1. A, as A is the shared vertex of both triangles. and 2. The original is ABC, and the dilated version is AED. as triangle ABC's half is represented by triangle AED.
How do you calculate a triangle's dilation?The following is a basic formula to determine a dilated figure's scale factor: Scale factor is equal to the difference between the dimensions of the old and new shapes.
What is the triangle's center of dilation?A fixed point in the plane around which all points are enlarged or contracted is the center of a dilation.
The center, which may be found within, outside, or on a figure, is the only invariant (constant) point under a dilation (k 1).
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In 2016 the Better Business Bureau settled 80% of complaints they received in the United States. Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is 0.80, the same as the overall proportion of complaints settled in 2016.In 2016 the Better Business Bureau settled 80% of complaints they received in the United States. Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is 0.80, the same as the overall proportion of complaints settled in 2016.
Using the binomial distribution, the mean and the standard deviation for the number of settled complaints among those received are given as follows:
Mean: 160 complaints.Standard deviation: 5.66 complaints.What are the mean and the standard deviation for the binomial distribution?The binomial distribution gives the probability of exactly x successes on n repeated trials, with p probability of a success on each trial. These parameters will be used to find the mean and the standard deviation, with formulas that are presented next.
The mean is given as follows:
[tex]E(X) = np[/tex]
The standard deviation is given as follows:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Considering that a sample of 200 complains are chosen, each with an 90% probability of being settled, the parameters are given as follows:
n = 200, p = 0.8.
Hence the mean is:
[tex]E(X) = np = 200 \times 0.8 = 160[/tex]
The standard deviation is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200 \times 0.8 \times 0.2} = 5.66[/tex]
What is the missing information?The problem states that 200 complaints were received, and asks for the mean and the standard deviation for the number of settled complaints among those received.
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how do you find the equation of line passing through (0,0) and (4,4)
Answer:
y = mx
Step-by-step explanation:
It depends on what form of the line that you want. Usually the slope intercept form is wanted.
y = mx + b We need to have the m (slope) and the b (the y-intercept)
The slope is the change in y over the change in x.
Ordered pairs are in the form (x,y)
(0,0) and (4,4) Have x's of 4 and 0, and y's of 4 and 0. We subtract these to find the changes in y and x.
[tex]\frac{4-0}{4-0}[/tex] This is [tex]\frac{4}{4}[/tex] which is the same as 1. The slope (m) is 1.
Now we need to find the y -intercept. The y intercept is the point where x is 0 (0,b). They give us this point (0,0,) So the y -intercept is zero.
y = 1m + 0
or y =mx
Which value must be added to the expression x² - 8x to make it a perfect-square trinomial?
04
O-16
O-4
O 16
Answer: 16
Step-by-step explanation:
The standard form of a perfect square trinomial is:
[tex](x-a)^{2} = x^{2}-2ax+a^{2}[/tex]
Put the equation into standard form:
[tex]x^{2} -8x+c[/tex]
Compare to to the form of a perfect square trinomial:
[tex]-8x=-2ax\\\frac{-8x}{-2x}=a\\a=4[/tex]
Plug a back into the equation to get c:
[tex]c=a^{2}=4^{2}\\c=16[/tex]
Putting everything back together gives you:
[tex](x-4)^{2} = x^{2}-8x+16[/tex]
The required, we need to add 16 to the expression x² - 8x to make it a perfect square trinomial. Option D is correct.
A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the monomial, binomial, and trinomial, etc. ax+b is a polynomial.
To make the expression x² - 8x a perfect-square trinomial, we need to add the square of half of the coefficient of x to the expression.
The coefficient of x is -8, so half of it is -4. The square of -4 is 16.
Therefore, we need to add 16 to the expression x² - 8x to make it a perfect square trinomial.
Answer: 16.
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6
The exchange rate between pounds and US dollars is £1 = $1.27
a) Annie goes on holiday to the USA.
She buys £500 worth of dollars
She spends $550 and converts the rest back to £ at the same rate.
How much money does she receive?
Annie will receive 66.92 euros after converting the dollars into euros post her trip
The exchange rate between pounds and US dollars: 1 Euro = $1.27
Exchange rate: An exchange rate determines the price at which one currency will be exchanged for another and has an impact on international trade and money transfers.
Euro Annie spends to buy dollars = 500
Equivalent dollars received by Annie for 500 euros = 500*1.27
= $635
The money she spent in dollars = $550
Dollars remaining = 635-550 = $85
Euro she will receive after conversion = Dollars remaining/Conversion rate 85/1.27 = 66.92 Euros
So, After changing the dollars into euros after her vacation, Annie will receive 66.92 euros.
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Resting body temperatures are normally distributed with an average of 98.25 degreesFahrenheit and a standard deviation of 0.73 degrees Fahrenheit. A nurse examines 40 patients in one hour. What is the probability the average temperature of the 40 patients is between 98.0 degrees Fahrenheit and 98.50 degrees Fahrenheit? (Round to the hundredths)A)0.97B)0.11542313C)0.99D)Sample size is not larger than 40 so we cannot compute probability
Resting body temperatures are normally distributed with an average of 98.25 degrees
Fahrenheit and a standard deviation of 0.73 degrees Fahrenheit. A nurse examines 40 patients in one hour. What is the probability the average temperature of the 40 patients is between 98.0 degrees Fahrenheit and 98.50 degrees Fahrenheit? (Round to the hundredths)
A)0.97
B)0.11542313
C)0.99
D)Sample size is not larger than 40 so we cannot compute probability
step 1
Find the z-scores
For x=98.0 degrees
z=(98-98.25)/0.73 --------> z=-0.3425
For x=98.50
z=(98.50-98.25)/0.73 ------> z=0.3425
using a Z-score Calculator
we have that
P=0.26803
step 2
we have that
Four friends have $525 that they want to share equally. To start, they divide the money so that each friend gets a $100 bill. What is the most useful next step?
If four friends have $525 that they want to share equally and they divide the money so that each friend gets a $100 bill, then next step will be divide the remaining money so that each friend gets a $31.25
Total money the have = $525
they divide the money so that each friend gets a $100 bill
The amount of money they split equally = 4×100
= $400
Remaining money = 525-400
= $125
Split the remaining money into 4 = 125/4
= $31.25
Hence, If four friends have $525 that they want to share equally and they divide the money so that each friend gets a $100 bill, then next step will be divide the remaining money equally so that each friend gets a $31.25
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What is the unit rate for the situation represented in the table?
Hours 3 5 7 9
Wages $35.25 $58.75 $82.25 $105.75
a $7.05/hour
b $2/hour
c $11.75/hour
d $16.45/hour
Answer:
c $11.75/hour
Step-by-step explanation:
You want the unit rate represented by the table of (hours, wages) = (3, $35.25), (5, $58.75), ....
Unit rateThe unit rate of dollars per hour is found by dividing dollars by hours:
$35.25/(3 hour) = $11.75/hour
You can check the other table values to see if they represent the same unit rate. (They do.)
Well GIVE U BRAINLIEST HELP ASAP
Question
Drag the numbers to order them from least to greatest.
Answer : -4/9 , -4/7 , -3/5 , -5/6
Indira finds that on a typical day, 4 out of every 5 students at her school eat a
cafeteria lunch. The rest of the students bring their lunch from home. Indira's
school has 495 students. On a typical day, how many students at her school bring
their lunch from home? Show your work.
By using fractions, we can conclude that 99 students bring their lunch from home.
What is a fraction?Consider a collection of items from which some of their components have been stolen. A fraction is a name given to the portion that was taken. The denominator is the bottom portion of the fraction, and the numerator is the upper portion.So, the Fraction of students eating a cafeteria lunch at her school = 4/5
A fraction of students bring their lunch from home:
1 / 4/55/4/51/5495 students attend her school in total.
Several students bring their lunch from home, including:
1/5 × 49599Therefore, by using fractions, we can conclude that 99 students bring their lunch from home.
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The value of the ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ does not rely on the values of the other variables in an expression or function, and its value determines the values of the other variables.
The value of the independent variable does not rely on the values of the other variables in an expression or function, and its value determines the values of the other variables.
What is an independent variable?An independent variable can be defined as the variable that is being manipulated, controlled, and which varies in an experimental or research study for the exploration of its effects.
It is termed “independent” because it's not affected or changed by other variables in an experiment or study.
It is known as a variable that is unaffected in a function and cannot be determined by the other variables in that function.
Other names for an independent variable includes;
Explanatory variableInput variableExposure variableControlled variablePredictor variableHence, the variable is independent.
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Harry just deposited $1500 into a savings account giving 6% interest compounded monthly. How much will be in the account after 10 years and 20 years ?
Compound Interest
It occurs when the interest is reinvested rather than paying it out.
When it happens interest in the next period is then earned on the principal sum plus previously accumulated interest.
The formula is:
[tex]{\displaystyle A=P\mleft(1+{\frac{r}{n}}\mright)^{nt}}[/tex]Where:
A=final amount
P=initial principal balance
r=interest rate
n=number of times interest applied per time period
t=number of time periods elapsed
Harry deposited an initial amount of P = $1500.
The savings account gives r = 6% = 0.06 interest
Since the interest is compounded monthly, n = 12 (there are 12 months in a year)
The time is t = 10 years.
Now we apply the formula:
[tex]\begin{gathered} {\displaystyle A=1500(1+{\frac{0.06}{12}})^{12\cdot10}} \\ \text{Calculating:} \\ {\displaystyle A=1500(1+0.005)^{120}} \end{gathered}[/tex]Using a calculator:
A = $2729.095
Rounding to two decimals,
A = $2729.10
Harry will have $2729.10 in his account after 10 years
Now for t = 20 years:
[tex]{\displaystyle A=1500(1+{\frac{0.06}{12}})^{12\cdot20}}[/tex]Calculating again:
A = $4965.31
Harry will have $4965.31 in his account after 20 years
The sales tax is $52 on the purchase of a dining room set for $1040. Find the sales tax rate.
Answer:
Total price including tax: $ 1,092.00
Sales tax rate: 5%
Step-by-step explanation:
Brainlest, Please!
if we take 1040 to be the 100%, what is 52 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 1040 & 100\\ 52& x \end{array} \implies \cfrac{1040}{52}~~=~~\cfrac{100}{x} \\\\\\ 20=\cfrac{100}{x}\implies 20x=100\implies x=\cfrac{100}{20}\implies x=5[/tex]
Can anyone help me with this problem please and thank you !
Answer:
d = 7
For step by step explaintion I am so sorry but I don't rember enough of my geometry class to properly explain this, but triangles BDC and ABD are congruent (I swear I can prove this if I dig up my old notes but I really do not feel like doing that) so these 2 equations (sides) are equal. So we just solve for d!
6d + 3 = 10d - 25
(we all know how to solve something this simple so I won't bore you with the details of inverse operations and such)
d = 7
f(x)=-3x^2+3x, find f(f)x))
The value of the composite function f(f(x)) is -3(-3x^2 + 3x)^2 + 3(-3x^2 + 3x)
How to determine the composite function?The functions are given as
f(x) = -3x^2 + 3x
The definition of the composite function is given as
f(f(x))
This composite function is calculated using the following composite function formula
f(f(x))= (f o f)(x)
Substitute the known values in the above equation
So, we have the following equation
f(f(x)) = -3f(x)^2 + 3f(x)
So, we have
f(f(x)) = -3(-3x^2 + 3x)^2 + 3(-3x^2 + 3x)
Hence, the composite function is f(f(x)) = -3(-3x^2 + 3x)^2 + 3(-3x^2 + 3x)
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What is answer????????
Answer is 6
9 - 6 = 3
The difference of a number and 9 means to subtract said number from 9.
There are 4 corners at an intersection. A pole at each corner holds 2 traffic light, 1 streetlight, and 2 crosswalk light. How many lights are at the intersection in all ?
Using multiplication we calculate that there are 56 lights in the cross-section.
When two integers are multiplied together in mathematics, the result is a product, or an expression that describes the factors to be multiplied.
The commutative law of multiplication states that the outcome is unaffected by the sequence in which real or complex numbers are multiplied. For instance, the sum of 6 and 5 is 30. (the outcome of multiplication). Usually, the order of the factors determines the outcome of a multiplication of matrices or the constituents of other associative algebras. For instance, multiplication in general and in matrices are non-commutative operations in other algebras.There are many other kinds of products in mathematics: in addition to multiplying just numbers, polynomials, or matrices, one may also define products on a wide range of algebraic expressionsTotal number of lights in each pole = 2 + 1 + 2 = 5 lights
There are 4 corners
Total number of poles = 5 × 4 = 20
So by multiplication we get there are 20 lights in the intersection.
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If X - N(-3,4), find the probability that x is between -6 and 6. Round to 3 decimal places.
The probability that x is between -6 and 6 is 18.84%.
What is defined by the term normal distribution?The symmetry of the normal distribution is well known. This means that the distribution is just not skewed. We can easily calculate probabilities using this distribution; all we need are the z scores. The Standard Normal Distribution would be a probability distribution with known and constant parameters. That really is, the parameters remain unchanged.For the given question;
The probability of x should line between -6 and 6.
The formula for calculating the z-score is;
z = (x - μ)/σ
μ = mean (-3)
σ = standard deviation (4)
Put the values in the formula.
For x = -6
z = (-6 - (-3))/4
z = -3/4
z = -0.75
Now, x = 6
z = (-6 - 3)/4
z = -9/4
z = -2.25
P(-6 < x < 6) = P(-0.75 < x < -2.25)
Find the probability using negative z score.
P(-6 < x < 6) = 0.197 - 0.0122
P(-6 < x < 6) = 0.1848
P(-6 < x < 6) = 18.84%
Thus, the probability that x is between -6 and 6 is 18.84%.
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Apples are 99 cents a pound and pears are $1.25 a pound. Write an expression thatrepresents the total cost, in dollars, of a pounds of apples and p pounds of pears.
Answer
$(0.99 + 1.25p)
Explanation
Note: 100 cents = $1
Apples cost $(99/100) = $0.99 a pound
Pears cost $1.25 a pound
Since 1 pound of pears cost $1.25,
∴ p pounds of pears will cost $1.25p
Now total cost in $ of a pound of apples and p pound of pears = $(0.99 + 1.25p)
Hence, the expression that represents the total cost is $(0.99 + 1.25p)
Review and evaluate the following: By the given y = 2x + 1 ÷ x, what is the value of y when: 1. x=0 2. x = 1 3. x = 2.5 4.x = 1/3 5. x=a
ANSWER
[tex]\begin{gathered} 1)\text{ Undefined} \\ \\ 2)\text{ }3 \\ \\ 3)\text{ }2.4 \\ \\ 4)\text{ }5 \\ \\ 5)\text{ }2+\frac{1}{a} \end{gathered}[/tex]EXPLANATION
We want to find the value of y:
[tex]y=\frac{2x+1}{x}[/tex]for the values of x.
To do this, for each value of x, substitute the values of x into the equation and simplify.
1. x = 0:
[tex]\begin{gathered} y=\frac{2x+1}{x} \\ \\ y=\frac{2(0)+1}{0}=\frac{0+1}{0}=\frac{1}{0} \\ \\ y=\text{ Undefined} \end{gathered}[/tex]The value of y is undefined for x = 0 since any value divided by 0 is undefined.
2. x = 1:
[tex]\begin{gathered} y=\frac{2(1)+1}{1}=\frac{2+1}{1} \\ \\ y=\frac{3}{1} \\ \\ y=3 \end{gathered}[/tex]3. x = 2.5:
[tex]\begin{gathered} y=\frac{2(2.5)+1}{2.5}=\frac{5+1}{2.5} \\ \\ y=\frac{6}{2.5} \\ \\ y=2.4 \end{gathered}[/tex]4. x = 1/3:
[tex]\begin{gathered} y=\frac{2(\frac{1}{3})+1}{\frac{1}{3}}=\frac{\frac{2}{3}+1}{\frac{1}{3}} \\ \\ y=\frac{\frac{5}{3}}{\frac{1}{3}}=\frac{5}{3}*\frac{3}{1} \\ \\ y=5 \end{gathered}[/tex]5. x = a:
[tex]\begin{gathered} y=\frac{2(a)+1}{a}=\frac{2a+1}{a} \\ \\ y=2+\frac{1}{a} \end{gathered}[/tex]That is the answer.
Solve the system of equations
-2x - 6y + 8z = 14
3x + 2y - z = 4
2x - y + 2z = 10
in 2018, the population of los Angeles county, California, was 10,137,915. if los Angeles County covers 4,751 square miles, what's the average population density in the county?
The average population density in the county is:
10,137,915 people / 4,751 square miles = 2133.84 people / square mile
Rounding to nearest integer, we have: 2134 people / square mile
A data set has a correlation coefficient of 0.013. Which statement about the data is true? a. The data has little or no linear correlation. b. The data has a strong positive linear correlation. c. The data has a weak negative linear correlation. d. The data has a strong negative linear correlation.
Answer: Choice A
The data has little or no linear correlation
======================================================
Explanation:
r = correlation coefficient
The r values are within the interval [tex]-1 \le r \le 1[/tex]
In other words, r is between -1 and 1 inclusive of both endpoints.
r = -1 is the strongest negative correlationr = 1 is the strongest positive correlationr = 0 means there's no linear correlation at all. The data points are either randomly scattered about, or they perhaps fit on some kind of curve.For the case r = 0.013, it's very close to r = 0. This suggests there is very weak positive correlation or practically no linear correlation at all.
How to find the range of data. 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26
Answer:
22
Step-by-step explanation:
To find the rage, you subtract the smallest number from the largest number in the set of numbers.
So...
26 - 4 = 22
11. At Outdoor Adventures Clothing Company, all items are marked up to maximize
profit. Life preservers cost $25 to buy from the manufacturer. They sell for $35. What
is the percent increase on life preservers, to the nearest whole percent?
Using the percentages formula, we conclude that the percentage increase in life preserves is 40%.
What is the percentage?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement. By dividing the value by the total value and multiplying the result by 100, one can determine the percentage. The percentage calculation formula is (value/total value)100%.So, the percentage increase in life preserves:
Formula: (selling value - cost)/cost ×100Now, substitute the values in the formula as follows:
(selling value - cost)/cost ×100(35 - 25)/25×10010/25×1000.4×10040%Therefore, using the percentages formula, we conclude that the percentage increase in life preserves is 40%.
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Given that log 2 = a and log 3 = b, express the following in terms of a and b:
a) log 72
Answer:
Step-by-step explanation:
=a, log 3 = b Log 2 log 1.5= log 23/20 год 1.5 = = log 3-log 2 b-a The other terms log 1.2 log 0.24, log 0.5, log 0.836 cannot be expressed only. of in terms a or bor both. [Answer: Log 1.5 Option A
Answer:
[tex]\log 72=3a+2b[/tex]
Step-by-step explanation:
Given:
[tex]\log 2 = a[/tex][tex]\log 3 = b[/tex]Rewrite 72 as a product of 2s and 3s.
[tex]\implies 72 = 2 \times 2 \times 2 \times 3 \times 3[/tex]
[tex]\implies 72=2^3 \times 3^2[/tex]
Therefore:
[tex]\implies \log 72=\log(2^3 \times 3^2)[/tex]
[tex]\textsf{Apply the log product law}: \quad \log xy=\log x + \log y[/tex]
[tex]\implies \log 72=\log(2^3)+\log(3^2)[/tex]
[tex]\textsf{Apply the log power law}: \quad \log x^n=n\log x[/tex]
[tex]\implies \log 72=3\log2+2\log3[/tex]
Substitute the given values of log 2 and log 3:
[tex]\implies \log 72=3a+2b[/tex]
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Write the equation of the line that is parallel
to y = x-7 and passes through the point
(-3, 1)
Equation parallel to y = x+4,
How do you write an equation for a parallel line?Equations that are parallel have the same slope.The standard equation of an equation is written through slope intercept form, which is
y = mx + b
where m is your slope and b is the y intercept
So, in the equation provided, 1 is the slope.
To write an equation when given a slope and points, you use point slope form, which is
y −y1 =m(x−x1)
y1 is the y in the set of points you are given, same with x1
So,
y1 =1 and x1= -3
As stated before, m is the slope, and the slope is given as 1
Plug in the numbers into the equation
y −1 =1 (x+3)
y= x +4 ;
And there you have a equation parallel to
y=x +4
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Can u please help me solve this problem
Given that the initial point of vector "u" is:
[tex](4,8)[/tex]And the terminal point:
[tex](-12,14)[/tex]You need to find the Component Form of the vector with this formula:
[tex]u=\langle x_2-x_2,y_2-y_1\rangle[/tex]In this case:
[tex]\begin{gathered} x_2=-12 \\ x_1=4 \\ y_2=14 \\ y_1=8 \end{gathered}[/tex]Then, you get:
[tex]u=\langle-12-4,14-8\rangle=\langle-16,6\rangle[/tex]Find the Magnitude using this formula:
[tex]||u||=\sqrt{x^2+y^2}[/tex]In this case:
[tex]\begin{gathered} x=-16 \\ y=6 \end{gathered}[/tex]Therefore, by substituting values and evaluating, you get:
[tex]||u||=\sqrt{(-16)^2+(6)^2}\approx17.088[/tex]In order to find the direction of the vector "u", you need to use this formula:
[tex]\theta=tan^{-1}(\frac{y}{x})[/tex]Then, when you substitute the values of "x" and "y" into the formula and evaluate, you get:
[tex]\theta=tan^{-1}(\frac{6}{16})\approx20.556°[/tex]Hence, the answer is:
What is the solution to the system of equations? Use the substitution method to solve. 6=−4x+y− 5x−y=21 Enter your answer by filling in the boxes
The x and y solution of the system is x = -3 and y = -6
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
6 = −4x + y
− 5x − y = 21
Make -y the subject in the second equation, by adding 5x to both sides of the equation
5x − 5x − y = 21 + 5x
This gives
−y = 21 + 5x
Substitute −y = 21 + 5x in 6 = −4x + y
6 = −4x - 21 - 5x
Evaluate the like terms
5x + 4x = -6 - 21
This gives
9x = -27
So, we have
x = -3
Substitute x = -3 in −y = 21 + 5x
−y = 21 + 5 * -3
Evaluate
−y = 6
So, we have
y = -6
Hence, the solution for the system of linear equations 6 = −4x + y and − 5x − y = 21 is x = -3 and y = -6
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A coffee shop currently sells 440 lattes a day at $2.50 each. They recently tried raising the by price by $0.25 a latte, and found that they sold 60 less lattes a day.
a). Assume that the number of lattes they sell in a day, N, is linearly related to the sale price, p (in dollars). Find an equation for N as a function of p.
N(p)= (blank)
b). Revenue (the amount of money the store brings in before costs) can be found by multiplying the cost per cup times the number of cups sold. Again using p as the sales price, use your equation from above to write an equation for the revenue, R as a function of p.
R(p)= (blank)
c). The store wants to maximize their revenue (make as much money as possible). Find the value of p that will maximize the revenue (round to the nearest cent).
p= (blank) which will give a maximum revenue of $ (blank)
Show your work!
Explain your answer!
No incorrect answer!
No nonsense answers!
No spam answers!
Thanks!
Using linear function concepts, it is found that:
a) The amount of lattes sold function is: N(p) = -240p + 1040.
b) The revenue function is: R(p) = -240p² + 1040p.
c) The revenue is maximized when p = $2.17.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For this problem, we have a linear function with the points having the following format:
(price, lattes sold).
Hence two points are given as follows:
(2.50, 440), (2.75, 380).
The slope is given by change in y divided by change in x, hence:
m = -60/0.25 = -240.
Then:
N(p) = -240p + b.
When p = 2.50, N(p) = 440, hence we solve for b as follows:
440 = -240(2.5) + b
b = 1040.
Thus the function is:
N(p) = -240p + 1040.
The revenue function is:
R(p) = pN(p)
Hence:
R(p) = p(-240p + 1040)
R(p) = -240p² + 1040p.
Which is a concave down quadratic function, with a = -240 and b = 1040. A concave down quadratic function is maximized when:
p = -b/2a
Hence:
p = -1040/2(-240) = $2.17.
More can be learned about linear functions at https://brainly.com/question/24808124
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Find the equation of the line that passes through (-1,5) and (0,1)
We have to find the equation of the line that passes through the points (-1,5) and (0,1). We will write the equation in the slope-intercept form, which is given by:
[tex]y=mx+b[/tex]Where m represents the slope of the function, and b the y-intercept. We will find the slope, and then the y-intercept.
1. Finding the slope
For finding the slope we will use the formula:
[tex]m=\frac{y_2-y_1_{}}{x_2-x_1}[/tex]where (x₁,y₁) and (x₂,y₂) are two points that passes through the line. In this case, the points (-1,5) and (0,1).
Replacing, we obtain:
[tex]m=\frac{1-5}{0-(-1)}=\frac{-4}{1}=-4[/tex]Thus, the slope is -4.
2. Finding the y-intercept
For doing this step, we want to know the value of the function when x equals zero. But, as we have that the line passes through (0,1), this means that this value will be 1. This is, the y-intercept is 1.
3. Putting all together
Now, we just have to put the values obtained in the slope-intercept form:
[tex]\begin{gathered} y=mx+b \\ y=-4x+1 \end{gathered}[/tex]And this means that the equation of the line that passes through (-1,5) and (0,1) is y=-4x+1.