Answers
Recall that :
1) A function
[tex]f\mleft(x\mright)[/tex]translated n-units to the left is
[tex]f\mleft(x-n\mright).[/tex]2) A function
[tex]h\mleft(x\mright)[/tex]translated m-units up is:
[tex]h\mleft(x\mright)+m.[/tex]3) A function g(x) reflected over the x-axis is:
[tex]-g(x)\text{.}[/tex]The parent function is:
[tex]y=\sqrt[]{x}\text{.}[/tex]The function of the graph of the above function translated horizontally 3 units to the left is:
[tex]y=\sqrt[]{x+3}.[/tex]The function of the graph of the above function translated vertically 4 units up is:
[tex]y=\sqrt[]{x+3}+4.[/tex]The function of the graph of the above function reflected over the x-axis is:
[tex]y=-(\sqrt[]{x+3}+4)=-\sqrt[]{x+3}-4.[/tex]Finally, the function of the graph of the above function stretched vertically by a scale factor of 2 is:
[tex]y=-2\sqrt[]{x+3}-4.[/tex]Answer:
The graph of the function has a horizontal translation Left 3 and vertical translation Up 4. The graph has been reflected over the x-axis and has been Vertically stretched.
Related Questions
Christine ran a video game competition and recorded the scores of all the contestants. Score Number of people 426 4 572 1 859 2 900 1 1 951 2 X is the score that a randomly chosen person scored. What is the expected value of X? Write your answer as a decimal.
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The expected value is defined by
[tex]E=\Sigma x\cdot P(x)[/tex]We have to multiply each score by its probability
[tex]\begin{gathered} E=426\cdot\frac{4}{10}+572\cdot\frac{1}{10}+859\cdot\frac{2}{10}+900\cdot\frac{1}{10}+951\cdot\frac{2}{10} \\ E=170.4+57.2+171.8+90+190.2 \\ E=679.6 \end{gathered}[/tex]Hence, the expected value is 679.6.Determine the possible numbers of positive real zeros, negative real zeros, and imaginary zeros for the function. g(x) =x^5-2x^3-x^2+6
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Step-by-step explanation:
Note: The term root and zero are used interchangeably.
Use Descartes Rule of Signs,
For the function, f(x), For every sign change, we have a positive root. If we have at least 2 positive roots, we either have that said number of roots or 2 less number of roots until we reach 0.
For example if we have 8 positive roots, we either have 8,6,4,2, or 0 positive roots
For the function f(-x), For every sign change we have a negative root.. If we have at least 2 negative roots, we either have that said number of roots or 2 less number of roots until we reach 0.
For example, if we have 7 possible roots, we either have 7,5,3,1 possible negative roots.
For g(x), we have 2 sign changes, so 2 positives root or none
[tex]g( - x) = ( - x) {}^{5} - 2( - x) {}^{3} - ( - x) {}^{2} + 6[/tex]
[tex]g( - x) = - {x}^{5} + 2 {x}^{3} - {x}^{2} + 6[/tex]
We have 3 sign changes, so we have 3 or 1 negative roots.
The degree of the polynomial tells us the max possible of zeroes. So the total number of zeroes is 5. That will always be the case for this polynomial so fill every row under the total number columns as 5.
The following possible combinations
2 positive zeroes, 3 negative zeroes, 0 imaginary zeroes
2 positive zeroes, 1 negative zeroes, 2 imaginary zeroes
0 positive zeroes, 3 negative zeroes, 2 imaginary zeroes
0 positive zeroes, 1 negative zeroes, 4 imaginary zeroes
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. To keep in shape, Tisha exercises at a track near her home. She requires 24 minutes to do 6 laps running and 3 laps walking. In contrast, she requires 20 minutes to do 6 laps running and 2 laps walking. Assuming she maintains a consistent pace while running and while walking, how long does Tisha take to complete a lap? Tisha takes minutes to run a lap and minutes to walk a lap.
Answers
Let R be the minutes Tisha runs and W be the minutes Tisha walks. Since she requires 24 minutes to do 6 laps running and 3 laps walking, we have the following equation:
[tex]6R+3W=24[/tex]Now, when she requires 20 minutes to do 6 laps running and 2 laps walking, we have:
[tex]6R+2W=20[/tex]So, we have the following system of equations:
[tex]\mleft\{\begin{aligned}6R+3W=24 \\ 6R+2W=20\end{aligned}\mright.[/tex]We are going to solve it by elimination. Notice that the coefficients of R are the same, so we just have to multiply one equation by -1 and add it altogether to the other equation:
[tex]\begin{gathered} (6R+2W=20)(-1) \\ \Rightarrow-6R-2W=-20 \end{gathered}[/tex]Then:
[tex]\begin{gathered} 6R+3W=24\rbrack \\ -6R-2W=20 \\ \Rightarrow(6R-6R)+(3W-2W)=24-20 \\ \Rightarrow W=4 \end{gathered}[/tex]Now we use the value W=4 to find R:
[tex]\begin{gathered} W=4 \\ 6R+3W=24 \\ \Rightarrow6R+3\cdot4=24 \\ \Rightarrow6R=24-12=12 \\ \Rightarrow6R=12 \\ \Rightarrow R=\frac{12}{6}=2 \\ R=2 \end{gathered}[/tex]Therefore, it takes Tisha to complete a lap 2 minutes if she's running and 4 minutes if she's walking.
Consider the following graph of two functions.(8-1-2)Step 3 of 4: Find (8.5(-2)Enable Zoom/Pan866) = -3010-35SG) = x + 3
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The question requires that we evaluate the value of:
[tex](g\cdot f)(-2)[/tex]Recall that:
[tex]\left(g\cdot \:f\right)\left(x\right)=g\left(x\right)\cdot \:f\left(x\right)[/tex]Therefore, we have that:
[tex]\left(g\cdot\:f\right)\left(-2\right)=g\left(-2\right)\cdot\:f\left(-2\right)[/tex]We can get the values of g(-2) and f(-2) from the graph as shown below:
Therefore, we have:
[tex]\begin{gathered} g(-2)=5 \\ f(-2)=1 \end{gathered}[/tex]Hence, we can calculate the composite function to be:
[tex]\begin{gathered} (g\cdot f)(-2)=5\times1 \\ (g\cdot f)(-2)=5 \end{gathered}[/tex]QL An initial investment amount P, an annual interest rate r, and a time t are given. Find the future value of the investment when interest is compounde monthly, (c) daily, and (d) continuously. Then find (e) the doubling time I for the given interest rate. P = $2500, r=3.95%, t = 8 yr Te luture value ore vesmen we erst is Compouleu annually iS J400.29 (Type an integer or a decimal. Round to the nearest cent as needed.) b) The future value of the investment when interest is compounded monthly is $3,427.30 (Type an integer or a decimal. Round to the nearest cent as needed.) c) The future value of the investment when interest is compounded daily is $3429.02 (Type an integer or a decimal. Round to the nearest cent as needed.) d) The future value of the investment when interest is compounded continuously is $ 3429.08 (Type an integer or a decimal. Round to the nearest cent as needed.) e) Find the doubling time for the given interest rate. T= yr (Type an integer or decimal rounded to two decimal noon
Answers
User asks to solve part e of the problem.
We are asked to find the doubling time for the interest rate in the case of continuous compounding.
Recall that the formula for the continuously compounding interest rate is:
[tex]A=P\cdot e^{(r\cdot t\}}[/tex]Then, we need to solve when the value "A" (Accrued value) doubles the principal P, that is:
[tex]2P=P\cdot e^{(r\cdot t\}}[/tex]Dividing both sides by P and then applying natural logarithms (ln) on both sides, we get:
[tex]\begin{gathered} 2P=P\cdot e^{(r\cdot t\}} \\ 2=e^{(r\cdot t)} \\ \ln (2)=r\cdot t \\ \ln (2)=0.0395\cdot t \\ t=\frac{\ln l(2)}{0.0395} \\ t=17.548 \end{gathered}[/tex]which gives us approximately 17.548 years which we round to two decimals as: 17.55 years
Translate the sentence into an inequality.Twice the difference of a number and 10 is greater than 29.
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We will have the following:
[tex]2(x-10)>29[/tex]Which binomial is a factor of 49x2 + 84xy + 36y2?А. 7х + 6уВ. x+6yC. х- 6уD. 7х- 6уPLEASE HELP ASAP I WILL GIVE YOU BRAINLIEST!!!!!!
Answers
Factoring 2nd-degree polynomials make use of the factors of the numerical coefficient of the first and last term.
The numerical coefficient of our first term is 49. The possible factors of 49 are 1 and 49, 7 and 7, -1 and -49, and -7 and -7.
The numerical coefficient of our last term is 36. The possible factors of 36 are 1 and 36, 6 and 6, 12 and 3, 4 and 9, -1 and -36, -6 and -6, -3 and -12, and -4 and -9.
Since the choices only show 1,7 and 6,6, we will only be focusing on these factors. Our goal here would be for us to have a result of +84 when the two pairs of factors are multiplied and then multiplied to two.
The second row gives us the middle term +84. Therefore, the factors of the polynomial are (7x + 6y)(7x + 6y). The answer is Option A.
please help, and answer quickly my brainly keeps crashing. please answer quickly.
Answers
We will have the following:
We calculate the total surface area as follows:
[tex]A_s=4(\frac{11in\ast10in}{2})+(11in)^2\Rightarrow A_s=341in^2[/tex]So, the total surface area of the pyramid is 341 in^2.
An automobile battery manufacturer claims that its midgrade battery has amean life of 50 months with a standard deviation of 6 months. Suppose thedistribution of battery lives of this particular brand is approximately normal.ba. On the assumption that the manufacturer's claims are true, find theprobability that a randomly selected battery of this type will last less than 48months.Your answer6b. On the same assumption, find the probability that the mean of a randomsample of 36 such batteries will be less than 48 months.
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Given data:
The given mean life is m=50 months.
The given standard deviation is s=6 months.
The given value of battery life is x= 48 months.
The expression for the probability of that a randomly selected battery will last less than 48 months is,
[tex]\begin{gathered} P(Z<\frac{x-m}{s})=P(Z<\frac{48-50}{6}) \\ =P(Z<-\frac{1}{3}) \end{gathered}[/tex]Refere the Z-table the value of the above expression is 0.3707.
Thus, the probability that a randomly selected battery will last less than 48 months is 0.3707.
Students sold 342 tickets to the school carnival at $11.75 each. Nine tickets were refunded. Estimate the amount of money that the school took in. Is your estimate and over estimate or underestimate?
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Let:
x = Number of tickets
a = Price of each ticket
T = Total amount of money
so:
[tex]\begin{gathered} T=ax \\ \end{gathered}[/tex]Since nine tickets were refunded,
let:
y = Number of tickets refunded.
[tex]\begin{gathered} T=ax-ay \\ where\colon \\ a=11.75 \\ x=342 \\ y=9 \\ so\colon \\ T=11.75(342)-11.75(9) \\ T=4018.5-105.75 \\ T=3912.75 \end{gathered}[/tex]Answer:
$3912.75
PLEAS HELP ANSWER ASAP
The slopes of a quadrilateral are -1/2, 3/2, -1/2, and 3/2. What conclusion about this shape can be made?
A. The quadrilateral is a parallelogram, because there are two pairs of equal slopes, and Thus two pairs of parallel opposite sides.
B. The quadrilateral is a trapezoid, because there are two pairs of equal slopes, and thus two pairs of parallel opposite sides.
C. The quadrilateral is a parallelogram, because there is one pair of equal slopes, and thus one pair of parallel opposite sides.
D. The quadrilateral is a trapezoid, because there is one pair of equal slopes, and thus one pair of parallel opposite sides.
Answers
Answer
the first one, A.
Step-by-step explanation:
hope this helps
A car advertisement states that a certain car can accelerate from rest to 72 km/h in 12.5 seconds.
Initially the car is at rest, so the initial velocity is ______
m/s.
The car speeds up to 72 km/h which is equivalent to _______
m/s. Find the car’s average acceleration.
The acceleration of the car is _______
m/s2
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The motion of the car (velocity and acceleration) based on the advertisement can be described as follows;
The initial velocity of the car is 0 m/s
72 km/h is equivalent to 20 m/s
The acceleration of the car is 1.6 m/s²
What is velocity and acceleration?Velocity is the rate of change of displacement
Acceleration is the rate of change of velocity with time
The car accelerates from rest indicates that the initial velocity of the car is 0 m/sThe speed to which the car accelerates to is 72 k m/h
To convert from km/h to m/s, the conversion factor is1000/3600
Therefore;
72 km/h = 72 × 1000/3600 m/s = 20 m/s
The speed of the car of 72 km/h is equivalent to 20 m/sAcceleration can be found from the rate of change of the velocity as follows;
[tex]Acceleration = \dfrac{Change\, in \, \, velocity}{Time}[/tex]
The time it takes the car to increase from 0 to 72 kph (20 m/s) = 12.5 seconds
The acceleration of the car is therefore;
[tex]a = \dfrac{20 - 0}{12.5 - 0} = 1.6[/tex]
The acceleration of the car is 1.6 m/s²Learn more about velocity and acceleration here:
https://brainly.com/question/14344386
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2. Given that the quadrilateral PQRS is a parallelogram, ST = 6x + 3 andQT= 4x + 27, what is the length of QS?161145138150None of these answers are correct
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Given: The quadrilateral PQRS
To Determine: The value of QS
Solution
Please note that the diagonal of a quadrilaterals bisect each other. This is as shown below
Therefore ST equals QT
[tex]\begin{gathered} ST=QT \\ 6x+3=4x+27 \\ 6x-4x=27-3 \\ 2x=24 \\ x=\frac{24}{2} \\ x=12 \end{gathered}[/tex][tex]\begin{gathered} QS=ST+QT \\ QS=6x+3+4x+27 \\ QS=10x+30 \\ QS=10(12)+30 \\ QS=120+30 \\ QS=150 \end{gathered}[/tex]Hence QS = 150
Construct parametric equations describing the graph of the following equation.x = 3y +3If y = 4 + 1, find the parametric equation for x.
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Given:
[tex]x=4y+3,y=4+t[/tex]Required: Parametric equation of y.
Explanation:
Substitute 4+t for y into the equation of x.
[tex]\begin{gathered} x=4(4+t)+3 \\ =16+4t+3 \\ =4t+19 \end{gathered}[/tex]So, the parametric equation for x is x = 4t+19.
Final Answer: The parametric equation of x is x = 4t + 19.
square pyramid volume 225 cubic inches , base Edge 5 in . Determine the height of the pyramid
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The volume of a pyramid is:
[tex]V=\frac{1}{3}\times B\times h[/tex]Where B is the area of the base and h is the height.
Since it's a square pyramid, the base has the shape of a square. So it's area is:
[tex]B=5in\times5in=25in^{2}[/tex]And we have that the volume is 225in³. We can replace these values into the formula for the volume and solve for h:
[tex]\begin{gathered} 225in^3=\frac{1}{3}\times25in^2\times h \\ \frac{3\times225in^{3}}{25in^2}=h \\ h=27in \end{gathered}[/tex]The height of the pyramid is 27 inches
Write the equation of the line in slope-intercept form. Through the points (-8, 15) and (6, 15)
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Question: Write the equation of the line in slope-intercept form. Through the points (-8, 15) and (6, 15)
Solution:
The equation of the line in slope-intercept form is :
y = mx + b
where m is the slope of the line, and b is the y-coordinate of the y-intercept of the line. Now, the slope of the line is given by the following formula:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}[/tex]Where (X1,Y1) and (X2,Y2) are points on the line. In our case, we have that:
(X1, Y1) = (-8,15)
(X2,Y2) = (6,15)
Replacing these values in the equation of the slope we obtain:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}\text{ =}\frac{15-15}{6-(-8)}\text{ = 0}[/tex]then we have a horizontal line, because the slope is 0, for that, the equation of the line would be:
y = mx + b = 0(x) + b
then
y = b
now, take any point on the line, for example (x,y) = (6,15). Replacing this value in the previous equation, we obtain that the equation of the line is given by:
[tex]y\text{ = 15}[/tex]The legs of a right triangle have lengths of 15 cm and 112 cm. What is the length of the hypotenuse?
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ANSWER
113 cm
EXPLANATION
The Pythagorean Theorem states that for a right triangle with leg lengths a and b, and hypotenuse c, the square of the hypotenuse is equal to the sum of the squares of the legs,
[tex]c^2=a^2+b^2[/tex]In this case, the lengths of the legs are 15 cm and 112 cm, so the length of the hypotenuse is,
[tex]c=\sqrt{15^2+112^2}=\sqrt{225+12544}=\sqrt{12769}=113cm[/tex]Hence, the length of the hypotenuse is 113 cm.
Im trying to plot a slope function on a graph y=2x+3
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1) To plot a linear equation, like y=2x +3 let's visualize the graph
2) Set this function as an equation, to find the root of that function the x coordinate
y= 2x +3 Turn this to an equation
2x +3 =0 Subtract 3 from both sides
2x +3 -3 = -3
2x+0=-3 Divide both sides by 2
x=-3/2 -3/2 = -1.5
Looking at the function, we can see that the slope m=2, m>0, and the y-intercept is 3
Now we can set a table, where we can choose any value for x and then plug it into the function
x = 0 , y = 2(0) +3 y= 3
x= 1, y = 2(1) +3 y= 5
x=-1.5 y = 2(-1.5) +3 y=0
x | y
0 3
1 5
-1.5 0
At least 3 points already determine a line
Our graph must be like this:
Solve for y.2(y – 11) = 16HURRYYYY!!!
Answers
The initial expression is:
2 ( y - 11 ) = 16
Using the distributive property:
2y - 2*11 = 16
2y - 22 = 16
Adding 22 on both sides:
2y - 22 + 22 = 16 + 22
2y = 38
Dividing by 2 on both sides:
[tex]\begin{gathered} \frac{2y}{2}=\frac{38}{2} \\ y=19 \end{gathered}[/tex]Answer: y = 19
could u please help me by writing this out as a example ? solve for x
Answers
ANSWER:
In the given expression, we have to solve for 'x', and show the steps.
[tex]r\text{ =}\frac{5+x}{w}[/tex]Next, I am gonna solve it for 'x'
[tex]\begin{gathered} r=\frac{5+x}{w} \\ M\text{ultiplying both sides by 'w' and subtracting 5 from both sides gives.} \\ wr=5+x \\ x=wr-5 \end{gathered}[/tex]We have solved for 'x'.
multiple both sides by w
rw = 5 + x
subtract both sides by 5
rw - 5 = x
switch sides
x = rw - 5
Randall is buying house for $242,000. His down payment is 55% of the price. The mortgage ratefor a 5-year term is 8.2% per annum, compounded semi-annually, amortized over 25 years, andpaid monthly.a) For how much is the mortgage, once the down payment is deducted and compounded?b) How much are the monthly payments,,,,,
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given values
[tex]\begin{gathered} Total\text{ payment}=242000 \\ down\text{ payment}=55\% \\ rate\text{ for compunding}=8.2\%=\frac{8.2}{100}=0.082 \\ n=2\text{ since it is compounded semi-annually} \\ t=5\text{ years} \end{gathered}[/tex]STEP 2: Find the mortgage value
[tex]mortgage\text{ }value=Total\text{ payment}-Down\text{ payment}[/tex]Down payment will be calculated:
[tex]\begin{gathered} 55\%\text{ of \$242000} \\ \frac{55}{100}\cdot242000=0.55\cdot242000=\text{ \$}133100 \end{gathered}[/tex]To calculate the mortgage value, we first calculate the compounded amount,
[tex]\begin{gathered} A = P(1 + \frac{r}{n})^{nt} \\ A=108900\cdot(1+\frac{0.082}{2})^{2\cdot5} \\ A=108900\cdot(1.041)^{10} \\ A=162755.3131\approx\text{ \$}162755.31 \end{gathered}[/tex]Hence, the mortgage value will be approximately $162755.31
Then we calculate the monthly payments
Number of months between 25 years will be:
[tex]\begin{gathered} 1\text{ year}=12\text{ months} \\ 25\text{ years}=25\cdot12=300\text{ months} \end{gathered}[/tex]Therefore, the monthly payments will be:
[tex]\text{ }\frac{\text{ \$}162755.31}{300}=542.5177\approx\text{ \$}542.52[/tex]The monthly payments will be approximately $542.52
I you could just give me the answer that would be great no explanation needed:)
Answers
f(n) = -1.2n + 38.1
Hence, for an additional race
the finishing time, f(n+1), is given
f(n+1) = -1.2(n+1) + 38.1 = -1.2n + 38.1 -1.2
Which implies that
f(n+1) = f(n) - 1.2
This implies that the finishing time decreases by 1.2minutes
The model predicts that for each additional race a runner has run, the finishing time decreases by about 1.2 minutes
write each percent as a fraction in simplest form 1. 80%=
Answers
4/5
Explanation:
80%
[tex]\begin{gathered} \frac{80}{100}=\text{ }\frac{8}{10} \\ \text{this we divided both numerator an denominator by 10 } \end{gathered}[/tex]dividing both numerator an denominator by 2:
[tex]\frac{8}{10}=\text{ }\frac{4}{5}[/tex]fraction in simplest form = 4/5
triangle QRS is reflected across the y axis to create triangle QRS complete the rule that describes the coordinates of triangle QRS after the reflection has occurred
Answers
The rule for describing the reflection of the given figure QRS is as follow:
If the coordinate of each point of the triangle is (x,y), then, after the reflection across the y axis the new coordinates become:
(x,y) => (-x,y)
Answer:
[tex](x',y')=(-x,y)[/tex]
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into thecorrect position in the answer box. Release your mouse button when the item is place. If you change your mind, dragthe item to the trashcan. Click the trashcan to clear all your answers.y1098765B'C'43BсA'D'3456789 10ADХ-2 -1-2What is the length of CC' ?
Answers
as we can see from the graph coordinates of point C are (2,2) and coordinates of point C' are (7,4)
So by distance formula CC' will be
[tex]\begin{gathered} \text{length of cc'=}\sqrt[]{(7-2)^2+(4-2)^2}^{} \\ =\sqrt[]{25+4} \\ =\sqrt[]{29} \end{gathered}[/tex]So length of CC' is
[tex]\sqrt[]{29}[/tex]Evaluate expressions with parenthesesWhere can we put parentheses in 45 – 22 + 9 to make it equivalent to 14?Choose 1 answer:A45 – (22 +9)(45 – 22) +9Stuck? Review related articles/videos or use a hint.Report
Answers
Answer
45 – (22 +9)
Explanation
Given the expression
45 - 22 + 9
In order to rearrange the expression to get 14, this can be expressed as:
= 45 - (22 + 9)
= 45 - 31
= 14
Hence the required answer is 45 – (22 +9)
Problem 1. Find the measure of each angle in the diagram below 85° (2x) x 35°
Answers
Answer:
x =80 degrees
2x = 160 degrees
Explanation:
The sum of angles at a point is 360 degrees. Therefore:
[tex]\begin{gathered} 85\degree+2x+x+35\degree=360\degree \\ 3x=360\degree-85-35 \\ 3x=240 \\ x=\frac{240}{3} \\ x=80 \end{gathered}[/tex]Therefore, the measure of the other angle is:
[tex]2x=2\times80=160^0[/tex]Write an equivalent expression using the distributive property:
2(3x+4b)
Answers
Answer:
[tex]2(3x + 4b ) = 6x + 8b[/tex]
need help asap will give you 5 stars! need a quick worker!
Answers
Explanation
The question wants us to get the length of the missing side
To do so, we will use the trigonometric ratio:
[tex]undefined[/tex]Early last summer, Xavier planted a flower. Let y be the flower's height (incentimeters) x days after he planted it. Use the table to relate the independent variable x to thedependent variable y. First describe the relationship in words. Then write an equation. Use theequation to find the flower's height after 3 days.
Answers
i) The equation is; y = x + 16
ii) After 3 days, the height of the flower is 19 centimeters
Here, we want to describe a relationship
We start by describing the relationship between the flower's height and the number of days after it was planted
As we can see from the table, the value of x plus 16 equals the value of y
In the equation from, we have this as;
[tex]x+16\text{ = y}[/tex]To find the height of the flower after 3 days, we simply substitute the value of 3 for y
We have this as;
[tex]\begin{gathered} y\text{ = 16 + 3} \\ y\text{ = 19 } \end{gathered}[/tex]