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
Give the equation of the line parallel to a line through (-3, 4) and (-5, -6) that passes through the origin. y = 5x y = 5x + 1 y=-1/5x + 1 y = -1/5x y
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To solve for the equation of the line parallel :
[tex]\begin{gathered} (-3,4)\Longrightarrow(x_1,y_1) \\ (-5,-6)\Longrightarrow(x_2,\text{y}_2) \end{gathered}[/tex]For parallel line equation:
Slope-intercept form: y=mx+b, where m is the slope and b is the y-intercept
First let's find the slope of the line.
To find the slope using two points, divide the difference of the y-coordinates by the difference of the x-coordinates.
[tex]\begin{gathered} \text{slope =}\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{-6-4}{-5--3} \\ \text{slope=}\frac{-10}{-5+3}=\frac{-10}{-2} \\ \text{slope =5} \end{gathered}[/tex]Slope= 5
[tex]\begin{gathered} y=mx+c \\ y=5x+c \\ \text{where c = y-intercept} \end{gathered}[/tex]The y-intercept is (0, b). The equation passes through the origin, so the y-intercept is 0.
[tex]\begin{gathered} y=5x+0 \\ y=5x \end{gathered}[/tex]Hence the
Suppose that the future price p(t) of a certain item is given by the following exponential function. In this function, p(t) is measured in dollars and t is the number of years from today. p(t) = 3000 * (1.019) ^ t
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The growth or decay of an original quantity C that increases or decreases in a p% per year after t years is given by the following equation:
[tex]p(t)=C\cdot(1\pm\frac{p}{100})^t[/tex]If the quantity increases (i.e. it growths) we use the + symbol inside the parenthesis. If the quantity decreases we use the - symbol. This implies that for a growth the term that is raised to t is greater than 1 and for a decay that term is smaller than 1.
Now let's compare that generic equation with the function given by the question:
[tex]3000\cdot(1.019)^t=C\cdot(1\pm\frac{p}{100})^t[/tex]One of the first things you can notice is that C=3000 which means that the initial price was $3000. Just to be sure that this is correct we can evaluate p(t) at t=0:
[tex]p(0)=3000\cdot(1.019)^0=3000[/tex]So the initial price was $3000.
Now let's compare the terms inside parenthesis that are raised to t:
[tex]1.019=1\pm\frac{p}{100}[/tex]As I stated before, if the term raised to t is greater than 1 then we are talking about a growth. 1.019 is greater than 1 so this function represents a growth. What's more, in the right side of the equation we must use the + symbol. This way we have an equation for the yearly percentage of change of the price:
[tex]1.019=1+\frac{p}{100}[/tex]We can substract 1 from both sides of this equation:
[tex]\begin{gathered} 1.019-1=1+\frac{p}{100}-1 \\ 0.019=\frac{p}{100} \end{gathered}[/tex]And we multiply both sides by 100:
[tex]\begin{gathered} 100\cdot0.019=\frac{p}{100}\cdot100 \\ 1.9=p \end{gathered}[/tex]So each year the price increases in a 1.9%.
AnswerThen the answers in order are:
$3000
growth
1.9%
60 cars to 24 cars The percent of change is
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We can calculate the percent of change by means of the following formula:
[tex]change=\frac{x2-x1}{x1}\times100[/tex]Where x2 is the new value and x1 is the original value.
In this case, we go from 60 to 24, then the original value (x1) was 60 and the new value (x2) is 24, by replacing these values into the above equation, we get:
[tex]change=\frac{24-60}{60}\times100=-60[/tex]Then, the percent of change equals -60%
0 1 2 3 4 5 6 7 8 9 100 1 2 3 4 5 6 7 8 9 100 1 2 3 4 5 6 7 8 9 10401234 5 6 7 8 9 10OB.C.OD. +Reset Selection
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Okay, here we have this:
Considering the provided inequation, we are going to identify how can be represented on a number line, so we obtain the following:
So the first thing we will do is factor to find the solution intervals, we have:
[tex]\begin{gathered} 3x^2-27x\leq0 \\ x(x-9)\leq0 \\ 0\leq x\leq9 \end{gathered}[/tex]According to this, we finally obtain that the solution interval is option D, because it satisfies the found interval and its endpoints are closed.
A square pyramid has a volume of 108 cubic feet and a height of 4 feet.What is the length of each side of the base of the pyramid?A 4 ftOLOB. 9 ftC. 18 ftD. 27 ftO E. 81 ftHelp please very hard
Answers
okay so the answer is 9ft so option B
now we can take a look at how we arrived to that answer
do you know the formula for the volume?
14#An ecologist randomly samples 12 plants of a specific species and measures their heights. He finds that this sample has a mean of 14 cm and a standard deviation of 4 cm. If we assume that the height measurements are normally distributed, find a 95% confidence interval for the mean height of all plants of this species. Give the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)Lower limit:Upper limit:
Answers
Answer:
Lower limit: 11.7 cm
Upper limit: 16.263
Explanation:
The formula to find the lower and upper limits of the confidence interval (given the data is normally distributed) is :
[tex]CI=\mu\pm Z^*\frac{\sigma}{\sqrt{n}}[/tex]Where:
• μ = sample mean
,• σ = sample standard deviation
,• Z* = critical value of the z-distribution
,• n = is the sample size
In this case:
• μ = 14cm
• σ = 4cm
,• n = 12
The critical value of the z-distribution for a confidence interval of 95% is Z* = 1.96
Now, we can use the formula above to find the upper and lower limit:
[tex]CI=14\pm1.96\cdot\frac{4}{\sqrt{12}}=14\pm\frac{98\sqrt{3}}{75}=\frac{1050\pm98\sqrt{3}}{75}[/tex]Thus:
[tex]Lower\text{ }limit=\frac{1050-98\sqrt{3}}{75}\approx11.736cm[/tex][tex]Upper\text{ }limit=\frac{1050-98\sqrt{3}}{75}\approx16.263cm[/tex]Rounded to one decimal:
Lower limit: 11.7cm
Upper limit: 16.3cm
A whole pizza is cut into twelfths. If Dexter eats 1/2 of the pizza and Landry eats 1/3 of the pizza, then 3 what fraction of the pizza remains?
Answers
Explanation
Step 1
Let
A whole pizza = 1 pizza
Dexter eats 1/2
Landry eats 1/3
x= fraction of the pizza remains
Step 2
the r
7.2. I have a question about advanced trig equations that I really need help with picture included
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1) Let's start out isolating the cosine by dividing both sides by 2
[tex]\begin{gathered} 2\cos \mleft(\theta\mright)=\sqrt{3} \\ \frac{2\cos\left(θ\right)}{2}=\frac{\sqrt{3}}{2} \\ \cos \mleft(\theta\mright)=\frac{\sqrt{3}}{2} \\ \end{gathered}[/tex]2) From that we can find two general solutions in which the cosine of theta yields the square root of 3 over two:
[tex]\begin{gathered} \cos (30^{\circ})or\cos (\frac{\pi}{6})\text{ and }cos(330^{\circ}or\frac{11}{6}\pi)=\frac{\sqrt[]{3}}{2} \\ \theta=\frac{\pi}{6}+2\pi n,\: \theta=\frac{11\pi}{6}+2\pi n \end{gathered}[/tex]But not that there is a restraint, so we can write out the solution as:
[tex]\theta=\frac{\pi}{6},\: \theta=\frac{11\pi}{6}[/tex]Translate into a number sentence7. Four less than seven is greater than zero
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In order to translate the words into a number sentence, first let's translate each word or expression separately:
Four less than seven: "7 - 4"
Is greater than: ">"
Zero: "0"
Therefore the number sentence will be:
[tex]7-4>0[/tex]True or False? Every rectangle is a parallelogram. Every rhombus is a parallelogram. Every quadrilateral is a square. Every rectangle with four congruent sides is a square. X S True O False True O False O True False O True O False ?
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Given: Different statement relating different quadrilateral
To Determine: If true or false statement
Solution
The image below summarizes the properties of a quadrilateral
From the above, we can conclude that
what is the nessecary information you need to know about a cube?
Answers
Answer: the width, length and height
Step-by-step explanation: multiply the width length and height of a cube and you get the area
DATE IN OUT IN OUT HOURS TEMPORARY EMPLOYEE TIME CARD NAME: Eugene Mueller 8/8 7:00 4:10 8/9 6:50 11:00 DEPT Sales 8/10 8/11 12:00 4:35 Note: No overtime rate. 10:55 3:25 EMPLOYEE SIGNATURE RATE per hour: $8.50 TOTAL HOURS:
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6. Refer to the graph in question 5A) graph -f(x)B) graph f(x) -2
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Given the graph of f(x):
Where the points A, B, and C have the coordinates:
[tex]\begin{gathered} A=(0,-2) \\ B=(3,2) \\ C=(5,2) \end{gathered}[/tex]Now, the transformation -f(x) is just a reflection about the x-axis. This is equivalent to a change of sign on the y-coordinate. The new points A', B', and C' are:
[tex]\begin{gathered} A^{\prime}=(0,2) \\ B^{\prime}=(3,-2) \\ C^{\prime}=(5,-2) \end{gathered}[/tex]And the graph looks like this:
Now, for the f(x) - 2 transformation, we see that this is just a shift of 2 units down. Then:
Where:
[tex]\begin{gathered} A^{\prime}^{\prime}=(0,-4) \\ B^{\prime}^{\prime}=(3,0) \\ C^{\prime}^{\prime}=(5,0) \end{gathered}[/tex]What is the low end value, high end value, and does it have an outlier
Answers
Solution;
Given the results:
From the above data:
A) The low-end value is
[tex]0[/tex]B) The high end value is
[tex]95[/tex]C) Does this data set have outlier?
[tex]Yes[/tex]D) Outlier:
[tex]95[/tex]What is the distance between (-5, 5) and (1, -2)
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Answer:
[tex]\displaystyle d=\sqrt{85}\text{, or about 9.22 units}[/tex]
Step-by-step explanation:
We will use the distance formula to solve.
[tex]\displaystyle d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2}[/tex]
[tex]\displaystyle d=\sqrt{(1--5)^2 +(-2-5)^2}[/tex]
[tex]\displaystyle d=\sqrt{(6)^2 +(-7)^2}[/tex]
[tex]\displaystyle d=\sqrt{36+49}[/tex]
[tex]\displaystyle d=\sqrt{85}\text{, or about 9.22 units}[/tex]
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Write the nth rule for the following geometric sequence. Then find the fifth term. (you are given the first term and the common ratio)1-
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The formula for determining the nth term of a geometric sequence is expressed as
Tn = ar^(n - 1)
Where
a represents the first term
r represents the common ratio.
n represents the number of terms
From the information given,
a = 2, r = 3
Thus, the rule for the nth term of the geometric sequence is
Tn = 2 x 3^(n - 1)
To determine the fifth term, we would substitute n = 5 into the equation. It becomes
T5 = 2 x 3^(5 - 1)
T5 = 2 x 3^4
T5 = 162
The fifth term is 162
Question 5 of 10 Solve the proportion below. 23 A 6 B. 8 C. 9 D.
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solve for x
[tex]\begin{gathered} 12.6\times\frac{x}{12.6}=\frac{5}{7}\times12.6 \\ x=\frac{63}{7}=9 \end{gathered}[/tex]answer: C. 9
If a red and a blue fair six sided die are rolled what is the probability the result is 8 or divisible by 3?
Answers
SOLUTION:
Step 1:
In this question, we are given that;
If a red and a blue fair six-sided die are rolled.
What is the probability the result is 8 or divisible by 3?
Step 2:
The table for the two dice rolled together is as shown below:
Green 1 2 3 4 5 6
Red
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
Step 3:
The probability that the result is 8 =
[tex]\begin{gathered} =\text{ }\frac{\nu mber\text{ of 8}}{\text{Total number }} \\ =\text{ }\frac{5}{36} \end{gathered}[/tex]Next,
The probability that the result is divisible by 3
=
[tex]\frac{12}{36}[/tex]Finally, the probability that the result is 8 or divisible by 3, we have that:
[tex]\frac{5}{36}+\frac{12}{36}\text{ =}\frac{17}{36}[/tex]
I need help solving
This problem
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Weight required to destroy a bridge cable (in ponds) The type of variable is Nominal Categorical
A frequently used category variable is gender. Categorical variables can either be ordinal or numeric.
The closing price (in dollars) of the stock is a quantitative variable, and since the price involves an absolute zero, the scale of measurement is a ratio scale
Pounds is what type of variable?
Weight is a prime example of a ratio variable (e.g., in pounds). With certainty, we may state that 20 pounds weigh twice as much as 10 pounds. Ratio variables also have an important zero-point (e.g., exactly 0 pounds means the object has no weight)..
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Write an equation of the line with the given slope and y-intercept.
Slope
1
6
, y−intercept (0, −2)
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The equation of line is [tex]6y=6x$-$12[/tex].
The given slope is [tex]\frac{1}{6}[/tex].
The [tex]y $-$[/tex]intercept is [tex](0, $-$2)[/tex].
We have to write the equation of line using the given slope and [tex]y $-$[/tex]intercept.
The equation of line with the slope m and [tex]y $-$[/tex]intercept of [tex](0,a)[/tex] is [tex]y=mx+a[/tex].
From the question,
The value of [tex]m=\frac{1}{6}[/tex]
The value of [tex]a= $-$2[/tex]
Now putting the value of [tex]m[/tex] and [tex]a[/tex] in the equation of line.
[tex]y=\frac{1}{6}x+( $-$2)\\y=\frac{1}{6}x$-$2[/tex]
Multiply by [tex]6[/tex] on both side
[tex]y\times6=6\times(\frac{1}{6}x$-$2)\\6y=6\times\frac{1}{6}x$-$6\times2\\6y=6x$-$12[/tex]
The equation of line is [tex]6y=6x$-$12[/tex].
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In Abc,AB=5 feet and BC=3 feet.Which inequality represents all possible values for the length of AC,in feet?
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The smallest value of length AC would be 5 ft - 3 ft = 2 ft while the largest length would be 5 ft + 3 ft = 8ft. The answer will be
2 < Ac < 8
Solve the inequality -30 10-40x and write the solution using:
Inequality Notation:
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Answer:
Step-by-step explanation:
Lindsay gets paid $15 per hour at her job. If we let s be her salary and h be the number of hours she has worked, write an equation that represents the direct variation.
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A linear function or a direct variation function is represented by:
[tex]y=kx[/tex]where k is the constant rate of chante, in this case $15 per hour.
s=y= salary of Lindsay
h=x= hours she has worked
Then, the equation that represents the situation would be:
[tex]s=15h[/tex]Fifth grade > Y.5 Compare and convert Which is more, 1/2 of a pound or 6 ounces? of a pound 2. 6 ounces neither; they are equal Submit
Answers
We should know that :
1 pound = 16 ounces
The question is :
Which is more, 1/2 of a pound or 6 ounces?
so,
1/2 of a pound = 1/2 x 16 = 8 ounces
So,
8 ounces > 6 ounces
so, the answer is option 1
The more is 1/2 of a pound
See attached for the problem
Answers
The areas and volumes are given as follows:
a) Area of the four sides to be painted: 2448 m².
b) Area to be covered with shingles: 1140 m².
c) Volume of concrete needed to pour a floor 16 cm deep: 174.72 m³.
d) Total surface area: 5878.4 m².
Area -> Four sides paintedThe sides painted are divided as follows:
Two rectangles of dimensions 26 m and 18 m.Two rectangles of dimensions 42 m and 18 m.Hence the total area to be painted is found as follows:
Total area = 2 x 26 x 18 + 2 x 42 x 18 = 2448 m².
(Area rectangle = base x height)
Area to be covered with shinglesThis part of the problem seems incomplete, however the answer is correct.
Volume of concreteThe volume is given by:
Volume = base area x height.
Hence:
The base area is a rectangle of dimensions 26 m and 42 m.The height is of 16 cm = 0.16 m.Hence the volume is given by:
V = 26 x 42 x 0.16 = 174.72 m³.
Surface areaThe base is a rectangular prism of dimensions 26 m, 42 m and 18m, hence:
Surface area base = 2 x (26 x 42 + 26 x 18 + 42 x 18) = 4632 m².
The top is composed by:
Two rectangles of dimensions 13.6 m and 42 m.Two triangles of base 26 m and height 4 m.Hence:
Surface area top = 2 x 13.6 x 42 + 2 x 0.5 x 26 x 4 = 1246.4 m².
Then the total surface area is:
Total surface area = 4632 + 1246.4 = 5878.4 m².
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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.
Add.
47+13
Enter your answer as a fraction in simplest form by filling in the boxes.
Answers
Answer: 47+13 =60
60 as a fraction should be 3/5 in simplest form.
Step-by-step explanation:
write an expression such that if you apply the distributive property to your expression it would give the same result presented. 8x + 12
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Solution:
Let's find a expression such that if you apply the distributive property to your expression it would give the same result presented:
• 8x + 12 = 2 (4x + 6)
,• 8x + 12 = 4 (2x + 3)
,• 8x + 12 = 8 (x + 1.5)
Any of these expressions could be the solution to the question.
7(x+2)=
4(x+4)=
9(x+6)=
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Answer:
Step-by-step explanation:
7(x+2) = 7x+14
7(x+2)=7x+7 times 2
4(x+4)= 4x+16
4 times x = 4x
4 times 4 = 16
= 4x+16
9(x+6) = 9x+54
9 times x = 9x
9 times 6 = 54
= 9x+54
If the m< P is 65 degrees, then what is the measure of Arc XY
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Answer:
[tex]\text{ArcXY}=115\text{ degrees}[/tex]Step by step explanation:
We can solve this situation by the theorem of the angle formed outside of a circle by intersection:
*For two tangents:
[tex]mThen, if m
[tex]\begin{gathered} 65=\frac{1}{2}((360-mXY)-mXY) \\ 65=\frac{1}{2}(360-\text{mXY-mXY)} \\ 65=\frac{1}{2}(360-2\text{mXY)} \\ 65=180-\text{mXY} \\ \text{mXY}=180-65 \\ \text{mXY}=115 \end{gathered}[/tex]