Answer:
Purplemath
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.
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Given f (x) = 3x + 2 and g(x) = 4 – 5x, find (f + g)(x), (f – g)(x), (f × g)(x), and (f / g)(x).
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
Step-by-step explanation:
Purplemath
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.
MathHelp.com
Need a personal math teacher?
Given f (x) = 3x + 2 and g(x) = 4 – 5x, find (f + g)(x), (f – g)(x), (f × g)(x), and (f / g)(x).
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
12. Sydney Star bought a new sweatshirt for $42.00. Sales tax was 8%.
After tax, what was the total cost she paid for the sweatshirt? *
$8.00
$38.64
$3.36
$45.36
Answer:
$45.36
Step-by-step explanation:
100 + 8 = 108
42/100 X 108 = 45.36
100 + 8 = 108
42/100 X 108 = 45.36A tree grows three feet per year. What happens to the growth of the tree when the number of years changes?
O When the number of years increases, the number of feet decreases.
O When the number of years decreases, the number of feet stays the same.
O When the number of years increases, the number of feet increases.
O When the number of years decreases, the number of feet increases.
Answer:
The tree will keep growing each year 3 feet.
Answer:
Your Answer is When the number of years increases, the number of feet increases
What is the equation of the line that passes through the point (-8,-6) and
has a slope of 1/4
Answer:
y = 1/4x -4
Step-by-step explanation:
Since you know that that slope int. equation is y = mx+b, and the m is the slope just plug in the slope in the equation. So it will be y = 1/4x + b.
Then what you will do is solve for b in the equation. So what you do is plug in the x and y value from the coordinate given in the equation, so it will be like this: -6 = 1/4(-8) +b
-6 = -2 +b
-4 = b
b = -4
So then you plug back the b value into the equation with slope to wtite the equation. So it would be, y = 1/4x -4
Answer the following.
(a) A certain solution has a hydrogen ion concentration of 0.0000448 moles per liter. Write this number in scientific notation.
Answer:
35554555
Step-by-step explanation:
HURRYYYYY
What does "Slope-Intercept Form" look
like?
Xb+c=y
y = mx + b
y2 - 71
X2 - X1
AX + By = 2
Answer:
y=mx+b
Step-by-step explanation:
the second answer
This is my last 8th grade problem, again if you know the answer please interact :)
Answer:
same slope
parallel lines
Step-by-step explanation:
Convert: 16 c =________gal
Answer:
16 cups is 1 gallon
Step-by-step explanation:
because there are 16 cups in a gallon
help please, i don’t get this question .
The net of a triangular prism is show below.Find the rotal surface area of the triangular prism 4.6,4,5,15
Answer:
228.4cm²
Step-by-step explanation:
Find the diagram attached
Total surface area of the prism = Ph + 2B
P is the perimeter of the base (triangle)
h is the height of the prism
B is Base area
P = 5cm + 5cm + 4cm
P = 14cm
h = 15cm
B = 1/2 * base * height
B = 1/2 * 4.6 * 4
B = 4.6 * 2
B = 9.2cm²
Substitute the values into the formula;
Total surface area of the prism = Ph + 2B
Total surface area of the prism = 14(15)+2(9.2)
Total surface area of the prism = 210 + 18.4
Total surface area of the prism = 228.4cm²
Hence the total surface area of the triangular prism is 228.4cm²
Somone pls help if your good at math I’ll mark brainliest
Answer:
x=5
Step-by-step explanation:
(x--3)²+(4--2)²=10²
(x+3)²+36=100
(x+3)²=64
(x+3)²=8²
x=5
helppp asap pleaseeeeee
The number of seeds found in a sample of 7 different oranges were: 3, 3, 4, 5, 7, 8, and 12. What is the range of the number of seeds in the sample of oranges?
A:5
B:6
C:7
D:9
PLz help me i need this answer
Answer:
9
Step-by-step explanation:
Range is Biggest Number - Smallest Number.
12 is the biggest number and 3 is the smallest number.
So, 12 - 3 = 9
Answer:
9
Step-by-step explanation:
becauses 12-3=9
hope it helps
i need help like really bad
Answer:
A
Step-by-step explanation:
14/15 is less than 7/5
Answer:
dang me too I'm like almost failing
Tori has already jarred 1 liter of jam and will jar an additional 1 liter of jam every day. How
many days does Torì need to spend making jam if she wants to jar 10 liters of jam in all?
Answer:
9 days.
Step-by-step explanation:
We first subtract the amount already done from the total needed.
10 - 1 = 9.
Next, we take the remainder and divide it by the amount being made per day to get our final answer.
9 / 1 = 9.
The answer is 9 days.
pls help ;/ not hard btw
Simplify the following and write with positive exponents:
5z-5(3z)-2
Answer:
[tex] - 10z - 2[/tex]
Step-by-step explanation:
this is simplify
Need Help 20 points plz.
9514 1404 393
Answer:
the correct choices are shown
Step-by-step explanation:
Statement . . . . . Reason
1. c ║ d; ∠4 = ∠5 . . . . . Given
2. ∠4 = ∠7 . . . . . Alternate interior angles are equal
3. ∠5 = ∠8 . . . . . Vertical angles are equal
4. ∠7 = ∠8 . . . . . Substitution
Find the value of x in the equation 2(x +1)=14
Answer:
the x=6
Step-by-step explanation:
2(6+1)=14
2(7)=14
14=14
The midpoint of \overline{\text{AB}} AB is M(5, 1)M(5,1). If the coordinates of AA are (3, 6)(3,6), what are the coordinates of BB?
Answer:
(7, -4)
Step-by-step explanation:
The formula for calculating midpoint is expressed as;
M(X, Y) = (x2+x1)/2, (y1+y2)/2
X = x1+x2/2
Y = y1+y2/2
Given
X = 5, Y = 1, x1 = 3, y1 = 6
Get x2
X = x1+x2/2
5 = 3+x2/2
10 = 3+x2
x2 = 10-3
x2 = 7
Get y2;
Y = y1+y2/2
1 = 6+y2/2
2 = 6+y2
y2 = 2-6
y2 = -4
Hence the coordinate of B is at (7, -4)
Divide. Enter the quotient in simplest form.
9/10 divided by 3/8
Need help on this please help
Answer:
280m³
i hope this is help for you
Help me I need the answer ASAP I’ll give brainliest
Answer:
number 2
Step-by-step explanation:
4/10 and 10/25 are equal : proportionate
please help
it due in a lil bit
Kristin bought a snowboard for $60. The sales tax rate for the snowboard is $0.04 for every dollar spent. How much did Kristin pay in all for the snowboard?
The distance from your home to the school is 4 9/10 miles. From your house to the pool is 3 1/2 miles. How much farther are you from the school than from the pool?
if 3x =9 what is x ?
Answer:
3
Step-by-step explanation:
All you have to do is divide 9 by 3 and you get 3!
I hope this helps, and have a great day! :)
the answer is 3 hope this helped
If the mLD = 3x - 8 and mZL = 2x + 17, find the
value of x that would make ZDE ZL.
Answer:
x = 25
Step-by-step explanation:
For ∠ D and ∠ L to be congruent, then
3x - 8 = 2x + 17 ( subtract 2x from both sides )
x - 8 = 17 ( add 8 to both sides )
x = 25
Which one is longer?
Aslinky that is 26 inches long
Bslinky that is 2 feet long
C they are equal
Answer: A.
Step-by-step explanation:
Slinky A is 26 inches there are 24 inches in two feet so slinky B isn’t longer. Then they are obviously not equal because we figured out they have different lengths
cuál es el resultado de 1/3 + 5/6?
Answer:
it will be 1 1/6 or 7/6
Step-by-step explanation:
Hope this helped
Evaluate the following expression: 8x - 6 - 7y + 3 use x=3 and y=6
Answer:
-27
Step-by-step explanation:
8x - 6 - 7y + 3
X = 3 Y = 6
8(3) - 6 - 7(6) + 3
8 x 3 = 24
7 x 6 = 42
24 - 6 - (42 + 3)
(24 - 6) - 45
18 - 45 = -27
what is the equation of the following? Someone could help me to understand this? thank you
Answer:
y=(1/5)x
Step-by-step explanation:
First, we must find the slope of the line.
The slope of a line can be found using the formula: (y2-y1)/(x2-x1)
(3-0)/(15-0)
(3)/(15)
1/5
The slope is 1/5.
Next we find the y-intercept, or where the line crosses the y-axis. In this case, the y-intercept is 0.
This gives us the equation: y=(1/5)x
Let me know if this helps!
