Given a polynomial function f(x) = 2x2 – 3x + 5 and an exponential function g(x) = 2x - 5, what key features do f(x) and g(x) have in common?
A. Both f(x) and g(x) have the same domain of (9,-infinity).
B. Both f(x) and g(x) have the same range of [0,-infinity).
C. Both f(x) and g(x) have the same x-intercept of (2,0).
D. Both f(x) and g(x) increase over the interval of (-4, infinity).
Answers
Both f(x) and g(x) have the same range of [0,-infinity).
What is a function?A function is an expression that shows the relationship between two or more numbers and variables.
Plotting the functions f(x) = 2x² – 3x + 5 and g(x) = 2ˣ - 5:
Both f(x) and g(x) have the same range of [0,-infinity).
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Answer: A. Both f(x) and g(x) have the same domain of (9,-infinity).
Step-by-step explanation:
Related Questions
Twelve trees are equally spaced along one side of a straight road. The distance from the first tree to the sixth tree is 60 feet. What is the distance in feet between the first and last trees?
Answers
Answer:
120 feet
Step-by-step explanation:
because 60 feet x2 is 120
The distance between the first and the last tree is 132 feet.
What is an Arithmetic Progression?An arithmetic progression(A.P.) is a series, where the difference between consecutive numbers is constant.
The first term of an A.P. is denoted by a, and the common difference is denoted by d.
The nth term of an A.P. series is found using the formula:
aₙ = a + (n-1)d.
The sum of n terms of an A.P. series is found using the formula:
Sₙ = (n/2)(2a + (n-1)d)
How do we solve the given question?We are said that every tree is equally spaced. So the distance between the trees is in arithmetic progression.
With the first tree being at 0 feet from itself, our a = 0.
The distance from the first tree to the sixth tree is 60 feet, so we can say that the 6th term is 60
6th term = a + 5d
or, 60 = 0 + 5d
or, d = 60/5 = 12 feet.
To find the distance between the first tree and the last tree(12th tree), we will find the 12th term of the series,
12th term = a + (12-1)d = 0 + 11(12) = 132 feet.
∴ The distance in feet between the first and last tree is 132 feet.
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13. The value of a boat is depreciating at a rate of 7% per year. In 2004, the
boat was worth $192,000. Find the value of the boat in 2013.
Answers
Answer: Depreciating at 7% 100 - 7 = 93%
93% = 93/100 = 0.93
0.93 is your factor of depreciation.
There are 9 years between 2004 and 2013
So, you set 9 as power on your factor
0.93^9
Multiply your original value
$192,000 x 0.93^9
= $99,918.93
This is the value of the boat in 2013.
Step-by-step explanation: Hope this helps
Urgent. Please show all work
Answers
Answer:
[tex]\displaystyle f'(x) = \frac{4}{x^2}[/tex]
General Formulas and Concepts:
Calculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]Differentiation
DerivativesDerivative NotationThe definition of a derivative is the slope of the tangent line: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle f(x) = -\frac{4}{x}[/tex]
Step 2: Differentiate
[Function] Substitute in x: [tex]\displaystyle f(x + h) = -\frac{4}{x + h}[/tex]Substitute in functions [Definition of a Derivative]: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{-\frac{4}{x + h} - \big( -\frac{4}{x} \big)}{h}[/tex]Simplify: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{4}{x(x+ h)}[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle f'(x) = \frac{4}{x(x+ 0)}[/tex]Simplify: [tex]\displaystyle f'(x) = \frac{4}{x^2}[/tex]∴ the derivative of the given function will be equal to 4 divided by x².
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Calculate the volume. Round your answers to the nearest tenth if necessary.
Answers
Answer:
need to see problem please
Below is a list of
grades on a test.
| What is the mean?
he
100 100 75 60
55
80
85
90
100
75
Answers
Answer:
82
Step-by-step explanation:
The mean is just the average Add all individual numbers together then divide by how many numbers you added.
find the volume of the solid
Answers
V=5✖️3✖️6➕5✖️3✖️5➕5✖️3✖️3=210
The cafeteria sold 15 more turkey sandwiches than ham sandwiches. They sold 63 sandwiches in all. How many ham sandwiches did the cafeteria sell?
Answers
Answer:
48
:)
Step-by-step explanation:
63-15 = 48
48+15= 63
h+15=t
h+t=63
simplify to get 24 and 39
A rectangles length is 8 feet longer than twice its width. The rectangles perimeter is 316 feet. Find the rectangles length and width.
The rectangles length is ______ feet, and its width is_____feet.
Answers
Answer:
length= 108 feet,
width= 50 feet
Overview of steps:
Define variablesForm two equations using given informationSolve for one variable through substitution/ eliminationSolve for the other variable through substitutionWorking:
Let the length and the width of the rectangle be L and W feet respectively.
L= 2W +8 -----(1)
Perimeter= 2(length) +2(width)
316= 2L +2W
2L +2W= 316
Divide both sides by 2:
L +W= 158 -----(2)
Substitute (1) into (2):
2W +8 +W= 158
Simplify:
3W +8= 158
3W= 158 -8
3W= 150
Divide both sides by 3:
W= 150 ÷3
W= 50
Substitute W= 50 into (1):
L= 2(50) +8
L= 100 +8
L= 108
Thus, the rectangle's length is 108 feet, and its width is 50 feet.
Can someone help me with this?
Answers
Answer:
Example 1 = ?
Example 2 = x = 3.22
Example 3 = 10.963 = x
Example 4 = ?
Alma makes 5 cups of her favorite shade of purple paint by mixing 3 cups of blue paint, 11/2 cups of red paint, and 1/2 a cup of white paint. Alma has 2 cups of white paint.
Assuming she has enough red paint and blue paint, how much purple paint can Alma make?
Answers
Answer:
8 1/2 cups
Step-by-step explanation:
Add the blue and red cups of paint together to get 8 1/2 cups of paint.
Since we can assume she has enough, the answer is eight and a half cups of purple paint.
Alma can make 20 cups of purple paint.
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: For every 5 cups of purple paint alma needs to add 1/2 cup of white paint .
Thus with 2 cups white paint she could make 4 batches of 5 cups of purple paint.
Therefore, total number of purple paint cups from 2 cups of white paint is
4×5=20 cupa
Hence, Alma can make 20 cups of purple paint.
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What is the perimeter of rectangle efgh? startroot 10 endroot startroot 29 endroot units 2 startroot 10 endroot 2 startroot 29 endroot units 22 units 39 units
Answers
The perimeter of the rectangle is the length of the boundary of the perimeter of the rectangle. The perimeter of the rectangle is 2(√29+√10).
What is the perimeter of the rectangle?The perimeter of the rectangle is the length of the boundary of the perimeter of the rectangle.
In order to find the perimeter of the rectangle, we need to find the third side(Hypotenuse) of each triangle, therefore,
In ΔA,
[tex](Hypotenuse)^2 =(Perpendicular)^2+(Base)^2[/tex]
[tex]GF^2 = 3^2+1^2\\GF=\sqrt{10}[/tex]
In ΔB,
[tex](Hypotenuse)^2 =(Perpendicular)^2+(Base)^2[/tex]
[tex]EF^2 = 2^2+5^2\\EF=\sqrt{29}[/tex]
In ΔC,
[tex](Hypotenuse)^2 =(Perpendicular)^2+(Base)^2[/tex]
[tex]GH^2 = 2^2+5^2\\GH=\sqrt{29}[/tex]
In ΔD,
[tex](Hypotenuse)^2 =(Perpendicular)^2+(Base)^2[/tex]
[tex]EH^2 = 3^2+1^2\\EH=\sqrt{10}[/tex]
Now, the perimeter of the rectangle is,
[tex]Perimeter\ EFGH = EF+ GF + GH +EH[/tex]
[tex]=\sqrt{29}+\sqrt{10}+\sqrt{29}+\sqrt{10}\\\\=2\sqrt{29}+2\sqrt{10}\\\\=2(\sqrt{29}+\sqrt{10})[/tex]
hence, the perimeter of the rectangle is 2(√29+√10).
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Find the slope of the line through (2. – 3) and (5. – 3).
Answers
Answer:
Step-by-step explanation: Explanation:
You need to use the formula for slope:
m
=
y
2
−
y
1
x
2
−
x
1
m
represents the slope.
You need to assign each coordinate, but it must correspond.
For example:
In the coordinate
(
2
,
−
3
)
,
2
is
x
1
and
−
3
is
y
1
.
In the coordinate
(
5
,
2
)
,
5
is
x
2
and
2
is
y
2
.
Now you plug this in.
m
=
2
−
(
−
3
)
5
−
2
After this, you need to simplify
m
=
5
3
This may be wrong so double check.
let's solve:-
[tex]the \: formula \:to \: find \: slope \: \bold \green{m = \frac{y2 - y1}{x2 -x1}} \\ \\ \sf{(where \: m \: represents \: the \: slope.)} \\ \\ [/tex]
_________________________Here:-
[tex] \bold \red{\boxed{y2 = - 3} }\\ \bold \red{\boxed{y1 = - 3} }\\ \bold \red{\boxed{x2 = 5}} \: \: \: \\ \bold \red{\boxed{ x1 = 2} }\: \: \: [/tex]
[tex] \large\boxed {\sf{↬putting \: values \: according \: to \: formula}}[/tex]
[tex] \large \bold{↬m = \frac{ - 3 - ( - 3)}{5 - 2}} \\ \\\large \bold{↬m = \frac{ - 3 + 3}{5 - 2} } \: \: \: \: \: \: \: \\ \\ \large \bold{↬m = \frac{0}{3} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large \bold\blue{↬m = 0} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
_________________________Find the missing value for x.
Answers
Answer:
x is 62 degrees i think
Step-by-step explanation:
wow how do i know how to do this. ANYWAYS:
since it says that the whole two angels is 152 and that one of the angles is 90 degrees we can write the equation:
90 + x = 152
x = 62
you may ask "but thats the degree of the angle next to 90.." but it is also x because it is parallel (i think thats the word)
Lamar filled a measuring cup with 3 cups of vegetable oil. Then he poured 1 4/5 cups of the oil into a frying pan. How much oil is left in the measuring cup?
Answers
Answer:
1, 1\5 left
Step-by-step explanation:
Please Help Will mark brainliest
Answers
Answer:
○ [tex]\displaystyle -6x^2 + 6x + 5[/tex]
Step-by-step explanation:
Since the divisor is in the form of [tex]\displaystyle x - c,[/tex]use what is called Synthetic Division. Remember, in this formula, -c gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so do not forget it. Anyway, here is how it is done:
2| −6 18 −7 −10
↓ −12 12 10
________________
−6 6 5 0 [tex]\displaystyle \hookrightarrow -6x^2 + 6x + 5[/tex]
You start by placing the c in the top left corner, then list all the coefficients of your dividend [−6x³ + 18x² - 7x - 10]. You bring down the original term closest to c then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than your dividend, so that −6 in your quotient can be a [tex]\displaystyle -6x^2,[/tex]the [tex]\displaystyle 6x[/tex]follows right behind it, then you end it off with [tex]\displaystyle 5,[/tex]giving you the quotient of [tex]\displaystyle -6x^2 + 6x + 5.[/tex]
I am joyous to assist you at any time.
PLEASE HELP WILL GIVE BRAINLIEST
Answers
The inequalities are option B, C and D which are;
B. 11 > (w - 4)² C. y < 3⁴ D. 5+9 < 5×9
Define the term inequalities?Imbalances are numerical articulations that think about two qualities and express that they are not equivalent.
The inequalities are:
B. 11 > (w - 4)²
C. y < 3⁴
D. (5+9) < (5×9)
Here, option A and E are not inequalities. A is a quadratic expression and E is a rational function.
Inequality B says that 11 is greater than the square of the difference between w and 4.
⇒ √(11) > (w - 4)
⇒ w - 4 < √(11) or w - 4 > -√(11)
⇒ w < 4 + √(11) or w > 4 - √(11)
So the solution for inequality B is: w < 4 + √(11) or w > 4 - √(11)
Inequality C says that y is less than 3 to the fourth power (81).
⇒ y < 81
Inequality D says that the sum of 5 and 9 is less than the product of 5 and 9. This is clearly true:
⇒ (5 + 9) < (5 × 9)
⇒ 14 < 45
So the solution for inequality D is: 14 < 45
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This is the same triangle you used for Question 2.
Triangle ABC has angle measures as shown below. Using the information in the
diagram, and the value of x that you calculated in Question 2, find the measure
of Angle C.
In your answer, give the measure of Angle C and explain how you calculated it.
Answers
Answer:
93
Step-by-step explanation:
in your answer, give the measure of Angle C and explain how you calculated it.
i dont know the answer but i just added 3(29+2) and got 29 sorry if its wrong
What is the product represented by this model? [Hint: Remember that the green overlapping area represents the numerator]. Write your answer in simplest form.
Answers
The product represented by the model is 2/3, the correct option is A.
What is a Fraction?A fraction is a part of the whole, It is represented in the terms of p/q, where q is not equal to zero.
To form the fraction from the given graph
The number of green boxes needs to be counted = 20
Total number of boxes = 30
The green boxes represent the numerator
Fraction = 20/30
Fraction = 2/3
Therefore, the product represented by the model is 2/3.
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What are the coordinates of A’ after reflecting across the line x = 3?
On a coordinate plane, figure A B C D has points (3, 2), (2, 4), (6, 3), and (1, 0).
(2, 3)
(3, 2)
(3, 4)
(3, –2)
Mark this and return
Answers
Answer: (3,2)
Step-by-step explanation:
(3,2) lies on the line x=3, so it is an invariant point.
Answer:
c
Step-by-step explanation:
Teslim is designing a cover for a book. He wants to have a rectangular grid with x2 – 10x + 21 squares in it, for some positive whole number x. What are the possible side lengths for the grid? A. (x – 3) and (x – 7) B. (x – 3) and (x + 7) C. There are no possible whole number side lengths. D. (x + 3) and (x + 7)
Answers
Answer:
A. (x – 3) and (x – 7)
Step-by-step explanation:
A. (x – 3) and (x – 7) = x^2 - 10x + 21
x*x = x^2
x*-7 = -7x
-3*x = -3x
-3*-7 = 21
x^2 - 7x + 3x + 21
x^2 - 10x + 21
Using six random samples, the average number of catfish in the samples was 5. 7. If the total population of fish in the pond is 200, the proportion of catfish in the pond will be 5. 7 20 = x 200. What is the predicted number of catfish in the pond?.
Answers
Answer:
the answer is 57 I got it right hope you do to!
Step-by-step explanation:
Pl help
THIS IS DUE VERY SOON
CROWN FOR CORRECT ANSWER
Answers
Answer:
5.634
Step-by-step explanation:
Side BC = 12
Side AC = 10.59537
Side AB = 5.63366
90° = 1.5708 rad = π/2
62° = 1.0821 rad
28° = 0.48869 rad
Please let me know if this helped <3
What expression represents the profit? 27x – 650 27x 390 33x – 650 33x 390.
Answers
The expression that represents profit in the given example is
33x+390.
It is given that
Revenue function = [tex]2x^3 +30x-130[/tex]
Cost function = [tex]2x^3-3x-520[/tex]
What is the relationship between revenue, cost, and profit functions?Profit function = revenue function- cost function
Profit function= [tex]{2x^3 +30x-130}-{2x^3+3x+520[/tex]
profit function= 33x+390
Therefore, the expression that represents profit in the given example is
27x-650
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Answer:
33x+390.
Step-by-step explanation:
I took the test
QUICK whoever gives correct answer will get brainliest please and thank you.
Answers
Answer:
D. (The one with a graph and line)
You can use the vertical line test.
Two laser beams originating from the same source pass through a glass cylinder parallel to its base. The arc intercepted by the lasers closest to the source measures 60. The arc intercepted by the lasers on the other side of the cylinder measures 80. What is the measure of the angle formed by the two laser beams ?
A. )10
B. )20
C. )30
D. (40
Answers
The measure of the angle formed by the two laser beams is 20°
What is an angle?
An angle is formed when two or more lines intersect. Acute angles are angles less than 90 degrees, obtuse angles are greater than 90 degrees while right angles are 90 degrees.
The arc intercepted by the lasers closest to the source measures 60. The arc intercepted by the lasers on the other side of the cylinder measures 80. Hence:
The measure of the angle formed by the two laser beams = 80 - 60 = 20°
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lodine-131 has a half-life of 8 days. How much of the original 40-gram sample would be left
after 40 days?
Answers
Answer:
1.25 grams would be left
Step-by-step explanation:
40/2=20
20/2=10
10/2=5
5/2=2.5
2.5/2=1.25
What is an
equation of the line that passes through the points (1, 3) and (7, -3)?
Answers
Answer: y=-x+4
Step-by-step explanation:
Write an equation for each line.
Answers
Answer:
Step-by-step explanation:
Equation of blue line:
blue line is parallel to y-axis
⇒ x = 5
Equation of green line:
Green line is parallel to x-axis.
y = 2
Equation of red line:
At y-intercept x = 0. Point on red line is (0,5)
So, y-intercept = 5
y = mx + b Here, m is slope any b is y-intercept.
y = mx + 5
Now, choose any other point in red line. ((1,7)
Substitute this value in the above equation and we can find m
7 = m*1 + 5
7 - 5 = m
m = 2
y = 2x + 5
Equation of black line:
Black line and red line are parallel and so, they have same slope.
y = 2x + b
y-intercept (0,-6) ; b = -6
y = 2x - 6
PLEASE HELP!!!!!! The length of a rectangle is three times its width. If the perimeter of the rectangle is 56 cm, find its area.
Answers
Step-by-step explanation:
l = length
w = width
l = 3w
perimeter p = 2l + 2w = 56
using the identity of the first equation
p = 2(3w) + 2w = 56
6w + 2w = 56
8w = 56
w = 7 cm
l = 3w = 3×7 = 21 cm
so, the area is
l×w = 21×7 = 147 cm²
80 points. Help please.
4. Test the residuals of two other points to determine how well the line of best fit models the data.
Slope is y = 1x + 2
Answers
Answer:
[tex]\red{ \rule{10pt}{9999999pt}}[/tex]
Step-by-step explanation:
[tex]\red{ \rule{10pt}{999999pt}}[/tex]
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