required:
We need to find the best way for him to purchase his drinks.
Explanation:
Here we need to find the cost per oz for this
take
8 oz. bottles for $0.49
so 1 oz. bottles for ?
[tex]\frac{1*0.49}{8}=0.06125[/tex]similarly for all
[tex]\frac{1*0.69}{12}=0.0575[/tex][tex]\frac{1*0.99}{20}=0.0495[/tex][tex]\frac{1*1.59}{32}=0.0496875[/tex]Final answer:
best way for him to purchase his drinks is 20 oz. bottles for $0.99