Answer:
Faelyn should realize that her work shows that the polynomial is prime.
Explanation:
The only difference between her factors in Step 2 is that the 4 in the first group is negative, while the 4 in the second group is positive.
Rearranging the polynomial to factor it will not change the end result.
Factoring out a negative will make not only one, but both terms, in one of the binomials the opposite sign; this will not make the factors the same.
Factoring only 2x out of the first group will result in having (3x³+4x); this is not the same either.
She should realize that when this happens, her polynomial is prime.
The precision of what Faelyn should do is that Faelyn should realize that her work shows that the polynomial is prime. Hence, the option A is the correct option.
How to find the factors of polynomial?Factors of the polynomial which are multiplied to produce the original polynomial.
The polynomial which can not be factored is known as prime polynomial.
The standard form of the polynomial with highest power of 2 can be given as,
Given information-
The given polynomial equitation in the problem is,
[tex]6x^4 -8x^2 + 3x^2 + 4[/tex]
1) First step of Faelyn is[tex](6x^4- 8x^2) + (3x^2 + 4)[/tex]
2) Second step of Faelyn is[tex]2x^2(3x^2 - 4) + 1(3x^2 + 4)[/tex]
Faelyn noticed that she does not have a common factor. The polynomial which can not be factored is known as prime polynomial.
Thus Faelyn should realize that her work shows that the polynomial is prime. Hence, the option A is the correct option.
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A car traveled 48.36 miles in one hour. What was it's average speed per minute?
0.806 miles per minute
Step-by-step explanation:There are 60 minutes in an hour, so replace the unit "hour" by 60 minutes and recompute.
... 48.36 mi/h = 48.36 mi/(60 min) = (48.36/60) mi/min = 0.806 mi/min
The car's average speed was calculated by dividing the total distance of 48.36 miles by the total time of 60 minutes, resulting in an average speed of 0.806 miles per minute.
Explanation:To compute the car's average speed per minute, we need to divide the total distance covered by the total time in minutes. This is because speed is defined as the rate at which an object covers distance. The distance travelled by the car is 48.36 miles (the total distance), and the time is 1 hour. To transform this hour into minutes, we multiply by 60, as there are 60 minutes in an hour. So,
1 hour = 60 minutes
Therefore, to find the average speed, we take the total distance and divide by the total time in minutes. Using this, we find:
Average speed = Total distance / Total time
Average speed = 48.36 miles / 60 minutes = 0.806 miles per minute.
Therefore, the car's average speed was approximately 0.806 miles per minute.
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Help!
Could it be...??
a. /_ A
b. /_ BCA
c. /_ b
d. /_ CBA
which of the following values of x makes the rational expression below equal to zero? 2x+16/x+5
a. 5
b. -5
c. 8
d. -8
Answer:
d. -8
Step-by-step explanation:
Remember that you cannot possibly divide anything by 0, so if the denominator gives as a result 0, you are dealing with an impossibility, in order for a franction to give as a result 0, the numerator has to be 0, so we just need to equalize the numerator to 0 and solve for x to know how can we make the rational expression 0:
2x+16=0
2x=-16
x=-16/2
x=-8
So in order to make the expression equal to 0 x needs to be equal to -8,
1. Solve w=x+y/z for y.
2. Solve the equation above for z.
Answer:
y = z(w -x)z = y/(w -x)Step-by-step explanation:
As in any "solve for ..." problem, you reverse (undo) the operations done to the variable of interest. Generally, you do that in reverse order.
1. y is divided by z then the quotient added to x. To solve for y, we subtract x, then multiply by z.
... w - x = y/z . . . . . . . subtract x from the given equation
... z(w -x) = y . . . . . . . multiply by z
___
2. To solve for z, it is more convenient to start with the equation for y that is the result of the first question. We divide that by the coefficient of z.
... z = y/(w -x)
From w=x+y/z, the value of y = z(w - x)
w=x+y/z
This is changing the subject formula. The first thing to do is to subtract x from both sides. This will be:
w - x = x + y/z - x
w - x = y/z
Then, we cross multiply
z(w - x) = y
Therefore, y = z(w - x)
Since y = z(w - x)
Then, to get the value of z goes thus:
z = y/(w - x)
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add or subtract.
[tex] \binom{7 \sqrt{2} }{2} - \binom{ \sqrt{8} }{2} [/tex]
In a probability experiment, Craig rolled a six-sided die 57 times. The die landed on a number greater than three 36 times. What is the ratio of rolls greater than three to rolls less than or equal to three?
The ratio of rolls greater than three to rolls less than or equal to three is 36:21, which simplifies to 12:7 after dividing both terms by the greatest common divisor of 3.
Since Craig rolled the die 57 times, and it landed on a number greater than three 36 times, then it landed on a number less than or equal to three the remaining number of times. Subtracting the number of greater rolls from the total rolls:
Total rolls: 57
Rolls greater than three: 36
Rolls less than or equal to three = 57 - 36 = 21
Now, we can establish the ratio of rolls greater than three to rolls less or equal to three:
Ratio = Rolls greater than three : Rolls less than or equal to three = 36 : 21
And if needed, we can simplify this ratio by dividing both sides by their greatest common divisor, which is 3:
Simplified Ratio = 12 : 7
Please help me with question 5
How would you write the following phrase as a number expression eight more than triple a number
Can anyone help me on this question?:) tysm ily
Question 7 plz help me saner this question
Determine the equation for the parabola graphed below.
Which equation could be the equation of this parabola?
A. y = -2x^2
B. x = -2y^2
C. x = 2y^2
D. y = 2x^2
In 2015, the price of a business math text rose to $150. This is 8% more than the 2014 price. What was the old selling price?
Answer: old selling priceof businesss math text rose = $138.89
Explanation:
In year 2015, Price of business math text rose = $150
Suppose privious price (year 2014)= x dollars
Previous price is 8% less than the price in 2015 because given that $150 is 8% more than previous year price.
Now write the linear equation for the given information:
x + 8% of x = 150
Solve for x
x + [tex] \frac{8}{100} [/tex]x = 150
x + 0.08x = 150
1.08x = 150
divide 1.08 both the side
x = [tex] \frac{150}{1.08} [/tex]
x = $138.89
Old selling price = $138.89
How do you turn 43% into a fraction
To write a percent as a fraction in lowest terms, first remember that a percent is a ratio that compares a number to 100. 43% can be written as the ratio 43 to 100 or 43/100.
Therefore, 43% can be written as the fraction 43/100.
The heights in centimeters of 5 students are: 165, 175, 176, 159, 172 find the sample median, sample mean and sample variance.
The value of the sample median is 172.
The value of the sample mean is 169.4.
The value of the sample variance is 52.3
What is a median?It is the middle value of the given set of numbers after arranging the given set of numbers in order.
We have,
The heights in centimeters of 5 students are: 165, 175, 176, 159, 172
Now,
Arrange the heights in order.
159, 165, 172, 175, 176
Median = 172
Mean = (159 + 165 + 172 + 175 + 176) / 5 = 847 / 5 = 169.4
Sample variance.
= ∑ (x - Mean)² / (n - 1)
= 209.2 / 4
= 52.3
∑ (x - Mean)²
= (159 - 169.4)² + (165 - 169.4)² + (172 - 169.4)² + (175 - 169.4)² + (176 - 169.4)²
= 108.16 + 19.36 + 6.76 + 31.36 + 43.56
= 209.2
Thus,
The sample mean = 169.4
The sample median = 172
The sample variance = 52.3
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Simplify this equation.
(equation and choices in image)
b.)x³-7x²+3x+36
(x-4)(x²-3x-9)
Distribute x and -4 to x²-3x-9
=x²(x)-3x(x)-9(x)+x²(-4)-3x(-4)-9(-4)
=x³-3x²-9x-4x²+12x+36
Combine all liked terms
=x³-7x²+3x+36
One-third the sum of 6 and 3 (u get 10 points)
Hurry
Final answer:
The sum of 6 and 3 is 9, and one-third of this sum is 3 when you divide 9 by 3.
Explanation:
In mathematics, a sum is the result of adding two or more numbers or quantities together. It represents the total or aggregate of those quantities. The process of finding this total is called addition.
Thus,
To calculate one-third the sum of the numerals 6 and 3, we first find the sum of 6 and 3, which is 9.
Then, we need to take one-third of 9.
To find one-third of a number, you divide the number by 3.
So one-third of 9 is 9 divided by 3, which equals 3.
Therefore, one-third the sum of 6 and 3 is 3.
What is the value of x?
Enter your answer in the box.
_____ units
Answer:
x=28
Step-by-step explanation:
We can use similar triangles and proportions to solve this problem. Put the side of the small triangle over the same side of the larger triangle.
x 42
---------- = ----------
x+10 42+15
Simplify
x 42
---------- = ----------
x+10 57
Using cross products
57x = 42 (x+10)
Distribute
57x = 42x+420
Subtract 42x from each side
57x-42x = 42x-42x +420
15x = 420
Divide each side by 15
15x/15 = 420/15
x=28
Answer: The value of x is 28 units.
Step-by-step explanation:
Since we have given that
DC ║ PA
So, By Basic Proportionate theorem, if a line drawn parallel to the third side and intersect the other two sides, then the other two sides are divided into same ratio.
So, it becomes,
[tex]\frac{RC}{CA}=\frac{RD}{DP}\\\\\frac{x}{10}=\frac{42}{15}\\\\15\times x=10\times 42\\\\x=\frac{420}{15}=28\\\\x=28[/tex]
Hence, the value of x is 28 units.
Which describes the difference between the graph of f(x) = 3x2 + 2 and g(x) = 9x2?
B) The graph of f(x) is obtained by shifting g(x) up 2 units and compressing vertically by a factor of 3.
C) The graph of g(x) is obtained by shifting f(x) right 2 units and stretching vertically by a factor of 3.
D) The graph of f(x) is obtained by shifting g(x) right 2 units and stretching vertically by a factor of 3.
The solution is, the graph of f(x) is vertically stretched by a factor of 3 and shifted 7 units down, as f(x) = x changes to h(x) = 3x² - 7.
What is transformation of graph?Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.
here, we have,
Given that,
here is a graph of f(x) = x which is transformed into h(x) = 3x² - 7.
The graph of a the equation -
f(x) = x
is a straight line.
now, we get, When it is squared and multiplied by 3, we get -
h(x) = 3x²
which is a parabola stretched by a factor of 3 in vertical direction along
+ y axis.
When 7 is subtracted, it will shift the graph down by 7 units.
h(x) = 3x² - 7
Therefore, the graph of f(x) is vertically stretched by a factor of 3 and shifted 7 units down, as f(x) = x changes to h(x) = 3x² - 7.
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Complete question:
What is the effect on the graph of f(x) = x when it is transformed to
h(x) = 3x2 - 7?
A. The graph of f(x) is vertically stretched by a factor of 3 and shifted
7 units down.
B. The graph of f(x) is horizontally compressed by a factor of 3 and
shifted 7 units to the right.
C. The graph of f(x) is horizontally stretched by a factor of 3 and
shifted 7 units down.
D. The graph of f(x) is vertically stretched by a factor of 3 and shifted
7 units to the right
The purchase price of an IPad is 650. What is the total price oif the sales tax rate is 8%
miss Roberts simplified this ratio 2:6 explain how you know she is incorrect can you tell where she might have made a mistake
HELP MEEE!!! PLEASE!!!
Va doctor prescribes 10 mg of cough syrup. available is 5 mg/5 ml. how many teaspoons would you give?
Assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an lg smartphone survey). if 12 adult smartphone users are randomly selected, find the probability that fewer than 3 of them use their smartphones in meetings or classes.
Using the binomial probability formula, sum up the probabilities for 0, 1, and 2 smartphone users using their phones in meetings, which will give you the total probability for fewer than 3.
Explanation:The subject of this question appears to be probability theory, a branch of mathematics that studies the likelihood of different outcomes. The problem presented involves calculating the probability of a certain number of smartphone users behaving in a specified way. In this case, it's about finding the likelihood that fewer than 3 out of 12 selected individuals use their smartphones in meetings or classes.
To solve this, we'll use a binomial probability formula: P(X=r) = (nCr) * p^r * (1-p)^(n-r), where:
n is the number of trials (in this case, 12 smartphone users),r is the desired number of successful outcomes,p is the probability of success on a single trial (54%), andnCr is the combination of n items taken r at a time.
You will need to sum up the probabilities for 0, 1, and 2 smartphone users using their phones in meetings or classes to get the total probability for fewer than 3.
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You are wearing a pair of cargo pants with six pockets. You've put $10 in one of the pockets, but you cannot remember which one. After checking two pockets without success, what is the probability that the money will be in the next pocket you check? NextReset
The probability that the money will be in next pocket is 0.25.
We have a pair of cargo pants with six pockets and $10 in one of the pockets.
We have to find out the probability that the money will be in the next pocket you check after checking two pockets without success.
What is the formula to calculate the probability of an event ?The formula to calculate the probability of an event is -
[tex]P(A) = \frac{Total\;number\;of\;favorable\;outcomes}{Total\;number\;of\;outcomes\;in \;sample\; space} =\frac{n(A)}{n(S)}[/tex]In the question it is given -
Total money = $10
Total no. of pockets = 6 = n(S)
After two unsuccessful check in two pockets, new sample space =
n(S') = n(S) - 2 = 4
Hence, the probability that the money will be in the next pocket you check is -
P(A) = [tex]\frac{1}{4} = 0.25[/tex]
Hence, the probability that the money will be in next pocket will be 0.25.
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In a survey, 60 baseball fans were asked whether they thought the designated hitter rule should be changed. Forty-one fans thought the rule should be changed. WHat percent of the fans surveyed said that the designated hitter rule should be changed.
Shirley is drawing triangles that have the same area. The base of each triangle varies inversely with the height. What are the possible base and height of a second triangle if the first triangle's base is 16 and its height is 6 ?
the least common denominator of 2 fractions is 12 if you add the two denominators their sum is 7 what are the denominators
Which trinomial is the product of the expression below ? (2R-3) (R+12)
Which of these is equivalent to 92 + 42? (9 + 4)2 (9 × 4)2 (9 × 9) + (4 × 4) (9 + 9) + (4 + 4)