Answer:
The solution of the equation are 3 , -11
Step-by-step explanation:
* Lets revise how to make the completing square
- The form of the completing square is a(x - h)² + k, where a , h , k
are constant
- The general form of the quadratic is ax² + bx + c, where a , b , c
are constant
- To change the general form to the completing square form equate
them and find the constant a , h , k
* Now lets solve the problem
∵ x² + 8x = 33 ⇒ subtract 33 from both sides
∴ x² + 8x - 33 = 0
- lets change the general form to the completing square
∴ x² + 8x - 33 = a(x - h)² + k ⇒ solve the bracket of power 2
∴ x² + 8x - 33 = a(x² - 2hx + h²) + k ⇒ multiply the bracket by a
∴ x² + 8x - 33 = ax² - 2ahx + ah² + k ⇒ compare the two sides
∵ x² = ax² ⇒ ÷ x²
∴ a = 1
∴ -2ah = 8 ⇒ substitute the value of a
∴ -2(1)h = 8 ⇒ -2h = 8 ⇒ ÷ (-2)
∴ h = -4
∵ ah² + k = -33 ⇒ substitute the value of a and h
∴ (1)(-4)² + k = -33
∴ 16 + k = -33 ⇒ subtract 16 from both sides
∴ k = -49
∴ x² + 8x - 33 = (x + 4)² - 49
* Now lets solve the completing square
∵ (x + 4)² - 49 = 0 ⇒ add 49 to both sides
∴ (x + 4)² = 49 ⇒ take square root for both sides
∴ (x + 4) = ± 7
∵ x + 4 = 7 ⇒ subtract 4 from both sides
∴ x = 3
∵ x + 4 = -7 ⇒ subtract 4 from both sides
∴ x = -11
* The solution of the equation are 3 , -11
Answer:
{-11, 3}
Step-by-step explanation:
How to rename 8 2/3 = 7 ?/3
let's firstly convert the mixed fractions to improper fractions and proceed from there.
[tex]\bf \stackrel{mixed}{8\frac{2}{3}}\implies \cfrac{8\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{26}{3}}~\hfill \stackrel{mixed}{7\frac{x}{3}}\implies \cfrac{7\cdot 3+x}{3}\implies \stackrel{improper}{\cfrac{21+x}{3}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \cfrac{26}{3}=\cfrac{21+x}{3}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3\left( \cfrac{26}{3} \right)=3\left( \cfrac{21+x}{3} \right)}\implies 26=21+x\implies \boxed{5=x} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 8\frac{2}{3}=7\frac{5}{3}~\hfill[/tex]
7 5/3 if that’s what your asking
8 2/3 is equal to 7 5/3
Glowmart marked down it's stock 32%. What will be the sale price of a $60 jacket
Answer: $40.80
Explanation: 60*.68=40.8
Answer:
Sale price = $40.80
Step-by-step explanation:
The original price = $60
After mark down of 32% is applied,
The selling price becomes 100% - 32% = 68%
The selling price = 68% of $60 = [tex]\frac{68}{100}[/tex] × $60 = $40.80
im taking the flvs test and need the answer asapppppp
During a certain time of the year, the angle of the sun's rays at location C is smaller than the angle of the sun's rays at location D. Which location experiences cooler temperatures at that time?
Location C, because the smaller angle means the sunlight is spread out over more area
Location D, because the larger angle means the sunlight is spread out over more area
Location C, because Earth is tilted away from the sun at this time
Location D, because Earth is tilted towards the sun at this time
Answer:
d
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
I just finished the quiz, and this was my only incorrect one. The correct answer is A. Also, think logically. If the sun is spread out over more area, then it must be at a smaller angle. This leads to cooler temperatures, of course.
Triangle ABC is dilated so that the side lengths of the image are three times the lengths of their corresponding sides. Which of the following statements are true? Select all that apply.
AB ≅ A'B'
CB ~ C'B'
∠A ≅ ∠A'
CA ≅ C'A'
∠B ~ ∠B'
Answer:
∠A ≅ ∠A' and CB ~ C'B'
Step-by-step explanation:
In a dilation, you get a SIMILAR figure. It will have the same shape, but a different size.
Similar figures have the same angle measures but the side lengths will change.
Any of the answers with congruent (≅) angles are correct:
∠A ≅ ∠A'
Any of the answers with SIMILAR (~) side lengths are correct:
CB ~ C'B'
Answer:
∠A ≅ ∠A' and CB ~ C'B'
Step-by-step explanation:
(08.01)
Line R is represented by the following equation: x + y = 2
Which equation completes the system that is satisfied by the solution (1, 1)?
2x + y = 2
4x − 2y = 2
2x − 2y = 2
x + y = 4
Answer:
B: 4x − 2y = 2
B: 4x − 2y = 2 equation completes the system that is satisfied by the solution (1, 1).
What is a linear equation?A linear equation has one or two variables.
No variable in a linear equation is raised to a power greater than 1.No variable is used as the denominator of a fraction. A linear equation is defined as an equation that is written in the form of ax+by=c. When solving the system of linear equations, we will get the values of the variable, which is called the solution of a linear equation.solving this we will get the valve of Y if x is given.
explanation:
line R = x + y = 2
putting the value of X=1 & y=1 as given (1,1)
x+y =2
1+1= 2
therefore, 4x - 2y = 2
4(1) - 2(1)= 2 answer
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Which expression shows how to convert 60 hours to days?
Answer:
2.5 Days
Step-by-step explanation:
Answer:
2.5 days
Step-by-step explanation:
Write an equation to describe the variation. Use k for the constant of proportionality.
y varies directly as u and inversely as p^4
[tex]\bf \qquad \qquad \textit{joint compound proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with \underline{z}} \end{array}\implies y=\cfrac{kx}{z}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{\underline{y} varies directly as \underline{u} and inversely as }p^4}{y=\cfrac{ku}{p^4}}[/tex]
Which geometric term is best described as a straight path between two points?
A. Angle
B. Point
C. vertex
D. Line Segment
Answer:
the answer is d
Step-by-step explanation:
A line segment is best described as a path between two points.
What is a line segment?A line segment is a line that is definite from one point to another. The length of a line segment can be measured and it is not infinite.
We can choose the correct answer below:Four options are given.
We have to find the geometric term that is best described as a straight path between two points.
From the given options, the only term that satisfies these conditions is a line segment.
A line segment is a line that is definite from one point to another. The length of a line segment can be measured and it is not infinite.
Therefore, we have found that a line segment is best described as a path between two points. The correct answer is option D.
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Write an equation for the perpendicular line in slope intercept form for (-3,5);y=1/3x-2
Hey there! :)
We're given the equation : y = 1/3x - 2 & coordinates : (-3, 5)
If we're looking for an equation for a perpendicular line, then we know that the slope of our new equation MUST be the negative reciprocal of the original slope. This means that you flip the slope and add or remove a negative. Example : slope = -2 ⇒ negative reciprocal slope = 1/2
Before using this information, we must first find the slope of our original equation.
Using slope-intercept form, which is : y=mx+b ; where m=slope, b=y-intercept
Ask yourself : which value is in the "m" spot and which value is in the "b" spot?
Using this, we now know that 1/3 is our slope, and -2 is our y-intervept.
So, our negative reciprocal is -3.
Use point-slope form to find the y-intercept, and coordinates (-3, 5)
Point-slope = y - y1 = m(x - x1)
y - 5 = -3(x - (-3))
Simplify.
y - 5 = -3(x + 3)
Simplify.
y - 5 = -3x - 9
Add 5 to both sides.
y = -3x + 4 ⇒ slope-intercept form
~Hope I helped! :)
The work of a student to find the dimensions of a rectangle of area 8 + 12x and width 4 is shown below:
Step 1: 8 + 12x
Step 2: 4(2) 4x2)
Step 3: 4(4 + 8x)
Step 4: Dimensions of the rectangle are 4 and 4 + 8x
In which step did the student first make an error and what is the correct step?
Step 2: 4(2) + 4x(2)
Step 2: 4(2) + 4(3x)
Step 3: 4 + (4+8x)
Step 3: 4 + (4• 8x)
Answer:
Step 2: 4(2) + 4(3x)
Step-by-step explanation:
By definition, the area of a rectangle is given by:
Area = Length × Width
In this case, we know that:
Area = 8 + 12x
Width = 4
Therefore:
Step 1: 8 + 12x
Step 2: 4(2) + (4)(3x)
Step 3: 4(2 + 3x)
Therefore, the dimensions of the rectangle are 4 and 2 + 3x.
The mistake was made in STEP 2. Instead of 4(2) + 4(x2) it should be 4(2) + 4(3x). Which is the second option.
Two stores have movies to rent
The first store charges a $12.50-per-month membership fee plus
$1.50 per movie rented
The second store has no membership fee but charges $3.50 per movie
rented.
What is the minimum number of movies a person would need to rent in a month
for the first store to be a better deal?
Answer:7
Step-by-step explanation:
In the first store, you pay 12.5+1.5x per x movies
In the second store, you pay 3.5x per x movies
The first store offers a better deal when:
12.5 + 1.5x > 3.5x
12.5 > 2x
6.25 > x
Which means if you rent minimum 7 movies in month, you should go to the first store
Answer:
7Step-by-step explanation:
We know that the first store charges $12.50 per month, which is a initial condition, and charges additionally $1.50 per movie, which is variable, this represents the ratio of change, so this can be expressed as
[tex]\$12.50 + \$1.50x[/tex]
Where [tex]x[/tex] represents movies.
Now, the second store doesn't charge and membership fee, just it charges a cost per movie which is $3.50.
Then, to solve the minimum number of movies needed to Plan A be the best choice, we just have to solve the following inequality
[tex]\$12.50 + \$1.50x> \$3.50[/tex]
Which expresses the case where Plan A is a better choice, solving for [tex]x[/tex], we have
[tex]\$12.50 + \$1.50x> \$3.50x\\\$1.50x - \$3.50x >-\$12.50\\(-1)(-2x)>(-12.50)(-1)\\2x<12.50\\x<\frac{12.50}{2}\\ x<6.25[/tex]
Which means that the minimum number of movies is 7, which is the next whole number after 6.
The number of frogs in a certain lake is inversely related to the number of snakes in the lake. If x represents the number of snakes in the lake, then y = 100/x represents the number of frogs in the lake. Describe the reasonable domain and range values. Graph the function.
1. Domain: The set of natural numbers / Range: The set of natural numbers
2. Shown below
Step-by-step explanation:1. Domain and Range.In this problem, we have that the number of frogs in a certain lake is inversely related to the number of snakes in the lake. Hence we are facing an Inverse Variation, so this means that if the number of snakes in the lake increases then the number of frogs in the lake decreases, because snakes eat frogs! The function that describes this is a rational function defined as:
[tex]y=\frac{100}{x}[/tex]
Where:
[tex]x: \ represents \ the \ number \ of \ snakes \ in \ the \ lake \\ \\ y: \ represents \ the \ number \ of \ frogs \ in \ the \ lake[/tex]
As you can see, [tex]x[/tex] is in the denominator, therefore [tex]x\neq 0[/tex]. Since we need to provide a reasonable domain, we say that the domain is the set of natural numbers and this doesn't include the number 0. Why aren't negative values included in the domain as well? Well, although negative values are included in the function, they aren't reasonable because [tex]x[/tex] represents the number of snakes and you always get positive numbers when counting things.
To get the range, let's take the inverse of this function, so:
[tex]y=f(x)=\frac{100}{x} \\ \\ \\ Interchange \ x \ and \ y: \\ \\ x=\frac{100}{y} \\ \\ \\ Isolate \ y: \\ \\ y=\frac{100}{x} \\ \\ f^{-1}(x)=\frac{100}{x}[/tex]
So the domain of [tex]f^{-1}(x)[/tex] is the range of our given function [tex]y=f(x)[/tex]. As you can see the inverse function is the same as our given function, then the range is the set of natural numbers as well.
2. Graph.First of all, we can define the pattern of the rational function as:
[tex]y=g(x)=\frac{1}{x}[/tex]
So our function will be:
[tex]f(x)=100g(x)=100\frac{1}{x}=\frac{100}{x}[/tex]
So the graph of [tex]f(x)[/tex] will be the same graph of [tex]g(x)[/tex] but it's been stretched vertically by a constant of 100, that is, each y-value is multiplied by 100. Also, since [tex]x \neq 0[/tex] and [tex]y \neq 0[/tex] then at [tex]x=0[/tex] there is a vertical asymptote and at [tex]y=0[/tex] there is an horizontal asymptote. Finally, the graph is shown below for [tex]x>0 \ and \ y>0[/tex], but remember: Whenever [tex]x \ and \ y[/tex] are natural numbers.
Answer:
Both the number of snakes and the number of frogs will be positive, so positive values are reasonable for the domain and range.
Step-by-step explanation:
anyone can solve this question?
Answer:
see explanation
Step-by-step explanation:
Given the 2 equations
x² + y² = 5 → (1)
2x + y = 4 → (2)
Rearrange (2) expressing y in terms of x by subtracting 2x from both sides
y = 4 - 2x → (3)
Substitute y = 4 - 2x in (1)
x² + (4 - 2x)² = 5 ← expand factor on left side
x² + 16 - 16x + 4x² = 5
5x² - 16x + 16 = 5 ( subtract 5 from both sides )
5x² - 16x + 11 = 0 ← in standard form
(5x - 11)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
5x - 11 = 0 ⇒ 5x = 11 ⇒ x = [tex]\frac{11}{5}[/tex]
Substitute each of these values into (3) for corresponding values of y
x = 1 : y = 4 - 2 = 2 ⇒ P(1, 2)
x = [tex]\frac{11}{5}[/tex] : y = 4 - [tex]\frac{22}{5}[/tex] = - [tex]\frac{2}{5}[/tex]
Hence Q( [tex]\frac{11}{5}[/tex], -[tex]\frac{2}{5}[/tex] )
Evaluate the following expression (-5+7x1)-9x5
Final answer:
To evaluate the expression (-5+7x1)-9x5, follow the order of operations: calculate inside the parentheses, multiply, and then subtract, resulting in a final answer of 47.
Explanation:
To evaluate the expression (-5+7×1)-9×5, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction). Let's break down the expression step by step:
Inside the parentheses: -5 + (7 × 1) = -5 + 7 = 2.
Multiply: -9 × 5 = -45.
Subtract the value obtained from step 2 from the result of step 1: 2 - (-45).
Change the subtraction of a negative value to addition: 2 + 45 = 47.
Thus, the expression (-5+7×1)-9×5 evaluates to 47.
Round 96 cent. Amount. To the nearest dollar
Answer:
About 1 dollar.
Step-by-step explanation:
First we must establish the possible values that 96 cents can be rounded to.
We know that 96 cents is more than nothing, or 0. We also know that a dollar is 100 cents. This means 96 cents is in between 0 and 1 dollar. We just have to determine whether 96 is closer to 100 cents or 0 cents.
To do this find the difference between 96 and each value.
100-96 = 4
96-0 =96
The difference between 96 and 100 is smaller, so the values are closer and 96 should be rounded to a dollar.
I don't know how to graph y=6/5x+1
can someone help me?
So this equation is in slope intercept form:
y = mx + b
m is slope
b is y-intercept
This means that for this equation the slope is 6/5 and the y-intercept is (0 , 1)
Look at image below for the graph
Hope this helped!
~Just a girl in love with Shawn Mendes
Determine which diagram could be used to prove ABC - EDC using similarity transformations.
Answer: A The first Answer to the left
Step-by-step explanation:
The diagram could be used to prove that ABC-EDC using similarity transformations is option A.
The first Answer to the left
We have given that,
The diagram could be used to prove ABC - EDC using similarity transformations.
What is the transformation?
A similarity transformation is one or more rigid transformations (reflection, rotation, translation) followed by a dilation.
We have to determine which diagram could be used to prove ABC-EDC.
Therefore the answer is the first diagram.
The diagram could be used to prove that ABC-EDC using similarity transformations is option A.
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What is the approximate value of f(5) for the function f(x)=6.87(2.5)(x – 1)?
Answer:
68.7
Step-by-step explanation:
We need only estimate (approximate) the value of f(x) at x = 5:
f(x)=6.87(2.5)(x – 1) → f(5)=6.87(2.5)(5 – 1).
Note that 2.5(4) = 10, so now we have (exactly) f(5)=6.87(10), which, in turn, is
equal to 68.7.
I need help please
Answer:
b
Step-by-step explanation:
it makes sense because they all are going down by 1 side each time
B) the triangle because each figure is loosing one side
if Mark wants to see how the price of gas has increased over the last five years, which type of graph would best illustrate this data line graph circle graph bar graph pictograph
Line graph because it shows differences
What is the series using summation notation?
36+69+102+...+267
first term =36
second term=69
So common difference=69-36=33
checking. 69+33=102
36=3+33
so the series in AP Becomes as...
(3+33) ,(36+33) ,(36+2(33)) ... (36+7(33))
So The Answer is...
(refer above attachment.)
Hope it helps...
Regards,
Leukonov/Olegion.
A circle has its center at (6,-3) and a radius of 5 units. What is the equation of
the circle?
[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{6}{ h},\stackrel{-3}{ k})\qquad \qquad radius=\stackrel{5}{ r}\\[2em] [x-6]^2+[y-(-3)]^2=5^2\implies (x-6)^2+(y+3)^2=25[/tex]
Answer:
Step-by-step explanation:
The x value for the center is part of the x^2 part of the equation.
The y value for the center is part of the y^2 part of the equation.
The radius is squared.
(x - 6)^2 + (y + 3)^2 = 5^2
Notice the sign change for the center. When you move horizontally the sign of the center changes sign in the circle's equation.
The graph is included to show you that.
What is the area, in square inches, of the figure shown here?
25 POINTS PLEASE HELP A parallelogram with a height of 2 inches is shown. The height of the parallelogram is used to divide the side of the parallelogram into 5 inches, which is the length (or side) of the rectangle, and into 2 inches, which is the base of the triangle formed by the division.
10 in2
14 in2
16 in2
20 in2
Answer:
B.[tex]14in^{2}[/tex]
Step-by-step explanation:
Solve this by using one of two methods.
Split up into different shapes:
This method uses the sum of the areas of a rectangle and two triangles to find the area of the parallelogram:
[tex]A=(b*h)_{rectangle} +2*(0.5*b*h)_{triangle} \\A=(5*2)+2(0.5*2*2)\\A=10+4\\A=14in^{2}[/tex]
Use Parallelogram formula:
This formula is the same as the formula for a rectangle where you multiply the base by the height.
[tex]A=b*h\\A=(5+2)*2\\A=14in^{2}[/tex]
Answer: The answer is 14 in2
Leila is considering buying her first home. The house she is interested in buying is priced at $125,000. Leila can put down a $20,000 payment, and she qualifies for a 30-year mortgage at 6%. What will her monthly mortgage payment be?
Answer:
* The monthly mortgage payment is $629.53 ⇒ answer C
Step-by-step explanation:
* Lets explain how to solve the problem
- Leila is considering buying her first home
- The house she is interested in buying is priced at $125,000
∴ She can put $20000 down payment
* Lets find the balance to be paid off on mortgage
∴ The balance = 125000 - 20000 = 105000
- She qualifies for a 30-year mortgage at 6%
* Lets find the rule of the monthly payment
∵ [tex]pmt=\frac{\frac{r}{n}[P(1+\frac{r}{n})^{tn}]}{(1+\frac{r}{n})^{tn}-1}[/tex] , where
- pmt is the monthly mortgage payment
- P = the initial amount
- r = the annual interest rate (decimal)
- n = the number of times that interest is compounded per unit t
- t = the time the money is invested or borrowed for
∵ P = 105000
∵ r = 6/100 = 0.06
∵ n = 12
∵ t = 30
∴ [tex]pmt=\frac{\frac{0.06}{12}[105000(1+\frac{0.06}{12})^{30(12)}}{(1+\frac{0.06}{12})^{30(12)}-1}[/tex]
∴ [tex]pmt=\frac{0.005[105000(1.005)^{360}]}{(1.005)^{360}-1} =629.528[/tex]
* The monthly mortgage payment is $629.53
#5! And #4 revisions!
Answer:
4. Your working and answers are correct: x = 44, y = 43.
5. GH = 60°
Step-by-step explanation:
5. Arc GH is double the inscribed angle GFH, so we have ...
2(4x+2) = 9x-3
8x +4 = 9x -3 . . . . . simplify
7 = x . . . . . . . . . . . . add 3-8x
Then the arc's measure is ...
(9·7 -3)° = (63 -3)° = 60°
Answer:
Step-by-step explanation:
Your working and answers are correct: x = 44, y = 43.
5. GH = 60°
a bottle holds z ounces of water. a second bottle holds 16 ounces, which is 8/5 times as much water. how much does the first bottle hold?
Answer:
10 ounces of water
Step-by-step explanation:
16=8/5
z=1
16*1=16
8/5*z=8/5z
16=8/5z
16/1.6z=10
z = 10
Answer:
10 ounces of water
Step-by-step explanation:
PLEASE ANSWER THIS AND EXPLAIN HOW YOU GOT THE ANSWER.
9 - 3 ÷ 1/3 + 1 =
Answer:
Step-by-step explanation:
If you use pemdas, you would do 3÷1/3 which equals 9. Then do 9-9, which equals 0. Then, do 0+1, which equals 1. Hope this helps! <3
[tex]9 - 3 \div \frac{1}{3} + 1 = [/tex]
Divisions go first, to do it we have to reverse the fraction and turn ÷ into ×
[tex] = 9 - 3 \times 3 + 1 = [/tex]
Now the multiplication
[tex] = 9 - 9 + 1 = [/tex]
[tex] = 1[/tex]
Which trigonometric function is being used if we get the fraction 6/10 as our answer? Question 3 options: sin(A) cos(A) tan(A) tan(gerine)
Answer:
cos(A)Step-by-step explanation:
For angle A we have
opposite = 8
adjacent = 6
hypotenuse = 10
sin A = opposite/hypotenuse
cos A = adjacent/hypotenuse
tan A = opposite/adjacent
cot A = adjacent/opposite
6/10 = adjacent/hypotenuse = cos A
The trigonometric function of the triangle is given by cos A = 6/10
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ΔABC
where the measure of ∠ABC = 90°
Now , from the trigonometric relations ,
cos θ = adjacent / hypotenuse
So , on simplifying , we get
The measure of BC = 6 units
The measure of AB = 8 units
The measure of AC = 10 units
cos A = 6 / 10
Hence , the measure of cos A of triangle is cos A = 6 / 10
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Write the expression in terms of cosine. Please help.
Answer:
sin(81)
Step-by-step explanation:
Since the sine of something is the ratio of the opposite side to the hypotenuse, to get the same ratio in cosine, you take the complement of the angle. So the answer is sin(90 - 9) or sin(81).
The expression in terms of cosine cos 81°. The expression is obtained by the trigonometric rules.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
The given expression is;
sin9°
The expression in terms of cosine.
sin 9°= sin(90-81°)
sin 9°= cos 81°
Hence,the expression in terms of cosine cos 81°.
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Can someone answer this for me ASAP please ?
Answer:
The expression which is equivalent to (k ° h)(x) is [tex]\frac{1}{(5 + x)}[/tex] ⇒ 2nd answer
Step-by-step explanation:
* Lets explain the meaning of the composition of functions
- Composition of functions is when one function is inside of an another
function
# If g(x) and h(x) are two functions, then (g ° h)(x) means h(x) is inside
g(x) and (h ° g)(x) means g(x) is inside h(x)
* Now lets solve the problem
∵ h(x) = 5 + x
∵ k(x) = 1/x
- We need to find (k ° h)(x), that means put h(x) inside k(x)
* Lets replace the x of k by the h(x)
∵ k(x) = [tex]\frac{1}{x}[/tex]
∵ h(x) = 5 + x
- Replace the x of k by 5 + x
∴ k(5 + x) = [tex]\frac{1}{5 + x}[/tex]
∴ The expression which is equivalent to (k ° h)(x) is [tex]\frac{1}{5+x}[/tex]