Use the functions f(x)=2x and g(x)= x^2+1 to find the value of each expression.
7. f(3)+g(4) 8. g(3)+f(4)
Answers
Answer:
First, you learned (back in grammar school) that you can add, subtract, multiply, and divide numbers. Then you learned that you can add, subtract, multiply, and divide polynomials. Now you will learn that you can also add, subtract, multiply, and divide functions. Performing these operations on functions is no more complicated than the notation itself. For instance, when they give you the formulas for two functions and tell you to find the sum, all they're telling you to do is add the two formulas. There's nothing more to this topic than that, other than perhaps some simplification of the expressions involved.
Step-by-step explanation:
To find the answers, all I have to do is apply the operations (plus, minus, times, and divide) that they tell me to, in the order that they tell me to.
(f + g)(x) = f (x) + g(x)
= [3x + 2] + [4 – 5x]
= 3x + 2 + 4 – 5x
= 3x – 5x + 2 + 4
= –2x + 6
(f – g)(x) = f (x) – g(x)
= [3x + 2] – [4 – 5x]
= 3x + 2 – 4 + 5x
= 3x + 5x + 2 – 4
= 8x – 2
(f × g)(x) = [f (x)][g(x)]
= (3x + 2)(4 – 5x)
= 12x + 8 – 15x2 – 10x
= –15x2 + 2x + 8
\left(\small{\dfrac{f}{g}}\right)(x) = \small{\dfrac{f(x)}{g(x)}}(
g
f
)(x)=
g(x)
f(x)
= \small{\dfrac{3x+2}{4-5x}}=
4−5x
3x+2
My answer is the neat listing of each of my results, clearly labelled as to which is which.
( f + g ) (x) = –2x + 6
( f – g ) (x) = 8x – 2
( f × g ) (x) = –15x2 + 2x + 8
\mathbf{\color{purple}{ \left(\small{\dfrac{\mathit{f}}{\mathit{g}}}\right)(\mathit{x}) = \small{\dfrac{3\mathit{x} + 2}{4 - 5\mathit{x}}} }}(
g
f
)(x)=
4−5x
3x+2
Related Questions
does the number 15/3 belong to the set of natural/counting numbers?
Answers
What is 4 less than three sevenths of y
Answers
Answer:
[tex]\frac{3}{7}y - 4[/tex]
Step-by-step explanation:
Let's start with the part "three sevenths of y". In this statement, "of" means multiply or times. So, let's apply that. It would now be three sevenths times y. Three sevenths times y looks like this: 3/7y"4 less than" means subtraction because less than means subtractions. So our first part is 3/7y. Now let's add less 4 less than: 3/7y - 4.I hope this helps!
WORTH 85 POINTS!!
explain in FULL sentences!!!
A student conducted an experiment to test whether talking to plants would help them to grow faster. He set up the following two groups: Group 1: spoken to and hand watered Group 2: not spoken to and hand watered After three weeks, the plants in Group 1 showed much more growth than those in Group 2.
Name the independent and dependent variable.
Answers
Answer: Group 1 is the dependent variable, and group 2 is the independent
Step-by-step explanation: The dependent variable is the variable that is being measured or tested in an experiment. So, Group 1 would be the dependent variable, because as it says the the group 1 plants were spoken to and hand watered as in they changed the outcome of the experiment.
The independent variable is the variable the experimenter changes or controls. So, the independent variable would be group 2 because the group 2 plants outcome was not determines anything but it's self.
a saline solution has a concentration ratio of 2.5mg of salt in 100ml of solution. How many mg of salt will be needed to produce 500ml of a saline solution having the same concentration?
Answers
Answer:
12.5mg
Step-by-step explanation:
500ml÷100ml= 5
2.5mg×5= 12.5mg
I NEED HELP ASAP
Evaluate the expression for r = –3.
15 + 6r =
Answers
Answer: -3
Step-by-step explanation:
Since we are given the value of r, we can plug that value into the expression and solve.
15+6(-3) [multiply]
15-18 [subtract]
-3
Now, we know that the expresison is equal to -3.
Nina’s total trip to and from work is 14 miles. If she works 243 days this year, how many miles will she drive to and from work?
Answers
Answer:
3,402
Step-by-step explanation:
Step 1:
243 × 14
Answer:
3,402
Hope This Helps :)
Answer:
3402
Step-by-step explanation:
ANSWER ASAP FOR QUIZ
Answers
Peter purchases a baseball card for $150 as an investment. His research tells him that the value of
the card should double every 3 years. When will the card reach a value of $ 4000?
Answers
Answer:
6 years
Step-by-step explanation:
Given
[tex]Initial\ Investment = 150[/tex]
[tex]Ratio = double[/tex]
Required
When will it get to 4000
This question illustrates a geometric progression and will be solved using:
[tex]T_n = ar^{n-1}[/tex]
In this case;
[tex]T_n = 4000[/tex]
[tex]r = double = 2[/tex]
[tex]a = 150[/tex]
So, we're to solve for n
[tex]4000 = 150 * 2^{n - 1}[/tex]
Divide through by 150
[tex]\frac{4000}{150} = 2^{n-1}[/tex]
[tex]26.67= 2^{n-1}[/tex]
Take Log of both sides
[tex]Log26.67= Log2^{n-1}[/tex]
Apply law of logarithm
[tex]Log26.67= ({n-1})Log2[/tex]
Take Log values
[tex]1.42602301569 = (n - 1) * 0.30102999566[/tex]
Make n - 1 the subject
[tex]n - 1 = \frac{1.42602301569}{0.30102999566}[/tex]
[tex]n - 1 = 4.73714591984[/tex]
Add 2 to both sides
[tex]n = 1 + 4.73714591984[/tex]
[tex]n = 5.73714591984[/tex]
[tex]n = 6[/tex] (Approximated)
Hence, it'll take 6 years
#3 - Simplify the expression. Type your answer with all lowercase letters and no spaces. Type your p variable first and g variable second in your answer. * 2(5p+2g)+5g
Answers
Answer: 10p+9g
Step-by-step explanation:
2(5p+2g)+5g
10p+4g+5g
10p+9g
Please hurry! :) Its a get more math question.
Answers
The sales price is 44. 37 dollars.
Answer: $44.37
Step-by-step explanation:
63.38 x 30/100 (or x 0.3)
You save: $19.01
$63.38 - $19.01 = Final price of $44.37
Kendra earns $11.60 per hour working at the movie theater. Each week, she donates of
10
her earnings to Best Friends Animal Society, her favorite charity. If Kendra worked 8 hours
2
last week, how much money did she donate to the charity?
Answers
Answer:
$9.86
Step-by-step explanation:
First, write both numbers in the same form. Convert 8
1
2
to a decimal.
8
1
2
= 8+
1
2
= 8+
1×5
2×5
= 8+
5
10
= 8+0.5
= 8.5
Multiply.
11.6
× 8.5
580
+ 9280
98.60
Kendra earned $98.60 last week.
Now multiply to find how much money Kendra donated to the charity last week. She earned $98.60, and she donates
1
10
of her earnings each week.
First, write both numbers in the same form. Convert
1
10
to a decimal.
1
10
=0.1
Multiply.
98.6
× 0.1
9.86
Kendra donated $9.86 to the charity last week.
Perform matrix subtraction to find the values of w,
x, y, and z.
Answers
Answer:
w = ⇒ 21
x = ⇒ 13
y = ⇒ -11
z = ⇒ -16
Step-by-step explanation:
The value of the matrix will be [tex]\left[\begin{array}{ccc}w &x&\\y&z\end{array}\right] = \left[\begin{array}{ccc}21&13&\\5&-16\end{array}\right][/tex]
What is the matrix?A matrix is a rectangular array of numbers that are arranged in rows and columns. The numbers are referred to as the matrix's elements or entries. Engineering, physics, economics, and statistics, as well as various disciplines of mathematics, all use matrices.
[tex]=\left[\begin{array}{ccc}17&12&\\-3&-2\end{array}\right] - \left[\begin{array}{ccc}-4&-1&\\8&14\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}w &x&\\y&z\end{array}\right] = \left[\begin{array}{ccc}21&13&\\5&-16\end{array}\right][/tex]
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Jordan will hike a 10 mile trail at a rate of 2 mi/h. Write a linear equation to represent the distance of the trail that Jordan still has to hike after x hours. What does the y-intercept of the equation represent?
Answers
Answer:
y = 10 -2x; 10 is the length of the trail
Step-by-step explanation:
Jordan's remaining distance starts at 10 miles, and decreases 2 miles each hour:
y = -2x +10
The y-intercept is the length of the trail.
5^7/5^5 hurrrrrrrrryyyyyyyyyyyyy
Answers
Answer:
25
Step-by-step explanation:
Reduce each fraction below 6/6= 10/2= 2/6=
Answers
Answer:
6/6 = to 1
10/2=to 5
2/6= to 1/3 or 0.3333333333
Step-by-step explanation:
6/6 divide by 1
10/2 10 divide by 2
2/6 reduce to 1/3 or o.3333333333
work out 6d + 8 = 14 + 3d
Answers
In 6d + 8 = 14 + 3d , D=2
Isolate the variable by dividing each side by factors that don't contain the variable.
what is another way to represent this solution set?
Answers
Answer:
What solution set? I think you forgot to add a picture..
What solution do you need help with? :)
A map scale shows that 3 km = 2 cm. How many cm would represent 15 km on the map?
cm
Answers
Answer:
3 = 2
15 = 10
10 cm
Step-by-step explanation:
Is the sum of √16 and 1.5 rational or irrational?" Justify and explain your answer.
Answers
Answer:
Rational
Step-by-step explanation:
The square root of 16 is 4, and 4 + 1.5 is = to 5.5. An irrational number is defined as infinite and never-ending. Since 5.5 is not infinite, we can conclude that it isn't irrational.
the mean number of goals scored is 2.5 the mean number of away goals scored is 1.8 how many home and away games have been played in total
Answers
Question 4 -
Next >
What is the mode given the data set: 97, 82, 87, 97, 100, 75, 81?
A
81
B.
82
C.
97
D.
100
what’s the mode
Answers
On his first day of school, Kareem found the high temperature in degrees Fahrenheit to be 76.1°. He plans to use the function C of F = five-ninths (F minus 32) to convert this temperature from degrees Fahrenheit to degrees Celsius. What does C(76.1) represent?
Answers
Answer: the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius
Step-by-step explanation:
Answer:Aka) A
Step-by-step explanation:
PLZ HELLLLLLPPPPPPPP!
WILL MARK BRAINLIEST!!!!!
Answers
Answer:
more than one than its a and b but only one than its a
find the length of the missing side
a) 17 cm
b) 22 cm
c ) 15 cm
d) 13 cm
Answers
5^2 + 12^2= c^2
25 + 144= 169
/169= 13
The answer is D
The missing side of the triangle is measure 13 cm.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
We have to given that;
Two sides of right triangle are,
⇒ 5 cm, 12 cm
Since, The triangle is a right triangle.
So, We can apply the Pythagoras theorem as;
Let the measure of missing side = x
⇒ x² = 5² + 12²
⇒ x² = 25 + 144
⇒ x² = 169
⇒ x = √169
⇒ x = 13 cm
Learn more about the triangle visit:
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find the value of x if h is the midpoint of gj, gj equals 4x-6, and gh=27 - huryyyyyyy please.
Answers
Answer: X=15
Step-by-step explanation:
GH+HJ= GJ
27+27=4x-6
54=4x-6
60=4x
15=x
HELP ME PLS
A media research survey showed that one evening, 2/3 of all U.S. households had their televisions on, and 3/8 of them were watching a World Series baseball game. What fraction of the U.S. households was watching the game?
Answers
Answer:
sfhjty
Step-by-step explanation:
Solving equations to find angle measure
Show work please
Answers
Step-by-step explanation:
2x + 1 + x - 13 = 180° because these angles are supplementary
3x - 12 = 180°
3x = 180 + 12
3x = 192 divide both sides by 3
x = 64
2x + 1 ➡ 2 × 64 + 1 = 129°
x - 13 ➡ 64 - 13 = 51°
PLEASE HELP! An angle's measure is equal to 24 less than its complement. Find the measure of the angle.
Answers
The Larger complement angle is 57 degrees and Small angle is 33 degrees.
Given about the complement angles.
Complement angles means, the two angles will add up to 90 degrees.
Then angles is x+(x-24)=90
⇒2x=90+24
⇒2x=114
⇒x=57
So, the larger angle is 57 degrees.
small angle is 90-57=33 degrees.
Learn more about complementary angles in https://brainly.ph/question/3668.
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write a word phrase for
[tex] - 5 - 4n[/tex]
Answers
-5: negative five
-: minus
4n: a number times four
Put everything together.
Negative give minus a number times four.
Best of Luck!
If r=8 units and h=11 units, what is the volume of the cylinder shown above? Use 3.14 for pi. HELP ME
Answers
Answer:
The answer is
2210.56 units³Step-by-step explanation:
Volume of a cylinder is given by
V = πr²hwhere
r is the radius of the cylinder
h is the height
From the question
r = 8 units
h = 11 units
Substitute the values into the above formula and solve
V = 3.14(8)²(11)
= 3.14(64)(11)
= 3.14 × 704
We have the final answer as
V = 2210.56 units³
Hope this helps you