Exponential Transformations: Identify if they represent growth or decay, range, horizontal move, vertical move, flip, stretch or shrink Y = 3(1/2) ^x+3 Y = 4^x-3 + 6Y = -2^x - 5 Y = (2/3)^x-2 +1
Answers
If b > 1 then it's an exponential growth
If b < 1 then it's an exponential decay
Y = 3(1/2)^(x+3) decay
Y = 4^(x-3) + 6 growth
Y = -2^x - 5 decay
Y = (2/3)^(x-2) +1 decay
The y-intercept is found replacing x = 0 into the equation.
Y = 3(1/2)^(0+3)
Y = 3(1/2)^3
Y = 3(1/8)
Y = 3/8
Y = 4^(0-3) + 6
Y = 4^(-3) + 6
Y = 1/64 + 6
Y = 385/64
Y = -2^0 - 5
Y = -1 - 5
Y = -6
Y = (2/3)^(0-2) +1
Y = (2/3)^(-2) +1
Y = (3/2)^(2) +1
Y = 9/4 +1
Y = 13/4
The vertical movement is found identifying k in the equations.
Y = 3(1/2)^(x+3) k = 0 no vertical move
Y = 4^(x-3) + 6 k = 6 vertical move 6 units up
Y = -2^x - 5 k = -5 vertical move 5 units down
Y = (2/3)^(x-2) +1 k = 1 vertical move 1 unit up
If the equation is flipped or not is seen in the a parameter. If a < 0, it's flipped, if a > 0, it isn't flipped
Y = 3(1/2)^(x+3) a > 0 not flipped
Y = 4^(x-3) + 6 a > 0 not flipped
Y = -2^x - 5 a < 0 flipped
Y = (2/3)^(x-2) +1 a > 0 not flipped
The range is found with help of the vertical move and the flip
Y = 3(1/2)^(x+3) no vertical move, not flipped range: [0, ∞]
Y = 4^(x-3) + 6 vertical move 6 units up, not flipped range: [6, ∞]
Y = -2^x - 5 vertical move 5 units down range: [-5, -∞]
Y = (2/3)^(x-2) +1 vertical move 1 unit up, not flipped range: [1, ∞]
The horizontal movement is found identifying h in the equations.
Y = 3(1/2)^(x+3) h = 3 horizontal move 3 units left
Y = 4^(x-3) + 6 h = -3 horizontal move 3 units right
Y = -2^x - 5 h = 0 no vertical move
Y = (2/3)^(x-2) +1 h = -2 horizontal move 2 units right
If the equation is stretched or shrunk is seen in the a parameter. If a > 1, the function stretches, if 0 < a < 1, 1, the function shrinks
Y = 3(1/2)^(x+3) a = 3 stretches
Y = 4^(x-3) + 6 a = 1 doesn't stretch nor shrink
Y = -2^x - 5 a = -1 doesn't stretch nor shrink
Y = (2/3)^(x-2) +1 a = 2/3 shrinks
Related Questions
The maximum grade allowed between two stations in a rapid transit rail system is 3.5%. Between station a and station b which are 290 feet apart, the tracks rise 8 ft. What is the grade of the tracks between these stations ? Round the answer to the nearest tenth of a percent. Does this grade meet the rapid transit rails standards?
Answers
Given,
Station A and Station B are 290 feet apart.
Tracks rise 8 feet.
We need to find the slope of the tracks, because the slope of the track is the gradient of the track.
The slope is rise over run.
The rise is "8"
The run is "290"
Hence, the slope is >>>>>
[tex]\frac{8}{290}\approx0.027586[/tex]To convert it to a percentage, we multiply by 100. Thus,
[tex]0.027586\times100\approx2.76\%[/tex]This is within the tolerance range of less than 3.5%.
So, this grade meets the rapid transit rail standards.
AnswerGrade of tracks = 2.8%Yes, it does meet the rapid transit rail standards.Inequality statement for -13,-25,-8
Answers
The inequality statement for -13,-25,-8 is -13 > -25 < -8.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
It should be noted that -13 is greater than -25 while -25 is less than -8.
In this case, -13 > -25 < -8.
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Sandy was shopping and saw that 4lbs of meat costs $8.00. Calculate the unit price for 1 oz of the meat. $____
Answers
To answer this question first we convert from lbs to oz.
Recall that:
[tex]1\text{ lb = 16 oz.}[/tex]Therefore,
[tex]4\text{ lbs= 64 oz.}[/tex]Now, since 64 oz cost $8.00, then the cost of 1 oz of meat is:
[tex]\frac{8.00}{64}\text{dollars}\approx0.13\text{ dollars.}[/tex]Answer: $0.13.
A ferris Wheel has a radius of 65 feet. What is the circumference of the wheel?
Answers
Circumference of the wheel = 408.2 ft
Explanation:radius = 65 ft
Circumference of the wheel = circumference of a circle
Circumference of a circle = 2πr
π = 3.14
Circumference of a circle = 2 × 3.14 × 65
Circumference of a circle = 408.2 ft
Circumference of the wheel = 408.2 ft
The function h(x) shown is the result of adding two functions, f(x) and g(x).
Which statement could be used to describe the functions?
Answers
The domains of both f(x) and g(x) must be (–∞, ∞).
What is a domain?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x).
Here, we concluded that
The domains of both f(x) and g(x) must be (–∞, ∞).
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Earn,deposit, increase and raise all have positive valuesTrue or False
Answers
We will have the following:
*Earn: By definition represents a positive value, since you cannot "earn" a negative quantity.
*Deposit: Deposits are "neutral" since they represent the movement of money but not neccesarily an increase, and sometimes it can be also a payment, so it can also be net negative.
*Increase: By definition is a positive value.
*Raise: By definition is a positive value.
So, it is false. Reason:
A deposit represents a net neutral, since it is refering to the movement of money but not it's increase neccesarily, and sometimes is also a negative, since it can be used as payment, thus representing a net negative value.
A box contains the name of every student in the school. One hundred names are drawn from the box and students are asked their opinion of the new pizza served in the cafeteria. (A) biased or(B) unbiased
Answers
This is an unbiased sampling because there is not a systematically opinion that favors some outcomes over others. So the answer is B
solve the system of linear equations by substitution 3y=-2x and y=x-5
Answers
Step 1
Given;
[tex]\begin{gathered} 3y=-2x--(1) \\ y=x-5--(2) \end{gathered}[/tex]Required; To solve the system of linear equations
Step 2
Find the value of y and x
[tex]\begin{gathered} Substitute\text{ 2 into 1} \\ 3(x-5)=-2x \\ 3x-15=-2x \\ 5x=15 \\ \frac{5x}{5}=\frac{15}{5} \\ x=3 \end{gathered}[/tex][tex]\begin{gathered} From\text{ 2, y=x-5} \\ y=3-5=-2 \end{gathered}[/tex]Answers;
[tex]x=3,\text{ y=-2}[/tex]Subtract.7x2 - 5x+3(2x2 +7x-4)A. 5x2 - 2x + 7B. 5x2 - 12x +7C. 5x2 + 12x-1D. 5x2 + 2x-1
Answers
We have to evaluate the expression 7x^2 - 5x + 3 - (2x^2 +7x-4):
[tex]\begin{gathered} 7x^2-5x+3-(2x^2+7x-4) \\ (7-2)x^2+(-5-7)x+(3-(-4)) \\ 5x^2-12x+(3+4) \\ 5x^2-12x+7 \end{gathered}[/tex]Answer: B. 5x2 - 12x +7
Use my radians find the amplitude and period of each function then graph
Answers
For a function of the form:
[tex]y=acos(b\theta)[/tex]a = amplitude = 2
b = angular frequency = 1/4
The period can be calculated as follows:
[tex]\begin{gathered} T=\frac{2\pi}{b} \\ So: \\ T=\frac{2\pi}{1/4} \\ T=8\pi \end{gathered}[/tex]Now, we can graph the function easily:
Find the value of x. 14 6 / 110° 9 70
Answers
We are given a triangle crossed by two parallel lines. The lines are parallel since their corresponding angles are the same. Therefore, from Thale's theorem we have the following relationship:
[tex]\frac{14}{6}=\frac{x}{9}[/tex]Now we solve for "x" by multiplying by 9 on both sides of the equation:
[tex]\frac{14}{6}\times9=x[/tex]Solving the operations we get:
[tex]21=x[/tex]Therefore, x = 21
The two triangles below are similar. Also, m A = 15° and m ZC - 35° as shown below Find m2P, m 2Q, and m ZR. Assume the triangles are accurately drawn
Answers
Answer
Angle R = 15°
Angle P = 130°
Angle Q = 35°
Explanation
First noting that the sum of angles in a triangle is 180°.
We first need to calculate the Angle B for the first triangle.
Angle A + Angle B + Angle C = 180°
15° + Angle B + 35° = 180°
Angle B + 50° = 180°
Angle B = 180° - 50°
Angle B = 130°
We are then told to find Angles P, Q and R.
We are told that the two triangles are similar .
Two similar triangles will have the same angle measures.
So, we just need to note the corresponding angles and equate the unknowns.
Triangle ABC is similar to Triangle RPQ
Angle R = Angle A = 15°
Angle P = Angle B = 130°
Angle Q = Angle C = 35°
Hope this Helps!!!
If we consider only the cost of gasoline, how much does it cost ( in dollars) to drive each mile ? Round to the nearest cent.
Answers
Given:
The cost of gasoline, c=$2.20/gallon.
The car gets x=26 miles per gallon.
The cost to drive each mile if gasoline costs $2.20/gallon is
[tex]\begin{gathered} T=\frac{c}{x} \\ =\frac{\frac{2.20\text{ dollars}}{1\text{ gallon}}}{\frac{26\text{ miles}}{1\text{ gallon}}} \\ =\frac{2.20\text{ dollars}}{1\text{ gallon}}\times\frac{1\text{ gallon}}{26\text{ miles}} \\ =0.08 \end{gathered}[/tex]Therefore, the two fractions for obtaining the solution is,
[tex]\begin{gathered} \frac{2.20\text{ dollars}}{1\text{ gallon}} \\ \frac{1\text{ gallon}}{26\text{ miles}} \end{gathered}[/tex]The cost in dollars to drive each mile is $0.08 per mile (rounded to nearest cent).
fill in the blank with the correct answer. the number _______is divisibel by 2, 3, 4, 5, and 6
a)44
b)180
c)280
d)385
Answers
Answer:
b) 180
Explanation:
[tex]180 / 2 = 90\\180 / 3 = 60\\180 / 4 = 45\\180 / 5 = 36\\180 / 6 = 30[/tex]
Hope you have a nice day and a nice Thanksgiving!
A brainiliest would also be nice. thx.
Which of the following is the co-function of cos 58 degrees?tan 58°sin 58°cos 32°sin 32°
Answers
ANSWER
[tex]\sin 32^o[/tex]EXPLANATION
We want to find the cofunction of the given function.
The cofunction of a cosine function is:
[tex]\cos (\theta)=\sin (90-\theta)[/tex]Therefore, the cofunction of cos(58) is:
[tex]\begin{gathered} \cos (58)=\sin (90-58) \\ \cos (58^o)=\sin (32^o) \end{gathered}[/tex]That is the answer.
Hello,Can you please help with question 33 on the photo? Thank you
Answers
With the help of the given formula, we can find the first four terms of the sequence:
[tex]\begin{gathered} a_1=30 \\ a_2=a_{2-1}-10=a_1-10=20 \\ a_3=a_{3-1}-10=a_2-10=10 \\ a_4=a_{4-1}-10=a_3-10=0 \end{gathered}[/tex]Then, the first four terms of the sequence are 30, 20, 10, 0, ...
Now, as we can see, this is an arithmetic sequence because there is a common difference between each term. The explicit formula of an arithmetic sequence is shown below:
[tex]\begin{gathered} a_n=a_1+d(n-1) \\ \text{ Where} \\ \text{ d is the common difference} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} a_1=30 \\ d=-10 \end{gathered}[/tex][tex]\begin{gathered} a_n=a_1+d(n-1) \\ a_n=30-10(n-1) \\ \text{ Apply the distributive property} \\ a_n=30-10*n-10*-1 \\ a_n=30-10n+10 \\ a_n=-10n+40 \end{gathered}[/tex]Thus, a formula for the general term of the sequence is:
[tex]a_{n}=-10n+40[/tex]Now, we substitute n = 20 in the above formula to find the 20th term of the sequence:
[tex]\begin{gathered} a_{n}=-10n+40 \\ a_{20}=-10(20)+40 \\ a_{20}=-200+40 \\ a_{20}=-160 \end{gathered}[/tex]AnswerA formula for the general term of the sequence is:
[tex]a_{n}=-10n+40[/tex]The 20th term of the sequence is -160.
A data set has these values: 6, 8, 8, 10, 10, 10, 10, 12, 12, 14. The histogram ofthe distribution is shown.Aanb542<-057 9 11 13 15Data valuesWhich statement does not describe the data set?
Answers
It has a range of [tex]$15^{\prime \prime}$[/tex] is not describe the data set.
The data set is Symmetric.
it has a mode m=10= median = mean.
[tex]$$\begin{aligned}\text { Range } &=14-6 \\&=8\end{aligned}$$[/tex]
So option (c) is correct.
"It has a range of [tex]$15^{\prime \prime}$[/tex]
A data set is, for example, each student's test scores in a specific class. A data set is the number of fish consumed by each dolphin in an aquarium.
A data set is a grouping of data. A data set refers to one or more database tables in the case of tabular data, where each column of a table represents a specific variable and each row corresponds to a specific record of the data set in question.
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a. 10x-6=44b. (x+3)-15=48c. 4(x+6)-10=26d. 3(x+3)-15=48e.Which two equations have the same solution set? Write a sentence explaining how the properties of equality can be used to determine the pair without having to find the solution set for each.
Answers
a.
[tex]\begin{gathered} 10x-6=44 \\ 10x=44+6 \\ 10x=50 \\ x=\frac{50}{10} \\ x=5 \end{gathered}[/tex]b.
[tex]\begin{gathered} 9(x+3)-15=48 \\ 9x+27-15=48 \\ 9x+12=48 \\ 9x=36 \\ x=\frac{36}{9} \\ x=4 \end{gathered}[/tex]c.
[tex]\begin{gathered} 4(x+6)-10=26 \\ 4x+24-10=26 \\ 4x+14=26 \\ 4x=26-14 \\ 4x=12 \\ x=\frac{12}{4} \\ x=3 \end{gathered}[/tex]d.
[tex]\begin{gathered} 3(x+3)-15=48 \\ 3x+9-15=48 \\ 3x-6=48 \\ 3x=48+6 \\ 3x=54 \\ x=\frac{54}{3} \\ x=18 \end{gathered}[/tex]The answer in set notation
[tex]x=\mleft\lbrace5,4,3,18\mright\rbrace[/tex]e. Equation b and Equation d have the same solution set . Both of the equations is equals to 48.
1593 concert tickets were sold for a total of $22,491. If students paid $11 and nonstudents paid $17, how many student tickets were sold?
Answers
765 student tickets were sold
Explanation:Let the number of student tickets be represented by x
Let the number of nonstudent tickets be represented by y
1593 concert tickets were sold
x + y = 1593....................(1)
The total amount made = $22491
Cost of each student ticket = $11
Cost of each nonstudent ticket = $17
This can be interpreted mathematically as:
11x + 17y = 22491...............(2)
Mulitipy equation (1) by 17
17x + 17y = 27081...........(3)
Subtract equation (2) from equation (3)
6x = 4590
x = 4590/6
x = 765
765 student tickets were sold
Write the standard form of the equation of the circle described below. (6,-7) r=9
Answers
Solution
Step 1
write out the expression for the equation of a circle
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where the centers are (h,k)
h = 6
k = -7
r = 9
Step 2
Write out the required equation of the circle using the parameters
[tex]\begin{gathered} \text{The required equation thus is} \\ (x-6)^2+(y-(-7))^2=9^2 \\ (x-6)^2+(y+7)^2=81_{} \end{gathered}[/tex]A local bakery has determined the probability distribution for the number of cheesecake that they sell in a given day let X equal the number of cheesecake sold on a randomly selected day
Answers
1) First, from the question we see that we have a table with the probability distribution p(X) for the number of cheesecakes (X) sold on a randomly selected day. We know that the numbers in the table for P(X) should sum up to 1, that's because the total probability always sums 1. So using this fact we can see that:
[tex]P(x=15)=0.28[/tex]2) The probability of selling at least 10 cheesecakes is the sum of probabilities P(x) for x ≥ 10, using the data from the table and the probability obtained above we have:
[tex]\begin{gathered} P(x\ge10)=P(x=10)+P(x=15)+P(x=20) \\ P(x\ge10)=0.21+0.28+0.1 \\ P(x\ge10)=0.59 \end{gathered}[/tex]3) The probability of selling 5 or 15 cheesecakes is the joint probability of the events of selling 5 cheesecakes P(x = 5) or 15 cheesecakes P(x = 15) because they are independent events (i.e. P(x=5 ∩ x=15) = 0), we have:
[tex]\begin{gathered} P(x=5orx=15)=P(x=5)+P(x=15)-P(x=5andx=15) \\ P(x=5orx=15)=0.3+0.28-0 \\ P(x=5orx=15)=0.58 \end{gathered}[/tex]4) From the table we see that we don't have an assigned value for the probability of selling x = 25 cheesecakes, so the probability for this event is zero:
[tex]P(x=25)=0[/tex]5) The probability of selling at most 10 cheesecakes is the sum of the probabilities P(x) for x ≤ 10, using the data from the table we have:
[tex]\begin{gathered} P(x\leq10)=P(x=0)+P(x=5)+P(x=10) \\ P(x\leq10)=0.11+0.3+0.21 \\ P(x\leq10)=0.62 \end{gathered}[/tex]6) Finally, we must compute the expected value μ of cheesecakes sold on any given day, applying the following formula and the data of the table we get:
[tex]\begin{gathered} \mu=\sum ^{}_iX_i\cdot P(X_i) \\ \mu=0\cdot0.11+5\cdot0.3+10\cdot0.21+15\cdot0.28+20\cdot0.1 \\ \mu=9.8 \end{gathered}[/tex]Answers summary:
1) P(x = 15) = 0.28
2) P(x ≥ 10) = 0.59
3) P(x = 5 or x = 15) = 0.58
4) P(x = 25) = 0
5) P(x ≤ 10) = 0.62
6) μ = 9.8
can you please help me
Answers
Answer:
15
Explanation:
The y-intercept of a line is the point where it intersects the y-axis. This happens when x = 0; therefore, the y-coordinate of the y-axis is found by putting x = 0 in the equation given. This gives
[tex]18(0)-y=-15[/tex][tex]-y=-15[/tex][tex]y=15[/tex]which is our answer!
Factor 2x^2 - 10x - 12.2(x + 2)(x - 3) 2(x - 6)(x + 1)2(x - 1)(x + 6)
Answers
The factor is 2(x+1)(x-6).
From the question, we have
2x²-10x-12
=2x²-12x+2x-12
=2x(x-6)+2(x-6)
=(2x+2)(x-6)
=2(x+1)(x-6)
Factors :
The positive integers that can divide a number evenly are known as factors in mathematics. Let's say we multiply two numbers to produce a result. The product's factors are the number that is multiplied. Each number has a self-referential element. There are several examples of factors in everyday life, such putting candies in a box, arranging numbers in a certain pattern, giving chocolates to kids, etc. We must apply the multiplication or division method in order to determine a number's factors.The numbers that can divide a number exactly are called factors. There is therefore no residual after division. The numbers you multiply together to obtain another number are called factors. A factor is therefore another number's divisor.
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in a circle the radius is 11.5 which is the circumference??
Answers
The circumference of a circle is the perimeter or external measure.
Given a circle of radius r, the circumference is calculated as:
C=2 π r
The circle has a radius of r=11.5 units
The circumference is:
C=2 π (11.5) = 72.26 units
The circumference is 72.26 units
Select all of the expressions that are less than 10103O A 103хB. 1x 10oC 103 x 2OD } x 103O E 103
Answers
Let's check every option:
[tex]10\frac{2}{3}=\frac{32}{3}\approx10.667[/tex]A.
[tex]10\frac{2}{3}\times\frac{9}{10}=9.6<10.667[/tex]This option is correct
------------------------
B.
[tex]1\times10\frac{2}{3}=10.667=10.667[/tex]This option is not correct.
----------------------
C.
[tex]10\frac{2}{3}\times2\frac{1}{3}\approx24.888>10.667[/tex]This option is not correct
-------------------
D.
[tex]\frac{1}{8}\times10\frac{2}{3}\approx1.33<10.667[/tex]This option is correct
----------------------------
E.
[tex]10\frac{2}{3}\times\frac{3}{5}=6.4<10.667[/tex]This option is correct
Answer:
A
D
E
Find each unknown function value or x value for f(x) = 4x - 7 and g(x) = -3x + 5
Answers
Step 1
Find f(2)
[tex]To\text{ do this we substitute for f= 2 in f(x)}[/tex][tex]\begin{gathered} f(x)\text{ = }4x-7 \\ f(2)\text{ = 4(2) -7 = 8 - 7 = 1} \end{gathered}[/tex]Step 2
Find f(0)
[tex]f(0)\text{ = 4(0) -7 = 0 - 7 = -7}[/tex]Step 3
Find f(-3)
[tex]f(-3)\text{ = 4(-3) -7 = -12 -7 = -19}[/tex]Step 4
Find x, when f(x) = -3
[tex]\begin{gathered} f(x)\text{ = -3}--------------(1) \\ f(x)\text{ =4x-7}---------------(2) \\ \text{Equate both equations} \\ -3=4x-7 \\ -3+7\text{ = 4x} \\ 4x\text{ = 4} \\ x\text{ = }\frac{4}{4}=1 \end{gathered}[/tex]For questions 6 – 10, find the unknown side length. number 10
Answers
10) Given:
hypotenuse = 20
angle = 45°
To find:
length of s
angle = 45
opposite = side opposite the angle = s
To find the value of s, w will apply sine ratio (SOH)
[tex]sin\text{ 45 = }\frac{opposite}{hypotenuse}[/tex][tex]\begin{gathered} sin\text{ 45 = }\frac{s}{20} \\ s\text{ = 20sin45} \\ sin\text{ 45 = }\frac{\sqrt{2}}{2} \\ \\ s\text{ = 20}\times\frac{\sqrt{2}}{2} \\ s\text{ = 10}\sqrt{2}\text{ \lparen exact answer\rparen} \end{gathered}[/tex][tex]\begin{gathered} s\text{ = 20sin45} \\ s\text{ = 20\lparen0.7071\rparen} \\ s\text{ = 14.142 \lparen decimal approximation\rparen} \end{gathered}[/tex]6. Which of the following statements are true? 4 is a perfect cube 8 is a perfect square 100 is a perfect square 35 is a perfect cube
Answers
First statement: 4 is NOT a perfect cube, because it cannot be written as the cube of a rational number.
Second statement: 8 is NOT a perfect square because it cannot be written as the square of a rational number.
Third statement: 100 IS a PERFECT square, because ic can be written as 10^2 *the square of the number 10)
Fourth statement: 35 is NOT aperfect cube because it cannot be written as the cube of a rational number.
Therefore the only TRUE statement is the third one:
"100 is a perfect square".
What is the y-intercept in this equation: -1.5= y-12/0-4
Answers
The y-intercept in this equation: -1.5= y-12/0-4 is 18.
What is equation?
Equation: A statement stating the equality of two expressions with variables or integers. Essentially, equations are questions, and attempt to systematically find the answers to these questions have been the inspiration for the development of mathematics.
Given Equation:
-1.5 = y - 12 / 0-4
Solve the above equation, and we get,
-1.5 = y - 12 / (-4)
y -12 = 6.0
y = 18
Therefore, the y-intercept in this equation: -1.5= y-12/0-4 is 18.
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Daniel opened a small business. His profit for the first month was -$503. If his average profit for months 2-4 was $-421, what was the total profit for months 1-4?Please help me
Answers
If Daniel profit for the first month was -$503. If his average profit for months 2-4 was $-421, then $924 was the total profit for months 1-4
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Daniel opened a small business.
Profit for the first month was -$503 five hundred and three
Average profit for months 2-4 was $-421, four hundred and twenty one.
We need to find the total profit for months 1-4
Add profit for 1s month and 2-4 months.
$503+$421
$924
Hence $924 was the total profit for months 1-4
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