One of the five quadratics below has a repeated root. (The other four have distinct roots.) What is the repeated root?
\begin{align*}
&-x^2 + 18x + 81 \\
I need his answer fast!!
&3x^2 - 6x + 9 \\
&8x^2 - 32x + 32 \\
&25x^2 - 30x - 9 \\
&x^2 - 14x + 196
\end{align*}
Answers
Answer:
(c) 8x^2 -32x +32, repeated root is x=2.
Step-by-step explanation:
A quadratic with repeated roots will be a multiple of a perfect square trinomial. The form of it will be ...
a(x -b)² = ax² -2abx +ab² = a(x² -2bx +b²)
Dividing by the leading coefficient will leave a monic quadratic whose constant is a (positive) perfect square, and whose linear term has a coefficient that is double the root of the constant.
__
-x^2 + 18x + 81Dividing by the leading coefficient gives ...
x^2 -18x -81 . . . . . a negative constant
__
3x^2 - 6x + 9Dividing by the leading coefficient gives ...
x^2 -2x +3 . . . . . . constant is not a perfect square
__
8x^2 - 32x + 32Dividing by the leading coefficient gives ...
x^2 -4x +4 = (x -2)^2 . . . . . has a repeated root of x=2
__
25x^2 - 30x - 9Dividing by the leading coefficient gives ...
x^2 -1.2x -0.36 . . . . . . a negative constant
__
x^2 - 14x + 196The x-coefficient is not 2 times the root of the constant.
14 = √196 ≠ 2√196
Related Questions
An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.
P(high-quality oil)=0.45
p(medium-quality oil)=0.15
p(no oil)=0.40
a. What is the probability of finding oil (to 2 decimals)?
b. After 200 feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil identified by the test are given below.
p(soil | high-quality oil)=0.15
p(soil | medium-quality oil)= 0.75
P(soil | no oil)=0.15
Given the soil found in the test, use Bayes' theorem to compute the following revised probabilities (to 4 decimals).
What is the new probability of finding oil (to 4 decimals)?
According to the revised probabilities, what is the quality of oil that is most likely to be found?
Answers
The total probability of filling oil is 0.60
a. P(oil) = 1 - P(no oil) = 1 - 0.40 = 0.60
b.P(soil ∩ high quality oil) = (0.45)(0.15) = 0.067
P(soil ∩ medium quality oil) = (0.15)(0.15) = 0.022
P(soil ∩ no oil) = (0.40)(0.40) = 0.16
New probabilities,
P(high quality oil | soil) = 0.067 / (0.067+0.022+0.16) = 0.067/0.269 = 0.269
P(medium quality oil | soil) = 0.022 / (0.067+0.022+0.16) = 0.022/0.269 = 0.088
P(no oil | soil) = 0.09 / (0.067+0.022+0.16) = 0.09/0.269 = 0.361
New probability of finding oil,
P(oil|soil)= 1 - P(no oil | soil) = 1 - 0.361 = 0.639
So the company has a lower chance of finding oil given that they find the particular soil.
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at a store 40% of all the refrigerators are silver. there are 50 silver refrigerants at the store . how many refrigerants are at the store?
Answers
Answer:
125
Step-by-step explanation:
50 refrigerators are 40% of all the refrigerators in the store.
5 refrigerators are 4% of refrigerators in the store
125 refrigerators are 100% of refrigerators in the store
therefore there are 125 refrigerators at the store.
What measurement would be use to describe how much water a pot can hold
Answers
Answer:
I'd say liters or gallons! Hope this helps!! (:
Answer:
Hi Uh I Forgot but i know my teacher showed me
Step-by-step explanation:
In the square pyramid shown, points and are midpoints of the edges of one face. If the figure is sliced through points and and through the base, which best describes the shape of the resulting cross section? The picture shows a triangular prism. M and N are the points on the prism. A. rectangle B. trapezoid C. quadrilateral D. parallelogram
Answers
Based on the given information, we have a square pyramid with points M and N being the midpoints of the edges of one face. and forms a parallelogram. Option D
Since the base of the pyramid is a square, the cross section will consist of a square shape. Additionally, since the slice is made through the midpoints of the edges of the face, the resulting cross section will have parallel sides.
Considering these characteristics, we can conclude that the shape of the resulting cross section is a parallelogram. A parallelogram is a quadrilateral with opposite sides parallel. In this case, the opposite sides of the square cross section will be parallel, as the slice passes through the midpoints of the edges.
Therefore, the correct answer is D. parallelogram.
It's important to note that a triangular prism is not the correct answer because a triangular prism is a three-dimensional figure with two triangular bases and three rectangular faces. The cross section resulting from the given slice will not have the characteristics of a triangular prism. Option D.
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There are 24 hours in a day, At 7 a.m. how many hours are left in the day?
Answers
Answer:
17
Step-by-step explanation:
Answer:17
Step-by-step explanation:
24-7=17
What is cos(tan^-1(-2/3))=
Answers
cos(tan^(-1)(-2/3)) simplifies to 3√13 / 13.
To evaluate the expression cos(tan^(-1)(-2/3)), we can use the trigonometric identity:
cos(tan^(-1)(x)) = 1 / √(1 + x^2)
In this case, x is -2/3. Substituting the value into the identity:
cos(tan^(-1)(-2/3)) = 1 / √(1 + (-2/3)^2)
Now, let's calculate the value:
cos(tan^(-1)(-2/3)) = 1 / √(1 + 4/9)
= 1 / √(13/9)
= 1 / (√13/3)
= 3 / √13
= 3√13 / 13
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Someone please help asap!
Answers
Answer:
in order u put them in, 8 top, 12 bottem, 32 top, 30 bottem
eight hundred twenty nine and six tenths as a decimal
Answers
Any other questions ask :)
A salesperson made a sale worth $17,000.00 and his commission is 2% on the sale. How much commission will he get?
Answers
hi brainly user! ૮₍ ˃ ⤙ ˂ ₎ა
⊱┈────────────────────────┈⊰
\(\large \bold {ANSWER}\)
2% of $17,000 are 340.\(\large \bold {SOLUTION}\)
Well, as we are going to work with percentage, there are two ways to do this. Percentage is a ratio of a number by 100. Since it's a ratio with the number 100, I can divide the percentage value I want to know by 100 and then I multiply it by the value where I want to know the percentage. Another way would be using rule of 3, I'll do it both ways, it will generate the same result.
\(\begin{gathered}\frac{2}{100}=0,02\\ 0,02*17.000=340\end{gathered}\)
Now let's do it with the rule of 3.
\(\dfrac{17.000}{x} \large \text{$\searrow\!\!\!\!\!\!\nearrow\!\!\!\!\!$}\normalsize= \dfrac{100}{2}\)
\(\begin{gathered}100x=17.000*2\\100x=34.000\\x=\frac{34.000}{100}=340\end{gathered}\)
Hence, the 2% of $17,000 are 340.
2 points
6. The drawing below shows a ladder leaning against a building. Part B:
Suppose an identical ladder was put against a building that was 18 feet
high and the ladder reached the top of the building. How far away would
the bottom of the ladder be from the base of the building? Use
mathematics to justify your reasoning.
SUS
20 ft
CREARE
10 ft
Answers
Answer:
4.9 feet
Step-by-step explanation:
First, we need to determine the height of the building using the following:
\(L^2 = H^2 + B^2\)
Where
H = Height of the building
L = Length of the first ladder = 20ft
B = Distance from the base of the building = 10ft
So, we have:
\(20^2 = H^2 + 10^2\)
\(400 = H^2 + 100\)
\(H^2 = 400 - 100\)
\(H^2 = 300\)
\(H = \sqrt{300\)
Next, is to determine the distance of the new ladder from the base of the building (B) using Pythagoras theorem using:
\(L_2^2 = H^2 + B_2^2\)
Where
\(L_2 = 18\) --- Length of the second ladder
\(H = \sqrt{300\) ----- Height of the building
So, we have:
\(18^2 = \sqrt{300}^2 + B_2^2\)
\(324 = 300 + B_2^2\)
\(B^2_2 = 324 - 300\)
\(B^2_2 = 24\)
Solving for B2, we have:
\(B_2 = \sqrt{24\)
\(B_2 = 4.9\)
Is this correct. Please let me know thank you
Answers
Answer:
Yes it is correct, the amount of flour is 1.5 times larger than eggs needed
Step-by-step explanation:
what is 3 squared ÷ 48 - 6
Answers
Answer:
\( {3}^{2} \div 48 - 6 \\ 9 \div 48 - 6 \\ = - 5.8125\)
Cristina keeps track of how many items are sold each week so she can figure
out how much she needs to bake for the next week. Pretzel rolls are her best-
selling bread. Here are the weekly sales of pretzel rolls in March.
Week
Number of Pretzel Rolls Sold
March 1-7
287
March 8-14 304
March 15-21271
March 22-28 316
Rounding to the nearest 10, what is the best estimate of the number of
pretzel rolls sold in March? Enter your answer in the box.
Answers
The estimate of the number of pretzel rolls sold in March will be 890.
How to illustrate the information?The following can be deduced based on the information that given:
March 8-14. 304
March 15-21 271
March 22-28. 316
Therefore, it should be noted that 304 to the nearest ten is 300.
271 to the nearest ten will be 270
316 to the nearest ten will be 320
Therefore, the total number sold in March will be:
= 300 + 270 + 320
= 890
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Malcolm has $50 gift card to a local car wash and order is the ultimate car wash each visit is $8.95
Answers
The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.
The correct answer choice is option B.
How much cheaper is the car washes Malcolm orders than the car washes Martha's order?Malcolm's gift card = $50.
Cost Malcolm's car wash per visit = $7
Martha's gift card = $180
Cost Martha's car wash per visit = Difference between gift card balance of first and second visit
= $180 - $160
= $20
How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7
= $13
Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13
The complete question is attached in the diagram.
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What is the measure of FOL in the following circle?
Answer choices
a = 110
b = 120
c = 60
d = 55
Answers
9514 1404 393
Answer:
(d) ∠FOL = 55°
Step-by-step explanation:
The measure of inscribed angle FOL is half the measure of the intercepted arc FL. The same is true of angle FGL. Inscribed angles that intercept the same arc have the same measure, so ...
∠FOL = 55°
Let x be the number of bratwursts and y thenumber of hamburgers. Which system ofinequalities represents this situation?You are serving bratwurst andhamburgers at your annual picnic. Youwant at least three bratwursts orhamburgers for each of your 30 guests.Bratwursts cost $1.25 each andhamburgers $0.75 each. Your budget is$120.Click on the correct answer.x + y s 301.25x + 0.75y s 120x + y s 301.25x + 0.75y = 120x + y 2 901.25x + 0.75y2 120x + y 2 901.25x + 0.75y = 120
Answers
The first condition is that there must be at least 3 hamburgers or 3 bratwursts for each of the 30 participants. This means that the sum of hamburgers and bratwurst must be at least 90. This can be expressed as:
\(x+y\ge90\)The second condition says that the maximum amount to pay is $120, this means that the total cost of hamburgers and bratwurst must be less than $120. This can be expressed as:
\(1.25x+0.75y\le120\)Therefore, the system that represents the situation is:
\(\begin{gathered} x+y\ge90 \\ 1.25x+0.75y\le120 \end{gathered}\)Sand for use on icy roads is stored in a conical pile 14.2 m high and with a base diameter of 34.4 m calculate the volume of the pile if one sander can take 6.9 m of sand, how many sanders can be filled from the pile
Answers
Answer:
1. The volume of the pile is 4,399.7719 m^3
2. The number of sanders to be filled from a pile is 638
Step-by-step explanation:
Here, we firstly would calculate the volume of the pile
Mathematically, that will be;
V = 1/3 * pi * r^2 * h
from the question, h = 14.2
Mathematically, r = d/2
r = 34.4/2 = 17.2 m
So the volume will be:
V = 1/3 * 3.142 * 17.2^2 * 14.2
V = 4,399.7719 m^3
To find the number of sanders to be filled,
we simply divide the volume obtained by the volume a sander can take
That will be;
4,399.7719/6.9
= 637.6 which is 638
Ralph is an electrician. He charges an initial fee of $37.50, plus $25 per hour. If Ralph earned $187.50 on a job, how long did the job take?
Answers
Answer:
6
Step-by-step explanation:
25x+37.5=187.5; x as hours
IAn Individual Retirement Account (IRA) has $22,000 in it, and the owner decides not to add any more money to the account other than interest earned at 8%compounded daily. How much will be in the account 29 years from now when the owner reaches retirement age?There will be in the account.(Round to the nearest cent. Use a 365 day year.)
Answers
Given:
\(\begin{gathered} \text{Principal (P)= \$22000} \\ \text{Rate of interest= 8\%} \\ n=29\text{ years} \end{gathered}\)\(\begin{gathered} \text{Amount in the account after 9 years=}P(1+\frac{r}{365})^{365\times n} \\ =22000(1+\frac{8}{100\times365})^{365\times29} \\ =22000(1+0.0002)^{10585} \\ =22000(8.3044) \\ =\text{ \$182696}.80 \end{gathered}\)Amount in the account after 29 years is $182696.80
Using the graph below, determine the employee's hourly wage.
Answers
By using the graph, the employee's hourly wages is calculated as $10.6
Graph:
Basically, a graph is a collection of points, called vertices, and lines between those points, called edges.
Given,
Here we have the graph with straight line.
And we need to determine the employee's hourly wage.
While we looking into the graph we have identified that the x axis refers the number of hours the employ is working and the y axis refers the money earned by them.
In order to find the wages for one hour, we need to select one point from the graph.
Here we have take the point (5,53)
The first point refers the number of hours that is 5.
And the second one refers the wages for 5 hours that is 53.
So, the one hour wages is calculated as,
=> 53/5
=> 10.6
Therefore, the employee's hourly wage is $10.6.
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An artist is making a scale model of a statue. On the model 2 inches represent 1 foot on the actual state witch graph best represents this relationship
Answers
Answer:
C
Step-by-step explanation:
i have the same question i found it on quizzes
In certain deep parts of oceans, the pressure of sea water,P, in pounds per square foot, at a depth of d feet below the surface, is given by the following equation P=14+ 4d/9
If a scientific team uses special equipment to measure the pressure under water and find it to be 306 pounds per square foot, at what depth is the team making their measurements?
Answers
It is important to note that this equation assumes a constant density of seawater, which is not always the case in the deep ocean. In addition, the pressure at a given depth can vary depending on factors such as temperature and salinity. This equation should be used with caution and in conjunction with other measurements and data analysis techniques.
The given equation for pressure in pounds per square foot at a depth of d feet is P = 14 + 4d/9. We are given that the pressure measured by the scientific team is 306 pounds per square foot. To find the depth at which this pressure is measured, we need to solve the equation for d.
Substituting P = 306 in the equation, we get:
306 = 14 + 4d/9
Multiplying both sides by 9, we get:
2754 = 126 + 4d
Subtracting 126 from both sides, we get:
2628 = 4d
Dividing both sides by 4, we get:
d = 657 feet
The scientific team is measuring the pressure at a depth of 657 feet below the surface of the ocean.
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Isaac wants to play miniature golf. Go Golf charges $2.50 for ball and club rental and $4.25 per game. Golf Games charges $3.25 for ball and club rental and $8.50 for two games. For how many games would the cost be the same? Write and solve an equation to determine the number of games for which the cost would be the same.
NEED FAST RESPONSE EQUATION AND SOLUTION
Answers
The equation is 6.75x = 5.875y
The price will be the same for 47 Go Golf games and 54 Golf Games
Go Golf charges for the ball and club rental = $2.50
Go Golf charges per game = $4.25
Total charges for Go Golf for one game = $6.75
Golf Games charges for the ball and club rental = $3.25
Golf Games charges for two games = $8.50
Total charges for Golf Game for two games = $11.75
Per game charges = $11.75/2 = $5.875
Let x be the number of games for Go Golf and y be the number of games for Golf Games
Formulating the equation we get:
6.75x = 5.875y
Converting into fractions we get:
675/100x = 5875/1000y
27/4x = 47/8y
After cross multiplication
x/y = 57/48
x = 57 and y = 48
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Solve for x and graph the answer on a number line
2
Answers
The solution to the system of inequalities in interval notation is [-2, 1].
How to solve the system of inequalities?Based on the information provided in the image below, we have the following system of inequalities;
-12 < 3x - 6
-3 ≥ 3x - 6
By adding 6 to both sides of the equation (inequality), we have;
-12 < 3x - 6
-12 + 6 < 3x - 6 + 6
-6 < 3x
-2 < x
x > -2 (flip)
-3 ≥ 3x - 6
-3 + 6 ≥ 3x - 6 + 6
3 ≥ 3x
1 ≥ x
x ≤ 1
Therefore, the solution to the system of inequalities is given by:
-2 < x ≤ 1
In interval notation, we have [-2, 1].
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
ixl prediction! URGENT, PLEASE.
Answers
The expected number of not blue is 54
How to evaluate the expected number of valueFrom the question, we have the following parameters that can be used in our computation:
Spinner
Using the above as a guide, we have the following probability
P(Not Blue) = Not Blue/Total
So, we have
P(Not Blue) = 6/9
When it is spun 81 times, the expected number of times is
Times = 6/9 * 81
Evaluate
Times = 54
Hence. the number of times is 54
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10 oranges cost $7.50. What is the unit rate?
Answers
Answer:
$0.75
Step-by-step explanation:
You need to do 7.5 divided by 10 becuse you need to find the cost per one
9. It is estimated that a certain model rocket will reach an altitude of 200 ft. A photographer is setting up a camera 50 ft away from the launch pad. At what angle should he set the tripod to get a picture at the maximum altitude?
Answers
The photographer should set the tripod at an angle of approximately 75.96 degrees to get a picture of the rocket at its maximum altitude.
We have,
We can use trigonometry to solve this problem.
C
/ \
/ \
/θ \
/ \
/ \
A-------------B
50 ft
In this diagram, A represents the launch pad, B represents the maximum altitude of the rocket, C represents the position of the photographer, and θ represents the angle at which the tripod should be set.
We want to find θ.
First, we can find the height of the triangle ABC using the Pythagorean theorem:
AB² = AC² + BC²
200² = AC² + 50²
AC² = 200² - 50²
AC = √(200² - 50²)
AC = 190.526 ft
Next, we can use the tangent function to find θ:
tan(θ) = opposite/adjacent = AB/BC = 200/50 = 4
Taking the arctangent of both sides, we get:
θ = \(tan^{-1}(4)\)
θ = 75.96 degrees
Therefore,
The photographer should set the tripod at an angle of approximately 75.96 degrees to get a picture of the rocket at its maximum altitude.
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It takes 20 days using 12 machines to produce a batch of pens.
due to a fault only 3 machines were used for the first 8 days, all 12 machines were used from day 9 onwards.
how many days in total to produce the batch of pens
Answers
It would take a total of 20 days to produce the batch of pens.
Let's calculate the work done by the 3 machines for the first 8 days:
Work done by 3 machines in 8 days = (3/12) * 8 = 2 days' worth of work
The remaining work that needs to be done by all 12 machines is:
Remaining work = 1 - (2/20) = 0.9
Now, we can use the work formula to find the total number of days needed to complete the remaining work with 12 machines:
Total work = 0.9
Work done by 12 machines in one day = 12/20 = 0.6
Total number of days needed = 0.9/0.6 = 1.5
Therefore, the total number of days needed to produce the batch of pens is:
8 (days with 3 machines) + 1.5 (days with 12 machines) = 9.5 days
However, we also need to add the 10.5 days it would take for all 12 machines to complete the batch from the beginning:
10.5 + 9.5 = 20 days
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Megan's gas fireplace uses propane. The liquid propane is stored in a spherical tank. The tank has a radius of 1 foot, 6 inches. The tank contains 7,741,000 Btu of energy when it is filled to 80% of its total volume. How much energy does 1 gallon of liquid propane in the tank contain?
Hint: There are exactly 231 cubic inches in 1 gallon.
If necessary, round your answer to the nearest hundred.
Answers
Answer:
First, we need to find the total volume of the spherical tank. We can use the formula for the volume of a sphere:
V = (4/3)πr³
We are given that the radius is 1 foot, 6 inches, which is 1.5 feet.
V = (4/3)π(1.5)³
V ≈ 14.14 ft³
To find the volume of propane in the tank when it is filled to 80%, we multiply the total volume by 0.8:
V_propane = 0.8 × 14.14
V_propane ≈ 11.31 ft³
We are also given that the tank contains 7,741,000 Btu of energy. To find the energy per gallon, we need to know how many gallons are in the tank. One gallon is equal to 231 cubic inches.
1 ft³ = 12³ = 1,728 in³
11.31 ft³ = 11.31 × 1,728 in³
11.31 ft³ ≈ 19,536 in³
19,536 in³ ÷ 231 in³/gal ≈ 84.5 gallons
So, the tank contains approximately 84.5 gallons of propane. To find the energy per gallon, we divide the total energy by the number of gallons:
7,741,000 Btu ÷ 84.5 gal ≈ 91,580 Btu/gal
Therefore, 1 gallon of liquid propane in the tank contains approximately 91,580 Btu of energy.
ou are going to estimate how long a person holds down a button on their calculator by randomly selecting people and asking them to do something on your calculator (which has a special timer to record how long the enter button is pressed). You practiced on the people at work and found a standard deviation of about 0.59 seconds. You want to get a 95% confidence interval that is only 0.12 in width. How many people do you need to have in your study
Answers
Answer:
Привет! Кто-нибудь читал Криспину крест ведущего? Если да, то может ли кто-нибудь дать мне представление о том, как он изменился в этой истории! Спасибо за ваше время!
Step-by-step explanation: