The expression will be; part (a) (f o g)(-2) = 2 and part (b) (g o f)(-2) = -95
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given the functions as;
f(x)=4x-2
g(x)=5-x^2
We need to find (f o g)(-2)
So, first, we will find the function (f o g)(x) as follows:
[tex]\begin{gathered} \mleft(f\circ g\mright)(x)=f\lbrack g(x)\rbrack=4(5-x^2)-2 \\ (f\circ g)(x)=20-4x^2-2 \\ (f\circ g)(x)=18-4x^2 \end{gathered}[/tex]
Now, substitute with x = -2 then we get;
[tex](f\circ g)(-2)=18-4\cdot(-2)^2=18-4\cdot4=18-16=2[/tex]
Thus, the answer to the part is (a) (f o g)(-2) = 2
b) (g o f)(-2)
We need to find (g o f)(x) as follows:
[tex](g\circ f)(x)=g\lbrack f(x)\rbrack=5-(4x-2)^2[/tex]
Now Substitute with x = -2, then we get;
[tex]\begin{gathered} (g\circ f)(-2)=5-(4\cdot-2-2)^2 \\ =5-(-8-2)^2 \\ =5-(-10)^2 \\ =5-100 \\ =-95 \end{gathered}[/tex]
Thus, the answer to the part (b) is (g o f)(-2) = -95
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What’s the answer???
Answer:
2nd
Step-by-step explanation:
Simone and Harper go canoeing. Simone sees 12 storks. Simone seeks 4 times as many storks as harper. How many storks does Harper see?
Answer:48
Step-by-step explanation:12x4=48
Explain the steps for (-1/5) divided by 3/10 x (-2.4).
Answer: The correct answer is 14/7
Step-by-step explanation: This is the correct answer because it's explaining how to do it
Which expression is equivalent to 5x - 5x + 3x - 3x?
Answer:
0
Step-by-step explanation:
subtracting same numbers give you zero
Calculate (A) amount to be credited and (B) balance outstanding: (Round your answers to the nearest cent.) Invoice: $3,000; Terms 2/10, n/30 Invoice date: July 5 Payment amount $600 Date paid: July 14
The amount to be credited, based on the invoice amount and the payment, is $612.24. The balance outstanding is $2, 387.76
How to find the balance outstanding?Credit terms of 2/10, n/30 mean that if a buyer pays their payables in 10 days, they get a 2% discount. If they don't, then they'd have to pay the full thing in 30 days.
The days till the partial payment was made was:
= July 14 - July 5
= 9 days
The discount of 2% would apply on the payment of $600 so the amount to be credited is:
= 600 / (1 - 2%)
= $612.24
The balance would then be:
= Invoice amount - credited amount
= 3, 000 - 612.24
= $2, 387.76
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simplify tana+cota help asap
Using trigonometric ratios, tan a + cot a = (cos a + sin a) / sin a * cos a
Trigonometric RatioThe six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trigonometric ratios are evaluated with respect to sides and angles.
In the question given, the trig ratio is
tan a + cot a
We can simplify this as
tan a = sin a / cos a
cot a = 1 / tan a = 1 / sin a / cos a = cos a / sin a
Adding both ratios together
tan a + cot a = (sin a / cos a) + (cos a / sin a)
tan a + cot a = (cos a + sin a) / sin a * cos a
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Which set of real numbers includes positive integers but not negative integers or zero?
A set of real numbers which includes positive integers but no negative integers or zero is set of natural numbers.
What are Real numbers?
The set of real numbers is represented by the letter R.
Every number (except complex numbers) is contained in the set of real numbers. For example: 2, -8, 33/5, -1/5, 0, etc.
What are Integers?
The set of integers is represented by the letter Z.
An integer is any number in the infinite set, Z = (..., -3, -2, -1, 0, 1, 2, 3, ...}
Integers can further be divided into
positive integers i.e. 2, 6, 3456, etc.zeronegative integers i.e. -4, -17, -57385, etc.What are Natural numbers?
The set of natural numbers is represented by the letter N.
A natural number is a positive integer.
N = { 1, 2, 3, 4, ... }
According to the given question:-
Set of real numbers comprises of Rational numbers, irrational numbers, integers, whole numbers, etc.
Hence a set of real numbers which includes positive integers but no negative integers or zero is set of natural numbers i.e.
N = { 1, 2, 3, 4, ... }
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Hiroshi spends 30 minutes on history homework, 60 minutes on English homework, and x minutes on math homework. One fourth of his total homework time is spent on math. Which equation can be used to find the amount of time Hiroshi spends on his math homework?
StartFraction one-fourth EndFraction left-parenthesis x plus 30 plus 60 right-parenthesis equals x.(x + 30 + 60) = x
StartFraction one-fourth EndFraction left-parenthesis x right-parenthesis equals x left-parenthesis 30 plus 60 right-parenthesis.(x) = x(30 + 60)
StartFraction one-fourth EndFraction x left-parenthesis 30 plus 60 right-parenthesis equals x.x(30 + 60) = x
StartFraction one-fourth EndFraction left-parenthesis x right-parenthesis equals left-parenthesis 30 plus 60 right-parenthesis.(x) = (30 + 60)
An equation that can be used to find the amount of time Hiroshi spends on his math homework would be 1/4(30 + 60 + x) = x
In this question, Hiroshi spends 30 minutes on history homework, 60 minutes on English homework, and x minutes on math homework.
So, his total homework time would be,
(30 + 60 + x)minutes
Also, we have been given One fourth of his total homework time is spent on math.
We need to find an equation that can be used to find the amount of time Hiroshi spends on his math homework.
So, we get an equation,
1/4(30 + 60 + x) = x
Therefore, an equation that can be used to find the amount of time Hiroshi spends on his math homework would be 1/4(30 + 60 + x) = x
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Answer:
c
Step-by-step explanation:
(8/10)=(9/n)
Solve for n
Answer:
n=90/80
Step-by-step explanation:
you make n the subject of the formular
f(x) = -x³ + 3x² +9
x=4
[tex]{ \pink{ \boxed{ \red{ \sf{f(4) = - 7}}}}}[/tex]
Step-by-step explanation:
[tex]{ \green{ \sf{f(x) = { - x}^{3} + 3 {x}^{2} + 9}}}[/tex]
[tex]{ \green{ \sf{f(4) = ( { - 4})^{3} + 3( {4})^{2} + 9}}}[/tex]
[tex]{ \green{ \sf{f(4) = - 64 + 3(16) + 9}}}[/tex]
[tex]{ \green{ \sf{ f(4) = - 64 + 48 + 9}}}[/tex]
[tex]{ \green{ \sf{f(4) = - 64 + 57}}}[/tex]
[tex]{ \blue{ \boxed{ \orange{ \sf{f(4) = - 7}}}}}[/tex]
What is the image point of (-8, 1) after the transformation D₂ 0 R180 ?
The image point of (-8, 1) after the transformation D₂ о R180° is equal to (16, -1).
Given that,
The point is (-8,1)
We must locate the point's picture.
In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has the coordinates (-x, -y).
We have the following for a 2 scale factor dilation:
Point A (-8, 1)
= (-8 × 2, 1 × 2)
= Point A' is (-16, 2)
By applying a rotation of 180° to the given point, the coordinates of its image is given by:
(x, y)→(-x, -y)
Points A' = (-16, 2)
Points A' = (-(-16), -(1)) = (16, -1).
Therefore, The image point of (-8, 1) after the transformation D₂ о R180° is equal to (16, -1).
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(PLEASE OPEN) Need help with triangle proofs, please.
The triangle proof that shows that angle Q and angle S are congruent to each other is explained below.
What is the Side-angle-side Congruence Theorem (SAS)?The side-angle-side congruence theorem (SAS) states that if the two sides and an included angle in one triangle is congruent to two corresponding sides and an included angle in the other triangle, then both triangles are congruent to each other.
If two triangles are congruent to each other, the CPCTC theorem states that all their corresponding parts are also equal or congruent to each other.
The triangle proof is given as:
Statements Reasons
1. PR bisects ∠PQS 1. Given
2. ∠1 ≅ ∠2 2. Definition of bisection
3. PQ ≅ PS 3. Given
4. RP ≅ PR 4. Reflexive property
5. ΔQPR ≅ ΔSPR 5. SAS theorem
6. ∠Q ≅ ∠S 6. CPCTC
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Write an equation of the line that passes through (-3,1) and is perpendicular to y= 1/2x +3
Answer: y=-2x-5
Check this in desmos
Directions
Read the instructions for this self-checked activity. Type in your response to each question, and check your answers. At the end of the activity, write a
brief evaluation of your work.
Activity
In the first Lesson Activity, you derived an equation to model a car wash. The equation is y = 5x - 75. In this activity, you will graph this equation.
Question 1
Is it possible to graph the line that represents this equation by using two points found in the previous Lesson Activity, (15, 0) and (0, -75)? Explain
your answer.
Yes, the graph goes through those two points.
What is Graph?
In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
The points on the graph often represent the relationship between two or more things.
What is linear equation?
A linear equation is an algebraic equation of the form y=mx + b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
Explanation for the answer:
The equation can be graphed by plotting the two given points and drawing a line through them. Such a graph is shown in the attachment.
You can graph a line for any linear equation from any two points that fit the equation. So you can use the points (0, -75) and (15, 0) to graph the line representing the situation.
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=
4(7x), what is the value of a(-2)
The value of the function f(x) = 4 ( 7x ) for x = -2 is equal to f( -2 ) = -56.
As given in the question,
Given expression is equal to :
f(x) = 4 ( 7x )
Calculate the value of the given function for x = -2 is given by :
Substitute value of x = -2 we get.
f(-2)
= 4 ( 7 ( -2) )
Seven is positive and 2 is negative , multiplication of positive to negative is always negative.
So, 7 ( -2 ) is -14 Substitute in above equation we get,
= 4 ( -14 )
= -56
Therefore, the value of the function f(x) = 4 ( 7x ) for x = -2 is equal to
f( -2 ) = -56.
The complete question is :
If f(x) = 4 (7x) , what is the value of f(-2)?
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Given m || n, find the value of x and y.
(3y-17) (6x+20)°
(7x+13)
n
Answer:
Value of x = 7° & y = 45°
Step-by-step explanation:
According to the question m || n.
For x:
[tex] \rm \implies (7x + 13) \degree = (6x + 20) \degree \\ \\ \rm \implies 7x - 6x = 20 \degree - 13\degree \\ \\ \rm \implies x = 7 \degree[/tex]
For y:
[tex] \rm \implies (3y - 17)\degree + (6x + 20) \degree = 180\degree \\ \\ \rm \implies (3y - 17)\degree + (6 \times 7 + 20)\degree = 180\degree \\ \\ \rm \implies (3y - 17)\degree + (42 + 20)\degree = 180\degree \\ \\ \rm \implies 3y - 17\degree + 62\degree = 180\degree \\ \\ \rm \implies 3y + 45\degree = 180\degree \\ \\ \rm \implies 3y = 180\degree - 45\degree \\ \\ \rm \implies 3y = 145\degree\\ \\ \rm \implies y = \bigg( \frac{145}{3} \bigg) ^\degree \\ \\ \rm \implies y = 45\degree[/tex]
2x−4y=6
Step 2 of 2 : Determine the missing coordinate in the ordered pair (?,5) so that it will satisfy the given equation.
A family wants to save $100 each month. They record their progress toward this goal at the end of each month. What would a recording of $0 mean?
A recording of $0 for the family simply means that they have not saved anything or have spent all the savings.
What is savings?Savings simply means keeping of miney for a period of time in order to cater for future expenses. Saving is defined as income that is not spent or deferred consumption. Saving methods include putting money aside in a deposit account, a pension account, an investment fund, or as cash. Saving also entails lowering expenses, such as recurring costs.
Here, the family wants to save $100 each month and they record their progress toward this goal at the end of each month.
A recording of $0 simply means no savings.
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factor and graph the equation -0.01x² +0.5x
The graph and factor to the given equation are x= 50 or x=0.
What is equation?
An equation may be a formula in arithmetic that expresses the equality of 2 expressions by connecting them with the sign =.
Main body:
I am assuming the equation as : -0.01[tex]x^{2}[/tex] + 0.5x =0
Now first removing the decimal from the equation ,
-[tex]x^{2}[/tex]/100 + 5x/10 = 0
-[tex]x^{2}[/tex] + 50 x = 0
switching signs , we get
[tex]x^{2}[/tex] - 50x= 0
taking x as common
x(x-50) =0
so either x = 0
or
x- 50 = 0
x =50
Hence the value of x are 0 or 50.
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hi some 1 help me out
Answer:
3(3+4) IS NOT EQUAL TO 3^3
Step-by-step explanation:
3(3+4)
Expand brackets to get 21 (3x3 = 9, 3x4 = 12, 9 + 12 = 21)
3^3 = 3 x 3 x 3
3x3 = 9
9 x 3 = 27
21 < 27
A relation contains the points (1,-4), (3, 2), (4, -3), (x, 7), and (-4, 6).
For which value of a will the relation be a function?
O-4
O-3
O 3
O 4%
For x = -3 the relation will be a function.
We know that a relation is a function when for each input there is exactly one output.
In this question, we need to find the value of x for which the relation will be a function.
We need to select the value of x such that x ≠ 1, 3, 4, -4
This means x must be -3
Therefore, For x = -3 the relation will be a function.
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The revenue function is given by R(x)=x⋅p(x) dollars where x is the number of units sold and p(x) is the unit price. If p(x)=26(4)−x5, find the revenue if 15 units are sold. Round to two decimal places.
If price p(x) =26(4)^{-x/5}, the revenue when 15 units are sold is equal to $6.09.
How to calculate the amount of revenue at p(15)?From the information provided, the amount of revenue with respect to price that's being generated in this scenario can be calculated by using the following function (expression):
R(x) = x × P(x)
Where:
x represents the number of units sold.p(x) represents the unit price.Since the revenue function, we would simply substitute the value of the unit price and evaluate as follows:
Revenue, R(x) = x × 26(4)^{-x/5}
Substituting the given parameters into the formula, we have;
Revenue, R(x) = 15 × 26(4)^{-15/5}
Revenue, R(x) = 15 × 26(4)^{-3} or (15 × 26)/4³
Revenue, R(x) = 15 × 26(0.015625) or 390/64
Revenue, R(x) = 6.09375 ≈ $6.09.
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Complete Question:
The revenue function is given by R(x)=x⋅p(x) dollars where x is the number of units sold and p(x) is the unit price. If p(x)=26(4)^{-x/5}, find the revenue if 15 units are sold. Round to two decimal places.
The owner buys jackets for $45 and sells them how many jackets must the owner buy for the total jacket sales to be at least $390
Isabelle wanted to arrange her baseball cards in pairs but was one card short . she tried to arrange them by fives and was still one card short. she finally arranged her cards by sevens. what is the least number of cards she could have had?
The Least number of baseball cards Isabella could have is 49
How to determine the least number of cardsTo solve the problem, the multiples of seven will be necessary to ascertain the one that will:
have remainder 1 when divided by 2 remainder 4 or fall short by 1 when divided by 5multiples of 7: 7 , 14 , 21 , 28 , 35 , 42 , 49 , 56 , 63....
14 is short of 1 when divided by 5 but it is divisible by 2 without remainder
49 is the least number that fall short of 1 card to make it a multiple of 5 and have a remainder one when divided by 2
Hence the answer is 49
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You pick a card at random.
5678
What is P(not divisor of 45)?
Write your answer as a percentage.
%
As a percentage, a card at random 5, 6, 7, 8 9, 7.5, 6.42, 5.62. Per cent is derived from the Latin adverbial phrase per centum, which means "by the hundred." The Latin phrase made its way into English in the 16th century.
What is meant by percentage?A percentage is a number or ratio that is expressed as a fraction of one hundred. The percent sign, "%," is commonly used, but the abbreviations "pct.", "pct.," and sometimes "pc" are also used. A percentage is a number with no dimensions; it has no unit of measurement. Percentage = (Original number/Another number) x 100 is the formula for calculating the percentage of one number from another. A percentage is a value or ratio that represents a fraction of 100 in mathematics. Percentage means one hundred percent. There are no units in it. A percentage is a number that tells us how much out of 100 we are talking about, and it can also be written as a decimal or a fraction - three for the price of one.Therefore,
45/5 = 9
45/6 = 7.5
45/7 = 6.42
45/8 = 5.62
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The equation of line s is y= – 4x– 5/3 . Line t includes the point ( – 3,3) and is parallel to line s. What is the equation of line t?
The equation of the parallel line t is y = -4x - 9
How to determine the line equation?The equation of line s given as
y = -4x - 5/3
Also, from the question
The point on line t is given as
Point = (-3, 3)
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = -4
This means that the slope of y = -4x - 5/3 is -4
The slopes of parallel lines are equal
This means that the slope of the line t is -4
The equation of the parallel line is then calculated as
y = m(x - x₁) +y₁
Where
m = -4
(x₁, y₁) = (-3, 3)
Substitute the known values in the above equation
y = -4(x + 3) + 3
Evaluate
y = -4x - 12 + 3
Evaluate the sum
y = -4x - 9
Hence, the parallel line has an equation of y = -4x - 9
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convert the following percents to a decimal. show steps. help fast pls
10%
15%
17.5%
0.125%
113%
202.125%
Answer:
below
Step-by-step explanation:
0.1
0.15
0.175
0.00125
1.13
2.02125
{ ( - 4, 2 ), ( - 1, 0 ), ( - 3, 1 ), ( 2, - 3 ) } Write the set using set notation and in ascending order.
By using set notation, the elements of the given data set in ascending order include {-4, -3, -3, -1, 0, 1, 2, 2}.
What is a listing method?In Mathematics, a listing method can be defined as a technique which is used to list all the elements or members of a data set, while separating each of them with a comma and enclosing the data set within curly braces.
Generally speaking, set notation is typically used in mathematics for listing the elements of a set such as objects, numbers, or outcomes, especially by making use of curly brackets.
For this exercise, the elements of the given data set would be listed in ascending order as follows:
Set = {-4, -3, -3, -1, 0, 1, 2, 2}
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Help with this precalc question
The principal amount invested at the rate of 6% for 3 years, then the investment results in $717.38.
What is compound interest?Interest that is added to a loan and deposit sum is known as compound interest. In our everyday lives, it is the notion that is employed the most frequently. Compound interest is calculated as a sum using the interest and principal accrued over time. Compound interest versus simple interest differ primarily in this way.
As per the given information in the question,
Principle, P = $600
Rate, r = 6%
Time, t = 3 years.
Compound quarterly, r = 6/4
t = 4 × 3 = 12
Use the formula,
[tex]A = P(1+\frac{r}{100} )^t[/tex]
A = 600(1 + 6/4 × 100)¹²
A = 600 × (203/200)¹²
A = $717.38
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A firm manufactured 1000 Tv sets during its first year.the total firms production during the 10 year of operationis 29035 sets .
For each the level of output for 15th year using per year constant increase in production .
Answer:
6922 TV sets
Step-by-step explanation:
You want the production in the 15th year if production in the first year is 1000 and it increases yearly by a constant amount. The total production in the first 10 years is 29035.
Arithmetic seriesAn arithmetic series is one that has a constant difference from one term to the next. If a1 is the first term of the series, and d is the common difference between terms, the n-th term is ...
an = a1 +d(n -1)
And the sum of n terms is ...
Sn = (2a1 +d(n-1))(n/2)
ApplicationTo find the 15th term, we can make use of the given values to find the common difference, then use the formula for the n-th term.
S10 = (2(1000) +d(10 -1))(10/2) . . . . . sum formula with a1=1000
29035 = 10000 +45d . . . . . . . . . . . simplified
d = (29035 -10000)/45 = 423 . . . . the increase in production each year
Production in the 15th year is ...
a15 = 1000 +423(15 -1) = 1000 + 5922 = 6922
The output in the 15th year was 6922 TV sets.