Let f(x) = 16 – x^2, g(x) = 4 – x. Find (fg)(x) and its domain.
Answers
Answer:
x+4; all real numbers except =-4
Step-by-step explanation:
f(x)/g(x) = (x2-16)/(x+4)
The domain is all real numbers except x = -4 (because the denominator is zero at x = -4 and division by zero is undefined.)
We can simplify by factoring the numerator:
(x2-16)/(x+4) = (x-4)(x+4)/(x+4) = (x-4)
The domain is the same as the original expression: all real numbers except x = -4
Related Questions
How can you use the double number line diagram to find what percent 120 is of 150?
Answers
We can say that 120 is 80% of 150.The percentage that 120 is of 150 will be the length of this line divided by the length of the entire double number line (which is 100%).
To use the double number line diagram to find what percent 120 is of 150, we first need to plot the two numbers on the double number line. We can do this by drawing a horizontal line and labeling it with the two numbers, 120 and 150, and then dividing the line into equal segments.
Next, we can find the difference between the two numbers (150-120=30) and use this to label the corresponding points on the double number line. The point representing 120 should be 3/4 of the way between the two numbers (since 120 is 3/4 of 150).
Finally, we can use the double number line to find the percentage that 120 is of 150. To do this, we can draw a vertical line from the point representing 120 up to the top of the double number line.
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How do the areas of the parallelograms compare?
O The area of parallelogram 1 is 4 square units
greater than the area of parallelogram 2.
O The area of parallelogram 1 is 2 square units
greater than the area of parallelogram 2.
O The area of parallelogram 1 is equal to the area of
parallelogram 2.
O The area of parallelogram 1 is 2 square units less
than the area of parallelogram 2.
Answers
Answer:The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2. Then the correct option is A.
What is the area of the parallelogram?
The vertices of the parallelogram are (x₁, y₁), (x₂, y₂), (x₃, y₃), and (x₄, y₄).
Then the area of the parallelogram will be
Area = 1/2 [(x₁y₂ + x₂y₃ + x₃y₄ + x₄y₁) - (y₁x₂ + y₂x₃ + y₃x₄ + y₄x₁)]
(x₁, y₁) ⇒ (0, 2)
(x₂, y₂) ⇒ (2, 6)
(x₃, y₃) ⇒ (4, 6)
(x₄, y₄) ⇒ (4, 0)
Then the area of parallelogram 1 will be
A₁ = 1/2 [(0 x 6 + 2 x 6 + 4 x 0 + 4 x 2) – (2 x 2 + 6 x 4 + 6 x 4 + 0 x 0)]
A₁ = 16 square units
(x₁, y₁) ⇒ (2, 0)
(x₂, y₂) ⇒ (4, -6)
(x₃, y₃) ⇒ (2, -6)
(x₄, y₄) ⇒ (0, -2)
Then the area of parallelogram 2 will be
A₂ = 1/2 [(2 x -6 + 4 x -6 + 2 x -2 + 0 x 0) – (0 x 4 + -6 x 2 + -6 x 0 + -2 x 2)]
A₂ = 12 square units
The difference of area will be
A₁ - A₂ = 16 – 12
A₁ - A₂ = 4 square units
Then the correct option is A.
Step-by-step explanation:
Based on the image given, the area of parallelogram 1 is option A: 4 square units greater than the area of parallelogram 2.
What is the parallelogram?
To know the problem, one need the calculate the area of all of the parallelogram. So it will be:
Area of first Parallelogram (lets call it P-1) ,
Area of P-1 = Area of the red-figure - Area ΔA - Area ΔB - Area ΔC - Area ΔD
= (6 x 6) - (0.5 x 4 x 2) - (0.5 x 2 x 4)- (0.5 x 4 x 2) - (0.5 x 2 x 4)
= 36 - 4 - 4 - 4 - 4
= 20 units²
Area of Parallelogram 2 (lets call it P-2) ,
Area of P-2 = Area of the Blue-figure - Area ΔP - Area ΔQ - Area ΔR - Area ΔS
(8 x 4) - (0.5 x 2 x 2) - (0.5 x 6 x 2) - (0.5 x 2 x 2) - (0.5 x 6 x 2)
= 32 - 2 - 6 - 2 - 6
= 16 units²
The differences that is seen in the area of the parallelogram are:
= Area of P-1 - Area of P-2
= 20 - 16
= 4 units²
So, the area of parallelogram 1 is option A: 4 square units greater than the area of parallelogram 2.
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What’s the correct answer answer asap
Answers
Answer:
The answer should be B.
Find the equation of the parabola that has a vertex at (2,0) and a y-intercept of (0,12).
Question 19 options:
A)
y = 3(x + 2)2
B)
y = (x – 2)2
C)
y = (x + 2)2
D)
y = 3(x – 2)2
Answers
Answer:
D
Step-by-step explanation:
standard form would be 3x^2-12x+12
vertex form y=3(x-2)^2
Answer:
y = 3(x + 2)2
Step-by-step explanation:
For the following figure, complete the statement for the specified points.
Point A, B, and Q
O both collinear and coplanar
O coplanar
• neither collinear nor coplanar
• collinear
Answers
EXPLANATION
Coplanar means the three points A , B and Q are on the same plane.
They are not colinear, because they are not in a straight line. It is only A and Q that are on the same straight line. If B had fallen in line with them, the three points would have been collinear as well.
What is the mode?
6 5 3 5 5 6
Submit
Answers
Answer: 5
Step-by-step explanation:
5 is the most common recurring number so it is the mode of the data set
Answer: the mode is the number that appears the most so in this case it would be
Apply the distribute property, substitute the given numerical value given:
9(-3r -11), r=10
Answers
Answer:
-369
Step-by-step explanation:
Replace r with 10.
9(-3(10)-10))
9(-30-11)
9*-30+9*-11
-270+ -99
-369
Hope this helped. :)
Name the two functions used to form the rational function.
Answers
Answer:
A rational function is defined as the quotient of polynomials in which the denominator has a degree of at least 1 . In other words, there must be a variable in the denominator. The general form of a rational function is p(x)q(x) , where p(x) and q(x) are polynomials and q(x)≠0 ..
Explanation:
Well, Hope it helps you..
Y-your welcome in advance..
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Thinking about the geoboard shown, Klay says it is impossible to make a triangle with an area of 5. Kevin says he can make a triangle with an area of 5
If you agree with Kevin, make a triangle with an area of 5 and explain below how you know it is an area of 5.
If you agree with Klay, make a triangle with an area as close as possible to 5 and convince us below that 5 is not possible.
Answers
Kevin make a triangle with an area of 5 is Correct.
To construct a triangle with an area of 5, we need to consider the formula for the area of a triangle: Area = (1/2) x base x height.
Let's choose a base of 4 units and a height of 2.5 units.
Plugging these values into the area formula, we have:
Area = (1/2) x 4 x 2.5
Area = 5
Therefore, we have constructed a triangle with a base of 4 units and a height of 2.5 units, resulting in an area of 5.
This confirms that it is indeed possible to make a triangle with an area of 5 units.
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Write the equation of the line in fully simplified slope-intercept form
Answers
Answer:
y = (-1/6)x+2
Step-by-step explanation:
The general form is y=mx + b where m is the slope and b is the y intercept.
Notice that the graph is sloping down - - - as x increases, y decreases, so make sure that that m (slope) ends up being negative.
We can see the y intercept is 2.
So y=mx+2
Now let's calc the slope.
We have a couple of choices. We can use the slope formula OR we can substitute. I'm going to do both.
Slope formula = (y2-y1)/(x2-x1). Pick any 2 points. (-6,3) and (6,1) are plotted with dots on your graph.
slope = (3-1)/(-6-6)
= 2/-12 = -1/6
so y = (-1/6)x+2
Here's another way to solve: use any point and solve for m.
y=mx+2
We'll use the point (6,1)
1 = m*6+2
1-2 = 6m
-1 = 6m
-1/6 = m
Same slope!
No matter how you solve, the equation is y = (-1/6)x+2.
A person leaves home and walks 4 miles west, then 5 miles southwest.
How far from home is she?
miles
In what direction must she walk to head directly home?
degrees North of East
Answers
The person is approximately 8.43 miles from home, and they need to walk in the direction of approximately 26.6 degrees east of north to head directly home.
To determine the distance from home, we can use the concept of vector addition. The person walks 4 miles west, which can be represented as a vector (-4, 0) in a coordinate plane. Then, they walk 5 miles southwest, which can be represented as a vector (-3.54, -3.54) since southwest is a combination of west and south. Adding these two vectors together gives us (-7.54, -3.54).
To find the magnitude or distance from home, we use the Pythagorean theorem. The distance is given by sqrt((-7.54)^2 + (-3.54)^2) = 8.43 miles (approximately).
To determine the direction to head directly home, we need to find the angle between the vector (-7.54, -3.54) and the positive x-axis. We can use trigonometry to find this angle. The tangent of the angle is given by the ratio of the y-coordinate to the x-coordinate, which is -3.54 / -7.54. Taking the inverse tangent of this value gives us approximately 26.6 degrees.
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I ate 6 pieces of my candy this is 75% of the candy I had how much candy did I have before
Answers
Answer:
8
Step-by-step explanation: pls don't delete again I need brain points
I NEED HELP!! I'll give you brainliest!! A high school wants to expand its P.E. schedule. To better understand the needs of the students, the principal looked at which forms of exercise are preferred by the 18 students in the sample group.The Venn Diagram shows this information be gathered.a. How many students preferred swimming over running or walking?b. How many students choose running or walking?c. Which students preferred swimming and walking, but not running
Answers
Answer:
a. Three students preferred swimming over running and walking.
b. Fourteen students chose running or walking.
c. Alex and Jose preferred swimming and walking, but not running.
Given: f(x) = 2x^4 – 3x^3– 35x^2 – 9x + 45
Explain how you can show that (x-1) and (x+3) are factors.
Answers
Answer:
45-35-9-3+2 = 45-47+2 = 0
if the sum of coefficients is equal to 0, 1 is the factor of the polynomial
you can find other integer factors by looking on the integer factors of 45, so -3 will be a guess or you use use Horner, find how does this polynomial look like after factoring out (x-1) and try to group or other technic
A certain species of fish require 1.5 cubic feet of water per fish to maintain a healthy environment. Find the maximum number of fish you could put in a tank measuring 9 feet by 4 feet by 8 feet. 8 feet 9 feet 4 feet fish
Answers
the fish tank is a cuboid:
so volume of cuboid = wlh
v=4x9x8
v=288
1 fish requires 1.5 cubic feet
x fish requires 288 cubic feet
just cross mulitiply
288=1.5x
x=192
so the answer is 192 fishes
Suppose that mean retail price per gallon of regular grade gasoline is $3.45 with a standard deviation of $0.10 and that the retail
price per gallon has a bell-shaped distribution.
NOTE: Please use empirical rule approximations for this problem.
a. What percentage of regular grade gasoline sells for between $3.35 and $3.55 per gallon (to 1 decimal)?
Lololo
%
b. What percentage of regular grade gasoline sells for between $3.35 and $3.65 per gallon (to 1 decimal)?
%
c. What percentage of regular grade gasoline sells for less than $3.55 per gallon (to 1 decimal)?
%
Answers
The percentage of regular grade gasoline sells for between $3.35 and $3.55 per gallon is 64%
The percentage of regular grade gasoline sells for between $3.35 and $3.65 per gallon is 81.5%
The percentage of regular grade gasoline sells for less than $3.55 per gallon is 84%
Given :
Mean retail price is $3.45
Standard deviation is 0.10
Empirical rule states that 99.7% of data is observed in normal distribution that lies within 3 standard deviations.
68% of data lies under 1 standard deviation
95% lies under 2 standard deviations
99.7% lies under 3 standard deviations
there are 3 standard deviations on the left and right of mean . The graph is attached below
Mean is 3.45. standard deviation is 0.1
3.45+0.1=3.55
3.45-0.1=3.35
So 3.35 and 3.55 lies under first standard deviation
The percentage between $3.35 and $3.55 is 68%
3.45 +0.1+0.1=3.65
3.35 lies on 1 standard deviation on left and 2 deviations on the right of mean
So , 34+34+13.5=81.5%
The percentage between $3.35 and $3.65 is 81.5%
For gasoline sells for less than 3.55 , there are 3 standard deviation on the left of mean and 1 standard deviation on the right
0.15+2.35+13.5+34+34=84%
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2/5 of employees in a company drive to work, 1/3 travel by bus and the rest walk. 1. Find the fraction of who walk.
Answers
Answer:
4/15
Step-by-step explanation:
2/5 drive
1/3 bus
and rest walk
fraction of those who walk is 1-(2/5+1/3)
2/5+1/3=(6+5)/15=11/15
15/15-11/15=4/15
if f(x) =g(x) + 10 and g(x) = 3(x) - 18
Answers
Step-by-step explanation:
This is called a nested function. Remember, math is a language.
We define a function where x is whatever we want it to be, f(x) = g(x) +10
but we have yet another function inside and itvs defined as g(x) = 3x - 18
if we were to write it out, it woukd be
f(x) = (3x - 18) + 10
Round 386.565 to the nearest hundredth.
Answers
Hope this helps^^^^
Explanation: the 5 was 5 or higher so you turn it into a 0 and pump the number your rounding up.
HELP PLEASE GEOMETRY!!
Answers
Answer:
<G = <J
Step-by-step explanation:
SAS means two sides and the included angle
WE know two sides and need the included angle
<G must equal < J
What is the equation in slope intercept form of the line that passes through the point (2,0) and is parallel to the line represented by y = 4.5x + 2.7?
Answers
The equation of a line in the slope intercept form is expressed as
y = mx + c
Where
m represents slope
c represents y intercept
The equation of the given line is
y = 4.5x + 2.7
By comparing the equation with the slope, intercept form, it means that
slope, m = 4.5
If two lines are parallel, it means that they have the same slope. Given that the line that passes through the point(2, 0) is parallel to the given line, t means that the slope of ths line is 4.5
We would substitute x = 2, y = 0 and m = 4.5 into the slope intercep equation to determine c. It becomes
0 = 2 * 4.5 + c
0 = 9 + c
c = 0 - 9 = - 9
Substituting c = - 9 and m = 4.5 into the slope intercept equation, t
The equation of the line would be
y = 4.5x - 9
Suppose that your boss must choose three employees in your office to attend a conference in Jamaica. Because all 27 of you want to go, he decides that the only fair way is to draw names out of a hat. What is the probability that you, Rebecca, and John are chosen
Answers
Answer:
1/2925 = 0.0003 = 0.03% probability that you, Rebecca, and John are chosen.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, the order in which the people are chosen is not important, so the combinations formula is used to solve the question.
Combinations formula:
\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
Desired outcomes:
Only 1 outcome in which these 3 people are selected, so \(D = 1\)
Total outcomes:
3 people from a set of 27, so
\(T = C_{27,3} = \frac{27!}{3!(27-3)!} = 2925\)
Probability:
\(p = \frac{D}{T} = \frac{1}{2925} = 0.0003\)
1/2925 = 0.0003 = 0.03% probability that you, Rebecca, and John are chosen.
Warm-Up
Jug
Use the diagram below to answer the questions.
Intro
K
P
M
Which are shown on the diagram? Check all that apply.
O
OKM
Ojk
OPK
OLJK
COM
Dong
Answers
KM, JK, PK, and MJ are shown on the diagram.
Then the correct options are B, C, D, and F.
Since, Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
A line segment in mathematics has two different points on it that define its boundaries.
All the line segments will be
JK, JM, KM, MP, PK, and KL
The triangle KPM.
And the angle will be ∠LKJ, ∠PKM. ∠KMP. and ∠MPK.
Then the correct options are B, C, D, and F.
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which of the following ordered pairs are solutions to the system of inequalities? check all that apply
3x > y
y < 5
a. (9,4)
b. 1,3
c. 4,10
d. -2,-7
3. -12,50
f. 1,2
Answers
Answer: A and C
Step-by-step explanation:
What is the midpoint of the line segment with endpoints (-2,-4) and (4.6)?
Answers
-0.7 im guessing
it might not be right but i tried because
at a coffee shop, the first 100 customers’ orders were as follows
Answers
Answer:
81%
Step-by-step explanation:
22+5=27
22/27
For the diagram below ,The Value of q , r is
Answers
Answer:
angle r= 45°
angle r+angle q=180°
45°+ angle q=180°[linear pair]
angle q=180°- 45°
angle q= 135°
Let \(f(x)=2(3)^x^+^1\). Evalulate \(f(2)\) without using a calculator. Do not include \(f(2)\) in your answer.
Answers
\(f(x)=2(3)^{x+1} \\\\[-0.35em] ~\dotfill\\\\ f(2)=2(3)^{(2)+1}\implies f(2)=2(3)^3\implies f(2)=2(3^3) \\\\\\ f(2)=2(27)\implies f(2)=54\)
consider the function what are the values
Answers
Answer:
i cant see the numbers...
Step-by-step explanation:
Answer:
F(-3) = -5/2
F(-1) = 3/2
F(3) =3/4
how many 1 1/4 inch pieces can I cut a candy bar into if it is 5 1/3 inches long?
Answers
We can cut 4 4/15 pieces from 5 1/3 inches candy bar if the length of each candy is 1 1/4 inch.
Length of candy bar is 5 1/3 which can be written as 16/3 in
Length of piece that is to be cut from long candy bar is 1 1/4 or 5/4 in
Number of pieces
= length of piece/ total length of candy bar
= (16/3) / (5/4)
= 16/3 × 4/5
= 64/15
= 4 4/15 pieces
4 4/15 number of pieces can be cut from 5 1/3 inches long candy bar
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