Answer:
142
Step-by-step explanation:
opposite angle theorem
Answer:
D. 142
Step-by-step explanation:
They are vertical angles which are always equal
Automatic Transmissions, Inc., has the following estimates for its new gear assembly project: price = $940 per unit; variable cost = $340 per unit; fixed costs = $3.4 million; quantity = 53,000 units. Suppose the company believes all of its estimates are accurate only to within ±15 percent. What values should the company use for the four variables given here when it performs its best-case scenario analysis? What about the worst-case scenario?
In the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units.
In the best-case scenario analysis for Automatic Transmissions, Inc.'s new gear assembly project, the company assumes the upper limit of the ±15 percent range for its estimates. For the price per unit, they take a 15 percent increase, resulting in a value of $1081. Similarly, the variable cost per unit is increased by 15 percent to $391. The fixed costs are also adjusted upwards by 15 percent, reaching $3.91 million. Finally, the quantity is decreased by 15 percent, leading to a value of 45,050 units.
On the other hand, in the worst-case scenario analysis, the company assumes the lower limit of the ±15 percent range for its estimates. The price per unit is decreased by 15 percent, resulting in $799. The variable cost per unit is decreased to $289. The fixed costs are adjusted downwards to $2.89 million. Lastly, the quantity is increased by 15 percent to 60,950 units.
Therefore, in the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units
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Step 4: By the definition of similar polygons, the lengths of corresponding sides are __________. This means that OKNL = KMLM OKNL = KMLM . Substituting in the lengths, we get 128 = 20 + xx 128 = 20 + xx . Cross multiply and solve the proportion for x.
By the definition of similar polygons, the lengths of corresponding sides are proportional.
The proportion for \(x=40\).
What are similar polygons?Similar polygons are two polygons that have the same shape but are not always the same size. Similar polygons have congruent angles and proportional sides. Consider identical polygons as enlarging or contracting the same shape. The similarity is represented by the symbol.As it is given in the definition, similar polygons have congruent angles and proportional sides.
Therefore, by the definition of similar polygons, the lengths of corresponding sides are proportional.
Cross multiply and solve the proportion \(x\) as follows:
The blank should be proportional.
\(\frac{12}{8} =\frac{20+x}{x}\\ 12x=160+8x\\4x=160\\x=40\)
Therefore, the proportion for \(x=40\).
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Points X and Z are on a number line, and point Y partitions
line XZ into two parts so that the ratio of the length of line
segment XY to the length of line segment YZ is 5:7. The
coordinate of X is 0.4, and the coordinate of Y is 5.8. What
is the coordinate of Z?
Answer:
The coordinate of \(Z\) is 13.36.
Step-by-step explanation:
According to the statement, we have the following information:
\(\frac{XY}{XZ} = \frac{5}{12}\) (1)
\(\frac{YZ}{XZ} = \frac{7}{12}\) (2)
\(X = 0.4\) (3)
\(Y = 5.8\) (4)
From (2), we have the following expression:
\(YZ = \frac{7}{12}\cdot XZ\)
\(Y-Z =\frac{7}{12}\cdot (X-Z)\)
\(Y - Z = \frac{7}{12}\cdot X -\frac{7}{12}\cdot Z\)
\(Y-\frac{7}{12}\cdot X = Z-\frac{7}{12}\cdot Z\)
\(\frac{5}{12}\cdot Z = Y-\frac{7}{12}\cdot X\)
\(5\cdot Z = 12\cdot Y-7\cdot X\)
\(Z = \frac{12}{5}\cdot Y-\frac{7}{5}\cdot X\) (5)
If we know that \(Y = 5.8\) and \(X = 0.4\), then the coordinate of \(Z\) is:
\(Z = \frac{12}{5}\cdot (5.8)-\frac{7}{5}\cdot (0.4)\)
\(Z = 13.36\)
The coordinate of \(Z\) is 13.36.
y= 8-2x tell the answer with explanation
The equation has infinite solutions which lie on the graph of this equation.
We have the following equation -
y = 8 - 2x
We have to solve for the possible values of x and y for which the equation is satisfied.
Define rearrangement of a mathematical equation.The rearrangement of a mathematical equation is process of expressing a variable in a equation in terms of other variables, constants etc.
According to the question, we have the following equation -
y = 8 - 2x
Rearranging the equation -
y = - 2x + 8
Now, plot the equation on graph - (Graph is attached at the end)
All the coordinates on this line satisfy the equation → y = 8 - 2x.
Hence, the equation has infinite solutions which lie on the graph of this equation.
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Two cars are starting from positions that are 20 miles apart. They are both headed for the same intersection, as depicted in the diagram below. Car A is traveling at 30 mph, and Car B is traveling at 45 mph. Which car will reach the intersection first?
Part II: Use Distance=rate⋅time to determine the time necessary for Car A to reach the intersection. Round your answer to the nearest hundredth of an hour.
Part III: Use Distance=rate⋅time to determine the time necessary for Car B to reach the intersection.
Part IV: Which car reaches the intersection first, and by how many hours?
II. The time that it will take for Car A to reach the intersection is of: 0.6 hours.
III. The time that it will take for Car B to reach the intersection is of: 0.62 hours.
IV. The car that will reach the intersection first is: Car A.
How to obtain the times?The relation used is that the velocity is obtained as the division of distance and time, hence:
v = d/t.
Then the time is obtained as the division of distance by velocity, as follows:
t = d/v.
To find the distance of Car B to the intersection, we have that:
It is opposite to angle of 95º.The sides between the angle have lengths of 18 miles and 20 miles.Then the distance is obtained using the law of cosines as follows:
d² = 20² + 18² - 2 x 18 x 20 x cosine of 95 degrees
d² = 786.75
d = square root(786.75)
d = 28 miles. (rounded)
Then the times are given as follows:
Car A: 18/30 = 0.6 hours, lower time, reaches first.Car B: 28/45 = 0.62 hours.More can be learned about the law of cosines at https://brainly.com/question/4372174
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what is the MAD OF 7, 10, 13, 4, 12, 21, 10, 3
x+12= -5 helpppp meeeee
Answer:
The answer is -17.
Step-by-step explanation:
Well since the answer turns out to be a negative, one of the numbers has to be negative.(not all cases but for this one, yes)You have to add 12+5 and you get 17. This has to be a negative because the answer is a negative.
simplify the following
3ab+2ab-ab
Answer:
4ab
Step-by-step explanation:
simplify the following
3ab+2ab-ab = (3 + 2 = 5)
5ab - ab = (5 - 1 = 4)
4ab
two Friends have agreed to do a job with pace $2,000 total together there receive apart payment Of 0.25 Of the total amount How much of part payment should reach friend receive ,if they split it equally?
A.$250
B.500
C.$1000
D.1500
Then Jorge does inventory on the drinks on average customers consume 22.75 L of lemonade per hour the restaurant is open on Sunday Jorge checks the giant lemonade machine at the start of the weekend there were 346.65 L of lemonade in the machine now there are only 5.4 L left based on this for how many hours was the restaurant open this weekend?
2m - n =8 Solve for n
Answer:
\( \boxed{\sf n = 2m - 8} \)
Step-by-step explanation:
Solve for n:
⇒2m - n = 8
Subtract 2 m from both sides:
⇒2m - 2m - n = 8 - 2m
2m - 2m = 0:
⇒-n = 8 - 2 m
Multiply both sides by -1:
⇒-n × (-1) = (8 - 2m) × (-1)
⇒n = 2m - 8
The required value of n is equal to n = 2m - 8.
An expression is given in the question ; i.e., 2m - n = 8.
We have to find the value of the 'n' .
What is algebra ?
Algebra is the branch that deals with various symbols and the arithmetic operations such as addition , subtraction , etc.
As per the question ;
The given expression is 2m - n = 8.
Let's solve it to get the value of n.
The value of n can be find out , if we bring n to the left side of equal sign and 8 to the right of equal sign.
So ,
2m - n = 8 can be written as ;
2m = 8 + n
or
n = 2m - 8
Thus , the required value of n is equal to n = 2m - 8.
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The Wagner Corporation has a $22 million bond obligation outstanding, which it is considering refunding. Though the bonds were initially issued at 12 percent, the interest rates on similar issues have declined to 10 percent. The bonds were originally issued for 20 years and have 16 years remaining. The new issue would be for 16 years. There is a 7 percent call premium on the old issue. The underwriting cost on the new $22 million issue is $680,000, and the underwriting cost on the old issue was $530,000. The company is in a 40 percent tax bracket, and it will allow an overlap period of one month ( 1/12 of the year). Treasury bills currently yield 5 percent. (Do not round intermediate calculations. Enter the answers in whole dollars, not in millions. Round the final answers to nearest whole dollar.) a. Calculate the present value of total outflows. Total outflows b. Calculate the present value of total inflows. Total inflows $ c. Calculate the net present value. Net present value $ d. Should the old issue be refunded with new debt? Yes No
The answer are: a. Total outflows: $2,007,901, b. Total inflows: $827,080, c. Net present value: $824,179, d. Should the old issue be refunded with new debt? Yes
To determine whether the old bond issue should be refunded with new debt, we need to calculate the present value of total outflows, the present value of total inflows, and the net present value (NPV). Let's calculate each of these values step by step: Calculate the present value of total outflows. The total outflows consist of the call premium, underwriting cost on the old issue, and underwriting cost on the new issue. Since these costs are one-time payments, we can calculate their present value using the formula: PV = Cash Flow / (1 + r)^t, where PV is the present value, Cash Flow is the cash payment, r is the discount rate, and t is the time period.
Call premium on the old issue: PV_call = (7% of $22 million) / (1 + 0.1)^16, Underwriting cost on the old issue: PV_underwriting_old = $530,000 / (1 + 0.1)^16, Underwriting cost on the new issue: PV_underwriting_new = $680,000 / (1 + 0.1)^16. Total present value of outflows: PV_outflows = PV_call + PV_underwriting_old + PV_underwriting_new. Calculate the present value of total inflows. The total inflows consist of the interest savings and the tax savings resulting from the interest expense deduction. Since these cash flows occur annually, we can calculate their present value using the formula: PV = CF * [1 - (1 + r)^(-t)] / r, where CF is the cash flow, r is the discount rate, and t is the time period.
Interest savings: CF_interest = (12% - 10%) * $22 million, Tax savings: CF_tax = (40% * interest expense * tax rate) * [1 - (1 + r)^(-t)] / r. Total present value of inflows: PV_inflows = CF_interest + CF_tax. Calculate the net present value (NPV). NPV = PV_inflows - PV_outflows Determine whether the old issue should be refunded with new debt. If NPV is positive, it indicates that the present value of inflows exceeds the present value of outflows, meaning the company would benefit from refunding the old issue with new debt. If NPV is negative, it suggests that the company should not proceed with the refunding.
Now let's calculate these values: PV_call = (0.07 * $22,000,000) / (1 + 0.1)^16, PV_underwriting_old = $530,000 / (1 + 0.1)^16, PV_underwriting_new = $680,000 / (1 + 0.1)^16, PV_outflows = PV_call + PV_underwriting_old + PV_underwriting_new. CF_interest = (0.12 - 0.1) * $22,000,000, CF_tax = (0.4 * interest expense * 0.4) * [1 - (1 + 0.1)^(-16)] / 0.1, PV_inflows = CF_interest + CF_tax. NPV = PV_inflows - PV_outflows. If NPV is positive, the old issue should be refunded with new debt. If NPV is negative, it should not.
Performing the calculations (rounded to the nearest whole dollar): PV_call ≈ $1,708,085, PV_underwriting_old ≈ $130,892, PV_underwriting_new ≈ $168,924, PV_outflows ≈ $2,007,901,
CF_interest ≈ $440,000, CF_tax ≈ $387,080, PV_inflows ≈ $827,080. NPV ≈ $824,179. Since NPV is positive ($824,179), the net present value suggests that the old bond issue should be refunded with new debt.
Therefore, the answers are:
a. Total outflows: $2,007,901
b. Total inflows: $827,080
c. Net present value: $824,179
d. Should the old issue be refunded with new debt? Yes
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if i run 5280 feet in 5.00 minutes, what is my speed in miles per hour (to the appropriate number of significant figures)?
When I run 5280 feet in 5.00 minutes my speed is 12 miles per hour
What is velocity?It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).
The formula and procedure we will use to solve this exercise is:
v = x /t
Where:
x = distancet = timev = velocityInformation about the problem:
x = 5280 feett = 5 minutesv (miles/hour) = ?Applying the velocity formula, we get:
v = x /t
v = 5280 feet / 5 minutes
v = 1056 feet/ minutes
By converting the unit from feet to miles and from hours to minutes, we have:
1056 feet/ minutes * (1 miles / 5280 feet) * (60 minutes / 1 hour) = 12 miles/hour
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What is the equation X+y>3 in the slope interceptform (ie y=mx+b)?
A company’s profit, P(t) , in thousands of dollars, from 2000 to 2015 , is represented by the graph provided, where t=0 corresponds to the year 2000 . In what year interval was the profit of the company decreasing? Select your answers from the drop-down lists.
Answer:
Company B follows linear profit function while company A follows exponential profit function. Company B has more profit after 4 months while company A has more monthly profit after year-end. Option A is correct.
Given information:
Company A earns monthly profit based on the profit function, where t is the number of months.
Company B earns profit based on a linear function. The data in the below table shows the profit after each month:
Month 3 4 7
Profit 5 10 25
Now, the profit earned by company A after 4 months will be,
Also, the profit earned after a year will be,
Now, the linear function which represents the profit of company B is,
So, the profit earned after 4 months and 1 year (by company B) will be,
Now, comparing the profit of companies A and B:
After 4 months, company B has more monthly profit which is 10 hundred dollars or 1 thousand dollars. After the year-end, company A earns more monthly profit as it is 102.04 hundred dollars. This is because company A follows an exponential function to predict the profit while company B uses a linear profit function.
Therefore, option A should be correct.
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Company B follows linear profit function while company A follows - 1
The profit of the company was decreasing in the year interval 2010 to 2015.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given that,
A company’s profit, P(t) , in thousands of dollars, from 2000 to 2015 , is represented by the graph provided.
Here t=0 corresponds to the year 2000.
The X axis has been marked from 0 to 15, which corresponds to the year from 2000 to 2015.
It is clear that from 0 to 10, the profit is increasing. So from 2000 to 2010 the graph is increasing.
From 10 to 15, the graph is decreasing or the profit is decreasing and finally the profit is 0.
So the graph is decreasing in the interval 2010 to 2015.
Hence the interval where the graph is decreasing is 2010 to 2015.
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You may need to use the appropriate appendix table to answer this question. Suppose that the mean daily viewing time of television is 8.35 hours. Use a normal probability distribution with a standard deviation of 2.5 hours to answer the following questions about daily television viewing per household (a) What is the probability that a household views television between 5 and 11 hours a day? (Round your answer to four decimal places.) Incorrect: Your answer is incorrect. (b) How many hours of television viewing must a household have in order to be in the top 3% of all television viewing households? (Round your answer to two decimal places.) Incorrect: Your answer is incorrect. hrs (c) What is the probability that a household views television more than 3 hours a day? (Round your answer to four decimal places.)
The probability of household views between 5 and 11 hours will be 0.7653. Number of hours needed in order to be in top 3% will be 13.03 hours. Probability of views more than 3 hours will be 0.9838.
a) The probability of television views between than 5 and 11 hours.
P( 5≤X≤11) = P[ (5-μ)/σ ≤ (X-μ)/σ ≤ (11-μ)/σ]
= P [ (5-8.35)/2.5 ≤ z ≤ (11-8.35)/2.5)
= P ( -1.34 ≤ z ≤ 1.06)
= P ( z≤ 1.06) - P(z ≤ -1.34)
Substituting values from the z-table
P ( 5≤X≤11) = 0.85543 - 0.09012 = 0.76531
Probability that household views between 5 and 11 hours is 0.7653.
b) Hours needed to be in top 3% of all households.
P( X> h) = 0.03
P[ (X-μ)/σ > (h-μ)/σ] = 0.03
P ( z >h-8.35/2.5) = 0.03
P ( z ≤ h-8.35/2.5) = 0.97
From the table
(h - 8.35)/ 2.5 = 1.87
h = (1.87× 2.5) + 8.35
= 13.025 = 13.03 hours
So if the viewing time is more than 13.03, the household will be in the top 3%.
c) Probability of viewing more than 3 hours
P(X> 3) = P[ (X-μ)/σ > (3-μ)/σ]
= P( z < -2.14) = 0.9838
So probability the household will have views more than 3 hours will be 0.9838.
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Is this graph a function or not a function *?
A graph is a function if it passes the vertical line test, meaning that no vertical line intersects the graph at more than one point. If the graph does not pass this test, it is not a function.
The graph is a function if each input value (x-coordinate) corresponds to exactly one output value (y-coordinate). To determine if a graph is a function, we can apply the vertical line test. If a vertical line intersects the graph at more than one point, then the graph is not a function.
Let's consider an example. If we draw a vertical line that intersects the graph at multiple points, then it is not a function. However, if the vertical line intersects the graph at most one point for any given x-coordinate, then it is a function.
In a function, each x-coordinate has a unique y-coordinate. For instance, the point (1, 3) represents that when x=1, y=3. If there is another point on the graph that has the same x-coordinate but a different y-coordinate, then the graph is not a function.
In summary, a graph is a function if it passes the vertical line test, meaning that no vertical line intersects the graph at more than one point. If the graph does not pass this test, it is not a function.
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Without computing, decide whether the value of each expression is much smaller than
1, close to 1, or much greater than 1.
a. 100 - 1000
b. 504 + 50-
C. 4.7-5.2
d. 2= 7335
Jan and jamie are starting a nonprofit store. they plan to sell handmade scarves and jewelry. which basic economic question do they still need to answer?\
Answer:
How much will the handmade scarves and jewellery cost?
How much are they planning to spend on operating costs for their business every year?
Step-by-step explanation:
At which root does the graph of f x x 4 6 * x 7 5 cross the x axis?
The roots of the graph of f(x) = (x+4)⁶(x+7)⁵ crosses the x axis at x = -7 .
The Roots of the Graph of the equation is defined as the point at which the curve crosses the x axis , and also the roots satisfy the equation .
the function is given as : f(x) = (x+4)⁶(x+7)⁵ ;
let the function be denoted by y = f(x) .
If the graph crosses x - axis , then the value of y is 0 .
that means ; (x+4)⁶(x+7)⁵ = 0 ;
which implies that , (x + 4) = 0 (x + 7) = 0 ,
simplifying ,
we get ; x = -4 and x = -7 .
we know that if the power of function is even the function bounces from the x axis ,
and if the power of function is odd the function crosses the x axis ,
Therefore , the graph crosses the x axis at x = -7 .
The given question is incomplete , the complete question is
At which root does the graph of f(x) = (x+4)⁶(x+7)⁵ cross the x axis ?
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Question 6 of 13
Incorrect
2 tries left. Please try again.
Which transformations are displayed in the graph of g(x) = (x-1)-3 as it relates to the graph of the parent function? Select all that apply.
The translations to the parent function f(x) = x² to generate the function g(x) = (x - 1)² - 3 are given as follows:
Shift right one unit.Shift down three units.What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The changes to the parent function in this problem are given as follows:
g(x) = f(x - 1) = translation right one unit.g(x) = f(x - 1) - 3 = translation down three units.More can be learned about translations at brainly.com/question/28174785
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2. Simplify 5/7 + 126 - 107 56 . (1 point)
0 514 -712
( 57 -76
() 712 - 514
76 - 57
Answer:
-5/7+7/6
Step-by-step explanation:
plz i need help. I know this is probably easy but I need help with this!
go to desmos graphing calculator
hit the "+" button in the top left
click table
put in the x and y values
after u do that click under the blue line surrounding number 1 and type in
y1~mx1+b
after u do that look in the number 2 box there should be the word parameters
under that there will be what m and b equals
I need help with this algebra problem
Answer:
C
Step-by-step explanation:
A round brass bar is 5m long and 14mm in radius, calculate its volume in cm^3
Answer:
3080 cm³
Step-by-step explanation:
length = 5m = 500 cm
radius = 14 mm = 1.4 cm
The equation to find the volume is: 3.14 (r)^2 h
= 3.14 x (1.4)^2 x 500
= 3080 cm³
So, the answer is 3080 cm³
If f'(c) < 0 then f(x) is decreasing and the graph of f(x) is concave down when x = c. True False Question 4 (1 point). A local extreme point of a polynomial function f(x) can only occur when f'(x) = 0. True False Question 5 (1 point) If f'(x) > 0 when x < c and f'(x) < 0 when x > c, then f(x) has a maximum value when x = C. True False
Question 3: True
Question 4: False
Question 5: True
If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c.
This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.
Question 3: If f'(c) < 0 then f(x) is decreasing and the graph of f(x) is concave down when x = c.
True
When the derivative of a function, f'(x), is negative at a point c, it indicates that the function is decreasing at that point. Additionally, if the second derivative, f''(x), exists and is negative at x = c, it implies that the graph of f(x) is concave down at that point.
Question 4: A local extreme point of a polynomial function f(x) can only occur when f'(x) = 0.
False
A local extreme point of a polynomial function can occur when f'(x) = 0, but it is not the only condition. A local extreme point can also occur when f'(x) does not exist (such as at a sharp corner or cusp) or when f'(x) is undefined. Therefore, f'(x) being equal to zero is not the sole requirement for a local extreme point to exist.
Question 5: If f'(x) > 0 when x < c and f'(x) < 0 when x > c, then f(x) has a maximum value when x = c.
True
If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c. This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.
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What determines where the graph will cross the x-axis?.
The graph will cross the x-axis if the multiplicity of the real root is odd.
What is polynomial?
In arithmetic, a polynomial is an expression consisting of indeterminates and coefficients, that involves solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
Main body:
For polynomials, the graph will cross the x-axis if the multiplicity of the real root is odd, and just touch the x-axis if the multiplicity of the real root is even. (The multiplicity of the root is the number of times it occurs as a root)
(a) y=(x+1)^2(x-2) The graph crosses at x=2 (multiplicity 1) but touches at x=-1 (mulitplicity 2)
(b) y=(x-4)^3(x-1)^2 The graph crosses at x=4 (multiplicity 3) but touches at x=1 (m=2)
(c) y=(x-3)^2(x+4)^4 The graph touches at x=3 and x=-4 as the multiplicities are both even.
The graphs: (a) black, (b) red, (c) green
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(08.07 HC)
An expression is shown below:
f(x) = 2x² - x - 10
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the
coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers
obtained in Part A and Part B to draw the graph. (5 points)
(10 points)
Answer:
\(\textsf{A)} \quad x=-2, \:\:x=\dfrac{5}{2}\)
\(\textsf{B)} \quad \left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)\)
C) See attachment.
Step-by-step explanation:
Given function:
\(f(x)=2x^2-x-10\)
Part ATo factor a quadratic in the form \(ax^2+bx+c\) , find two numbers that multiply to \(ac\) and sum to \(b\) :
\(\implies ac=2 \cdot -10=-20\)
\(\implies b=-1\)
Therefore, the two numbers are -5 and 4.
Rewrite \(b\) as the sum of these two numbers:
\(\implies f(x)=2x^2-5x+4x-10\)
Factor the first two terms and the last two terms separately:
\(\implies f(x)=x(2x-5)+2(2x-5)\)
Factor out the common term (2x - 5):
\(\implies f(x)=(x+2)(2x-5)\)
The x-intercepts are when the curve crosses the x-axis, so when y = 0:
\(\implies (x+2)(2x-5)=0\)
Therefore:
\(\implies (x+2)=0 \implies x=-2\)
\(\implies (2x-5)=0 \implies x=\dfrac{5}{2}\)
So the x-intercepts are:
\(x=-2, \:\:x=\dfrac{5}{2}\)
Part B
The x-value of the vertex is:
\(\implies x=\dfrac{-b}{2a}\)
Therefore, the x-value of the vertex of the given function is:
\(\implies x=\dfrac{-(-1)}{2(2)}=\dfrac{1}{4}\)
To find the y-value of the vertex, substitute the found value of x into the function:
\(\implies f\left(\dfrac{1}{4}\right)=2\left(\dfrac{1}{4}\right)^2-\left(\dfrac{1}{4}\right)-10=-\dfrac{81}{8}\)
Therefore, the vertex of the function is:
\(\left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)\)
Part CPlot the x-intercepts found in Part A.
Plot the vertex found in Part B.
As the leading coefficient of the function is positive, the parabola will open upwards. This is confirmed as the vertex is a minimum point.
The axis of symmetry is the x-value of the vertex. Draw a line at x = ¹/₄ and use this to ensure the drawing of the parabola is symmetrical.
Draw a upwards opening parabola that has a minimum point at the vertex and that passes through the x-intercepts (see attachment).
Find the interquartile range for a data set having the five-number summary: 7.8, 17.1, 23.6, 31.1, 36.9
Answer:
Interquartile Range: 21.549999999999997 = 21.55
Step-by-step explanation:
Please help
2.01, 2.1, 2.001
Answer:
2.01
Step-by-step explanation:
i got the question easily i hope it helps