Which of the following is equal to the rational expression below when x+112x² – 121x +11A. +11B.X+ 11c. -11XD. X-11
Answers
SOLUTION
From the question we have
[tex]\frac{x^2-121}{x+11}[/tex]from difference of two squares, we have
[tex]\begin{gathered} \frac{(x-11)(x+11)}{x+11} \\ x+11\text{ above cancels the one below, we have } \\ x-11 \end{gathered}[/tex]Hence the answer is option D
Related Questions
Tools Pencil Guideline Eliminator Sticky Notes Formulas Graphing Calculator Graph Paper Х y 5 Clear Mark 3 -4.5 5 -9.5 7 - 14.5 9 - 19.5 What are the slope and the y-intercept of the graph of this function? A Slope = 2, y-intercept = -4.5 5 B Slope = y-intercept = 3 2 © Slope = 2, y-intercept = -5 D Slope = 2 5 y-intercept = 3
Answers
Explanation:
The equation for a line in the slope-intercept form is:
[tex]y=mx+b[/tex]Where 'm' is the slope and 'b' is the y-intercept.
We can find both with only two points from the line. The slope is:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_1-y_2}{x_1-x_2}[/tex](x1, y1) and (x2, y2) are points on the line.
With only one of these points, once we know the slope, we can find the y-intercept by replacing x and y by the point. For example:
[tex]y_1=mx_1+b[/tex]And then solve for b.
In this problem we can use any pair of points from the table. I'll use the first two:
• (3, -4.5)
,• (5, -9.5)
The slope is:
[tex]m=\frac{-4.5-(-9.5)}{3-5}=\frac{-4.5+9.5}{-2}=\frac{5}{-2}=-\frac{5}{2}[/tex]And the y-intercept - I'll use point (3, -4.5) to find it;
[tex]\begin{gathered} -4.5=-\frac{5}{2}\cdot3+b \\ -4.5=-\frac{15}{2}+b \\ b=-4.5+\frac{15}{2}=-\frac{9}{2}+\frac{15}{2}=\frac{6}{2}=3 \end{gathered}[/tex]Answer:
• Slope: -5/2
,• y-intercept: 3
The correct answer is option B
Calculate the probabilities of each of these situations. A standard deck of cards has 52 cards and 13 cards cards in each suit (Spades, Clubs, Hearts, & Diamonds). Which of the following is LEAST likely to occur? a) Selecting any spade card from a standard deck of cards, keeping it, then selecting the queen of hearts. b) Selecting a spade from a standard deck of cards, not putting it back, then selecting another spade. c) Selecting an ace from a standard deck of cards, not replacing it, then selecting a king.Event CEvent AEvent B
Answers
Answer
The least likely to occur is Event C
Explanation
A.
P(spade card) = 13/52
P(queen) = 4/51 Note: Without replacement
⇒ 13/52 x 4/51
= 52/2652
= 0.0196
B.
P(a spade) = 13/52
P( another spade) = 12/51 Note: Without replacement
⇒ 13/52 x 12/51
= 156/2652
= 0.0588
C.
P(an ace) = 4/52
P(king) = 4/51
⇒ 4/52 x 4/51
= 16/2652
= 0.006
∴ The least likely to occur is Event C
5)Which of the following is a critical number of the inequality x^2+5x-6<0 ?
Answers
Answer:
B. 1
Explanation:
Given the inequality:
[tex]x^2+5x-6<0[/tex]To find the critical number, first, change the inequality sign to the equality sign :
[tex]x^2+5x-6=0[/tex]Next, solve for x:
[tex]\begin{gathered} x^2+6x-x-6=0 \\ x(x+6)-1(x+6)=0 \\ (x-1)(x+6)=0 \\ x-1=0\text{ or }x+6=0 \\ x=1\text{ or }x=-6 \end{gathered}[/tex]Therefore, from the options, 1 is the critical number.
The correct option is B.
I need help with finding the rational approximation of 37 using perfect squares
Answers
SOLUTION
For rational approximation of 37, it means we are to obtain the close estimate for the square root of 37.
using perfect squares,
The perfect square number immediately lower than 37 is
[tex]36[/tex]The perfect square number immediately higher than 37 is
[tex]49[/tex]Then we set up the problem as in the image below
The distance between 36 to 37 is lower than the distance between 49 to 37, hence the rational aproximation of 37 will be closer to the square root of 36 than the square root of 49.
This accouunt for the sqaure root of 37 in the image above
[tex]\sqrt[]{37}=6.08\approx6.1[/tex]Therefore
The rational aprosimation of 37 using perfect square is 6.1
19. The table below shows the population of Florida from 2010 to 2019.YearPopulation (millions)201018.7201119.1201219.3201319.6201419.9201520.2201620.6201721.0201821.2201921.5(a) Use a graphing calculator to build a logistic regression model that best fits this data, letting t=0 in 2010. Round each coefficient to two decimal places.Pt = (b) What does this model predict that the population of Florida will be in 2030? Round your answer to one decimal place. million people(c) When does this model predict that Florida's population will reach 23 million? Give your answer as a calendar year (ex: 2010).During the year (d) According to this model, what is the carrying capacity for Florida's population? million people
Answers
The formula for the logistic regression model that best fits the data is,
[tex]y_1=\frac{a}{1+b\cdot e^{t\cdot x_{1}}}[/tex]The graph, tables and details of the population data will be shown below
a) The equation that best fits the regression model is,
[tex]\begin{gathered} P_t=y_1 \\ t=x_1 \\ a=93.2861\approx93.29(2\text{ decimal places)} \\ b=3.98291\approx3.98(2\text{ decimal places)} \\ t=-0.0198742\approx-0.02(2\text{ decimal places)} \end{gathered}[/tex]Substitutes the data above into the equation
[tex]P_t=\frac{93.29}{1+3.98\cdot e^{-0.02t}}[/tex]Hence,
[tex]P_t=\frac{93.29}{1+3.98\cdot e^{-0.02t}}[/tex]b) In the year 2030, t = 20
[tex]\begin{gathered} P_{20}=\frac{93.29}{1+3.98\cdot e^{-0.02\times20}}=\frac{93.29}{1+3.98\cdot e^{-0.4}}=\frac{93.29}{1+3.98\times0.67032} \\ P_{20}=\frac{93.29}{1+2.6678736}=\frac{93.29}{3.6678736}=25.43435521\approx25.4(1\text{ decimal place)} \\ P_{20}=25.4million\text{ people} \end{gathered}[/tex]Hence, the answer is
[tex]P_{20}=25.4\text{million people}[/tex]c) Given that
[tex]\begin{gathered} _{}P_t=23\text{million people} \\ 23=\frac{93.29}{1+3.98\cdot e^{-0.02t}} \end{gathered}[/tex]Multiply both sides by 1+3.98e^{-0.02t}
[tex]\begin{gathered} 23(1+3.98e^{-0.02t})=1+3.98e^{-0.02t}\times\frac{93.29}{1+3.98\cdot e^{-0.02t}} \\ \frac{23(1+3.98e^{-0.02t})}{23}=\frac{93.29}{23} \\ 1+3.98e^{-0.02t}=4.056087 \end{gathered}[/tex]Subtract 1 from both sides
[tex]\begin{gathered} 1+3.98e^{-0.02t}-1=4.056087-1 \\ 3.98e^{-0.02t}=3.056087 \end{gathered}[/tex]Divide both sides by 3.98
[tex]\begin{gathered} \frac{3.98e^{-0.02t}}{3.98}=\frac{3.056087}{3.98} \\ e^{-0.02t}=0.767861055 \end{gathered}[/tex]Apply exponent rule
[tex]\begin{gathered} -0.02t=\ln 0.767861055 \\ -0.02t=-0.264146479 \end{gathered}[/tex]Divide both sides by -0.02
[tex]\begin{gathered} \frac{-0.02t}{-0.02}=\frac{-0.264146479}{-0.02} \\ t=13.20732\approx13(nearest\text{ whole number)} \\ t=13 \end{gathered}[/tex]Hence, the population will reach 23million in the year 2023.
d) The carrying capacity for Florida's population is equal to the value of a.
[tex]\begin{gathered} \text{where,} \\ a=93.29\text{ million people} \end{gathered}[/tex]Hence, the carrying capacity fof Florida's population is
[tex]93.29\text{million people}[/tex]
A. What is the common ratio of the pattern?B. Write the explicit formula for the pattern?C. If the pattern continued how many stars would be in the 11th set?
Answers
Given:
The sequence of number of stars is 2,4,8,16
a) To find the common ratio of the pattern.
[tex]\begin{gathered} \text{Common ratio=}\frac{2nd\text{ term}}{1st\text{ term}} \\ r=\frac{4}{2} \\ r=2 \end{gathered}[/tex]Hence the common ratio is 2.
b) To find the explicit formula for the pattern.
The general for a geometric progression sequence is,
[tex]a_n=a_1(r)^{n-1}_{}_{}[/tex]Hence, the formula for the above pattern will be,
[tex]a_n=2(2)^{n-1}[/tex]c) To find the number of stars in 11th set.
Substitute n=11 in the explicit formula of the pattern.
[tex]\begin{gathered} a_{11}=2(2)^{11-1} \\ a_{11}=2(2)^{10} \\ a_{11}=2(1024) \\ a_{11}=2048 \end{gathered}[/tex]Hence, the number of stars in 11th set will be 2048.
Кр2.345 67 8Identify each angle as acute, obtuse, or right123345678.
Answers
we have the following:
Therefore:
Find the solution to following system of equations A+ 10C = 54 A +9C = 50 A. A=10 C= 4 B. A= 14 C= 4 C. A=4 C= 14 D. A= 10 C= 6
Answers
Answer:
B. A = 14
C = 4
Explanation:
The system of equation is:
A + 10C = 54
A + 9C = 50
So, we can solve for A using the first equation:
A + 10C = 54
A + 10C - 10C = 54 - 10C
A = 54 - 10C
Now, we can replace A by (54 - 10C) on the second equation, so:
A + 9C = 50
(54 - 10C) + 9C = 50
54 - 10C + 9C = 50
54 - C = 50
54 - C + C = 50 + C
54 = 50 + C
54 - 50 = 50 + C - 50
4 = C
Then, we can replace C by 4 and calculate A, so:
A = 54 - 10C
A = 54 - 10(4)
A = 54 - 40
A = 14
Therefore, the solution of the system is:
A = 14
C = 4
Convert €3.2 per kilogram to unit price dollars per pound
Answers
We get 1.45 dollars per pound when we convert 3.2 Euros per kilogram to dollar per pound.
According to the question,
We have the following information:
3.2 Euros per kilogram
We need to convert its units into dollars per pounds.
We know that 1 Euro is approximately equal to 1 US dollar and 1 kilogram of weight is equal to 2.205 pounds.
(Note that there are various conversions from Euro to dollars which have 1 Euro equal to 1.00755 and many other values. In this case, we have rounded it off to 1 to avoid any confusion.)
(We know that per means the unit given is in divide.)
So, we have:
(3.2*1)/(1*2.205)
3.2/2.205
1.45 dollar per pounds
Hence, the conversion to dollars per pounds is 1.45 dollar per ponds from Euros per kilogram.
To know more about dollars here
https://brainly.com/question/28547396
#SPJ1
Solve fort 30 on t =(Type (Type an integer or a simplified fraction)
Answers
Multiply both sides by t:
[tex]\frac{12t}{10}=30[/tex]Multiply both sides by 10:
[tex]12t=300[/tex]Divide both sides by 12:
[tex]\begin{gathered} t=\frac{300}{12} \\ t=25 \end{gathered}[/tex]how many km/h equals 880ft/min? Explain how you solved this problem
Answers
The number of kilometers per hour in 880 feet / minute can be found to be 16.09 kilometers per hour
How does km/h relate to ft/ min?Based on the conversion rates between kilometers and feet, the number of feet per minute for each kilometer per hour is 54.6807 feet per minute.
In other words, 1 km / h is equal to 54.6807 feet per minute.
If there are 880 ft / minute therefore, the number of kilometers per hour is:
= Speed in feet per minute / feet per minute per kilometer per hour
= 880 / 54.6807
= 16.09 kilometers per hour
Find out more on kilometers per hour at https://brainly.com/question/17263672
#SPJ1
the remainder when f(x)is divided by x-3 is 15. Does f(-3) =15? explain why or why not
Answers
We will see that the function f(x) is:
f(x) = 15*(x - 3)
Evaluating it in x = -3 we can see that:
f(-3) = -90
Is the statement true?We know that when we divide f(x) by (x - 3), the quotient is 15. (that is the statement given in the question)
so we can write the equation:
f(x)/(x - 3) = 15
And we can solve this for f(x) as if it were a variable, then we get:
f(x) = 15*(x - 3)
Now, if we evaluate the function in x = -3 (this is replacing the variable x with the number -3), we will get:
f(-3) = 15*(-3 - 3) = 15*(-6) = -90
So the statement:
f(-3) = 15
Is false
Learn more about evaluating functions:
https://brainly.com/question/1719822
#SPJ1
which are thrwe ordered pairs that make the equation y=7-x true? A (0,7) (1.8), (3,10) B (0,7) (2,5),(-1,8) C (1,8) (2,5),(3,10)D (2,9),(4,11),(5,12)
Answers
In order to corroborate that the points belong to the equation, we must subtitute the points into the equation.
If we substitute the points from option A, we get
[tex]\begin{gathered} 7=7-0 \\ 7=7 \end{gathered}[/tex]for (1,8), we have
[tex]\begin{gathered} 8=7-1 \\ 8=6\text{ !!!} \end{gathered}[/tex]then, option A is false.
Now, if we substitute the points in option B, for point (2,5), we have
[tex]\begin{gathered} 5=7-2 \\ 5=5 \end{gathered}[/tex]which is correct. Now, for point (-1.8) we obtain
[tex]\begin{gathered} 8=7-(-1) \\ 8=8 \end{gathered}[/tex]Since all the points fulfil the equation, then option B is an answer.
Lets continue with option C and D.
If we substitute point (1,8) from option C, we have
[tex]\begin{gathered} 8=7-1 \\ 8=6\text{ !!!} \end{gathered}[/tex]then, option C is false.
If we substite point (4,11) from option D, we get
[tex]\begin{gathered} 11=7-4 \\ 11=2\text{ !!!} \end{gathered}[/tex]then, option D is false.
Therefore, the answer is option B.
what would be the value if m in a angle on 50 degrees and 10m
Answers
50 + 10m = 90 Reason: This is a right angle, which sum up to 90 degree.
10m = 90 - 50
10m = 40
m = 40/10
m = 4
Given slope of m=2/3 and y-intercept b=1 graph the line
Answers
ok! to graph your first point, you know the y-intercept is 1, so your point is (0,1)
graph that
because we knkow the slope is 2/3 and it's y change/x change, move up 2 and left 3 for your next point, which is (2,4)
we can graph a third point for accuracy, and move up 2 and left 3 again to get (4,7)
create a line connecting all the points
Hello! I'm hitting a bit of a snag on this. I think I'm reading it too many times
Answers
The solution:
Given:
[tex]\begin{gathered} \text{ A sphere of radius 4m.} \\ \\ A\text{ cube of side 6.45m} \end{gathered}[/tex]Required:
To compare the volume and area of bot shapes.
The Sphere:
[tex]\begin{gathered} Area=4\pi r^2=4(4)^2\pi=64\pi=201.062m^2 \\ \\ Volume=\frac{4}{3}\pi r^3=\frac{4}{3}\times\pi\times4^3=268.083m^3 \end{gathered}[/tex]The Cube:
[tex]\begin{gathered} Area=6s^2=6\times6.45^2=249.615m^2 \\ \\ Volume=s^3=6.45^3=268.336m^3 \end{gathered}[/tex]Clearly, we can see that:
Both shapes have approximately the same volume.
But the cube has a greater volume than that of the sphere.
Therefore, the correct answer is [option 4]
What does the slower car travel at Then what does the faster car travel at
Answers
Given that two cars are 188 miles apart, travelling at different speeds, meet after two hours.
To Determine: The speed of both cars if the faster car is 8 miles per hour faster than the slower car
Solution:
Let the slower car has a speed of S₁ and the faster car has a speed of S₂. If the faster speed is 8 miles per hour faster than the slower car, then,
[tex]S_2=8+S_1====\text{equation 1}[/tex]It should be noted that the distance traveled is the product of speed and time. Then, the total distance traveled by each of the cars before they met after 2 hours would be
[tex]\begin{gathered} \text{distance}=\text{speed }\times time \\ \text{Distance traveled by the faster car after 2 hours is} \\ =S_2\times2=2S_2 \\ \text{Distance traveled by the slower car after 2 hours is} \\ =S_1\times2=2S_1 \end{gathered}[/tex]It was given that the distance between the faster and the slower cars is 188 miles. Then, the total distance traveled by the two cars when they meet is 188 miles.
Therefore:
[tex]\begin{gathered} \text{Total distance traveled by the two cars is} \\ 2S_1+2S_2=188====\text{equation 2} \end{gathered}[/tex]Combining equation 1 and equation 2
[tex]\begin{gathered} S_2=8+S_1====\text{equation 1} \\ 2S_1+2S_2=188====\text{equation 2} \end{gathered}[/tex]Substitute equation 1 into equation 2
[tex]\begin{gathered} 2S_1+2(8+S_1)=188 \\ 2S_1+16+2S_1=188 \\ 2S_1+2S_1=188-16 \\ 4S_1=172 \end{gathered}[/tex]Divide through by 4
[tex]\begin{gathered} \frac{4S_1}{4}=\frac{172}{4} \\ S_1=43 \end{gathered}[/tex]Substitute S₁ in equation 1
[tex]\begin{gathered} S_2=8+S_1 \\ S_2=8+43 \\ S_2=51 \end{gathered}[/tex]Hence,
The slower car travels at 43 miles per hour(mph), and
The faster car travels as 51 miles per hour(mph)
I would like to make sure my answer is correct ASAP please
Answers
step1: Write out the formula for exponential growth
[tex]y=a(1+r)^n[/tex][tex]\begin{gathered} a=\text{initial population} \\ r=\text{rate} \\ n=\text{years} \end{gathered}[/tex]Hence we have
[tex]a=800,r=3\text{ \%, n=x}[/tex]Step2: substitute into the formula in step 1
[tex]\begin{gathered} y=800(1+\frac{3}{100})^x \\ y=800(1+0.03)^x \\ y=800(1.03)^x \end{gathered}[/tex]Hence the right option is A
3. The sum of two consecutive odd integersis 168. What are the integers?
Answers
Integers are numbers such as
[tex]N=\text{ }.\ldots\text{-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9}\ldots.[/tex]And odd numbers are
[tex]1\text{ 3 5 7 9 11 13 }\ldots[/tex]Referring to the figure, find the value of x in circle C.
Answers
The tangent-secant theorem states that given the segments of a secant segment and a tangent segment that share an endpoint outside of the circle, the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment.
Graphically,
[tex]PA\cdot PB=(PD)^2[/tex]In this case, we have:
[tex]3x\cdot5=10^2[/tex]Now, we can solve the equation for x:
[tex]\begin{gathered} 3x\cdot5=10^2 \\ 15x=100 \\ \text{ Divide by 15 from both sides of the equation} \\ \frac{15x}{15}=\frac{100}{15} \\ \text{Simplify} \\ x=\frac{20\cdot5}{3\cdot5} \\ x=\frac{20}{3} \\ \text{ or} \\ x\approx6.67 \end{gathered}[/tex]Therefore, the value of x is 20/3 or approximately 6.67.
Solve this system of equations by elimination. Enter your answer as an ordered pair (x,y). Do not use spaces in your answer. If your answer is no solution, type "no solution". If your answer is infinitely many solutions, type "infinitely many solutions".
Answers
5x + 2y = -12 (a)
3y + 5x =-8 (b)
First, write (b) in the ax+by=c form:
5x + 3y = -8 (b)
Now, subtract (b) to (a) to eliminate x
5x + 2y = -12
-
5x + 3y = -8
__________
-y = -4
solve for y:
Multiply both sides by -1
y=4
Replace y=4 on (a) and solve for x:
5x + 2 (4) = -12
5x + 8 = -12
5x = -12-8
5x = -20
x = -20/5
x = -4
Solution: (-4,4)
Find the perimeter and area of the polygon with given vertices
Answers
Let's begin by listing out the information given to us:
[tex]\begin{gathered} A(-3,3),B(-3,-1),C(4,-1),D(4,3) \\ AB=3-(-1)=3+1=4_{} \\ BC=|-3-4|=|-7|=7 \\ CD=|-1-3|=|-4|=4 \\ AD=|-3-4|=|-7|=7 \\ \\ Perimeter=2(l+w)=2(7+4)_{}=2(11)=22 \\ Perimeter=22unit \\ \\ Area=lw=7\cdot4=28unit^2 \\ Area=28unit^2 \end{gathered}[/tex]Find the real solutions of the equation by graphing. 4x^3-8x^2+4x=0
Answers
x = 0,1 are the real solutions of the equation .
What are real solutions in math?
Any equation's solution that is a real number is known as a "real solution" in algebra.Discriminant b2 - 4ac is equal to zero when there is only one real solution. One solution, x = -1, exists for the equation x2 + 2x + 1 = 0.There are a number of solutions to the given quadratic equation depending on whether the discriminant is positive, zero, or negative. The existence of two unique real number solutions to the quadratic is indicated by a positive discriminant. A repeating real number solution to the quadratic equation is indicated by a discriminant of zero.4x³ - 8x² + 4x = 0
x( 4x² - 8x + 4 ) = 0
x( 4x² - 4x - 4x + 4 ) = 0
x ( 4x ( x - 1) -4 ( x - 1 )) = 0
x ( ( 4x - 4 ) ( x - 1 ) ) = 0
x = 0
4x - 4 = 0 ⇒ x = 1
x - 1 = 0 ⇒ x = 1
Learn more about real solution
brainly.com/question/4526506
#SPJ13
2+2=im in kendergardenin. pls help.
Answers
The addition is the operation that puts together two quantities of numbers. It is represented by the signal "+". To add the two numbers we can use a visualization method as shown below:
We have two sticks on the left and two sticks on the right, we need to add them both, this is the same as joining them together, the result is 4 sticks. The answer is 4.
Answer:
the answer is 11
duuuh
Step-by-step explanation:
I got the first part I’m not sure of the 2nd is it 38.5
Answers
We will have the following:
The surface area of the onion can be best modeled by a sphere. Base on the model, the approximate area of the onion is 38.5 square inches:
[tex]A_s=4\pi(\frac{3.5}{2})^2\Rightarrow A_s\approx38.5[/tex]what is 3/8 * 1/5 and 6/10 * 3/4
Answers
Answer
(3/8) × (1/5) = (3/40)
(6/10) × (3/4) = (9/20)
Explanation
We are asked to solve the given expressions
(3/8) × (1/5)
And
(6/10) × (3/4)
For (3/8) × (1/5)
[tex]\frac{3}{8}\times\frac{1}{5}=\frac{3\times1}{8\times5}=\frac{3}{40}[/tex]For (6/10) × (3/4)
[tex]\begin{gathered} \frac{6}{10}\times\frac{3}{4}=\frac{6\times3}{10\times4}=\frac{18}{40} \\ We\text{ can now reduce this to the simplest form} \\ \text{Divide numerator and denominator by 2} \\ \frac{18}{40}=\frac{9}{20} \end{gathered}[/tex]Hope this Helps!!!
Choose the left side that makes a True statement, and shows at the sum of the given complex numbers is 10Choose the left side that makes a true statement, and shows that the product of the given complex numbers is 40
Answers
For statement one:
We need to add up to complex numbers and their sum must give us equal to 10.
Also, we need to use the complex numbers:
5+i√15 and 5-i√15.
Then, we can use:
(5+i√15)+( 5-i√15) =
5+i√15+5-i√15 =
5+5+ i√15-i√15 =
= 10 + 0
= 10
For the second statement:
We need to show the product of complex numbers:
Then, we use:
(5+i√15)(5-i√15))=
5*5 - 5*i√15) +5*i√15) +√15*√15=
25 + 0 + 15=
40
Put the equation y = x2 - 10x + 16 into the form y = =(x - h)² + ki Answer: y = > Next Question
Answers
To complete the perfect square ((x-h)²) we add and subtract constants:
[tex]\begin{gathered} y=x^{2}-10x+16 \\ y=x^{2}-10x+25-25+16 \\ y=x^{2}-10x+5^{2}-9 \\ y=(x-5)^{2}-9 \end{gathered}[/tex]g(x) = 2x - 5f(x) = 4x + 2Find g(f(x))
Answers
Explanation
Step 1
Let
[tex]\begin{gathered} g(x)=2x-5 \\ \text{and} \\ f(x)=4x+2 \end{gathered}[/tex]then
[tex]\begin{gathered} g(f(x))= \\ g(x)=2x-5 \\ g(f(x))=2(4x+2)-5 \\ \text{apply distributive property} \\ g(f(x))=8x+4-5 \\ g(f(x))=8x-1 \end{gathered}[/tex]I hope this helps you
Find the present value that will grow to $6000 if the annual interest rate is 9.5% compounded quarterly for 9 yr.The present value is $(Round to the nearest cent as needed)
Answers
We need to know how to calculate compound interest to solve this problem. The present value is $2577.32
Compound interest is the interest that is earned on interest. Inorder to calculate the compound interest we need to know the principal amount, the rate of interest, the time period and how many times the interest is applied in per time period. In this question we know the amount after 9 years and the rate of interest is 9.5% and the interest is compounded quarterly. We will use the formula for compound interest get the principal value.
A=P[tex](1+\frac{r}{n}) ^{nt}[/tex]
where A= amount, P= principal, t=time period, n= number of times interest applied per time period, r=rate of interest
A=$6000
r=9.5%
t=9 yrs
n=4
6000=P[tex](1+\frac{9.5}{400} )^{36}[/tex]
6000= P x 2.328
P=6000/2.328=2577.32
Therefore the present value that will grow to $6000 in 9 years is $2577.32
Learn more about compound interest here:
https://brainly.com/question/24274034
#SPJ1