Therefore , the solution of the given problem of function comes out to be f(g(x)) = x[tex]X^{2}[/tex]−4[tex]X^{2}[/tex]−28x−32/(x−4)
What is function?Each x value in the domain has one but only one y value range, according to the rule of a function. Definition. If there is only one and only one value of x such that f(x) = y, then the function is one-to-one
Here,
Given : f(x) =X² - 8x+16/2 + 2x
g(x) =(6x)/(x-4)
To find the f(g(x)) :
=> f(g(x)) = f(6x/(x-4))
=> f(6x/(x-4)) = (6x/(x-4) )^2 - 8((6x)/(x-4)) +16/2 + 2(6x)/(x-4)
=> f(6x/(x-4)) = 36[tex]x^{2}[/tex]/ ( [tex]x^{2}[/tex]+ 16 - 8x) - 36[tex]x^{2}[/tex]/(x+4) +8
=> f(6x/(x-4)) = x[tex]X^{2}[/tex]−4[tex]X^{2}[/tex]−28x−32/(x−4)
Therefore , the solution of the given problem of function comes out to be
f(g(x)) = x[tex]X^{2}[/tex]−4[tex]X^{2}[/tex]−28x−32/(x−4)
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For which function is the average rate of change over the interval 1 < x < 5 greater than the average rate of change over the same interval for the function g(x) = 1. 8x2?
The function g(x) = 1. 8x2 greater than the average rate is k(x) = 2x^2
How to calculate average rate?
The average rate is a measure of how quickly a quantity changes over a specific period of time. It can be calculated by dividing the change in the quantity by the change in time. The formula for calculating the average rate is:
Average rate = (final value - initial value) / (final time - initial time)
Given a function y, the average rate of change S of y = f(x) in an interval (Xs, Xf) will be given by the following equation:
In this problem, we have that:
Interval (1,5), so
Then
S = f(5) - f(1)/4
All options are compared to g(x).
g(5) = 1.8*(5)^2 = 45
g(1) = 1.8*(1)^2 = 1.8
An average rate of change greater than 10.8.
D.=k(x) = 2x^2
k(5) = 2*(5)^2 = 50
k(1) = 2*(1)^2 = 2
Greater than 10.8, this is the answer.
Hence, The function g(x) = 1. 8x2 greater than the average rate is k(x) = 2x^2
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An automobile manufacturer has given its car a 48.3 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this car since it is believed that the car has an incorrect manufacturer's MPG rating. After testing 150 cars, they found a mean MPG of 48.2. Assume the population variance is known to be 6.76. A level of significance of 0.02 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places
The p-value of the test statistic is calculated as follows:
0.6386.
What are the hypothesis tested?At the null hypothesis, it is tested if the mean is actually of 48.3 miles per gallon, that is:
[tex]H_0: \mu = 48.3[/tex]
At the alternative hypothesis, it is tested if the mean is different of that, hence:
[tex]H_1: \mu \neq 48.3[/tex]
What is the test statistic?The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.
The equation is given as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.The parameters for this problem are given as follows:
[tex]\overline{x} = 48.2, \mu = 48.3, \sigma = \sqrt{6.76} = 2.6, n = 150[/tex]
Hence the test statistic is obtained as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{48.2 - 48.3}{\frac{2.6}{\sqrt{150}}}[/tex]
z = -0.47.
The p-value is found using a z-distribution calculator, with a two-tailed test, as we are testing if the mean is different of a value, with z = -0.47, hence it is of:
0.6386.
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What is the difference between polynomials and not polynomials equation explain your answer?
By noticing which formulas only contain the operations of addition, subtraction, multiplication, and non-negative integer exponents, the polynomials may be located. Expressions with additional operations are considered non-polynomial expressions.
Expressions are polynomials, but expressions that equal zero are polynomial equations.
A polynomial may be written as the sum of a finite number of terms, where each term is the product of one or more variables raised to a positive integer exponent and a constant coefficient (or power).
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
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Please help meeeeeeeee
Answer:
24 units²
Step-by-step explanation:
Surface area of a cube = 6a² , where a = the side given
=> 6(2)²
=> 6(4)
=> 24 units²
Hope this helps!
Answer:
2(length) x 2(width) = 4(area of 1 square),
4(area of one square) x 6(there are six sides of a cube) = 24 squared
9,16,21
is a right triangle
Answer: Yes
Step-by-step explanation:
a right triangle is ... 9, 12, 15, 40, 41. 10, 24, 26. 12, 16, 12, 35, 37. 14, 48, 50. 15, 20, 25. 15, 36, 39. 16, 30, 34. 18, 24, 21, 29, 28, 35, 32, 40. 27, 36, 45. 40, 50
Choose the graph that represents the equation y = –|x – 1|.
What is the product of 6.3 and 5? 315 31.5 3.15 0.315
Answer: 31.5
Step-by-step explanation:
6.3 x 5
hope this helps :)
Please Simplify the phrase the first two and find the last one
Answer:
1) 23x + 6y
2) 8x - 4y
3) 4x - x² + 7
Step-by-step explanation:
Simplify:
Multiply each term of (3x + 6y) by 5 and multiply each term of (2x - 6y) by 4.
5(3x + 6y) + 4 (2x - 6y) = 5*3x + 5*6y + 4*2x - 4*6y
= 15x + 30y + 8x - 24y
Now, combine like terms. Like terms have same variable with same power.
= 15x + 8x + 30y - 24y
= 23x + 6y
2) 3(4x - 2y) - 2*(2x -y) = 3*4x + 3*(-2y) + (-2)* 2x + (-2)*(-y)
= 12x - 6y - 4x + 2y
= 12x - 4x - 6y + 2y
= 8x - 4y
3) f(x) = 3x + 2
To find f(x +1), replace x with (x +1)
f(x +1) = 3*(x + 1) + 2
= 3*x + 3*1 + 2
= 3x + 3 + 2
=3x + 5
f(2x) = 3*(2x) + 2
= 6x + 2
f(2x) + h(x) = 6x + 2 - x² - 2x + 5
= 6x - 2x - x² +2 + 5
= 4x - x² + 7
6. Angle A and Angle B are vertical angles. If the measure of Angle A is 30 degrees, what is the measure of Angle B?
Answer:
Angle B is 30 degrees
Step-by-step explanation:
Vertical angles are always congruent
Vertical angles are always of same measure. The measure of angle B in this case is evaluated as: [tex]m\angle B = 30^\circ[/tex]
What are vertical angles?Each of the pairs of the opposite angles made by two intersecting lines are called vertical angles.
They are always of same measure.
We can think about this fact as: "there were two lines overlaying on each other. Then, there was a finite point chosen, from where both decided to rotate by a certain degree. Since angle is measure of rotation, and as vertically opposite sides were equally rotated, so they get same measure:"
Its diagram is attached below. The vertical angles are congruent (denoted by ≅) (which is another way to say that they are of same measure)
Since the angle A and angle B specified in this case are pair of vertical angles, and since measure of angle A = 30 degrees, thus, angle B is also of measure 30 degrees.
The measure of an angle is written by writing small m in its left as: [tex]m\angle B = 30^\circ[/tex]
Therefore, the measure of angle B in this case is evaluated as: [tex]m\angle B = 30^\circ[/tex]
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A circle has a diameter of 12 centimeters. A sector of the circle is 9 square centimeters. What is the measure of the central angle whose radii define the sector?
Answer:
sector area = [central angle / 360] * PI * radius²
central angle = sector area * 360 / [PI * radius²]
central angle = 9 cm² * 360 / [3.14159 * 6²]
central angle = 28.6479139544 degrees
Source: http://www.1728.org/radians.htm
Step-by-step explanation:
The function
h
defined by
h(t) = (49 + 4. 9t)(10 – t)
models the height, in meters, of an object
t
seconds after it is dropped from a helicopter.
1. Find or approximate the time when the object hits the ground. Explain or show your
reasoning
2. From what height is the object dropped? Explain or show your reasoning.
Answer:
55555555546776546567
what is the distance between the points (4,-2) and )-5,3)?
Answer:
10.3
Step-by-step explanation:
Let the given points be the endpoints of a right triangle. The horizontal change in x is from 4 to -5 and is negative 9; the vertical change in y is from -2 to+ 3 and is +5.
The desired distance is found using the Pythagorean theorem:
d = √(9² + 5²) = √106, or 10.3 (to the nearest tength)
One angle of a triangle meaure 140°. The other two angle are in a ratio of 3:5. What are the meaure of thoe two angle
One angle of a triangle measure 140°. The other two angles are in a ratio of 3:5.The smaller angle would measure 84°, and the larger angle would measure 56°. This can be found through the use of basic trigonometry.
A triangle is a three-sided polygon with three angles that add up to 180°. Since one of the angles is already known, the remaining two angles can be calculated by subtracting 140° from 180°, which equals 40°. This 40° can then be divided by the ratio 3:5, which is 8° and 32°.
If 8° is the smaller angle, then 32° must be the larger angle. To convert 8° and 32° to the final answer of 84° and 56°, 8° must be multiplied by 10 and 32° must be multiplied by 5. This gives a total of 84° and 56° for the other two angles.
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One angle of a triangle measures 140°. The other two angles are in a ratio of 3:5. What are the measures of that two angles?
Rewrite 21/3 as a whole number
Answer:
7
Step-by-step explanation:
As we want to find the whole number, and to do so we divide the numerator by the denominator. Since we are only interested in whole numbers, we ignore any numbers to the right of the decimal point.
21/3 = 7
What is the surface area of the pyramid?
Answer:
166
Step-by-step explanation:
1) the area of triangles on the left and right sides: 2*13
2) the area of triangles on top and bottom sides: 10*12
3) the area of the rectangle in the middle: 10*2
4) Altogether: 2*13+10*12+10*2=166
What type of triangle is a 50/50 80?
50-50-80 is a Isosceles acute triangle.
An isosceles acute triangle is a triangle in which all three angles are less than 90°, and at least two of its angles are equal in measurement. One example of the angles of an isosceles acute triangle is 50°, 50°, and 80°.
Properties of Isosceles Acute Triangle
It is easy to point to an isosceles acute triangle if we know its properties. The properties of the isosceles acute triangle are noted below:
Two angles and two sides opposite those angles are equal.All three angles are less than 90° (acute angles).The summation of all the interior angles is 180°.Read more about the Isosceles acute triangle.:
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Rebecca carries a balance on her credit card each month. Today is the first day of the new, 28-day billing cycle. The current balance is x and the APR is 24%. Rebecca is buying a friend an expensive gift that cost $1,400 that she plans to put on her credit card. this will be her only purchase this month, and she will be making this purchase on the last day of the month
Part A
If her Finance charge will be $51, write and solve an equation to determine her current balance on her credit card. Show work
Part B
How much in finance charges can she save by making the purchase on the last day of the billing cycle versus the first day of the billing cycle? Explain how you determined your answer
Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the laset day of the billing cycle instead of on the first day
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The billing cycle for the month = 28 days
Current beginning balance = x
Annual percentage rate (APR) = 24%
Monthly percentage rate (MPR) = 2% (24% ÷ 12)
Purchase on the last day = $1,400
Total finance charge for the month = $51
Finance charge for the last-day purchase = $1 ($1,400 x 2% x 1/28)
Finance charge for the beginning balance = $50 ($51 - $1)
The current beginning balance, x = $2,500 ($50 ÷ 2%)
Equation for current beginning balance, x = 51 - 1 ÷ 0.02
Total finance charge for the last-day purchase = $28 ($1,400 x 2%)
Savings in finance charge by purchasing on the last day = $27 ($28 - $1)
Hence, Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the last day of the billing cycle instead of on the first day.
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What is 2 4 reflected across the Y?
The point (2, -4) is reflected across the line y = -1.
The coordinates of the image is (4, -4).
coordinates
Any of a set of numbers used in specifying the location of a point on a line, on a surface, or in space.
Coordinates are a pair of numbers which are used to determine the position of a point or a shape in a 2-dimensional plane. We define the position of a point on a 2D plane using two numbers, called the x-coordinate and the y-coordinate.
Numbers
A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.
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EMERGENCY NEED HELP PLEASE HELP THE QUESTION IS ATTACHED TO THE QUESTION THING PLEASE HELP!!!
Graph of given system of equations is shown in figure with intersection point (2, 4).
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The system of equation is,
⇒ 2x + y = 8
⇒ - x + 2y = 6
By solving both equation , we get;
⇒ (x, y) = (2, 4)
Thus, The graph of system of equation intersect on point (2, 4).
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How can you tell if a graph is linear or logarithmic?
A linear graph will have a straight line, whereas a logarithmic graph will have a curved line.
1. Look at the graph and identify the shape of the line.
2. If the line is straight, then the graph is linear.
3. If the line is curved, then the graph is logarithmic.
When looking at a graph, you can tell if it is linear or logarithmic by examining the shape of the line. A linear graph will have a straight line, whereas a logarithmic graph will have a curved line. This is due to the fact that a linear graph is plotted by plotting the points of a linear equation, whereas a logarithmic graph is plotted by plotting the points of a logarithmic equation. The linear equation is of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The logarithmic equation is of the form y = logb(x), where b is the base of the logarithm. Thus, the shape of the line will depend on the form of the equation used to plot the graph. If the line is straight, then it is a linear graph, and if it is curved, then it is a logarithmic graph.
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Solve each system by graphing
I’m looking for the answer but also a explanation of how you solved it so I can solve the other 1s without help
Answer: its hard to give an answer but read explanation
Step-by-step explanation: so the first number (1/3x) is your slope and the second number is the y-intercept (5). so for example, you're going to put positive 5 on the y-axis and because you slope is a fraction, rise/run will make you go 3 to the right and 1 up. Then you do the same with the second equation except, the slop is negative and you'll have to go down.
Use scientific notation to find the product of 7.13 • 10^-3 and 40 (help please)
Answer:
2.852 • 10⁻⁵
Step-by-step explanation:
Solve for 40(7.13 • 10⁻³)
285.2 • 10⁻³ = 2.852 • 10⁻⁵
I WILL GIVE BRAINLY! PLEASE HELP!
3x + 1 over 4y2
What is the value of the expression above when x = 3 and y = 4?
Answer:
he expression is undefined where the denominator equals
0
, the argument of an even indexed radical is less than
0
, or the argument of a logarithm is less than or equal to
0
.
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Step-by-step explanation:
JUST ONE MORE PLZ! THANK YOU BTW
Answer:
Sorry, it's actually the third one, 4.8 feet
Step-by-step explanation:
First, you divide the length of the family room tv by the length of the tv in Louise's room
5 divided by 1.5 equals 3.33
Then, you divide the width of the family room tv to get the width of Louise's tv
3 divided by 3.33 is 0.9
Now, you follow the formula for perimeter.
(0.9 + 1.5) x 2 = 4.8
The perimeter of Louise's tv is 4.8 feet.
Answer:
H. 4.8 ftStep-by-step explanation:
Similar figures have same ratio of corresponding sides.
The scale factor is:
1.5/ 5 = 3/10The width of the smaller television is:
3*3/10 = 9/10 = 0.9Perimeter:
P = 2(w + l)P = 2(1.5 + 0.9) = 4.8 ftCorrect choice is H
if you measure angle is 80 is an acute?
An auditorium has 30 seats in the first row, 38 seats in the second row, 46 seats in the third row, and so on. how many seats are in the 10th row?
a. 60
b. 93
c. 102
d. 110
Answer:
Step-by-step explanation:Its actually 102, not 110
can someone help me out!! show work and i’ll make brainliest!!
Answer:
X=3
Y=2
X=-2
Step-by-step explanation:
Since the graph appears to be moving in a straight line on the y axis
Since the graph appears to be moving in a straight line on the x axis
Since the graph on the y axis appears to be moving in a straight line.
Solve the inequality. Graph the solution.
-1/3h > or equal to 8
(step by step equation)
We can solve the inequality to get:
h ≤ -3
And its graph can be seen below.
How to solve the inequality?Here we have the following inequality:
-(1/3)*h ≥ 8
To solve the inequality, we need to isolate h.
So we can multiply both sides by -3 (notice that this will change the sign of the inequality symbol)
So we will get:
-3*(-1/3)*h ≤ -3*h
h ≤ -3
Now to graph this, we need to draw a closed circle at -3, and draw an arrow that gose to the left.
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what is the percent change from 99 to 71?
To calculate the percent change of two numbers such as 99 to 71, you use the Percent Change Formula, where a is the start value and b is the end value. When we insert a = 99 and b = 71 in the formula above, then we get the following that we can simplify and solve to get the percent change from 99 to 71.
Change ≈ -28.2828%
Brenna owns 9 T-shirts, 3 of which are red.
If Brenna randomly selects a T-shirt to wear, what is the probability it will be red?
Answer:
1/3
Step-by-step explanation:
9 Shirts, 3 are Red
Probability: 3/9
Simplify: 1/3