f(x)=x²−4x−21
The degree is the biggest power of x. That's a polynomial of degree 2, also called a quadratic function. Let's find its zeros.
0 = x²−4x−21 = (x - 7)(x+3)
x=7 or x=-3
The fundamental theorem guarantees every non-constant polynomial with complex coefficients has a complex zero, let's call it r. If we divide the polynomial by x-r there won't be any remainder and we'll get a new polynomial, one degree less. The fundamental theorem again applies and (if it's not a constant polynomial) we are assured of another zero, s. We divide by x-s and get a new polynomial of degree one less. We repeat all this until we get a constant polynomial (degree zero). So we get a zero for every degree. They're not necessarily all different.
Answer:
The degree of f(x) is 2. The Fundamental Theorem of Algebra guarantees that a polynomial equation has the same number of complex roots as its degree. This means that f(x) has exactly 2 zeros. Those zeros are 7 and -3.
Find the y-intercept of the following equation. Simplify your answer.
y = 6x + 4
y-intercept =
Answer:
The slope is 6 and the y intercept is 4
(0,4)
Step-by-step explanation:
y = 6x + 4
This is in the form y = mx+b
where m is the slope and b is the y intercept
The slope is 6 and the y intercept is 4
(0,4)
Please help there’s a picture to explain more
110
70
X=?
Answer:
Step-by-step explanation:
110 = 70 + X [ extarior angle property]
or, 110 - 70 = X
or , 40 = X
HOPE IT HELPS ...
MARK ME AS BRAINLIEST IF IT DOES SO
Please please please answer this if you do this i will give you brain list I’ll give a thank you and I’ll rate you five star. It’s due soon so pls answer FAST!!
Answer:
b) 30^2 + b^2 = 40^2
Step-by-step explanation:
This is cuz the diagonal is the hypotenuse of the diagonal formed so it'll be c^ 2
c ^ 2 always is on the right hand side of the equation.
In this case since 40^2 is c^2 is should be on the right side of the equation.
Use set notation to denote the elements, subsets, and complements of the following given sets.
N is the set of odd natural numbers greater than 11 and less than 21. Use set notation to write the elements of N.
N = {13, 15, 17, 19)
N = {12, 14, 16, 18, 20}
N- {11, 12, 14, 16, 18, 20, 21)
N = {11, 13, 15, 17, 19, 21}
Answer:
N = {13, 15, 17, 19} is the correct answer.
Step-by-step explanation:
We are given with the following details:
N is the set of odd natural numbers.
N contains the elements which are greater than 11 and less than 21.
To write: The set notation for the elements of set N.
Solution:
First of all, let us see what are odd natural numbers.
Natural numbers are the positive integers i.e. {1,2,3,4, ........ }
Odd Natural numbers are the natural numbers which leave remainder as 1 when divided by 2 i.e. {1,3,5,7,9,11,13, ...... 21, 23, 25, 27.....}
Here, set N is odd natural numbers greater than 11 (so 11 will not be included) and less than 21 (so 21 will not be included). Odd natural numbers between 11 and 21 will be included.
So the answer will be N = {13,15,17,19}.
Analyze the diagram below and complete the instructions that follow.
N
In the diagram, 212 22 22 = 23, and m41 = 609. Give the reasons that best support the following statements used to show
that m43 = 60°
1. 21 = 22 and 22 = 23; therefore, 2133
2. m 1 = 60° and 2123; therefore, 60° =m23
3. 60º = m/3; therefore, mx3 = 60°
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Helen and her sister started watching a cartoon movie at 10:26 A.M. The movie was 2 hours and 51 minutes long. After the movie, they played a card game for 32 minutes and then played soccer in the backyard for 1 hour and 6 minutes. What time was it when Helen and her sister finished playing soccer?
Answer:
2:55 P.M
Step-by-step explanation:
After the movie: 10:26 A.M. + 2 hours and 51 minutes --> 1:17 P.M.
After the card game: 1:17 P.M. + 32 minutes --> 1:49 P.M.
After playing soccer: 1:49 P.M. + 1 hour and 6 minutes --> 2:55 P.M.
Are the following figures similar? (1 point)
Yes; the corresponding angles are congruent
No; the corresponding angles are not congruent
yes; the corresponding sides are proportional
no; the corresponding sides are not proportional
Answer:
yes the corresponding angles are congruent...
it can be wrong
Is -415 rational or irrational
Answer:
Rational
Step-by-step explanation:
Can convert it to a ratio (-415/1)
Answer:
Rational
Step-by-step explanation:
-415 is an integer. All integers are rational. It can be written as a fraction p/q, where p and q are integers and q is not equal to zero.
-415 can be written as [tex]-\frac{415}{1}[/tex].
Please help me with my question!!
Answer:
C
Step-by-step explanation:
Equation:
[tex]\frac{x}{-2}+\frac{y}{10}=1\\\\\frac{x*5}{-2*5}+\frac{y}{10}=1\\\\\frac{-5x}{10}+\frac{y}{10}=1\\\\-5x+y=10\\\\y=5x+10[/tex]
What are the zeros of the function g(x)=2(x+2)(x-9) located at
Answer:
x = - 2, x = 9
Step-by-step explanation:
Given
g(x) = 2(x + 2)(x - 9)
To find the zeros let g(x) = 0, that is
2(x + 2)(x - 9) = 0
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x - 9 = 0 ⇒ x = 9
The zeros of the function g(x)=2(x+2)(x-9) are -2 and 9.
What is the zeros and y-intercept of a function?Zeros is the Intersection points of the considered function's curve on input axis(usually represented by values of x)
y-intercept = Intersection points of the considered function's curve on output axis. On x-axis, value of y-coordinate is 0, On y-axis, value of x-coordinate is 0.
Thus, if function is y=f(x) then putting y = 0 gives zeros of the function.
And putting x = 0 gives the y-intercept of the function. (if any, for both cases).
Given the function as;
g(x) = 2(x + 2)(x - 9)
To find the zeros let g(x) = 0, that is;
2(x + 2)(x - 9) = 0
Then Equate each factor to zero and solve for x;
x + 2 = 0 ⇒ x = - 2
x - 9 = 0 ⇒ x = 9
Hence, the zeros of the function g(x)=2(x+2)(x-9) are -2 and 9.
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What is the area of a rectangle with length (3^2)^2 meters and width of 3^2 meters?
Answer:
729m^2
Step-by-step explanation:
Area of rectangle = length x width
From the question, we know that length = 3^2^2 = 81 ( three squared is 9. Nine squared is 81)
width = 3^2 = 9.
Now for the area: length x width = 81 x 9 = 729m^2.
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The members of a basketball team need to
raise $895 for new uniforms. They already
have $351 from food sales. To raise the
remainder, they are planning a shoot-out
challenge. If 34 teams sign up, how much
must they charge per team to meet their
goal?
Answer:
$16
Step-by-step explanation:
First subtract $351 from $895 to find the dollar amount we're considering.
($895 - $351 = $544)
Then, divide the 34 teams into the $544 to yield the dollar amount each team should be charged. ($544 / 34 = $16)
Find the length of a. The length of the of the unknown leg is?
Answer:
10
Step-by-step explanation:
Pythagorean theorem
c² = a² + b²
26² = a² + 24²
a² = 26² - 24² = 100
a = √(100) = 10
The length of unknown leg will be a = 10 units
ConceptThe right angle triangle is given and the length of one side and length of hypotenuse are givenWe have to find the length of second sideSince the triangle given is right angle triangle we will use pythagorean theorem to find the length of third side.How to solve this problem?The steps are as follow:
The length of first side is 24 units and length of hypotenuse is 26 units and the second side is unknown which is taken as 'a' According to pythagorean theorem:(hypotenuse)^2 = (Side)^2 + (Side)^2
(26)^2 = (24)^2 + (a)^2
676 = 576 + (a)^2
(a)^2 = 676 - 576
(a)^2 = 100
a = 10 units
So the length of unknown leg will be a = 10 units
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please help , factor 6x^2-33x+15 A. 3(2x-5)(x+1) B. 3(x+1)(2x+5) C. 3(2x-1)(x+5) D. 3(x-5)(2x-1)
Answer:
D
Step-by-step explanation:
Since the end term is positive, we know the 1 and 5 must both be positive or negative. However since -33x is negative, we know 1 and 5 are both negative too
Answer:
3(2x-1 )(x-5 )
Step-by-step explanation:
6x^2-33x+15
Factor out the greatest common factor
3(2x^2 -11x +5)
Factor inside the parentheses
3(2x )(x )
We need to get to -11 so the the only factors of 5 are 1 and 5 and they have to be negative
3(2x-1 )(x-5 )
2 * -5 + -1 = -10-1 = -11
f(0) = g(0)
f(-2) = g(-2)
f(0) = g(-2)
f(-2) = g(0)
Answer:
f(-2) = g(-2)
PLEASE HELP. A Ferries wheel has a diameter of 100 ft. The center of the wheel is 60 feet off the ground. If it takes the Ferries wheel 12 seconds to make a full rotation, find the height of a rider 2 seconds after he passes position A, the right most point on the wheel.
Answer choices:
A. 103.30 ft
B. 80.34 ft
C. 74.40 ft
D. 101.96 ft
Answer:
lresaputa es la C
Step-by-step explanation:
If /61 is the longest side length in the triangle, find the value of x that makes the triangle above a right triang
answer in simplest radical form.
A. 5
B. 6
C. 2V15
D. 6V10
Answer:
A. 5
Step-by-step explanation:
The longest side of the right triangle is the hypotenuse and it is √61 units. The other legs of the triangle is x unit and (x + 1) units.
From Pythagoras theorem for right angle triangle, the square of the hypotenuse is equal to the sum of the square of the other sides of the triangle. This implies that:
(√61)² = (x)² + (x + 1)²
x² + x² + 2x + 1 = 61
2x² + 2x + 1 - 61 = 0
2x² + 2x -60 = 0
Dividing through by 2 gives:
x² + x - 30 = 0
x² + 6x - 5x - 30 = 0
x(x + 6) -5(x + 6) = 0
(x-5)(x+6) = 0
x-5 = 0 or x+6 = 0
x = 5 or x = -6
Since the length of a side cannot be negative, x = 5 units
Answer:
The correct answer is A.
Step-by-step explanation:
X=5
Sue invests £9000 in an account for one year.
At the end of the year, interest is added to her account.
Sue pays tax on this interest at a rate of 20%
She pays £30.24 tax.
Work out the percentage interest rate for the account.
Answer:
£151.20
Step-by-step explanation:
20%= 100%divided by 5
To find 100% from 20% you x by 5
so you times 30.24 by 5
30.24x 5 = 151.2
So the answer is £151.20
interest percentage rate would be 1.6754%
The interest rate for the account is 1.68%
What is interest rate?The interest rate is the amount a lender charges a borrower and is a percentage of the principal the amount loaned.
Given that,
Sue invests £9000 in an account for one year.
She pays £30.24 at a rate of 20%
So, 20% of the interest = £30.24
Let the interest be x,
X0.2 = 30.24
X = £151.2
The total interest was = £ 151.2
The rate R at which generated this interest =
R = (100 × 151.2)/(1 × 9000)
R = 15120/9000
R = 1.68%
Hence, the interest rate = 1.68%
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For the graph of the rational function
f(x)=x^2-15+56 over
x+7, identity all discontinuities as either a removable discontinuity or a vertical asymptote
A.removable discontinuity at x=-7
B. Vertical asymptote is x=7
C.vertical asymptote is at x=-7
D. Removable discontinuity at x=7
There are 40 nickels in a roll. If you have 250 rolls of nickels, how many nickels do you have?pls help me
Answer:
10,000 nickles
Step-by-step explanation:
Since there are 40 nickles in a roll and you have 250, think that you have 250 sets of 40. This means that this question is a multiplication problem.
Multiply 40 x 250. This would give you 10,000.
Don't forget units.
The number of nickels in 250 rolls is 10000
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here, There are 40 nickels in a roll. If I have 250 rolls of nickels, then the number of nickels in total is = 250×40
= 10000
Hence, The number of nickels in 250 rolls is 10000
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A sphere has a radius of 16 in. Which statements about the sphere are true? Check all that apply. The sphere has a diameter of 8 in. The volume of the sphere is . The sphere has a diameter of 32 in. The radius’s length is one-half the length of the diameter. The volume of the sphere is . The diameter’s length is one-half the length of the radius.
Answer:
The sphere has a diameter of 32 in.
The radius’s length is one-half the length of the diameter.
Step-by-step explanation:
The diameter is the measurement of the line that starts at one end of a circle or a sphere and ends at the other end.
The radius is half the diameter. The radius goes from one end of the circle or sphere to the center.
So, if a sphere has a radius of 16 inches, it would have a diameter of 32 inches.
16 * 2 = 32
I cannot see the volume of the sphere.
[tex]V = \frac{4}{3}\pi r^3[/tex]
Using 3.14 for pi and 16 for 'r':
[tex]4/3 * 3.14 * 16^3\\\\4/3*3.14 *4096\\\\4.1866...*4096\\\\17148.3136[/tex]
The volume of the sphere is about 17148 cubic centimetres.
Answer:
c
Step-by-step explanation:
i did the test
8y⁷÷4y⁵ what is this answer
Answer:
Step-by-step explanation:
Terms with the exponents are like terms, we can subtract the exponents from each other when we divide.
(8y^7)/(4y^5) = 2y^(7-5) = 2y^2
Answer: [tex]2y^{2}[/tex]
Step-by-step explanation:
8/4=2
[tex]y^{7} / y^{5} =y^{7-5} =y^{2}[/tex]
so the answer is 2y^2
If 65% of the light are on what percent of the lights are off
Answer:
since 100% is everything
100 - 65 = 35%
Step-by-step explanation:
35% of the lights are off
Answer:
35% are off
Step-by-step explanation:
The lights are either on or off
That is 100%
100 -65 = 35
65% are on
35% are off
Please answer correctly !!!!!!!! Will mark brianliest !!!!!!!!!!!!
Answer:
Step-by-step explanation:
Since length times width = the area, you know that the area divided by the length is the width. This means that 6x^2 + 10 / 2 = the length.
6x^2 / 2 = 3x^2
10/2 = 5
You end up with 3x^2 + 5 as the length.
Answer & Step-by-step explanation:
Since you trying to find the width when you are given the length and the area, then you are going to divide the area by the length to get the width.
(6x² + 10) ÷ 2
We can also put this into a fraction so it will be easier to know what you are dividing.
[tex]\frac{6x^2+10}{2}[/tex]
Divide 6x² by 2 and divide 10 by 2. Keep the exponent because 2 does not have a variable.
So, your width will be 3x² + 5
Analyze the set below and answer the question that follows. (KUM) n (KUL) Which Venn diagram has shading that represents the given set?
Answer:
Choice A. The shading in the Venn Diagram shown in the first attachment represents the set [tex](K \cup M) \; \cap \; (K \cup L)[/tex].
Step-by-step explanation:
Let [tex]A[/tex], [tex]B[/tex], and [tex]C[/tex] be sets. By the distributive law of sets, [tex]A \cup (B \cap C)[/tex] and [tex](A \cup B) \cap (A \cup C)[/tex] refer to the same set.
Apply this property to simplify the given expression:
[tex]\begin{aligned}(K \cup M) \; \cap\; (K \cap L) = K\cup (M \cap L)\end{aligned}[/tex]
[tex]M \cap L[/tex] refers to the intersection between the two lower circles. The union of that intersection with set [tex]K[/tex] (the upper circle) would be the shaded region seen in choice A.
. 4/18 times 2/92. 1/9 times 3/63. 12/14 times 1/84.1/7 times 5/65. 17/20 times 1/61. 4 1/4 times 3 1/22. 3 5/6 times 4 1/23. 2 1/2 times 4 7/84.3 3/5 times 2 3/85. 3 1/2 times 3 3/8Whoever can solve at least 2 from each set is awesome!
Answer:
Step-by-step explanation:
4/18×2/92
=1/9×1/23
=1/207
1/9×3/63
=1/3×1/23
=1/69
12/14×1/84
=1/14×1/7
=1/98
1/7×5/65
=1/7×1/13
=1/91
17/20×1/61
=17/1220
4 1/4 ×3 1/22
=17/4×67/22
=1,139/88
=12 83/88
3 5/6×4 1/23
=23/6×93/23
=93/6
=15 3/6
=15 1/2
2 1/2×4 7/84
=5/2×343/84
=1715/168
=10 35/168
I have answered more than 2 from each set
Choose the kind(s) of symmetry: point, line, plane, or none.
(A)
none
plane
point
line
it would be a Line
The line would be vertical right through the middle
can i get brainliest?
NEED HELP ASAP! Arianna correctly simplified an expression. When she substituted \ into the simplified expression, the value was –4. Which could be Arianna’s original expression? One-sixth (negative 3 x minus 24) One-sixth (negative 5 x minus 8) One-sixth (negative 10 x minus 4) One-sixth (negative 12 x minus 16).
Answer:
(1/6)(-10x - 4) = -4
Step-by-step explanation:
(1/6)(-3x - 24) = -4
=> -3x - 24 = -4 x 6
=> -3x - 24 = -24
=> -3x = 24 - 24
=> -3x = 0
=> x = 0 (not 2) => Incorrect option
(1/6)(-5x - 8) = -4
=> -5x - 8 = -4 x 6
=> -5x - 8 = -24
=> -5x = 8 - 24
=> -5x = -16
=> x = 16/5 (not 2) => Incorrect option
(1/6)(-10x - 4) = -4
=> -10x - 4 = -4 x 6
=> -10x - 4 = -24
=> -10x = 4 - 24
=> -10x = -20
=> x = 2 => Correct option
(1/6)(-12x - 16) = -4
=> -12x - 16 = -4 x 6
=> -12x - 16 = -24
=> -12x = 16 - 24
=> -12x = 8
=> x = -3/4 (not 2) => Incorrect option
=> Option C is correct
Hope this helps!
Answer: C. One-sixth (negative 10 x minus 4)
Step-by-step explanation: On Edgenuity!!!!!!!!!!!!!
A boy is playing ball in a garden surrounded by a wall 2.5 m high kicks the ball vertically up from a height of 0.4 m with a spee d of 14 m/s.For how long is the ball above the height of the wall .
Answer:
2.5 sec
Step-by-step explanation:
Height of wall = 2.5 m
initial speed of ball = 14 m/s
height from which ball is kicked = 0.4 m
we calculate the speed of the ball at the height that matches the wall first
height that matches wall = 2.5 - 0.4 = 2.1 m
using [tex]V^{2}[/tex] = [tex]U^{2}[/tex] + 2as
where a = acceleration due to gravity = -9.81 m/s^2 (negative in upwards movement)
[tex]V^{2}[/tex] = [tex]14^{2}[/tex] + 2(-9.81 x 2.1)
[tex]V^{2}[/tex] = 196 - 41.202
[tex]V^{2}[/tex] = 154.8
v = [tex]\sqrt{154.8}[/tex] = 12.44 m/s
this is the velocity of the ball at exactly the point where the wall ends.
At the maximum height, the speed of the ball becomes zero
therefore,
u = 12.44 m/s
v = 0 m/s
a = -9.81 m/s^2
t = ?
using V = U + at
0 = 12.44 - 9.81t
-12.44 = -9.81
t = -12.44/-9.81
t = 1.27 s
the maximum height the ball reaches will be gotten with
[tex]V^{2}[/tex] = [tex]U^{2}[/tex] + 2as
a = -9.81 m/s^2
0 = [tex]14^{2}[/tex] + 2(-9.81s)
0 = 196 - 19.62s
s = -196/-19.62 = 9.99 m. This the maximum height reached by the ball.
height from maximum height to height of ball = 9.99 - 2.5 = 7.49 m
we calculate for the time taken for the ball to travel down this height
a = 9.81 m/s^2 (positive in downwards movement)
u = 0
s = 7.49 m
using s = ut + [tex]\frac{1}{2}[/tex]a[tex]t^{2}[/tex]
7.49 = (0 x t) + [tex]\frac{1}{2}[/tex](9.81 x [tex]t^{2}[/tex] )
7.49 = 0 + 4.9[tex]t^{2}[/tex]
[tex]t^{2}[/tex] = 7.49/4.9 = 1.53
t = [tex]\sqrt{1.53}[/tex] = 1.23 sec
Total time spent above wall = 1.27 s + 1.23 s = 2.5 sec
The standard form of the equation of a parabola is y=1/2x^2 - 4x+21. What is the vertex form of the equation?
Answer:
y=1/2*(x-4)^2+13
Step-by-step explanation:
Answer:
y=1/2*(x-4)^2+13
Step-by-step explanation:
