Three men went into a second-hand shop to buy a
television.
It was priced in the window at £30.
Each of them handed over £10 to the shop assistant.
As the assistant opened the till, the manager had a quiet
word with him, "that TV is in the sale and is only £25
now, you will have to give them £5 back."
The assistant was very lazy and couldn't be bothered to
count out the right change for each man.
Instead, he took 5 £1 coins out of the till.
He put two of them in his own pocket and gave each
man £1 back.
Here's the problem:
The men have now paid £9 each for the TV.
The assistant has kept £2 for himself.
3 x £9 = £27.
£27 + £2 = £29.
But £30 was handed over in the first place.
WHERE IS THE MISSING £1?
Answers
Step-by-step explanation:
The trick here is to realize that this is not a sum of the money that the three people paid originally, as that would need to include the money the clerk has ($25). This is instead a sum of a smaller amount the people could have paid ($9 × 3 people = $27), added with the additional money that the clerk would not have needed had they paid that smaller amount ($27 paid - $25 actual cost = $2). Another way to say this is, the $27 already includes the bellhop's tip. To add the $2 to the $27 would be to double-count it. So, the three guests' cost of the room, including the bellhop's tip, is $27. Each of the 3 guests has $1 in his pocket, totaling $3. When added to the $27 revised cost of the room (including tip to the bellhop), the total is $30.
To obtain a sum that totals to the original $30, every dollar must be accounted for, regardless of its location.
Thus, the sensible sum can be expressed in this manner:
Related Questions
Hey guys, Im on this homework, and i dont know how to find this answer, its a 7th grade question, so if anyone can help, that will help a lot
Answers
Prime factorise 1950.
1950 = 2 × 5 × 5 × 3 × 13
Multiply the numbers 5 × 13...you'll get 65.
Now, multiply 2 × 5 × 3 = 30.
If you check,
65 × 30 = 1950.
Also, they have the digits 0, 3, 6 & 5 as asked in the question.
So, your required numbers are 65 & 30.
_______
Hope it helps!
RainbowSalt2222 ☔
Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production
process. Assume a production process produces items with a mean weight of 15 ounces.
a. The process standard deviation is 0.20, and the process control is set at plus or minus 0.75 standard deviation. Units with
weights less than 14.85 or greater than 15.15 ounces will be classified as defects. What is the probability of a defect (to 4
decimals)?
In a production run of 1000 parts, how many defects would be found (round to the nearest whole number?
b. Through process design improvements, the process standard deviation can be reduced to 0.07. Assume the process control
remains the same, with weights less than 14.85 or greater than 15.15 ounces being classified as defects. What is the probability of
a defect (round to 4 decimals; if necessary)?
In a production run of 1000 parts, how many defects would be found (to the nearest whole number)?
c. What is the advantage of reducing process variation, thereby causing a problem limits to be at a greater number of standard
deviations from the mean?
Answers
Using the normal distribution, it is found that:
a) The probability of a defect is of 0.4532, and out of 1000 parts, 453 will be classified as defective.
b) The probability of a defect is of 0.0324, and out of 1000 parts, 32 will be classified as defective.
c) The reduction in the variability also reduces the number of defective parts.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean given by \(\mu\) and standard deviation represented by \(\sigma\) is given as follows:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score measures how many standard deviations the measure X is above(in case the score is positive) or below(in case the score is negative) the mean. From the z-score table, the p-value associated with the z-score is found, which represents the percentile of the measure X.For item a, the mean and the standard deviation are given as follows:
\(\mu = 15, \sigma = 0.2\)
The proportion of defectives is two times the p-value of Z when X = 14.85, as 14.85 and 15.15 are the same distance from the mean and the normal distribution is symmetric, hence:
\(Z = \frac{X - \mu}{\sigma}\)
Z = (14.85 - 15)/0.2
Z = -0.75
Z = -0.75 has a p-value of 0.2266.
2 x 0.2266 = 0.4532 = 45.32%
Out of 1000, the number of defectives is:
0.453 x 1000 = 453.
For item b, we have that \(\sigma = 0.07\), hence:
\(Z = \frac{X - \mu}{\sigma}\)
Z = (14.85 - 15)/0.07
Z = -2.14
Z = -2.14 has a p-value of 0.0162.
2 x 0.0162 = 0.0324.
Out of 1000, the number of defectives is:
0.032 x 1000 = 32.
For item c, we can see that the reduction of variability will make the parts having measures closer to the desired, hence reducing the number of defectives.
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The table below represents a function. ху 011 25 5 26 750 Which equation makes the table true? x) = 2x + 1 Rx) = x² + 1 fx) = 2x-1 f(x) = x2-1
Answers
Answer: 3rd
Step-by-step explanation:
PLS HELP
WILL GIVE BRAINIEST
The points plotted below are on the graph of a polynomial. Which of the
following x-values is the best approximation of a root of the polynomial?
Check all that apply.
A. X-1.1
B. X= 4.3
C. x=2.4
D. X=6
E.X=1
Answers
Answer:
I don't know the answer but have a site that helps me with math, its called
Step-by-step explanation:
Just check it out
The pentagons ABCDE and JKLMN are similar.
Find the length x of JK.
Answers
The value of x in the pentagon JKLMN is 7.2.
What is Polygon?A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.
The pentagons ABCDE and JKLMN are similar.
when two figures have the same shape but their sizes are different, then such figures are called similar figures.
We need to find the value of x.
1/1.8=4/x
Apply cross multiplication
x=4×1.8
x=7.2
Hence, the value of x in the pentagon JKLMN is 7.2.
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Highschool geometry please answer questions 8-10 in the attachment added
Answers
PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!
Answers
Using functions,
Part A: f (3) = 6(3) + 14 = 32.
g (3) = 3 + 2 = 5
Part B: (f/g) (3) will be 6.4.
What are functions?The core concept of calculus in mathematics is a function. The relations are certain kinds of the functions. In mathematics, a function is a rule that produces a different result for every input x. In mathematics, a function is represented by a mapping or transformation. Letters like f, g, and h are widely used to indicate these operations. The set of all potential values that can be passed into a function while it is specified is known as the domain. The entire set of values that the function's output is capable of creating is referred to as the "range." The range of potential values for a function's outputs is known as the co-domain.
Here in the question,
f (x) = 6x + 14
g (x) = x + 2
Now we have to find for the value of x,
f (3) = 6(3) + 14 = 32.
g (3) = 3 + 2 = 5
So, f (3) = 32 and g (3) = 5.
Now,
(f/g) (3) will be 32/5 = 6.4.
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Glenn bought a game system and 3 video games for $375. Jim bought a game system and 4 videogames at the same store for $410.-Each game system costs the same.-Each video game costs the same.What is the cost, in dollars, of one game system?
Answers
To obtain the cost of one game system, the following steps are necessary:
Step 1: Let the unknown costs of a game system and a video game be represented by the variables x and y, respectively.
That is :
\(\begin{gathered} x\Rightarrow\text{ cost of one game system} \\ y\Rightarrow\text{ cost of one video game} \end{gathered}\)Step 2: Transform each of the first two sentences of the question into mathematical equations, as follows:
\(\begin{gathered} \text{Sentence 1:} \\ x+(3\times y)=375 \\ \text{Sentence 2:} \\ x+(4\times y)=410 \end{gathered}\)Step 3: Assign the equations numbers, and solve them simultaneously, as below:
\(\begin{gathered} x+(3\times y)=375 \\ \Rightarrow x+3y=375\ldots\ldots\text{.(1)} \\ x+(4\times y)=410 \\ \Rightarrow x+4y=410\ldots\ldots\ldots(2) \\ \end{gathered}\)Now:
\(\begin{gathered} \text{Subtract equation 1 from equation 2:} \\ (x+4y)-(x+3y)=410-375 \\ x+4y-x-3y=35 \\ x-x+4y-3y=35 \\ 0+y=35 \\ \Rightarrow y=35 \end{gathered}\)Finally:
\(\begin{gathered} \text{substitute the value of y into equation 1 and solve for x:} \\ x+3y=375\ldots\ldots\text{.(1)} \\ \Rightarrow x+3(35)=375 \\ \Rightarrow x+105=375 \\ \Rightarrow x=375-105 \\ x=270 \end{gathered}\)Therefore the cost, in dollars, of one game system is 270
Question 13(Multiple Choice Worth 4 points)(06.04 MC)The function f(x) = 4x + 30 represents the length of a rectangle. The function g(x) = x - 1 represents the width of the rectangle. Use (f•g)(5) to determine the area of the rectangle.44650200
Answers
From the problem, the length of the rectangle is f(x) = 4x + 30 and the width is g(x) = x - 1.
To find the area, use (f · g)(5)
That will be :
\(\begin{gathered} (f\cdot g)(x)=(4x+30)(x-1) \\ (f\cdot g)(5)=(4\times5+30)(5-1) \\ (f\cdot g)(5)=50(4) \\ (f\cdot g)(5)=200 \end{gathered}\)ANSWER :
The area is 200
Determine whether the following individual events are independent or dependent. Then find the probability of the combined event.
In a town where 1/4 of the days are sunny and 3/4 are cloudy, the next six days are all sunny.
Answers
The probability of the combined event that the next six days are all sunny is 1/4096
How to determine the probability all days being sunny?From the question, we have the following parameters that can be used in our computation:
Probability that it is sunny = 1/4
Probability that it is cloudy = 3/4
Number of days = 6
The probability for all six days, it is sunny is represented as
Probability = Probability that it is sunny^Number of days
Substitute the known values in the above equation, so, we have the following representation
Probability = (1/4)⁶
Express as decimal
Probability = (0.25)⁶
Evaluate the exponent
Probability = 1/4096
Hence, the probability is 1/4096
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3) a. Graph the quadrilateral WXYZ with vertices (3.-5), (1.-3), 7(-1, -5), and Z(1.-7).b. Graph the quadrilateral after a 90 degree rotation clockwise about the origin and state the ruleand the coordinates of the vertices.(x,y) →W'X'Y'Z'
Answers
a) Graph for Quadrilateral
When we rotate a figure of 90 degrees clockwise, each point of the given figure has to be changed from (x, y) to (y, -x) and graph the rotated figure.
W' = (-5, -3)
X' = (-3, -1)
Y = (-5, 1)
Z = (-7, -1)
In a network of 30 computers, 4 have a copy of a particularly critical file to sustain an organization's regular operations. Suppose that 9 computers at random fail. What is the probability that all 4 computers with the critical file fail in this incident? (
Answers
The probability that all 4 computers with the critical file fail in this incident
P(x=4)=0.00085
This is further explained below.
What is the probability that all 4 computers with the critical file fail in this incident?Generally, is mathematically given as
\($H \rightarrow(n, m)$\)
p.d.F. of Hyper Geometric distribution
given, $N=39, n=4, M=8, x=4$
\(\begin{aligned}P(x=4) &=\frac{8}{4} \frac{39}{39} \\&=\frac{70 \times 1}{82251}\end{aligned}$$\)
\(\begin{aligned}&P(x=4)=8.5106 \times 10^{-4} \\&P(x=4)=0.00085\end{aligned}\)
In conclusion, P(x=4)=0.00085
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PLS HELP ME ASAP ILL GIVE BRAINIEST:)
Which equation can be used to find the area of the of the parallelogram?
Responses
A A = 10(5 + 7)
B A = (7)(5)
C A = (15)(7)
D A = (15)(5)
Answers
Answer:The answer is D (15)(5)
Step-by-step explanation:
To find the area of a parallelogram the formula it b×h. Base and height and the base is 15cm and the height is 5cm so the answer is d because 7 isn't the base or height it is a slant.
Answer: C
Area = Base x Height (15)(5)
For each pair of functions f, g below, find f(g(x)) and g(f(x))
Then, determine whether and are inverses of each other.
Simplify your answers as much as possible.
(Assume that your expressions are defined for all in the domain of the composition.
You do not have to indicate the domain.)
Answers
Answer:
See below
Step-by-step explanation:
Part A
\(f(g(x))=f(\frac{x}{3})=3(\frac{x}{3})=x\\g(f(x))=g(3x)=\frac{3x}{3}=x\)
Since BOTH \(f(g(x))=x\) and \(g(f(x))=x\), then \(f\) and \(g\) are inverses of each other
Part B
\(f(g(x))=f(\frac{x+1}{2})=2(\frac{x+1}{2})+1=x+1+1=x+2\\g(f(x))=g(2x+1)=\frac{(2x+1)+1}{2}=\frac{2x+2}{2}=x+1\)
Since BOTH \(f(g(x))\neq x\) and \(g(f(x))\neq x\), then \(f\) and \(g\) are NOT inverses of each other
Of all the soft drink consumers in a particular sales region, 30% prefer Brand A and 70% prefer Brand B. Of all these soft drink consumers, 20% prefer Brand A and are female, and 40% prefer Brand B and are female. What is the probability that a randomly selected consumer is female, given that the person prefers Brand A? A. 0.18 B. 0.21 C. 0.34 D. 0.67
Answers
Answer:
The answer to this question should be D. 0.67
Hope this helped.
Which of these events is not mutually exclusive?
A) the chance that you will get a heads or tails when you flip a coin once.
B) the chance that you will only study for the test alone or with a friend.
C) the chance that you will meet your friends for pizza or at a chinese restaurant for dinner today at 6.
D) the chance that you will answer the ringing phone or take a walk.
Answers
The chance that you will get a heads or tails when you flip a coin once (option A) is not mutually exclusive.
Mutually exclusive events are events that cannot occur at the same time, or that do not have any overlap. In the case of flipping a coin, the possibility of getting a head and the possibility of getting tails are independent of each other, and both can occur simultaneously. Therefore, the chance that you will get heads or tails when you flip a coin once is not mutually exclusive.
On the other hand, the other events listed (B, C, and D) are mutually exclusive. The chance that you will only study for the test alone or with a friend cannot occur simultaneously, as you can either study alone or with a friend, but not both. Similarly, the chance that you will meet your friends for pizza or at a Chinese restaurant for dinner today at 6 cannot occur at the same time, as you can either go to the pizza place or the Chinese restaurant, but not both. And the chance that you will answer the ringing phone or take a walk cannot occur simultaneously, as you can either answer the phone or take a walk, but not both.
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The chance that you will get a heads or tails when you flip a coin once (option A) is not mutually exclusive.
this question is related to probability.
mutually exclusive
Mutually exclusive events are those events that do not occur at the same time.
For example, when a coin is tossed then the result will be either head or tail, but we cannot get both the results. Such events are also called disjoint events since they do not happen simultaneously.
probability
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
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A drawer of shirts contains 3 solid red, 2 striped red, 4 solid blue, and 3 striped green. What is the probability of picking a shirt that is red or striped?
Answers
The probability of picking a shirt that is red or striped is 2/3.
Given, that a drawer of shirts contains 3 solid red, 2 striped red, 4 solid blue, and 3 striped green.
We have to find the probability of picking a shirt that is red or striped,
P(R ∪ S) = P(R) + P(S) - P(R∩S)
where, R be the event that the shirt is red.
and S be the even that the shirt is striped.
P(R) = 5/12 (as, there are 5 red shirts)
P(S) = 5/12 (as, there are 5 striped shirts)
P(R∩S) = 2/12 (as, there are 5 striped red shirts)
P(R ∪ S) = 5/12 + 5/12 - 2/12
P(R ∪ S) = 8/12
P(R ∪ S) = 2/3
The probability of picking a shirt that is red or striped is 2/3.
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On Monday a team of street sweepers cleaned 4 city blocks. Tuesday, the team cleaned 2 1/6 times as many blocks as on Monday. How many city blocks did the street sweepers clean on Tuesday?
Answers
1/5 is the answer :0000
There will be twelve and a half city blocks of the street sweepers clean on Tuesday.
What is a fraction?The numerator, which is found at the top of the fraction number, and the denominator, which is located at the bottom, are its two component components.
It is given that, four city blocks were cleaned by a crew of street sweepers on Monday. The crew cleaned 2 1/6 as many blocks on Tuesday as they did on Monday.
Suppose the number of city blocks the street sweepers cleaned on Tuesday will be x,
x = 4 + 2 1/6 × 4
x=4+13/6×4
x=12.6≈ 12 1/2
Thus, the street sweepers will clean twelve and a half city blocks on Tuesday.
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Which of the following points satisfies y < 3x - 6?
(2, -4)
(1,0)
Answers
The point (2,-4) satisfies y < 3x - 6
Explanation: The coordinates are in the form (x,y) so 2 is the x value, and -4 is the y value. You substitute these values into the equation:
y<3x-6
-4<3(2)-6
-4<6-6
-4<0
Now let’s substitute (1,0) into the inequality:
y<3x-6
0<3(1)-6
0<3-6
0<-3
This is false as 0 is greater than -3, not less than. Hope this helps :)
How many terms are in the expression 5 - 3c + 21?
A
one
B
two
C
three
D
four
Answers
Answer:
B. two
Hope this helps you!
\( \qquad \qquad\huge \underline{\boxed{\sf Answer}}\)
The given expression is :
\(\qquad \sf \dashrightarrow \: 5 - 3c + 21\)
Now, first simplify the expression ~
\(\qquad \sf \dashrightarrow \: 5 + 21 - 3c\)
\(\qquad \sf \dashrightarrow \: 26 - 3c\)
Count the number of terms ~
Hence, we get the two terms in the given expression.
What is the weight of the y, in grams?
y 1
1 1
1 1
1 1
1
1
answers=
-1/3
-1
-4
-3
Answers
Answer:
-1
Step-by-step explanation:
Find the sum of the first 20 arithmetic progression 2, 7, 12, 17, 22
Answers
Answer: 5
Step-by-step explanation: 2 + 5 = 7, 7 + 5 = 12, 12 + 5 = 17, 17 + 5 = 22
i need help!!!! does anyone know this..!!???
Answers
The period of the frequency factor b that is given in the diagram above would be = 0.2 sec.
How to determine the period of the frequency factor b given above?The frequency of a water wave is defined as the number of times the wave completes a cycle within a given period of time. While the period is the time it takes for the completion of a cycle.
The dot the represents the frequency factor b is the green dot on the wave table. Therefore the period as traced from the graph= 0.2 sec.
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Joy wants to buy strawberries and raspberries to bring to a party. Strawberries cost $1.60 per pound and raspberries cost $1.75 per pound. If she only has $10 to spend on berries, which inequality represents the situation where she buys x pounds of strawberries and y pounds of raspberries?
A.1.60x+1.75y≤10
B.1.60x+1.75y≥10
C.1.75x+1.60y≤10
D.1.75x+1.60y≥10
Answers
Answer: 1.60x + 1.75y is less than or equal to 10
Step-by-step explanation:
Since the strawberries cost $1.60 per pound, it would be x pounds times $1.60 for the total cost of strawberries. Since the raspberries cost $1.75 per pound, it would be y pounds times $1.75 for the total cost of the raspberries. The total cost of both, or 1.60x + 1.75y, must be equal to or less than 10 because she cannot spend over 10 dollars.
1.60x + 1.75y ≤ 10 inequality represents the given situation.
What is linear inequality?"Linear inequality is the mathematical expression where linear expression are relate using inequality >, <, ≥, ≤ ."
According to the question,
Given,
x pounds represents the weight of strawberries
y pounds represents weight of raspberries
Cost of strawberries per pound = $1.60
⇒Cost of x pounds strawberries = 1.60x
Cost of raspberries per pound = $1.75
⇒Cost of y pounds of raspberries = 1.75y
Total amount Joy can spend = $10
Substitute the conditions to represent a linear inequality we get,
1.60x + 1.75y ≤ 10
Hence, Option(A) is the correct answer.
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Let f(x) = v= -6 and g(x) = 22 +5.(fog)(x) =m(gof)(x) =
Answers
Ok, so
Given:
\(\begin{gathered} f(x)=\sqrt[]{x}-6 \\ g(x)=x^2+5 \end{gathered}\)We want to find (fog)(x) and (gof)(x).
First, let's find (fog)(x).
This is:
\((fog)(x)=f(g(x))=f(x^2+5)\)So we're going to evaluate f in (x2 + 5).
\(f(x^2+5)=\sqrt[]{x^2+5}-6\)Now, let's find (gof)(x). This is:
\((gof)(x)=g(f(x))=g(\sqrt[]{x}-6)_{}\)So we're going to evaluate g in the function f.
\(g(\sqrt[]{x}-6)=(\sqrt[]{x}-6)^2+5\)Which of the following lines is perpendicular to the line y=3/4x-2
Answers
Answer:
A. y = -⁴/3x + 4
Step-by-step explanation:
The line y = ¾x - 2 is given in the slope-intercept form, y = mx + b, where,
Slope (m) = ¾
y-intercept (b) = -2
Therefore, the equation of the line that is perpendicular to the line y = ¾x - 2 will have a slope (m) that is the negative reciprocal of ¾, which is -⁴/3.
Thus, the only equation that has a slope of -⁴/3 is y = -⁴/3x + 4.
That's the answer.
Elena receives $95 per year in simple interest from three investments totaling $2100 . Part is invested at 3%, part at 4%, and part at 5%. There is $1000 more invested at 5% than at 4%. Find the amount invested at each rate.
The amount invested at 3% is $
the amount invested at 4% is $
and the amount invested at 5% is $
Answers
The amount invested at 3% is $400, the amount invested at 4% is $700, and the amount invested at 5% is $1000.
Let's assume the amount invested at 4% is x dollars.
According to the given information, the amount invested at 5% is $1000 more than the amount invested at 4%.
So, the amount invested at 5% is (x + $1000).
The total amount invested is the sum of the amounts invested at each rate, which is $2100.
Therefore, we can write the equation:
x + (x + $1000) + (amount invested at 3%) = $2100
Now, we can calculate the amount invested at 3%.
We subtract the sum of the amounts invested at 4% and 5% from the total investment:
(amount invested at 3%) = $2100 - (x + x + $1000) = $2100 - (2x + $1000)
Given that Elena receives $95 per year in simple interest from the investments, we can use the formula for simple interest:
Simple Interest = Principal × Interest Rate
The interest earned from the investment at 3% is (amount invested at 3%) × 0.03, the interest earned from the investment at 4% is (amount invested at 4%) × 0.04, and the interest earned from the investment at 5% is (amount invested at 5%) × 0.05.
According to the problem, the total interest earned is $95.
So we can write the equation:
(amount invested at 3%) × 0.03 + (amount invested at 4%) × 0.04 + (amount invested at 5%) × 0.05 = $95
Now we can substitute the expression for (amount invested at 3%) and solve for x.
Once we have the value of x, we can calculate the amounts invested at 3%, 4%, and 5% using the given information.
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Two rectangles of the same shape have areas of 676 and 3,457 square centimetres. If the shorter side of the larger rectangle is 41 centimetres, what are the dimensions of the smaller one?
Answers
The dimensions of the smaller rectangle are 13 centimeters by 52 centimeters.
Let's assume the dimensions of the smaller rectangle are length L and width W (in centimeters).
We know that the area of the smaller rectangle is 676 square centimeters:
L * W = 676 ----(1)
We also know that the larger rectangle has a shorter side of 41 centimeters. Let's say the corresponding longer side of the larger rectangle is H centimeters.
The area of the larger rectangle is 3457 square centimeters:
41 * H = 3457 ----(2)
Our current set of equations contains two unknowns. In order to get the smaller rectangle's dimensions, we can simultaneously solve these equations.
In order to find H, we can use equation (2):
H = 3457 / 41
H ≈ 84.22
Now we can substitute this value of H into equation (1):
L * W = 676
We need to find the dimensions (L and W) that multiply to give 676. We can start by looking for factors of 676.
Factors of 676: 1, 2, 4, 13, 26, 52, 169, 338, 676
By trial and error, we can see that the factors that give a close match to the dimensions of the larger rectangle (41 and 84.22) are 13 and 52:
L = 13
W = 52
Therefore, the smaller rectangle has measurements of 13 by 52 centimetres.
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Which is the solution to the inequality below?
Answers
The solution to the inequality will be x ≤ -3. The correct option is B.
What is inequality?Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
The given inequality : | x + 2 |+ 5 ≤ 4 will be calculated as below:-
| x + 2 | + 5 ≤ 4
x + 2 ≤ 4 - 5
x + 2 ≤ -1
x ≤ -1 - 2
x ≤ -3
Therefore, the solution to the inequality will be x ≤ -3. The correct option is B.
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Write the equation of the quadratic function that contains the point (1,1) and has the same shape as f(x)=2x. The vertex is on the y-axis.
Answers
The equation of the quadratic function that contains the point (1,1) is
y = 2x² - 1.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree. A quadratic function must contain at least one term of the second degree.
Given the quadratic function that contains the point (1,1)
x = 1 and y = f(x) = 1
the shape of the equation is the same as f(x) = 2x²
a quadratic equation is given by
y = a(x - k)² + h
here (k, h) is the vertex of the function
given vertex is on the y-axis,
so k = 0
y = ax² + h
and a = 2 from f(x) = 2x²
y = 2x² + h
substitute x= 1 and y = 1
1 = 2 + h
h = 1 - 2 = -1
equation of function is y = 2x² - 1
Hence equation of the function is y = 2x² - 1.
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