Answer:
6
Step-by-step explanation:
(f / g)(x)
= [tex]\frac{f(x)}{g(x)}[/tex]
= [tex]\frac{10x}{2x-1}[/tex] ← substitute x = 3
= [tex]\frac{10(3)}{2(3)-1}[/tex]
= [tex]\frac{30}{6-1}[/tex]
= [tex]\frac{30}{5}[/tex]
= 6
please help If f(x)=sinx, then f′(π/3) =
Answer:
[tex]f' \left(\dfrac{\pi}{3}\right) =\dfrac{1}{2}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=\sin x[/tex]
The differentiation of sin(x) is cos(x).
[tex]\implies f'(x)=\cos x[/tex]
Therefore:
[tex]\implies f' \left(\dfrac{\pi}{3}\right) = \cos \left(\dfrac{\pi}{3}\right)[/tex]
[tex]\implies f' \left(\dfrac{\pi}{3}\right) =\dfrac{1}{2}[/tex]
Let f(x)=4 x, g(x)=1/2 x+7 , and h(x)=-2 x+4 . Perform each function operation. (h⁰ g)(x)
The value of the composite function (h⁰ g)(x) calculated by function operation is -x-10 .
A function is defined as the relation between element of two sets, domain and range. A function is usually denoted using f, g or h .
A algebraic function is defined as y=g(x) such that each element y is related to a single value of x.
(h ∘ g)(x) is also written as h[g(x)] is called a composite function where which means the value of x=g(x) will be substituted in the function h(x).
Composite function is a process that joins two functions to create a third, unique function.
The output of one function becomes the input of another function in h of g of x.
Given functions are:
g(x)=1/2 x+7 and h(x)=-2 x+4
Therefore (h ∘ g)(x)=h[g(x)]
=h(1/2 x+7)
=-2(1/2 x+7)+4
=-x-14+4
=-x-10
Hence the value of the function operation (h⁰ g)(x) is -x-10 .
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Find the two consecutive asymptotes, the period (in radians), the phase shift (in radians) and the vertical shift of the function: y = 4csc(5θ - 3π/4)
Answer:
Phase shift = [tex]\frac{3\pi }{5}[/tex]
Vertical shift = [tex]0[/tex]
Step-by-step explanation:
Shift Definition
[tex]\text{For\:}f\left(x\right)=A\cdot g\left(Bx-C\right)+D\text{,\:where\:}g\left(x\right)\text{\:is\:one\:of\:the\:basic\:trig\:functions,\:}[/tex] [tex]\frac{C}{B}\text{\:is\:phase\:shift}[/tex], [tex]D\text{\:is\:vertical\:shift}[/tex]
Here we have
[tex]\left(x\right)=4\csc \left(\frac{5\theta-3\pi }{4}\right)[/tex]
which can be written in the form [tex]g\left(Bx-C\right)=\csc \left(\frac{5\theta-3\pi }{4}\right)[/tex]
So comparing the two we get [tex]B=\frac{5}{4}, C=\frac{3\pi }{4},\:D=0[/tex]
Phase shift = [tex]\frac{C}{B} = \frac{\frac{3\pi }{4}}{\frac{5}{4}}[/tex] [tex]= \frac{3\pi }{5}[/tex]
Vertical shift [tex]D = 0[/tex]
Plssss help this is harder than my hw and I am helping a second grader
Answer:
Ballio's goal is to read 23 books.
Step-by-step explanation:
9+9+9=27
27-4=23
27
9 9 9 (9x3=27)
31 (27+4)
27 4
23 (27-4)
Brainlist Pls!
Which of the following numbers are solutions to -2x-3≤11
a: -7 b: -10 c: 7 d: 10 e: -4
A) c,d,e
B) a,c,d,e
C) a,b
D) none
The numbers that are solutions to -2x - 3 ≤ 11 are (b) a, c, d and e
How to determine which of the numbers are solutions to -2x - 3 ≤ 11?The inequality expression is given as
-2x - 3 ≤ 11
Add 3 to both sides of the inequality
So, we have:
-2x ≤ 14
Divide through the inequality by -2
So, we have
x ≥ - 7
The above means that all numbers from -7 (inclusive) are in the solution
Hence, the numbers that are solutions to -2x - 3 ≤ 11 are (b) a, c, d and e
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A canteen has fixed cost of 1500 per week.meal costs 5 each are sold at a fixed price of 9 each.write down the eq for total cos
An equation for the total cost is TC = 1500 + 5x
In this question, a canteen has fixed cost of $1500 per week.
A meal costs $5 each are sold at a fixed price of $9 each.
We need to write the equation for the total cost.
Let x be the number of individuals.
Let TC represents the total cost.
So, an equation for the total cost would be,
TC = 1500 + 5x
Therefore, an equation for the total cost is TC = 1500 + 5x
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How did you determine whether a fraction was equivalent to 2/5 Explain.
Answer:
An equivalent Fraction is obtained by multiplying both the numerator and denominator of the given fraction by the same number.
Step-by-step explanation:
So, the Equivalent Fraction of 2/5 = 4/10, 6/15, 8/40. An equivalent Fraction is obtained by dividing both the numerator and denominator of the given fraction by the same number.
Determine whether the vectors in each pair are normal to each other. [1 8 4 -2}
Since their dot product is not equal to zero, then vectors (1,8) and (4, -2) are not normal to each other.
Two vectors are said to be normal or perpendicular to each other if the result of their dot product is equal to zero.
These two vectors are also called orthogonal to each other.
Let u = (u₁, u₂) and v = (v₁, v₂), then the dot product u . v is defined as:
u . v = u₁v₁ + u₂v₂
To check whether the vectors are normal to each other, let us check their dot product.
The given vectors are: (1,8) and (4, -2).
Let u = (1, 8) and v = (4, -2), then,
u . v = 1 . 4 + 8 . (-2)
= 4 + (-16) = -12 (not equal to zero)
Since u.v ≠ 0, then (1,8) and (4, -2) are not normal to each other.
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For each function, find the inverse and the domain and range of the function and its inverse. Determine whether the inverse is a function. f(x)=(x-4)²
The inverse function returns the original value for which the output of a function was given.
The inverse of the function f(x) = (x - 4)² is f(x) = √x - 4
What is the inverse formula?The inverse function returns the original value for which the output of a function was given. When it comes to functions, f and g are inverse, with f(g(x)) = g(f(x)) = x. A function that is made up of its inverse returns the original value.
An inverse in mathematics is a function that serves to "undo" another function. That is, if f(x) produces y, then putting y into the inverse of f yields x. Invertible functions are those that have an inverse, which is denoted by f1.
Consider F(x) = y,
The x and y value is switched giving the necessary equation of
x = (y - 4)²
Then solve for y
√x = y - 4
simplifying the above equation, we get
y = √x - 4
The domain of the expression is all real numbers except where the expression is undefined, In this case, there are no real numbers that make the expression undefined.
Interval Notation: (-∞,∞)
Set-Builder Notation: {x| x ∈ R}
The range is the set of all valid y values, use the graph to find the range
Interval Notation: [0,∞)
Set-Builder Notation: {y| y ≥ 0}
The domain and range be
Domain: (-∞,∞) {x| x ∈ R}
Range: [0,∞) {y| y ≥ 0}
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A box is filled with 12 red crayons, 5 blue crayons, and 7 yellow crayons.
A crayon is chosen at random from the box. Find the probability that it is a blue or a yellow crayon.
Write your answer as a fraction in simplest form.
Answer:
Red or blue crayon - 11/16
Step-by-step explanation:
Red crayon - 9/16
Blue crayon - 2/16
Red or blue crayon - 11/16
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
There are 24 total crayons in the box. You want to know the probability of picking a blue or yellow crayon. Since there are 7 yellow crayons and 5 blue you add those together and get 12. You now have your numerator in your fraction. There are also 12 red crayons12+12 = 24 and now you have your denominator. The fraction now reads 12/24. You simplify by dividing the top and bottom by 12 and get 1/2. Hope this helps.439x39=
Please help
Because no one has done this one yet
Answer:
Answer= 17,121
Step-by-step explanation:
439
x39
3951
1317 then you add
Find the value of 1.36 divided by 0.081
Answer: 16.7901
Step-by-step explanation: when dividing decimals, you need to make the divisor a whole number.
So, in this case you move the decimal point on 0.081 until it is a whole number.
then it would be 81 after moving the point 3 times to the right.
Now to make it even, you need to move the decimal point on 1.36: 3 times. You will then get: 1,360 divided by 81
And add back the decimal point once you divide.
Point G is the center of the small circle. Point X is the center of the large circle. Points G, H, and X are all on line segment GX.
what should be the area of a new circle that has a line segment GX as the diameter
The area of a new circle that has line segment GX as its diameter is 121 pi cm² .
Suppose that,
The radius of the small circle (GH) = 10 cm.
The radius of the big circle (HX) = 12 cm.
We will add the line GH and HX to get the total length of line segment GX.
So, GX = GH + HX
= 10 + 12
GX = 22 cm.
So, the diameter of new circle will be equal to line segment GX as it is given in the question.
Then, the area of new circle = π r² ( r = radius)
Radius = D/2 = 22/2 (D = Diameter)
r = 11
Now, Area = π × 11²
= 121π cm²
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What is the measure of line AD
suppose you invested $20,000 and it grew by 15% every year for 20 years. how much would this investment be worth after 20 years?
1. $300,000
2. $308,140.43
3. $6.65 x 10^27
4. $327,330.74
If you can explain how you got your answer please, thank you!!
lyft charges 1.50 for the initial fee and 0.88 per mile traveled for an lyftX write and solve an inequality to determine how many miles jazlyn can travel if she has 25$ to spend. round your answer to the nearest hundreth.
16+56 divided by 2^3-17 order operations
Answer: The answer is -9
Step-by-step explanation: so the equation is 16+56/2^3-17. First we multiply 2^3 which makes 8 and now we have 16+56/8-17 and then continue with addition and subtraction were left with 72/-9 then we divide it and were left with -8 as our total!
Hoped this helped! C:
The value of the expression is 6.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
16 + 56 ÷ 2³ - 17
Applying PEMDAS.
= 16 + 56 ÷ 8 - 17
= 16 + 56/8 - 17
= 16 + 7 - 17
= 16 - 10
= 6
Thus,
The value of the expression is 6.
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Morgan spent $42 for a jacket. This was $14 less than twice what she spent for a a pair of jeans. How much were the jeans?
Responses
$28
$28
$21
$21
$22
$22
$31
Rotation 90° counterclockwise around the origin
Translation 17 units right and 12 units up
The point after all the rotation and translation will become (17 - y, x + 12) from (x, y).
We need to first rotate the point 90° counterclockwise around the origin.
Let the point be (x, y)
When rotating a point 90° counterclockwise about the origin, the coordinate of the point (x, y) will become (-y, x). In other words, x and y will be switched and y will become negative.
Now, we need to translate the point 17 units right.
So, it means that the x - coordinate of the point will become x + 17
So, the point now becomes:
( -y , x ) = ( - y + 17 , x)
(17 - y, x)
Now we have to translate the point 12 units up.
So, we get that:
(17 - y, x + 12)
Therefore, the point after all the rotation and translation will become (17 - y, x + 12) from (x, y).
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Which angles are complementary to each other?
Answer:
C. <3 and<4
Step-by-step explanation:
Complementary angles are angles whose two angles make the sum 90°.
Guess bestie slay you'll do great!
1. if parallel lines are intersected by a transversal then alternate interior angles
Answer:
They are conguent.
Step-by-step explanation:
10,12,14 please help
Answer:
Step-by-step explanation:
I cannot tell which points are which. We need a clearer picture if you do not mind
I need help with this
The first 4 terms of the geometric sequence are 12 , 36 , 108 and 324.
In a geometric sequence, each term following the first is found by multiplying the preceding one by a constant, non-zero quantity known as the common ratio.
The nth term of a geometric series with first term a and common ratio r is given by [tex]a_n=ar^{n-1}[/tex] .
Given the first term of the geometric sequence is 12 .
And given [tex]a_n=a_{n-1}\times 3[/tex]
Now using the above formula:
a₂ = a₁ × 3
or, a₂ = 12 × 3 = 36
Again using the above formula:
a₃ = a₂ × 3
or, a₃ = 36×3 = 108
Similarly
a₄ = a₃ × 3
or, a₄ = 108 × 3 = 324
Hence the first four terms of the geometric sequence are 12 , 36 , 108 and 324 .
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The left and right page numbers of an open book are two consecutive integers whose sum is 277. Find these page numbers.
The two page numbers are
(Use a comma to separate answers as needed.)
Answer:
138, 139
Step-by-step explanation:
You want the consecutive page numbers whose total is 277.
Consecutive numbersConsecutive integers differ by 1. If the lesser of two consecutive integers is represented by x, then the next one is (x+1). The sum of these two integers will be ...
x + (x +1) = 2x +1
We want to find the numbers whose sum is 277:
2x +1 = 277
2x = 276
x = 138
x+1 = 139
The two page numbers are 138, 139.
__
Additional comment
It is customary for the odd page number to be on the right when the book is open. Fortunately, this problem makes that be the case.
Therefore, two page numbers are 138, 139 of a left and right page numbers of an open book are two consecutive integers whose sum is 277.
What is integers?Positive numbers, negative numbers, and zero are examples of integers. 'Integer' is a Latin word that means 'complete' or 'completely'. This means that integers exclude fractions and decimals. In this article, we'll learn more about integers, their definition, and their properties.
All whole numbers & negative numbers are considered integers. This means that if we combine negative and whole numbers, we get a set of integers.
The difference between two consecutive integers is 1. The following integer is (x+1) if x is the lesser of two subsequent integers. These two integers' sum will be
x + (x +1) = 2x +1
So for 277 the equation will be
⇒ 2x +1 = 277
⇒ 2x = 276
⇒ x = 138
⇒ x+1 = 139
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Determine whether the vectors in each pair are normal to each other. (6,-3) and (2,4).
Since their dot product is zero, then (6,-3) and (2,4) are normal to each other.
Step-by-step explanation:
Two vectors are said to be normal or perpendicular to each other if the result of their dot product is equal to zero.
These two vectors are also called orthogonal to each other.
Let u = (u₁, u₂) and v = (v₁, v₂), then the dot product u . v is defined as:
u . v = u₁v₁ + u₂v₂
To check whether the vectors are normal to each other, let us check their dot product.
The given vectors are: (6,-3) and (2,4).
Let u = (6, -3) and v = (2, 4), then,
u . v = 6 . 2 + (-3) . 4
= 12 + (-12) = 0
Since u.v = 0, then (6,-3) and (2,4) are normal to each other.
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is –10 an irrational number?
can someone help me pls !!!!!!!
Learning task 2. Complete the following to make a true statements. Then, determine the property applied.
1. 18 + _______ = 6 + 18
2. -40 + ________ = 0
3. ( 10 + 3 ) + 6 = 10 + ______
4. -15 + ________ = -15
5. _______ + 0 = 42
6. -2 ( 5 + 8 ) = ___________ + ( -16 )
7. 30 ( _____ ) = 30
[( 4 )( 6 )] 2 = 4 [ ___________ ]
9. 15 * ______________ = 0
10. ( 12 )(-4 ) = ________ 12
SOMEONE PRETTY PLEASE HELP MEE
The value of x in the angles is 14.
How to find angles when parallel lines are cut by transversal?When parallel lines are cut by a transversal, angle relationships are formed.
The angle relationships that are formed includes corresponding angles, alternate angles, vertical angle etc.
Therefore, the value of x can be found as follows;
m∠1 = m∠7 (vertical angles)
Therefore,
m∠7 = m∠15(corresponding angles)
Hence,
m∠1 = m∠15
m∠1 = 8x - 4
m∠15 = 6x + 24
Therefore,
8x - 4 = 6x + 24
8x - 6x = 24 + 4
2x = 28
divide both sides by 2
x = 28 / 2
x = 14
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On a math test, Anna writes 9 as a solution to 3/27. Find the correct solution what error did Anna likely make on her test?
Answer:
[tex]\frac{1}{9}[/tex]
Step-by-step explanation:
Ana forgot to do prime factorisation of [tex]\sqrt{27}[/tex] and bring out one three from the pair of square root of 3.
Answer: she used 3 as the denominator and 17 as the numerator and/or she didn't make it a fraction which would make the correct answer be 3/27=1/9
Step-by-step explanation:hope it helps, brainliest? i could really use it