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Which are the solutions of the quadratic equation?
x2 = 9x + 6
The solutions of the quadratic equation x^2 = 9x + 6 are (9 + sqrt(105))/2 and (9 - sqrt(105))/2.
Explanation:To find the solutions of the quadratic equation x^2 = 9x + 6, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b +- sqrt(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -9, and c = -6. Plugging in these values, we get:
x = (-(-9) +- sqrt((-9)^2 - 4(1)(-6))) / (2(1))
Simplifying further:
x = (9 +- sqrt(81 + 24)) / 2
x = (9 +- sqrt(105)) / 2
So the solutions of the quadratic equation x^2 = 9x + 6 are:
x = (9 + sqrt(105)) / 2
x = (9 - sqrt(105)) / 2
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The solutions to the quadratic equation x² = 9x + 6 are x = 3 and x = 6. This is done by rearranging the equation and then factoring into two binomials (x - 3) and (x - 6) equals 0, then set each binomial equal to zero.
Explanation:The given quadratic equation is x² = 9x + 6. To find the solutions of the quadratic equation, we first move all the terms to one side. This gives us: x² - 9x - 6 = 0. This is now a standard quadratic equation, and can be solved by either factoring or using the Quadratic Formula.
If we opt to solve via factoring, we're looking to factorize the original expression into two binomial expressions, essentially looking for two numbers which both add up to -9 and multiply to -6. These two numbers are -3 and 6. Therefore, the quadratic equation can be factored as follows: (x - 3)(x - 6) = 0. Setting each factor equal to 0 gives the possible solutions for x, in this case, x = 3 and x = 6.
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how to solve x^2-4y^2=7
Estimate the area of the irregular shape. Explain your method and show your work. Can someone explain this to me?
Answer:
Approximate area: 27.5 square units
Step-by-step explanation:
The irregular shape is very similar to a trapezium with coordinates (-3,3), (2, 2), (2, -2) and (-3, -4).
Area of a trapezium: [(a+ b)/2]*h
where a and b refer to the two parallel sides and h is the distance between them. From the above coordinates: a = 7 length units, b = 4 length units and h = 5 length units. Therefore, approximate area = [(7+ 4)/2]*5 = 27.5 square units
A publishing company has a weekly cost equation of C=96,000+20x and a weekly revenue equation of R=26x, where x is the number of books produced and sold in a week. The company loses money when R
To find when a publisher makes or loses money, compare the cost function C=96,000+20x to the revenue function R=26x. The break-even point is at x=16,000 books produced and sold weekly. Below this, the company incurs losses.
When determining when a publishing company makes or loses money, we investigate the relationship between cost and revenue functions. The cost function given is C=96,000+20x and the revenue function is R=26x, with x representing the number of books produced and sold per week. A company loses money when costs exceed revenues, that is when C > R.
To find the quantity of books where this happens, we equate the two equations:
C = R96,000 + 20x = 26x96,000 = 26x - 20x96,000 = 6xx = 96,000 / 6x = 16,000Therefore, at the production and sale of 16,000 books, the company will break even. Producing fewer than 16,000 books would result in a loss because the cost would be higher than the revenue generated.
explain why counting by tens might be faster than counting by ones
A conical tent made of canvas has a base that is 34 feet across and a slant height of 12 feet. To the nearest whole unit, what is the area of the canvas, including the floor? Use 3.14 for π.
Answer:
The area of the canvas, including the floor is 1548 sq. feet.
Step-by-step explanation:
Given : A conical tent made of canvas has a base that is 34 feet across and a slant height of 12 feet.
To find : What is the area of the canvas, including the floor?
Solution :
A conical tent made of canvas has a base that is 34 feet.
The diameter of the base is D=34 feet.
The radius of the base is [tex]r=\frac{34}{2}=17[/tex]
The slant height l=12
The area of the canvas, including the floor is
[tex]A=\pi r l+\pi r^2[/tex]
[tex]A=\pi r(l+r)[/tex]
[tex]A=3.14\times 17(17+12)[/tex]
[tex]A=3.14\times 17\times29[/tex]
[tex]A=1548.02[/tex]
In nearest whole unit, A=1548 sq. feet.
Therefore, The area of the canvas, including the floor is 1548 sq. feet.
Find the dimensions of a triangle given the following information. The perimeter is equal to 36cm, side 1 is 4 less than side 2 and side 3 is twice the length of side 2.
Jim has half a pizza left over from dinner. If he eats of this for breakfast, what fractional part did he eat for breakfast
Lesley raised $25 for the food bank last year and she raised 8 times as much money this year how much money did she raise this year
Find the perimeter of the following rectangle. Write your answer as a mixed number in simplest form. Be sure to include the correct unit in your answer. length is 7/10 and 2 1/4
Seven weightlifters are competing in the dead-lift competition. In how many ways can the weightlifters finish first, second, and third ( no ties)?
F=9/5C+32 What Does C And F represent
A bag contains 1 gold marbles, 6 silver marbles, and 30 black marbles. Someone offers to play this game: You randomly select on marble from the bag. If it is gold, you win $4. If it is silver, you win $2. If it is black, you lose $1. You can expect to lose an average of ________ cents every time you play. (round to the nearest cent)
How many diameters can a circle have?
Charlie is making a scale model of his kitchen. If the kitchen measures 12 feet by 11 feet, and his scale is two inches = three feet, what is the scale measure of the kitchen? Round to the nearest tenth.
A. 8 in by 7.3 in
B. 18 in by 16.5 in
C. 0.5 in by 0.4 in
D. 10 in by 9 in
Answer:
Option A. is the answer.
Step-by-step explanation:
Charlie is making a scale model of his kitchen.
The kitchen measures 12 feet by 11 feet.
We can use the unitary method to get the scale measures.
Since his scale is 3 feet = 2 inches.
So 1 feet = [tex]\frac{2}{3}[/tex] inches
and 12 feet = [tex]\frac{(2)(12)}{3} = 8[/tex] inches
Similarly 11 feet = [tex]\frac{(11)(2)}{3}=7.3[/tex] inches
Therefore, scale measures of the kitchen will be = 8 in by 7.3 in
Option A. is the correct answer.
The _______ form of a quadratic equation is written y = a(x - h)2 + k
Answer:
Correct Answer: vertex form
Step-by-step explanation:
"to find x in part a, you would need" to solve the equation x 2 – 25 =0. wh
20.301_____ 20.31 is this equal or greater
a baseball team plays 83 games in a season. if the team won 17 more than twice as many as they lost how many times did the did lose?
Final answer:
By creating an equation based on the information provided and solving for L, which represents the number of games lost, it was determined that the baseball team lost 22 games during the season.
Explanation:
To determine how many games the baseball team lost during the season, let us denote the number of lost games as L. The problem states that the baseball team won 17 more than twice the number of games they lost, which can be expressed as 2L + 17. Since the team played a total of 83 games in the season, we have the following equation to represent the total number of games played:
L + (2L + 17) = 83.
Combining like terms, we get:
3L + 17 = 83.
Now, subtract 17 from both sides of the equation:
3L = 66.
Then, we divide both sides of the equation by 3:
L = 22.
So, the baseball team lost 22 games during the season.
To find the number of times the team lost, set up an equation using the given information. The team won 17 more than twice the number of times they lost. The team lost 22 times.
Explanation:To find the number of times the team lost, we can set up an equation using the given information.
Let's assume the number of times the team lost is x.
According to the given information, the team won 17 more than twice the number of times they lost. So, the number of times the team won is 2x + 17.
The total number of games played is 83, which is the sum of the number of games won and lost.
So we have the equation 83 = x + (2x + 17).
Simplifying this equation, we get 83 = 3x + 17.
Subtracting 17 from both sides, we have 66 = 3x.
Dividing both sides by 3, we get x = 22.
Therefore, the team lost 22 times.
From a sample of 500 items, 30 were found to be defective. the point estimate of the population proportion defective will be
Final answer:
The point estimate of the population proportion defective, given 30 defects in a 500 item sample, is 0.06 or 6%.
Explanation:
The point estimate of the population proportion defective can be calculated by dividing the number of defective items in the sample by the total number of items in the sample.
In this case, there are 30 defective items out of a sample of 500 items.
So the point estimate of the population proportion defective is:
Point estimate = Number of defective items / Total number of items
Point estimate = 30 / 500 = 0.06
Factor 27x+9y
using the GCF.
The greatest common factor for the expression 27x+9y will be 9.
What is the greatest common factor?The highest number that is a factor of all the numbers is known as the greatest common factor of two or more numbers. The largest factor that splits both numbers is said to be the greatest common factor.
List the prime factors of each integer before calculating the greatest common factor.
It is given that the expression is,
27x+9y
We can take out 9 commons in the expression because it does not affect the expression,
The greatest common factor is,
9( 3x + y)
We obtain 9 as the value that we can take commonly from the complete expression. As a result, it is the greatest common factor.
Thus, the greatest common factor for the expression 27x+9y will be 9.
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Find the reference angle when o= 420 degrees
A) 30 degrees
B) 45 degrees
C) 50 degrees
D) 120 degrees
one stae leads the country in tart cherry production producing 78 out of every 100 tart cherries each year what percent of tart cherries are produced in this state
The state in question produces 78% of the country's total annual tart cherry production.
Explanation:The state in question produces 78 out of every 100 tart cherries annually, which is the same as 78 out of 100 or 78/100. When written as a fraction, this can be turned into a decimal by dividing the numerator (78) by the denominator (100). This will give 0.78. To convert this decimal into a percentage, we then multiply by 100 which leads to 78%. This means the state produces 78% of the total tart cherries grown in the country each year.
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nearly 4 of 5 people choose vanilla as their favorite ice cream flavor. if 120 people attend an ice cream social, how many would you expect to choose vanilla?
Forty percent of all registered voters in a national election are female. a random sample of 5 voters is selected. the probability that there are no females in the sample is
To calculate the probability of selecting no female voters in a sample of 5, given that 40% of the registered voters are female, we multiply the probability of selecting a male voter (60%) five times, which equals to (0.6)⁵ or 7.776% probability.
The question involves calculating the probability that none of the five randomly selected voters are female, given that 40% of registered voters are female. To find this probability, we need to use the complementary probability, which is the probability of the opposite event occurring (that is, selecting a male voter).
The probability of selecting one male voter randomly is 60% (or 0.6), as females account for 40% of the registered voters. When we select 5 voters independently, we multiply the individual probabilities together because the events are independent. Therefore, the probability of selecting no female voters in 5 trials is calculated as:
(0.6) × (0.6) × (0.6) × (0.6) × (0.6) = (0.6)⁵ = 0.07776 or 7.776%.
This is the probability that a random sample of 5 voters will contain no females.
Find the thirtieth term of the following sequence.
-6, -4, -2, 0, ...
Answer: 52
Step-by-step explanation:
To find the 30th number sequence with the given values of: -6,-4,-2,0.
Multiply 30 by 2 because we add 2 to the sequence every time we go up.
30*2 gives us 60, then we subtract however many 2's were in the given sequence.
From -6 to -4 to -2 to 0, we get 8.
60-8 = 52.
Thank you and I hope this helps. Even if my math is wrong somewhere, I got the answer right on my assignment so this is 100% correct.
There are 25 squares in the pattern. What fraction of the squares have these number of edges free?
A college professor noted that the grades of his students in an introductory statistics class were normally distributed with a mean of 76.5 and a standard deviation of 9. if 67.36% of his students received grades of c or above, what is the minimum score of those students receiving a grade of at least a c?
Using the properties of normal distribution and the Z-score related to the given percentile, it can be inferred that the minimum grade for a 'C' in this college statistics class is approximately 72.
Explanation:In this scenario, the professor's grades reflect a normal distribution, therefore, we can utilize the properties of normal distribution to answer your question. The probability given, 67.36%, corresponds to a Z-score of -0.45 (you can find this in standard statistical tables).
We'll utilize the formula Z = (X - μ) / σ, Z is the Z-score, X is the data point, μ is the mean, and σ is the standard deviation. Therefore, if we rearrange the formula to find X (the data point,or in this case, the lowest grades for students receiving a C or above), it will be X = Z * σ + μ. Substituting the given values in the equation gives X = -0.45 * 9 + 76.5. This results in a minimum score approximately equal to 72.45, or 72 if we consider only whole marks. Hence, our conclusion that the minimum grade for a 'C' is 72.
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The minimum score required to receive at least a grade of C in this normally distributed class is approximately 72.54.
To determine the minimum score that students need to receive at least a grade of C in a class where grades are normally distributed, we analyze the problem with a mean [tex](\mu)[/tex] of 76.5 and a standard deviation [tex](\sigma)[/tex] of 9.
We know that 67.36% of the students received a grade of C or above.
This corresponds to the top 67.36% of the distribution.
The bottom 32.64% of the distribution received less than a C.
The z-score associated with the 32.64th percentile can be found using z-tables or a standard normal distribution calculator:
z = -0.44
Next, we convert this z-score to the actual score using the formula:
[tex]X = \mu + z\cdot \sigma[/tex]
Substituting the given values:
X = 76.5 + (-0.44 * 9) = 76.5 - 3.96 = 72.54
Thus, the minimum score required for a grade of at least C is approximately 72.54.
If $3000 is deposited in an account that pays 5% interest, what is the difference in the amount after 4 years between the amount earned if the principal is compounded annually and the amount earned calculated using simple interest?
A. $30.72
B. $41.12
C. $46.52
D. $53.76
What is 3/7 divided by 6?
2.) Simplify a fraction:
342 = 1 × 314 × 3 = 1143/7 divided by 6 is equal to 1/14.
To divide 3/7 by 6, you can multiply the numerator (3) by the reciprocal of the denominator (6).
The reciprocal of 6 is 1/6.
So, (3/7) divided by 6 can be calculated as:
(3/7) × (1/6)
= (3 × 1) / (7× 6)
= 3/42
Divide numerator and denominator by 3:
= 1/14
Therefore, 3/7 divided by 6 is equal to 1/14.
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