i think it’s 6......... Sorry if I got it wrong I’m trying to help people out Answer:
Step-by-step explanation:
Practice Question:
f(x)= 3x^2 + 4x - 6
g(x)= 6x^3 - 5x^2 - 2
Find (f + g)(x)
Answer Options (Choose one):
A. (f+g)(x) = -6x^3 + 8x^2 + 4x -4
B. (f+g)(x) = 6x^3 + 3x^2 - x - 8
C. (f+g)(x)= 6x^3 - 2x^2 + 4x - 8
D. (f+g)(x)= 9x^3 - x - 8
The correct option of the function is C. (f+g)(x)= 6x^3 - 2x^2 + 4x - 8.
What is a function?The function is a type of relation, or rule, that maps one input to specific single output.
Given;
f(x)= 3x^2 + 4x - 6
g(x)= 6x^3 - 5x^2 - 2
So,
(f + g)(x) = (3x^2 + 4x - 6) + (6x^3 - 5x^2 -2)
(f + g)(x) = 3x^2 + 4x - 6 + 6x^3 - 5x^2 - 2
Now, like terms and in order of exponent
(f + g)(x) = 6x^3 - 2x^2 + 4x - 8
Therefore, the correct option is C. (f+g)(x)= 6x^3 - 2x^2 + 4x - 8.
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removing this account, any words
Answer: Cya
Step-by-step explanation:
Answer:
Thanks for the free points. Sayonara, mate.
Step-by-step explanation:
The winning team
in a 400-meter relay race had a time of
198.608 seconds. Suppose all 4 of the split
times were the same. Write and solve an
equation to find the split times.
The equation for split times is 4x= 198.608 and the value of x is 49.652
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
Let x be the split time
all 4 of the split times were the same.
4x= 198.608
=> x= 198.608/4 = 49.652
The equation for split times is 4x= 198.608 and the value of x is 49.652
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A line is perpendicular to y = -1/5x + 1 and intersects the point negative (-5,1) what is the equation of this perpendicular line?
Answer: y = 5x + 26
Step-by-step explanation:
To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.
We can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Substituting the values, we get:
y - 1 = 5(x - (-5))
Simplifying further:
y - 1 = 5(x + 5)
Expanding the brackets:
y - 1 = 5x + 25
Rearranging the equation to the slope-intercept form (y = mx + b):
y = 5x + 26
Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.
(2,1)
Which of the following could be the quadratic function graphed in the xy-plane above?
f(x) = 2x2
f(x) = x2 + 1
f(x) = (x - 2)2 + 1
f(x) = (x - 1)2 + 2
Answer:
the correct answer is f(x)=(x-2)^2 + 1
Step-by-step explanation:
lets loof for f(2) :
f(2)=(2-2)^2 + 1
f(2)=(0)^2 + 1
f(2)= 1 ---> (2,1)
A city has a population density of approximately 6,300 people /km2. The population is about 552,200 people. What is the approximate area of the city
Answer:
Step-by-step explanation:
552,200 people × (1 km²)/6,300 people) ≈ 87.65 km²
Expand and simplify (x-3)(2x+1)(x+1)
Step-by-step explanation:
(x-3)(2x+1)(x+1)
(2x² - 6x + x - 3)(x+1)
(2x² - 5x - 3) (x+1)
2x³ -5x² -3x + 2x² -5x - 3
2x³ - 3x² - 8x -3
---------------------------FOLLOW MEFind the area of this circle. Use 3.14 for . A circle has diameter 62 feet. 62 ft
PLS HELP
Answer:
3017.54
Step-by-step explanation:
Volume for area of circle is A = Pie ( Or in this case 3.14 ) * radius ^ 2
Plug in the numbers 3.14 * 31 ^2
31 is half the diameter or the radius
Answer = 3017.54
Ethan writes 1/6 pages in 1 1/2 minutes.How long will it take him to write a full page?
Answer:
33 Minutes
Step-by-step explanation:
Just take 11/2 time 6 and get 33 minutes.
determine whether the relation r on the set of all integers is reflexive, symmetric, antisymmetric, and/or transitive, where (x,y) in r if and only if: x = y − 1 or y = x − 1.
The relation R is symmetric and antisymmetric, but not reflexive or transitive.
Let's examine each property of the relation R separately:
Reflexive: A relation R is reflexive if every element in the set is related to itself. In this case, we have (x, x-1) or (x-1, x) for any integer x. Therefore, the relation is not reflexive since x is not related to itself.
Symmetric: A relation R is symmetric if for any pair of elements x and y in the set, (x,y) being in R implies that (y,x) is also in R. In this case, we have (x, y-1) or (y, x-1) for any integers x and y. It is clear that if (x, y-1) is in R, then (y, x-1) is also in R, and vice versa. Therefore, the relation is symmetric.
Antisymmetric: A relation R is antisymmetric if for any distinct elements x and y in the set, if (x,y) is in R, then (y,x) cannot also be in R. In this case, if we have (x, y-1) and (y, x-1), then x = y-1 and y = x-1. This implies that x = y, which contradicts our assumption that x and y are distinct. Therefore, the relation is antisymmetric.
Transitive: A relation R is transitive if for any elements x, y, and z in the set, if (x,y) and (y,z) are in R, then (x,z) is also in R. In this case, we have (x, y-1) and (y, z-1) for any integers x, y, and z. If we add these two relations, we get (x, z-2).
However, this does not satisfy the original relation, which requires that (x, z-1) be in R. Therefore, the relation is not transitive.
In summary, the relation R is symmetric and antisymmetric, but not reflexive or transitive.
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Help with special right triangles rounding
Answer:
9.8 units-----------------------------------
Hypotenuse of an isosceles triangle is √2 times the leg:
x = √12 × √2 = √24 = 4√6 ≈ 9.8 units (rounded to the nearest tenths)a paint can is 10 cm tall and holds approximately 535 cubic centimeters of paint. what is the approximate area of the base of the can? responses 5350 square centimeters 5350 square centimeters 53.5 square centimeters 53 point 5 square centimeters 100 square centimeters 100 square centimeters 5.35 square centimeters
the approximate area of the base of the paint can is 53.5 square centimeters.by using Volume formula is Base Area × Height
To find the approximate area of the base of the paint can, we can use the formula for the volume of a cylinder:
Volume = Base Area × Height
We are given the volume (535 cubic centimeters) and the height (10 cm). We need to solve for the Base Area. Rearranging the formula to solve for Base Area, we get:
Base Area = Volume ÷ Height
Now, substitute the given values:
Base Area = 535 cubic centimeters ÷ 10 cm
Base Area ≈ 53.5 square centimeters
So, the approximate area of the base of the paint can is 53.5 square centimeters.
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The approximate area of the base of the can is 53.5 square centimeters
How to determine the area of the base of the can?From the question, we have the following parameters that can be used in our computation:
Volume = 535 cubic centimeters of paint
Height of container = 10 cm
The area of the base of the can is calculated as
Base area = Volume/Height
Substitute the known values in the above equation, so, we have the following representation
Base area = 535/10
Evaluate
Base area = 53.5
Hence, the base area is 53.5 square centimeters
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if r(t) = 3e2t, 3e−2t, 3te2t , find t(0), r''(0), and r'(t) · r''(t).
As per the given data, r'(t) · r''(t) = \(108e^{(2t)} - 72e^{(-2t)} + 72te^{(2t)\).
To discover t(zero), we want to alternative 0 for t inside the given feature r(t). This offers us:
\(r(0) = 3e^{(2(0)}), 3e^{(-2(0)}), 3(0)e^{(2(0)})\\\\= 3e^0, 3e^0, 0\\\\= 3(1), 3(1), 0\\\\= 3, 3, 0\)
Therefore, t(0) = (3, 3, 0).
To find r''(0), we need to locate the second one derivative of the given feature r(t). Taking the by-product two times, we get:
\(r''(t) = (3e^{(2t)})'', (3e^{(-2t)})'', (3te^{(2t)})''= 12e^{(2t)}, 12e^{(-2t)}, 12te^{(2t)} + 12e^{(2t)}\)
Substituting 0 for t in r''(t), we have:
\(r''(0) = 12e^{(2(0)}), 12e^{(-2(0)}), 12(0)e^{(2(0)}) + 12e^{(2(0)})\\\\= 12e^0, 12e^0, 12(0)e^0 + 12e^0\\\\= 12(1), 12(1), 0 + 12(1)\\\\= 12, 12, 12\)
Therefore, r''(0) = (12, 12, 12).
Finally, to discover r'(t) · r''(t), we need to calculate the dot made of the first derivative of r(t) and the second spinoff r''(t). The first spinoff of r(t) is given by using:
\(r'(t) = (3e^{(2t)})', (3e^{(-2t)})', (3te^{(2t)})'\\\\= 6e^{(2t)}, -6e^{(-2t)}, 3e^{(2t)} + 6te^{(2t)\)
\(r'(t) · r''(t) = (6e^{(2t)}, -6e^{(-2t)}, 3e^{(2t)} + 6te^{(2t)}) · (12, 12, 12)\\\\= 6e^{(2t)} * 12 + (-6e^{(-2t)}) * 12 + (3e^{(2t)} + 6te^{(2t)}) * 12\\\\= 72e^{(2t)} - 72e^{(-2t)} + 36e^{(2t)} + 72te^{(2t)\)
Thus, r'(t) · r''(t) = \(108e^{(2t)} - 72e^{(-2t)} + 72te^{(2t)\).
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Please Help!!!
What method would allow you find the area of the given triangle?
Answer:
the method we follow is area of the triangle is 12bh b is base and h is the height of the triangle
pls help asappp you will get brainliest
Answer:
32 units.
Step-by-step explanation:
look up a picture of a 306090 triangle, it will make sense :)
Answer:
32
Step-by-step explanation:
cos 30 = \(\frac{\sqrt{3} }{2}\)
\(\frac{\sqrt{3} }{2}\) = 16\(\sqrt{3}\) / n
n = 16\(\sqrt{3}\) * \(\frac{2}\sqrt{3} }\)
n = 32 units
What operation is the inverse of the one in the equation 9 = p/8 ?
A.subtraction
B.division
C.multiplication
D.addition
Multiplication operation is the inverse of the one in the given equation which is 9 = p/8.
What is an inverse?
The opposite of another operation is referred to as the "inverse" in mathematics. The operations that cancel out or are the opposite of one another are referred to as inverse operations. The work of a pair is reversed by an inverse operation.
We are given an equation as 9 = p/8.
In this equation, we can see that the operation used is division.
We know that inverse of division is multiplication.
Hence, multiplication operation is the inverse of the one in the given equation.
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Find an equation for the hyperbola with foci (0,±5) and with asymptotes y=± 3/4 x.
The equation for the hyperbola with foci (0,±5) and asymptotes y=± 3/4 x is:
y^2 / 25 - x^2 / a^2 = 1
where a is the distance from the center to a vertex and is related to the slope of the asymptotes by a = 5 / (3/4) = 20/3.
Thus, the equation for the hyperbola is:
y^2 / 25 - x^2 / (400/9) = 1
or
9y^2 - 400x^2 = 900
The center of the hyperbola is at the origin, since the foci have y-coordinates of ±5 and the asymptotes have y-intercepts of 0.
To graph the hyperbola, we can plot the foci at (0,±5) and draw the asymptotes y=± 3/4 x. Then, we can sketch the branches of the hyperbola by drawing a rectangle with sides of length 2a and centered at the origin. The vertices of the hyperbola will lie on the corners of this rectangle. Finally, we can sketch the hyperbola by drawing the two branches that pass through the vertices and are tangent to the asymptotes.
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2+2-1 the kkkjdscdvxbcfvgbhnjimklimugytfdrseawzesxrctgvyhbjnkm
Answer:
Hello! the answer is 3.......
I feel as though the question was a joke.. But no matter I will accept the points.
Anyway have a great day and take mental health breaks!
Evaluate the expression when y=6 y²-9y-7
Answer:
The answer would be Y= 5 ± √67 / 6
Step-by-step explanation:
Name
Period
13. The volleyball team is accepting donations and
having a car wash to raise funds for an out-of-
state tournament and purchase new equipment.
The team plans to use 25% of all donations and
car wash proceeds for new equipment. The table
shows the results from over the weekend where
w represents the amount charged per car wash. If
the team charged $5 per car wash, how much
money will they have to spend on new equipment?
The total amount of money spend on new equipment after using 25% of the total donations and car wash proceeds is $93.75.
On Saturday,
The team raised 21w + 75 dollars,
And on Sunday
Team raised 18w + 105 dollars.
Percent of donations and car wash proceeds for new equipment used
= 25%
The total amount raised over the weekend,
Total amount raised
= (21w + 75) + (18w + 105)
= 39w + 180
Amount for new equipment
= 25% ( 39w+ 180)
= 0.25(39w + 180)
= 9.75w + 45
If the team charged $5 per car wash that is w = 5
Substitute this value into the equation ,
Amount for new equipment
= 9.75w + 45
= 9.75(5) + 45
=48.75 + 45
= $93.75
Therefore, the amount of money spend on new equipment is equal to $93.75.
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The above question is incomplete , the complete question is:
The volleyball team is accepting donations and having a car wash to raise funds for an out-of-state tournament and purchase new equipment.
The team plans to use 25% of all donations and car wash proceeds for new equipment. The table shows the results from over the weekend where w represents the amount charged per car wash. If the team charged $5 per car wash, how much money will they have to spend on new equipment?
Day Donations and car wash proceeds
Saturday 21w + 75
Sunday 18w + 105
Please help me with edge question .
\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)
Help me plzz!!!!!!!!!!!!!!!
You have $50,000 in a retirement account, you plan to deposit $3,000 at the end every year until your account reaches $350,000. you expect to earn 6% annually on your savings how many years will you have to work before you retire?
a. 27
b.24
c.15
d.11
e.18
You will have to work for 27 years before you retire.
How many years do you need to work until retirement?To determine how many years you will have to work before you retire, we can use the formula for calculating the future value of an ordinary annuity. The formula is:
\(FV = P * ((1 + r)^n - 1) / r\)
We need to solve for n, so we'll rearrange the formula:
n = (log(FV * r / P + 1)) / log(1 + r)
Plugging in the values:
n = (log(350000 * 0.06 / 3000 + 1)) / log(1 + 0.06)
Calculating this expression:
n ≈ 27.24
Therefore, you will have to work approximately 27.24 years before you retire.
Since we're dealing with a whole number of years, the closest option is:
a. 27
So the answer is 27 years.
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What is the GCF of 24 and 42?
Answer:
6
Step-by-step explanation:
To find the GCF by factoring, list out all of the factors of each number and select the largest that both have in common.
Type the correct answer in each box, starting with the intercept with the lower value.
-x^2 + 5x + 24
x-intercept(s): ( 8 , 0 ) , ( − 3 , 0 )
y-intercept(s): ( 0 , 24 )
Help please.... I haven't done this in like 5 years.
Y = -1/8X +2
When X is 1, Y = -0.125+2, or 1.875
When X is -5, Y = 0.625+2, or 2.625
When X is -9, Y = 1.125+2, or 3.125
When X is -2, Y = 0.25+2, or 2.25
When X is -4, Y = 0.5+2, or 2.5
---
hope it helps
Lines x and y intersect to form adjacent angles 2 and 3. If m/_2 = 3a - 27 and m/_3 = 2b + 14, find the values of a and b so that x is perpendicular to y.
Answer:
Step-by-step explanation:
The required values of a and b is -
a = 39° ; and
b = 38°
What are adjacent angles?The two angles are said to be adjacent angles when they share the common vertex and side.
Lines x and y intersect to form adjacent angles 2 and 3.
and the given two angles are,
m/_2 = 3a - 27
m/_3 = 2b + 14
Since x and y are perpendicular to each other. Therefore,
m/_2 = 90°
m/_3 = 90°
Therefore we have,
3a - 27 = 90°
⇒ 3a = 90° + 27
⇒ 3a = 117°
⇒ a = 117°/3
⇒ a = 39°
Also,
2b + 14 = 90°
⇒ 2b = 90° - 14
⇒ 2b = 76°
⇒ b = 76°/2
⇒ b = 38°
Hence,The required values of a and b is-
a = 39° ; and
b = 38°
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simplify -2.7+0.8f-16-5
If p and q vary inversely and p is 29 when q is 25, determine q when p is equal to 5.
Answer:If p and q vary inversely, it means that their product remains constant. So we can set up the equation:
p * q = k
where k is the constant of variation.
Given that p is 29 when q is 25, we can substitute these values into the equation:
29 * 25 = k
725 = k
Now, let's determine the value of q when p is equal to 5:
p * q = k
5 * q = 725
Dividing both sides of the equation by 5:
q = 725 / 5
q = 145
Therefore, when p is equal to 5, q is equal to 145.
Step-by-step explanation:
Answer:p1q1=p2q2
q1=25,p1=29;
p2=5,q2=?;
q2=p1q1/p2;
q2=25*29/5;
q2=29*5;
q2=145.
Step-by-step explanation:
Solve for x.
3x^2 / x^2 - 16 = (3 / x - 4) + (4x / x + 4)
For the quadratic equation 3x² / (x² - 16) = (3 / x - 4) + (4x / x + 4), x = 16 is not a solution to the original equation.
We can begin by simplifying both sides of the equation and getting a common denominator:
3x² / (x² - 16) = 3/(x-4) + 4x/(x+4)
Multiplying both sides by (x² - 16), we get:
3x² = 3(x+4) + 4x(x-4)
Expanding the right side, we get:
3x² = 3x + 12 + 4x² - 16x
Simplifying and rearranging terms, we get:
x² - 19x + 12 = 0
We can factor this quadratic equation as:
(x - 3)(x - 16) = 0
Therefore, the solutions are x = 3 and x = 16.
However, we need to check if these solutions satisfy the original equation. For x = 3, we get:
3x² / (x² - 16) = (3 / x - 4) + (4x / x + 4)
3(3)² / (3² - 16) = (3 / 3 - 4) + (4(3) / 3 + 4)
27/1 = -1 + 12/7
27 = 20/7
This is not true, so x = 3 is not a solution to the original equation.
For x = 16, we get:
3x² / (x² - 16) = (3 / x - 4) + (4x / x + 4)
3(16)² / (16² - 16) = (3 / 16 - 4) + (4(16) / 16 + 4)
3(256) / 240 = (-45/16) + 20/5
64/15 = 1/16
This is also not true, so x = 16 is not a solution to the original equation.
Therefore, there are no solutions to the equation.
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