2. The graph of the basic quartic function m(x) = x is shown. a. The function h(x) = 3x - 6)" is a transformation of m(x). Complete the table. Reference Corresponding Points on m(x) Points on h(x) (-2, 16) (-1,1) (0,0) (1,1) (2.16) b. Graph the function h(x) = (x - 6)* on the same coordinate plane as mix). c. Is the function h(x) even, odd, or neither? Explain your reasoning.
1. The complete table is shown below.
2. The graph is attached below.
3. the function h(x) is an odd function.
What is Transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
Given:
m(x)=[tex]x^4[/tex]
and, h(x)= [tex]1/4 (x-6)^4[/tex]
So, the -6' in the h(x) there is Horizontal transformation on right side by 6 units, i.e., (x, y)--->(x +6, y)
and, 1/4 in h(x) shows there is Vertical stretch in h(x).
So, (x, y)--->(x, y/4)
Now, Points on m(x) points on h(x)
(x, y) (x+6, y/4)
(-2, 16) (4, 4)
(-1, 1) (5, 1/4)
(0, 0) (6, 4)
(2, 16) (8, 4)
2. The graph is attached below.
3. Replace h(x) by h(-x) we get
h(-x) = [tex]1/4 (x-6)^4[/tex]
h(-x) = [tex]1/4 (-x-6)^4[/tex] will give an odd function.
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Solve for y. Assume the equation has a solution for y. py + qy = -4y + 8
Answer:
y = [tex]\frac{8}{p+q+4}[/tex]
Step-by-step explanation:
py + qy = - 4y + 8 ( add 4y to both sides )
py + qy + 4y = 8 ← factor out y from each term on the left side
y(p + q + 4) = 8 ← divide both sides by p + q + 4
y = [tex]\frac{8}{p+q+4}[/tex]
The higher your credit score, the
A) lower your savings interest rate
B) higher your car loan rate
C) lower your mortgage interest rate
D) higher risk you are to a creditor
Answer: c lower your mortgage interest rate
Step-by-step explanation
The higher your credit score, the less risk you represent for a lender.
My dad taught me this.
Line JK passes through points J(–4, –5) and K(–6, 3). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b?
–21
–4
11
27
The value of b in the Line JK passes through points J(–4, –5) and K(–6, 3) is
b = –21
How to find the value of bThe graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of variable to suit the problem
y = output variable
m = slope
x = input variable
c = y intercept
The slope, m of the linear function is calculated using the points J(–4, –5) and K(–6, 3)
m = (y₀ - y₁) / (x₀ - x₁)
m = (3 + 5) / (-6 + 4)
m = (8) / (-2)
m = -4
equation passing through point K(–6, 3)
(y - y₁) = m' (x - x₁)
y - 3 = -4(x + 6)
y - 3 = -4x - 24
y = -4x - 24 + 3
y = -4x - 21
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Match The Description Below With Its Symbol(S) The Mean Of The Y-Values Select The Correct Choice Below. O A. B O B. Y O C. Y_i O D. M O E. Y_i O F. (X, Y)
The mean of y-values is referred to as [tex]\bar{y}[/tex]. So, option b is the correct choice.
A variable in a set of sample data in statistics is symbolized by the little Latin letter x. If a letter has a horizontal bar above it, it means the variable it is placed over is considered the average or mean.
We would add all of the sample data points, divide by the sample size, and then compute the x-bar, or sample mean. This is given by [tex]\bar{x}=\frac{x_1+x_2+x_3+\cdots\cdots+x_n}{n}[/tex] where n is referred to as the sample size and [tex]\bar{x}[/tex] is the sample mean.
Therefore, the central tendency of the data is represented by this [tex]\bar{x}[/tex] or the x bar. Therefore, the mean of y-values is represented by y bar or [tex]\bar{y}[/tex].
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Select the correct answer. The given equation has been solved in the table. Step Statement 1 2 3 x − 9 = − 13 2 2 3 x − 9 + 9 = − 13 + 9 3 2 3 x = − 4 4 3 2 ⋅ 2 3 x = 3 2 ⋅ ( − 4 ) 5 x = − 6 In which step was the addition property of equality applied? A. step 2 B. step 3 C. step 4 D. The addition property of equality was not applied to solve this equation.
In step 2 the addition property of equality was applied. Thus, the correct option is A.
What is addition property of equality?When the same amount is added to both sides of an equation, according to the addition property of equality, the equation remains the same. An equation that reads as A = B still holds true if a number x is added to both sides. The equation is A + x = B + x in mathematics.
When the same amount is added to both sides of an equation, the equation remains true, which is known as the addition property of equality. One of the basic characteristics of equality in mathematics, it is also very significant. The division, multiplication, and addition properties of equality are the additional characteristics.
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Full question:-
Select the correct answer. The given equation has been solved in the table. (see attachment)
(PLEASE HELP)The graph of F(x), shown below, resembles the graph of G(x)=x^2, but it has changed somewhat. Which of the following could be the equation of F(x)?
By analyzing the graph, we can see that the transformed function, F(x), is the one in option D.
F(x) = 2*x^2 + 3
Which of the following could be the equation of F(x)?On the graph, we can see the graphs of both equations, F(x) and G(x), where G(x) = x^2
First, we can see that the vertex of the quadratic of F(x) is at the point (0, 3).
So first we have a translation of 3 units upwards, we also can see that the parabola of F(x) is narrower (horizontally) than the one of G(x), then we must have a scale factor larger than 1 multiplying the function.
Then we have something like:
F(x) = k*G(x) + 3 = k*x^2 + 3
Where k > 1.
The only option that has this form is option D.
F(x) = 2*x^2 + 3
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Brenna is considering which brand of cereal to buy. She knows some brands contain a lot of sodium, or salt, which she is trying to avoid. Crispee Flakes has 0.23 grams of sodium per cup. Corn Puffers has 0.28 grams of sodium per cup. Energy Doodles has 0.26 grams of sodium per cup.
How many of the brands have less than 1\4
of a gram of sodium per cup?
Using mathematical operations, we can say that only 1 brand has less than 1/4 grams of sodium per cup which is Crispy Flakes.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.
The operation's arity is determined by the number of operands.
Basic arithmetic operations or calculations, such as addition, subtraction, multiplication, and division, are covered in Fundamentals of Mathematics and are concepts we learn in primary school.
Students will eventually study fundamental ideas like algebra, geometry, factors, ratios, etc. in upper classes.
So, we have that:
Crispy Flakes have 0.23 grams of sodium per cup.
Corn Puffers have 0.28 grams of sodium per cup.
Energy Doodles have 0.26 grams of sodium per cup.
Now, brands that have less than 1/4 gram of sodium per cup:
100 * 1/4 = 25
Then, 1/4 of 1.00 = 0.25
0.23 > 0.25
Therefore, using mathematical operations, we can say that only 1 brand has less than 1/4 grams of sodium per cup which is Crispy Flakes.
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22. Represent Real-World Problems The railroad
tracks meet the road as shown. The town will
allow a parking lot at angle Jif the measure of
angle Jis greater than 38: Can a parking lot be
built at angle? Why or why not?
++++
Green
50°
Park
Ave.
Ave.
On observing the provided question, we can say that the the provided equation f(x) = is the basic cubic function.f(x) = 8100
What is function?An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable). A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.
basic cubic function is = f(x) = x^2
x = 90
f(x) = 8100
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On solving the provided question, we can say that It is possible to construct a parking lot since the angle J's measurement is 180 - (50 + 90) = 40. More than 38 degrees, 40 degrees.
what are angles?An angle is a form in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a point in the middle known as the angle's vertex. In the plane where the rays are placed, two rays can produce an angle. An angle is also produced when two planes intersect. They're known as dihedral angles. In plane geometry, an angle is the form that two rays or lines with a common termination might take. The Latin word "angulus," which means "horn," is where the English word "angle" comes from. The two rays, also known as the sides of the angle, have a common termination known as the vertex.
It is possible to construct a parking lot since the angle J's measurement is 180 - (50 + 90) = 40. More than 38 degrees, 40 degrees.
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Figure R was rotated about the center shown by 180 Degrees.
Which figure is the image of R?
The rotation of figure R about its center will produce the image of R as given in option C.
Rotation of solid figures.Rotation is a type of rigid transformation which involves turning a given figure or object at a an angle about a reference point to produce an image. This process can be used to explain the question given.
Some other types of rigid transformation are; dilation, translation, reflection.
Dilation implies either increasing or decreasing the dimensions of a given object.Translation requires moving a given object in a specific direction and units. Reflection involves turning a given object about a reference point or line.All these have their distinct procedures and would be applied as expected or stated in the question.
When figure R is rotated about the center at 180 degrees, it would produce an image of R as shown in option C.
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Use the number line below, where RS=4y+4, ST=3y+8, and RT=54.
a. What is the value of y?
b. Find RS and ST.
The value of y is 6 and the length of RS and ST are 28, 26 respectively.
What is a line ?
line is a straight one dimensional figure having no thickness is called as the line.
Given , number lines
RS = 4y+4
ST = 3y+8
RT = 54
From the given figure ,
RS+ST = RT
4y+4+3y+8 = 54
7y+12 = 54
7y = 54-12
7y = 42
y =42/7
y = 6
The RS = 4y+4 = 4*6+4 = 28
ST = 3y+8 = 3*6+8 = 26
Hence, The value of y is 6 and the length of RS and ST are 28, 26 respectively.
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You spend 100 minutes in 2 classes. How many minute will you spend in 3 classes?
Answer:150
Step-by-step explanation:
Answer:
150
Step-by-step explanation:
since half of 100 is 50, 2 classes will have 50 minutes. If you add 100+50 you get 150. So therefore ur answer is 150!
Lara puts pictures of the same size on each page in a scrapbook.
. She has 48 large pictures, and each page can fit 3 large pictures.
. She has 24 small pictures, and each page can fit 6 small pictures.
Which equation shows how to find p, the greatest number of pages Lara can fill in the scrapbook?
OA. 48 24+6÷3=p
OB. 48-6 +24÷3=p
OC. 48 x 3 + 24 x 6=p
OD.
48+3+24+6=p
Reset
Next
Answer:
d
Step-by-step explanation:
I think the a answer is d
Recall the equation for a circle with center (h, k) and radius r. At what point in the first quadrant does
the line with equation y = x + 1 intersect the circle with radius 4 and center (0, 1)?
The point of intersection of the line [tex]y = x + 1[/tex] and the circle with radius 4 and center [tex](0,1)[/tex] is [tex](x, y) = (-1, 0)[/tex] which is in the first quadrant.
How to find the point in the first quadrant?The equation of a circle with center (h, k) and radius r is:
[tex](x - h)^2 + (y - k)^2 = r^2.[/tex]
The equation of the line is given as [tex]y = x + 1[/tex].
Given the center of the circle is (0,1) and the radius is 4, the equation of the circle is [tex](x-0)^2 + (y-1)^2 = 4^2[/tex]
This can be simplified as [tex]x^2 + y^2 - 2y + 1 = 0[/tex]
Now we can substitute [tex]y = x + 1[/tex] in the circle equation:
[tex]x^2 + (x+1)^2 - 2(x+1) + 1 = 0\\x^2 + x^2 + 2x + 1 + 2x + 1 = 0\\2x^2 + 4x = -2\\x^2 + 2x = -1\\(x+1)^2 = 0\\x = -1[/tex]
Now that we have the value of x, we can substitute it in the equation [tex]y = x + 1[/tex] to find the corresponding y value:
[tex]y = -1 + 1\\y = 0[/tex]
So, the point of intersection of the line [tex]y = x + 1[/tex] and the circle with radius 4 and center (0,1) is [tex](x, y) = (-1, 0)[/tex] which is in the first quadrant.
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A map of a rectangular park has a length of 4 inches and a width of 6 inches. It uses a scale of 1 inch for every 30 miles.
What is the actual area of the park? Show how you know.
The map needs to be reproduced at a different scale so that it has an area of 6 square inches and can fit in a brochure. At what scale should the map be reproduced so that it fits on the brochure? Show your reasoning.
Answer:
Step-by-step explanation:
L = 4 in real life = 4*30 =120 miles
W=6 in real life =6*30=180 miles
actual area = 120*180 = 21600sq miles
to fit into a 6sq in paper it'll need to shrink to 2x3 inches, 1/2 of what it was before, so the scale becomes 1" for every 60miles.
A nurse sets an intravenous
fluid drip rate at 1000 mL
every 8 hr. How much fluid would the patient receive in
3 hr? Step by step (applications of rational equations)
Answer:
375 mL
Step-by-step explanation:
Let x = Amount of fluid patient receives in 3 hours
Fluid drip rate: 1000 mL --------- 8hr
x --------- 3 hr
Cross multiplication is applied:
(x).(8 hr) = (1000 mL).(3hr)
x = [(1000mL).(3 hr)]/ (8 hr)
x = 375 mL
tarren estimates that the product of 10 and 4 is about 120. Is his answer reasonable?
No, His answer is not reasonable.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Tarren estimates that the product of 10 and 4 is about 120.
Now, We know that;
The product of 10 and 4 is,
⇒ 10 × 4 = 40
Thus, His answer is not reasonable.
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Please please please answer
98 degrees
50 degrees
60 degrees
88 degrees
On using the exterior angle theorem the value of ∠G is obtained as option D: 88 degrees.
What is exterior angle theorem?
The measure of an exterior angle is equal to the sum of the measures of the two opposite(remote) interior angles of the triangle, according to the external angle theorem.
The measure of ∠F = (6x - 10)°
The measure of ∠E = 38°
The measure of ∠G = (7x + 18)°
But, in the given image it can be seen that the ∠G lies outside the triangle.
Apply the exterior angle theorem to solve the value for x.
According to the exterior angle theorem, the equation will be -
∠F + ∠E = ∠G
Substitute the values into the equation -
(6x - 10)° + 38° = (7x + 18)°
Simplify the equation -
6x - 10 + 38 = 7x + 18
Collect the like terms -
6x - 7x = 18 + 10 - 38
-x = -10
x = 10
So, the value of x is obtained to be 10°.
Substitute the value of x in ∠F and ∠G -
∠F = (6x - 10)°
∠F = (6(10) - 10)°
∠F = (60 - 10)°
∠F = 50°
∠G= (7x + 18)°
∠G= (7(10) + 18)°
∠G= (70 + 18)°
∠G= 88°
Therefore, the values of angles are ∠F = 50° and ∠G= 88°.
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8.9 math question A train makes a round-trip from New Orleans to Los Angeles the train stops in Tucson during its return how many miles has the train traveled in all how many miles does the train have left to travel
When the train stops at Tucson in return trip, distance he travelled is 2378 miles and distance left for the train to travel is 1408 miles
What is distance?Distance is a measure of how far away two objects or points are from one another. In physics or daily life, the term "distance" can refer to a physical distance or an estimate based on other criteria (for example, "two counties over").
|AB| can be used to denote the distance between two points. In most situations, the distance from point B to point A can easily be used in place of the distance from point A to point B.
A distance metric or function is a way to explain what it means for elements of a space to be "far apart from" or "close to" each other. It is a generalisation of the idea of physical distance in mathematics.
If the train stops at Tucson in return trip, distance he travelled is,
d = 1893 + (1893 - 1408)
d = 2378 miles
And, miles the train have left to travel is
⇒ 1893 + 1893 - 2378
= 3786 - 2378
= 1408 miles
Thus, When the train stops at Tucson in return trip, distance he travelled is 2378 miles and distance left for the train to travel is 1408 miles.
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1
1
the graph.
a. y = 3x - 2
b. y = 3x-2
c. y = 3x+2
d. y = 3x + 2
e. y = ( )* - 2
Answer:
e
Step-by-step explanation:
A person invested $230 in an account growing at a rate allowing the money to double
every 7 years. How long, to the nearest tenth of a year would it take for the value of
the account to reach $390?
It would take 28.6 years for the value of the account to reach $390.
The equation reads A(t) = Ao (2) Where
A(t) = 3902, Ao = 230, and t =?, k = 7 years
Hence, 3902 = 230 × (2)
^t/7
We divide 230 on both sides (3902/230 = 230) (2)
^t/7/230
16.965217391 = (2) (2)
^t/7
Calculate the ln of both sides:
16.965217391 = ln (2)t/7
ln 16.965217391 = t/7 ln (2) (2)
In 16.965217391/ln 2 = t/7
t = 4.0874628413× 7
t = 28.612239889 years
Approximately = 28.6 years
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The height of △XYZ is the distance from point Yto XZ←→. Find the area of the triangle. Round your answer to the nearest tenth, if necessary.
The area of a rectangular floor is 80 square feet. The length of the floor is 2 feet less than the width of the floor.
What is the width of the floor?
Drag the answers into the boxes to correctly complete the statements.
The equation
floor is
8
10
40
feet.
78
, where w is the width of the floor in feet, can be used to solve this problem. The width of the
√78
√82
w²+2=80
w(w - 2) = 80
w²2=80
w(w + 2) = 80
Answer:
Step-by-step explanation: Umm multiply 80 by 2 and divied 78 after add 10
????What’s the answer??
one of the most common forms of the equation of lines called slope-intercept form along with derivation.
What is the slope-intercept for the linear function?The linear equation y = mx + c is a line with m as slope, m and c as the y-intercept. This form of the linear equation is called the slope-intercept form, and the values of m and c are real numbers.
The slope, m, represents the steepness of a line. The slope of the line is also termed as gradient, sometimes. The y-intercept, b, of a line, represents the y-coordinate of the point where the graph of the line intersects the y-axis.
We know that, the equation of a line in point slope form, where (x1, y1) is the point and slope m is:
(y – y1) = m(x – x1)
Here, (x1, y1) = (0, c)
Substituting these values, we get;
y – c = m(x – 0)
y – c = mx
y = mx + c
Therefore, the point (x, y) on the line with slope m and y-intercept c lies on the line if and only if y = mx + c
Slope Intercept Form Formula
As derived above, the equation of the line in slope-intercept form is given by:
y = mx + c
Here,
(x, y) = Every point on the line
m = Slope of the line
c = y-intercept of the line
Usually, x and y have to be kept as the variables while using the above formula
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Every day your heart creates enough energy to drive a truck for 32 kilometers. If you combined the energy created all the students in your math class for a week, how many meters could the truck drive?
PLEASE WRITE IN FULL SENTENCE AND SHOW FULL SHOW!!!
If we assume that each student's heart creates the same amount of energy as a single person, the energy created would be enough to drive the truck for 192000 meters.
How to do the calculations?If we assume that each student's heart creates the same amount of energy as a single person, we can estimate the total amount of energy created by the class.
If one person's heart creates enough energy to drive a truck for 32 kilometers,
Then six people's hearts would create enough energy to drive the truck for 32 x 6 = 192 kilometers.
In meters, it would be 192 x 1000 = 192000 meters.
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Every day your heart creates enough energy to drive a truck for 32 kilometers. If you combined the energy that is created by all the students in your math class for a week, how many meters could the truck drive?
Number of students is 6
-1/3x-9>1.5-4/5x
solve the inequality
Answer: x belongs to (0, 0.4444)
Step-by-step explanation:
PLEASE HELP! Determine the domain and range of the relation graphed below. Enter your answers using interval notation.
The domain and the range of the graphed relation are given as follows:
Domain: (-4,6).Range: [-6, 4).How to obtain the domain and the range of the function?The domain of a function is composed by the set that contains all possible values assumed by the input of the function. Hence, considering the graph of the function, the domain is given by the values of x of the graph.
As the graph contains open circles at both the ends of the domain, the domain is composed by an open interval.
The range of a function is composed by the set that contains all possible values assumed by the output of the function. Hence, considering the graph of the function, the range is given by the values of y of the graph.
The graph assumes a minimum value of -6, hence the lower bound is closed, however the upper bound at y = 4 is open, as the only point the graph reaches y = 4 is on the open circle.
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which of the following tests analyze the difference between the means of two independent samples?
a. Correlated T Test
B. T test for independent groups
c. sign test
d. all the above
T-test for independent groups analyzes the difference between the means of two independent samples. Hence, option B is the correct answer.
B. T-test for independent groups is the test that analyzes the difference between the means of two independent samples. This test assumes that the two samples are drawn from populations that have normal distributions and that the variances of the two populations are equal. The T-test for independent groups compares the means of the two samples and determines if there is a statistically significant difference between them. This test is also known as a two-sample T-test or independent T-test.
The other options A and C are not the correct ones.
A. Correlated T-Test is used when comparing means of dependent samples, it's also known as a dependent t-test
C. Sign test is a non-parametric test that is used to compare two dependent samples.
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Consider the following integral Sketch its region of integration in the xy-plane. Double integrate x/ln(x) dxdy (a) Which graph shows the region of integration in the xy-plane?____
(b) Write the integral with the order of integration reversed: Double integrate x/ ln(x) dx dy = double integrate x/ ln(x) dy dx with limits of integration A= D B= A C= D= (c) Evaluate the integral
a. Sketch the region of integration in the XY-plane.
b. Reverse the order of integration.
c. Evaluate the integral.
(a) The integral is a double integral, which means that the region of integration is a region in the XY plane. The region of integration is defined by the limits of integration for x and y. However, since the limits of integration are not given, it's not possible to sketch the region of integration in the XY plane.
(b) The integral is already written with the order of integration reversed.
(c) Without the limits of integration, it is not possible to evaluate the integral. The limits of integration are necessary to determine the region of integration, and thus the range of values for x and y over which the integral is to be taken. Without this information, it is not possible to carry out the evaluation of the integral.
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A sample proportion of 0.62 is found. To determine the margin of error for this statistic, a simulation of 200 trials is run, each with a sample size of 100 and a point estimate of 0.62.
The minimum sample proportion from the simulation is 0.73, and the maximum sample proportion from the simulation is 0.97.
What is the margin of error of the population proportion using an estimate of the standard deviation?
A simulation of 200 trials is run, each with a sample size of 100 and a point estimate of 0.62=0.08 to establish the margin of error for this statistic.
What is margin of error?Your results will vary from the actual population value by how many percentage points, as indicated by the margin of error.
A 95% confidence interval with a 4% margin of error, for instance, indicates that your statistic will, 95% of the time, be within 4% of the true population figure.
However, the official definition goes a little bit beyond. The range of values in a confidence interval that lie below and above the sample statistic is known as the margin of error.
The confidence interval is a tool for displaying the level of uncertainty surrounding a certain statistic (i.e. from a poll or survey).
According to our question-
Because the sample proportions' range is 0.97-0.73 = 0.24
Calculate the standard deviation:
Range = 6* (s-bar)
= 0.24
s-bar = 0.04
S/Sqrt (100) then equals 0.04
and s = 0.4
S.D = 0.04 + 0.04
= 0.08
Hence, A simulation of 200 trials is run, each with a sample size of 100 and a point estimate of 0.62=0.08 to establish the margin of error for this statistic.
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