To find an nth-degree polynomial function with real coefficients given certain conditions, we can write the polynomial as a product of its linear factors using the given roots.
Explanation:To find an nth-degree polynomial function with real coefficients, we need to use the given conditions. Let's say the conditions include the roots of the polynomial. If we have n distinct real roots, the polynomial will have n factors. So, if the roots are a, b, c, ..., we can write the polynomial as P(x) = (x - a)(x - b)(x - c)...
Example:To find a quadratic polynomial with roots 2 and -3, we can write the polynomial as P(x) = (x - 2)(x - (-3)) = (x - 2)(x + 3) = x² + x - 6.
Similarly, for higher-degree polynomials, we use the same approach. We write the polynomial as a product of its linear factors using the given roots.
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Working together, it takes two roofers 10 hours to put a new roof on a portable classroom. if the first roofer can do the job by himself in 12 hours, how many hours will it take the second roofer to do the job by himself?
Number of hours the second roofer to do the job by himself is 60 hours.
Given that, working together, it takes two roofers 10 hours to put a new roof on a portable classroom.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Working together 1/10 roofs per hour
First roofer 1/12 roofs per hour
So, equation is x + 1/12 = 1/10
x = 1/10 - 1/12
= 6/60 - 5/60 = 1/60
Together, they work 1/60 + 1/12
= 1/60 + 5/60
= 6/60 = 1/10
Therefore, number of hours the second roofer to do the job by himself is 60 hours.
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A stadium can seat 46,000 people for a baseball game. One day, 49,442 people attended a game. How many people had to stand because they did not have a seat? 3. Draw a picture or a chart that shows the information and the question
Which of the following are independent pairs of events? Check all that apply.
A.Flipping two coins and having one show a head and the other show a head
B.Being sneezed on and catching a cold
C.When rolling a pair of dice, getting a total of 6 and having one die show a 3
D.Rolling a 4 on one die and rolling a 2 on another die
E.Seeing clouds and winning the lottery,
The best answer for these question would be:
A. Flipping two coins and having one show a head and the other show a head
D. Rolling a 4 on one die and rolling a 2 on another die
E. Seeing clouds and winning the lottery
Independent events in math means that the first situation does not affect the other variable. It is generally the individual probability that will happen to the solution. Which means that you have to determine whether the first situation will be affected on the second events that will happen. While the dependent events, have the opposite effect.
For the function f(x) = (8-2x)2 ,find f-1 . Determine whether f-1 is a function.
A.
f-1(x) = ;f-1 is a function
B.
f -1 (x) = ; f-1 is not a function
C.
f-1(x) = ;f-1 is not a function
D.
f-1(x) = ; f-1 is a function
Its not A!,
f-1(x) = 8±√x/2; f-1 is not a function, is the answer
What is the scale factor used to create the dilation?
A: 1/2
B: -1/2
C: 2
D: -2
More than 450 students traveled to a state park for a field trip. The school allowed 6 students to travel by car, and the rest traveled on 11 buses, each of which held the same number of students. If there were S students in each bus, which inequality best represents this situation?
What is the factored form of the following expressions x^2-100xy+24y^2
19) What is the effect on the graph of the parent function f(x) = x when f(x) is replaced with f(x) + 3?
A) shifts the line 3 units up
B) shifts the line 3 units down
C) increases the slope of the line by a factor of 3
D) decreases the slope of the line by a factor of 3
What is the equation of a vertical line passing through (−5, −2)?
x = −5
y = −2
x = −7
y = −3
Answer:
x = -5
First option is correct.
Step-by-step explanation:
The vertical line is passing through the point (−5, −2).
The equation of a vertical line is in the form x = k
For vertical line, the x-coordinate of each point that lie on the line remains same. Only the y-coordinate is different
For the given point, the x-coordinate = -5
Hence, k = -5
Therefore, the equation of line is x = -5
First option is correct.
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What is the formula of quadratic equations?
Final answer:
The quadratic formula is used to find the solutions of quadratic equations. It is x = (-b ± √(b² - 4ac)) / (2a). The discriminant determines the nature of the solutions.
Explanation:
The formula for quadratic equations is:
x = (-b ± √(b² - 4ac)) / (2a)
Quadratic equations are equations of the form ax² + bx + c = 0. The quadratic formula is used to find the solutions or roots of these equations. The discriminant, b² - 4ac, determines the nature of the solutions: if it is positive, there are two real solutions; if it is zero, there is one real solution; and if it is negative, there are two complex solutions.
Olivia just graduated with an Associates degree and is working as a secretary in a firm earning 9.75 an hour.Her contract stipulates that she will get an annual rasie of 6% until she reaches the rate of $15.50 an hour. sheshow long would it take for Olivia to earn $15.50 an hour? math
Does the point (3,7) lie on inside or outside the circle
Michelle works at a store that sells clothing accessories. The supply function for baseball caps is P=Q-6, where P is the price and Q is the quantity of baseball caps. If Michelle sells the baseball caps for $19 apiece, how many baseball caps will the store make?
A. 31 baseball caps
B. 6 baseball caps
C. 19 baseball caps
D. 25 baseball caps
Answer:
25
Step-by-step explanation:
Given : The supply function for baseball caps is P=Q-6, where P is the price and Q is the quantity of baseball caps.
To Find: If Michelle sells the baseball caps for $19 apiece, how many baseball caps will the store make?
Solution:
The supply function for baseball caps is P=Q-6
where P is the price
Q is the quantity of baseball caps.
Now we are given that Michelle sells the baseball caps for $19 a piece.
So, P = 19
Substitute the value in the function:
19=Q-6
19+6=Q
25 =Q
Thus If Michelle sells the baseball caps for $19 apiece, the store make will make 25 baseball caps .
A drawer contains 4 red socks, 3 white socks, and 3 blue socks. Without looking, you select a sock at random, replace it, and select a second sock at random. What is the probability that the first sock is blue and the second sock is red?
Answer:
[tex]\texttt{Probability}=\frac{3}{25} [/tex]
Step-by-step explanation:
Probability is the ratio of number of favorable outcome to total number of outcomes.
Total number of socks = 4 + 3 + 3 = 10
Number of blue socks = 3
Number of red sock = 4
[tex]\texttt{Probability of selecting blue sock}=\frac{3}{10} \\ [/tex]
[tex]\texttt{Probability of selecting red sock}=\frac{4}{10} \\ [/tex]
For finding the combined probability we need to multiply both the values
[tex]\texttt{Probability that the first sock is blue and the second sock is red}=\frac{3}{10}\times \frac{4}{10}=\frac{12}{100}=\frac{3}{25} \\ [/tex]
[tex]\texttt{Probability}=\frac{3}{25} [/tex]
Using the graph below, calculate the average rate of change for f(x) from x = 2 to x = 6.
exponential function going through points 2, 2 and 6, 6
−4
−1
1
4
Answer:
The average ate of change for f(x) from x=2 to x=6 is one, (1). Also seen as choice c.
Step-by-step explanation:
A similarity transformation maps ABC to JKL. The measure of of preimage ABC is 105°. The scale factor of the dilation in the similarity transformation is 1.5. If in the preimage corresponds to in the image, what is m?
Name at least one advantage of credit cards
3. Use the description of each triangle to draw a picture of the triangle. Write and solve equations to find missing angle measures when necessary. Label the measures of all angles of the triangle and mark congruent sides and right angles. (You do not need to draw the triangle exactly to scale.) (a) right isosceles triangle (b) equiangular (all three angles congruent) isosceles triangle (c) acute scalene triangle with two angle measures of 57° and 82°
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In the figure, YX−→− and YZ−→− are tangents to circle A at points X and Z, respectively.
mXZ=140∘
mXSZ=220∘
What is the measure of ∠XYZ ?
The sum of three consecutive integers is -96. What is the larger integer
What is the simplified form of 8b^3c^ 2a + 4b^3c^2?
The number 12,089 is?
< 12,098.
= 12,098.
> 12,098.
Or none of these is correct
Final answer:
The numbers 12,089 is less than 12,098, as determined by comparing the ones place of each number., hence the correct option is A
Explanation:
The student asks for the correct comparison between the numbers 12,089 and 12,098. To generate an accurate answer, we compare the digits from left to right.
Since the thousands, hundreds, and tens places are the same, we look at the ones place to determine which number is greater. Comparing the ones digits, we see that 9 (in 12,098) is greater than 8 (in 12,089), therefore 12,089 is less than 12,098.
The correct answer is:
12,089 < 12,098.
Find two positive consecutive odd integers such that the square of the larger integer is one less than twice the square of the small integer.
Answer:
smaller integer = 5
Larger integer = 7
Step-by-step explanation:
Let the first odd integer be x
Then the next consecutive integer will be x + 2
Now, The square of larger integer is 1 less than twice the square of the smaller integer.
As, x < x + 2
Smaller integer = x
Larger integer = x + 2
⇒ (x + 2)² + 1 = 2·x²
⇒ x² + 4 + 4x + 1 = 2x²
⇒ x² - 4x - 5 = 0
⇒ x² - 5x + x - 5 = 0
⇒ x(x - 5) + 1(x - 5) = 0
⇒ (x - 5)(x + 1) = 0
⇒ x = 5 or x = -1
But we need positive integer so x = -1 is rejected.
Hence, x = 5
So, smaller integer = 5
Larger integer = 7
Jamal wrote the following statements: Statement 1: Perpendicular lines are two lines that intersect at 90° angles. Statement 2: All right angles are congruent. Which geometry term does each statement represent?
So I just wanna see if I got this one correct my question is.... Each volume of an encyclopedia is 2 1/3 inches wide. How many volumes will fit on a shelf 18 inches wide?
What do you need to do to solve x/6=18
given that cos 42° ~0.743 what is the sine of the complementary angle
The perimeter of a rectangle is 256 inches. How long are the sides if the length exceeds the width by 16 inches? mark X represent the width of the rectangle and write the Equation 2X +2(x+16)=256. Solving for X the width of the rectangle is what
The sum of 555 consecutive integers is 505505505.
What is the third number in this sequence?