Answers
The complete table of values is
x 1 1.5 2 3 3.5 4 5
y 1.33 -1.58 -2.17 -1.33 -0.43 0.71 3.57
The graph is attachedThe x values are {1.28, 4.76}The x values are undefined The x values are {1.15, 3.69}Completing the table of valuesThe equation of the function is given as
y = x²/3 + 6/x² - 5
To complete the table of values, we set x = 1, 1.5, 4 and 5
So, we have
y = 1²/3 + 6/1² - 5 = 1.33
y = 1.5²/3 + 6/(1.5²) - 5 = -1.58
y = 4²/3 + 6/(4²) - 5 = 0.71
y = 5²/3 + 6/(5²) - 5 = 3.57
Solving the x values from the graphThe x and the y intervals are given as
0 ≤ x ≤ 5 and -5 ≤ y ≤ 4
See attachment for the graph and the labelled points
Estimating x²/3 + 6/x² - x - 3 = 0
We have
y = x²/3 + 6/x² - 5
Set y = x - 2
x²/3 + 6/x² - 5 = x - 2
So, we have
x²/3 + 6/x² - x - 3 = 0
This means that y = x - 2
From the graph, we have x = {1.28, 4.76}
Estimating x²/3 + 6/x² - x = 0
We have
y = x²/3 + 6/x² - 5
Set y = x - 5
x²/3 + 6/x² - 5 = x - 5
So, we have
x²/3 + 6/x² - x = 0
This means that y = x - 5
From the graph, we have x = undefined
It has no solution because the line does not intersect with the curve
Estimating x²/3 + 6/x² - 5 = 0
We have
y = x²/3 + 6/x² - 5
This means that y = 0
From the graph, we have x = {1.15, 3.69}
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Related Questions
Casey is going to wear a gray sportscoat and is trying to decide what tie he should wear to work. In his closet, he has 22 ties, 13 of which he feels go well with the sportscoat. If Casey selects one tie at random, determine the probability and the odds of the tie going well or not going well with the sportscoat.
The probability the tie goes well with the jacket is?
The probability the tie will not go well with the jacket is?
The odds against the tie going well with the jacket is?
(Simplify your answer. Type an integer or a fraction.)
The odds in favor of the tie going well with the jacket is?
(Simplify your answer. Type a ratio using a colon.)
Answers
P(going well) = number of ties that go well / total number of ties
P(going well) = 13/22
P(going well) = 0.59 or 59%
The probability that the tie will not go well with the jacket is:
P(not going well) = 1 - P(going well)
P(not going well) = 1 - 0.59
P(not going well) = 0.41 or 41%
The odds against the tie going well with the jacket is:
Odds against = number of ties that do not go well / number of ties that go well
Odds against = (22-13) / 13
Odds against = 9/13
The odds in favor of the tie going well with the jacket is:
Odds in favor = number of ties that go well / number of ties that do not go well
Odds in favor = 13 / (22-13)
Odds in favor = 13/9 or 1.44:1
(If this doesn’t seem right to you comment!)
Malachi ask students in his class, “ how long does it take you to get to school?“ The histogram shows the data
Answers
Answer: C Distribution is symmetric
Step-by-step explanation:
An office manager orders one calculator or one calendar for each of the office's 80 employees. Each calculator costs $12, and each calendar costs $10. The entire order totaled $900.
Part A: Write the system of equations that models this scenario.
Part B: Use substitution method or elimination method to determine the number of calculators and calendars ordered. Show all necessary steps.
Answers
The system of equations is.
x + y = 80
12x + 10y = 900
And the solutions are y = 30 and x = 50
How to write and solve the system of equations?Let's define the two variables:
x = number of calculators.
y = number of calendars.
With the given information we can write two equations, then the system will be:
x + y = 80
12x + 10y = 900
Now let's solve it.
We can isolate x on the first equation to get:
x = 80 - y
Replace that in the other equation to get:
12*(80 - y) + 10y = 900
-2y = 900 - 960
-2y = -60
y = -60/-2 = 30
Then x = 50
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11. The spread of a drop of food dye throughout a glass of milk is called__________
Answers
Answer: Diffusion
Step-by-step explanation:
Write an expression for the sequence of operations described below.
Subtract three from the product of seven and eight
Type x if you want to use a multiplication sign. Type / if you want to use a division sign. Do not simplify any part of the expression.
Answers
An expression for the sequence of operations described "Subtract three from the product of seven and eight." is (7 × 8) - 3.
How to evaluate and solve the given expression?In order to evaluate and solve this expression, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right. Lastly, the mathematical operations of addition or subtraction would be performed from left to right.
Based on the information provided, we have the following mathematical expression:
Expression: (7 × 8) - 3
56 - 3
53
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What is the length of the segment indicated by the question mark
Answers
Check the picture below.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{6.6+x}\\ a=\stackrel{adjacent}{6.6}\\ o=\stackrel{opposite}{8.8} \end{cases} \\\\\\ (6.6+x)^2= (6.6)^2 + (8.8)^2\implies (6.6+x)^2=121\implies (6.6+x)^2=11^2 \\\\\\ 6.6+x=11\implies x=4.4[/tex]
Ivan created a scale drawing of the Grand Canyon using a scale of 1 inch for every 25
miles. His drawing is 11 inches long. What is the actual length of the canyon?
Answers
Answer:
275 miles
Step-by-step explanation:
A 2-quart carton of pineapple juice costs $8.08. What is the price per cup?
$
Answers
Answer:
$1.01
Step-by-step explanation:
We Know
A 2-quart carton of pineapple juice costs $8.08
1 quart = 4 cups
2 quarts = 8 cups
So, 8 cups of pineapple juice cost $8.08.
What is the price per cup?
We Take
8.08 / 8 = $1.01
So, the price per cup is $1.01
Graph the equation shown below by transforming the given graph of the parent function. 2^3x
Answers
The graph of the exponential function [tex]y = 2^{3x}[/tex] is given as follows:
How to define an exponential function?An exponential function has the definition presented as follows:
[tex]y = ab^x[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The function in this problem is given as follows:
[tex]y = 2^{3x}[/tex]
Hence the parameter values are:
a = 1, hence when x = 0, y = 1.b = 2, hence when x increases by 1/3, y is multiplied by 2 -> increases by 1/3 due to the horizontal compression with the multiplication by 3 in the domain.More can be learned about exponential functions at brainly.com/question/2456547
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A cake is in the shape of a rectangular prism. It has a length of 13 inches, a width of 8 inches, and a height
of 5 inches. A baker will put frosting on all sides of the cake except for the bottom. What is the total surface area
of the cake that will be covered in frosting?
Show Your Work
O 114 in.
0 334 in.
O 449 in?
O 573 in?
Answers
If the cake is in the shape of a rectangular prism, the total surface area of the cake that will be covered in frosting is 314 sq. inches.
To find the total surface area of the cake that will be covered in frosting, we need to calculate the area of all sides except the bottom. A rectangular prism has 6 sides, and we will be considering 5 of them.
Surface area of top: length × width = 13 × 8 = 104 sq. inches
Surface area of front: length × height = 13 × 5 = 65 sq. inches
Surface area of back: length × height = 13 × 5 = 65 sq. inches
Surface area of left side: width × height = 8 × 5 = 40 sq. inches
Surface area of right side: width × height = 8 × 5 = 40 sq. inches
Now, we will sum the areas of all these sides:
104 + 65 + 65 + 40 + 40 = 314 sq. inches
So, the total surface area of the cake that will be covered in frosting is 314 sq. inches. None of the provided options match this answer, so it is important to double-check the question for any discrepancies.
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A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 19. 1 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 18. 1, 21. 1, 22. 1, 23. 1, 21. 1, 27. 1, and 27. 1 pounds. If α = 0. 200, what is the critical value? The population standard deviation is unknown
Answers
Since the population standard deviation is unknown, we use a t-distribution to find the critical value. The degrees of freedom for the t-distribution is n-1, where n is the sample size. In this case, n = 7, so the degrees of freedom is 7-1 = 6. The critical value for a t-distribution with 6 degrees of freedom and a significance level of α = 0.200 (two-tailed) can be found using a t-table or calculator. The critical value is approximately ±1.94.
Victoria has $200 of her birthday gift money saved at home, and the amount is modeled by the function h(x) = 200. She reads about a bank that has savings accounts that accrue interest according to the function s(x) = (1. 05)x−1. Explain how Victoria can combine the two functions to model the total amount of money she will have in her bank account as interest accrues after she deposits her $200. Justify your reasoning.
WILL GIVE BRANLIEST
Answers
The reasoning behind this is that the initial amount (h(x)) is multiplied by the interest growth factor (s(x)) to calculate the total amount with interest over time.
To model the total amount of money Victoria will have in her bank account as interest accrues after depositing her $200, you can combine the two functions h(x) and s(x). The given functions are h(x) = 200 and s(x) = (1.05)^x−1.
First, note that s(x) represents the growth factor of the interest, which is 5% (1.05) compounded annually. To find the total amount after x years, you need to multiply the initial amount by the growth factor raised to the power of x.
So, the combined function T(x) can be written as T(x) = h(x) * s(x).
Substitute the given functions into the combined function:
T(x) = (200) * ((1.05)^x−1)
This function, T(x), models the total amount of money Victoria will have in her bank account after x years with interest accrued on her $200 deposit. The reasoning behind this is that the initial amount (h(x)) is multiplied by the interest growth factor (s(x)) to calculate the total amount with interest over time.
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Greg, Harry and Ian share their electricity bill in the ratio 2:4:5.
how much dies each of them pay when their electricity bill are 1) 110$ 2) 165$ 3) 352$
pls answer quickly
Answers
The amount each of them pays when their electricity bill is $110, $165, and $352 respectively, in the ratio 2:4:5, are:
1) $20, $40, $50
2) $30, $60, $75
3) $64, $128, $160
1. How much do they pay for a $110 electricity bill?To find out how much each of them pays, we'll use the given ratio of 2:4:5 and divide the total bill among them accordingly.
Total bill: $110
The total ratio is 2+4+5=11.
Greg's share: (2/11) * $110 = $20
Harry's share: (4/11) * $110 = $40
Ian's share: (5/11) * $110 = $50
Therefore, Greg pays $20, Harry pays $40, and Ian pays $50.
2. How much do they pay for a $165 electricity bill?Total bill: $165
The total ratio is still 2+4+5=11.
Greg's share: (2/11) * $165 = $30
Harry's share: (4/11) * $165 = $60
Ian's share: (5/11) * $165 = $75
Therefore, Greg pays $30, Harry pays $60, and Ian pays $75.
3. How much do they pay for a $352 electricity bill?Total bill: $352
The total ratio remains the same: 2+4+5=11.
Greg's share: (2/11) * $352 = $64
Harry's share: (4/11) * $352 = $128
Ian's share: (5/11) * $352 = $160
Therefore, Greg pays $64, Harry pays $128, and Ian pays $160.
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What is the missing value of G if G is two and one-half times smaller than 19. 02 cm? A. 7. 608 cm B. 7. 808 cm C. 8. 608 cm D. 9. 51 cm
Answers
Therefore, the missing value of G is 7.608 cm, which is option A.
What is the missing value of G?If G is two and one-half times smaller than 19.02 cm, we can find the value of G by multiplying 19.02 cm by 2/5, since two and one-half is equal to five halves, or 2/5 when expressed as a fraction.
G = (2/5) x 19.02 cm
Simplifying this expression:
G = 7.608 cm
Therefore, the missing value of G is 7.608 cm, which is option A.
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In the year 2001, a company made $7. 2 million in profit. For each consecutive year after that, their profit increased by 11%. How much would the company's profit be in the year 2005, to the nearest tenth of a million dollars?
Answers
The company's profit in the year 2005 would be approximately $10.5 million.
Let's calculate the company's profit for the year 2005 using the given information.
Initial profit in 2001: $7.2 million
Annual profit increase: 11%
We need to find the profit for 2005, which is 4 years after 2001.
Step 1: Identify the formula for compound interest, which can be applied to profit increase:
Future Profit = Initial Profit * (1 + Profit Increase Rate)^Number of Years
Step 2: Plug in the values:
Future Profit [tex]= $7.2 million * (1.11)^4[/tex]
Step 3: Calculate the result:
Future Profit [tex]= $7.2 million * (1.11)^4[/tex]
Future Profit = $7.2 million [tex]* 1.4641[/tex]
Future Profit = $10.54152 million
Step 4: Round the result to the nearest tenth of a million dollars:
Future Profit ≈ $10.5 million
So, the company's profit in the year 2005 would be approximately $10.5 million.
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John owns 10 shirts and needs to select 5 to wear to school next week. How many ways can he choose the shirts? (hint: combinations)
50 ways
B 252 ways
500 ways
D 792 ways
Answers
There are 252 different combinations of shirts, the correct option is B.
In how many ways he can choose the shirts?Remember that if you have N elements, and you want to select K of these, the number of combinations is given by:
[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]
Here we have 10 shirts and we want to select 5 of these, so the number of combinations is given by:
[tex]C(10, 5) = \frac{10!}{(10 - 5)!*5!} \\\\C(10, 5) = \frac{10*9*8*7*6}{5*4*3*2} = 252[/tex]
There are 252 different combinations, so the correct option is B.
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Edro, Lena, Harriet, and Yermin each plot a point to approximate StartRoot 0. 50 EndRoot.
Pedro A number line going from 0 to 0. 9 in increments of 0. 1. A point is between 0. 2 and 0. 3.
Lena A number line going from 0 to 0. 9 in increments of 0. 1. A point is between 0. 4 and 0. 5.
Harriet A number line going from 0 to 0. 9 in increments of 0. 1. A point is at 0. 5.
Yermin A number line going from 0 to 0. 9 in increments of 0. 1. A point is just to the right of 0. 7.
Whose point is the best approximation of StartRoot 0. 50 EndRoot?
Pedro
Lena
Harriet
Yermin
Answers
Yermin's point is the best approximation of the square root of 0.50.
To know whose point is the best approximation of the square root of 0.50 on a number line. We have the points plotted by Pedro, Lena, Harriet, and Yermin.
Step 1: Calculate the square root of 0.50.
[tex]\sqrt{0.50} = 0.707[/tex]
Step 2: Compare the plotted points to the calculated square root value.
Pedro: Between 0.2 and 0.3
Lena: Between 0.4 and 0.5
Harriet: At 0.5
Yermin: Just to the right of 0.7
Step 3: Determine the closest approximation.
Yermin's point (just to the right of 0.7) is the closest to the calculated value of 0.707.
Your answer: Yermin's point is the best approximation of the square root of 0.50.
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A cuboid is placed on top of a cube, as shown in the diagram, to form a solid.
2 cm
3 cm
The cube has edges of length 7 cm.
The cuboid has dimensions 2 cm by 3 cm by 5 cm.
Work out the total surface area of the solid.
Optional working
Ansv
cm²
+
5 cm
7 cm
Answers
Answer: 344cm²
Step-by-step explanation:
7x7=49
49x5=245
3x2=6
49-6=43
245+43=288
5x2=10 10x2=20
5x3=15 15x2=30
288+30+20+6=344
Lily's age is 2 years and 4 months.
Hugo's age is 1 year and 8 months.
Write Lily's age in months as a fraction of Hugo's age in months.
Give your answer in it's simplest form.
Answers
Answer:
7/5
Step-by-step explanation:
Lily's age in months: 2×12+4=28mo
Hugo's age in months=12+8=20
Lily's age over Hugo's age: 28/20
Simplify:
28/20=14/10=7/5
Write a function to model the volume of a rectangular prism if the length is 26cm and the sum of the width and height is 32cm. what is the maximum possible volume of the prism?
Answers
To model the volume of a rectangular prism with length 26cm and width w and height h such that the sum of the width and height is 32cm, we can use the following function:
V(w, h) = 26wh
subject to the constraint:
w + h = 32
We can solve for one of the variables in the constraint equation and substitute it into the volume equation, giving us:
w + h = 32 => h = 32 - w
V(w) = 26w(32 - w) = 832w - 26w^2
To find the maximum possible volume, we can take the derivative of this function with respect to w and set it equal to zero
dv/dw= 832 - 52w = 0
Solving for w, we get:
w = 16
Substituting this value back into the constraint equation, we get:
h = 32 - w = 16
Therefore, the maximum possible volume of the prism is:
V(16, 16) = 26(16)(16) = 6656 cubic cm
So the function to model the volume of the rectangular prism is V(w) = 832w - 26w^2, and the maximum possible volume is 6656 cubic cm when the width and height are both 16cm.
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Question 1 2 pts A researcher is interested in determining whether sugar consumption increases memory. She recruits 100 participants and randomly assigns them to one of two groups, sugar vs. No sugar. She then measures their word recall: Sugar group: M = 4. 5, SD = 1. 8, n = 55 • No sugar group: M = 2. 6, SD =. 68, n = 45 1. Is this an example of a quasi-experimental design? (yes or no) 2. What is the dependent variable? 3. What is the independent variable?
Answers
1. This is not an example of a quasi-experimental design because the researcher randomly assigned participants to the two groups. In a quasi-experimental design, the researcher does not have full control over the assignment of participants to groups.
2. The dependent variable in this study is the word recall. It is the variable that the researcher is interested in measuring and is expected to be affected by the independent variable.
3. The independent variable in this study is sugar consumption. It is the variable that the researcher manipulated by assigning participants to one of two groups, sugar vs. no sugar.
The purpose of manipulating the independent variable is to examine its effect on the dependent variable, word recall.
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What is the mean of the data set fifth grade jump distance
Answers
The mean of the fifth-grade jump distance data set.
How to calculate the mean of fifth-grade jump distances?To determine the mean of the data set for fifth-grade jump distances, we need the actual data values. Without the specific data set, it is not possible to calculate the mean.
The mean is the sum of all the values in a data set divided by the number of values. Therefore, we would need the individual jump distances for each fifth-grade student to calculate the mean accurately.
Once we have the complete data set, we can add up all the distances and divide by the total number of students to find the mean. Without the specific data, we cannot provide a numerical answer for the mean of the fifth-grade jump distance.
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The vertices of a quadrilateral in the coordinate plane are known. How can the perimeter of the figure be found?
O Use the distance formula to find the length of each side, and then add the lengths.
Use the slope formula to find the slope of each of side, and then determine if the opposite sides are parallel.
O Use the slope formula to find the slope of each of side, and then determine if the consecutive sides are perpendicul
O Use the distance formula to find the length of the sides, and then multiply two of the side lengths.
Answers
Answer:..
Step-by-step explanation:Use the distance formula to find the length of each side and then add the lengths.
Use the slope formula to find the slope of each of side, and then determine if the opposite sides are parallel.
Use the slope formula to find the slope of each of side, and then determine if the consecutive sides are perpendicular.
Use the distance formula to find the length of the sides, and then multiply two of the side lengths.
stressing outtt I need help its due in a few minuets
Answers
64e^2/5e = 64e^(2-1)/5 = 64e/5
Similarly, we can simplify the expression 3e/8e by dividing the numerator by the denominator and canceling out e:
3e/8e = 3/8
Now we can multiply the two simplified expressions to get the final answer:
(64e/5) * (3/8) = (64*3*e)/(5*8) = 24.96e
Therefore, the simplified expression is 24.96e.
(4,7);y=3x+6
Write an equation passing through the point and parallel to the given line.
Answers
The Equation of the line which is parallel to the line "y = 3x + 6", and also passes through (4,7) is "y = 3x - 5".
In order to find an equation of a line which passes through point (4,7) and is parallel to line "y = 3x + 6", we use the fact that parallel lines have the same slope.
The given line ""y = 3x + 6" has a slope of 3,
So, the "parallel-line" we want to find must also have a slope of 3.
Now, by using the "point-slope" form of the equation of a line, which is : y - y₁ = m(x - x₁),
where m is slope and (x₁, y₁) is a point on the line,
So, we substitute "m = 3" and (x₁, y₁) = (4,7) to get:
⇒ y - 7 = 3(x - 4),
⇒ y - 7 = 3x - 12,
⇒ y = 3x - 5
Therefore, the equation of the required line is y = 3x - 5.
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Josie had 12 beads on her necklace. Then she added b more beads. Write an expression that shows how many beads are on the necklace in all. please write a expression like b-12 or b+?
Answers
The expression that shows how many beads are on the necklace in all is:
b + 12.
What is expression?An expression in mathematics is a combination of numbers, variables, and/or operators that represents a mathematical relationship or quantity. It may contain constants, variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Expressions are often used to describe or represent real-world situations, and can be simplified, evaluated, or manipulated using algebraic rules and properties.
In the given question,
To write an expression that shows how many beads are on Josie's necklace in all after adding b more beads:
Start with the initial number of beads on the necklace, which is 12.
To this, add the number of beads Josie added, which is b.
Combine the two terms to form the final expression: 12 + b.
Therefore, the expression that shows how many beads are on Josie's necklace in all after adding b more beads is 12 + b.
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Determine the location and value of the absolute extreme values off on the given interval, if they exist 8x? f(x) - +22x2 - 24x on (-7,11 G What in are the absolute maximum maxime off on the given interval? Select the correct choice below and, if necessary, to in the answer bowen to completo your choice A. Tho absolute maximum/maxima isarea- (Use a comma to separato answers as needed. Type exact answers, using radicals as rended) B. There is no absolute maximum off on the given interval What are the absolute minimum/minima off on the given interval? Select the correct choice below and. If necessary, in the wwer boxes to complete your in O A The absolute minimum/minima is/are at (Use a comma to separate answers as needed. Type exact answers, using radical as needed) B. There is no absolute minimum off on the given interval
Answers
The absolute maximum will be at (11, 10373).
The absolute minimum is at (-1.963, -25.294).
What in are the absolute maximum maxime off on the given interval?
To determine the location and value of the absolute extreme values of the function f(x) = 8x³+ 22x² - 24x on the interval (-7, 11), follow these steps:
Find the critical points by taking the derivative of the function and setting it equal to zero:
f'(x) = 24x² + 44x - 24
Solve for x:
Factor the equation: 4(6x² + 11x - 6) = 0
Using the quadratic formula, x = (-11 ± √(121 + 144))/12
x ≈ -1.963, 0.630
Check the endpoints and the critical points to find the absolute maximum and minimum:
f(-7) ≈ 461
f(-1.963) ≈ -25.294
f(0.630) ≈ -16.102
f(11) ≈ 10373
Compare the values:
The absolute maximum is at x = 11, with a value of 10373.
The absolute minimum is at x ≈ -1.963, with a value of ≈ -25.294.
Answer:
The absolute maximum is at (11, 10373).
The absolute minimum is at (-1.963, -25.294).
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The number of revolutions
made by a tire traveling over a fixed distance
varies inversely with the radius of the tire. a
12-inch radius tire makes 100 revolutions to
travel a certain distance. how many
revolutions would a 16-inch radius tire require
a
to travel the same distance?
define variables
identify constant of variation
write an equation and show work (please can someone help with this stuff, my deadline is in 4 days)
Answers
A 16-inch radius tire would require 75 revolutions to travel the same distance as a 12-inch radius tire that made 100 revolutions.
Let's start by defining some variables. Let "r" represent the radius of the tire and "n" represent the number of revolutions it makes over a fixed distance. We are given that the number of revolutions is inversely proportional to the radius of the tire. This means that as the radius increases, the number of revolutions decreases, and vice versa. We can express this relationship mathematically as follows:
n = k/r
Here, "k" is the constant of variation, which remains the same for any given tire traveling over the same distance. To solve the problem, we need to find the value of "k" first. We know that a 12-inch radius tire makes 100 revolutions to travel a certain distance. Substituting these values into the equation, we get:
100 = k/12
Solving for "k," we get k = 1200. Now we can use this value to find the number of revolutions required by a 16-inch radius tire to travel the same distance:
n = 1200/16 = 75
Therefore, a 16-inch radius tire would require 75 revolutions to travel the same distance as a 12-inch radius tire that made 100 revolutions.
In summary, we defined the variables, identified the constant of variation, wrote the equation (n=k/r), found the value of the constant by using the given information, and used it to solve the problem by finding the number of revolutions required by a tire with a different radius.
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The sum of the roots of a quadratic is 1 and the product of the roots is -35/4.
a. find the quadratic.
b. find the roots
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If the sum of the roots of a quadratic equation is 1 and the product of the roots is -35/4 and the equation is [tex]4x^2-4x-35=0[/tex] and the roots are 3.5 and -2.5
If the quadratic equation is [tex]ax^2+bx+c=0[/tex]
The sum of the roots = [tex]-\frac{b}{a}[/tex]
The product of the roots = [tex]\frac{c}{a}[/tex]
Sum of the roots = 1 = [tex]-\frac{b}{a}[/tex]
Product of the roots = [tex]-\frac{35}{4}[/tex] = [tex]\frac{c}{a}[/tex]
If we assume a as 1, then the equation comes out to be:
[tex]x^2-x-\frac{35}{4} =0[/tex]
Multiply the equation by 4 to get a simplified equation:
[tex]4x^2-4x-35=0[/tex]
[tex]4x^2[/tex] - 14x + 10x - 35 = 0
2x (2x - 7) + 5 (2x - 7) = 0
(2x - 7)(2x + 5) = 0
x = 3.5 and -2.5
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Mohal is a waiter at a restaurant. Each day he works, Mohal will make a guaranteed wage of $25, however the additional amount that Mohal earns from tips depends on the number of tables he waits on that day. From past experience, Mohal noticed that he will get about $15 in tips for each table he waits on. How much would Mohal expect to earn in a day on which he waits on 16 tables? How much would Mohal expect to make in a day when waiting on
�
t tables?
Answers
Answer:
If Mohal waits on 16 tables, he can expect to earn $25 wages + ($15 tips x 16 tables) = $265 in a day.
If Mohal waits on 1 table, he can expect to earn $25 wages + ($15 tips x 1 table) = $40 in a day.
