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
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Step-by-step explanation:
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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
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Step-by-step explanation:
2x + 1 + x - 13 = 180° because these angles are supplementary
3x - 12 = 180°
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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!
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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.
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Answer:
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Step-by-step explanation:
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Answers
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Evaluate the expression for r = –3.
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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.
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find the length of the missing side
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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.
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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;
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⇒ x² = 25 + 144
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What is the mode given the data set: 97, 82, 87, 97, 100, 75, 81?
A
81
B.
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C.
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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
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r = 8 units
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Answers
Answer:
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Step-by-step explanation:
Step 1:
243 × 14
Answer:
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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
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write a word phrase for
[tex] - 5 - 4n[/tex]
Answers
-5: negative five
-: minus
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Negative give minus a number times four.
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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:
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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]
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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.
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Step-by-step explanation:
GH+HJ= GJ
27+27=4x-6
54=4x-6
60=4x
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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.
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
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.
#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
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.
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
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? :)