The value of the composite function f(f(x)) is -3(-3x^2 + 3x)^2 + 3(-3x^2 + 3x)
How to determine the composite function?The functions are given as
f(x) = -3x^2 + 3x
The definition of the composite function is given as
f(f(x))
This composite function is calculated using the following composite function formula
f(f(x))= (f o f)(x)
Substitute the known values in the above equation
So, we have the following equation
f(f(x)) = -3f(x)^2 + 3f(x)
So, we have
f(f(x)) = -3(-3x^2 + 3x)^2 + 3(-3x^2 + 3x)
Hence, the composite function is f(f(x)) = -3(-3x^2 + 3x)^2 + 3(-3x^2 + 3x)
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Given that AABC ADEF. Find the scale factor from AABC to ADEF.A2x24B20CDX-2E5
1) To find the scale factor for these triangles, we need to write a pair of ratios and then solve for x:
[tex]\begin{gathered} \frac{2x}{4}=\frac{20}{5} \\ \\ 10x=80 \\ \\ \frac{10x}{10}=\frac{80}{10} \\ \\ x=8 \\ \\ \end{gathered}[/tex]Now, we can plug x=8 into those:
[tex][/tex]The revenue for selling x units of a product is R = 113.95 x. The cost of producing x units is C = 93 x + 750. In order to obtain a profit, the revenue must be greater than the cost. For what values of x will this product produce a profit? (Enter a number. Round your answer up to the nearest whole unit.)
For profit with the revenue of R=113.95x and cost of C=93x + 750 the value of x is 36units.
As given in the question,
Revenue for selling x units of a product is R = 113.95 x
Cost of producing x units is C = 93 x + 750
For profit, the revenue must be greater than the cost.
R > C
113.95x > 93x +750
Subtract 93x from both the sides
113.95x -93x >93x-93x +750
⇒20.95x > 750
Divide by 20.95
⇒x > 750/20.95
⇒x>35.7995
Nearest whole number is 36.
Value of x to produce a profit is 36units
Therefore, to make a profit with the revenue of R=113.95x and cost of
C =93x + 750 the value of x is 36units.
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A student claimed that 0.045 m and 0.0045 m have the same number of significant digits. Do you agree or disagree?
Agree
Disagree
Examine angle ABC below.
Which of the following equations correctly represent the relationships between the segments?
A) AG= 2GD
B) GC= 1/2FG
C) BE= 2BG
D) GA= 1/2AD
Answer:
A
Step-by-step explanation:
The centroid cuts the median in a 2:1 ratio from vertex to side.
Please help me with that. Thank you
The logarithms in terms of a and b are:
a) log 72 = 3a + 2b
b) log √27 = [tex]\frac{3}{2} b[/tex]
c) log 360 = 3a + 2b + log 5
What are logarithms?The use of a logarithm can be utilized to solve problems that cannot be resolved using the concept of exponents alone. A logarithm is simply another way to describe exponents. It can be represented as:nˣ = a ⇔ logₙ a = x , log stands for logarithm here.
Where,
Two positive real numbers are a and n. x is a real number.
The "argument" is defined as a and is located inside the log.The "base," is denoted by the letter n at the bottom of the log.The rules of logs can be used to expand a logarithm, compress a collection of logarithms into a single one, or simplify a logarithm.Given:
log 2 = a
log 3 = b
a) log 72
= log (2³ × 3²)
= log 2³ + log 3² [ By product rule of logarithms, log mn = log m + log n]
= 3log 2 + 2log 3 [By power rule of logarithms, log mⁿ = nlog m]
Replacing with the values of log 2 and log 3.
= 3a + 2b
b) log √27
= [tex]\frac{1}{2}[/tex] log 27 [By power rule of logarithms, log mⁿ = nlog m]
= [tex]\frac{1}{2}[/tex] log 3³
= [tex]\frac{1}{2} *3 log3[/tex]
= [tex]\frac{3}{2} log 3[/tex]
= [tex]\frac{3}{2} b[/tex]
c) log 360
= log (2³ × 3² × 5)
= log 2³ + log 3² + log 5 [By product rule of logarithms,log mn = log m + log n]
= 3log 2 + 2log 3 + log 5 [By power rule of logarithms, log mⁿ = nlog m]
= 3a + 2b + log 5
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Adam has 18 counters.
He gives 10 of the counters to Lesley.
a) What fraction of the 18 counters does Lesley get?
Give your answer in its simplest form.
b) What fraction of the 18 counters does Adam have now?
Give your answer in its simplest form.
The fraction of counters Lesley get if Adam gives 10 counters out of 18 counters is 5/9.
The fraction of counters Adam have now is 4/9.
FractionThis is an expression which consists of a numerator and a denominator
A numerator is the upper of top value of a fraction
A denominator is the lower or bottom value of a fraction
Number of counters Adam has = 18Number of counters Adam gave to Lesley = 10Number of counters Adam has left = Number of counters Adam has - Number of counters Adam gave to Lesley
= 18 - 10
= 8
Fraction of the 18 counters Lesley get = Number of counters Adam gave to Lesley / Number of counters Adam has
= 10/18
= 5/9
Fraction of the 18 counters Adam have now = Number of counters Adam has left / Number of counters Adam has
= 8 / 18
= 4/9
In conclusion, the fraction of counters Adam have now after giving out 10 counters to Lesley is 4/9
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a. 161b.16c. -16116d.e.5
64 ^ (-2/3)
Rewrite 64 as 4^3
(4^3) ^ (-2/3)
Using the power rule a^b^c = a^(b*c)
4 ^(3*-2/3)
4^ -2
We know that a^ -b = 1/ a^b
1 / 4^2
1/16
The graph represents the projected profits for a
company, y, based on the number of units sold, x.
250
200
150
100
50
0
10 15
20
(25, 200)
25
(30, 150)
30
35
x
If the end-of-year analysis indicates that profits did not
meet expectations, which inequality in vertex form
represents the region containing the results of the
year?
Oy< -2(x+25)² - 200
O y> 2(x-25)² + 200
y> 2(x+25)² - 200
Oy< -2(x-25)² + 200
The inequality in vertex form represents the region containing the results of the year is y < -2(x - 25)² + 200 option (D) is correct.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
From the graph:
The vertex is:
(25, 200)
The vertex form of the parabola:
y = a(x - h)² + k
y = a(x - 25)² + 200
Plug x = 30 and y = 150
a = --2
y = -2(x - 25)² + 200
The inequality will be:
y < -2(x - 25)² + 200
Thus, the inequality in vertex form represents the region containing the results of the year is y < -2(x - 25)² + 200 option (D) is correct.
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Jenny put all her shoeboxes in a row. The width of each shoebox is 12.02 cm. What is the total width of all 14 shoeboxes?
Answer:
168.28
Step-by-step explanation:
Write an equation of the line that passes through (-5,4) and is perpendicular to the line that is defined by x-2y=-4
By using the equation of the line and properties of perpendicular lines, we find that the equation of the line is equal to y = - 2 · x - 6.
How to determine the equation of a line
Herein we need to find a line that passes through point (- 5, 4) and is perpendicular to a given line in implicit form: x - 2 · y = - 4. The complete procedure is shown below. First, rewrite the equation of the perpendicular line into explicit form:
x - 2 · y = - 4
2 · y = x + 4
y = (1 / 2) · x + 2
Second, determine the slope of the new line:
m · m' = - 1
(1 / 2) · m' = - 1
m' = - 2
Third, calculate the intercept of the new line:
b = y - m · x
b = 4 - (- 2) · (- 5)
b = 4 - 10
b = - 6
Fourth, complete the new equation of the line:
y = - 2 · x - 6
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You want to open an account with $2,000. You can earn 4% interest each year, and you plan to leave this account for 6 years. How much more would the account be worth after 6 years by calculating interest compounded daily versus calculating simple interest? (Assume 365 days in a year.) Do not round until the final answer. Round to the nearest cent.
The account would be worth more after 6 years if calculating interest compounded daily versus calculating simple interest by $62.46
How to calculate compound interest and simple interest?Principal, p = $2,000Interest rate, r = 4% = 0.04Time, t = 6 yearsNumber of periods, n = 365 daysCompound interest:
A = P(1 + r/n)^nt
= 2,000(1 + 0.04/365)^(365×6)
= 2,000.00(1 + 0.000109589041095)^(2190)
= 2000(1.0.000109589041095)^2190
= 2000 (0.00010958904109589)
= $2,542.46 to the nearest cent
Simple interest:
S.I = principal × rate × time
= 2,000 × 0.04 × 6
= $480
Total = Principal + simple interest
= $2,000 + $480
= $2,480
To find the amount more would the account would be worth after 6 years by calculating interest compounded daily versus calculating simple interest
= Compound interest - Simple interest
= $2,542.46 - $2,480
= $62.46
In conclusion, the account would be worth $62.46 more if compounded daily than simple interest.
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HELP! Alegbra 2
A soccer ball is kicked into the air so that its height, h, in feet, after t seconds is given by the function:
h(t)= -16t^2+96
What is the maximum height the ball reaches?
How long is the ball in the air?
The ball reaches a maximum height of 96 feet and it spent 0 seconds in the air
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the maximum height the ball reaches?The quadratic equation is given as
h(t) = -16t^2 + 96
Differentiate the equation of the function
So, we have
h'(t) = -32t
Set the differentiated function to 0
So, we have
-32t = 0
Divide both sides by -32
So, we have
t = 0
Substitute t = 0 in the equation h(t) = -16t^2 + 96
So, we have
h(0) = -16(0)^2 + 96
Evaluate
h(0) = 96
This means that the maximum height of the ball is 96 feet
How to determine the time spent in the air?Recall that the quadratic equation is given as
h(t) = -16t^2 + 96
Next, we differentiate the equation of the function
So, we have
h'(t) = -32t
Set the differentiated function to 0
So, we have
-32t = 0
Divide both sides by -32
So, we have
t = 0
Hence, the ball spent a total of 0 seconds in the air
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what are the transformations of this functions compared to the parent function
The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation.
Numerous different coordinate systems can be used to describe geometrical figures.
The connection between several systems is defined by coordinate transformations, which offer formulas for the coordinates in one system in terms of the coordinates in another system. The coordinate transformation from polar to Cartesian coordinates is given by the formulas x = r cos and y = r sin, for example, if the polar axis is the positive x axis on the plane and the origins of the Cartesian coordinates (x, y) and polar coordinates (r) are the same.Every bijection from the space to itself can be related to two coordinate transformations.The formulas for the new coordinates of each point's image are constructed in a way that the old coordinates of the original point's image are maintained.In particular, the change of algebraic equations, it is a typical kind of algebraic problem.To learn more about transformation visit:
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Write the equation of the line described.
through
(−1, 2)
and perpendicular to
5x + 3y = 15
Answer:
[tex]y = \frac{3}{5} x + \frac{13}{5} [/tex]
Step-by-step explanation:
The equation of a line can be written in the slope-intercept form y= mx +c, where m is the slope and c is the y-intercept.
Let's rewrite the given equation into the slope-intercept form, so that we can identify its slope.
5x +3y= 15
3y= -5x +15
Divide both sides by 3:
[tex]y = - \frac{ 5}{3} x + 5[/tex]
Thus, the slope of the given line is [tex] - \frac{5}{3} [/tex]
The slope of a perpendicular line is the negative reciprocal of the given line. In simpler terms, the slope of the perpendicular line can be found by flipping the denominator and numerator, and by multiplying -1 afterwards.
Slope of perpendicular line= [tex] \frac{3}{5} [/tex]
Substitute the value of the slope into the equation:
[tex]y = \frac{3}{5} x + c[/tex]
To find the value of c, substitute a pair of coordinates the line passes through.
When x= -1, y= 2,
[tex]2 = \frac{3}{5} ( - 1) + c[/tex]
Solve for c:
[tex]c = 2 + \frac{3}{5} [/tex]
[tex]c = \frac{13}{5} [/tex]
Thus, the equation of the line described is [tex]y = \frac{3}{5} x + \frac{13}{5} [/tex].
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−8+n3=6, what does the n equal?
Answer:
n=2.4
Step-by-step explanation:
The value of n is ∛14.
What is Equation?An equation is a mathematical statement that asserts the equality of two expressions. It consists of two sides, known as the left-hand side (LHS) and the right-hand side (RHS), connected by an equal sign (=).
To solve the equation −8 + n³= 6
Add 8 to both sides of the equation to isolate the term with n:
−8 + n³ + 8 = 6 + 8.
Simplifying the equation gives: n³ = 14.
Take the cube root of both sides to solve for n.
Taking the cube root of n³ = 14
∛(n^3) = ∛14.
Therefore, n = ∛14.
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Find the quotient of (+22)÷(+2)
Please help I’ll mark you as brainliest if correct!!
Answer:
1 hour, 28 minutes, 15 seconds
Step-by-step explanation:
How can you use the Power of a Quotient, Quotient of Powers, Zero Exponent Laws Identity Exponent and to evaluate numerical expressions with whole-number exponents?
The powers can be used in the following manner using multiplicative identity.
Powers are mathematical expressions of the kind where x is the base and n is the exponent. In powers, the exponent specifies how many times to multiply the base by itself whereas the base is the integer or variable that is continuously multiplied.
The quotient rule states that exponents should be subtracted when dividing powers by the same base. For instance, h(6-2) Equals h when h(6) is divided by h(2) (4). Subtracting the exponents is a quick and easy way to simplify the issue.
When separating similar words with exponents, using the Quotient of Powers Rule to minimize the number of terms. This rule states that when dividing words with the same base, the exponents should be removed in order to find the result. When separating similar words with exponents, using the Quotient of Powers Rule to minimize the number of terms. This rule states that when dividing words with the same base, the exponents should be removed in order to find the result. The trick is to eliminate only exponents with compatible bases.
Since the multiplicative identity, or one, is the simple outcome of no numbers at all, it follows that every integer raised to the power of zero equals one.
Thus, we came to the logical conclusions.
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Explain why when multiplying powers you add rather than multiply the exponents.Explain why when multiplying powers you add rather than multiply the exponents.
The gas tank in Margaret's car holds 27 gallons of gas, and she starts out with a full tank. She
drives her car every day, and each day she uses an average of 1.3 gallons. How may gallons wil
she have left after 3 days?
Answer:
She will have 23.1 gallons left after 3 days.
Step-by-step explanation:
We know Margaret uses an average of 1.3 gallons of gas every day and her car holds 27 gallons total. In three days, she would use 3 times her daily average, or 3 * 1.3 = 3.9 gallons consumed in 3 days. To find how many gallons are left in her tank after 3 days, we would subtract 3.9 gallons from 27 gallons. This equals exactly 23.1 gallons of gas.
HELP! ALgebra 2!
A rectangular swimming pool is twice as long as it is wide. The pool has an area of 450 feet. What are the dimensions of the pool?
======================================================
Explanation:
x = width
2x = length, since it is twice as long as it is wide
area = length*width = 2x*x = 2x^2
Set this equal to the area of 450 sq ft and solve for x
2x^2 = 450
x^2 = 450/2
x^2 = 225
x = sqrt(225)
x = 15 feet is the width
2x = 2*15 = 30 feet is the length
Check:
area = length*width = 30*15 = 450
The answers are confirmed.
NEED HELP.... Tom is planning a trip to three different cities this summer. When looking at amap, Tom has drawn in two of the distances between these cities. Which of youranswer choices is the correct way to represent the potential range for how manymiles City B is away from City C?- 3
we have that
the distance city B to city C is equal to
405+401=806 miles4
therefore
the answer is
3 < x < 807 -----> because is a potential range (Its not exact)help me!!! Write an equation of the line passing through the point (2, 8) that is perpendicular to the line 2x - 3y = 7
Answer:
y = -3/2x +11
Step-by-step explanation:
First you have to change the equation from standard form to slope form.
y = mx + b
2x-3y=7 --> subtract 2x from both sides
-3y = -2x + 7 --> now divide both sides by -3 to get y by itself
y = 2/3x - 7/3 --> the reason 2/3x is positive is because when there are two negatives it turns to a positive.
now you have to use point slope form y - y1 = m (x - x1)
x1 and y1 would be your point. 2 is x1 and 8 is y1
y - 8 = -3/2 (x - 2) --> the reason that m is -3/2 is because a perpendicular equation is the opposite reciprocal of the original slope
next distribute the -3/2
y-8 = -3/2x + 3 --> and now add 8 to 3 to get why by it self
now you have y = -3/2x + 11
PLEASE HELP I GIVE BRAINLYS TO THE FIRST ONE THAT GETS IT RIGHT
Answer: 6 blue, 6 yellow, 6 red
Step-by-step explanation:
A fair stack of cards is an equal amount of cards.
3 colors, 18 total
18 / 3 = 6
Therefore 6 of each
You are reading a study that reports selecting a random sample of hospitals and estimating admission delay times. You know this is an example of:
When you're reading a study that reports selecting a random sample of hospitals and estimating admission delay times, it's an example of C. probability sampling.
What is probability sampling?Probability sampling is the process of selecting a sample from a population when the selection is based on the randomization principle, often known as chance or random selection. In general, probability sampling is more difficult, time-consuming, and expensive than non-probability sampling.
Using a method based on probability theory, probability sampling is a strategy in which the researcher selects samples from a larger population.
Researchers can produce a sample that accurately represents the relevant real-world population by using probability sampling.
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You are reading a study that reports selecting a random sample of hospitals and estimating admission delay times. You know this is an example of:
a. Quota sampling
b. Convenience Sampling
c. Probability sampling
d. Sampling bias
A population forms a normal distribution with a mean of μ = 55 and a standard deviation of σ = 12. For each of the following samples, compute the z-score for the sample mean. a. M = 58 for n = 4 scores b. M = 58 for n = 16 scores c. M = 58 for n = 36 scores
It should be noted that the z-score for the sample mean that's given is 0.5.
What is the z score!A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.
The following can be seen from the information illustrated:
Mean ( u ) =55
Standard Deviation ( sd )=12
Number ( n ) = 4
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)
Z = (58-55)/12/ Sqrt ( 4 )
Z = 3/6= 0.5
Therefore, the z score is 0.5.
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how many groups of 1/2 are in 8
i think 16? 1/2+1/2=1 so 8*2=16
At a carnival, 5/8 of the games cost $1. Another 2.5% of the games cost $2. What percent of the games do not cost $1 or $2?
2.5% of 8 = .2
5/8 + .2/8 = 5.2/8
5.2/8 = .65 x 100 = 65%
65% of games cost 1 or 2 dollars
100% - 65% = 35%
!! after doing it i did realize I could've just converted 5/8 into a percent than added it.
or
5/8 = .625 + .025 = .65 x 100 = 65%; 100% - 65% = 35%
Explain how -6 2/5 + 7/3
Answer is -4.0
Answer:
Answer is - 4 1/15
Step-by-step explanation:
-6 2/5 = -32/5
-32/5 + 7/3 to add fractions they must have the same denominator
- 96/15 + 35/15 = ( -96 + 35) / 15 = - 61/15 = - 4 1/15
help me
look at the picture
The zeros of the quadratic are (1 and 3), the vertex is (2, -1). Draw the parabola with a "solid" line. Shade the "interior" of the parabola.
What is defined as the inequality?Inequalities are mathematical representations in which neither side is equal. Unlike equations, we consider the two values in inequality.When inequalities are connected together, it is possible to jump so over middle inequality.If, p < q and q < d, then p < dIf, p > q and q > d, then p > dFor the given question;
The inequality of the function is given as;
= x² - 4x + 3
Find the factors;
(x - 3)(x - 1) = 0
x = 1 and x = 3 are the zeros of the equation.
Now, to graph the equation find the point;
Put x = 0; y = 3
Put x = 1; y = 0
Put x = 2, y = -1
Plot the points on the graph and join the points with solid line.
The vertex of the parabola is found at (2, -1).
Thus, the graph of the parabola is plotted.
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