consider the parent function f(x)=x^2. a. graph y=f(x). b. write an equation for f(1/2x). Then sketch a graph of y=f(1/2x) and describe the transformation. c.write an equation for f(3x). Then sketch a graph of y=f(3x) and describe the transformation.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
f(x)=x²
f(1/2x) = ?
graph of y=f(1/2x) = ?
Step 02:
b. f(1/2x)
x ===> 1/2x
[tex]f\text{ (1/2 x) = (}\frac{1}{2}x)^2=\frac{1}{4}x^2[/tex]Step 03:
c. Graph:
We give values to x, and we obtain the values of y.
f(x) = 1/4 x²
e.g.
if x = 4
y = 1/4 (4)² = 1/4 * 16 = 4
That is the solution for b. and c.
Related Questions
solve and reduce 10÷2/9
Answers
We have the following:
[tex]10\div\frac{2}{9}[/tex]solving:
[tex]\frac{10}{\frac{2}{9}}=\frac{\frac{10}{1}}{\frac{2}{9}}=\frac{10\cdot9}{2\cdot1}=\frac{90}{2}=45[/tex]The answer is 45
How do I solve:7/8+y= -1/8
Answers
We are given the following equation
[tex]\frac{7}{8}+y=-\frac{1}{8}[/tex]Let us solve the equation for variable y
Our goal is to separate out the variable y
Subtract 7/8 from both sides of the equation.
[tex]\begin{gathered} \frac{7}{8}-\frac{7}{8}+y=-\frac{1}{8}-\frac{7}{8} \\ y=-\frac{1}{8}-\frac{7}{8} \end{gathered}[/tex]Since the denominators of the two fractions are the same, simply add the numerators.
[tex]\begin{gathered} y=-\frac{1}{8}-\frac{7}{8} \\ y=\frac{-1-7}{8} \\ y=\frac{-8}{8} \\ y=-1 \end{gathered}[/tex]Therefore, the value of y is -1
If the diameter of a quarter is 24.26 mm and the width of each quarter is 1.75 mm, to the nearest tenth, what is the approximate surface areaof the roll of quarters? Hint there are 40 quarters in a roll of quarters.A)14,366,2 mm
Answers
For this problem, we are given the dimensions of a quarter and we need to determine the surface area of a roll of quarters.
We can approximate the roll as a cylinder, where the height is the sum of the heights of all the quarters and the dimater is equal to the diameter of one quarter. Therefore we have:
[tex]\begin{gathered} A_{base}=\pi r^2=\pi(\frac{24.26}{2})^2=462.24\text{ mm^^b2}\\ \\ h=40\cdot1.75=70\text{ mm}\\ \\ L_{base}=2\pi(\frac{24.26}{2})=76.22\text{ mm}\\ \\ A_{lateral}=70\cdot76.22=5335.4\text{ mm^^b2}\\ \\ A_{surface}=2\cdot462.24+5335.4=6259.88\text{ mm^^b2} \end{gathered}[/tex]The surface area is equal to 6259.88 mm, the correct option is C.
Solve the system of equation by the elimination method {1/3x+1/2y=1/2{1/6x-1/3y=5/6(x,y)=(_, _)
Answers
Solution
- The solution steps to solve the system of equations by elimination is given below:
[tex]\begin{gathered} \frac{x}{3}+\frac{y}{2}=\frac{1}{2}\text{ \lparen Equation 1\rparen} \\ \\ \frac{x}{6}-\frac{y}{3}=\frac{5}{6}\text{ \lparen Equation 2\rparen} \\ \\ \text{ Multiply Equation 2 by 2} \\ 2\times(\frac{x}{6}-\frac{y}{3})=\frac{5}{6}\times2 \\ \\ \frac{x}{3}-\frac{2y}{3}=\frac{5}{3}\text{ \lparen Equation 3\rparen} \\ \\ \\ \text{ Now, }\frac{x}{3}\text{ is common to both Equations 1 and 3.} \\ \\ \text{ We can therefore subtract both equations to eliminate }x. \\ \text{ We have:} \\ \text{ Equation 1 }-\text{ Equation 3} \\ \\ \frac{x}{3}+\frac{y}{2}-(\frac{x}{3}-\frac{2y}{3})=\frac{1}{2}-\frac{5}{3} \\ \\ \frac{x}{3}-\frac{x}{3}+\frac{y}{2}+\frac{2y}{3}=\frac{1}{2}-\frac{5}{3}=\frac{3}{6}-\frac{10}{6} \\ \\ \frac{y}{2}+\frac{2y}{3}=-\frac{7}{6} \\ \\ \frac{3y}{6}+\frac{4y}{6}=-\frac{7}{6} \\ \\ \frac{7y}{6}=-\frac{7}{6} \\ \\ \therefore y=-1 \\ \\ \text{ Substitute the value of }y\text{ into any of the equations, we have:} \\ \frac{1}{3}x+\frac{1}{2}y=\frac{1}{2} \\ \frac{1}{3}x+\frac{1}{2}(-1)=\frac{1}{2} \\ \\ \frac{1}{3}x=\frac{1}{2}+\frac{1}{2} \\ \\ \frac{1}{3}x=1 \\ \\ \therefore x=3 \end{gathered}[/tex]Final Answer
The answer is:
[tex]\begin{gathered} x=3,y=-1 \\ \\ \therefore(x,y)=(3,-1) \end{gathered}[/tex]if 2 angles from a line
Answers
If two angles form a linear pair, then they form a straight line, and the sum of their measures is 180 degrees.
This illustrated below;
In the illustration above, angle measure 1 and 2 both equal to 180 degrees. Angle 1 and angle 2 are refered to as a linear pair.
When 80% of a number is added to the number, the result is 162.
Answers
Given:
80% of a number is added to the number, the result is 162.
Required:
To find the number.
Explanation:
80% of a number is added to the number
[tex]\begin{gathered} \frac{80}{100}x+x \\ \\ =0.8x+x \end{gathered}[/tex]The result is 162, so
[tex]\begin{gathered} 0.8x+x=162 \\ \\ 1.8x=162 \\ \\ x=\frac{162}{1.8} \\ \\ x=90 \end{gathered}[/tex]Final Answer:
The number is 90.
The first year shown the number of students per teacher fell below 16 was
Answers
Using the y axis, we want to find when it goes below 16
The x value when y is less than 16 for the first time is 2002
The mean mass of 8 men is 82.4 kg. What is the total mass of the 8 men?
Answers
Given:
The mean mass of 8 men is 82.4 kg.
Required:
To find the total mass of 8 men.
Explanation:
Let the total mass be x.
Now,
[tex]\begin{gathered} \frac{x}{8}=82.4 \\ \\ x=82.4\times8 \\ \\ x=659.2 \end{gathered}[/tex]Final Answer:
The total mass of 8 men is 659.2.
put the numbers in order from least to greatest2.3,12/5,5/2,2.2,21/10
Answers
Express the fraction in terms of decimal.
[tex]\frac{12}{5}=2.4[/tex][tex]\frac{5}{2}=2.5[/tex][tex]\frac{21}{10}=2.1[/tex]The numbers are,
2.3, 2.4, 2.5, 2.2, 2.1.
Now we arrange the number from least to greatest.
[tex]2.1,2.2,2.3,2.4,2.5[/tex]So answer is,
[tex]\frac{21}{10},2.2,2.3,\frac{12}{5},\frac{5}{2}[/tex]EspañolAt a football game, a vender sold a combined total of 249 sodas and hot dogs. The number of sodas sold was 55 more than the number of hot dogs sold. Findthe number of sodas sold and the number of hot dogs sold.Number of sodas sold:Number of hot dogs sold:1Х5?
Answers
Given:
Vender sold a combined total of 249 sodas and hot dogs.
The number of sodas sold was 55 more than the number of hot dogs sold.
Let x and y be the number of sodas and hot dogs sold.
[tex]x+y=249\ldots\text{ (1)}[/tex][tex]x=y+55\ldots\text{ (2)}[/tex]Substitute equation (2) in (1)
[tex]y+55+y=249[/tex][tex]2y=249-55[/tex][tex]2y=194[/tex][tex]y=97[/tex][tex]x=97+55[/tex][tex]x=152[/tex]Number of sodas sold is 152.
Number of hot dogs sold is 97.
A business could not collect $5,000 that it was owed. The total owed to the business was $100,000. What fraction of the total was not collected? (Express As Fraction)
Answers
Total owed to the business = $100,000
amount that could not be collected = $5000
Fraction of total not collected
[tex]\text{fraction not collected=}\frac{5000}{100000}=\frac{5}{100}=\frac{1}{20}[/tex]e) A client takes 1 1/2 tablets of medication three times per day for 4 days. How many tablets will the clienthave taken at the end of four days? Explain how your arrived at your answer.
Answers
Given
Client takes 1 1/2 of medication one time
Find
how many tablets will client have been taken at the end of 4 days.
Explanation
Client takes medication one time = 1 1/2
Client takes medication three times =
[tex]\begin{gathered} 1\frac{1}{2}\times3 \\ \frac{3}{2}\times3 \\ \frac{9}{2} \end{gathered}[/tex]medication for 4 days =
[tex]\begin{gathered} \frac{9}{2}\times4 \\ 18 \end{gathered}[/tex]Final Answer
The client takes 18 tablets at the end of four days.
A glacier in Republica was observed to advance 22inches in a 15 minute period. At that rate, how many feet will the glacier advance in one year?
Answers
To fins the rate in feet/year we must change first the measurements to the units required
inches to feat
minutes to years
[tex]22in\cdot\frac{1ft}{12in}=\frac{11}{6}ft[/tex][tex]15\min \cdot\frac{1h}{60\min}\cdot\frac{1day}{24h}\cdot\frac{1year}{365\text{days}}=\frac{1}{35040}\text{years}[/tex]to find the rate divide the distance over the time
[tex]\frac{\frac{11}{6}ft}{\frac{1}{35040}\text{year}}=\frac{11\cdot35040ft}{6\text{year}}=\frac{385440}{6}=\frac{64240ft}{\text{year}}[/tex]In the figure, ∆ABD ≅ ∆CBD by Angle-Side-Angle (ASA). Which segments are congruent by CPCTC? BC ≅ AD CB ≅ AB AB ≅ CD DB ≅ DC
Answers
By CPCTC this is the only valid answer:
CB ≅ AB
Another statement should be AD≅ CD
The cost of a pair of skis to a store owner was $700, and she sold the pair of skis for $1020.Step 3 of 3: What was her percent of profit based on selling price? Follow the problem-solving process and round your answer to thenearest hundredth if necessary.
Answers
Answer:
Explanation:
• The ,cost price ,of the pair of skis = $700
,• The ,selling price ,of the pair of skis = $1020
To calculate the percentage of profit, use the formula below:
[tex]\text{Percent of Profit=}\frac{Selling\text{ Price-Cost Price}}{\text{Selling Price}}\times\frac{100}{1}[/tex]Substitute the given values:
[tex]\text{Percent of Profit=}\frac{1020\text{-7}00}{\text{7}00}\times\frac{100}{1}\text{=}\frac{320}{\text{7}00}\times\frac{100}{1}=45.71\%[/tex]The percentage profit is % (correct to the nearest hundredth).
Drag the tiles to the correct boxes. Not all tiles will be used.
Match each equation with a value of x that satisfies it.
18
1
9
2
5
(x - 2) = 2
√²+7=4
V1-x
= -1
-3
Answers
For a given exponential expression, the determined value is x=3,0,6.
What are exponential expressions?A component of an exponential expression is an exponent. Powers can be expressed succinctly using exponential expressions. The exponent represents the number of times the base has been multiplied.Powers can be expressed succinctly using exponential expressions. The exponent represents the number of times the base has been multiplied. Exponential expressions or the representation of multiplication with exponents can be streamlined to produce the most efficient notation possible.Each exponential expression's x value is evaluated.
Therefore,
1. [tex]$ \sqrt{x^2+7}=4 \\[/tex]
[tex]&\left(x^2+7\right)=4^2 \\[/tex]
[tex]&\left(x^2+7\right)=16 \\[/tex]
simplifying the above equation, then we get
x² = 16 - 7 = 9
x = 3
2. [tex]$\sqrt[2]{1-x}=-1$[/tex]
(1 -x) = (-1)²
1 - x = 1
x = 0
3. [tex](x-2)^{\frac{1}{2}}=2 \\[/tex]
(x - 2) = 2²
x - 2 = 4
x = 6
The determined value is x=3,0,6 for a given exponential expression.
To learn more about exponential expression, refer to:
https://brainly.com/question/8844911
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Please help thank you sm it would be very helpful and very much appreciated ♥️‼️
2. Write the formula for the circumference of a circle.
a. Calculate the circumference of circle B if the diameter is 8 inches.
b. Calculate the radius of circle B if the circumference is 94.2 square centimeters.
Answers
Step-by-step explanation:
2. C = [tex] 2 \pi r [/tex]
a. to find radius from diameter in order to calculate the value of the circumference we have to divide the diameter by 2
d/2 = 8/2 = 4
Next, Find the circumference
C = [tex] 2 \pi r [/tex]
C = [tex] 2 \cdot 3.142 \cdot 4 [/tex]
C = 25.13
b. Rearrange formula for circumference to find the value of the radius
Where, C = [tex] 2 \pi r [/tex]
Make r the subject of formula
C/[tex] 2 \pi [/tex] = [tex] 2 \pi r [/tex] /[tex] 2 \pi [/tex]
94.2/2 × 3.142 = r
94.2/6.3 = r
r = 14.95 ≈ 15
2.circumference= pi×diameter
a)25.136 inches
b)14.99 cm
Step-by-step explanation:
a) pi × 8
3.142× 8= 25.136
b) diameter = radius × 2
circumference = pi × diameter OR pi × radius×2
because we are trying to find the radius we will use the pi × 2 radius.
94.2= 3.142 × 2 radius
94.2 ÷ 3.142= 2 radius
29.981 = 2 radius
29.981 ÷ 2 = radius
14.99 = radius
In the accompanying regular pentagonal prism, suppose that each base edge measures 7 in. and that the apothem of the base measures 4.8 in. The altitude of the prism measures 10 in.A regular pentagonal prism and a pentagon are shown side by side. The pentagon contains a labeled segment and angle.The prism contains a horizontal top and bottom and vertical sides. The front left face and front right face meet the bottom base at right angles.The pentagon is labeled "Base".A line segment starts in the center of the pentagon, travels down vertically, and ends at the edge. The segment is labeled a.The vertical segment forms a right angle with the edge.(a)Find the lateral area (in square inches) of the prism.in2(b)Find the total area (in square inches) of the prism.in2(c)Find the volume (in cubic inches) of the prism.in3
Answers
To determine the lateral area of the prism;
[tex]Lateral\text{ area=perimeter of the base}\times height[/tex][tex]Lateral\text{ area=5\lparen7\rparen }\times10=350in^2[/tex]To determine total area of the prism;
[tex]Total\text{ area=2\lparen area of base\rparen+Lateral area}[/tex][tex]\begin{gathered} Total\text{ area of the prism=2\lparen}\frac{1}{2}\times perimeter\text{ of the base}\times apotherm\text{\rparen+350} \\ \end{gathered}[/tex][tex]\begin{gathered} Total\text{ area of the prism=2\lparen}\frac{1}{2}\times5(7)\times4.8\text{\rparen+380=168+350=518in}^2 \\ \end{gathered}[/tex]To determine the volume of the prism;
[tex]Volume\text{ = base area }\times height[/tex][tex]Volume=\frac{1}{2}\times5(7)\times4.8\times10=840in^3[/tex]Hence
giving the figure below, what is the measure of angle JKL
Answers
The measure of < JKL = 25+25 = 50 degrees.
Angle JOK = 360 -230 = 130 degrees , (where O is the center of the circle)
< OLK = < OJK = 90 degrees ( tangent to a circle)
< LOK = < JOK = 180 - (90+65) = 180 - 155 = 25 degrees
The solution is: < JKL = 25 +25 = 50 degrees
There is a raffle with 250 tickets. One ticket will win a $320 prize, one ticket will win a $240 prize, one ticket will win a $180 prize, one ticket will win a $100 prize, and the remaining tickets will win nothing. If you have a ticket, what is the expected payoff
Answers
Given that: There is a raffle with 250 tickets. One ticket will win a $320 prize, one ticket will win a $240 prize, one ticket will win a $180 prize, one ticket will win a $100 prize, and the remaining tickets will win nothing.
The expected payoff will be:
[tex]\begin{gathered} EV=\frac{1}{250}(320)+\frac{1}{250}(240)+\frac{1}{250}(180)+\frac{1}{250}(100)+\frac{246}{250}(0) \\ EV=\frac{320+240+180+100}{250} \\ EV=\frac{840}{250} \\ EV=3.36 \end{gathered}[/tex]So the expected payoff will be $3.36.
Haley spent 1/2 oven hour playing on her phone that used up 1/9 of her battery how long would she have to play on her phone to use the entire battery
Answers
1/2 hour playing -- 1/9 battery
1 hour playing -- 2/9 battery
1 1/2 hours playing --- 3/9 battery
2 hours playing ------ 4/9 battery
2 1/2 hours playing ---- 5/9 battery
3 hours playing ----- 6/9 battery
3 1/2 hours playing --- 7/9 battery
4 hours playing -----8/9 battery
4 1/2 hours playing ---- 9/9 battery
9/9 represent the entire battery so che can play 4.5 hours on her phone
it can be represented into a fraction as
[tex]4.5=4\frac{1}{2}=\frac{9}{2}[/tex]△VWY is equilateral, VZ≅WX, and ∠XWY≅∠YVZ. Complete the proof that △VYZ≅△WYX.VWXYZ
Answers
The statement
[tex]VY\cong WX[/tex]is true because
[tex]\Delta VWY[/tex]is an equilateral triangle.
Now, the last statement is true because the triangles have 2 sides and one angle congruent, therefore, by the SAS criterion, the triangles are congruent.
Answer:4.- Triangle VWY is an equilateral triangle.
5.- SAS criterion.
A bridge AB is to be built across a river. The point C is located 62m from B, and angle A is 80 degrees, angle C is 60 degrees. How long is the bridge
Answers
The points A, B, and C form a triangle.
From the given information in the question, the triangle ABC can be drawn to have the following parameters:
Recall the Sine Rule. Applied to the triangle above, the rule is stated as follows:
[tex]\frac{BC}{\sin A}=\frac{AC}{\sin B}=\frac{AB}{\sin C}[/tex]The length of the bridge is AB. Given that the measures of angles A and C, and side BC are known, the following ratio is used to solve:
[tex]\frac{BC}{\sin A}=\frac{AB}{\sin C}[/tex]Substituting known values, the length of AB is calculated as follows:
[tex]\begin{gathered} \frac{62}{\sin80}=\frac{AB}{\sin60} \\ AB=\frac{62\times\sin60}{\sin80} \\ AB=54.52 \end{gathered}[/tex]The bridge is 54.52 m long.
Given that angle A lies in Quadrant III and sin(A)= −17/19, evaluate cos(A).
Answers
As we know;
[tex]sin^2(x)+cos^2(x)=1[/tex]We will use this equality. We take the square of the sine of the given angle and subtract it from [tex]1[/tex].
[tex]sin^2(A)=(-\frac{17}{19} )^2=\frac{289}{361}[/tex][tex]sin^2(A)+cos^2(A)=1[/tex][tex]sin^2(A)=1-cos^2(A)[/tex][tex]\frac{289}{361}=1-cos^2(A)[/tex][tex]cos^2(A)=1-\frac{289}{361} =\frac{72}{361}[/tex][tex]\sqrt{cos^2(A)} =cos(A)[/tex][tex]\sqrt{\frac{72}{361} }=\frac{6\sqrt{2} }{19}[/tex]In the third region the sign of cosines is negative. Therefore, our correct answer should be as follows;
[tex]cos(A)=-\frac{6\sqrt{2} }{19}[/tex]* #3: Write the mixed number shown below as a decimal. 6 3/4
Answers
Answer:
6.75
Hope it helps!
Let me know if its wrong
20 ping pong balls are numbered 1-20, with no repitition of any numbers. What is the probability of selecting one ball that is either odd or less than 5?
Answers
given 20 ping pong balls
numbered 1-20
odd numbers = 1, 3, 5, 7, 9, 11, 13, 15, 17, 19
total odd numbers = 10
numbers less than 5 = 1, 2, 3, 4
total numbers less than 5 = 4
since 1 and 3 are in both sides,
total number of porbabilities
= 10 + 4 - 2
= 12
the probability of selecting one ball
= 12/20
= 3/5
= 0.6
therefore the probabilty of selecting one ball that is either odd or less than 5 = 0.6
Find the measures of the sine and cosine of the following triangles
Answers
Let x be the side opposite to angle 62 degrees
Let y be the adjacent angle.
The sine of the angle is given as follows:
[tex]\begin{gathered} \sin62=\frac{Opposite}{Hypotenuse}=\frac{x}{10} \\ \end{gathered}[/tex]The cosine is given as:
[tex]\cos62=\frac{Adjacent}{Hypotenuse}=\frac{y}{10}[/tex]I need help with this answer can you explain it
Answers
The solution.
The correct answer is y-intercept at (0,1) and decreasing over the interval
[tex]\lbrack-\infty,\infty\rbrack[/tex]Hence, the correct answer is the last option (option D)
7. Find the slope of a line which passes through the origin and point (2,4).A 0.5B -0.5C 2D 4
Answers
Answer:
C
Step-by-step explanation:
the slope of a line is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.
in our case here we are going e.g. from the origin (0, 0) to (2, 4).
so, x changes by +2 (from 0 to 2).
y changes by +4 (from 0 to 4).
therefore, the slope is
+4/+2 = 2
FYI - the direction is not important. it works the same way in the other direction. but what is important : once you pick a direction for one coordinate, you have to use the same direction for the second one. you cannot go e.g. for x in one direction and for y in the other.
Х о 12 3 4 у -6 1 8 15 22what is the slope intercept form