According to the rational root theorem, -7/8 is a potential rational root of: A. f(x) = 24x⁷ + 3x⁶ + 4x³ - x - 28.
What is a rational root theorem?A rational root theorem is also referred to as rational root test and it states that when the coefficients of a polynomial are integers, all of the possible rational roots can be determined by dividing each factor of the constant term by each factor of the coefficient of the highest power (leading coefficient).
In Mathematics, the canonical form for a polynomial in one variable (x) is given by:
[tex]a_n x^n + a_{n-1} x^{n-1} +a_1 x^1 +a_0=0[/tex]
Therefore, the potential rational root of the above polynomial is ±factors of a₀ dividided by ±factors of [tex]a_n[/tex] i.e ([tex]\pm a_0/\pm a_n[/tex]).
For this exercise, -7/8 is a potential rational root of f(x) = 24x⁷ + 3x⁶ + 4x³ - x - 28 in accordance with rational root theorem;
Factors of the leading coefficient are: 24: ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.Factors of the constant term are: 28: ±1, ±2, ±4, ±7, ±14, ±28.Potential rational root is: ±7/8.Read more on rational root theorem here: https://brainly.com/question/10937559
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Find the remainder of 2338when divided by 55. b) What is the inverse of 23 modulo 55 i.e. which number a has the property that 23*a has the remainder 1 when divided by 55?
a) 2338 ≡ 42 • 55 + 28 ≡ 28 (mod 55)
b) We want to find a such that
23a ≡ 1 (mod 55)
Use the Euclidean algorithm:
55 = 2 • 23 + 9
23 = 2 • 9 + 4
9 = 2 • 4 + 1
⇒ 1 = 9 - 2 • 4
⇒ 1 = 9 - 2 • (23 - 2 • 9) = 5 • 9 - 2 • 23
⇒ 1 = 5 • (55 - 2 • 23) - 2 • 23 = 5 • 55 - 12 • 23
Solve for a :
5 • 55 - 12 • 23 ≡ 1 (mod 55)
⇒ -12 • 23 ≡ 1 (mod 55)
⇒ a ≡ -12 ≡ 43 (mod 55)
HELP PLEASE ILL GIVE BRAINLEST
Answer:
y= 40 degree
Step-by-step explanation:
ACD+CDA+DAC= 180 degree
y+ 90+30+20= 180 degree
y+140 = 180
y= 180- 140 degree
y= 40 degree
Hope it helps you :)))))
have a good day
A box of chocolates contains 10 milk chocolates, 8 dark chocolates and 6 white chocolates. Sung randomly chooses a chocolate, eats it, then randomly chooses another. What is the probability Sung chose a milk chololate then a white chocolate
Using it's concept, it is found that there is a 0.1087 = 10.87% probability Sung chose a milk chocolate then a white chocolate.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that:
Initially, there are 10 + 8 + 6 = 24 chocolates, out of which 10 are milk, hence the probability of eating a milk chocolate first is given by: [tex]\frac{10}{24} = \frac{5}{12}[/tex].Then, there will be 23 chocolates, out of which 6 will be white, hence the probability of eating a white chocolate first is given by: [tex]\frac{6}{23}[/tex].Thus, the probability of milk then white is given by:
[tex]p = \frac{5}{12} \times \frac{6}{23} = \frac{30}{12 \times 23} = 0.1087[/tex]
0.1087 = 10.87% probability Sung chose a milk chocolate then a white chocolate.
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How many pencils did kyle purchase?
Answer:
he purchased 12 pencils
Step-by-step explanation:
1.24x12=14.88
14.88-20= 5.12
also this kid i knew has the same pfp
What point can be found by taking the average of the endpoints of a line
segment?
O A. Endpoint
O B. Vertex
O C. Midpoint
O D. Center
Step-by-step explanation:
C. Midpoint
The average is the distance of the line divided by 2
Identify the CENTER: (x+3)^2 + (y-2)^2 = 64 *
(3,-2)
(9,4)
(-3,2)
8
Answer:
centre = (- 3, 2 )
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius )
(x + 3)² + (y - 2)² = 64 ← is in standard form
with centre (- 3, 2 )
I SWEAR IF YOU HELP ME ILL FRL LOVE YOU FOR FREAKING EVERRR
Drag each tile to the correct box. arrange the functions in ascending order, starting with the function that eventually has the least value and ending with the function that eventually has the greatest value. 3x 8 4x 3 x2 6 3x 4x x2 ↓ ↓ ↓ ↓ ↓
The functions in ascending orders are:
1. 3x
2. 3x + 8
3. x^2
4. x^2 + 6
5. 4^x
6. 4^x + 3
What is a function?A function is known to be that relation that is said to exist between a set of numbers that is known to be having one output each.
Note that in the above such as 3x, 3x + 8, the functions in ascending orders as it start with the function that has it least value.
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Nguyen makes two slices through a three-dimensional object. One plane is parallel to the base; the cross-section is a square. The other plane is perpendicular to the base; the cross-section is a triangle. What three-dimensional shape did Nguyen cut?
Answer:
the answer to your question is pyramid
PLEASE ANSWER 50 POINTS!!
what is [4^2+(5+3x4)]x3=
Answer:
[( 4² + 5 + 3 × 4 )] × 3
= ( 4 × 4 ) + 5 + 3 × 4 × 3
= 16 + 5 + ( 3 × 4 × 3 )
= 16 + 5 + ( 12 × 3 )
= 16 + 5 + 36
= 21 + 36
= 57
Answer:
99
Step-by-step explanation:
pemdas states:
PARENTHESIS
EXPONENTS
MULTIPLICATION/DIVISION (left to right)
ADDITION/SUBTRACTION (left to right)
the first equation you would do is 3*4 as it is in the most inner parenthesis and is a multiplication equation
3*4 = 12
then add 12 to 5
12 * 5 = 17
(4^2 + 17) * 3 is what you have left
the next thing you do is the exponent
4^2 is 4*4 or 16
then add 16 to 17
16 + 17 = 33
then at the end
you multiply it by 3
33 * 3 = 99
your answer is 99
Ali divided one fruit cake equally among six persons. What part of the cake he gave to each person?
Step-by-step explanation:
when we divide something equally among n people, it means we divide it equally into n parts, and every part is 1/n or 1 nth.
so, for six people or parts, everybody got 1/6 or 1 sixth of the cake.
Sam walks 100 m north and then 100 m east. How far is she from her starting position? Give your answer to a sensible degree of accuracy.
Answer- 200m
: Right now Sam is 200m far from her starting point
please help !!! its math problem i give brainlist What type of function is represented in the table below?
Answer:
linear is correct
Step-by-step explanation:
please solve this problem using the pythagorean theorem, and give me the right answer and I will give you brainliest. :)
========================================================
Explanation:
Check out the diagram below.
a = 6.3 inchesb = 6.3 inchesc = unknown hypotenuseUse the Pythagorean Theorem to find the length of c.
[tex]a^2 + b^2 = c^2\\\\c = \sqrt{a^2 + b^2}\\\\c = \sqrt{(6.3)^2 + (6.3)^2}\\\\c = \sqrt{39.69+39.69}\\\\c = \sqrt{79.38}\\\\c \approx 8.9095\\\\c \approx 8.9\\\\[/tex]
The distance from one corner to the opposite corner is about 8.9 inches.
So, I'm trying to solve this question but I can't quite jog my mind, A little help here maybe > Forest City has ordered 36 maple trees and 54 dogwood trees to be planted in groups in a city park. Each group will have the same number of maple trees and dogwood trees.
By finding common factors, we conclude that we can divide the trees in 6 or in 9 parts, but not in 8.
Can the trees be planted in 6, 8, or 9 parts?We know that each of these parts needs to have the same number of each type of trees.
So we need to see if 6, 8, or 9, are common factors between 36 and 54.
First:
6*6 = 36
9*4 = 36
So 9 and 6 are factors of 36.
And 9*6 = 54
So 9 and 6 are factors of 54.
(8 is not a factor of neither)
So 9 and 6 are common factors between 36 and 54.
Then we can divide the trees in 6 or in 9 parts, but not in 8.
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A rectangular room is 12 1/2 feet long and 10 1/3 feet wide. What is the area of the room?
Answer: 20
Step-by-step explanation: 12 1/2x10 1/3=20
A phone case comes in 8 different colors, and you can also pick from 10 different patterns. If you can only pick one of each, how many different phone cases can there be
Answer:
80
Step-by-step explanation:
8 different colors multiplied by 10 different patterns
pls answer the question i am mark in brainlist
Answer:
x = -2
Step-by-step explanation:
Given: [tex]\textsf{$\dfrac{x+3}{x+4}=\dfrac{x+5}{x+8}$}[/tex]
1. Cross-multiply
(x + 3)(x + 8) = (x + 5)(x + 4)
2. Distribute
⟹ (x + 3)(x + 8) = (x + 5)(x + 4)
⟹ x(x) + x(8) + 3(x) + 3(8) = x(x) + x(4) + 5(x) + 5(4)
⟹ x² + 8x + 3x + 24 = x² + 4x + 5x + 20
3. Combine like terms
⟹ x² + 8x + 3x + 24 = x² + 4x + 5x + 20
⟹ x² + 11x + 24 = x² + 9x + 20
4. Subtract x² from both sides
⟹ x² - x² + 11x + 24 = x² - x² + 9x + 20
⟹ 11x + 24 = 9x + 20
5. Subtract 24 from both sides
⟹ 11x + 24 - 24 = 9x + 20 - 24
⟹ 11x = 9x - 4
6. Subtract 9x from both sides
⟹ 11x = 9x - 4
⟹ 11x - 9x = 9x - 9x - 4
⟹ 2x = -4
7. Divide both sides by 2 to isolate the variable
⟹ 2x ÷ 2 = -4 ÷ 2
⟹ x = -2
What is the measure of "?"
Answer:
60
Step-by-step explanation:
The surface area of a cone is square units. the height of the cone is times greater than the radius. what is the length of the radius of the cone to the nearest foot? the radius is about feet.
The radius of the cone is 7 feet
How to determine the radius?The given parameters are:
Surface Area, A = 216π
h = 8/3r
The surface area of a cone is:
[tex]A = \pi r(r + \sqrt{h^2 + r^2})[/tex]
So, we have:
[tex]216\pi = \pi r(r + \sqrt{(8/3r)^2 + r^2})[/tex]
Factor out r
[tex]216\pi = \pi r(r + r\sqrt{(8/3)^2 + 1})[/tex]
Evaluate the exponent
[tex]216\pi = \pi r(r + r * 2.85)[/tex]
Evaluate the sum
[tex]216\pi = \pi r(3.85r)[/tex]
Divide both sides by pi
[tex]216 = 3.85r^2[/tex]
Divide both sides by 3.85
[tex]56.10 = r^2[/tex]
Take the square roots of both sides
r = 7 (approximately)
Hence, the radius of the cone is 7 feet
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Answer:
The radius is about 9 feet.
Hope this helps!
Step-by-step explanation:
( i will give brainlist ) What is the equation of the following graph?
Answer:
y= ⅓x +2
Step-by-step explanation:
Since the graph is a linear graph, let's use the slope-intercept form to find its equation.
Slope-intercept form
y= mx +c, where m is the slope and c is the y-intercept.
The y-intercept is the point at which the graph cuts through the y-axis. In this case, the y-intercept is 2.
Thus, y= mx +2.
Let's find the slope of the graph.
First, identify 2 pairs of coordinates from the graph:
(0, 2) and (3, 3)
Next, substitute these coordinates into the slope formula below:
[tex]\boxed{ \text{slope} = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
slope
[tex] = \frac{3 - 2}{3 - 0} [/tex]
[tex] = \frac{1}{3} [/tex]
Thus, the equation of the graph is y= ⅓x +2.
I have absolutely no idea what to do here. Can someone break this down for me please?
Answer:
Step-by-step explanation:
The task is to draw the parabola of the equation [tex]x^{2} -4x+4[/tex] on the given graph.
The first step we can take to doing this is to use the table on the left hand side to work out our x and corresponding y-values to use as plotting coordinates. To do this you want to substitute the given value for x which will give you a corresponding y-value.
E.g:
x | [tex]x^{2} -4x+4[/tex] | y
0 | [tex](0)^{2} -4(0)-4[/tex] | -4
Here we have gotten the coordinates (0, -4) so this will be a point on the graph.
Repeat with all other values on the table and you should get a bunch of dots which lead upwards in a curved line from a point. Extend the lines to form a parabola shape (A u-shape).
Once you have drawn the graph, label the parts.
Roots: The places where the line crosses the x-axis
Vertex: The lowest point of the parabola
Line of symmetry: The vertical line in which the parabola reflects/ is the same either side (Has equation x=_).
y-intercept: The point where the line crosses the y-axis.
Hope this helped!
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Length be x
width be x-5
So
Area=Length×Breadth
x(x-5)=750Or
If x turned y
y(y-5)=750750-y(y-5)=0Option C
Option A can be true as per commutatI've property
y²-5y=750Option B is true
Answer:
y² - 5y = 750
750 - y(y - 5) = 0
(y + 25)(y - 30) = 0
Step-by-step explanation:
Formula
Area of a rectangle = length × width
Given:
y = length of the room(y - 5) = width of the room750 ft² = area of the roomSubstituting the given values into the formula and rearranging in different way:
Equation 1
⇒ 750 = y(y - 5)
⇒ y(y - 5) = 750
⇒ y² - 5y = 750
Equation 2
⇒ 750 = y(y - 5)
⇒ 750 - y(y - 5) = 0
Equation 3
⇒ 750 = y(y - 5)
⇒ y(y - 5) - 750 = 0
⇒ y² - 5y - 750 = 0
⇒ y² - 30y + 25y - 750 = 0
⇒ y(y - 30) + 25(y - 30) = 0
⇒ (y + 25)(y - 30) = 0
The patel family went to a festival. the family is made up of 2 adults and 3 children. admission to the festival is $22.00 for adults and $15.00 for children. how much did the family spend to enter the festival? the family spent $ .00 to enter the festival. please help d:
Answer:$89.00
Step-by-step explanation:22 times 2 is 44.
15 times 3 is 45.
44 plus 45 is 89
Answer:
$89.00
Step-by-step explanation:
2 adults = $22 x 2 = $44
3 children = $15 x 3 = $45
$44 + $45 = $89.00
Hope this helps!
(I will mark brainliest) Will 3/8 + 2/8 be closer to 1/2 or 1? How do you know?
Answer:
1/2
Step-by-step explanation:
3/8 + 2/8 is 5/8, 1/2 is equal to 4/8, so 5/8 is only 1/8 away from 1/2 while 5/8 is also 3/8 away from 1 or 8/8 therefore, it is closer to 1/2
CAN SOMEONE PLS HELP ME
Answer:
no i cannot help you
Step-by-step explanation:
thats good
five numbers have a mean of 3. four of the numbers are 7,5,2,-4. what is the 5th number?
Answer: The fifth number is 5
Step-by-step explanation:
Evaluate 8 7/8 + (7 5/6−2 1/3)
Answer:
14.375 Or 115/8
Step-by-step explanation:
since 8 7/8 = 71/8 and 7 5/6 = 47/6 and 2 1/3 = 7/3
then 71/8 + ( 47/6 - 7/3) = 115/8
HELP PLEASE!!
5⁸/5³=
a. 5^-5
b. 1¹¹
c. 5⁵
d. 5 ¹¹
Answer:
C
Step-by-step explanation:
[tex] \frac{ {5}^{8} }{ {5}^{3} } \\ [/tex]
Now you may reduce the fraction
[tex] = {5}^{5} [/tex]
convert 221 quinary number into decimal number.
Step-by-step explanation:
______________________( First of all to convert quinary to decimal we need to multiply them by 5 )
So let's solve now.....
= 221
Solution,
Converting quinary number to decimal .....
= 2 × 5² + 2 × 5¹ + 1 × 5⁰
The value of any number to the power 0 is 1 ...
= 2 × 25 + 2 × 5 + 1 × 1
= 50 + 10 + 1
= 61..
______________________Hence the answer is 61....
______________________