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The Solution:
Given:
[tex]y=3^x[/tex]Required:
To translate it to become:
[tex]y=3^{x-4}+1[/tex]The Transformations:
A horizontal shift of 4 units to the right.
A vertical shift of 1 unit up.
Below is th graph:
Related Questions
¿Cual es el resultado de efectuar (2x+5)³ + (x-2)(x-2)?
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The equation (2x+5)³ + (x-2)(x-2) we get 8x³ + 60x² + 150x +129.
What is meant by binomial equation?A binomial number is an integer that can be produced by evaluating a homogeneous polynomial with two terms in mathematics, more specifically in number theory. It is a Cunningham number that has been generalized.
Let the equation be (2x + 5)² + (x -2)(x- 2)
By using binomial formula we get,
(a + b)³ = a³ + 3a²b + 3ab² + b³
The coefficient multipliers are located in row 3 of Pascal's triangle.
(2x + 5)³ + (x - 2)(x - 2)
= 8x³ + 60x² + 150x +125(x - 2)(x - 2)
8x³ + 60x² + 150x + 125 + x(x - 2) - 2(x-2)
8x³ + 60x² + 150x + 125 + x² - 2x - 2x +4
simplifying the above equation, we get
8x³ + 60x² + 150x + 125 + x² - 4x +4
8x³ + 60x² + 150x +129 + x² - 4x
8x³ + 60x² + 150x + 129 - 4x
8x³ + 60x² + 146x + 129
= 8x³ + 60x² + 150x +129
Therefore, by simplifying the equation (2x+5)³ + (x-2)(x-2) we get 8x³ + 60x² + 150x +129.
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Question 25 of 27Which of the following is an example of independent events?OA. Rolling a 6 on a number cube and spinning a 7 on a spinnerB. Drawing a jack from a standard deck of cards and then drawing a2 without replacing the jackC. Selecting a green marble from a bag of 10 different coloredmarbles and then selecting a second green marble without puttingthe first backOD. Owning cows and living on a dairy farm
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Independent events are events where one event occurring or not does not affect whether the other one happens.
Pulling two cards out of a deck of cards, when you don't replace the first card, or pulling two marbles from a bag, where you don't replace the first marble, are not independent. By removing the first card/marble, you've change the situation for the second draw.
Using a spinner and rolling a die are totally independent, since they are different objects and what happens on one does not impact what will happen on the other.
And if you live on a dairy farm, that creates a better chance of being involved with dairy production and cows, so those are not independent.
Option A has two independent events.
If Mason made 20 free throws, how many free throws did he attempt in all?
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Answer:
what is the shooting percentage?
Solve the equation.– 2y - 15 = 4y + 15y=
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Given the equation;
[tex]-2y-15\text{ = 4y+15}[/tex]You are to calculate the value of y. This is as shown below;
First collect the like terms;
[tex]\begin{gathered} -2y\text{ - 4y = 15+15} \\ \end{gathered}[/tex]Evaaluate the expression an find y;
[tex]\begin{gathered} -6y=30 \\ \end{gathered}[/tex]Divide both sides by -6;
[tex]\begin{gathered} \frac{-6y}{-6}=\frac{30}{-6} \\ y\text{ = -5} \end{gathered}[/tex]Hence the value of y is -5
What is the difference of the complex numbers below? (6+81)-(1-21 ) O A. 7+10) O O O B. 5+10) O C. 5+67 O 0 7 D. 7 +62
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we have the expression
[tex](6+8i)-(1-2i)[/tex]Remove parenthesis
[tex]6+8i-1+2i[/tex]Group similar terms
[tex](6-1)+(8i+2i)[/tex]Combine like terms
[tex]5+10i[/tex]The answer is option Bif x + 9 equals 13 what is the value of x
Answers
X + 9 = 13
To know the value of x you have to subtract 9 from both sides of the equation
x+9-9= 13-9
x= 4
31/32 - > Identify the ordered pairs in the graph. Then identify the domain and range. Is this a function? 7) 8) Domain: Domain: Range: that Range: Function? Function? O Type here to search gi 3
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7)
The ordered pairs are:
(-4, -2), (-2, 1), (0, -1), (-3, 0), and (-3,2)
Domain = {-4, -3, -2, 0}
Range = {-2, -1, 0, 1, 2}
A function must map every element of the domain to a unique number in the range
But here -3 is mapped to 0 and 2.
Hence it is not a function
8)
The ordered pairs are:
(-2, 3), (-1,-1), (0,-1), (1,-3), (3, 1)
Domain = {-2, -1, 0, 1, 3}
Range = {-3, -1, 1, 3}
In this case, every element of the domain is mapped to a unique
ut -The ordered pairs are:
3m^2-13m+20=0 what is the discriminant? use the discriminant to determine the number and type of solutions of the given equation ,3m^2-13m+20=0 is this equation one rational number, two irrational numbers, two nonreal complex numbers ,two rational numbers? The given equation ,3m^2- 13m+20=0, can be solved using the quadratic formula or zero-favtor property?
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The discriminant is -71
The discriminant is less than zero, the equation has no real roots
Explanation:Given the equation:
[tex]3m^2-13m+20=0[/tex]The discriminant is given as:
[tex]D=b^2-4ac[/tex]where a = 3, b = -13, c = 20
[tex]\begin{gathered} D=(-13)^2-4(3)(20) \\ \\ =169-240 \\ =-71 \end{gathered}[/tex]The discriminant is less than zero, the equation has no real roots
Sasha has $850 todeposit into twoaccounts.Sasha will deposit $450at First Oak Bank.She will deposit the restinto River Point Bank.Sasha will not make additionaldeposits or withdrawals.How much more money will bein her account at First Oak thanat River Point after 2 years?
Answers
Given
Sasha has $850 to deposit into two accounts.
Sasha will deposit $450 at First Oak Bank.
She will deposit the rest into River Point Bank.
Sasha will not make additional deposits or withdrawals.
To find how much more money will be in her account at First Oak than at River Point after 2 years.
Now,
It is given that,
In the first Oak bank the rate of interest is 6%.
Then, the amount in her account after 2 years is,
[tex]\begin{gathered} A=P+\frac{Pnr}{100} \\ A=450+\frac{450\times2\times6}{100} \\ A=450+54 \\ A=454 \end{gathered}[/tex]Hence, the amount in the First Oak bank is $454.
In the River point bank the rate of interest is 2% compounded annually.
Then, the amount in her account after 2 years is,
[tex]\begin{gathered} A=P(1+\frac{r}{100})^t \\ A=P(1+\frac{2}{100})^2 \end{gathered}[/tex]Since Sasha will deposit $450 at First Oak Bank and she will deposit the rest into River Point Bank.
Then, the amount deosited in the River point bank is,
[tex]\begin{gathered} P=850-450 \\ =400 \end{gathered}[/tex]Therefore,
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this is confusing isnt there supposed to be 2 numbers
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Let's begin by listing out the information given to us:
Angle U = 27°
TU is tangent to S implies this is a right triangle
Angle T = 90°
The sum of interior angles in a triangle is 180 degrees
U + T + S = 180°
⇒27 + 90 + S = 180
⇒S = 180 - (90 + 27) = 53
S = 53°
find (x) 76° 6x-9 47°
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There are two degrees, one variable and one number.
A full one- gallon container can beused to fill the one-liter containers, as shownbelow. Write a unit rate that estimates thenumber of liters per gallons.
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Explanation
Step 1
as we can see in the picture
[tex]1\text{ gallons}\rightarrow3\text{ liters}[/tex]so, to find the unit rate make
[tex]\begin{gathered} \text{unit rate=}\frac{Number\text{ of liters}}{Number\text{ of gallons}} \\ \text{replace} \\ \text{Unit rate=}\frac{3\text{ liters}}{1\text{ gallon}}=\text{ 3 liters per gallon} \end{gathered}[/tex]I hope this helps you
Latex paint sales for $25 per gallon and will cost you $175 to paint your room if each gallon will cover 330 ft.² how many square feet of wall space do you have in your room
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The square feet of wall space in your room if paint cost $25 per gallon and will cost you $175 to paint the room is 2,310 square feet
What is the square feet of wall space in your room?Cost of latex paint per gallon = $25Total cost of paint = $175Square feet covered by each gallon = 330 ft.²Number of latex paint need to paint your room = Total cost of paint / Cost of latex paint per gallon
= $175 / $25
= 7 gallons
Number of square feet of wall space in your room = Number of latex paint need to paint your room × Square feet covered by each gallon
= 7 × 330
= 2,310 square feet
In conclusion, the square feet of wall space in your room is 2,310 square feet
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Can you help me on what 6x equals? (Grade 10, angles)
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First we need to find the value of x, we can use the fact that the sum of the interior angles of a quadrilateral is 360°
[tex]6x+6x+9x+9x=360[/tex][tex]\begin{gathered} 30x=360 \\ \end{gathered}[/tex]then we isolate the x
[tex]x=\frac{360}{30}[/tex][tex]x=12[/tex]then for 9x and 6x, we substitute the value of x=12
[tex]6(12)=72[/tex][tex]9(12)=108^{}[/tex]if x =12, therefore, the angle 6x=72° and the 9x=108°
Please help me with the question and explain your work! 16 through 19 thank you please please please help
Answers
We have the following:
A.
First we find the slope of the line with the following points:
(0, 3) and (5,0)
[tex]m=\frac{0-3}{5-0}=-\frac{3}{5}[/tex]now, for b, with the point (0,3)
[tex]\begin{gathered} 3=-\frac{3}{5}\cdot0+b \\ b=3 \end{gathered}[/tex]The equation is:
[tex]y=-\frac{3}{5}x+3[/tex]B.
The area is:
[tex]\begin{gathered} A=\frac{AC\cdot CB}{2} \\ A=\frac{3\cdot5}{2}=\frac{15}{2} \\ A=7.5 \end{gathered}[/tex]The area is 7.5 square units
for, perimeter:
[tex]\begin{gathered} p=AC+CB+AB \\ AB^2=AC^2+CB^2 \\ AB^2=3^2+5^2=9+25=34 \\ AB=\sqrt[]{34} \\ p=3+5+\sqrt[]{34} \\ p=13.83 \end{gathered}[/tex]The perimeter is 13.83 units
C.
when two lines are perpendicular they fulfill the following
[tex]m_1\cdot m_2=-1[/tex]therefore,
[tex]\begin{gathered} -\frac{3}{5}\cdot m_2=-1 \\ m_2=\frac{5}{3} \end{gathered}[/tex]Therefore, the equation is:
[tex]y=\frac{5}{3}x+3[/tex]Statistic Questions
All of the following statements, except for one, contains an error.
Which statement does not contain an error?
A) The relationship between height and the ability to reach things is strong and positive. The correlation is 1.15.
B) The relationship between height and weight is strong and positive. The correlation is 0.95.
C) The relationship between height and gender is strong and positive. The correlation is 0.95.
D) The relationship between age and height is negative for the elderly. The correlation is –1.25 .
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The correct statement regarding the correlation coefficient is given as follows:
B) The relationship between height and weight is strong and positive. The correlation is 0.95.
What is a correlation coefficient?The correlation coefficient between two variables is an index that measures correlation between these variables, assuming values between -1 and 1.
As the values have to be between -1 and 1, statements A and D are false, as the coefficients have values greater than 1 or less than -1.
From the image given at the end of the answer, the variables are given as follows:
Height.Weight.The scatter plot is increasing, hence statement B is correct, as there is a positive correlation between the variables.
Missing InformationThe graph is given by the image at the end of the answer.
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Please help me and explain how to find the result
Answers
A family consumes 1.2kg of rice a day
If the family have 30ky of rice
Let the number of days be x
The minimum number of days required for the amount of rice remaining not to be more than 6kg can be expressed below as
[tex]30-1.2x\le6[/tex]Solve for x by collecting like terms
[tex]\begin{gathered} 30-1.2x\le6 \\ 30-6\le1.2x \\ 24\le1.2x \\ 1.2x\ge24 \\ \text{Divide both sides by 1.2} \\ \frac{1.2x}{1.2}\ge\frac{24}{1.2} \\ x\ge20\text{ days} \end{gathered}[/tex]Hence, the minimum number of days required for the amount of rice remaining not to be more than 6kg is 20 days
what is the volume of the cone? use Pi and round to the nearest tenth
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Let's begin by listing out the information given to us:
Radius (r) = 7ft
Height (h) = 25ft
The volume of a cone is calculated as shown below:
V = ⅓πr²h
V = ⅓ * 3.14 * 7² * 25 = 1282 1/6
V = 1282 1/6 or 1282.667 = 1282.7 = 1283 ft³
V = 1283 ft³
The data for the control group has a a. first common differenceb. second common difference c. common ratioTherefore the data is being generated by a a. linear functionb. quadratic function c. exponential functionThe data for the original formula has aa. first common difference b. second common differencec. common ratioTherefore the data is being generated by a a. linear functionb. quadratic functionc. exponential function The data for the improved formula has a a. first common difference b. second common difference c. common ratio Therefore the data is being generated by a a. linear functionb. quadratic functionc. exponential function
Answers
Answer:
The data for the control group has a first common difference, therefore the data is being generated by a linear function
The data for the original group has a second common difference, therefore the data is being generated by a quadratic function
The data for the Improved group has a common ratio, therefore the data is being generated by an exponential function
Explanation:
Given the table in the attached image.
The data for the control group has a common difference, that is the difference between consecutive values are the same.
[tex]d=13-6=20-13=27-20=34-27=41-34=7[/tex]Since the values have a common difference then it is a linear function.
The original formula has a second common difference, therefore the data is being generated by a quadratic function.
The improved formula has a common ratio;
[tex]r=\frac{18}{9}=\frac{36}{18}=\frac{72}{36}=\frac{144}{72}=\frac{288}{144}=2[/tex]Therefore, the data is being generated by an exponential function.
r(x)=−x−7 when x=−2,0, and 5
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Given,
The expression of the function,
[tex]r(x)=-x-7[/tex]The value of r(x) at x = -2 is,
[tex]r(-2)=-(-2)-7=2-7=-5[/tex]The value of r(x) at x = 0 is,
[tex]r(0)=-(0)-7=0-7=-7[/tex]The value of r(x) at x = 5 is,
[tex]r(5)=-(5)-7=-5-7=-12[/tex]Hence, the value of r(x) is -2, -7 and -12.
use basic trigonometric identities to simplify the expression: -tan (-x) cot (-x) = ?
Answers
-1
Explanation
let's remember the indentities
[tex]\begin{gathered} tan\theta=\frac{sen\text{ \lparen x\rparen}}{cos\text{ \lparen x\rparen}} \\ cot\theta=\frac{cos(x)}{sin(x)} \end{gathered}[/tex]so
Step 1
let the expression
[tex]-tan(-x)cot(-x)=?[/tex]rewrite the expression:
replace using the identity
[tex]\begin{gathered} -tan(-x)cot(-x)=? \\ -tan(-x)cot(-x)=-\frac{\sin(-x)}{cos(-x)}*\frac{cos(-x)}{\sin(-x)} \\ -tan(-x)cot(-x)=-\frac{\sin(-x)}{sin(-x)}\frac{cos\left(-x\right)}{\sin(*x)} \\ -tan(-x)cot(-x)=-1*1 \\ -tan(-x)cot(-x)=-1 \end{gathered}[/tex]therefore, the answer is
-1
I hope this helps you
use the distributive property to evaluate the expression (3+6)(-8)
Answers
We have the following:
The distributive property of multiplication over addition can be used when multiplying a number by a sum.
[tex]\begin{gathered} \mleft(3+6\mright)\mleft(-8\mright)=9\cdot-8 \\ -72=-72 \end{gathered}[/tex]An experiment consists of spinning the spinner shown. All outcomes are equally likely. Find P(<7). Express your answer as a fraction in simplest forn
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There are 8 total outcomes. Now, we need to find where P(<7).
This means the outcomes where the number is less than 7.
There are 6 numbers under the 7 = 1,2,3,4,5,6
The probability is given by the next formula:
[tex]P=\frac{\text{Number of favorable outcomes}}{\text{Total of possible outcomes}}[/tex]Where:
Number of favorable outcomes = 6
Total of possible outcomes = 8
Replacing these values:
[tex]P=\frac{6}{8}[/tex]Simplify the expression, divide both numbers by 2:
[tex]P=\frac{3}{4}[/tex]The correct answer is the second one.
If I work 4weeks on and one week off how many weeks per year
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We know that the year has 52 weeks
From 5 weeks, you work 4. So, we can use the rule of three
Number of weeks Weeks of work
5 4
52 x
[tex]\begin{gathered} 5x=4\cdot52 \\ 5x=208 \\ x=\frac{208}{5} \\ x=41.6\text{ w}eeks \\ or\text{ 41 complete w}eeks\text{ } \end{gathered}[/tex]Dawn's suitcase weighed 25 kilograms. Convert this weight to pounds. (Round youranswer to the nearest tenth.)
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Given: Dawn's suitcase weighed 25 kilograms.
Required: To convert the given weight to pounds.
Explanation: Since 1 kilogram is equivalent to 2.20462 pounds. Hence to convert 25 kg to pounds, we need to multiply by 2.20462.
Thus we have
[tex]\begin{gathered} 25\text{ kg}=25\times2.20462\text{ pounds} \\ =55.1156\text{ pounds} \\ \approx55.1\text{ pounds} \end{gathered}[/tex]Final Answer: Dawn's suitcase weighed 55.1 pounds.
Susan's Jewelry Shop is having a sale on necklaces. The store is offering a sale pack of 4 necklaces for $48.80. What is the unit price of a necklace in the sale pack?
Carly's ClothinStore is also having a sale on necklaces. The unit price of any necklace at Carly's Clothing Store is the same as the unit price of a necklace at Susan's Jewelry Shop How much would it
cost a customer for 10 necklaces at Carly's Clothing Shop?
Answers
Unit Price
The store offers a sales pack of 4 necklaces for $48.80. This means each necklace in this pack has a unit price of:
$48.80 / 4 = $12.20
Now we know the unit price of any necklace at Carly's Clothing Store is the same as the unit price at the competing store. This means each necklace at Carly's Clothing Store has a price of $12.20.
If a customer bought 10 of these necklaces, he would have to pay
10 * $12.20 = $122,00
For 10 necklaces at Carly's Clothing Store, a customer would pay $122
Calculate Jayden's simple interest on a 5-year car loan for $33,486 at 2.38%.
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Answer:
$3984.83.
Explanation:
[tex]Simple\: Interest=\frac{Principal\times Rate\times Time}{100}[/tex]In this particular case:
• The principal/loan amount = $33,486.
,• Rate = 2.38%.
,• Time = 5 years.
Substituting these into the formula above:
[tex]\begin{gathered} Simple\: Interest=\frac{33,486\times2.38\times5}{100} \\ =\$3984.83 \end{gathered}[/tex]Jayden's simple interest is $3984.83.
Consider the following graph. Explain why it is possible to find an Euler circuit for this graph. Then, using Fleury's algorithm, identify and draw an Euler circuit starting with point A and choosing the first edge as A to F. Show all work using the required method. Draw the graph properly. (If you choose not to draw on my graph, then draw a LARGE graph on your paper.)
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The Euler circuit for the graph using Fleury's algorithm is attached below.
The following steps are to be used to form the circuit.
Of the three edges coming from vertex "2" should I choose? We avoid choosing the edge "2-3" because it is a bridge and we cannot return to "3".
Any of the two remaining edges is ours to choose. Let's say we choose "2-0." By eliminating this edge, we can travel to vertex "0."
We pick the one edge from vertex "0" that is present, remove it, and then move to vertex "1." The Euler tour changes to "2-0 0-1."
We take the lone edge from vertex "1," delete it, and then move to vertex "2." The Euler tour is now "2-0 0-1 1-2."
Once more, vertex 2 has just one edge, so we pick it, remove it, and continue on to vertex 3.
Hence we get the required circuit.
The term "Eulerian graph" has two different meanings in graph theory. One interpretation applies to a graph with an Eulerian circuit, whereas the other applies to a graph where each vertex has an even degree. These definitions apply to linked graphs.
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2) Reflection across the line y = x. B(-2, 1), S(-2, 2), R(3, 3), H(2, -2) B'( ) S/ ) R (2) J( )
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Let's begin by identifying key information given to us:
[tex]B\mleft(-2,1\mright),S\mleft(-2,2\mright),R\mleft(3,3\mright),H\mleft(2,-2\mright)[/tex]Reflection is done over the line y = x, we have:
[tex]\begin{gathered} (x,y)\rightarrow(y,x) \\ B\mleft(-2,1\mright)\rightarrow B^{\prime}(1,-2) \\ S\mleft(-2,2\mright)\rightarrow S^{\prime}(2,-2)_{} \\ R\mleft(3,3\mright)\rightarrow R^{\prime}(3,3) \\ H\mleft(2,-2\mright)\rightarrow H^{\prime}(-2,2) \end{gathered}[/tex]f(x +h)-f(x)For the function defined as follows, find (a) f(x + h), (b) f(x + h) – f(x), and (c)f(x)= 4/x
Answers
Given the function:
[tex]f(x)=\frac{4}{x}[/tex]We will find the following:
a) f(x+h)
So, we will substitute with x = x+h
[tex]f(x+h)=\frac{4}{x+h}[/tex]b) f(x+h) - f(x)
[tex]\begin{gathered} f(x+h)-f(x)=\frac{4}{x+h}-\frac{4}{x} \\ \\ f(x+h)-f(x)=\frac{4x-4(x+h)}{x(x+h)} \\ \\ f(x+h)-f(x)=\frac{4x-4x-4h}{x(x+h)} \\ \\ f(x+h)-f(x)=\frac{-4h}{x(x+h)} \end{gathered}[/tex]c) [f(x+h) - f(x)]/h
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{-4h}{x(x+h)\cdot h} \\ \\ \frac{f(x+h)-f(x)}{h}=\frac{-4}{x(x+h)} \end{gathered}[/tex]