Please Help. Functions and Relations. What is the effect on the graph of f(x)= x^2 when it is transformed to h(x)= 2x^2 + 15??
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In general, given a function g(x), a vertical stretch/compression is given by the transformation below
[tex]\begin{gathered} g(x)\rightarrow a*g(x) \\ a>1\rightarrow\text{ stretch} \\ 0Therefore, in our case,[tex]x^2\rightarrow2x^2\Rightarrow\text{ vertical stretch by a factor of 2}[/tex]On the other hand, a vertical shift is given by the following transformation
[tex]\begin{gathered} g(x)\rightarrow g(x)+b \\ b>0\rightarrow\text{ b units up} \\ b<0\rightarrow\text{ b units down} \end{gathered}[/tex]Thus,
[tex]\begin{gathered} 2x^2\rightarrow2x^2+15=h(x)\Rightarrow\text{ 15 units up} \\ \end{gathered}[/tex]Hence, the answer is option C. Vertical stretch by a factor of 2 and a vertical shift by 15 units up.Related Questions
Find the diameter of a circle with a circumference of 28.26 centimeters. Use 3.14 for π.
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Answer:
The diameter of the circle is 9.0 cm.
[tex]d=9.0\text{ cm}[/tex]Explanation:
Given that the circumference of the circle is 28.26 centimeters.
[tex]C=28.26\text{ cm}[/tex]Recall that the formula for the circumference of a circle is;
[tex]\begin{gathered} C=2\pi r=\pi d \\ d=\frac{C}{\pi} \end{gathered}[/tex]Substituting the given values;
[tex]\begin{gathered} d=\frac{28.26\text{ cm}}{3.14} \\ d=9.0\text{ cm} \end{gathered}[/tex]Therefore, the diameter of the circle is 9.0 cm.
[tex]d=9.0\text{ cm}[/tex]TWO-Variable SystemsThe two lines graphed below are parallel. How many solutions are there to thesystem of equations?O A. TwoO B. ZeroO C. OneO D. Infinitely manyPREVIOUS
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Answer:
B. Zero
Explanation:
The solutions of a system of equations are the points where the graphs intersect. If the lines are parallel, the lines will not intersect, so there will be no solutions to the system.
Therefore, the solutions to the system of two parallel lines are
B. Zero
As the number manu fucture increase from soo+200. manufactute (ost increase from 350 to 650 birr. Assume that the given data establishes relationship between Cost. cand number of units made. Q and asume that the the relation This is linear. Assuum the thice unit is birr 13.
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y = 3x + 50 is the linear equation relating the total cost to the number of units produced.
We know that a linear equation is of the form
y = mx + b
Where m is the slope (rate of change of y with respect to x) and b is the value when x is 0.
With the given information, the cost increased by
$650 - $350 = $300
When the number of units produced increased by 200 - 100 = 100.
So the rate of change of cost (y) with respect to x (number of units) is 300/100=3.
So the equation is of the form
y = 3x + b
Use one of the two given data points to determine b.
When the production was 100, the total cost was $350:
So,
350 = 3(100) + b
350 = 300 + b
b = 50
Hence the answer is y = 3x + 50 is the linear equation relating the total cost to the number of units is produced.
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3. Which situation could be represented by the graph shown?3027242118A. Garrett buys limes for $0.80 each.B. Sophia buys 12-packs of soda for $1.75 each.C. Jacob buys packs of gum for $1.50 each.D. Allison purchases lemons for $0.75 each.15129631 2 3 4 5 6 7 8 9 10
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Find the slope of the graph, use 2 points on the line (0,0) and (4,3)
[tex]m=\frac{3-0}{4-0}=\frac{3}{4}=0.75[/tex]The equation of the graph is y=0.75x, it represents the situation in option D. Allison purchases lemons for $0.75 each
What is an obtuse angle?A) Angle COAB) Angle BOAC) Angle DOBD) Angle DOA
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An obtuse angle is an angle that measures more than 90° but not eauql or greater than 180°.
COA is the sum of COB and BOA, which is 90°, so COA is not obtuse.
BOA is 60°, so it is not obtuse.
DOA is a straight line, so it is 180°, so not obtuse.
DOB is COD plus COB. Since COA is 90°, DOC is also 90°, so DOC ples COB is 120°, which is between 90° and 180°, so DOB is obtuse and the correct alternative is C.
Glven: Circle P with center at (-2, 3) and a radius of 23. Identify the equation that could represent circle P. (3 – 2) + (y - 3)2 = 23 (2+2) + (y + 3)' = 23 (2 – 2)2 + (y + 3) = 23 (2+2)² + (y – 3)2 =23
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The correct option is:
[tex](x+2)^2+(y-3)^2=23[/tex]Because we need to remember that the equation for a circumference centered in (h,k) and with radius r is:
y = x2 + 5x - 10y=-x² + 2x + 10
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Since in both given equations, the variable y is already clear, then you can equal the two equations and then solve for x. So, you have
[tex]\begin{cases}y=x^2+5x-10\text{ (1)} \\ y=-x^{2}+2x+10\text{ (2)}\end{cases}[/tex][tex]\begin{gathered} x^2+5x-10=-x^2+2x+10 \\ \text{ Add }x^2\text{ to both sides of the equation} \\ \text{ Subtract 2x to both sides of the equation} \\ \text{ Subtract 10 to both sides of the equation} \\ x^2+5x-10+x^2-2x-10=-x^2+2x+10+x^2-2x-10 \\ 2x^2+3x-20=0 \end{gathered}[/tex]To solve for x you can use the quadratic formula, that is,
[tex]\begin{gathered} \text{ For }ax^2+bx+c=0\text{ where a}\ne0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]In this case
a=2
b=3
c=-20
So,
[tex]\begin{gathered} x=\frac{-3\pm\sqrt[]{(3)^2-4(2)(-20)}}{2\cdot2} \\ x=\frac{-3\pm\sqrt[]{9+160}}{4} \\ x=\frac{-3\pm\sqrt[]{169}}{4} \\ x=\frac{-3\pm13}{4} \\ x_1=\frac{-3+13}{4}=\frac{10}{4}=\frac{5}{2}=2.5 \\ x_2=\frac{-3-13}{4}=\frac{-16}{4}=-4 \end{gathered}[/tex]Now you can plug in the solutions found in any of the given equations to find their respective y-coordinates.
For the first solution, you have
[tex]\begin{gathered} x_1=\frac{5}{2} \\ y_{}=-x^2+2x+10\text{ (2)} \\ y_1=-(\frac{5}{2})^2+2(\frac{5}{2})+10 \\ y_1=-\frac{25}{4}+5+10 \\ y_1=\frac{35}{4} \\ y_1=8.75 \\ \text{ Then} \\ (2.5,8.75) \end{gathered}[/tex]For the second solution, you have
[tex]\begin{gathered} x_2=-4 \\ y=-x^2+2x+10\text{ (2)} \\ y_2=-(-4)^2+2(-4)+10 \\ y_2=-16-8+10 \\ y_2=-14 \\ \text{Then} \\ (-4,-14) \end{gathered}[/tex]Therefore, the solution set of the given system of equations is
[tex]\mleft\lbrace(-4,-14),(2.5,8.75)\mright\rbrace[/tex]which is the better buy and provide the unit price for your answer! $5.28 for 6 candy bars or $12.75 for 15 candy bars?
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Answer:
Explanation:
Given:
$5.28 for 6 candy bars
$12.75 for 15 candy bars
To determine the better buy, we simplify each option first:
For $5.28 for 6 candy bars:
5.28/6 = $0.88 per candy bar
For $12.75 for 15 candy bars:
12.75/15 = $0.85 per candy bar
Therefore,
Which situation can be represented by the equation y = 9x?Question 3 options:Michael drove x amount of hours in his car. This is 9 times the amount of miles as y.Michael drove x amount of miles in his car. He drove y amount of hours in 9 miles.Michael has y amount of miles to drive. This amount is 9 times x, the amount of miles to drive in hours.Michael has x amount of hours. This amount is 9 times y, the amount of miles to drive in hours.
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Solution:
Given:
[tex]y=9x[/tex]This is a linear equation that relates distance, speed, and time.
where;
[tex]undefined[/tex]Help meeee please!!!!
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The coordinates of B' are (1, 0) after transforming the parallelogram down 4 units and right 3 units.
What are coordinates?Coordinates are distances or angles, represented by numbers, that uniquely identify points on surfaces of two dimensions or in space of three dimensions. These are the set of values that shows the exact position. Coordinates are the set of points, or numbers, that locates a point on a line, on a plane, or in space. The points at the coordinates are called coordinate points. The coordinate plane has two axes. Those are horizontal and vertical axes. The two axes intersect each other at a point called the origin. Coordinate axes are one of the fixed reference lines of a coordinate system. It is a two-dimensional number line. It is used to locate the position of any point.
From the graph, the coordinates of B are (-2, 4).
Translating 4 units down means the value of the y-axis is changing. Therefore, new coordinates will be
(-2-0, 4-4)
=(-2, 0)
Then the parallelogram is translated to 3 units to the right. So, the x-axis is changing to a positive end.
The coordinates of B' will be
(-2+3, 0+0)
= (1,0)
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Use the intercepts to graph the equation. y = -6 x-intercept: Enter as a coordinate: such as (a, b). If there is no x-intercept, enter DNE. Enter as a coordinate: such as (a, b). If y-intercept: there is no y-intercept, enter DNE. 8 6 5 4 ربا
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Answer:
x -intercept: DNE
y-intercept: (-6, 0)
Explanation:
The x-intercept is the point where the line intersects the x-axis.
The y-intercept is the point where the line intersects the y-axis.
Now when we draw the line y = -6, we get
We see that the red line does not intersects the x-axis at any point; thereffore, the x-intercept does not exist.
x -intercept: DNE
The red line intersects the y-axis at y = -6; therefore, the y-intercept is the point (0, -6)
Find and graph the intercepts of the following linear equation: x-4y=16
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The given function is:
[tex]x-4y=16[/tex]The x-intercept is the value of x when y = 0.
[tex]\begin{gathered} x-4(0)=16 \\ x=16 \end{gathered}[/tex]The y-intercept is the value of y when x = 0.
[tex]\begin{gathered} (0)-4y=16 \\ -4y=16 \\ \text{ Dividing both sides of the equation by }-4 \\ y=-4 \end{gathered}[/tex].
Graph the line from the table you found in (5). Remember to scale and label your axes!
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We are asked to draw a line by using the values given in the table.
Let x denotes the first column of values and y denotes the second column of values
So, the (x, y) ordered pairs are
(0, 4), (2, 0), (1, 2), (3, -2), (-1, 6)
Let us plot these points on the graph then we would draw a line connecting these points.
Therefore, this is how the graph of the line looks like.
The y-intercept of the line is the point where the line intersects the y-axis.
From the above graph, we see that the line intersects the y-axis at y = 4
Therefore, the y-intercept of the line is 4
The slope of the line is given by
[tex]slope=\frac{\text{rise}}{\text{run}}[/tex]The rise is the vertical distance between the two points on the line.
The run is the horizontal distance between the two points on the line.
As you can see, we selected two points on the line. (you may select any two points)
The two points are (2, 0) and (3, -2)
The vertical distance is -2 (negative because it is going down) and the horizontal distance is 1
[tex]slope=\frac{\text{rise}}{\text{run}}=\frac{-2}{1}=-2[/tex]Therefore, the slope of the line is -2
Graph the solution to the following system of inequalities.ys-2x-3y> 4x + 710-8-4-Х?10
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Explanation
[tex]\begin{gathered} y\leq-2x-3 \\ y>4x+7 \end{gathered}[/tex]Step 1
First, graph the inequality 1
[tex]y\leq-2x-3[/tex]the related equation is
[tex]y=-2x-3[/tex]now, get 2 coordinates of the line
a) when x=1
[tex]\begin{gathered} y=-2x-3 \\ y=-2(1)-3 \\ y=-2-3 \\ y=-5 \\ so,\text{ the coordinate is (1,-5)} \end{gathered}[/tex]b)when x=0
[tex]\begin{gathered} y=-2x-3 \\ y=-2\cdot0-3 \\ y=0-3 \\ y=-3 \\ \text{coordinate P2}\Rightarrow(0,-3) \end{gathered}[/tex]now, draw a line that pases trought the coordinates we found.
Since the inequality is ≤ , not a strict one, the border line is solid
Step 2
Now, do the same for inequality 2
so
[tex]y>4x+7[/tex]the related equation is
[tex]y=4x+7[/tex]find 2 coordinates of the line
a)when x=0
[tex]\begin{gathered} y=4x+7 \\ y=4\cdot0+7 \\ y=0+7 \\ y=7 \\ so,\text{ the coordinate 3 is (0,7)} \end{gathered}[/tex]b) when x=-2
[tex]\begin{gathered} y=4x+7 \\ y=4\cdot-2+7 \\ y=-8+7 \\ y=-1 \\ so,\text{ the coordinate 4 is (-2},-1) \end{gathered}[/tex]now, draw the line 2, this lines passes trougth the coordiantes 3 and 4
Since the inequality is >, a strict one, the border line is dotted
Step 3
Graph:
in inequality (1) we need the values smaller r than -2x-3, it measn all values under the line,
and in Inequality 2 we need the values greater than 4x+7, it means all values over the line
so, the solution is the dark purple zone
I hope this helps you
7/8 of a watermelon weight is water. if the watermelon weighs 24 kilograms, how many of the kilograms come from water?
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ANSWER
21 kg of the watermelon are water.
EXPLANATION
We have to divide the weight of the watermelon by 8 and then multiply by 7 - or in other words, multiply by 7/8:
[tex]24\times\frac{7}{8}=\frac{24}{8}\times7=3\times7=21[/tex]21 of the 24 kilograms of the watermelon are from water.
Find the 55th term of the arithmetic sequence -7, -5, -3,
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The given numbers are -7,-5,-3.
The common differen
A car travels at a steady speed of 40 mph. How far will it go in 15 minutes?
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The distance travelled by the car in 15 minutes can be determined as,
[tex]\begin{gathered} D=s\times t \\ D=40\text{ mph}\times15\text{ min}\times\frac{1\text{ h}}{60\text{ min}} \\ D=10\text{ miles} \end{gathered}[/tex]Thus, the required distance is 10 miles.
is 0.5 a integer but not a whole number
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...
Natural Numbers are the numbers 1 through infinity.
Whole numbers.
So, they start from 1 and go on...
1, 2, 3, 4, .....
Now, Whole numbers are very same just that they start from 0, so it would be:
0, 1, 2, 3, ....
Integers would include the negatives fo the naturals and 0, so they would be:
...-2, -1, 0 , 1, 2, ....
We want a number NOT natural but integer, that would be 0.
So,
Natural Numbers = 1, 2, 3, 4, 5, ....
Whole Numbers = 0, 1, 2, 3, 4, 5, .....
Integers = ...-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...
7. Solve this riddle. I am an even number. I am between 10 and 20. And when I am divided by 7, I have no remainder. What number am I?
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
solve the riddle = ?
Step 02:
We must analyze the exercise to find the solution
a. even number
b. 10 ----- 20
c. x / 7 ===> no remainder
11 , 13 , 15 , 17 , 19 ===> even numbers
An arithmetic sequence has a 10th term of 15 and 14th term of 35. show that the equation (y=mx+b) of this graph equals an =-30+(n-1)5.
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The arithmetic sequence follows
[tex]a_n=-30+(n-1)5[/tex]Lets see if the 10th term is 15 by replacing the n for 10
n=10
[tex]a_{10}=-30+(10-1)5[/tex][tex]a_{10}=-30+(9)5=-30+45=15[/tex]Now, Lets see if the 14th term is 35 by replacing the n for 14
n=14
[tex]a_{14}=-30+(14-1)5[/tex][tex]a_{14}=-30+(13)5=-30+65=35[/tex]Then so, the sequence follows the equation an =-30+(n-1)5.what is the reference angle for four radians rounded to two decimal places?
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The reference angle can be calculated 4 radians is in the third quadrant, of the coordinate
reference angle=angle - 3.14
reference angle=4-3.14
the reference angle of 4 radians is 0.8584 rounded to two decimal places is 0.86 radians
Given the standard restricted domains, which of the following relationships does not hold for x=-1? (Assume angles are in radians.)
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Answer:
[tex]D:\text{ arccos\lparen cos\lparen-1\rparen\rparen= 1}[/tex]Explanation:
From the restricted domain, we want to check for the relationship that does not hold
All we have to do here is to substitute the value -1 for x, after which we evaluate each of the given equations
We proceed as follows:
[tex]\begin{gathered} a)\text{ sin\lparen}\sin^{-1}(-1))\text{ = -1} \\ b)\text{ arcsin\lparen sin\lparen-1\rparen\rparen = -1} \\ c)\text{ cos\lparen arc cos \lparen-1\rparen\rparen = -1} \\ d)\text{ arc cos\lparen cos\lparen-1\rparen\rparen = 1} \\ e)\text{ tan\lparen arc tan\lparen-1\rparen\rparen = -1} \\ f)\text{ arctan\lparen tan\lparen-1\rparen\rparen = -1} \end{gathered}[/tex]The correct option is thus D
The scatter plot below shows the average rent (in dollars per month) for a 1-bedroom apartment in NYC each year between 2000 and 2013. A line was fit to the data to model the relationship. Which of these linear equations best describes the given model?A) ŷ = ⅖x + 800B) ŷ = 40x + 800C) ŷ = 800x + ⅖D) ŷ = 800x + 40Based on the equation, use this equation to estimate the average rent in 2020.Round your answer to the nearest dollar.$___.
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From the graph, we can conclude:
[tex]\begin{gathered} b=y-intercept_{}\approx800 \\ m\approx\frac{900-800}{3-0}\approx33.33\approx40 \end{gathered}[/tex]So, the linear equation that best describes the given model is:
[tex]\hat{y}=40x+800[/tex]Therefore, for 2020 or x = 20:
[tex]\begin{gathered} \hat{y}(20)=40(20)+800 \\ \hat{y}(20)=1600 \end{gathered}[/tex]2. The following is a graph of the function f(x) = 2^x. Graph thetransformation f(x+3) on the blank coordinate axis.yy
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Explanation:
The transformation f(x+3) indicates that we have to translate the graph of f(x) 3 units to the left.
In the graph of f(x) the y-intercept is at y = 1. For f(x+3) this point is moved 3 units to the left, so it is (-3, 1).
Answer:
The graph of f(x+3) is
if H & J equals 7 and 10s equals 10 find LK
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The trapezoid HJKL has T and S as midpoints of the legs
The length of TS can be calculated as the mean or average of the lengths of HJ and LK, i.e.:
[tex]TS=\frac{HJ+LK}{2}[/tex]We are given the lengths HJ=14, LK=42, thus:
[tex]TS=\frac{14+42}{2}=\frac{56}{2}=28[/tex]Now if we have HJ=7 and TS=10, we can find LK by solving the equation for LK
[tex]LK=2TS-HJ[/tex][tex]LK=2*10-7=20-7=13[/tex]The length of LK is 13
Parallelogram ABCD is below. m
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The consecutive angles of a parallelogram are supplementary. therefore:
[tex]\begin{gathered} m\angle A+m\angle B=180 \\ 41+x+8.5=180 \\ x+49.5=180 \\ solve_{\text{ }}for_{\text{ }}x\colon \\ x=180-49.5 \\ x=130.5 \\ x\approx131 \end{gathered}[/tex]The average amount of water used per person each day in a country is 45 gallons. How much water does the average person use in one year?
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Proportions
It's assumed the amount of water consumed by one person is proportional to the time.
The contant of proportionality is given as 45 gal/day.
Since one normal year has 365 days, then we use the same proportion to calculate the water used in one year as follows:
Water used = 45 * 365 = 16,425 gallons.
The average person uses 16,425 gallons.of water in one year
Use the formula P(B\A)=n(A and B)÷n(A) to find the probability P(kinglface card) when a single. card is drawn from a standard 52 card deck. P(king face card)=
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In a deck of 52 cards, there 4 faces of Kings. These are the King of Hearts, King of Diamonds, King of Spades, and King of Clubs. Therefore, the chance of drawing a king face card in a deck of cards would be 4 out of 52 or 1 out of 13.
Answer: P(king face card) = 1/13
what is the intermediate in the form (x+a)^2=b as a result of completing the square for the following equation?Answer:()^2=
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Step 1: Write out the equation
[tex]x^2-12x+32=4[/tex]Step 2: Subtract 32 from both sides of the equation
[tex]\begin{gathered} x^2-12x+32-32=4-32 \\ x^2-12x=-28 \end{gathered}[/tex]Step 3: Complete the square by adding 1/2 of the square of the coefficient of x to both sides
That is
[tex]x^2-12x+(-6)^2=-28+(-6)^2[/tex]This implies that
[tex](x-6)^2=-28+36=8[/tex]Hence the intermediate step is (x - 6)² = 8
what is 7/8 - 3 1/5? i cant firgure it out
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Answer:
-93/40 or -2 13/40
Step-by-step explanation:
7/8 - 16/5
Adjust based on the LCM
35/40 - 128/40
35-128/40