consider the function f(x) = x^1/2 and the function G, shown below. g(x)= f(1/4 • x) = (1/4 •x)^1/2how will the graph of the function g differ from the graph of the function f?
Answers
ANSWER
The graph of function g is the graph of function f stretched horizontally by a factor of 4.
EXPLANATION
Function g(x) is a transformation of function f(x), obtained by multiplying the variable, x, by 1/4. This is described as a horizontal stretch by a factor of 4.
Hence, the graph of function g is the graph of function f stretched horizontally by a factor of 4.
Related Questions
You need a shelf for a small space in your house, so you make a measurement with your meter stick and head to the store. Once there, you find that the dimension of the shelves you want is given in cm.If your space measured 0.9 m, and the shelves at the store measure 30 cm, answer the following questions:1) How many meters wide is the shelf you want to buy?
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We will have the following:
[tex]0.9m=90cm[/tex]So, the number of shelves you need is 3.
Thus, the shelves you can buy are 0.3 m long each.
What are inequality? When do we use inequalities?What type of inequalities are there? Which symbols are used for each type?Are the following expressions variable inequalities? Why?a. 13z=27b. x<0c 3x+5x>11d. y+5≤11e. 7-1>- 32
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Inequalities are expressions that refer to non-equivalent quantities. Inequalities can express less than, more than, less than or equal to, more than or equal to.
The type of inequalities and symbols are:
[tex]<,>,\leq,\ge[/tex]So, there are four types of inequalities, for example:
[tex]\begin{gathered} x<2 \\ x>2 \\ x\leq2 \\ x\ge2 \end{gathered}[/tex]Each inequality is different from the other, this means that the symbol used represents a type of inequality.
At last, among the choices, the inequalities are
[tex]\begin{gathered} x<0 \\ 3x+5x>11 \\ y+5\leq11 \\ 7-1>-32 \end{gathered}[/tex]However, variable inequalities mean that the inequalities must have a variable in it. So, they are:
[tex]\begin{gathered} x<0 \\ 3x+5x>11 \\ y+5\leq11 \end{gathered}[/tex]Therefore, the variable inequalities are b, c, and d.
find the coordinates of the vertex of the following parabola algebraically. write your answer as an (x,y) point..y=x²+9
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using the parabola formula:
y = a(x-h)² + k²
vertex = (h, k)
We are given a parebola equation of: y = x²+9
comparing both equations to get the vertex:
y = y
a = 1
(x-h)² = x²
x² = (x + 0)²
(x-h)² = (x + 0)²
h = 0
+k = +9
k = 9
The vertex of the parabola as (x, y): (0, 9)
Aaron took out a 30-year mortgage for $70,000. His monthly mortgage payment is $466. How much will he pay over 30 years? Interest rate = 7%
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Answer:
[tex]\text{ \$167,760}[/tex]Explanation:
Here, we want to get how much will be ppaid over the course of 30 years
From the question, we have it that he pays $466 monthly
Now, to get the amount he will pay over the course of the years, we have to understand that there are 12 months in a year
The total number of months for which he will be paying will be:
[tex]30\times\text{ 12 = 360}[/tex]He will be paying $466 per month for a total of 360 months
So, the total amount he is to pay is the product of this two
Mathematically, that would be:
[tex]360\times466\text{ = 167,760}[/tex]The function c = 100+.30m represents the cost c (in dollars) of renting a car afterdriving m miles.How many miles would a customer have to drive for the cost to be $149.50?
Answers
149.5 = 100 + .30m
149.5 - 100 = .30m
49.5 = .30m
Divide both sides by 0.30
m = 49.5/0.3
m =165
Option D
A rock has a mass of 14 g and a volume of 2 cm3. What is the density of the rock? *
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We will determine the density of the rock as follows:
[tex]\rho=\frac{14g}{2cm^3}\Rightarrow\rho=7g/cm^3[/tex]So, the density of the rock is 7 g/cm^3.
What is the value of the expression below when w = 3?5W^2 – 5W – 8
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According to the given data we have the following expression:
5W^2 – 5W – 8
In order to calculate the value of the expression above when w=3 we would need to substitute the w with 3 and then calculate the expression.
So, if w=3 then:
5(3)^2 -5(3) -8
=45 - 15 -8
=22
The value of 5W^2 – 5W – 8 when w = 3 would be 22
Freiese Um Which of the following is the graph of F(x) = 3x2 ?
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To determine which is the graph of the function we can give some values to x to find point through the graph.
If x=0 then we have:
[tex]\begin{gathered} F(0)=3(0)^2 \\ F(0)=0 \end{gathered}[/tex]This means that the graph passes through the point (0,0).
If x=1 then we have:
[tex]\begin{gathered} F(1)=3(1)^2 \\ F(1)=3(1) \\ F(1)=3 \end{gathered}[/tex]This means that the graph passes through the point (1,3)
If x=-1 then we have:
[tex]\begin{gathered} F(-1)=3(-1)^2 \\ F(-1)=3(1) \\ F(-1)=3 \end{gathered}[/tex]This means that the graph passes through the point (-1,3)
Hence we conclude that the graph has to pass through the points (0,0) (1,3) and (-1,3)
Looking at the graphs given we notice that the third graph fullfils these condition; therefore, the graph of the function is shown in option C
NO LINKS!! Show all work where necessary to get full credit Part 2
Answers
21. Circle R
A circle is named using its center.22. RV
A radius connects the center to a point on the circle.23. ZV
A chord connects two points on the circle.24. TX
A diameter passes through the center of the circle and connects two points on the circle.25. RV
See 22 and 24.26. 4 feet
The diameter is twice the radius, 2(2)=4.Answer:
21. R
22. RU
23. VZ
24. BE
25. RU
26. 4 feet
Step-by-step explanation:
Question 21
A circle is named by its center.
Therefore the name of the given circle is R.
Question 22
The radius of a circle is a straight line segment from the center to the circumference.
Therefore, the radii of the given circle are:
RZ, RT, RU, RV, RW and RX.Question 23
A chord is a straight line segment joining two points on the circumference of the circle.
Therefore, the chords of the given circle are:
WZ, TX and VZ.Question 24
The diameter of a circle is the width of the circle at its widest part. It is a straight line segment that passes through the center of the circle and whose endpoints lie on the circumference.
Therefore, the diameters of the given circle are:
TX and WZ.Question 25
As the diameters are TX and WZ, they contain the radii RZ, RT, RW and RX.
Therefore, the radii that are not contained in the diameter is:
RU and RV.Question 26
The diameter is twice the length of the radius.
Therefore, if the radius of the circle is 2 feet:
⇒ Diameter = 2 × 2 = 4 feet.
Which of the following are rational numbers?A) 42/91B) 10.27C) 8.14 D) 0
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It's important to know that a rational number can be expressed as fractions, but also when they are expressed as decimals, the decimal part repeats infinitely, that is, it has a pattern or finite decimal digits.
Having said that, we can deduct that all the answer choices are rational numbers.This graph shows the amount of rain that falls in a given amount of time.
What is the slope of the line and what does it mean in this situation?
A line graph measuring time and amount of rain. The horizontal axis is labeled Time, hours, in intervals of 1 hour. The vertical axis is labeled Amount of rain, millimeters, in intervals of 1 millimeter. A line runs through coordinates 2 comma 5 and 4 comma 10.
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It is to be noted that the slope of the line is 5/2. This means that 5 mm of rain falls every 2 hours. See the calculation below.
What is a slope in math?In general, the slope of a line indicates its gradient and direction. The slope of a straight line between two locations, say (x₁,y₁) and (x₂,y₂), may be simply calculated by subtracting the coordinates of the places. The slope is often denoted by the letter 'm.'
To find the slope of the line in the graph, we use the following equation:
m = [y₂ - y₁]/[x₂-x₁]
Where (x1,y1) = coordinates of the first point in the line; and
(x₂,y₂) = coordinates of the second point in the line
Given that the points (2, 5) from the graph is (x₁, y₁) and the point on graph (4, 10) are (x₂,y₂) Hence,
m = [10-5]/[4-2]
The slope (m) = 5/2
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Full Question:
This is the complete question and the described graph is attached
This graph shows the amount of rain that falls in a given amount of time.
What is the slope of the line and what does it mean in this situation?
Select from the drop-down menus to correctly complete each statement
The slope of the line is ___
This means that ___ mm of rain falls every ___
28 * 81.5 can you help me
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so the answer is 2282
A bag contains 8 red marbles, 2 blue marbles, 5 white marbles, and 7 black marbles. What is the probability of randomly selecting:A white marble:A red marble:A red marble, white or blue marble: A black marble: A green marble:
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Which is an equivalent expression for 4 times d raised
to the negative third power all over quantity 18 times d
raised to the ninth power end quantity?
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Answer:
2d⁻³/9d⁻⁹
Step-by-step explanation:
4 times d raised to the negative third power = (4 × d)⁻³ = 4d⁻³
18 times d raised to the ninth power = (18 × d)⁻⁹ = 18d⁻⁹
the equation as a quotient:
Expression = 4d⁻³/18d⁻⁹
Expression = 2d⁻³/9d⁻⁹
There are 16 appetizers available at a restaurant. From these, Pablo is to choose 12 for his party. How many groups of 12 appetizers are possible?
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EXPLANATION
This is a combinatory, as there are 12 groups, the combinatory will be as follows:
16C12 = 16!/[12!*(16-12)!] = 1820
In conclusion, there will be 1820 possible groups of 12 appetizers.
Consider the parabola given by the equation: f ( x ) = − 2 x 2 − 12 x − 9 Find the following for this parabola: A) The vertex: B) The vertical intercept is the point C) Find the coordinates of the two x intercepts of the parabola and write them as a list of points of form (x, y) separated by commas: It is OK to round your value(s) to to two decimal places.
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Answer:
it is C) find the coordinated of two x intercept is
Find the volume of a cone. Round your answer to the nearest wholenumber.7 ft4 ft
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Answer:
117 cubic feet
Explanation:
From the diagram:
• The radius of the cone, r = 4 ft
,• The perpendicular height, h = 7 ft
[tex]\text{Volume of a cone=}\frac{1}{3}\pi r^2h[/tex]Substitute the given values:
[tex]\begin{gathered} V=\frac{1}{3}\times\pi\times4^2\times7 \\ =117.2ft^3 \\ \approx117\; ft^3 \end{gathered}[/tex]The volume of a cone is 117 cubic feet (to the nearest whole number).
Wich situation can be represented by 3 + 3s =5s - 7
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3 + 3s = 5s - 7
A. Three times a number increased by 3 ( can be represented by 3s + 3 ) is the same as ( = ) five times a number decreased by 7 ( can be represented by 5s -7 ). 3s + 3 = 5s - 7
Answer: A
Vincent turned his head 30° to the side. Which of the following shows the angle that he turned his head?
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Given data:
Vincent turned his head 30° to the side.
The figure in the option b is the angle that he turned his head.
Last year, Trey opened an investment account with $8800. At the end of the year, the amount in the account had decreased by 6.5%. How much is this decrease in dollars? How much money was in his account at the end of last year?Decrease in amount:$Year-end amount:$
Answers
ANSWER
[tex]\begin{gathered} decrease=572 \\ Year-end\text{ amount=8228} \end{gathered}[/tex]EXPLANATION
Initial amount is $8800
percentage decrease is 6.5%
Decrease amount (in dollars );
[tex]\begin{gathered} \frac{6.5}{100}\times8800 \\ =6.5\times88 \\ =572 \end{gathered}[/tex]The amount of money in the account at the end of last year= Initial amount - decrease
[tex]\begin{gathered} A=8800-572 \\ =8228 \end{gathered}[/tex]Decrease in amount: $572
Year-end amount: $8228
The coordinate pairs for triangle ABC are A(1,2), B(4,5), C(2,2). It undergoes a translation of 2 units right and 1 unit 1 up. Write down the coordinates of A'
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We will have the transformation rule (x, y) -> (x+2, y+1)
Then, for A' we will have:
A'(3, 3)
B'(6, 6)
C'(4, 3)
what is the value of x of the perimeter of the following figure is 30 miles?
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The Solution:
Given:
We are required to find the value of x if the perimeter is 30 miles.
[tex]Perimeter=2(3x-8)+2(6x+5)=6x-16+12x+10=30[/tex][tex]\begin{gathered} 6x+12x-6=30 \\ \\ 18x=30+6 \\ \\ 18x=36 \end{gathered}[/tex]Divide both sides by 18.
[tex]\begin{gathered} x=\frac{36}{18}=2 \\ \\ x=2 \end{gathered}[/tex]Therefore, the correct answer is 2.
I don't understand this. Proving and applying ASA and Salad congruence
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Given two triangles, we can say that they are congruent by the SAS postulate (Side Angle Side) if both triangles have two congruent sides and the angle that they form is also congruent
In this case, we have that triangle IHG and DFE have already two congruent sides, then, to make them congruent, the angle that they each form (angle IHG and angle DEF) must be congruent so we can use the SAS postulate
Jocelyn graphs a linear function that passes through three distinct points: A, B, and C. The coordinates ofpoint A (-3, -3) and point C (3,5) are shown.What are the possible coordinates of point B for Jocelyn’s linear function?
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(0,1) is a possible coordinite through the points (-3,-3), (3,5)
a triangular lot is 130 ft on one side and has a property line of length 700 ft. Find the area of the lot in acres.
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Area of the lot = 1.03 acres
Explanations:The line length of the triangular lot = 700 ft
The height of the triangular lot = 130 ft
Note:
Area of a triangle = 0.5 x base x height
Calculate the base of the triangular lot using the Pythagora's theorem
[tex]\begin{gathered} \text{Length}^2=Height^2+Base^2 \\ 700^2=130^2+Base^2 \\ \text{Base}^2=700^2-130^2 \\ \text{Base}^2\text{ = }490000\text{ - }16900 \\ \text{Base}^2\text{ = }473100 \\ \text{Base = }\sqrt[]{473100} \\ \text{Base = }687.82 \end{gathered}[/tex]The base of the triangular lot = 687.82 ft
Area of the triangular lot = 0.5 x 687.82 x 130
Area of the triangular lot = 44708.3 ft²
NB
1 ft² = 2.3 x 10^(-5) Acres
44708.3 ft² = 44708.3 x 2.3 x 10^(-5)
44708.3 ft² = 1.03 acres
Therefore:
Area of the lot = 1.03 acres
Type a counter example that would have to exist in order for the conclusion to be false.5>0,6> 0.12 > 0,16 > 0,20 > 0,100 > 0.Conclusion: All numbers are greater than 0.Counterexample: ?
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Here, we want to give a counter example which would exist to make the conclusion wrong.
To do this, we have to get the values which are in actual terms lesser in value to zero. These values include the negative integers i.e negative whole numbers. On the number line, these values exist before zero, to the left handside of the number line.
Examples of these values include -5, -4 , -3 , -2 etc
So the counter example can be in the form;
-3 < 0 , -5 < 0 , -2 < 0
With these set of examples, we have made the conclusion false.
PLEASE HELP!!
Write an equation of a quadratic function with the given properties: f(3)=f(-5)=0; f(-6)=-36
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The equation for a quadratic function with given properties is, f(x) = -201.5 (x² +2x - 15)
Given,
f(3) = f(-5) = 0;
f(-6) = -36
Here,
The x intercepts of the quadratic equation are;
x₁ = 3 , x₂ = -5
The quadratic equation in factored form is equal to
f(x) = a(x - x₁) (x - x₂)
Substitute x₁ = 3 , x₂ = -5 in f(x)
Then,
f(x) = a(x - 3) (x - -5)
f(x) = a(x - 3) (x + 5)
We have;
f(-6) = -36
That is, if x = -6 then f(x) = -36
So,
f(x) = a(x - 3) (x + 5)
-6 = a(-36 - 3) (-36 + 5)
-6 = a x - 39 x - 31
-6 = 1029a
a = -1029/6
a = -201.5
Here,
f(x) = -201.5(x - 3) (x + 5)
Apply distributive property;
f(x) = -201.5(x² +5x - 3x - 15)
f(x) = -201.5 (x² +2x - 15)
That is,
The equation for a quadratic function with given properties is, f(x) = -201.5 (x² +2x - 15)
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Find the next two terms in this sequence. 1 3 7 15 [?] 2'4'8' 16' T'I
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We will solve as follows:
*First: We identify the pattern, that is:
[tex]\frac{3}{4}-\frac{1}{2}=\frac{1}{4}[/tex][tex]\frac{7}{8}-\frac{3}{4}=\frac{1}{8}[/tex][tex]\frac{15}{16}-\frac{7}{8}=\frac{1}{16}[/tex]From this, we can see tat the pattern follows the rule:
[tex](\frac{1}{2})^{n+1}[/tex]So, the next terms of the sequence will be:
[tex]\frac{15}{16}+(\frac{1}{2})^{4+1}=\frac{31}{32}[/tex]And the next one is:
[tex]\frac{31}{32}+(\frac{1}{2})^{5+1}=\frac{63}{64}[/tex]And those are the next two terms of the sequence.
Liam's monthly bank statement showed the following deposits and withdrawals.If Liam's balance in the account was $62.45 at the beginning of the month, what was the account balance at the end of the month?
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First, let's take the inital balance and add all the deposits:
[tex]62.45+32.35+63.09+98.79=256.68[/tex]Then, we'll take this amount and substract all the withdrawals:
[tex]256.68-114.95-79.41=62.32[/tex]This way, we can conclude that the account balance at the end of the month was $62.32
The perimeter of a rectangular poster is 14 feet and the length is 4 feet. Describe how to use the perimeter formula to find the width.This calculator has a tray why the answer is not 3.2
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Explanation
We are told that the perimeter of a rectangular poster is 14 feet and the length is 4 feet.
Perimeter simply means the total sum of all the sides of the rectangle
[tex]\begin{gathered} From\text{ the above} \\ let\text{ the length = y} \\ width\text{ =x} \end{gathered}[/tex]So, the perimeter is
[tex]x+x+y+y=2x+2y[/tex]Since the perimeter is 14 then
[tex]2x+2y=14[/tex]Also, the length is 4 feet
Therefore y = 4, so that
[tex]\begin{gathered} 2x+2(4)=14 \\ 2x+8=14 \\ collecting\text{ like terms} \\ 2x=14-8 \\ 2x=6 \end{gathered}[/tex]Making x the subject of the formula
[tex]\begin{gathered} x=\frac{6}{2}=3 \\ \\ x=3 \end{gathered}[/tex]Therefore, the width of the rectangle is 3 feet
The rectangle is
[tex]4+3+4+3=14[/tex]
