Answer:
15/8
Step-by-step explanation:
Find the measure of angle 2
a 50°
b 90°
c 140°
d 40°
third-degree, with zeros of -3,-2, and 1, and y-intercept of -8
The polynomial y = (4 / 3) · x³ + (16 / 3) · x² + (4 / 3) · x - 8 is the cubic equation whose zeros are x₁ = -3, x₂ = - 2, x₃ = 1 and intercept is - 8.
How to derive a cubic equation associated with a given set of zeros and a intercept
Herein we must derive a cubic equation such that the zeros are x₁ = -3, x₂ = - 2, x₃ = 1 and its intercept is - 8. Cubic equations are polynomials of the form y = a · x³ + b · x² + c · x + d, where a, b, c, d are real coefficients.
If we know that (x₁, y₁) = (- 3, 0), (x₂, y₂) = (- 2, 0), (x₃, y₃) = (1, 0) and (x₄, y₄) = (0, - 8), then we solve the following system of linear equations to determine all real coeffcients by numerical methods:
- 27 · a + 9 · b - 3 · c + d = 0
- 8 · a + 4 · b - 2 · c + d = 0
a + b + c + d = 0
d = - 8
(a, b, c, d) = (4 / 3, 16 / 3, 4 / 3, - 8)
The cubic equation is y = (4 / 3) · x³ + (16 / 3) · x² + (4 / 3) · x - 8.
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what is the slope of a line that is parallel to the line shown on the graph?
PLEASE HURRY!
Answer:
-3
Step-by-step explanation:
A (0,2)
B (2,-4)
slope = (-4-2)/(2-0)
-6/2
-3
a parallel line has the same slope
let d be a positive integer. show that among any group of d 1 (not necessarily consecutive) integers there are two with exactly the same remainder when they are divided by d.
Among any group of d+1 integers there are two with exactly the same remainder when divided by d.
What are Positive Integers?Positive integers are those bigger than 0 that don't contain any fractional portions. On the number line, these figures are located to the right of 0.
Is 0 a Positive Integer?Since it is neither positive nor negative, 0 is not a positive integer. Positive integers are defined as numbers greater than 0 in mathematics.
The possible remainders after dividing an integer by d are 0, 1, 2,..., d-1.
The number of remainders that can be obtained is d, or |0, 1, 2,..., d-1|=d0,1,2,...,d-1=d.
According to the Pigeonhole Theory:
objects are the number of integers in d+1.
"holes" = "remainders" + "d"
[d+1/d]=2
According to the Pigeonhole Principle, there are always two d+1 integers in every group that have precisely the same residual after being divided by d.
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There are always two d+1 numbers in any group that have the exact same residual after division.
Examples of integers and what they are:An integer, pronounced "IN-tuh-jer," is an entire number which can be positive, minus, even zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, among 3,043. 1.43, 1 3/4, 3.14, and other values which aren't integers seem to be some examples.
Briefing:The potential remainders after dividing an integer by d are 0, 1, 2,..., d-1.
The possible number of remainders is d, or I{0,1,2,.......d-1}I = d
By the Pigeonhole Principle:
Objects = umber of integers = d+1
Holes = number of remainders = d
[tex]\frac{d+1}{d} = 2[/tex]
According to the Pigeonhole Principle, there are always two d+1 numbers in every group that have precisely the same residual after being divided by d.
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Consider the following graph:
What is the slope/rate of change between the inputs of 0 and 4? _______.
What is the slope/rate of change between the domain values of 4 and 8? ______.
Is the slope/rate of change constant (not changing/the same)? ______.
Is the function linear? _______.
The solution is
a) The slope/rate of change between the inputs in m = -1/2
b) Slope/rate of change between the domain values of 4 and 8 is m = -1/2
c) The slope/rate of change is constant
d) The function is a linear function
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be = A
Now , the value of A is
a)
when the inputs are 0 and 4 , the values of x = 0 and x = 4
So , the values of y = 5 and y = 3 respectively
Let the first point be P = P ( 0 , 5 )
Let the second point be Q = Q ( 4 , 3 )
Now , the slope of the line between the two points is given by
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 3 - 5 ) / ( 4 - 0 )
Slope m = -2/4
Slope m = -1/2
So , the slope of the line m = -1/2
b)
when the domain values are 4 and 8 , the values of x = 4 and x = 8
So , the values of y = 3 and y = 1 respectively
Let the first point be Q = Q ( 4 , 3 )
Let the second point be R = R ( 8 , 1 )
Now , the slope of the line between the two points is given by
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 1 - 3 ) / ( 8 - 4 )
Slope m = -2/4
Slope m = -1/2
So , the slope of the line m = -1/2
c)
The slope of the line m = -1/2 and it is constant
d)
The function is a linear function and the equation of line is given by
y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 5 = -1/2 ( x - 0 )
On simplifying the equation , we get
y - 5 = -1/2 ( x )
Adding 5 on both sides of the equation , we get
y = ( -1/2 )x + 5
Therefore , the equation of line is y = ( -1/2 )x + 5 and it is linear
Hence , the equation of line is y = ( -1/2 )x + 5 and it is linear where the slope of the line is m = -1/2
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In triangle DEF, line DE is congruent with line FD and the measurement of angle F is 55. Find the measurement of angle E. (isosceles triangle)
Step-by-step explanation:
because it is an isoceles triangle (both legs are equally long), E and F are the side angles in the baseline.
and because both leg sides are equally long, also both side angles must be equally large
therefore,
angle E = angle F = 55°.
How can you use rates to determine weather a situation is proportional relationship?
Answer: If the rate is constant, then the situation is a proportional relationship. If the rate is not constant, then the situation cannot be a proportional relationship.
find the length and the slope of each side of the triangle below. then, find the coordinates of the midpoint of each side. when the slope is undefined, write undefined in the response box.
The triangle has three side x,y and √(x²+y²), the slope of x is zero, the slope of y is undefined, the slope of √(x²+y²) is tanα. The coordinate of the midpoint of x is x/2,0 and y is 0, y/2
how to determine the length and slope of the side of a triangle?suppose the triangle is right-angled and the sum of other two angles are also 90 degrees. we know that the side opposite to the right angle is called hypotenuse. let the other two side is denoted by x and y. Now, x is the base of triangle, and the rest of the side is y. The angle between hypotenuse and base is denoted by α . As per Pythagorean theorem, hypotenuse = √(x²+y²).
slope can be calculated by tanα or using the formula (y₂-y₁)/(x₂-x₁)
according to trigonometric ratio, tanα = opposite side/base = x/y
tanα is the slope of hypotenuse.
the side length x is along the horizontal axis, so its y coordinate is zero and slope is also zero.
the side length y is along the vertical axis whose x coordinate is zero that means slope is undefined.
When does a slope is defined?As per the formula (y₂-y₁)/(x₂-x₁) used to calculate slope, whenever x coordinate is zero the result is written as undefined.
hence, the triangle is right-angled, and the biggest side has a slope only.
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Samson opened a bank account with 2.25% simple interest. The total amount of interest Samson will earn after 30 years is $812.50. How much did Samson deposit when he opened the account? Round if necessary.
Answer: The equation for simple interest is:
Future interest = Principal*(interest rate*number of years). Remember to write the interest rate of 1.25% as 0.0125 (rather than directly as 1.25)
812.50 = x(0.0125*20)
812.5 = x(0.25)
x = $3250
This means that Samson deposited $3250 when he opened the account.
Step-by-step explanation:
SIMPLIFY 2X+3Y^2(X-Y^2)
The required simplified expression is 2x + 3xy² - 3y⁴ which is determined by using the distributive property.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
The expression is given in the question as:2x + 3y²(x - y²)
We have to simplify the given expression.
As per the question, we have
⇒ 2x + 3y²(x - y²)
Apply the distributive property of multiplication
⇒ 2x + 3xy² - 3y⁴
Therefore, the simplified expression is 2x + 3xy² - 3y⁴.
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3(6x-4y)-5. Help i do not know how to do this it’s very confusing I need help
Answer:
3(6x-4y) -5 18x-12y-5MAY BE IT'S HELP UHHH=^._.^
Answer:
The answer to the expression 3(6x-4y)-5 is 18x - 12y - 5. This is the result of following the order of operations and performing the necessary operations in the correct sequence.
Step-by-step explanation:
To solve this problem, you need to follow the order of operations, which is a set of rules that dictate the sequence in which operations should be performed in a mathematical expression to get the correct result. The order of operations is often abbreviated using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
According to the order of operations, the first step in solving this problem is to evaluate anything inside parentheses. In this case, there are no parentheses, so we can move on to the next step, which is to evaluate any exponents. Again, there are no exponents in this expression, so we can move on to the next step, which is to perform any multiplication or division.
In this case, there is a multiplication operation: 3 * (6x - 4y). So we need to evaluate this first. To do that, we need to multiply 3 by each of the terms inside the parentheses: 3 * 6x and 3 * -4y. This gives us 18x - 12y.
Now that we have performed all of the multiplication and division operations, we can move on to the final step, which is to perform any remaining addition or subtraction operations. In this case, there is only one subtraction operation: 18x - 12y - 5. So we need to subtract 5 from 18x - 12y to get our final answer: 18x - 12y - 5 = 18x - 12y - 5.
Therefore, the result of evaluating the expression 3(6x-4y)-5 is 18x - 12y - 5. I hope this helps! Let me know if you have any other questions.
Order these number from least to greatest. 33 1/3%, 0.3125, 17/48
An airplane was flying at an altitude of 11,200 feet above sea level. The airplane then increased its altitude by 10,150 feet. The airplane will land at an airport that is located at sea level. What change in altitude must the airplane make in order to land?
With the application of Arithmetic operators altitude must the airplane make in order to land is 21350 feets.
What is Arithmetic operators ?
By combining operands with one arithmetic operator, an arithmetic operation is given. The built-in functions ADD, SUBTRACT, DIVIDE, and MULTIPLY additionally allow for the specification of arithmetic operations.
solution:
An airplane was flying at an altitude above the sea level is 11,200 feet
The airplane then increased its altitude by 10,150 feet.
By adding both the altitude 11,200 + 10,150 = 21350 feets
Therefore, altitude must the airplane make in order to land is 21350 feets
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100 POINTS PLEASE HELP Supply curves shift to the left when a product is more expensive to create. All of the following are examples of scenarios that would cause this EXCEPT:
A. higher materials cost
B. higher minimum wage for employees
C. higher demand from customers
Answer:
C. Higher Demand from customers
Step-by-step explanation:
Higher Materials cost leads to higher production cost
Higher minimum wage leads to higher production cost
The demand for the final product does not increase the production cost of the products
Answer: C. Higher Demand from customers
Step-by-step explanation:
MATHEMATICAL CONNECTIONS In Exercises 23 and 24,
use the given information to write and solve a system of
linear equations to find the values of x and y.
23. LMN = PQR, L = 40°, M = 90°,
P = (17x − y)°, R = (2x + 4y)º
The value of x and y are 3 and 11.
What is the congruent triangle?
Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.
Given that,
△LMN = △PQR
Thus ∠L = ∠P, ∠M = ∠Q, and ∠N = ∠R.
Also, ∠L = 40°, ∠M = 90°, ∠P = (17x − y)°, ∠R = (2x + 4y)°.
The sum of interior angles of a triangle is 180°.
∠L + ∠M + ∠N = 180°
40° + 90° + ∠N = 180°
∠N = 50°.
Therefore,
17x − y = 40 .....(i)
2x + 4y = 50 .....(ii)
Multiply equation (i) with 4 and add with equation (ii)
68x - 4y = 160
2x + 4y = 50
_________
70x = 210
x = 210/70
x = 3
Putting x = 3 in equation (ii)
6 + 4y = 50
4y = 44
y = 11
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Brianna has 34 m of fencing to build a three-sided fence around a rectangular plot of
land that sits on a riverbank. (The fourth side of the enclosure would be the river.)
The area of the land is 140 square meters.
The dimensions of the field are 17 meters and 8.5 meters.
What is dimensions?
The minimal set of coordinates required to specify any point within a mathematical space is known as the dimension of the space in physics and mathematics. As a result, a line has a dimension of one because a point on it can be specified by a single coordinate, such as the point at 5 on a number line.
Given:
Brianna has 34 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank.
Since,
Area of rectangle = A = l x w ..(1)
where l = length and w = width
Perimeter = 2w + l
34 = 2w + l
l = 34 - 2w ..(2)
Plug this value in equation (1).
A = (34 - 2w) x w
140 = 34w - 2w^2
2w^2 - 34w + 140 = 0
The dimension w can be found as follows;
w = - b / 2a
Here a = 2, b = -34
⇒ w = -(-34)/2(2) = 34/4 = 8.5
Hence, the width is 8.5 meters.
Now to find the length.
Plug w = 8.5 in equation (2)
l = 34 - 2(8.5)
l = 34 - 17
l = 17
Hence, the dimensions of the field are 17 meters and 8.5 meters.
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Complete question:
Brianna has 34 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 140 square meters.
List each set of possible dimensions (length and width) of the field.
9
LBCA and LACD form a linear pair. LBCA is
represented by (2x - 5)° and LACD is
represented by (3x + 10)°.
What is the mLACD?
A. 35°
B. 61°
C. 65°
D. 115°
Answer:
D
Step-by-step explanation:
[tex]m\angle BCA+m\angle ACD=180^{\circ} \\ \\ 2x-5+3x+10=180 \\ \\ 5x+5=180 \\ \\ 5x=175 \\ \\ x=35 \\ \\ \\ m\angle ACD=3(35)+10=115^{\circ}[/tex]
Triangle KLM is formed by connecting the midpoints of the side of triangle HIJ.
The lengths of the sides of triangle KLM are shown. What is the length of HJ?
Figures not necessarily drawn to scale.
Applying the triangle midsegment theorem, the length of HJ is: 8 units.
What is the Triangle Midsegment Theorem?The triangle midsegment theorem states that when a line connects the midpoints of two sides of a triangle, it is parallel to the third side and also has a length that is half of the length of the third side.
In the image attached below, segment LK is a midsegment of the triangle which is parallel to a third side, segment HJ.
Therefore:
LK = 1/2(HJ) [triangle midsegment theorem]
Substitute
4 = 1/2(HJ)
Multiply both sides by 2
4 × 2 = 1/2(HJ) × 2
8 = HJ
Length of HJ = 8 units.
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How many square feet of tiles do you need to purchase to cover the floor of a 10.5 foot by 8.5 foot bathroom
You would need to purchase 89.25 square feet of tiles to cover the floor of a 10.5-foot by 8.5-foot bathroom.
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
To determine the number of square feet of tiles needed to cover a 10.5-foot by 8.5-foot bathroom floor, we can use the formula for the area of a rectangle, L × W
As per the question, the length of the floor is 10.5 feet and the width is 8.5 feet, so the total area of the floor is 10.5 feet × 8.5 feet = 89.25 square feet.
Therefore, you would need to purchase 89.25 square feet of tiles to cover the floor of a 10.5-foot by 8.5-foot bathroom.
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Keith buys 3 yards of material to make a blanket. He trims off a total of 1/6 yard before he begins sewing. How much material remains for the blanket?
The remaining material for sewing is 5/2 material.
What is fraction?Fractions are used to represent smaller pieces (or parts) of a whole.
Given that, Keith buys 3 yards of material to make a blanket. He trims off a total of 1/6 yard before he begins sewing.
1/6 of 3 = 3x1/6 = 1/2
The remaining material = 3-1/2
= 5/2
Hence, The remaining material for sewing is 5/2 material.
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jonah and haley made brownies to bring as a class treat. some were plain and some had sprinkls the class ate 3/4 of one pan and 1/6 of another pan of plain brownies they ate 5/6 of one pan and 1/10 of another pan of brownies with sprinkles. if the brownies were the same sie dud the class eat more plain brownies or more brownies with sprinkles
Answer:
5/6
Step-by-step explanation:
he class ate 3/41 = <<3/41=3/4>>3/4 of one pan of plain brownies
They also ate 1/61 = <<1/61=1/6>>1/6 of another pan of plain brownies
The total amount of plain brownies they ate is 3/4 + 1/6 = <<3/4+1/6=5/6>>5/6
The class ate 5/61 = <<5/61=5/6>>5/6 of one pan of brownies with sprinkles
They also ate 1/101 = <<1/101=1/10>>1/10 of another pan of brownies with sprinkles
The total amount of brownies with sprinkles they ate is 5/6 + 1/10 = 5/6 + 1/10 = 41/60
The class ate more plain brownies because 5/6 > 41/60. Answer: {5/6}.
A marine biologist is studying the growth of a particular species of fish. She writes the following equation to show the length of the fish, f(m), in cm, after m months:
f(m) = 3(1.09)m
Part A: When the marine biologist concluded her study, the length of the fish was approximately 5.98 cm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(m) represent? (2 points)
Part C: What is the average rate of change of the function f(m) from m = 2 to m = 8, and what does it represent? (4 points)
The solution is
A) The domain to plot the growth function is Domain = [ 0 , 8 ]
B) The y-intercept of the graph of the function f ( a ) is f ( 0 ) = 3 cm
C) The average rate of change of the function f ( a ) from m = 2 to m = 8 is given by T = 0.4022 cm per month
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation be represented as A
Now , the value of A is given by
f ( a ) = 3 ( 1.09 )ᵃ
A)
To find the domain of the function f ( a )
The length of the fish was approximately 5.98 cm
So , substituting the value of f ( a ) as 5.98 cm , we get the value of m,
And , f ( a ) = 5.98 cm
So , 5.98 = 3 ( 1.09 )ᵃ
Solving for a , we get
Divide by 3 on both sides of the equation , we get
1.9933 = ( 1.09 )ᵃ
a = 8
So , the value of a is 8
So , the domain of the function is [ 0 , 8 ]
B)
The y-intercept of the graph is given by substituting the value of a = 0,
So , f ( a ) = 3 ( 1.09 )ᵃ
when a = 0 , we get
f ( 0 ) = 3 ( 1.09 )⁰
f ( 0 ) = 3 cm
Therefore, the value of f ( 0 ) = 3 cm
C)
The average rate of change from m =2 to m = 8 is given by the equation ,
when m = 2 ,
f ( a ) = 3 ( 1.09 )ᵃ
f ( 2 ) = 3 ( 1.09 )²
f ( 2 ) = 3 x 1.1881²
f ( 2 ) = 3.5643
And , when a = 8
f ( a ) = 3 ( 1.09 )ᵃ
f ( 8 ) = 3 ( 1.09 )⁸
f ( 8 ) = 3 x 1.99256
f ( 8 ) = 5.97768
So , the average rate of change is the slope of the graph
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope = f ( 8 ) - f ( 2 ) / ( 8 - 2 )
Slope = ( 5.97768 - 3.5643 ) / 6
Slope = 2.4133879 / 6
Slope = 0.40223 cm per month
Therefore ,
The average rate of change of the function f ( a ) from a = 2 to a = 8 is given by T = 0.4022 cm per month
Hence ,
A) The domain to plot the growth function is Domain = [ 0 , 8 ]
B) The y-intercept of the graph of the function f ( m ) is f ( 0 ) = 3 cm
C) The average rate of change of the function f ( m ) from m = 2 to m = 8 is given by T = 0.4022 cm per month
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It says to find the surface area of the figure and to round to nearest hundredth. confused..
How to solve-2–(-12)
Answer:
10
Step-by-step explanation:
[tex]-2-(-12)\\=-2+12\\=12-2 \\=10[/tex]
5 Bob is 5 years younger than twice Mark's age. Bob is 31. How old is Mark?
Answer:
57 years old
Step-by-step explanation:
Bob=31
Mark= 31 x 2 - 5
31 x 2= 62
62- 5 = 57
Mark is 57 years old
Answer:
Mark is 18
Step-by-step explanation:
Could someone help me answer this multiple-answer question? I'm stuck
Answer:
x = 2
<1 = 28
Step-by-step explanation:
The two angles equal each other.
4x + 20 = 5x + 18 Subtract 4x from both sides
20 = x + 18 Subtract 18 from both sides
2 = x
4x + 20
4(2) + 20
8 + 20
28
The sphere is a geometric body generated by turning a semicircle around its diameter ?
The theory tells us that the sphere is a three-dimensional body that arises by rotating a semicircle around its diameter.
¿What is the sphere?The sphere has been a three-dimensional body. The main characteristics of this body are:
All the points that make up the surface of the sphere are at the same distance from a particular point known as the center. It is a geometric field that arises when a semicircle rotates around its own diameter.In the attached image let's see an example of a sphere.
¡Hope this helped!
100 POINTS WILL GIVE BRAINLIEST What is the target percent change for Growth Domestic Product?
A. 2-3% growth per period
B. 1-5% growth per period
C. 3-6% growth per period
Answer:A
Step-by-step explanation:
U V||R T{. Find ST
ST=
Submit
Using the congruence angel theorem, the value of ST is 38.
In the given question given that, UV||RT.
We have to find the value of ST.
Given: UV||RT
Prove: Value of ST.
From the given diagram we can see that;
UT = 19
VS = 39
RS = 26
Using the Congruence Triangle Theorem;
∆USV≈∆TSR
So using the theorem;
US/VS = ST/RS………………(1)
From the given diagram we can see that
US = UT+ST
US = 19+ST
Now putting the value to the condition 1
(19+ST)/39 = ST/26
Simplifying
26(19+ST) = 39ST
494+26ST = 39ST
Subtract 26TS on both side, we get
13ST = 494
Divide by 13 on both side, we get;
ST = 38
Hence, the value of ST is 38.
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If
f(x) = 2x² – 5
and
g(x) = 5x + 7
Find
g(f(x)) = 10x² + [? ]
Answer:
The missing term in the output of the function [tex]g(f(x))[/tex] is -18.
[tex]g(f(x))=10x^2-18[/tex]
Step-by-step explanation:
Function CompositionIn mathematics, function composition is a term that encompasses a relationship between two functions wherein the output of one function is used as the input for another function. This relationship combines two functions to form a single function, known as a composite function. For future reference, function composition may also be denoted by a small circle, see below:
[tex](g\circ f)(x)=g(f(x))[/tex]
In the given problem, we must evaluate the composite function [tex]g(f(x))[/tex] / [tex](g\circ f)(x)[/tex] to identify the unknown term.
With composite functions, we begin evaluating from the inside. To evaluate [tex]g(f(x))[/tex], we must substitute the output of the function [tex]f(x)[/tex] (given as the expression [tex]2x^2-5[/tex]) as the input ([tex]x[/tex]) for the function [tex]g(x)[/tex]:
[tex]g(f(x))=g(2x^2-5)[/tex]
Now, using [tex]f(x)[/tex] as the input ([tex]x[/tex]) for the function [tex]g(x)[/tex] (given as the expression [tex]5x+7[/tex]), we can substitute [tex]2x^2-5[/tex] into the output for the function [tex]g(x)[/tex]:
[tex]g(f(x))= 5(2x^2-5)+7[/tex]
From here, we can go ahead and distribute the 5:
[tex]g(f(x))=10x^2-25+7[/tex]
Combine like terms:
[tex]g(f(x))=10x^2-18[/tex]
With the composite function evaluated, we can identify our missing term as [tex]-18[/tex].