Answer:
expression for (g + h)([tex]x\\[/tex]) = [tex]2x[/tex] + [tex]3x^2\\[/tex] and for (g - h)([tex]x[/tex]) = [tex]2x[/tex] - [tex]3x^2[/tex]
value of (g .h)(2) = 24
Step-by-step explanation:
function operations: Functions with overlapping domains can be added, subtracted, multiplied and divided. If f(x) and g(x) are two functions, then for all x in the domain of both functions we can find the sum, difference, product and quotient
given :
g([tex]x[/tex]) = [tex]2x[/tex]
h([tex]x[/tex]) = [tex]3x^2[/tex]
we know that ;
(g + h)([tex]x[/tex]) = g([tex]x[/tex]) + h([tex]x[/tex])
= [tex]2x[/tex] + [tex]3x^2[/tex]
similarly;
(g - h)([tex]x[/tex]) = g([tex]x[/tex]) - h([tex]x[/tex])
= [tex]2x[/tex] - [tex]3x^2[/tex]
now,
(g . h)([tex]x[/tex]) = 2([tex]3x^2\\[/tex])
= 6[tex]x^2\\[/tex]
for (g .h)(2) = 6([tex]2^2[/tex])
= 6 × 4
= 24
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Determine the number of zeros of the polynomial function. f(x) = x^4 − 6x
The factor of the function will be x and (x³ – 6). Then the zeroes of the function will be 0 and √6.
What is a factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The polynomial function is given below.
f(x) = x⁴ − 6x
Then the factor of the function will be
f(x) = x(x³ – 6)
Then the zeroes of the function will be
x = 0, √6
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On a number line, 6.87 would be located
6.87
A. To the right of 6.81
B. Between 6 and 6.5
C. Between 6.5 and 7
D. To the left of 6.81
Check all that apply.
Lashawn makes scrambled eggs with 3 spoonfuls of salsa for every 2 eggs. Gilberta adds 7 spoonfuls of salsa for every 5 eggs.
Whose scrambled eggs have a stronger salsa taste?
A. Lashawn's eggs
B. Gilberta's eggs
C. The dishes of scrambled eggs have equal salsa tastes
Lashawn's scrambled eggs have a stronger salsa taste than Gilberta's scrambled eggs. Then the correct option is A.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Lashawn makes scrambled eggs with 3 spoonfuls of salsa for every 2 eggs.
Gilberta adds 7 spoonfuls of salsa for every 5 eggs.
Then the scrambled eggs have a stronger salsa taste will be
Lashawn's eggs = 3/2 = 1.5
Gilberta's eggs = 7/5 = 1.4
Lashawn's scrambled eggs have a stronger salsa taste than Gilberta's scrambled eggs.
Then the correct option is A.
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Joshua has a job that pays $2,265 biweekly. How much is withheld annually for Medicare? A.$853.91 B.$32.84 C.$16.42 d.$35.58 E.$71.16
Answer:
09999kjht
Step-by-step explanation:
tttttttttgtgr312345678909ytrewq
A sphere has a radius of 24 centimeters. What is its volume
Answer:
57905.8
Step-by-step explanation:
Use the formula:Plug in:
V = 4/3 * 24³π
= 4/3 * 13824π
= 18432π
= 57905.83579cm³
Rounded to nearest tenth:
57905.8
Answer: 18,432
Step-by-step explanation: ANSWER ON EDMENTUM/PLUTO
calculus piecewise function.
Part A
The notation [tex]\lim_{x \to 2^{+}}f(x)[/tex] means that we're approaching x = 2 from the right hand side (aka positive side). This is known as a right hand limit.
So we could start at say x = 2.5 and get closer to 2 by getting to x = 2.4 then to x = 2.3 then 2.2, 2.1, 2.01, 2.001, etc
We don't actually arrive at x = 2 itself. We simply move closer and closer.
Since we're on the positive or right hand side of 2, this means we go with the rule involving x > 2
Therefore f(x) = (x/2) + 1
Plug in x = 2 to find that...
f(x) = (x/2) + 1
f(2) = (2/2) + 1
f(2) = 2
This shows [tex]\lim_{x \to 2^{+}}f(x) = 2[/tex]
Then for the left hand limit [tex]\lim_{x \to 2^{-}}f(x)[/tex], we'll involve x < 2 and we go for the first piece. So,
f(x) = 3-x
f(2) = 3-2
f(2) = 1
Therefore, [tex]\lim_{x \to 2^{-}}f(x) = 1[/tex]
===============================================================
Part B
Because [tex]\lim_{x \to 2^{+}}f(x) \ne \lim_{x \to 2^{-}}f(x)[/tex] this means that the limit [tex]\lim_{x \to 2}f(x)[/tex] does not exist.
If you are a visual learner, check out the graph below of the piecewise function. Notice the gap or disconnect at x = 2. This can be thought of as two roads that are disconnected. There's no way for a car to go from one road to the other. Because of this disconnect, the limit doesn't exist at x = 2.
===============================================================
Part C
You'll follow the same type of steps shown in part A.
However, keep in mind that x = 4 is above x = 2, so we'll deal with x > 2 only.
So you'd only involve the second piece f(x) = (x/2) + 1
You should find that f(4) = 3, and that both left and right hand limits equal this value. The left and right hand limits approach the same y value. The limit does exist here. There are no gaps to worry about when x = 4.
===============================================================
Part D
As mentioned earlier, since [tex]\lim_{x \to 4^{+}}f(x) = \lim_{x \to 4^{-}}f(x) = 3[/tex], this means the limit [tex]\lim_{x \to 4}f(x)[/tex] does exist and it's equal to 3.
As x gets closer and closer to 4, the y values are approaching 3. This applies to both directions.
A recipe that makes 18 chocolate chip cookies calls for 2.5 cups of flour. How many cookies can you make if you have 3.75 cups of flour (and enough of the other ingredients)?
Answer:
27
Step-by-step explanation:
3.75/2.5x18=27
Determine the values of x and y.
Answer: x = 23, y = 40
Step-by-step explanation:
By the same-side interior angles theorem, y+30 and 110 are supplementary.
110 + y + 30 = 180 [supplementary angles add to 180 degrees]y + 140 = 180 [combine like terms]y = 40 [subtract 140 from both sides]We know that the 3x + 1 angle and y + 30 are also congruent, so:
3x + 1 = y + 30 [congruent angles have equal measure]3x + 1 = 40 + 30 [substitute y = 40]3x + 1 = 70 [combine like terms]3x = 69 [subtract 1 from both sides]x = 23 [divide both sides by 3]please help me. 50 pts
Which quantity is multiplied by pi () in the formula for the area of a circle?
A. d
OB. 2
O c. d
D. r
Option: B
The area of a circle is pi times the radius squared (A = π r²).
can you help me to solve this
Answer:
Is the question even complete ?
Step-by-step explanation:
thanks to you all for you help
Answer:yw
Step-by-step explanation:
Which of the numbers below are whole numbers?
A. 0
B. 0.388
C. 2454
D. 602.49
E. 996
F. 719557
Answer:
a whole number is a number with no decmils other than .0000 and is not a fraction where the top and bottom are equal
whole: a,c,e&f
not:b&d
pls someone help me asap :)
Answer:
right angle
acute
acute
obtuse
obtuse
Step-by-step explanation:
Since angle <ABC is a straight line, the angle is 180 degrees. This means all the angles in between should also add up to 180 degrees. Using this knowledge you can solve for the value of angle <FBE which is going to be equal to 180 - (40 + 25 + 50) = 65.
< DBF = <DBE + <EBF
< DBF = 25 + 65 = 90 (right angle)
<EBD = 25 (given) (acute)
<DBC = 50 (given) (acute)
<ABE = <ABF + <FBE
<ABE = 40 + 65
<ABE = 105 (obtuse)
<CBF = <CBD + <DBE + <EBF
<CBF = 50 + 25 + 65
<CBF = 140 (obtuse)
Comparing Fractions Choose the correct symbol to compare the fractions please see attached image
Answer:
>
Step-by-step explanation:
Given: [tex]\frac{1}{2} ? \frac{1}{3}[/tex]
Want: Which fraction is larger?
To identify the size of a fraction, converting it into a fraction is easier
[tex]\frac{1}{2}[/tex] = 0.5
[tex]\frac{1}{3}[/tex] = 0.33
where 0.5 is greater than 0.33
Choices:
< is less than symbol
> is greater than symbol
= is equal to
[tex]\frac{1}{2} > \frac{1}{3}[/tex]
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Visual Representation:
There are 5 white balls. 8 red balls, 7 yellow balls, and 4 green balls in a container. A ball is chosen randomly. Find the probability of the following events.
1.What is the probability of choosing
green?
Answers:________ work space:______
2. What is the probability of choosing
red?
Answers:________ work space:______
3. What is the probability of choosing
neither white nor green?
Answers:________ work space:_______
4. . What is the probability of choosing
other than yellow?
Answers:________ work space:_______
5. What is the probability of choosing
purple?
Answer:_________ work space:_______
Given :
White balls = 5 Red balls = 8 Yellow balls = 7Green balls = 4Answer 1 :-
We know that,
P (E) = No. of favourable outcomes / Total number of outcomes.>> Total no. of outcomes = 5 + 8 + 7 + 4
>> Total no. of outcomes = 24
As there are 4 green balls. Therefore,
P (E) = 4 / 24P (E) = 2 / 12 P (E) = 1 / 6Answer 2 :-
We know that,
P (E) = No. of favourable outcomes / Total number of outcomes.>> Total no. of outcomes = 5 + 8 + 7 + 4
>> Total no. of outcomes = 24
As there are 8 red balls. Therefore,
P (E) = 8 / 24 P (E) = 4 / 12 P (E) = 2 / 6 P (E) = 1 / 3Answer 3 :-
We know that,
P (E) = No. of favourable outcomes / Total number of outcomes.>> Total no. of outcomes = 5 + 8 + 7 + 4
>> Total no. of outcomes = 24
As there are 15 balls that are neither green nor white. (Red balls+ yellow balls)
P (E) = 15 / 24 P (E) = 5 / 8which law would you use to simplify the expression...
Answer:
Power of a quotient
What is the period of this graph?
Answer:
Look at the pic for answer.
Step-by-step explanation:
Solve the following word problem.
Money is invested at two rates of interest. One rate is 8 % and the other is 2%. If there is $1300 more invested at 8 % than at 2 %. find the amount invested at
each rate if the total annual interest received is $350. Let x = amount invested at 8% and y = amount invested at 2 %. Then the system that models the problem
[x = y + 1300
is
Solve the system by using the method of addition.
0.08x +0.02y = 350,
Answer:
at 8%: $3760at 2%: $2460Step-by-step explanation:
You are given a system of equations and asked to solve it by the method of addition. That method requires you add a multiple of one equation to the other so that one of the variables is eliminated. In some cases, this is easier if multiples of both equations are added together. The resulting single-variable equation is then solved in the usual way.
__
lookThe given system of equations is ...
x = y +13000.08x +0.02y = 350We notice the first equation has the variables on opposite sides of the equal sign, and both their coefficients are 1. The second equation has the variables on the same side of the equal sign, and their coefficients are 0.08 and 0.02.
planTo eliminate a variable by the "addition method," we need to have the variable on the same side of the equal sign with opposite coefficients. Or, we need to have the variable on opposite sides of the equal sign with the same coefficient.
Both of the x-variables are on the left side, so we need opposite coefficients. We can get that by multiplying the first equation by -0.08, or by multiplying the second equation by -12.5. We judge the first of these choices to be easier.
The y-variables are on opposite sides of the equal sign, so we need equal coefficients. We can get that by multiplying the first equation by 0.02, or the second equation by 50.
solutionWe choose to multiply the first equation by 0.02, so we can eliminate the y-variable. Here is the result of doing that, then adding the results
(0.02)(x) +(0.08x +0.02y) = (0.02)(y +1300) +(350)
0.10x +0.02y = 0.02y +376 . . . . . eliminate parentheses
0.10x = 376 . . . . . . . . . subtract 0.02y from both sides. y is eliminated
x = 3760 . . . . . . . . . divide by 0.10
y = x -1300 = 2460
__
The amount invested at 8% was $3760; the amount invested at 2% was $2460.
_____
Additional comment
We chose to eliminate y for a couple of reasons. x is the amount at the higher rate. We have found that solving for the higher-rate amount usually works best for preventing errors. The other reason is that multiplying by 0.02 results in smaller numbers, which we consider easier to deal with.
Had we multiplied by -0.08 to eliminate x, we would have ...
-0.08(x) +(0.08x +0.02y) = -0.08(y +1300) +(350)
0.02y = -0.08y +246
We judge -0.08(1300) +350 harder to calculate mentally, than 0.02(1300) +350.
0.10y = 246
y = 2460; x = 2460+1300 = 3760
HURRY Given f(x) = - 3/4x + 2, find ƒ(16). The solution is
Answer: Read attachment.
Step-by-step explanation: Attached is my work. Hope it helps!
If my answer was helpful, please mark as brainliest. Or not, it's fine.
Answer:
[tex]\fbox {f(16) = -10}[/tex]
Step-by-step explanation:
Given :
f(x) = -3/4x + 2
Substitute x = 16 :
f(16) = -3/4(16) + 2
f(16) = -12 + 2
f(16) = -10
An 8-pack of clay pots costs $15.76. What is the unit price?
At the city museum child admission is $6.10 and adult admission is $9.20. On Wednesday, 144 tickets were sold for a total sales of 1083.00. How many adult tickets were sold that day
Construct the truth table and determine the truth value of the following compound statement.
a)p⟾¬(p ʌ r)
b) (q ʌ r) ⟾(p ⇔ q)
See the attached truth tables.
• A ∧ B is true only when both A and B are true
• A ⇒ B is true only when both A and B are true, or A is false. This logically equivalent to ¬A ∨ B
• ¬A is true only when A is false
• A ⇔ B is true only when both A ⇒ B and B ⇒ A are true. Equivalently, (¬A ∨ B) ∧ (¬B ∨ A)
Help with this math problem
Answer:
The minimum cost of the X-ray machines is 12,197dollars.
Step-by-step explanation:
First, we check whether it’s a Quadratic Equation or not
The general form of the Quadratic equation [tex]f(x) =[/tex] [tex]ax^{2} + bx + c[/tex]
Let’s compare it with the given equation, we get
a = 1
b = -520
c = 79,79
Hence, it’s a quadratic equation.
Now, we will use the VERTEX FORMULA as we are asked to find the ‘minimum’ unit cost.
X = [tex]\frac{-b}\[2a[/tex] = [tex]\frac{-(-520)}\[2(1)[/tex] = [tex]260[/tex]
So , number of X-ray machines are = 260 (value of x)
To find the minimum unit cost, plug the value of x into the given equation, and we get
[tex]f(260) = (260)^{2} -520(260) + 79,797[/tex]
[tex]=12,197[/tex]
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Which of the function correctly expresses the exponential model f(x)=6(14)^x with base of e
The exponential equation with a base of e is:
[tex]f(x) = 6*e^{2.639*x}[/tex]
How to change the base?
We start with:
[tex]f(x) = 6*(14)^x[/tex]
We want to rewrite this to:
[tex]f(x) = 6*(e^n)^x[/tex]
So we only need to find the value of n such that:
[tex]e^n = 14[/tex]
If we apply the natural logarithm to both sides:
[tex]ln(e^n) = ln(14)\\n = ln(14) = 2.639[/tex]
Then the exponential equation with base of e is:
[tex]f(x) = 6*e^{2.639*x}[/tex]
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the equation of the line that goes through (3, 0) and (6, 2) in slope-intercept form???
the slope intercept form of the given points is y = 2/3 (x-3).
What is Straight Line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined on both sides of a point. A straight line does not have any curve in it.
Here, given passing points
(3, 0) and (6, 2)
We know that,
(y - y₁) = (y₂-y₁)/(x₂-x₁) (x - x₁)
(y - 0) = (2-0)/(6-3) (x-3)
y = 2/3 (x-3)
Thus, the slope intercept form of the given points is y = 2/3 (x-3).
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Determine the number of crawlers and rovers to make,that will maximize the company profit in a given week
Answer:
jjjijijijiiijijijijijijij no pliss inglés. ;D.
The points (-15, r) and (-3, 16) lie on a line with slope 5/4. Find the missing coordinate r.
Answer:
r = 1
Step-by-step explanation:
we know that :
[tex]Slope=\frac{y_{B}-y_{A}}{x_{B}-x_A}[/tex]
Then
[tex]\frac{5}{4} =\frac{16-r}{-3-(-15)}[/tex]
Then
[tex]\frac{5}{4} =\frac{16-r}{12}[/tex]
Then
5×12 = 4×(16-r)
Then
60 = 64 - 4r
Then
4r = 64 - 60
Then
4r = 4
Then
r = 1
A teacher asked her students how many pets they own. Here
are the results:
0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 8
On a piece of paper, draw a dot plot to represent the data.
Then determine which answer choice matches the dot plot
you drew.
Step-by-step explanation:
the answer is (c)
because 0 is 3 in number,
1 is 4 in number,
2 is 3in number
3 is 2 in number,
4 is 2 in number,
no 5,6,7
8 is 1 in number
and no 9
The dot plot ( C )is solved and each dot represents one student's response
What is a dot plot?A dot plot, also known as a dot chart or dot graph, is a type of data visualization that displays the frequency of values in a dataset. It is a simple graphing technique that uses dots to represent data points on a horizontal or vertical axis.
Each data point in the dataset is represented by a dot placed above the corresponding value on the axis. If there are multiple data points with the same value, the dots are stacked vertically above that value. The resulting plot shows the distribution of data points along the axis, with the height of the stack of dots representing the frequency of each value.
Given data ,
Let the data of the number of pets owned by student be represented as A
Now , the value of A = { 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 8 }
The frequency of 0 = 3
The frequency of 1 = 4
The frequency of 2 = 3
The frequency of 3 = 2
The frequency of 4 = 2
The frequency of 8 = 1
In this dot plot, each dot represents one student's response. The number on the left indicates how many pets the students reported owning, and the dots are arranged vertically above that number.
For example, three students reported owning 2 pets, so there are three dots arranged above the number 2. This type of plot is useful for displaying the frequency of different values in a dataset.
Hence , the dot plot is solved
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If $4500 is invested at 10% annual interest, which is compounded continuously, what is the account balance after 3 years, assuming no additional deposits or withdrawals are made?
Answer:
$6074.36
Step-by-step explanation:
The formula for continuous compounding is
F = Pe^(rt)
F = $4500 × e^(0.1 × 3)
F = $6074.36
Answer: $6074.36
Which one is it I need to finish this page fast
Answer:
E; 10% off %20 sweater with $6 shipping
Step-by-step explanation:
Similar to what I said last time,
this time is with percentages,
How to calculate percent off?
Divide the number by 100 (move the decimal place two places to the left).
Multiply this new number by the percentage you want to take off.
Subtract the number from step 2 from the original number. This is your percent off number.
________________________________________________________
A. 35% off a $35 sweater with 4 dollar shipping is basically
0.35 x 35 = 12.25 and 35-12.25 = $22.75 + the $4 shipping fee (if no tax)
which the total would be $26.75
B. 20% off $35 is
0.2x35=7 and 35-7 = 28 so your total is $28
C. 30% off $30 with $6 for shipping is
0.3x30=9 and 30-9 is $21 plus the shipping fee
$27
D. $20 sweater with $5 shipping is $25 no discount involved :D
E. 10% off %20 sweater with $6 shipping is
0.1x20 is 2 which 20 - 2 = 18 and plus shipping fee 18+6 is $24
________________________________________________________
Hope this helped again.