What is (f⁰f)(3) ?
(F) 1 (G) 5 (H) 21 (I) 77
The value of (fof)(3) is 21.
When two or more functions are combined to form a new function, the new function is known as a composite function. For example- if there is a function f(x), then fof(x) is a composite function formed by repeating f(x) twice.
Here, we are given a function- f(x) = x + 9
if we put the value of x = 3, we get-f(3) = 3 + 9f(3) = 12
now, we need to find the value of (fof)(3)
This can also be written as- {f(f(3)}
we know that f(3) = 12
⇒ {f(f(3)} = f(12)
f(12) = 12 + 9f
(12) = 21
Thus, the value of (fof)(3) is 21.
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f(x) = x + 9
What is (fof)(3)?
(F) 1 (G) 5 (H) 21 (I) 77
What's the distance between 3/4 and 1/8 on a number line?
Answer:
5/8
Step-by-step explanation:
3/4 = 6/8. so 6/8-1/8= 5/8. 5/8 is the answer.
.Two angles form a linear pair. The measure of one
angle is 1/3 the measure of the other angle.
Answer:
45o and 135o
Step-by-step explanation:
The sum of angles of a linear pair is always equal to 180°.
So if the first angle is x,
then the second angle is 3x
x + 3x = 180
4x = 180
x = 45
then 3x = 135
If 6x = 1/216 what is the value of x
Answer:
The answer is in the attached screenshot (I wanted to show properly formatted fractions)
Explanation:
The explanation is in the attached screenshot (I wanted to show a properly formatted fraction)
The question is in the picture
There is a 18-ft fence on one side of a rectangular garden. the gardener has 43 ft of fencing to enclose the other three sides. what is the length of the garden's longer dimension? there is a 18-ft fence on one side of a rectangular garden. the gardener has 43 ft of fencing to enclose the other three sides. what is the length of the garden's longer dimension?
The required dimension of the longer side of the fencing is 18 ft.
As given in the question, there is an 18-ft fence on one side of a rectangular garden. the gardener has 43 ft of fencing to enclose the other three sides.
What is the perimeter?Perimeter is the measure of the figure on its circumference.
Here,
Total length of the fencing = 18 + 43
The total length of the fencing = 61
Perimeter of rectangle = 2 length + 2 width
61 = 2 * 18 + 2 width
2 width = 61 - 36
2 width = 25
width = 12.5 ft
Thus, the required dimension of the longer side of the fencing is 18 ft.
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Use the Change of Base Formula to rewrite each expression using common logarithms.
log₇8
The stated logarithm equation log₇8 in changed by the Base Formula is logₓ8 - logₓ 7.
What is termed as logarithmic?A logarithmic notation is one where variable x contains a logarithm.
The variable in an exponential equation is depicted by an exponent. To solve exponential equations, first see if both sides of the formula could be written as powers of the same number. If you can't, consider taking the common logarithm of both equation sides and solve the problem using property.
Quotient Rule: ㏒(A/B) = ㏒A - ㏒BProduct Rule : ㏒A + ㏒B = ㏒(AB)Power Rule: n㏒A = ㏒AⁿBase Rule = ㏒ₐb = ㏒ₓb/㏒ₓaNow, as per the stated conditions;
The given equation is; log₇8
Apply the Base Rule and re-write the equation;
= logₓ8 / logₓ 7
This obtained equation can also be written on the form by applying product rule.
= logₓ8 - logₓ 7
Therefore, the logarithm equation log₇8 in expressed by the Base Formula is logₓ8 - logₓ 7.
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The length of each side is increased by 2 units. Calvin says that would double the perimeter of the rectangle.
Is he correct? If not, state his error.
A.
Calvin is correct.
B. Calvin is incorrect. He should have squared the 2, so the perimeter would be quadrupled (multiplied
by a factor of 4).
C. Calvin is incorrect. He should add 2 to each side not multiply each side by 2.
D. Calvin is incorrect. He should have cubed the 2, so the perimeter would be multiplied by a factor of 8.
First step: Find the old area. What is the formula for area of a rectangle?
Next step: Find the new area by increasing the measurements 2.
Last: Find new area.
Calvin is incorrect. He should add 2 to each side not multiply each side by 2.
The correct answer is an option (C)
For given question,
Let l be the length of the rectangle and w be the width of the rectangle.
Assume that l = 10 units and w = 4 units
The perimeter of the rectangle is,
P = 2(length + width)
So, for above values the perimeter of the rectangle would be,
⇒ P1 = 2×(10 + 4)
⇒ P1 = 28 units
The length of each side is increased by 2 units.
so, l = 12 and w = 6 units
Then the perimeter of the rectangle would be,
P2 = 2(12 + 6)
P2 = 36 units
According to Calvin, if the length of each side of rectangle is increased by 2 units, the perimeter of the rectangle would double.
But from P1 and P2 we can clearly observe that, Calvin is incorrect.
Calvin possibly double the each side of the rectangle instead of increasing by 2 units.
If he double each side then l = 20 and w = 8
The perimeter of the rectangle would be,
P3 = 2(20 + 8)
P3 = 56
From P1 and P3, the perimeter of the rectangle is doubled.
Therefore, Calvin is incorrect. He should add 2 to each side not multiply each side by 2.
The correct answer is an option (C)
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Use this method to write each equation in logarithmic form. Show your work.
6⁸=a+1
The equation 6 ⁸ = a + 1 in the logarithm form will be given as log ₆ ( a + 1 ) = 8 .
Logarithms are another form of exponents.
For example, we know that 2 raised to which power is equal to 8,
this is expressed by the exponential form as follows 2³ = 8 is equal to log ₂ 8 = 3
Both equations describe the same relationship between the numbers 2, 3, 8 where 2 is the base and 3 is the exponent
The difference is that while the exponential form isolates the power 8,the logarithmic form isolates 3
So by writing given equation in logarithmic form we get -log₆ ( a + 1 ) = 8.
Therefore, the equation 6 ⁸ = a + 1 in the logarithm form will be given as log ₆ ( a + 1 ) = 8 .
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Students at a middle school take an elective during the last hour of the school day. There are 11 students who take an art class. There are 3 times as many students who take a music class as students who take an art class. What is a ratio that relates the number of students who take a music class to the number of students who take an art class.
The ratio that relates the number of students who take a music class to the number of students who take an art class is 3 : 1 .
A ratio is defined as a comparison of two sets of the same unit, showing how much of one set is contained in the other. A common form to express the relationship between two quantities, such as 'a' and 'b', is a:b, read as 'a follows b'.Let the number of students taking arts class be "x"
and number of students taking music class be "y".
It is given that 11 students take an art class which can be given by
x = 11 ...(1)
There are 3 times as many students who take a music class as students who take an art class which can be given by
y = 3x = 3(11) = 33 ....(2)
On dividing equation (1) by (3) , we get
x/y = 11/33 = 1/3
This can be written as x : y = 1 : 3 but here we are asked about the ratio of music class to the art class then ratio is given by y : x = 3 : 1
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he scale factor of △RST to △DEC is 3 ∶ 13. What is the scale factor of △DEC to △RST?
The scale factor of △DEC to △RST is 13 : 3.
The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.
A multiplicative inverse or reciprocal for a number y, denoted by 1/y or y⁻¹, is a number that when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction b/a is a/b.
The scale factor of △RST to △DEC is 3 : 13.
Now, △DEC to △RST is the inverse of △RST to △DEC
Therefore,
[tex]\frac{\Delta RST}{\Delta DEC} = \frac{3}{13}[/tex]
[tex]\frac{\Delta DEC}{\Delta RST} =\frac{13}{3}[/tex]
Hence, the scale factor of △DEC to △RST is 13 : 3.
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1. Which of the following is NOT a use of resistance bands?
muscular strength
muscular endurance
O stretching
speed
Answer:
speed
Step-by-step explanation:
speed is the right answer hope its right
3. Evaluate.
3
8-8
11
The value of the given fraction 3/8 - 8/11 after the evaluation is -31/88.
What are fractions?A fraction is a portion of a larger whole. The number is expressed in arithmetic as a quotient, which is the numerator divided by the denominator. Both are integers in a simple fraction. A complex fraction contains a fraction in either the numerator or the denominator. There are three major types of fractions in mathematics. Proper fractions, improper fractions, and mixed fractions are the three types. Fractions are terms that have a numerator and a denominator.So, evaluation of 3/8 - 8/11:
First, we will take the LCM of 8 and 11.LCM of 8, 11 = 88Now,
3/8 - 8/11[11(3) - 8(8)]/88(33 - 64)/88-31/88Therefore, the value of fraction 3/8 - 8/11 after the solution is -31/88.
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a diagram of a bookcase in an instruction booklet uses a scale of 1:30 if the diagram is 7.8 cm tall 5.4 wide and 1 cm deep what are the actual dimensions of the bookcase
The actual dimensions of the bookcase is 234 cm tall, 162 cm wide and 30 cm deep
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The scale of 1:30 is used to produce a diagram of a bookcase in an instruction booklet.
If the diagram is 7.8 cm tall 5.4 wide and 1 cm deep, hence:
Height of bookcase = 7.8 cm * 30 = 234 cm
Width of bookcase = 5.4 cm * 30 = 162 cm
Depth of bookcase = 1 cm * 30 = 30 cm
The actual dimensions of the bookcase is 234 cm tall, 162 cm wide and 30 cm deep
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Write each equation in logarithmic form. 5⁴=625
The logarithmic form of the given equation (5⁴=625)is = log₅(625) = 4.
logarithmic exponential form:Logarithmic functions are the inverses of exponential functions. So a log is an exponent! y=logbx if and only if by=x for every x>0 and 0b1.
Why we employ logarithms?Logarithms depict changes in terms or multiplication: in the instances above, each step is 10x larger. Each step on the natural log is "e" (2.71828...) times longer. When dealing with a sequence of multiplications, logarithms let us "count" them in the same way that addition counts on our behalf when effects are added.
According to the given data:using the property of log:
5⁴=625
Apply logarithmic definition: aⁿ = b gives logₐᵇ = n
so,
a = 5
b = 625
n = 4
equation would be as follows:
log₅(625) = 4
The logarithmic form of the given equation (5⁴=625)is = log₅(625) = 4
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Answer: [tex]log_{5} 625 = 4[/tex]
Step-by-step explanation:
solve the following equation: 4(n+2)-2n=0
Answer:
Step-by-step explanation:4n+8-2n=0. 2n=-8. n=-4.
HOPE THIS HELPSSSS!!!!!!!!!!!!!+
Answer:
-4
Step-by-step explanation:
4n+8-2n=0 2n=-8.n=-4
Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it.
f(x)
f(x) = −4(x − 8)2 + 3
h(x)
graph of negative 1 times the quantity of x minus 3 squared, plus 2
The axes of symmetry of the functions are f(x): x = 8 and h(x): x = 3
How to determine the axis of symmetry for each function?The functions are given as
f(x) = -4(x - 8)^2 + 3
h(x) = -(x - 3)^2 + 2
A quadratic function is represented as
y = a(x - h)^2 + k
Where the equation of the axis of symmetry of the function is
x = h
This means that the axes of symmetry of the functions are
f(x): x = 8
h(x): x = 3
Hence, the axes of symmetry of the functions are f(x): x = 8 and h(x): x = 3
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I’m stuck please help.
Answer:
Step-by-step explanation:
PS =5 because PS's line is parallel to 5 the line.
So now all that is left is the angle one
m∠Q =105° we can come to this conclusion because 105° is parallel to m∠Q
If you are still confused please, let me know! :)
1.44 make-up exam: in a class of 20 students, 19 of them took an exam in class and 1 student took a make-up exam the following day. the professor graded the first batch of 19 exams and found an average score of 79 points with a standard deviation of 7.3 points. the student who took the make-up the following day scored 60 points on the exam.
a) Since the new score is less than the average score, it will decrease the average.
What a standard deviation means?The degree of data dispersion from the mean is indicated by the standard deviation. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.Think about the following data: 2, 1, 3, 2, 4. The average and the total square of the observations' departures from the mean will be 2.4 and 5.2, respectively. There will be a standard deviation of (5.2/5) = 1.01.Statistics experts have established that measures that are within plus or minus 2 SD of the true value are more accurate than those that fall outside of this range. For data points that frequently fall outside of the 2SD range, the majority of QC programs mandate that remedial action be taken.a) Since the new score is less than the average score, it will decrease the average.
b) Sum of 27 scores = 27*79
Hence,
New average = (79*27 + 63)/28 = 78.43
c) Since the variability would increase in the overall data, the standard deviation increases.
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Please help ASAPPPPPP
EXPLAIN WHY ANSWER IS CORRECT
Answer:
3.7
Step-by-step explanation:
Triangles BDE and BCE are congruent, so BC=BD=3.7.
what operation will you use to solve the x - 3 = 12
Answer: addition
Step-by-step explanation: add three to both sides to eliminate the 3 on the X side and isolate the X
Answer:
X=9
In order to find X u must subtract 3 from 12
12-3=9
so X=9
360(-45)+25 what is the answer for this problem
Answer:
The answer is -16175
Step-by-step explanation:
-First multiply 360 by -45, which equals -16200
-Then add 25 to -16200, and you get -16175
-15.7 and 2.6 are
both greater than
-18
What is a algebraic expression of a number 5 time a number
What is an equation of the line that passes through the point (8,-2) and is perpendicular to the line 4x+3y=3
Answer:
y = 3/4x - 8
Step-by-step explanation:
is it possible to be a rational number that is not an integreter but is a whole?
No, it is not as a result of all whole numbers are integers, thus there's no number that's not associate degree whole number.
A rational number may be outlined as any number that may be expressed or written within the p/q type, wherever 'p' and 'q' area unit integers and Q could be a non-zero number.The whole numbers area unit the numbers while not fractions and it's a group of positive integers and nil. it's diagrammatical by the image “W” and also the set of numbers area unit . Zero as a full represents nothing or a null worth.These numbers area unit positive integers as well as zero and don't embody aliquot or decimal elements (3/4, 2.2 and 5.3 don't seem to be whole numbers). Also, arithmetic operations like addition, subtraction, multiplication and division area unit attainable on whole numbers.
Hence , it is not possible.
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Please help --> 0.42b - 8.3 + 9.14b = -5.91 Show your work please!!!
Answer:
0.25
Step-by-step explanation:
group like terms: 0.42b+9.14b-8.3=-5.91
add similar elements: 9.56b-8.3=-5.91
multiply both sides by 100: 956b-830=-591
add 830 to both sides: 956b-830+830=-591+830
simplify: 956b=239
divide each side by 956: you know what that looks like
simplify: b=1/4
convert to decimal: 0.25
Answer:
b = 0.25
Step-by-step explanation:
Given:
[tex]\sf 0.42b - 8.3 + 9.14b = -5.91[/tex]
Collect like terms:
[tex]\implies\sf 0.42b+ 9.14b - 8.3 = -5.91[/tex]
Combine like terms:
[tex]\implies \sf 9.56b - 8.3 = -5.91[/tex]
Add 8.3 to both sides:
[tex]\implies \sf 9.56b - 8.3+8.3 = -5.91+8.3[/tex]
[tex]\implies \sf 9.56b=2.39[/tex]
Multiply both sides by 100:
[tex]\implies \sf 9.56b \times 100=2.39 \times 100[/tex]
[tex]\implies \sf 956b=239[/tex]
Divide both sides by 956:
[tex]\implies \sf \dfrac{956b}{956}=\dfrac{239}{956}[/tex]
[tex]\implies \sf b=\dfrac{239}{956}[/tex]
Write 956 as 4 × 239:
[tex]\implies \sf b=\dfrac{1 \times 239}{4 \times 239}[/tex]
Cancel the common factor 239:
[tex]\implies \sf b=\dfrac{1}{4}[/tex]
[tex]\implies \sf b=0.25[/tex]
Write each logarithmic expression as a single logarithm.
x log₄m+1/y log₄n - log₄p
The value of logarithmic expression x log₄m+1/y log₄n - log₄p is log₄(m^x * n^1/4)/p.
By considering the given logarithmic expression
x log₄m+1/y log₄n - log₄p
log₄m^x+ log₄n^1/4- log₄p
log₄(m^x * n^1/4)- log₄p
log₄(m^x * n^1/4)/p
The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.
Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).
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Please help me with this assignment.
Answer:D
Step-by-step explanation: 3 over 9 = .333 repeating which is greater then .22 and lower then 33
What does 100000k mean?
You have 153,183K of something.
Does that mean I have 100 million? Or 1 million?
Answer: 100 million.
Step-by-step explanation:
It is 100 million because if you forget the K which means three zeros, it would be like this. 100000000. After three digits, you put a comma, so it would be 100,000,000.