Answers
Part 1
[tex](g\circ h)(x)=g(x-4)=(x-4)^2 + 1=x^2 - 8x+16+1=\boxed{x^2 - 8x+17}[/tex]
Part 2
[tex](-\infty, \infty)[/tex]
The answers in the box are:
First box: [tex]\mathbf{x^2-8x+17}[/tex]Second box: [tex]\mathbf{(-\infty,\infty)}[/tex].Given that the functions are
[tex]g(x)=x^2+1[/tex]
[tex]h(x)=x-4[/tex]
Since clearly g(x) and h(x) exist for all real values of x so the domain of g(x) and h(x) both are all real numbers.
Now the composition of function is given by,
[tex](g\circ h)(x)=g(h(x))[/tex]
[tex]=g(x-4)[/tex]
[tex]=(x-4)^2+1[/tex]
[tex]=x^2-8x+16+1[/tex], since we know that [tex](a-b)^2=a^2-2ab+b^2[/tex]
[tex]=x^2-8x+17[/tex]
So, [tex](g\circ h)(x)=x^2-8x+17[/tex]
It is a polynomial function so it is defined for all real values of x.
Hence the domain of composition is all real numbers, that is [tex](-\infty,\infty)[/tex]
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Related Questions
Inside the box of every cereal box contains a surprise gift. The store manager assures employees that 18 of the 48 boxes on the shelf have a secret decoder ring and inside the other 30 boxes on the shelf contain a different gift. If two cereal boxes are randomly selected from the shelf to purchase, what is the probability that both of them have the secret decoder ring? (Give answer as a decimal correct to least three decimal places.)
Answers
The probability that both of them have the secret decoder ring will be 0.1356.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
Inside the box of every cereal box contains a surprise gift.
The store manager assures employees that 18 of the 48 boxes on the shelf have a secret decoder ring.
And inside the other 30 boxes on the shelf contain a different gift.
If two cereal boxes are randomly selected from the shelf to purchase.
Then the probability that both of them have the secret decoder ring will be
The total events will be
Total event = ⁴⁸C₂
Total event = 1128
The favorable events will be
Favorable event = ¹⁸C₂
Favorable event = 153
Then the probability will be
P = 153 / 1128
P = 0.1356
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what are the intercepts of x^2 +8x+16
Answers
Answers:
x intercept = -4
y intercept = 16
The graph is shown below.
=======================================================
Explanation:
To determine the x intercept(s), we set the expression equal to zero and solve for x. In other words, we plug in y = 0 and solve for x.
y = x^2 +8x+16
0 = x^2 +8x+16
x^2 +8x+16 = 0
(x+4)^2 = 0
x+4 = 0
x = -4
There's only one x intercept. It's located at the vertex of the parabola.
The location of the x intercept is the point (-4,0)
------------
To find the y intercept, we plug in x = 0 and compute like so:
y = x^2 +8x+16
y = (0)^2 +8(0)+16
y = 16
The y intercept is 16 which is located at (0,16)
Check out the graph below. It was made using the free app Desmos.
Is the point (11, 15) on the circle defined by (x-9)² + (y-15)² = 4?
O Yes
O No
Answers
The center would always be at the perpendicular bisector of two chord or one chord and a tangent.
That's why first one is wrong and second one right.
Find the radius of a circle with area 345 square centimetres
30 pts need in like 10 mins!!
Please say the answer like-
… divided by … = ……
Or
… times … = …..
Answers
Answer:
5.9
Step-by-step explanation:
It's because area is 345
Formula , A=πr2Find the √ of 34518.6=3.14×f2fR = 5.9Step-by-Step Solution:
Radius (r) = ?
Area (A) = πr² = 345 sq. cm
Therefore,
πr² = 345
3.14 * r² = 345
r² = 345/3.14
r² = 109.87
r = √109.87
=> r = 10.48
Radius (r) = 10.48 cm
Simplify completely!!!
Answers
Answer:
h^24
Step-by-step explanation:
hope that helpssndbfbsb
show how to simplify y-8 = 3/4x [x-(-6)]
Answers
To simplify the equation, we have y = [tex]\frac{3}{4x^2 + 24x} + 8[/tex]
How to simply the expressionGiven the expression
y-8 = 3/4x [x-(-6)]
First, expand the bracket
[tex]y - 8[/tex]= [tex]\frac{3}{4x^2 + 24x}[/tex]
Make 'y' the subject of formula
y = [tex]\frac{3}{4x^2 + 24x} + 8[/tex]
Thus, to simplify the equation, we have y = [tex]\frac{3}{4x^2 + 24x} + 8[/tex]
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please help! due very soon!
Answers
Answer:
{x | x = -6, -1, 0, 3}
(first option listed)
Step-by-step explanation:
The domain of a function is all possible x-values for that function
So, we can see (from the x-value portion of our table) that the possible x-values are:
-6 , -1, 0, and 3
We write domain and range in lowest - highest number value order, so we write our domain as such:
{x | x = -6, -1, 0, 3}
{range is all possible y-values, and this would include -7 , 1, 9, and -2}
hope this helps!!
Vector g is shown below.
Vector h is parallel to g, in the same direction and
half as long.
Work out h as a column vector.
9
Answers
Answer:
h = [tex]\left[\begin{array}{ccc}5\\1\\\end{array}\right][/tex]
Step-by-step explanation:
g = [tex]\left[\begin{array}{ccc}10\\2\\\end{array}\right][/tex] , then
h = [tex]\frac{1}{2}[/tex] [tex]\left[\begin{array}{ccc}10\\2\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}5\\1\\\end{array}\right][/tex]
14. What is the measure of ZABC in the image shown? OE A B 10x - 10 100 - 2x 2x + 10 C 14. What is the measure of ZABC in the image shown ? OE A B 10x - 10 100 - 2x 2x + 10 C
Answers
Answer: 110 degrees
Step-by-step explanation:
By the exterior angle theorem.
[tex]10x-10=100-2x+2x+10\\\\10x-10=110\\\\\therefore \angle ABC=110^{\circ}[/tex]
The accompanying frequency distribution represents the square footage of a random sample of 500 houses that are owner occupied year round. Approximate the mean and standard deviation square footage.
Savings Lower Limit Upper Limit Frequency
0-199 0 199 345
200-399 200 399 97
400-599 400 599 52
600-799 600 799 21
800-999 800 999 9
1000-1199 1000 1199 8
1200-1399 1200 1399 3
Answers
The mean and the standard deviation are 233 and 208.95 respectively.
The mean of a distribution is its average, while the standard deviation is the summary of how far each data in the dataset, is to the mean.
First, we calculate the class midpoint (x) from the given intervals.
The class midpoint is the average of the intervals. So, we have:
X1 = (0+199)/2 = 99.5
X2 = (200+399)/2 = 299.5
X3 = (400+599)/2 = 499.5
X4 = (600+799)/2 = 699.5
X5 = (800+999)/2 = 899.5
X6 = (1000+1199)/2 = 1099.5
X7 = (1200+1399)/2 = 1299.5
So, the table becomes:
X values Frequency (f)
99.5 345
299.5 97
499.5 52
699.5 21
899.5 9
1099.5 8
1299.5 3
The mean of the distribution is:
This gives:
Mean = (99.5*345)+(299.5*97)+(499.5*52)+(699.5*21)+(899.5*9)+(1099.5*8)+(1299.5*3)/(345+97+52+21+9+8+3)
Mean = 124832.5/535 = 233
Therefore, Mean = 233
The standard deviation is calculated as follows:
So, we have:
Б =
√(99.5*(345-233)²+((299.5-233)² * 97)+((499.5-233)² * 52)+((699.5-233)² * 21)+((899.5-233)² * 9)+((1099.5-233)² * 8)+((1299.5- 233)² * 3)/ (345+97+52+21+9+8+3)
Standard Deviation = √(23357155.5)/535
= √43658.23
= 208.95
Б = 208.95
Hence, the mean and the standard deviation are 233 and 208.95 respectively.
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Suppose that the electricity consumption in your home last month was 354 kWh. In your contract with the electricity company, you agreed to pay 11.3 cents per kWh. If you also have to pay a regular fixed charge of $15.63, determine the total amount due on your electricity bill.
Answers
The total amount due on the electricity bill is $55.64.
Here given that the last month's electricity consumption is 354 kWh
According to my contract with the electricity company, I agree to pay 11.3 cents per kWh.
So for 354 kWh of last month, I have to pay [tex]=11.3\times354=4000.2[/tex] cents
Now we know that 1 dollar = 100 cents
100 cents = $1
1 cent = [tex]\$\frac{1}{100}[/tex]
4000.2 cents [tex]=\$\frac{4000.2}{100}=\$40.002[/tex]
also, I have to pay a fixed charge of $15.63
So the total bill for last month will be [tex]=\$40.002+\$15.63=\$55.632\approx\$55.64[/tex]
Hence the total due amount on the electricity bill is $55.64 approximating the amount to the next two decimal place number.
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Solve for x: |x − 2| + 10 = 12 (1 point)
Answers
Answer:
I think that would be 1
Step-by-step explanation:
Do everything in the lines before anything else. -2 becomes a 2 and then you add that with the 12 and divide 12 on both sides to get one.
Answer:
x = 0 or 4
Step-by-step explanation:
The absolute value function can be resolved into two equations. These one- or two-step equations can be solved in the usual way.
__
negative argument-(x -2) +10 = 12
-x = 0 . . . . . . . . . simplify, subtract 12
x = 0 . . . . . . . . . multiply by -1. Check: 0 -2 is negative.
positive argumentx -2 +10 = 12
x = 4 . . . . . . . . . simplify, subtract 8. Check: 4 -2 is positive.
The two solutions are x=0 and x=4.
)The width of a rectangle is shown below:
A coordinate plane with a point A at negative 3, 3 and C at negative 3, negative 2.
If the area of the rectangle to be drawn is 20 square units, where should points B and D be located if they lie to the right of points A and C?
B(1, 3) and D(1, −2)
B(3, 3) and D(3, −2)
B(2, 3) and D(2, −2)
B(1, 2) and D(1, −3)
Answers
Answer: B(1, 3) and D(1, −2)
Step-by-step explanation:
The distance from A to C is 5, meaning we need the length to be 4.
If they lie to the right, we need to add 4 to the x coordinates, so the x coordinates should be 1, and the y coordinates should be 3 and -2.
The locations of B and D are given by (A) B(1,3) and D(1,-2).
The area of rectangle is given by the product of the length and width of that rectangle.
Area = Length*Width
Distance between two points (a,b) and (c,d) is given by,
[tex]d=\sqrt{(c-a)^2+(d-b)^2}[/tex]
Here in the given question it is mentioned that AC forms width of a rectangle and A is at (-3,3) and C is at (-3,-2)
Now the width is [tex]=\sqrt{(-3-(-3))^2+(-2-3)^2}=\sqrt{0^2+(-5)^2}=\sqrt{25}=5[/tex] unit.
Also it is given that, the area of the rectangle is 20 square units.
So the length is = 20/5 = 4 units
B and D lie to the right of points A and C respectively.
We have to go 4 units right to the A to find B and 4 units right to C to find D.
A is at (-3,3)
then B is at (-3+4,3) = (1,3)
C is at (-3,-2)
So D is at (-3+4,-2) = (1,-2)
Hence correct option is (A) B(1,3) and D(1,-2)
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A Store-It-All storage facility requires users to enter a four digit code, using numbers 0-9, to get through the
gate. You need to get a box of winter clothes from your storage container, but you forgot the code.
1. How many possible codes are there if the digits cannot be repeated?
There are
possible codes.
2. What is the probability that you will guess the correct code on your first try?
P(correct code) =
3. If the digits can be repeated, how many possible codes are there?
There are
different codes.
Answers
Answer:
Step-by-step explanation: 1. 5040 because 10x9x8x7
3. 10000 because 10^4=1000
1)There are 5040 possible codes are there if the digits cannot be repeated.
2)The probability that you will guess the correct code on your first try will be (1/5040).
3) Possible code = 10000 .
Given,
Numbers : 0 to 9
Here,
Total number of digit = 0,1,2,3,4,5,6,7,8,9
Given condition;
a)
Four digit card must be drawn;
The total possible ways there if the digits cannot be repeated will be;
⇒10×9×8×7
⇒5040
b)
The probability that you will guess the correct code on your first try is;
P(A) = n(A)/n(S)
Where,
n(A) is the event has the right code
n(S) is the total possible ways;
P(A) =1/5040
Hence the total possible ways there if the digits cannot be repeated and the probability that you will guess the correct code on your first try will be 5040 and (1/5040) respectively.
c)
If the gits can be repeated then we have 10 digits for each place :
Possible code = 10 * 10 * 10 *10
Possible code = 10000
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Model 3xfx Write the inverse of the rational function used to represent the situation in model 3, .
A biologist has tracked the population of Antarctic penguins in a marine reserve since 2012. He represents the population with the rational function f(x)=15x+50/x+5, where is the number of years that have passed since 2012 and () is the number of penguins.
Answers
y = (15x + 50)/(x + 5)
Swap the x and y and make y the subject again
x = (15y + 50)/(y + 5)
x(y + 5) = 15y + 50
xy + 5x = 15y + 50
xy - 15y = 50 - 5x
y(x - 15) = 50 - 5x
y = (50 - 5x)/(x - 15)
So inverse function f^-1(x) = (50 - 5x)/(x - 15)
help me pls i dont understand it
Answers
Answer:
Step-by-step explanation:
x×4=2x²(x-1)
2x³-2x²-4x=0
2x(x²-x-2)=0
x≠0
x²-x-2=0
x²-2x+x-2=0
x(x-2)+1(x-2)=0
(x-2)(x+1)=0
x=2
or
x=-1 (rejected)
Answer:
Step-by-step explanation:
Formula
The following relationship exists between the parts of each chord.
(x - 1)(2x^2) = 4*x
Solution
The easiest way to start is to divide both sides of the equation by x.
(x - 1)(2x^2)/x = 4x / x Divide by x
( x-1)(2x) = 4 Remove the brackets
2x^2 - 2x = 4 Subtract 4 from both sides
2x^2 - 2x - 4 = 4 - 4 Combine
2x^2 - 2x - 4 = 0 Pull out the common factor
2(x^2 - x - 2) = 0 Divide by 2
x^2 - x - 2 = 0 Factor
(x - 2)(x + 1)
Answer:
x can be 2 or x can be - 1 on paper. The x on the upper right prohibits that. A line can't have a length of - 1. So - 1 is called an extraneous solution.
The answer is x = 2
How do I solve this problem? The green dots can be moved
Answers
Answer :
Points at (1, 3) and (3, 3) and (2, 1)
Explanation:
The original graph (dashed) is an absolute value function meaning f(x) = |x|
Given: y = 2f(x - 2) + 1
f(x - 2) means you plug in x - 2 for x in f(x) function
the new graph equation is: y = 2|x - 2| + 1
The graph will shift up 1 because +1The graph will shift right because -2The graph has a scale factor of 2The graph is V shaped because it is an absolute value graphLearn more about Absolute Value here: https://brainly.com/question/729268
Visual:
13. Find the values of x and y in the diagram below.
א
9
13
7
y
3
10
17
Answers
Answer:
x = 2
y = 4
Step-by-step explanation:
Let's start with the 7 in the middle. Subtract the 1 on its upper left to get 6.
Add the 3 on its lower left to get 10.
so, 3 - x = 1. x = 2
17 - y = 13. y = 4
What mistake did he make ?! I need everybody Anwser
Answers
Answer:
he subtracted the wrong coordinates to find the horizontal leg
Step-by-step explanation:
It should be 4-(-3) but he labeled 4-(-1)
graph g(x) = -8|x| +1
Answers
Answer:
look the attachment in the above
Urgent algebra 2 help needed
Answers
Answer:
The area for the trapezoid is
A=h/2(a+b)
A=8/2(10+15)
A=100 cm square
Hope it helps!
Order these numbers from least to greatest.
3.3661, 3.5, 3.36, 3.036
Answers
Answer:
3.036, 3.36, 3.3661 , 3.5
Step-by-step explanation:
Look at the first 2 numbers
3.3661, 3.5, 3.36, 3.036
We can order them as 3.0 , 3.3 , 3.3 . 3.5
So 3.036 is first one
Now we have 2 of the 3.3's
One is 3.3661 and the other one is 3.3600
Because if you add a number to the end it will always be a zero and it wont change the answer
So 3.36 is second and 3.3661 is third one
3.5 is bigger than 3.3
So 3.5 is last
3.36
3.3661
3.5 greatest
what is the equation
Answers
Answer:
[tex]y = \sin( \frac{2\pi}{3} x) [/tex]
Step-by-step explanation:
The equation of a sine function is y = a sin(bx), where a = amplitude (aka height) and b equals period (aka time). I'm assuming there isn't any information other than the graph shown, so let's assume that our amplitude is 1 and our period is 2pi/3. Plugging these values into the equation, we get:
[tex]y = (1) \sin(( \frac{2\pi}{3})x ) = \sin(\frac{2{\pi} }{3}x )[/tex]
Which of the following graphs shows the solution set for the inequality below?
|x + 2| + 7 > 10
Answers
Work Shown:
|x+2| + 7 > 10
|x+2| > 10-7
|x+2| > 3
x+2 > 3 or x+2 < -3
x > 3-2 or x < -3-2
x > 1 or x < -5
The graph for x > 1 has an open circle at 1 and shading to the right.
The graph for x < -5 has an open circle at -5 and shading to the left
Both of these facts combine to describe Choice C
In other words, we have open circles at -5 and 1, with nearly everything shaded except for the region between the open circles.
The open circles are used to exclude those x values mentioned.
Ms. Mather filled 8 3/4 gallons of gas in her car's fuel tank. The car used up 3 1/2 gallons when she visited a friend in a neighboring town. How many gallons of gas are left in Ms. Mather's fuel tank?
Answers
Answer: [tex]5\frac{1}{4}[/tex] gallons are left
Step-by-step explanation:
convert to mixed number...
[tex]8\frac{3}{4} = \frac{35}{4}[/tex]
[tex]3 \frac{1}{2} = \frac{7}{2}[/tex] or [tex]\frac{14}{4}[/tex]
[tex]\frac{35}{4} -\frac{14}{4}=\frac{21}{4}[/tex]
[tex]\frac{21}{4} =5\frac{1}{4}[/tex]
therefore, [tex]5\frac{1}{4}[/tex] gallons are left in Ms. Mather's fuel tank
Answer:
5 1/4 gallons are left... correct
Please answer BOTH the questions xoxo <3
Answers
Answer:
First Image: Choice B
Second Image: Choice B
Step-by-step explanation:
The equation of the line is written in the slope-intercept form,
y = mx + b
where m represents the slope
b represents the y-intercept
First Image:
In our equation, y = 0.1x + 1,
we see that the y-intercept of the line is 1 and the slope is 0.1
We can simple plug in the x values to test if the table is true:
x = -1
y = 0.1x + 1 → y = 0.1(-1) + 1 → y = -0.1 + 1 → y = 0.9
This proves choices A and C are INCORRECT
The next point is at x = 10
y = 0.1x + 1 → y = 0.1(10) + 1 → y = 1 + 1 → y = 2
Making choice D INCORRECT
Hence, you've selected the correct choice (B)!
Second Image:
In our equation, y = 3x + 2,
we see that the y-intercept of the line is 2 and the slope is 3
Choice A is INCORRECT due to (0,0) not logical as the y-intercept is 2
Choice B is CORRECT due to (1/3, 3) not logical as that 3 = 3(1/3) + 2
6 = 3(4/3) + 2 → 6 = 4 + 2. → 6 = 6
3 = 3(1/3) + 2 → → 3 = 1 + 2. → 3 = 3
20 = 3(6) + 2 → 20 = 18 + 2. → 20 = 20
Choice C is INCORRECT due to (-6, 20) not logical as that 20 = 3(-6) + 2
Choice D is INCORRECT due to (10, 4) not logical as that 10 = 3(4) + 2
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AABC=AADC, LACB=143, AC=33 LACD=?
Answers
Answer:
I think the best answer is 143
A Ferris wheel at an amusement park is modeled by (x – 100)2 + (y – 75)2 = 4,900, where the measurements are in feet. A slingshot attraction is modeled by y = –3x2 + 48x – 30. Which attraction reaches a greater height, and what does it represent in terms of the context?
Answers
The attraction that reaches a greater height and what it represent in terms of the context is:
The slingshot reaches a greater height at 162 ft, which is the vertex of the parabola.The Ferris wheel reaches a greater height at 145 ft, which is the highest point on the circle.HeightFerris wheel
(x – 100)2 + (y – 75)2 = 4,900
y max= 75+70
y max=145 ft
Sling shot
y = –3x² + 48x – 30
dy/dx=-6+48=0
x=48/6
x=8
Hence:
y max = –3(8)² + 48(8) – 30
y max = –3×64+48(8)-30
y max = –192+384-30
y max =162 ft
Therefore slingshot reaches a greater height at 162 ft and Ferris wheel reaches a greater height at 145 ft.
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Help please I need it asap and thank you
Answers
Answer: 2.5
Step-by-step explanation:
The altitude of an equilateral (or isosceles) triangle bisects the side to which it is drawn.
What is the solution to the linear equation?
-12 +3b-1-5-b
b=-2
b = -1.5
b = 1.5
b = 2
Answers
Answer:
[tex]b = 2[/tex]
Step-by-step explanation:
[tex]( - 12 - 1 - 5) + (3b - b) \\ - 18 + 2b \\ 2b - 18 \\ b = 2[/tex]
