Answer:
(fg)(x) = x^3-4x^2-16x+64, D: All Real Numbers
Step-by-step explanation:
(fg)(x) = f(x) x g(x)
= 16-x^2(4-x)
=64-16x-4x+x^3
(fg)(x) = x^3-4x^2-16x+64
Domain is all real numbers because you can substitute any real number for x and the function would still work.
Thus the value of [tex](fg)(x) = x^3 -4x^2 -16x -64[/tex] , and the domain is a set of real numbers.
The domain is a set of all real numbers because by substituting any value in the equation we only get real numbers.
The function is defined as a relationship between two variables a dependent and an independent variable. A function consists of a domain and a co-domain. The set of codomains is called a range.
Example : [tex]f(x) = 4x+ 3[/tex]
All those values of a set for which a function is defined are called a domain.
According to the question :
[tex]f(x) = 16 - x^2\\ g(x) = 4 - x.[/tex]
[tex](fg)(x) = (16- x^2) (4-x)\\(fg)(x) = [16(4-x) -x^2(4- x)]\\\(fg)(x) = [64- 16x -4x^2+x^3]\\(fg)(x) = x^3 -4x^2 -16 x -64[/tex]
Thus the value of [tex](fg)(x) = x^3 -4x^2-16x-64.[/tex]
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who can solve these!!!
Answer:
1. 5 months2. 147 pagesStep-by-step explanation:
1....................................
Company A
75 + 20xCompany B
35xTime required:
75 + 20x = 35x15x = 75x = 5 months2....................................
Set up fee = $15
Additional fee= $0.17 per page
Max amount= $40
0.17x + 15 < 400.17x < 25x < 25/0.17x < 147Max number of pages is 147
Step-by-step explanation:
the solution is attached
have a good day
Use the Distributive Property to simplify. s 5 a solution to 2t - 1 = 11?
Answer:
5 is NOT a solution to the equation.
t = 6
Step-by-step explanation:
Step 1: Write out equation
2t - 1 = 11
Step 2: Add 1 to both sides
2t = 12
Step 3: Divide both sides by 2
t = 6
Euclid relied on five basic axioms to build the propositions in his book Elements. The first axiom states, “Things that are equal to the same thing are also equal to one another.” Which modern mathematical statement is equivalent to this axiom? Will give brainiest Asap If a = b, then b = a. If a = b and b = c, then a = c. If a ≠ b, then b ≠ a. If a = b, then a + c = b + c.
Answer: B
Step-by-step explanation:
Answer:
B. If a = b and b = c, then a = c.
Step-by-step explanation:
I just did it.
The slope of the line represented by the equation 2(x - 3) - 6y = 10 is
equal to what?
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
The equation of the line is;
2(x - 3) - 6y = 10
Placing the line in slope intercept form we get;
6y = 2x - 6 - 10
6y = 2x - 16
Dividing throughout by 6 we get;
y = [tex]\frac{2}{6}[/tex]x - [tex]\frac{16}{6}[/tex]
Simplifying gives;
y = [tex]\frac{1}{3} x +2 \frac{2}{3}[/tex]
So the slope of this line = [tex]\frac{1}{3}[/tex]
ASAP!!!!! A square pyramid and its net are shown below. What is the surface area of the pyramid?
Answer:
800
Step-by-step explanation:
16x16=256
17x16=272
272/2=136
136x4=544
544+256=800
Are the equations – 2x = 10 and -5x = 25 equivalent?
Answer: [tex]Yes[/tex]
Q: How are they the same answer?
A: You divide both of them by the number with x.
Divide both sides by -2
[tex]-2x/-2=10/-2\\x=-5[/tex]
Divide both sides by -5
[tex]-5x/-5=25/-5\\x=-5[/tex]
That's how both of them are equivalent to each other.
[tex]\text{Hey there!}[/tex]
[tex]\text{Are the equations -2x = 10 \& -5x = 25 equivalent?}[/tex]
[tex]\text{-2x = 10}[/tex]
[tex]\text{DIVIDE both sides by -2}[/tex]
[tex]\bf{\dfrac{-2x}{-2} = \dfrac{10}{-2}}[/tex]
[tex]\text{Cancel out \dfrac[-2x}{-2} because it gives 1}[/tex][tex]\text{Cancel out:}\ \bf\dfrac{-2x}{-2} \text{ because it gives you 1}[/tex]
[tex]\text{Keep:} \bf{\dfrac{10}{-2}}\text{ because it gives you the result of x}[/tex]
[tex]\bf{\dfrac{10}{-2} = -10\div2 \rightarrow -5}[/tex]
[tex]\boxed{\underline{\text{\bf{x = -5}}}}\checkmark[/tex]
[tex]\text{-5x = 25}[/tex]
[tex]\text{DIVIDE both sides by -5}[/tex]
[tex]\bf{\dfrac{-5x}{-5}= \dfrac{25}{-5}}[/tex]
[tex]\text{Cancel out:}\ \bf{\dfrac{-5x}{-5}}\text{ because it gives you 1}[/tex]
[tex]\text{Keep:}\ \bf{\dfrac{25}{-5}}\ \text{ because it gives you the result of x }[/tex]
[tex]\bf{\dfrac{-25}{5} = -25 \div 5 \rightarrow -5 }[/tex]
[tex]\boxed{\underline{\bf{x = -5}}}\checkmark[/tex]
[tex]\boxed{\text{To answer your question: \boxed{\bf{YES}} because both x's equal to -5}}[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Find a rational number and an irrational number that are between 9.5 and 9.7. Include the decimal approximation of the irrational number to the nearest hundredth. plz help
Answer:
9.6 - rational√91, √92 or √93 - irrationalStep-by-step explanation:
Rational number between 9.5 and 9.7:
An easy one is 9.6Irrational number between 9.5 and 9.7
Let's find 9.5^2, 9.6^2 and 9.7^2:
9.5^2 = 90.259.6^2= 92.169.7^2= 94.09One of the numbers could be √91, it is not a perfect square.
Approximate value:
√91 = 9.54A rectangular prisms base has an area of 40cm2.the prisms height is 5cm .what is the volume of the prism?
Answer:
5
Step-by-step explanation:
5679
4a−2(3a+8)=6 what is the answer
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{a = - 11}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{4a - 2(3a + 8) = 6}[/tex]
Distribute 2 through the parentheses
[tex] \longrightarrow{ \sf{4a - 6a - 16 = 6}}[/tex]
Collect like terms
[tex] \longrightarrow{ \sf{ - 2a - 16 = 6}}[/tex]
Move 16 to right hand side and change it's sign
[tex] \longrightarrow{ \sf{ - 2a = 6 + 16}}[/tex]
Add the numbers: 6 and 16
[tex] \longrightarrow{ \sf{ - 2a = 22}}[/tex]
Divide both sides by 2
[tex] \longrightarrow{ \sf{ \frac{ - 2a}{ - 2} = \frac{22}{ - 2}}} [/tex]
Calculate
[tex] \longrightarrow{ \sf{a = - 11}}[/tex]
Hope I helped !
Best regards! :D
Parallel lines s and t are cut by a tranversal r. Which angles are alternate interior angles? <3 and <5 <1 and <7 <3 and <7 <4 and <5
Answer:
it Would be easier to answer with a picture but since these Question are normaly the same picture but it is Angle 3 and 7
Step-by-step explanation:
#NO ADDS
What does constant growth and double mean
What is -8-__=-5
And how do i do it step by step?
Answer:
-3
Step-by-step explanation:
-5 is greater than -8, so in order for a subtraction problem to give a higher number is if it is negative, because a negative negative is a positive.
-8--3=-5
This is another way of saying
-8+3=-5
HELP ME PLEASE WILL OD ANYTHUNIGN
Answer:
5.4ft²
Step-by-step explanation:
Area of yellow region
= area of square - area of circle
Area of square= side ×side
Area of circle= πr²
5ft is the length of a side of the square, as well as the diameter of the circle.
Diameter= 2 ×radius
Radius or circle, r
= 5 ÷2
= 2.5 ft
Area of yellow region
= (5 ×5) - π(2.5²)
= 25 -6.25π
= 5.4 ft² (to nearest tenth)
Find the value of the expression -1/3-(-5/12).
Answer:
1/12
Step-by-step explanation:
A text font fits 12 characters per inch. Using the same font, how many characters can be expected per yard of text? There are 12 inches in a foot, and 3 feet in a yard. 36 characters 144 characters 360 characters 432 characters
432 characters can be expected to fit per yard of text. Therefore, option D is the correct answer.
Given that, a text font fits 12 characters per inch.
We need to find how many characters can be expected per yard of text.
How to convert yards to inches?To convert a yard measurement to an inch measurement, multiply the length by the conversion ratio. The length in inches is equal to the yards multiplied by 36.
Let x be the number of characters to be used in a yard.
12 characters / in = x/ 36 in
(12 characters * 36 in) / in = x
x = 432 characters
Therefore, option D is the correct answer.
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the answer is 432 characters
How do i find the vertex of the equation y=(x+5)(x+4)?
Answer:
Step-by-step explanation:
y=(x+5)(x+4)=x²+5x+4x+20=x²+9x+20=x²+9x+(9/2)²-(9/2)²+20
[tex]y=(x+\frac{9}{2} )^2-\frac{81}{4} +20\\y=(x+\frac{9}{2})^2-\frac{81}{4}+\frac{80}{4}\\y=(x+\frac{9}{2})^2-\frac{1}{4}[/tex]
vertex is (9/2,-1/4) or(4.5,-0.25)
HELPP!!! Which of the following is a negative externality of a parent taking afternoon and
evening classes at a local college?
A potential career change and income decrease
A tighter schedule limiting time with children
The list of assignments due for each semester
The number of future job postings
can someone help me with this geometry question?
Answer:
(-1,4.5)
Step-by-step explanation:
You would have to use the formula for midpoint. 5+-3/2= -1
3+6/2= 4.5 which would be -1 for x and 4.5 for y.
If y is directly proportional to x and y = 6 when x = 2, what is the proportion equation?
Answer:
y = 3x
Step-by-step explanation:
Direct proportion equation is
y = kx
6 = k*2
Divide each side by 2
6/2 = 2k/2
3 =k
The equation is y = 3x
Formula for direct proportion: y = kx
Solution:
6 = 2k
~Divide 2 to both sides
3 = k
Best of Luck!
For a given recipe, 10 cups of flour are mixed with 20 cups of sugar. How many cups of flour should be used if 4 cups of sugar are used? Assuming a constant ratio, fill out the table of equivalent ratios until you have found the value of x.
Answer:
2
Step-by-step explanation:
If 20 cups are used on the first recipe then 4 are used on the second, the way to find the answer is to divide 20 by 4. 20 divided by 4 will get 5. Now we have to divide the 10 cups of flour by 5 which in the end will get 2.
A movie club charges a one-time fee membership fee of $25. This allows members to purchase movies for $7 each. Lincoln is a member of the movie club and has spent a total of $60. How many movies has Lincoln purchased
Answer:
he purchased 5 movies bro
Step-by-step explanation:
Can v11 be classified as a rational
Answer:
yes it should
Step-by-step explanation:
Find the reciprocal of 5.
Answer:
0.2 is the answer
Step-by-step explanation:
Answer:
0.2
Step-by-step explanation:
5^-1=0.2
What kind of triangle?
Answer:
I think it's an obtuse scalene.
Step-by-step explanation:
Amy buy 5 pounds potatoes for $2.50. How much does 1 pound of potatoes weight? (What is the unit rate?)
Answer:
$0.50
Step-by-step explanation:
If there are 5 pounds of potatoes for $2.50, you must divide to find the unit rate.
$2.50 / 5 = $0.50
1 pound of potatoes costs $0.50
Answer:
0.5 $/pound
Step-by-step explanation:
[tex]5[/tex] pounds ⇒ [tex]2.50$[/tex]$to khow much dollars one 1 pound costs, we must divide the price of 5 pounds by 5
[tex]\frac{2.50}{5} = 0.5[/tex] $/ pound2.5 is in dollars and 5 is in pounds so the rate unit is $/pound
the cost of a camp is $300 for the first week and $125 for each week beyond the first. the total cost can be modeled by the expression 300+125(x-l). what does (x-l) repreasent
Answer: hopefully this helps
D. The number of weeks after the first week
Step-by-step explanation:
will give brainliest and 20 points:
f(x+1) = 8(x+1)^2+3(x+1)-8
Answer:
Step-by-step explanation:
what is 125.2 X 3 3/4=?
Answer: 31.3x33
Step-by-step explanation:
Did the test :)
The measure of two vertical angles are given by the expressions (x+3) and (2x-7). Find the value of x.
Answer:
61.3
Step-by-step explanation:
two vertical angles add up to 180°
so (x+3)+(2x+7)=180°
open brackets & collect like terms
x+3+2x-7=180°
3x+-4=180°
3x=184°
x=61.3 after dividing by 3 on both sides
Need help please guys
Answer:
B.
Explanation:
π ≈ 3.142
22/7 ≈ 3.143
square root of ten ≈ 3.162
