Writing a Polynomial Function Given a y-Intercept:
Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, –5).
Describe the steps for writing the equation of this cubic polynomial function.
We are given
a cubic polynomial function has the same zeroes
Let's assume that zeros as 'a'
so, we can write it as
[tex]f(x)=(x-a)^3[/tex]
now, we are given y-intercept
(0,-5)
at x=0 , y=-5
we can use it and then find 'a'
[tex]-5=(0-a)^3[/tex]
[tex]a=\sqrt[3]{5}[/tex]
now, we can plug it
and we get
[tex]f(x)=(x-\sqrt[3]{5})^3[/tex]..................Answer
Answer:
Use the zeroes to determine the roots.
Write the polynomial as a product of the leading coefficient, a, and the factors, where each factor is x minus a root.
Use the y-intercept (0, –5) to solve for the leading coefficient.
Substitute the leading coefficient into the polynomial function for a and simplify.
Step-by-step explanation:
Which of the following are measures of complementary angles? A. 50° and 41° B. 100° and 80° C. 77° and 13° D. 35° and 10°
Complimentary angles equal 90 degrees. So the answer would be C because 77+13= 90.
Answer: Two angles are complementary when they add up to 90°
then, doing all the options:
A) 50° + 41° = 91°, so this angles are non complementary.
B) 100° + 80° = 180°, so this aren't complementary, but they are Supplementary (because their addition is 180°) angles.
C) 77° + 13° = 90°, si this angles are complementary
D) 35° + 10° = 45°, this pair is not complementary.
So the only correct answer is C.
What is the length of the hypotenuse of the triangle of 7ft and 4ft
To find the length of the hypotenuse in a right-angled triangle with sides measuring 7ft and 4ft, use the Pythagorean Theorem: 7² + 4²= c², which gives us the hypotenuse length of approximately 8.06 feet.
The question is asking for the length of the hypotenuse of a right-angled triangle when the lengths of the other two sides are known (7ft and 4ft).
To find the hypotenuse, we use the Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is expressed as a² + b² = c².
By applying the Pythagorean Theorem:
72 + 42 = c²
49 + 16 = c²
65 = c²
c = √65 ≈ 8.06 ft
Therefore, the length of the hypotenuse is approximately 8.06 feet.
Which ordered pairs are solutions to the inequality 2y−x≤−6 ?
Select each correct answer.
(−3, 0)
(6, 1)
(1, −4)
(0, −3)
(2, −2)
To determine which ordered pairs are solutions to the inequality 2y - x ≤ -6, substitute the x and y values of each ordered pair into the inequality and check if it is satisfied.
Explanation:To determine which ordered pairs are solutions to the inequality 2y - x ≤ -6, we substitute the x and y values of each ordered pair into the inequality and check if the inequality is satisfied:
For the ordered pair (-3, 0): 2(0) - (-3) ≤ -6 → 0 + 3 ≤ -6 → 3 ≤ -6 (not satisfied)For the ordered pair (6, 1): 2(1) - 6 ≤ -6 → 2 - 6 ≤ -6 → -4 ≤ -6 (satisfied)For the ordered pair (1, -4): 2(-4) - 1 ≤ -6 → -8 - 1 ≤ -6 → -9 ≤ -6 (not satisfied)For the ordered pair (0, -3): 2(-3) - 0 ≤ -6 → -6 - 0 ≤ -6 → -6 ≤ -6 (satisfied)For the ordered pair (2, -2): 2(-2) - 2 ≤ -6 → -4 - 2 ≤ -6 → -6 ≤ -6 (satisfied)Therefore, the correct answers are (6, 1), (0, -3), and (2, -2).
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A group of employees were asked whether they drive or walk to work.
The table shows the probabilities of results.
Answer:
Independent.
Step-by-step explanation:
Answer: Picture
Step-by-step explanation:
You have $1 bills and $5 bills in your wallet. There are 7 bills worth a total of $19
You have 3 $5s and 4 $1 bills. Hope this helps :)
You have 3 $5s and 4 $1 bills.
Hope this helps you, if it does, please mark brain! <3
-SHOBE-
please help on this one?
The answer is (-3,0) if you plug the coordinates into the equation you will find that it satisfies it and indicates that you should shade below the line
:)
Please help asap 28 pts
What is five billion two hundred fifty four million seventy one thousand nine hundred twenty six written in standard form
5,254,071,926
Is the standard form
The number 'five billion two hundred fifty four million seventy one thousand nine hundred twenty six' can be written in standard form as 5,254,071,926.
Explanation:The number 'five billion two hundred fifty four million seventy one thousand nine hundred twenty six' is written in words. In standard form, we write it as a numeric value instead. So,
5,254,071,926
is the standard form of 'five billion two hundred fifty four million seventy one thousand nine hundred twenty six'. The standard form simply means writing the number as we typically would in mathematics or everyday usage.
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How do i divide 806 by 9 with long division, im getting 9 remainder 6
The length of a rectangle room is 6 feet longer than twice the width. If the room's perimeter is 132 feet, what are the room's dimensions?
Answer:
The width of the room is 20 feet.
The Length of the room is [tex]46[/tex] feet.
Step-by-step explanation:
Lets take the width of the room as [tex]x[/tex] feet
Then the length of the room will be [tex]2x+6[/tex] feet
Perimeter of a room is the addition of all the walls making the boundary of the room.
Perimeter of the rectangular room = 2 * Width + 2 * Length
⇒[tex]132=2*x+2*(2x+6)[/tex]
⇒[tex]132=2x+4x+12[/tex]
⇒[tex]132=6x+12[/tex]
⇒[tex]132-12=6x[/tex]
⇒[tex]120=6x[/tex]
⇒[tex]20=x[/tex]
Therefore,
The width of the room is 20 feet.
The Length of the room is,
[tex]2x+6[/tex] = [tex]2*20+6[/tex] = [tex]46[/tex] feet
Please help!
Factor.
9x^4−64y^2
To factor 9x^4 - 64y^2, use the difference of squares formula. The factored form is (3x^2 + 8y)(3x^2 - 8y).
To factor 9x^4 - 64y^2, we can use the difference of squares formula: a^2 - b^2 = (a + b)(a - b). Applying this, we get: 9x^4 - 64y^2 = (3x^2 + 8y)(3x^2 - 8y)
Therefore, the factored form of 9x^4 - 64y^2 is (3x^2 + 8y)(3x^2 - 8y).
The vertex of this parabola is at (3,-2). when the x-value is 4, the y-value is 3. whatis the coefficient of the squared expression in the parabolas equation
Answer:
The coefficient of the squared expression in the parabolas equation will be 5.
Step-by-step explanation:
The vertex form of parabola is: [tex]y=a(x-h)^2 +k[/tex] , where [tex](h,k)[/tex] is the vertex point and [tex]a[/tex] is the coefficient of [tex]x^2[/tex] term.
The vertex is given as [tex](3,-2)[/tex]. That means, [tex]h=3[/tex] and [tex]k=-2[/tex]
So, the vertex form will be: [tex]y=a(x-3)^2-2[/tex]
Given that, when the x-value is 4, the y-value is 3. So, plugging these values into the above equation, we will get.....
[tex]3=a(4-3)^2-2\\ \\ 3=a(1)^2-2\\ \\ a=3+2=5[/tex]
Thus, the coefficient of the squared expression in the parabolas equation will be 5.
PLEASE HELP I NEED TO SEND THIS SOON
Screenshot attached below
Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.
{Nine times the difference of 8 and a number.}
Nine times the difference of 8 and a number.
To represent the sentence 'Nine times the difference of 8 and a number.' as an algebraic expression, we can use the expression 9(8 - x), where x represents 'a number'.
Explanation:To represent the sentence 'Nine times the difference of 8 and a number.' as an algebraic expression, we can start by assigning the letter x to represent a number. Then, we can write the expression as 9(8 - x), where 8 - x represents the difference of 8 and the number x.
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The given sentence 'Nine times the difference of 8 and a number' can be translated into the algebraic expression 9(8 - x).
Explanation:The given sentence, 'Nine times the difference of 8 and a number' can be represented as an algebraic expression as follows: First, identify the operation for 'difference' which is subtraction. Then, identify the 'number', which is given as x. So, 'the difference of 8 and a number' would be 8 - x. 'Nine times the difference' implies multiplication, so the entire expression would be 9(8 - x). Therefore, the algebraic expression to represent the sentence in question is 9(8 - x).
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Simplify the following expression:
-5a⁷ b⁻³ • 4a⁻⁶ b⁶
Perform the indicated operation and then simplify 4m-3-9m+8
Final answer:
To simplify 4m - 3 - 9m + 8, combine like terms to get -5m + 5, which is the simplified expression.
Explanation:
To perform the indicated operation and simplify 4m - 3 - 9m + 8, we need to combine like terms. The terms 4m and -9m are like terms, as are the constants -3 and +8. So, let's combine them.
First, combine the m terms:
4m - 9m = -5m
Next, combine the constant terms:
-3 + 8 = 5
Putting it all together, we have:
-5m + 5
This is the simplified form of the original expression.
The height of a football during a punt is modeled by h=-16t^2+60t+3. If the football hits the ground, how long did it stay in the air?
"how long..." is asking for time (t). "The amount of time spent in the air" is the time from when the ball was kicked (0 seconds) to the time it landed on the ground. Need to find the x-intercepts (one will be negative which will be invalid). You can do this by factoring ... or by using the quadratic formula. With the equation you provided, it is not factorable, so you must use the quadratic formula.
h = -16t² + 60t + 3
a=-16 b=60 c=3
[tex]t = \frac{-b +/- \sqrt{b^{2}-4ac } }{2a}[/tex]
[tex]t = \frac{-60 +/- \sqrt{60^{2}-4(-16)(3) } }{2(-16)}[/tex]
[tex]t = \frac{-60 +/- \sqrt{3600 + 192} }{-32}[/tex]
[tex]t = \frac{-60 +/- \sqrt{3792} }{-32}[/tex]
[tex]t = \frac{-60 +/- 61.6}{-32}[/tex]
[tex]t = \frac{-60 + 61.6}{-32}[/tex] or [tex]t = \frac{-60 - 61.6}{-32}[/tex]
[tex]t = \frac{1.6}{-32}[/tex] or [tex]t = \frac{-121.6}{-32}[/tex]
t = -0.05 or t = 3.8 disregard the negative
Answer: 3.8 seconds
If m ∡2 = 138°, find m ∡1, m ∡4, and m ∡3
Which of the following is a binomial?
A. b²-14
B. x²
C. s⁴-s+12
D. f³+f²-f+16
Binomial: A polynomial that is the sum of two terms, each of which are monomials. The answer here would be A. b² - 14, because it is comprised of two terms. Answer B is a monomial because it only has ONE term, C is a trinomial because it has three terms, and D. is a multinomial, or a polynomial because it has more than three terms. Hope that helps!
Students were asked to rank their preferences for watching the following sports: baseball, football, soccer, volleyball, hockey, and softball. How many different rankings are possible?
A.
720
B.
36
C.
6
D.
46,656
5/100‚3/100‚75/100,5/100 listed from least to greatest
3/100, 5/100, 5/100 75/100
Find the median of the data set 3 35 23 37 45 5 49 27 48
median = 35
the median is the middle entry of the data arranged in ascending order
rearranging the data in ascending order
3 5 23 27 35 37 45 48 49
the middle value = 35 ← median
what is the solution of 3x+8/x-4 >;= 0
The division between two numbers is positive if and only if they have the same sign. So, this fraction is positive if numerator and denominator are either both positive or both negative.
For this reason, you want to study the sign of numerator and denominator separately first.
As for the numerator, you have
[tex] 3x+8 \geq 0 \iff 3x \geq -8 \iff x \geq -\dfrac{8}{3} [/tex]
Similarly, for the denominator you have
[tex] x-4 > 0 \iff x > 4 [/tex]
(note that we used strict inequality for the denominator, since it can't be zero).
So, the sign of the fraction works like this:
If [tex] x \leq -\frac{8}{3} [/tex] both numerator and denominator are negative (or, at most, the numerator is zero if [tex] x = -\frac{8}{3} [/tex]), so the ratio is greater than or equal to zero.If [tex] -\frac{8}{3} \leq x < 4 [/tex] the numerator is positive and the denominator is negative (or, at most, the numerator is zero if [tex] x = -\frac{8}{3} [/tex]), so the ratio is less than or equal to zero.If [tex] x >4 [/tex] both numerator and denominator are positive, so the ratio is greater than or equal to zero.Answer:
A. x ≤ −8/3 or x>4
Step-by-step explanation:
Edge 2020 answer is A
Carlos graphed the system of equations that can be used to solve x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12
What are the roots of the polynomial equation?
–3, –2, 3
–3, 2
18, 32
18, 32, 66
Answer:
The roots are [tex]-3,-2,3[/tex]
Step-by-step explanation:
Let [tex]f(x)=x^3-2x^2+5x-6[/tex] and [tex]g(x)=-4x^2+14x+12[/tex].
The graph of the two functions are in the attachment.
The x-values of the points of intersection are the roots of the polynomial equation.
[tex]x^3-2x^2+5x-6=-4x^2+14x+12[/tex]
The roots are
[tex]-3,-2,3[/tex]
Answer:
-3,-2,3
Step-by-step explanation:
edge
I'd really appreciate if anyone helped! :)
Which set of ordered pairs represents a function?
A. (1, 2), (1, 3), (1, 4), (1, 5)
B. (4, 1), (3, 2), (3, 3), (1, 4)
C. (1, 6), (2, 2), (4, 7), (3, 2)
D. (1, 6), (3, 2), (4, 7), (3, 4)
In order for the data set to represent a function, there can be no duplicates of the first value.
A. 1 is used as the first value more than once it is NOT a function
B. 3 is used as the first value more than once it is NOT a function
C. no first number is used more than once it IS a function
D. 3 is used as the first value more than once it is NOT a function
Answer: C
Two squares, each with an area of 25units are placed side by side to form a rectangle. What is the perimeter of the rectangle?
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!
The graph shows the solution to which system of equations?
A) y = x + 2 and y = -x - 4
B) y = 3x + 7 and y = x + 12
C) y = 2x - 3 and y = −2x + 1
D) y = -x + 4 and y = −2x + 5
A car is purchased for $29500. After each year, the resale value decreases by %35. What will the resale value be after 4 years
Using the exponential decay formula, the resale value of a car initially purchased at $29,500 and depreciating at 35% per year will be approximately $5,266.08 after 4 years.
To calculate the resale value of a car after depreciation, we can use the formula for exponential decay, which is [tex]V = P (1 - r)^t[/tex], where V is the future value of the car, P is the initial purchase price, r is the rate of depreciation, and t is the time in years. In this case, P = $29,500, r = 35% or 0.35, and t = 4 years.
Following the formula, the resale value after 4 years would be:
V = $29,500 (1 - 0.35)⁴
V = $29,500 (0.65)⁴
V = $29,500 (0.17850625)
V = $5,266.08 approximately
Therefore, the resale value of the car after 4 years will be around $5,266.08.
helpppppppppppppppppppppppp
To find the total amount of snow accumulated after one month, simply add in the inches recorded.
9.2 in. + 0.5 in. + 6 in. + 5.9 in. = 21.6 total inches of snow fell over the one month period