Find the zeros of each function.
h(x) = 6x² + x − 1
Answers
The zeros of the function h(x) = 6x² + x − 1 are x = 1/3 and x = -1/2.
What are the zeros of the given function?Given the function in the question:
h(x) = 6x² + x − 1
To determine the zeros of the function, we need to solve for x when h(x) equals zero.
Plug in h(x) = 0
0 = 6x² + x − 1
6x² + x − 1 = 0
We can use the quadratic formula to solve for x:
x = [-b ± √(b² - 4ac)] / 2a
where a, b, and c are the coefficients of the quadratic equation.
In the function, a = 6, b = 1, and c = -1.
Plug these values into the above formula
x = [-1 ± √(1² - 4(6)(-1))] / 2(6)
x = [-1 ± √(1 + 24)] / 12
x = [-1 ± √(25)] / 12
x = [-1 ± 5] / 12
Hence, the zeros of the function are:
x = (-1 + 5) / 12 = 4/12 = 1/3
and
x = (-1 - 5) / 12 = -6/12 = -1/2
Learn more about quadratic equations here: https://brainly.com/question/4038687
#SPJ1
Related Questions
Given the simultaneous equations 2x - y = 1 x² + 4ky + 5k = 0 where k is a non-zero constant show that x² + 8kx + k = 0. Given that x² + 8kx + k = 0 has equal roots.
Answers
a) \(x^{2}\)+8kx +k=0, b) k=1/16
Here we have equation is 2x -y = 1 , \(x^{2}\)+4ky+5k=0
To show that \(x^{2}\) +8kx +k =0, we have two equation 2x-y=1 and \(x^{2}\) +4ky + 5k=0
So from the equation 2x - y = 1 we can find y
Therefore y = 2x-1
Now we will put the value of y in the equation \(x^{2}\) + 4ky + 5k =0
a) We have \(x^{2}\) + 4k(2x-1) +5k=0
\(x^{2}\) + 8kx -4k + 5k=0
\(x^{2}\) +8kx +k=0
b) Now we have to find the value of k, and as from the question it is given that \(x^{2}\) + 8kx +k =0 have equal roots
Therefore we get \(b^{2}\) + 4ac = 0 is the condition of the linear equation in two equal roots.
So from this we have b= 8k, a = -1, c= k
\((8k)^{2}\) - 4× 1×k =0
64\(k^{2}\) -4k =0
4k(16k -1) =0
16k-1=0
k = 1/16
As k is a non-zero constant therefore we have not taken k=0. Therefore the value of k is 1/16.
To know more about the linear equation refer to the link given below:
https://brainly.com/question/2030026
#SPJ1
The complete question is:
Given the simultaneous equations 2x - y = 1 x² + 4ky + 5k = 0 where k is a non-zero constant a)show that x² + 8kx + k = 0. Given that x² + 8kx + k = 0 has equal roots., b) find the value of k.
Whats The Answer Marking Brainliest, Please explain your answer:D..............................Please HELP!!!!
Answers
Answer:
A
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
Someone please help me asapp
Answers
1. 3*7= 21
2. 4*a= 4a
3. m*m= m^2
What is the equation of this circle in general form?
Responses
x2+y2−2x−6y−26=0
x squared plus y squared minus 2 x minus 6 y minus 26 equals 0
x2+y2+2x+6y−26=0
x squared plus y squared plus 2 x plus 6 y minus 26 equals 0
x² + y² + 2x + 6y + 4 = 0
x, ² +, y, ² + 2, x, + 6, y, + 4 = 0
x2+y2−2x−6y+4=0
x squared plus y squared minus 2 x minus 6 y plus 4 equals 0
Answers
The equation of this circle in general form is: (x - 1)^2 + (y - 3)^2 = 36
How to find the equation of the circle in general formTo find the equation of a circle in general form, we need to complete the square for both x and y terms.
x^2 + y^2 - 2x - 6y - 26 = 0
First, we will complete the square for x terms:
x^2 - 2x + y^2 - 6y - 26 = 0
(x - 1)^2 - 1 + y^2 - 6y - 26 = 0
(x - 1)^2 + y^2 = 27
Now, we will complete the square for y terms:
(x - 1)^2 + (y - 3)^2 = 36
Therefore, the equation of this circle in general form is: (x - 1)^2 + (y - 3)^2 = 36
Learn more about equation at https://brainly.com/question/14107099
#SPJ1
Answer:
x2+y2−2x−6y−26=0
Step-by-step explanation:
Just took the test.
oscar is thinking of a number he says my number is between 200 and 220 it is divisible by 6 the sum of all the digits is 3 how to sole such a question
Answers
The answer is: Oscar's number is 210.
What is Sum?
In mathematics, the sum is the result of adding two or more numbers or quantities together. It is a basic arithmetic operation and is often denoted by the symbol "+".
To solve this question, we need to find a number that satisfies the following conditions:
The number is between 200 and 220.
The number is divisible by 6.
The sum of all the digits is 3.
Let's start by finding all the multiples of 6 that are between 200 and 220:
204 = 2 + 0 + 4 = 6
210 = 2 + 1 + 0 = 3
216 = 2 + 1 + 6 = 9
Out of these numbers, only 210 has a sum of digits that is equal to 3. Therefore, the number that Oscar is thinking of is 210.
To check that 210 is between 200 and 220, we can see that it is indeed between the two numbers:
200 < 210 < 220
And to check that 210 is divisible by 6, we can see that:
210 ÷ 6 = 35
Therefore, the answer is: Oscar's number is 210.
Learn more about Sum
https://brainly.com/question/24205483
#SPJ1
Given points B(−12,2), T(−8,10), A(−7,12), F(−6,10), and G(−2,2), which of the following proves that △BAG~△TAF?
Answers
Answer:
By the Distance Formula, BA=5√5, TA=√5, A F=√5, and AG=5√5. Since, BA/TA = AG/A F = 5/1, and ∠A≅∠A by the Reflexive Property, △BAG∼△TAF by SAS ∼.
Hope this helps!
Step-by-step explanation:
An expert witness for a paternity lawsuit testifies that the length of a pregnancy is normally distributed with a mean of 280 days and a standard deviation of 13 days. An alleged father was out of the country from 240 to 306 days before the birth of the child, so the pregnancy would have been less than 240 days or more than 306 days long if he was the father. The birth was uncomplicated, and the child needed no medical intervention. What is the probability that he was NOT the father? What is the probability that he could be the father? Calculate the z-scores first, and then use those to calculate the probability.
Answers
The probability that the alleged father was not the father is: 0.024, or 2.4% and The probability that the alleged father could be the father is: 0.953, or 95.3%.
To calculate the probability that the alleged father was not the father, we first need to calculate the z-score for a pregnancy length of 240 days and for a pregnancy length of 306 days. The z-score formula is:
z = (x - mu) / sigmawhere x is the pregnancy length, mu is the mean pregnancy length, and sigma is the standard deviation of pregnancy length.
For a pregnancy length of 240 days, the z-score is:
z = (240 - 280) / 13 = -3.08For a pregnancy length of 306 days, the z-score is:
z = (306 - 280) / 13 = 2.00To calculate the probability that the alleged father was not the father, we need to find the area under the normal distribution curve to the left of the z-score for a pregnancy length of 240 days and to the right of the z-score for a pregnancy length of 306 days, and then add these probabilities together. Using a standard normal distribution table or calculator, we find that the probability to the left of z = -3.08 is approximately 0.001, and the probability to the right of z = 2.00 is approximately 0.023. Therefore, the probability that the alleged father was not the father is:
0.001 + 0.023 = 0.024, or 2.4%To calculate the probability that the alleged father could be the father, we need to find the area under the normal distribution curve between the z-scores for a pregnancy length of 240 days and a pregnancy length of 306 days. Using a standard normal distribution table or calculator, we find that the probability between z = -3.08 and z = 2.00 is approximately 0.953. Therefore, the probability that the alleged father could be the father is:
0.953, or 95.3%Learn more about probability
https://brainly.com/question/24756209
#SPJ4
A spinner used in a board game is divided into 12 equally sized sectors. Seven of these sectors indicate that the player should move his token forward on the board, three of these sectors indicate that the player should move his token backward, and the remaining sectors award the player bonus points but do not move his token on the board.
The total area of the sectors that do not allow the player to move his token is 45. 1 inches squared.
What is the radius of the spinner?
Enter your answer, rounded to the nearest tenth of an inch, in the box
Answers
Answer:
The radius is 9.28 inches.
Step-by-step explanation:
Since there are 7 Move Ahead zones, and 3 Go Backwards zones on the spinner, there must be 2 other zones (the Freeze! +Bonus pts)
2 out of 12 zones are Freeze! +Bonus pts. That is 1/6 of the spinner. They said the area of the the Freeze!+Bonus pts is 45.1 inches squared.
45.1 × 6
= 270.6
The entire spinner has the area 270.6
The area of a circle is:
A = pi•r^2
We are looking for r. Thats the radius they asked for in the question.
270.6 = pi•r^2
pi is a number, I'm using the pi button on the calculator bc it is most exact.
270.6 = pi•r^2
Divide both sides by pi.
86.134655 = r^2
square root both sides.
9.28 = r
The radius is 9.28 inches.
What is the midpoint of the horizontal line segment graphed below?10(-6,3)(10,3)10A. (2,6)В. (4, 6)ОООC. (2, 3)D. (4, 3)
Answers
Therefore,
(-6, 3)(10, 3)
\(\begin{gathered} (x_m,y_m)=(\frac{-6+10}{2},\frac{3+3}{2}) \\ (x_m,y_m)=(\frac{4}{2},\frac{6}{2}) \\ (x_m,y_m)=(2,3) \end{gathered}\)
A housepainter mixed 4 gal of red paint with every 3 gal of blue paint in order to make a purple paint. Which
ratio of gallons of red paint to gallons of blue paint will make the same shade of purple paint?
28: 15
15:20
28:21
12:3
Answers
Reason:
The purple paint has 4 parts red and 3 parts blue.
The ratio of red to blue is 4:3
Multiply both parts of that ratio by 7 and we end up with 28:21
The two ratios 4:3 and 28:21 will produce the same shade of purple.
Express the function as the sum of a power series by first using partial fractions and find the interval of convergence f(x) = 10/ x^2-6x-16 please show work
Answers
The interval of convergence \(f(x) = 10/ x^2-6x-16\) is (-8, 2)
How to calculate the interval of convergenceBy expressing the function as a partial fraction, we have;
\(f(x) = 10/[(x - 8)(x + 2)]\)
The next thing is to write f(x) as a sum of two fractions when denominators are (x - 8) and (x + 2), we have;
\(f(x) = A/(x - 8) + B/(x + 2)\)
Multiplying both sides by (x - 8)(x + 2), we have;
10 = A(x + 2) + B(x - 8)
Given that x = 8, we have;
10 = A(10),
A = 1
Given that x = -2, we have;
10 = B(-10)
B = -1
Hence, we have \(f(x) = 1/(x - 8) - 1/(x + 2)\)
Power series for each term.
The power series for 1/(x - 8) is:
\(1/(x - 8) = -1/8 × 1/(1 - x/8) = -1/8 × ∑(x/8)^n, n=0\) to infinity
The power series for -1/(x + 2) is:
\(-1/(x + 2) = -1/2 × 1/(1 + x/2) = -1/2 × ∑(-x/2)^n\), n=0 to infinity
Thus, power series for f(x) is:
\(f(x) = 1/(x - 8) - 1/(x + 2) = -1/8 × ∑(x/8)^n - 1/2 ×∑(-x/2)^n\\= ∑[(-1/8)(x/8)^n + (-1/2)(-x/2)^n]\\= ∑[(-1/8)^{n+1} × x^n + (-1/2)^{n+1} × x^n]\)
We can therefore say that, the power series converges for values of x such that |x/8| < 1 and |-x/2| < 1, or equivalently, for -8 < x < 2.
Hence, the interval of convergence for the power series is (-8, 2).
Learn more on Power series on https://brainly.com/question/28158010
#SPJ4
Solve 2y - 3 = 4y +6.
I
y=
Answers
Answer:
-9/2
Step-by-step explanation:
Begin by subtracting 2y from both sides
(2y - 2y) - 3 = (4y - 2y) + 6
-3 = 2y + 6
Then, subtract 6 from both sides
(-3 - 6) = 2y + (6 - 6)
-9 = 2y
Finally, divide by 2 on each side
(-9/2) = (2y/2)
y = -9/2
the point at which the medians intersect in a triangle
Answers
Hope this helps
2) Currently: 37, 30, 24, 30, 37, 30, 55, 16
Mean
Median
Mode
Range
Answers
Answer: mean: 32.375 median: 30 mode: 30 range: 39
Step-by-step explanation:
Please help me with this!!!!
Answers
Answer:
Give me the written answer and I can solve it for you
Step-by-step explanation:
Type the missing number in this sequence: 50, 42, 34, 18, 10, 2 what comes after 34?
Answers
Answer:
The answer is 26 is after 34.
The pattern is x - 8 = y.
Step-by-step explanation:
Good luck! <3
If George's mom needs 3 kilograms of sliced cheese for a family party, how many
packages will she need to buy?
Answers
Answer:
1 package of cheese = 500 gram
6 packages
Step-by-step explanation:
H E L P- A G A I N (im dum ok? also no scam answers please.)
Answers
Answer:
a.Equation :y=40-2.5x
b.straight, decreases, the same
Step-by-step explanation:
please helpp . i need this asap it is due todayyy
Answers
Answer:
2 and X=2
Step-by-step explanation:
X-8=-6
Add 8 to both sides
X=-6+8
8-6=2
So X=2
Since X=2 the value of X is 2
Answer:
x=3 because if 8-6 is 2 then 2-8 is -6 and the equation would turn into 2-8
( 74 GUIDED Name:
PRACTICE Using Dot Plots to Make Inferences
1.
Joseph asks 10 of his friends how many baseball trading cards each friend has.
The data is shown in the dot plot. How many friends have more than five cards?
1
2
3
8
9
10
4 5 6 7
baseball trading cards
11
A. 3
C. 10
B. 5
Answers
Answer:
2 friends have more than 5 cards
Step-by-step explanation:
Incomplete question;
I will answer this question with the attached dot plot
The horizontal axis represents the friends, the vertical represents the number of baseball trading cards and the dots represent the frequency
So, we have:
\(Friend\ 1 = 2\)
\(Friend\ 2 = 3\)
\(Friend\ 3 = 7\)
\(Friend\ 4 = 4\)
\(Friend\ 5 = 2\)
\(Friend\ 6 = 6\)
\(Friend\ 7 = 2\)
\(Friend\ 8 = 5\)
\(Friend\ 9 = 1\)
\(Friend\ 0 = 0\)
The friends that has more than 5 are:
\(Friend\ 3 = 7\)
\(Friend\ 6 = 6\)
Hence, 2 friends have more than 5 cards
peter has probability 2/3 of winning each game. peter and paul bet $1 on each game. they each start with $400 and play until one of them goes broke. what is the probability that paul goes broke?
Answers
k = 0 to 399 By calculating this summation, we will obtain the probability that Paul goes broke. To find the probability that Paul goes broke when Peter has a 2/3 probability of winning each game, we can use the concept of probability, game, and bet in our explanation.
First, we need to determine the probability of Paul winning a game, which can be found by subtracting Peter's winning probability from 1:
Probability of Paul winning = 1 - Probability of Peter winning = 1 - 2/3 = 1/3
Now, let's denote the number of games required for one of them to go broke as 'n'. Since they each start with $400, the total number of games would be n = 400 + 400 = 800.
We will use the binomial probability formula to calculate the probability of Paul going broke after 'n' games:
P(Paul goes broke) = (n! / (k!(n-k)!)) * (p^k) * (q^(n-k))
Here, n is the total number of games (800), k is the number of games Paul wins, p is the probability of Paul winning (1/3), and q is the probability of Peter winning (2/3).
To find the probability of Paul going broke, we need to calculate the probability of Paul winning fewer than 400 games out of 800:
P(Paul goes broke) = Σ [P(Paul wins 'k' games)] for k = 0 to 399
By calculating this summation, we will obtain the probability that Paul goes broke.
Learn more about probability here:
brainly.com/question/27342429
#SPJ11
If 59 of a tank can be filled in 2 minutes, how many minutes will it take to fill the whole tank?.
Answers
When 5/9 of the tank is filled in 2 minutes, then it will take 3.6 minutes to fill the entire tank.
The definition of a fraction is a fraction multiplied by another fraction, integer, or a group of variables. Given that the 5/9 tank fills in 2 minutes. The duration of this period in seconds is 60×5= 120 seconds.
So the time taken to fill a 1/9 tank is calculated as follows,
Time taken = 120/5
=24 seconds
The time taken to fill the 9/9 tank (full) is calculated by multiplying 24 seconds and 9, we get,
24×9 = 216 seconds
= 3.6 minutes.
Therefore, the required answer is 3.6 minutes.
The complete question is -
If 5/9 of a tank can be filled in 2 minutes, how many minutes will it take to fill the whole tank?
To know more about the time taken:
https://brainly.com/question/29364966
#SPJ4
20% = 0.2 (true or false)
Answers
Answer:
TRUE
Step-by-step explanation:
20% is a 5th part of 100% which means that the same part of 1 is 0.2
Answer: its true
Step-by-step explanation: took the test
Help with geometry homework with rectangles. Quadrilateral ABCD is a rectangle. Which of the following must be true? Choose all that apply.
Answers
A and C are the two true statements.
According to Thomson Financial, last year the majority of companies reporting profits had beaten estimates. A sample of 162 companies showed that 98 beat estimates, 29 matched estimates, and 35 fell short. (a) What is the point estimate of the proportion that fell short of estimates
If required, round your answer to four decimal places. pshort = (b) Determine the margin of error and provide a 95% confidence interval for the proportion that beat estimates. If required, round your answer to four decimal places. ME = (c) How large a sample is needed if the desired margin of error is 0.05?
Answers
Use the remainder theorem to find the remainder when P(x) x^4 - 9x^3 - 5x^2 - 3x + 4 is divided by x + 5
Answers
Answer:
1644 I guess?
Step-by-step explanation:
I hope it helps
Frank has been driving at a constant speed for 3 hours, during which time he traveled 195 miles. Frank would like to know how long it will take him to complete the remaining 455 miles, assuming he maintains the same constant speed. Help Frank determine how long the remainder of the trip will take. Include a table or diagram to support your answer
Answers
Answer:
10.6 hours
Step-by-step explanation:
Suppose two utilites, People's Electric and Muricipal Energy, each produce 900 tons of pollution per year. The government has a goal of eliminating haf the pclution, and, in turn, provides 450 pollution permits to each utlity. A pollution permit is required to legally produce a ton of poliubon. However, the tao utities are allowed to trade permas. Suppose the cost of eliminating one ton of pollution for People's Electric is $400 and the cost of eliminating a ton of polution for Municipal Energy is $350. The total cost of each utility eliminating 450 tons of pollution is $ (Enter your response as a whole number)
Answers
The total cost of each utility eliminating 450 tons of pollution is $180,000.
To calculate the total cost for each utility to eliminate 450 tons of pollution, we need to multiply the cost per ton of pollution elimination by the number of tons each utility needs to eliminate.
For People's Electric, the cost of eliminating one ton of pollution is $400. So, to eliminate 450 tons, the total cost would be 450 tons * $400/ton = $180,000.
For Municipal Energy, the cost of eliminating one ton of pollution is $350. Again, to eliminate 450 tons, the total cost would be 450 tons * $350/ton = $157,500.
Therefore, the total cost for each utility to eliminate 450 tons of pollution is $180,000 for People's Electric and $157,500 for Municipal Energy.
The cost calculation is based on the given information that each utility is provided with 450 pollution permits by the government. These permits allow them to legally produce a ton of pollution. By setting a limit on the number of permits, the government aims to reduce pollution by half. The utilities have the option to trade permits with each other.
In this scenario, People's Electric has a higher cost of eliminating pollution per ton compared to Municipal Energy ($400 vs. $350). It means that People's Electric would find it more expensive to reduce pollution through internal measures like investing in cleaner technology or implementing environmental initiatives. On the other hand, Municipal Energy has a lower cost, indicating that they have relatively more cost-effective methods for pollution reduction.
Given these costs, it is more beneficial for People's Electric to purchase permits from Municipal Energy rather than eliminating the pollution themselves. By purchasing permits, People's Electric can meet the pollution reduction target at a lower cost. Conversely, Municipal Energy can generate additional revenue by selling their permits.
This permit trading mechanism allows for cost efficiency in achieving the government's pollution reduction goal. The total cost for each utility is determined by multiplying the cost per ton of pollution elimination with the number of tons they need to eliminate.
Learn more about the Pollution
brainly.com/question/23857736
#SPJ11
Find the measure of.. (image included)
I don't get this :(
Answers
David made a scale drawing of an Olympic-sized pool the pool is 20.5 in long and the drawing that I can shoot pool is 164 ft long what is the correct scale of the drawing
Answers
Answer:
\(Scale = 1\ in : 8\ ft\)
Step-by-step explanation:
Given
\(Scale\ Measurement = 20.5in\)
\(Actual\ Measurement = 164ft\)
Required
Determine the scale
The scale is calculated using the following ratio:
\(Scale = Scale\ Measurement : Actual\ Measurement;\)
Substitute values for Scale and Actual Measurements
\(Scale = 20.5\ in : 164\ ft\)
Divide ratio by 20.5
\(Scale = 20.5/20.5\ in : 164/20.5\ ft\)
\(Scale = 1\ in : 8\ ft\)
This implies that: 1 inch on scale represents 8 ft in actual measurement
Answer:
1.8
Step-by-step explanation: