Consider the given equation,
[tex]y=(x-a)(x-b)^2(x-c)^3[/tex]Put x = a in the equation,
[tex]\begin{gathered} y=(a-a)(a-b)^2(a-c)^3 \\ y=(0)(a-b)^2(a-c)^3 \\ y=0 \end{gathered}[/tex]So the graph of the function passes through (a,0), which is a valid point.
So, option (I) is correct.
Similarly, when substituting the other values, it is obtained that the curve of the given function passes through points (b,0) and (c,0).
But this contradicts with the statements in (II) and (III) respectively.
Therefore, it can be concluded that only statement (I) is correct.
Justin has $200 in a bank account that earns 3% in annual interest. Does this describe a linear or exponential function? Select the equation.
Justin has $200 in a bank account that earns 3% in annual interest.
This can be modeled using an exponential function given by
[tex]f(x)=P(1+r)^x[/tex]Where P is the invested amount, r is the interest rate in decimal, and x is the number of years.
For the given case,
P = $200
r = 3% = 0.03
So, the exponential function becomes
[tex]\begin{gathered} f(x)=200(1+0.03)^x \\ f(x)=200(1.03)^x \end{gathered}[/tex]Therefore, the given situation describes an exponential function.
[tex]Exponential\colon f(x)=200(1.03)^x[/tex]Isabella painted a water colour design on gridpaper. Some of the points were at A (-4, 8),B (-2, 8), C(-1,6), D (-2, 4), E (-4, 4), andF (-5, 6). She folded the paper along y = 3 toreflect the design. The image points are A', B',C', D', E', and F.a) Draw the line y = 3. (Hint: The x-axisis the line y = 0. For which line is they-coordinate 3 for every point?)b) Determine the coordinates of A', B',C.D', E', and F'.c) Draw the image, and label A', B', C',D', E', and F'.y8-7-€6-4.32-5•1 C
EXPLANATION
Drawing the line y=3 give us the following graph:
Reflecting over the axis y=3 give us the following image points:
A' = (-4,2)
B' = (-2,-2)
C' = (-1,0)
D' = (-2,2)
E' = (-4,2)
F'= (-5,0)
Drawing the points in the graph calculator:
Daria bought a bracelet at original cost $14 to sell in her handicraft store. She marked the price up 45%. What was the list price of the bracelet? Round to the nearest cent.
Daria bought a bracelet at original cost $14 to sell in her handicraft store. She marked the price up 45%. What was the list price of the bracelet? Round to the nearest cent.
Remember that
100%+45%=145%=145/100=1.45
Multiply the original cost by the factor 1.45
so
$14*1.45=$20.30
the answer is $20.305. The sum of two numbers is 24. The second number is 4 less than the first. Write a system of equations andsolve it to find the numbers.A. (16,8)B. (14, 10)C (18, 14)D (6,4)
Take x and y as the two numbers, the sum of these is 24:
[tex]x+y=24[/tex]It is also stated that the second number, y, is 4 less than the first, x, it means:
[tex]y=x-4[/tex]The system of equations is:
[tex]\begin{gathered} x+y=24 \\ y=x-4 \end{gathered}[/tex]Use the second equation, which is solved for y and replace this expression for y in the first equation, then solve for x:
[tex]\begin{gathered} x+y=24 \\ x+(x-4)=24 \\ x+x-4=24 \\ 2x=24+4 \\ 2x=28 \\ x=\frac{28}{2} \\ x=14 \end{gathered}[/tex]x has a value of 14. Use this value and the second equation to find the value of y:
[tex]\begin{gathered} y=x-4 \\ y=14-4 \\ y=10 \end{gathered}[/tex]The solution for the system is (14,10). The correct answer is B.
Points B and C lie on line segment AD, with AB < AC. If AD = 76, CD = 24 and AB = BC, what is the value of BC?
ANSWER
[tex]BC=26[/tex]EXPLANATION
First, let us make a sketch of the problem:
Since AB is equal in length to BC, they both have a value of x.
The total length of AD is 76. This implies that:
[tex]\begin{gathered} AB+BC+CD=AD \\ x+x+24=76 \end{gathered}[/tex]Solve for x by simplifying the equation above:
[tex]\begin{gathered} 2x+24=76 \\ 2x=76-24=52 \\ \\ x=\frac{52}{2} \\ \\ x=26 \end{gathered}[/tex]Therefore, the value of BC is:
[tex]BC=26[/tex]That is the answer.
[tex] 4\sqrt{109.6} [/tex]find the quotient
The given division is
[tex]\frac{109.6}{4}[/tex]If we use the long division method, we get the following
As you can see in the image above, the quotient is 27.4.3. The results of the primary election are shown. Smith 15% Goron 35% Other 10% Fishman 40% (a) Order the popularity of the choices from greatest to least. (b) It was estimated that 280 people were going to vote. If this was true, how many people would have voted for Goron? Show your work. (c) 40 people voted for "Other." Was the estimate of total voters from Part (b) accurate? Explain. Answer: I C Focus 33
a) The order is;
Fishman
Goron
Smith
Other
b) 98 people would have voted for Goron if the estimation was true
c) The estimate was not correct as the actual value obtained (40) is not same as what was estimated (28)
a) We want to order the popularity of choices from greatest to least
What we have to know and understand here is that the higher the percentage, the greater the popularity
Thus, we have it that;
Fishman
Goron
Smith
Other
b) As we can see from the data presented, Goron had 35% of the votes
So, the number of people that voted for Goron will be;
[tex]\begin{gathered} 35\text{ \% of 280} \\ =\text{ }\frac{35}{100}\times280\text{ = 98} \end{gathered}[/tex]98 people would have voted for Goron if the estimation was true
c) Here, we want to evaluate if the total we had from part B was correct
What we have to do here is get the number that would have been correct if at all 280 people voted
We have this as;
[tex]\begin{gathered} 10\text{ \% of 280} \\ =\text{ }\frac{10}{100}\times280\text{ = 28} \end{gathered}[/tex]The estimate was not correct as the actual value obtained (40) is not same as what was estimated (28)
write each in scientific notation with the answer simplified:(8•10^13) ÷ (2•10^8)(5•10^8) (6•10^9) ÷ (15•10^14)
To write in scientific notation we must follow the formula below:
[tex]N=a\times10^b[/tex]where:
a is a number between 1 and 9;
b is a integer, i.e., can be a positive or negative number
We have also to do some power properties.
For the first question, we get:
[tex]\begin{gathered} \mleft(8•10^{13}\mright)\div2•10^8= \\ =\frac{8}{2}\times\frac{10^{13}}{10^8}= \\ =4\times10^{13-8}= \\ =4\times10^5 \end{gathered}[/tex]So the final answer is 4 x 10^5
For the second one:
[tex]\begin{gathered} \mleft(5•10^8\mright)6•10^9\div15•10^{14}= \\ =\frac{5\cdot6\cdot10^{8+9}}{15\cdot10^{14}}= \\ =\frac{30\cdot10^{17}}{15\cdot10^{}^{14}}= \\ =\frac{30}{15}\cdot10^{17-14}= \\ =2\cdot10^3 \end{gathered}[/tex]Our final answer here is 2 x 10^3.
A) lena entered a raffle to win a movie ticket. The probability that she wins a movie ticket is 8/17. Find the odds in favor of her winning a movie ticket.B) keth is watching his favorite soccer team playing a match. The odds against his favorite team winning are 9/4. What is the probability of his favorite team winning?
A) The given information is:
The probability that Lena wins a movie ticket is 8/17.
This probability is given by:
[tex]P(winning)=\frac{favorable\text{ number of outcomes}}{total\text{ number of outcomes}}[/tex]The odds is favor are given by:
[tex]\text{ Odds in favor}=\frac{favorable\text{ outcomes}}{unfavorable\text{ outcomes}}[/tex]We can find the unfavorable outcomes by subtracting the number of favorable outcomes from the total number of outcomes, so:
Unfavorable outcomes=17-8=9.
So, the odds in favor are:
[tex]Odds\text{ }in\text{ }favor=\frac{8}{9}[/tex]B) The given information is:
The odds against Keith's favorite team winning are: 9/4
The odds against are given by:
[tex]Odds\text{ }against=\frac{\text{ unfavorable outcomes}}{\text{ favorable outcomes}}[/tex]The total number of outcomes is: unfavorable+favorable = 9+4=13
So, the probability of his favorite team winning is:
[tex]\begin{gathered} P(winning)=\frac{favorable\text{ outcomes}}{total\text{ number of outcomes}} \\ P(winning)=\frac{4}{13} \end{gathered}[/tex]The floor of a square closet measures 7 feet on each side, as sho 7 feet What is the area of the floor of the closet?
The formula to find the area of a square is:
[tex]\begin{gathered} A=s^2 \\ \text{ Where A is area and} \\ s\text{ is a side of the square} \end{gathered}[/tex]So, in this case, you have
[tex]\begin{gathered} s=7ft \\ A=s^2 \\ A=(7ft)^2 \\ A=49ft^2 \end{gathered}[/tex]Therefore, the area of the floor of the closet is 49 square feet.
Plan A minutes: Plan B minutes:monday-10 monday-30tuesday-20 tuesday-40wednesday-30 wednesday-50thursday-40 thursday-60friday-50 friday-70Prove that linear functions grow by equal differences over equal intervals.
the linear function,
of plan A,
initital term a = 10
second term = 20
common difference = 20 - 10 = 10
for plan B
initial term a = 30
second term =40
the common difference = 40 - 30 = 10
thus the both linear function grow by equal difference over equal interevals.
The equation V=31600(0.92)tV=31600(0.92)t represents the value (in dollars) of a car t years after its purchase. Use this equation to complete the statements below.
Notice that:
[tex]0.92=1-0.08.[/tex]Therefore, we can rewrite the given equation as follows:
[tex]V=31600(1-0.08)^t.[/tex]From the above equation, we get that the price of the car is decreasing an 8% per year.
Evaluating the given equation at t=0, we get the purchase price:
[tex]V(0)=31600(0.92)^0=31600(1)=31600.[/tex]Answer:
The value of this car is decreasing at a rate of 8 percent per year.
The purchase price of the car was 31600 dollars.
Which best represents the transformations for the coordinates of the verticals of the given pairs of triangles (1,6), (-1,3), (5,2), and (-1,6), (-3,3), (3,2) Is it a rotation (that my educated guess)Reflection or translation?
No. It's not a rotation. It's translation.
for translation, there is a formula that is
[tex]x^{\prime}=x+a\text{ }[/tex]and
[tex]y^{\prime}=b+y[/tex][tex]y^{\prime}=b+y[/tex]where (x',y') is the new coordinate and (x,y) is the old one and (a,b) is the increasing value of (x,y)
so here we have the new coordinates are (-1,6), (-3,3), (3,2)
and the olds are (1,6), (-1,3), (5,2)
[tex]\begin{gathered} -1=a+1 \\ and\text{ }6=b+6 \\ this\text{ gives } \\ a=(-2)\text{ and b=0} \\ similarly\text{ you take each case you will get the value of a is \lparen-2\rparen and the value of b is 0.} \end{gathered}[/tex]Thus we can say that the triangle is translated by adding the horizontal value (a) =(-2) to the x-coordinate of each vertex and the vertical value (b)=0 to the y-coordinate.
now you can see
[tex]\begin{gathered} 1+(-2)=1\text{ \& 6+\lparen0\rparen=6 ie \lparen1,6\rparen+\lparen-2,0\rparen=\lparen-1,6\rparen} \\ similarly \\ (-1,3)+(-2,0)=(-3,3) \\ (5,2)+(-2,0)=(3,2) \end{gathered}[/tex]so the right answer is translation.
Bridget's father is building Champion a new stable,
and he needs to drive a nail through a 4 x 6 board
with an actual thickness of 31¹/2 inches. What length
of nail should he use? (Give your answer in inches and
write it as a mixed number.)
lesson 55)
Answer:
Step-by-step explanation:
4x6 meaning the length is 4 and the width is 6 while as the thickness all around is 31 1/2 inches.
4x6=24
the area is 24 inches
He should use a 24 inch wide nail and the length should be 33/2 so it doesnt unloosen.
the statue of liberty is approximately 305 feet tall. if the angle of elevation of a ship to the top of the statue is 20.5°, how far, to the nearest foot, is the ship from the statue's base?
The situation forms a right triangle:
Since it's a right triangle, we can apply the trigonometric function:
Tan α = opposite side / adjacent side
Replacing:
Tan 20.5= 305/x
Solve for x:
x = 305/tan 20.5
x= 816 ft
I would like to go step by step with this
The dice simulation method will be suitable according to the given sample space for Kwang to select which night of the week he will go to the shelter.
Step 1: What is the sample space of the outcome?
The sample space will be {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}.
Step 2: Choose a simulation method that matches the sample space.
The dice simulation method will be suitable. Because a dice has 6 faces and the given sample space has 6 elements.
Step 3: Assign each outcome to a random number.
Let's assign randomly:
1 = Monday,
3 = Tuesday,
5 = Wednesday,
2 = Thursday,
6 = Friday,
4 = Saturday.
Step 4: Run 4 simulations to select a night to volunteer for each of the next 4 weeks. List the result for each simulation is below:
1st Simulation: Let's say Kwang rolls the dice and got 4.
2nd Simulation: Let's say Kwang rolls the dice and got 6.
3rd Simulation: Let's say Kwang rolls the dice and got 3.
4th Simulation: Let's say Kwang rolls the dice and got 2.
Step 5: Based upon the simulations state the real-world outcomes for each event. Which day of the week will Tom volunteer for each of the next 4 weeks?
Week 1: Saturday
Week 2: Friday
Week 3: Tuesday
Week 4: Thursday
Thus, the dice simulation method will be suitable according to the given sample space for Kwang to select which night of the week he will go to the shelter.
To learn more about sample space visit:
https://brainly.com/question/24273864
#SPJ9
Can you please help me out with a question
Tangents to a circle that intersects at a point are equal in length.
Therefore,
|AB| = |AC|
Where
|AC| is the length of line AC
and
|AB| is the length of line AB
Hence,
[tex]\begin{gathered} 4x+2=2x+8 \\ \text{this implies that} \\ 4x-2x=8-2 \\ 2x=6 \\ \text{Dividing both sides by 2, we have} \\ \frac{2x}{2}=\frac{6}{2} \\ \text{thus} \\ x=3 \end{gathered}[/tex]x = 3 units
Find the area of the rhombus9 in12 inA = [ ? ] in2?=Enter
The formula for calculating the area of a rhombus is expressed as
Area = d1d2/2
where
d1 is the length of one diagonal
d2 is the length of the other diagonal
From the information given,
length of one diagonal = 12 + 12 = 24
length of other diagonal = 9 + 9 = 18
By substituting these values into the formula,
Area = 1/2 x 24 x 18
Area = 216 in^2
#9 - A card is drawn from a standard deck of playing cards. Find the probability that youdraw an ace.O 7.7%O 6.8%O 5.5%O 6.2%
Answer:
7.7%.
Explanation:
The number of cards in a standard deck, n(S)= 52
The number of aces in a standard deck, n(A) = 4 i.e 1 per suit.
Therefore, the probability that you draw an ace:
[tex]\begin{gathered} P(A)=\frac{n(A)}{n(S)} \\ =\frac{4}{52} \\ \approx0.0769 \\ \approx7.7\% \end{gathered}[/tex]The probability that you draw an ace is 7.7%.
We are stuck on this I will need some help trying to figure out which one is the right answer
The general form of represented of a number in scientific notation is,
[tex]a\times10^n[/tex]Here, the required conditions are,
[tex]\begin{gathered} 1\leq a<10 \\ n\in N \end{gathered}[/tex]Note that N represents the set of all possible natural numbers.
Consider the given numbers and match them with the above form.
Clearly, the rightmost number in the given image is in the proper form of the scientific notation,
[tex]8.98\times10^6[/tex]Here, 'a' is 8.98 and 'n' is 6.
Both the values satisfy the required conditions.
Therefore, it can be concluded that out of all the given numbers, the number represented in scientific notation is,
[tex]8.98\times10^6[/tex]Point M is the point of reflection for point A. Find the coordinates of the image A' A(-3, 2) M(-1,5)
You know that the distance between each point on the preimage and the point of reflection M(-1,5) are equal to the distance between M(-1,5) and each point on the image.
So, you can observe this graph
Therefore, the coordinates of the image A' will be (1,8).
4 Surfboards atMorgun's Surf Shopcost $792. If they areall priced the sameamount, how muchdoes 1 surfboardcost?$198
Given that:
- The cost of 4 surfboards is $792.
- All the surfboards cost the same.
Therefore, in order to find the cost of 1 surfboard at Morgun's Surf Shop, you only need to divide the total cost of the four surfboards, by 4.
Let be "x" the cost (in dollars) of 1 surfboard.
You get that:
[tex]\begin{gathered} x=\frac{792}{4} \\ \\ x=198 \end{gathered}[/tex]Hence, the answer is: 1 surfboard costs $198.
Yolanda bought 14 books. Yolanda bought 2 times as many books as Hans. Let n be the number of books that Hans bought.(a) Write an equation that relates the number of books that they bought.Use 2, 14, and n.
number of books Yolanda bought = 14 books
Yoland bought 2 times as many books as Hans. Therefore, Yolanda number of books can be represented as 2n. Where n is the number of books Han bought.
n = number of books Hans bought
2n = 14
divide btoh
Refer to the line for Exercises 17-22.17. If RS 19 and RV = 71, find SV.
Solution:
(17) Given;
[tex]RS=19,RV=71,SV=RV-RS[/tex]Thus;
[tex]\begin{gathered} SV=71-19 \\ \\ SV=52 \end{gathered}[/tex]ANSWER: SV = 52
The width of a picture frame is 16 3/5 centimeters. It’s length is 4 4/5 centimeters longer than the width . Find the length and the perimeter of the picture frame. Write the answer in simplest form.
ANSWER:
[tex]\begin{gathered} \text{Length = 21}\frac{2}{5}\text{ centimeters} \\ \\ \text{Perimeter = 76 centimeters} \end{gathered}[/tex]EXPLANATION:
Since the length is 4⅘ longer than the width, the length will be:
Length = 4⅘ + 16⅗
[tex]\begin{gathered} W\text{ = 16}\frac{3}{5}\text{ centimeters} \\ Length\text{ = 4}\frac{4}{5}\text{ }_{}+\text{ 16 }\frac{3}{5} \end{gathered}[/tex]Let's solve for length:
[tex]\begin{gathered} Length\text{ = 4}\frac{4}{5}\text{ }_{}+\text{ 16 }\frac{3}{5}\text{ = }\frac{24}{5}\text{ + }\frac{83}{5}\text{ = }\frac{107}{5}\text{ = 21}\frac{2}{5}\text{ centimeters} \\ \\ \text{Length = 21}\frac{2}{5}\text{ centimeters} \end{gathered}[/tex]From the given dimensions, it shows the picture frame is a rectangle.
To find the perimeter, use the perimeter of a rectangle formula:
Perimeter of a rectangle = 2(Length + Width)
[tex]\begin{gathered} \text{Perimeter = 2(}\frac{107}{5}+\frac{83}{5}) \\ \\ \text{ = 2(}\frac{190}{5}) \\ \\ \text{ = }2(38) \\ \\ \text{ = 76 centimeters} \end{gathered}[/tex]scores on a test are normally distributed with a mean of 81 and a standard deviation of 8. Find the probability that a randomly chosen score will be between 70 and 93.
Answer:
0.8486
Explanation:
To find the probability that a score will be between 70 and 93, we first need to standardize these values, so we will use the following
[tex]z=\frac{value-mean}{standard\text{ deviation}}[/tex]Therefore, for 70 and 93, we get
[tex]\begin{gathered} z=\frac{70-81}{8}=-1.375 \\ \\ z=\frac{93-81}{8}=1.5 \end{gathered}[/tex]Then, we need to find the following probability
P(-1.375 < z < 1.5)
This probability can be calculate using a standard normal table, so
P(-1.375 < z < 1.5) = P(z < 1.5) - P(z < -1.375)
P(-1.375 < z < 1.5) = 0.9332 - 0.0846
P(-1.375 < z < 1.5) = 0.8486
Therefore, the probability is 0.8486
the linear function f(x)=mx+b is one to one for all slopes, expect when m=____ then find f exponent negative 1(x).
Quiz 1 Write an addition equation or a subtraction equation (your choice!) to describe the diagram. _15 10 -5 0 5 Report a prob
Each arrow represents a subtraction. The beginning of the arrow is the number where the subtraction should start and the point of the arrow is the point where the subtraction should end. The first arrow begins in "0" and ends in "-4", while the second arrow begins on the point of the second one and ends in "-13".
We should first represent the arrow number 1, which is shown below:
[tex]0\text{ -4}[/tex]Because the arrow starts at 0 and go "4" units to the left, therefore we need to subtract 4.
The second arrow starts from the first and goes 9 units to the left, so we have:
[tex](0\text{ - 4) - 9}[/tex]The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is less than or equal to 2". Find P(not A). Outcome Probability 1 0.26 2 0.45 3 0.06 4 0.04 5 0.15 6 0.04
A Probability
1 0.26
2 0.45
3 0.06
4 0.04
5 0.15
6 0.04
Probability to be less or equal than 2 = 0.45 + 0.26
= 0.71
f (x) = x² + x - 1 F (X + 2)