PLEASEEE HELP I NEED ONE MORE
The solution of the function is as follows:
(f o g)(x) = 16x² + 17x + 1
(g o f)(x) = 4x² + 36x + 1
How to solve composite function?Composite functions are when the output of one function is used as the input of another.
Therefore, let's solve the composite functions as follows:
f(x) = x² + 9x
g(x) = 4x + 1
Therefore,
(f o g)(x) = f(g(x))
Therefore,
f(g(x)) = (4x + 1)² + 9x = (4x + 1)(4x + 1) + 9x = 16x² + 4x + 4x + 1 + 9x = 16x² + 17x + 1
(g o f)(x) = g(f(x))
g(f(x)) = 4(x² + 9x) + 1 = 4x² + 36x + 1
Therefore,
(f o g)(x) = 16x² + 17x + 1
(g o f)(x) = 4x² + 36x + 1
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A farmhouse shelters 23 animals. Some are goats and some are ducks. Altogether there are 58 legs. How many of each animal are there?
There are 6 goats and 17 ducks present in the farmhouse
How to calculate the number of goats and ducks ?Let x represent the number of goats
Let y represent the number of ducks
x + y= 23....equation1
Goats have 4 legs and ducks have 2 legs
4x + 2y= 58.......equation 2
From equation 1
x + y= 23
x= 23-y
Substitute 23-y for x in equation 2
4(23-y) + 2y = 58
92- 4y + 2y= 58
92-2y= 58
-2y= 58-92
-2y= -34
y- 34/2
y= 17
Substitute 17 for y in equation 1
x + y= 23
x + 17= 23
x= 23-17
x= 6
Hence there are 6 goats and 17 ducks in the farmhouse shelter
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You could take a 15-week, three credit college course, which requires 10 hours per week of your time for $740 per credit hour in tuition. Or during those hours you could have a job paying $10 per hour. What is the net cost of the class compared to working? Based on your answer and the fact that the average college graduate earns nearly $28,000 per year more than a high school graduate, write a few sentences giving your opinion as to whether the college course is a worthwhile experience.
The cost of the class would be $740 x 3 = $2220. If you were to work instead, at $10 per hour for 10 hours per week for 15 weeks, you would earn $1500. So, the net cost of the class would be $2220 - $1500 = $720.
In general, a college degree can lead to higher earning potential and greater career opportunities, so in most cases, it can be considered a worthwhile investment. However, the decision to take a particular class should be based on individual circumstances and goals. If the class is relevant to your future career aspirations and you can afford the cost, it may be a good investment. However, if the class is not directly related to your career goals, or you are not able to afford the cost, it may not be worth it.
Which graph represents the function on the interval [−3,3]?
f(x)=⌊x⌋−3
The function f(x)=⌊x⌋−3 in interval [−3,3] is represented by following graph:
The correct option is D.
What is floor function?The floor function floor(x) is defined as the function that gives the highest integer less than or equal to x.
Given function
f(x)=⌊x⌋−3 in interval [−3,3]
Above function is floor function.
x = 3f(x) = ⌊x⌋−3
f(3) = 3 - 3
f(3) = 0
x = 2f(2) = 2 - 3
f(2) = -1
x = 1f(1) = 1 - 3
f(1) = -2
x = 0f(0) = 0 - 3
f(0) = -3
x = -1f(-1) = -1 -3
f(-1) = -4
x = -2f(-2) = -2 -3
f(-2) = -5
x = -3f(-3) = -3 -3
f(-3) = -6
Plotting above points the graph we get is as follows:
Hence, Graph that represents the function f(x)=⌊x⌋−3 in interval [−3,3] is below.
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Examine the triangle below, solve for x and y, rounded to two decimal places.
X=
y=
X
30°
y
16
[tex]30 + 60[/tex]
I am pretty sure I'm wrong
[tex]30 \div 60[/tex]
[tex]30 \times 60[/tex]
[tex]30 - 60[/tex]
four granola bars and three drinks cost $12.50. Two granola bars and five drinks cost $15.00. At Snacks To Go, three granola bars and three drinks cost $10.50. Four granola bars and two drinks cost $10.00. Part A Write a system of equations for each concession stand that models the price of its items. Part B Solve each system of equations. What do the solutions represent? Part C You decide to open a new concessions stand and sell granola bars and drinks. Determine a price for each item that differ from the prices at Snacks To Go. Then write a system of equations to model the prices at your snack bar.
Using substitution method to solve the system of linear equations, the granola and drinks cost $1.25 and $2.5 respectively while the modelled system of linear equation is attached below
What is System of Linear EquationA grouping of two or more linear equations that share the same set of variables is known as a system of linear equations. When a, b, and c are constants and x and y are variables, the equations can be written as ax + by = c. Elimination, substitution, and graphing are just a few of the techniques that can be used to solve these problems.
In this given problem, we have to define our variables and then set our system of equations.
a)
Let;
x = granola bardrinks2x + 5y = 15 ...eq(i)
4x + 3y = 12.50 ...eq(ii)
b)
Using substitution method;
From equ(i)
2x + 5y = 15
2x = 15 - 5y
x = (15 - 5y) / 2 ...eq(iii)
Put eq(iii) into eq(ii)
4x + 3y = 12.50
4(15 - 5y) /2 + 3y = 12.50
y = 2.5
Put y = 2.5 into eq(i)
2x + 5(2.5) = 15
x = 1.25
c)
Granola = 1.0
drinks = 3.0
The system of linear equations will be
x + y = 4
2x + 3y = 11
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Rewrite (6+3)9 using the distribute property of multiplication over addition
(2)9
6(9)-3(9)
(9)9
6(9)+3(9)
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{(6 + 3)9}\leftarrow\text{Your given equation}\\\mathsf{= 9(6 + 3)}\leftarrow\text{Convert your equation to this to make it easier to solve}\\\mathsf{= 9(6) + 9(3)}\leftarrow\text{What you are looking for because it is your answer to this question}\\\mathsf{= 54 + 27}\leftarrow\text{Making it more easier to solve for the overall answer} \\\mathsf{= 81}\leftarrow\text{This is your overall answer to the whole equation}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{Option\ D. \ 6(9) + 3(9)}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Question 39 of 40
Simplify the expression below. If your answer is not a whole number, enter it
as a fraction in lowest terms, using the slash mark (/) as the fraction bar.
8 divided by (4-6) - 15 divided (-5)
Answer: its -1
Step-by-step explanation:
Simplify the expression below. If your answer is not a whole number, enter it
as a fraction in lowest terms, using the slash mark (/) as the fraction bar.
5/6 divided by 7/18
Answer:
2.14 rounded ............
Aria invested $40,000 in an account paying an interest rate of 8\tfrac{3}{8}8 8 3 % compounded daily. Olivia invested $40,000 in an account paying an interest rate of 8\tfrac{1}{8}8 8 1 % compounded quarterly. To the nearest hundredth of a year, how much longer would it take for Olivia's money to triple than for Aria's money to triple?
To the nearest hundredth of a year (period), it will take Olivia's money 0.54 years more to triple than Aria's money to triple.
How the period is determined?The additional period it will take Olivia's money to triple than Aria's is determined as the difference between the two investment periods.
The investment periods are computed using an online finance calculator as follows:
Aria Investment:I/Y (Interest per year) = 8.375%
PV (Present Value) = $40,000
PMT (Periodic Payment) = $0
FV (Future Value) = $-120000
Results:
Number of Periods (N) = 4,788.531
= 13.119 years (4,788.531/365) or 13 years and 1 month
Total Interest = $80,000.00
Olivia's Investment:I/Y (Interest per year) = 8.125%
PV (Present Value) = $40,000
PMT (Periodic Payment) = $0
FV (Future Value) = $-120000
Results:
N = 54.633
= 13.65825 years (54.633 quarters/4) or 13 years and 8 months
Total Interest $80,000.00
The difference in investment period:
13.66 - 13.12
= 0.54 years
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Write an
explicit formula for an, the nth term of the sequence 8, 40, 200, ....
Answer:
1,000
Step-by-step explanation:
Formula: An=8/5x5(4)
If the mean of this data is 95, find the missing data. 103, 99, 90, 86, 105, 96, ___
Answer: The missing value is 86
Step-by-step explanation: The mean of a data set is the same as the average. The formula for mean is the sum of the data values/(the number of data values). Right now there are only 6 data values and we are looking for a seventh. If we sum the 6 current values and divide by 6, we get a data set with a mean of 96.5. We need a lower mean. The data set we need has 7 points so the sum of all 7 points should be 7(95) since if we divide 7(95) by the number of points which is 7, we get 95 which is the mean we want. 7(95) is 665. We can subtract the sum of the current 6 points from 665 to find the value we want.
What is the equation of a line with a slope of 3 and a point (3, 1) on the line?
Express the equation in the form of y-ma+bwhere m is the slope and b is the y-intercept
Enter your answer in the box
Answer: y = 3x - 8
Step-by-step explanation: Given slope m = 3, and point x = 3, y = 1
y -1 = 3(x-3)
y = 3x - 9 + 1
y = 3x - 8
Ridge City is smaller than Peak City. Desert City is smaller than Peak City but larger than Ridge City. Peak City is smaller than Oak City. Which city is the largest?
Answer:
Desert city is the largest city.
Help the picture has everything you need to know 20 points
Answer:
Triangle VWX and triangle IGH are congruent
Step-by-step explanation:
problem 1.9. (know your theory) write the precise definition of the following: (1) {xn}nn0 is a sequence of reals. (2) give an example of a sequence of rational numbers. (3) (give the recursive definition of) p ` i
1) A sequence of real numbers is an ordered list of real numbers where each number in the list is assigned a specific position or index, usually denoted by n. The sequence is denoted by {xn} n>n0, where xn represents the nth term of the sequence and n ranges from 0 to infinity.
2)An example of a sequence of rational numbers is {2, 1.5, -0.5, -1.25, ...}, where each term in the sequence is a rational number.
3) The recursive definition of the summation of ai is a mathematical formula that defines the nth term of the summation in terms of the previous terms. It is typically denoted as:
∑(i=1)^ni = a1 + (a2 + (a3 + ....(an-1 + an)...)),
Where a1 is the first term of the summation, a2 is the second term, and so on and so forth. This recursive definition is used to calculate the nth term of the summation by adding the previous term to the current term. It is generally used in mathematical induction and recursion.
4)The associative property of summation notation states that the order in which the summation is performed does not affect the final result. In other words, for any three indices a, b, and c, and any sequence of numbers {xn}, the following equation holds:
∑(a=b)c xn = ∑(a=c)b xn = ∑(a=b)c xn
This property allows us to group the terms in a summation in different ways without changing the final result.
5) The translation invariance property of summation notation states that the value of a summation is unchanged when the index of summation is translated (shifted) by a constant value. In other words, for any indices a and b, any constant k, and any sequence of numbers {xn}, the following equation holds:
∑(a=b)xn = ∑(a+k=b+k)xn
This property allows us to shift the index of summation without affecting the final result of the summation.
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The doctor has ordered a 5% saline solution to be prepared. How many grams of pure drug will be needed to make 115 mL of solution at the 5% strength?
Answer:
(115 x 5) / 100 = 0.575 grams of the pure drug.
Step-by-step explanation:
To make a 5% solution, the concentration of the pure drug is 5 grams per 100 mL of solution.
To find the amount of pure drug needed for a specific volume, such as 115 mL, you can use the formula:
(volume of solution x concentration of pure drug) / 100
So in this case:
(115 x 5) / 100 = 0.575 grams of the pure drug.
This calculation shows that 0.575 grams of the pure drug would be needed to make 115 mL of a 5% solution.
Answer:
5.75 g
Step-by-step explanation:
First calculate 5% of the total amount of solution, 115 ml:
[tex]\implies \sf 5\%\;of\;115\;ml=\dfrac{5}{100} \times 115=5.75\;ml[/tex]
As we have not been told any information about the drug, assume the standard equivalent that 1 ml equals 1 gram. Therefore, the amount of pure drug needed to make 115 ml of solution at the 5% strength is 5.75 g.
What is the quotient of -4/5-2
Answer:
-1.3
Step-by-step explanation:
find the common ratio of the geometric sequence. 14, 7, 7/2, 7/4
The common ratio for the sequence is 1/2.
What is Geometric Sequence?Sets of numbers that adhere to a pattern or norm are known as number sequences. A geometric sequence is one where the rule is to multiply or divide by the same number each time.
Formula : [tex]a_n[/tex] = a[tex]r^{n-1[/tex]
where a is the first term, r is the common ratio.
Given:
Sequence: 14, 7, 7/2, 7/4
To calculate the common ratio = [tex]a_1/ a_2[/tex]
Now, the common ratio
= 7/14
= 1/2
Hence, the common ratio is 1/2.
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Nya rode her bike about 2 ½ miles in ¼ hour. What was her average speed in miles per hour?
Nya's average speed was 10 miles per hour.
What is the speed, distance, and time?
Speed, distance, and time are related concepts in physics that are used to measure and describe motion.
Speed is a measure of how fast an object is moving. It is typically measured in units of distance per unit of time, such as miles per hour or kilometers per hour. Speed can be calculated using the formula:
Speed = Distance / Time
To find Nya's average speed in miles per hour, we need to divide the distance she traveled by the time it took her to travel that distance.
Average speed = distance/time
We know that Nya rode her bike 2 ½ miles in ¼ hour. To use these measurements in the formula, we need to convert the units to the same unit of measurement. In this case, we need to convert the distance to miles and the time to hours.
Average speed = (2.5 miles) / (0.25 hour)
To find out the speed in miles per hour, you need to multiply by the conversion factor 1 hour/60 minutes, so
Average speed = (2.5 miles) / (0.25 hour) * (1 hour/60 minutes)
Average speed = (2.5 miles) / (0.25 hour) * (4)
Average speed = 10 miles per hour.
Hence, Nya's average speed was 10 miles per hour.
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HELP ME OUT PLEASE!!!!!!!
Simplify
Answer:
I believe it is -2a⁶b¹² (the first option)
What is the length of the unknown
leg of the right triangle?
5 ft
6 ft
(The figure is not drawn
to scale.)
The length of the unknown leg of the right triangle is
(Round to one decimal place as needed.)
ft.
Answer:
a = 3.31ft.
Step-by-step explanation:
Pythagorean TheoremThe Pythagorean Theorem explains the connection between a right triangle's three sides. The area of the square produced on the hypotenuse of any right triangle is equal to the sum of the areas of the squares formed on its legs: a2 + b2 = c2.a, is the shortest leg of the triangle or the opposite.b, is the adjacent leg of the triangle. This leg typically forms the right angle of the triangle.c, is the hypotenuse. This is the longest leg of the triangle.Applying the theorem[tex]a^{2} + b^{2} = c^{2}[/tex][tex]a^{2} +5^{2} = 6^{2}[/tex][tex]a^{2} = 6^{2} - 5^{2}[/tex][tex]a^{2} = 36-25[/tex][tex]\sqrt{a^{2} } = \sqrt{11}[/tex][tex]a = 3.31 feet[/tex]The opposite is 3.31 feet.
Please let me know if this helped!!!
match the volume formula to the description
Answer:
145236 4236. b. fjdjfjfjfjfjdjfjfjfjfjfnfjfjfjfnfjgjfjfnfjf
pleasee hellppp
-9=6m+15
solution:
check:
The solution to the equation -9 = 6m + 15 is m = -4.
What is the solution to the given equation?Given the equation in the question;
-9 = 6m + 15
Rewrite the equation as 6m + 15 = -9
Move all terms not containing m to the right side of the equation by subtracting 15 from both sides
6m + 15 - 15 = -9 - 15
6m = -9 - 15
Add -9 and -15
6m = -24
Divide both sides by 6
6m/6 = -24/6
m = -24/6
m = -4
Solution check
Plug m = -4 into the equation and check
-9 = 6m + 15
-9 = 6( -4 ) + 15
-9 = -24 + 15
-9 = -9
Correct.
Therefore, the numerical value of m is -4.
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z-2<22 solve the inequality for z
The factor z-8 is less than zero when z<8. Similarly, the factor z-3 is less than zero when z>3. Combining the two solutions,[tex]$z \in(3,8)$[/tex]
.
What is meant by inequality?A connection in mathematics that compares two numbers or other mathematical expressions in an unequal way is known as an inequality. It is most frequently used to compare the sizes of two numbers on the number line. A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. So inequality emerges from an imbalance. You can solve an inequality by: adding the same amount to each side; taking the same amount away from each side; multiplying or dividing each side by the same positive amount. The inequality symbol needs to be turned around if you multiply or divide each side by a negative number.Given inequality:
[tex]$$z^2-11 z+24 < 0$$[/tex]
Factor the left-hand side.
[tex]z^2-11 z+24 & < 0 \\[/tex]
[tex]z^2-8 z-3 z+24 & < 0 \\[/tex]
[tex]z(z-8)-3(z-8) & < 0 \\[/tex]
[tex](z-8)(z-3) & < 0[/tex]
The factor z-8 is less than zero when z<8. Similarly, the factor z-3 is less than zero when z>3. Combining the two solutions,[tex]$z \in(3,8)$[/tex].
The complete question is,
Solve the following inequality:
[tex]$$z^2-11 z+24 < 0$$[/tex]
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Select the correct answer . Which property of equality was used to solve this equation ? - 5x = 4; (- 5x)/- 5 = 4/- 5; x = - 4/5
The property of equality that was used to solve the equation is the division property of equality
Determining the property of equalityFrom the question, we are to determine the property of equality that was used to solve the given equation
From the given information,
The equation is
-5x = 4
and
The solution is
(- 5x)/- 5 = 4/- 5
x = - 4/5
From the solution step, we can observe that both sides of the equation were divided by -5.
Thus,
The property of equality that was used is the division property of equality
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The general strategy for solving an equation of the form x/a=b is to?
We have discussed the general strategy for solving an equation of the form x/a = b.
What is an equation?
An equation is a mathematical statement that shows that two expressions are equal. An equation is composed of two sides, separated by an equal sign (=), with each side containing one or more variables, numbers, and/or mathematical operations.
The general strategy for solving an equation of the form x/a = b is to:
Multiply both sides of the equation by a, in order to cancel out the fraction on the left side. This will isolate the variable x on one side of the equation.
Simplify the equation by combining like terms if necessary.
Check the solution by substituting it back into the original equation and verifying that it makes the equation true.
For example, consider the equation x/2 = 4
Multiply both sides by 2: x/2 * 2 = 4 * 2
x = 8
To check the solution, substitute it back into the original equation: x/2 = 4, 8/2 = 4. The equation is true, so x = 8 is the correct solution.
It's important to keep in mind that when solving equations, it is important to follow the order of operations, and also to be careful when dividing or multiplying by zero.
Hence, we have discussed the general strategy for solving the equation.
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What is the quotient when 2 x 2 + 4 x – 14 is divided by 2 x
The quotient when 2x² + 4x – 14 is divided by 2x is [tex]x + 2 - \frac{7}{x}[/tex] .
What is Quotient in Division?When two numbers are divided by each other, the result is known as a quotient. For instance, when we divide 8 by 2, the result will be 2, where 2 is the quotient.
As we know division is a mathematical operation that involves dividing items into equal groups. It is represented by the symbol (÷). When we divide a number, the result we ultimately get is the quotient.
Here we have
2x² + 4x – 14 is divided by 2x
=> [tex](2x^{2} + 4x - 14) \div {2x}[/tex]
=> [tex]\frac{(2x^{2} + 4x -14)}{2x}[/tex]
Take 2x as common
=> [tex]\frac{2x(x + 2 - \frac{7}{x} )}{2x}[/tex]
=> [tex]x + 2 - \frac{7}{x}[/tex]
Therefore,
The quotient when 2x² + 4x – 14 is divided by 2x is [tex]x + 2 - \frac{7}{x}[/tex] .
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How to solve the inequality:
-6 > z/-2 +1
The solution to the inequality is z > 14
What is inequality?Mathematical expressions with inequalities include those in which the two sides are not equivalent. Contrary to equations, we assess and contrast two values in inequality. The inequality signs that are used in place of the equal signs are:
Less than (or less than or equal to), Larger than (or greater than or equal to), or Not equal to.Given:
-6 > z/-2 + 1
Rewrite so "z" is on the left side of the inequality.
z/-2 + 1 < -6
Move the negative in front of the fraction.
-z/2 + 1 < -6
Move all terms not containing z to the right side of the inequality.
-z/2 < - 6 - 1
-z/2 < - 7
Multiply both sides by 2
z < -14
Interchange the sign since z cannot be negative;
z > 14
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solve the system
2x+y-3z=0
x-4y+z=0
4x+16y+4z=0
Answer:
x=0
y=0
z=0
Step-by-step explanation: