Answer:
[tex] y \geq 15[/tex]
Step-by-step explanation:
The range of the inverse is the same as the domain of the original function.
Answer:y>15
Step-by-step explanation:
Consider the following polynomial function.
f(x) = (x+3)(x+1)²(x-1)
Answer the questions regarding the graph of f.
Then, use this information to graph the function.
(a) Choose the end behavior of the graph of f.
Choose One
(b) List each real zero of faccording to the behavior of the graph at the X-axis near that
zero. If there is more than one answer, separate them with commas. If there is no
answer, click on "None".
Zero(s) where the graph crosses the X-axis:
Zero(s) where the graph touches, but
does not cross the X-axis:
(c) Find the y-intercept of the graph of f:
(d) Graph f(x) = (x+3)(x+1)²(x-1) by doing the following.
Plot all points where the graph of f intersects the x-axis or y-axis.
For each point on the X-axis, select the correct behavior.
Click on the graph icon.
The end points behavior of the function:
(a) If x goes to positive infinity then the function goes to positive infinity. If x goes to negative infinity then the function goes to negative infinity.
(b) The zeros of the function f(x) are -3, -1, -1, and 1.
(c) The y-intercept is at (0,-3).
What is the endpoint behaviors of a polynomial?
A polynomial function's final behaviour is how its graph behaves as x gets closer to positive or negative infinity. The graph's final behavior is determined by a polynomial function's degree and leading coefficient.
What are zeros of a polynomial?
The locations where a polynomial becomes zero overall are known as the zeros of the polynomial. The term "zero polynomial" refers to a polynomial with a value of zero (-1). The highest power of the variable x is referred to as a polynomial's degree. A linear polynomial is a polynomial with degree 1.
Given function is f(x) = (x+3)(x+1)^2(x-1).
If x = ∞, then f(x) = ∞. The one endpoint of the function will go positive infinity.
If x =- ∞, then f(x) = -∞. The one endpoint of the function will go negative infinity.
To find the zeros of the polynomial, equate f(x) with zero.
(x+3)(x+1)^2(x-1) = 0
Either, x + 3 =0 → x = -3
or, (x+1)^2 =0 → x = -1
or, x-1 = 0 → x = 1
The zeros of the function are -3, -1, and 1.
To find y-intercept, put x=0 in the given function:
f(0) = (0+3)(0+1)^2(0-1)
→ f(0) = -3
The y-intercept is at (0,-3).
The x-intercepts of the function are zeros of the function.
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The length of a rectangle is six times its width. If the perimeter of the rectangle is 112 ft, find its length and width.
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answer:
Unless you wrote the wrong expressions, non of your choice answers are correct!
Step-by-step explanation:
Solve for x:
2 (x - 7) = 36
Divide both sides of (x - 7)×2 = 36 by 2:
(2 (x - 7))/2 = 36/2
2/2 = 1:
x - 7 = 36/2
The gcd of 36 and 2 is 2, so 36/2 = (2×18)/(2×1) = 2/2×18 = 18:
x - 7 = 18
Add 7 to both sides:
x + (7 - 7) = 7 + 18
7 - 7 = 0:
x = 18 + 7
18 + 7 = 25:
Answer: x = 25
Daisy has one cucumber that is 3 inches long and another that is 5inches long. She cuts the cucumber into 3/8 inch thick slices and adds them to a salad. How many 3/8 inch thick slices does Daisy have? How much of a slice will be left over?
If She cuts the cucumber into 3/8 inch thick slices and adds them to a salad. The number of 3/8 inch thick slices that Daisy have 21 1/3.
How to find the thickness ?Given data:
Cucumber length = 3 inches
Second cucumber length = 5 inches
Cucumber slices = 3/8
Now let find the the number of thickness that daisy have
Thickness = (3+5) ÷ 3/8
Thickness = 8× 3/8
Thickness = 64/3
Thickness = 21 1/3
Therefore the thickness is 21 1/3.
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Wayne rents a car from a company that charges $35 per day plus $0.10 per mile he drives. What is a linear equation for the monthly charge, C, dollars, in terms of the number of miles driven, n?
The linear equation for the monthly charge C dollars , in terms of the number of miles driven(n) is C(n) = 35 + 0.10×n .
In the question ,
it is given that ,
the fixed rent for a car is = $35 .
the per mile charge for the car is = $0.10 miles
let the number of miles driven is = n miles
the function C that represents the linear equation for the monthly charge C dollars , in terms of the number of miles driven(n) is given by
C(n) = fixed charge + (per mile charge)×(number of miles)
Substituting the values , we get
C(n) = 35 + 0.10×n
Therefore , The linear equation for the monthly charge C dollars , in terms of the number of miles driven(n) is C(n) = 35 + 0.10×n .
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Answer:
id say, C=0.10=35
Step-by-step explanation:
not really sure, but I tried!
Write an equation for the trend line shown on the scatter plot.
Answer:
y = 5x + 15
Step-by-step explanation:
You can pick any two points on the graph that intersect the trend line. For instance (5,40) and (3,30)
Formula for Slope:
[tex]y = \frac{y_2 - y_1}{x_2 - x_1} = \frac{40 - 30}{5 - 3} = \frac{10}{2} = 5[/tex]
y intercept:
[tex]y = 15[/tex]
Equation of a line:
[tex]y = mx + b\\m = slope \\b = intercept \\\\y = 5x + 15[/tex]
** also be cautious of the different scaling of the x and y axis.
A rectangular wall is √240 ft by
√50 ft. You need to paint the wall twice to
cover the area with two coats of paint. If
each can of paint can cover 60 square feet,
how many cans of paint will you need?
Answer:
Step-by-step explanation: √240 = 15.49…. √50 = 7.07…
15.5 x 7.07 = 109.58 rounded to 110. Therefore the area is 110 feet so at least 2 can is needed to fill up the wall. But if the problem is being precise it’s 1 can and 5/6 of a can.
2 cans of paint will be needed to cover 110 square feet area.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given,
A rectangular wall is √240 ft by √50 ft.
Need to paint the wall twice to cover the area with two coats of paint.
Area of wall=Length×Width
=√240×√50
=√12000
=109.5=110
Given that each can of paint can cover 60 square feet,
110/60=1.83
=2
Hence, 2 cans of paint will be needed to cover 110 square feet area.
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5+4+7+5+3-4=?
helpppppppp
Answer: 20
Step-by-step explanation:
6 to the power of -3 as a simplified fraction or integer
Answer:
Step-by-step explanation:
1. Make Words into Math
6 to the power of -3 =
6^-3=
-6*-6*-6=
0.00462962962
Answer:0.00462962962
Given that -5 is a zero of the polynomial P(x) = x³ + 3x²-12x-10, find the other zeros.
Answer:
Below
Step-by-step explanation:
If -5 is one of the roots then that means (x+5) is one of the factors
divide (x+5) into x^3 + 3x^2 -12x -10
to get x^2-2x-2 which you can easily (using Quadratic Formula) find the roots 1 + sqrt 3 and 1 -sqrt 3
('roots' and 'zeroes' are the same thing)
Which is the best estimate for 2 2/3 × 3 1/4
An athlete swings a 7.9 kg ball horizontally on the end of a rope. The ball moves in a circle of radius 0.9 m at an angular speed of 0.27 rev/s.
What is the tangential speed of the ball? Answer in units of m/s.
part 2
What is its centripetal acceleration? Answer in units of m/s2.
this is physics
The tangential speed of the ball is 1.5267
The centripetal acceleration is 2.5897 m/s²
How to solve for the tangential speedMass of the ball is m = 7.90 kg
ball moves in a circle having radius r = 0.9 m
angular speed is ω = 0.27 rev /s
given that 1 revolution = 6.283 rad / sec
0.27 rev / sec = ?
ω = 1.696 rad / sec
a. The tangential speed Velocity = rω
w = 1.696
r = 0.9
= 1.696 * 0.9 m
= 1.5267 m / s
b ) centripetal acceleration a = v² / r
= (1.5267 m/s)^2 / 0.9 m
= 2.3308 / 0.9
= 2.5897 m/s²
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Determine whether the equation 2+y=x+4 represents a linear or nonlinear function.
Answer:
linear
Step-by-step explanation:
Because if you graph it. It creates a line which makes it a linear
Rewrite (55•44)•33 using the
Associative Law of Multiplication.
Rewriting the given term (55.44).33 using the Associative Law of Multiplication, we have 55.(44.33). Therefore, 1st option is correct.
The given terms are written as -
(55.44).33
We have to rewrite the given term using the Associative Law of Multiplication.
According to the Associative Law of Multiplication, the terms or factors can be associated in any expected ways, i.e.,
a(bc) = (ab)c
So, our given term in the question (55.44).33 can be rewritten according to the Associative Law of Multiplication as -
(55.44).33 = 55.(44.33)
Thus, rewriting the given term (55.44).33 using the Associative Law of Multiplication gives us 55.(44.33). Therefore, 1st option is correct.
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The sum of $5400 was borrowed from a bank
at the rate of 10% per annum for 3 years. How much would the simple interest payable would be?
(A) $1800
(B) $540
(C) $1620
(D) $486
The simple interest on $5400 at a rate of 10% per annum for 3 years is $ 1620
Simple interest:The interest on a loan at a fixed rate per annum. The formula used for simple interest is given by
Simple interest (I) = ptr
Where p = principal amount
t = time period
r = rate of interest per year.
Here we have
The sum of $5400 was borrowed from a bank at a rate of 10% per annum for 3 years
Find the simple interest that can be payable
From above observations
Principal amount, P = $5400
Rate of interest = 10% = 10/100 = 0.1
Time period, t = 3 years
The simple interest that can be payable = $5400(3)(0.1) = $ 1620
Therefore,
The simple interest on $5400 at a rate of 10% per annum for 3 years is $ 1620
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Let the vector v have an initial point at (4, 8) and a terminal point at
(-2, 3). Plot the vector v and afterwards follow the guided steps to analyze
the vector.
The vector having a magnitude √61 and direction 140.2° has been shown in the figure.
Given,
Let the vector v have an initial point at (4, 8) and a terminal point at
(-2, 3).
we are asked to Plot the vector v .
Given that the initial point of the vector is (4,8) and the termination point of the vector is (-2,3).
So, the tail of the vector is at point (4,8) and the head of the vector is at (-2,3).
The vector , v, has been shown.
I v I = √(4-(-2))²+(8-3)²
= √(4+2)²+(8-3)²
= √(6)²+(5)²
= √36+25
= √61
The direction of a vector is the angle made by a vector with the positive direction of the x-axis.
θ = 180° tan⁻¹ I 3-8/-2-4I
θ = 180° tan⁻¹ (5/6)
θ = 180° - tan⁻¹(5/6)
θ = 180° - 39.80°
θ = 140.2°
Hence, the required vector having a magnitude √61 and direction 140.2° has been shown in the figure.
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See question in screenshot below:
The point only can be on the unit circle and on the second quadrant if:
x = -√55/8
How to get the value of the x-coordinate?
We know that we have a point of the form:
P = (x, y)
And the value of y is:
y = 3/8
Then our point is:
P = (x, 3/8)
And it is on the unit circle, then the values of x and y are solutions of:
x^2 + y^2 = 1
x^2 + (3/8)^2 = 1
x^2 = 1 - (3/8)^2 = 1 - 9/64 =
x^2 = 64/64 - 9/64
x^2 = 55/64
x = ±√(55/64) = ±√55/8
And P is on the second quadrant, then we take the negative option:
x = -√55/8
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write an equation in slop intercept form to represent the relationship in a table
The equation of the table is y=2x+8 when the slope and intercept are 2 and 8.
Given that,
In the picture we can see the table.
We have to find the equation of the table.
We know the equation is in the form
y=mx+b
Here,
m is rise/run
Which is slope
b is intercept.
Take the point as (0,8) and (1,10)
Slope is m =(10-8)/(1-0)
m= 2/1
m=2
Then b is
8=2(0)+b
b=8
The equation will be y=2x+8
Therefore, The equation of the table is y=2x+8 when the slope and intercept are 2 and 8.
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A standard deck of playing cards contains 52 total cards, 13 of which are "spades".
Suppose you and a friend are playing a game. You can choose any two cards from the deck without looking. If the two cards you choose are both spades, you win!
You pull out one card, and then another, without putting the first one back.
What is the approximate probability that you win? Are your two choices independent or dependent events?
6%, Independent
6%, Dependent
11%, independent
11%, Dependent
The probability that you win is 6%, and the two choices are dependent events option (B) is correct.
What is probability?
It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that:
A standard deck of playing cards contains 52 total cards, 13 of which are "spades".
The probability of the first draw:
Probability = favorable outcomes/total outcomes
First draw: 1/4
For the second draw:
Second draw = 12/51
The probability that you win = (1/4)(12/51) = 3/51
In percent:
= (3/51)x100
= 5.88 = 6%
Thus, the probability that you win is 6%, and the two choices are dependent on events option (B) is correct.
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Which of the following mixed numbers is equal to the improper fraction 29/4
A: 7 1/4
B: 7 1/2
C: 7 3/4
D: 7
Answer: A
Step-by-step explanation:
If y=-2x^3+4x+9, what is y when x=3?
Answer:
39
Step-by-step explanation:
2*3^3+4*3+9
= 39
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How do I figure the total of a 4:3 ratio?
Step-by-step explanation:
If you take the 4:3 aspect ratio and divide 4 by 3, the result is 1.33. Therefore, you could alternately describe the 4:3 aspect ratio as 1.33:1, meaning that for every 1.33 units in width, there is 1 unit in height. Again, the same applies for the 16:9.
Learn at brainlyIdentify the change in the parent function that will produce the related function shown as a dashed line. f(x) = x
For f(x)=x+4 and g(x)=3x+2, find the following functions.
Someone please explain how to solve this
The values of the following functions are:
a. (f ºg)(x) = x+2
b. (g º f)(x) = 3x + 14
c. (f º g)(-1) = 3
d. (g º f)(-1) = 11
Given:
f(x) = x+4 and
g(x) = 3x+2
we are asked to determine the following functions:
a. (f º g)(x)
⇒ f(g(x))
⇒ f(3x+2)
⇒ (f º g)(x) = (3x+2)+4
= 3x+6
divide by 3
= x+2
b. (g º f)(x)
⇒ g(f(x))
⇒ g(x+4)
⇒ (g º f)(x) = 3(x+4)+2
= 3x+12+2
= 3x+14
c. (f º g)(-1)
⇒ f(g(-1))
⇒ f(3(-1)+2)
⇒ f(-3+2)
⇒ f(-1)
⇒ (f º g)(-1) = -1+4
= 3
d. (g º f)(-1)
⇒ g(f(-1))
⇒ g(-1+4)
⇒ g(3)
⇒ (g º f)(-1) = 3(3)+2
= 11
Hence we get the required answer.
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30x43x54545454545455454x82409284x098908098x8908089808x56678909876543-32131273138x1000 =
Answer:
7,036,363,636,363,635,660,000
Step-by-step explanation:
this one hert my head
Write the prime factorization for each of the following numbers using exponents if possible.
2. Choose the correct answer to 2,412 ÷ 25. 96 96 R12 97 95 R37
Answer: 96 R12
Step-by-step explanation:
What are m and b in the linear equation y = 18x + 25?
Answer: m=18 and b=25
Step-by-step explanation:
y = mx + b ==> standard slope intercept equation
y = 18x + 25
Notice any similarities?
y = 18x + 25
m=18 and b=25
Can anyone help me with number 2?
Friday: Nabil had $80.50 on a gift card before buying four journals at a bookstore. The bookstore charges 50¢ to use the card. He had $44.00 left on the gift card after buying the journals. If each journal cost the same amount, what was the price of each journal?
Answer:
$9.00 a journal.
Step-by-step explanation:
First off, you can start by subtracting $0.50 from $80.50 because it costs $0.50 to use the card.
You’re left with a new value of $80.00. Since Nabil had $44.00 left over on his card, you can subtract $44.00 from $80.00 to figure out how much he spent.
$80.00
-$44.00
————
$36.00
Since Nabil bought four journals, and they are all equal in cost, you can divide $36.00 by 4 (36/4) and get $9.00.