Theorem : Let p be a prime number. If p divides a² , (where a is a positive integer), then p divides aLet say prime factors of a area = p₁ , p₂ , p₃ ........., pₓ where p₁ to pₓ are prime numbera = (p₁ × p₂ × p₃ ×.........× pₓ)a² = (p₁ × p₂ × p₃ ×.........× pₓ) (p₁ × p₂ × p₃ ×.........× pₓ)if p divides a² then it is one of (p₁ × p₂ × p₃ ×.........× pₓ)as a = (p₁ × p₂ × p₃ ×.........× pₓ) so p divides aVerification forp = 2, p = 5 and for a square = 1, 4, 9, 25, 36, 49, 64 and 81.2 is factor of 4 , 36 & 642 is factor of 2 , 6 & 85 is factor of 255 is a factor of 5 also
Which second degree polynomial function has a leading coefficient of –1 and root 4 with multiplicity 2? f(x) = –x2 – 8x – 16 f(x) = –x2 8x – 16 f(x) = –x2 – 8x 16 f(x) = –x2 8x 16
Using the Factor Theorem, the second degree polynomial function that has a leading coefficient of –1 and root 4 with multiplicity 2 is given by:
f(x) = -x² + 8x - 16
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
In this problem, we have that:
The leading coefficient is of a = -1.There is a root of 4 with multiplicity 2, hence [tex]x_1 = x_2 = 4[/tex].Thus, the polynomial is given by:
f(x) = -(x - 4)(x - 4)
f(x) = -(x² - 8x + 16)
f(x) = -x² + 8x - 16
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number 1 is the question
Which of the following is an example of a theorem?
A. Two points determine a line.
B. Vertical angles are congruent.
C. Any angle is congruent to itself.
D. If two planes intersect, then their intersection is a line.
Answer:
D
Step-by-step explanation:
Just ask :)
Help with this trying to get extra credit
Answer: 21 is the range
Step-by-step explanation: You keep asking questions about things like this so I deliver
Range is the Largest number and then subtract it by the smallest number, the largest is 44 and smallest is 23 so 44 - 23 is 21
Find the volume of the figure.
____cm3
What is the area of this circle?
Answer:
pie * r^2 bro where r= 10mi
The volume of a cylinder with a radius of 15 m and a height of 7 m.
radius (r) = 15m
height (h) = 7m
To find: The volume of cylinder We know that,Volume of cylinder:[tex]\pi {r}^{2} h[/tex]
By the using the formula,we get[tex] \frac{22}{7} \times (15) \times (15) \times 7 \\ \\ = 22 \times 225 \\ \\ = 4950[/tex]
Therefore, the volume of the cylinder is 4950 m³Hope it helpsThe midpoint of EF is M(2, -3). One endpoint is E(-3, 2). What is the x-value of the coordinate of endpoint F.
Answer: 7
Step-by-step explanation:
The scatterplot shows the amount of sunlight some tomato plants received and the amount each plant grew.
The scatterplot shows the amount of sunlight some tomato plants received and the amount each plant grew
Based on the data there is no association between the number of hours of sunlight a plant receives and how much it grows.
Based on the data there is no association between the number of hours of sunlight a plant receives and how much it grows.
True or False
Answer:
false
Step-by-step explanation:
an item is regularly priced at 60$ Carmen bought it at a discount of "70 %" off the regular price. How much did carmen play?
Factor x2 + x – 42.
An x-method chart shows the product negative 42 at the top of x and 1 at the bottom of x. 7 is on the left side of x and negative 6 is on the right side.
Use the completed X diagram to replace the x-term in the trinomial with two x-terms.
x2 + x – 42 = x2 +
– 42
Next, use double grouping to factor the four terms.
= x(
)–
(x + 7)
=
To verify,
the factors.
-- - - -- - - - - - - - - -- - - - - - - - - - - - -- - - - - - - - - - - - - - -- - - - - - -- - - - --
[tex]\blue\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]
Factor x²+x-42
[tex]\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}[/tex]
First, think of two numbers such that
If we multiply them we'll get -42If we add them we'll get 1These numbers are:-
7 and -6
Write them here:-
(x+7)(x-6)
Note:-
We don't have to use the Big X method, since the coefficient of x² is 1.
If it's greater than 1, like 2, then the Big X method comes in handy.
Good luck.- - - - -- -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Answer:
1. 7x-6x
2. x+7
3. 6
4.(x-6)(x+7)
5. multiply
Step-by-step explanation:
Your+required+return+is+14%. +should+you+accept+a+project+with+the+following+cash+flows
By using an excel spreadsheet and IRR function, the cross over rate = 14.85%
Year Cash Flow (A) Cash Flow (B)
0 -58,000 -58,000
1 34,000 21,200
2 28,000 25,200
3 20,000 30,000
4 13,600 25,200
What is the IRR for each of these projects?using an excel spreadsheet and the IRR function:
Project A's IRR = 28.3%
Project B's IRR = 25.7%
(b) If you apply the IRR decision rule, which project should the company accept?
Project A (its IRR is higher)
Requirement 2:
(a) Assume the required return is 14 percent. What is the NPV for each of these projects?
using an excel spreadsheet and the NPV function:
Project A's NPV = $14,921.37
Project B's NPV = $15,156.64
(b) Which project will you choose if you apply the NPV decision rule?
Project B (its NPV is higher)
Requirement 3:
(a) Over what range of discount rates would you choose Project A?
higher than 14.85%
(b) Over what range of discount rates would you choose Project B?
lower than 14.85%
(c) At what discount rate would you be indifferent between these two projects?
crossover rate calculation
Year Cash Flow (A) Cash Flow (B) differential amount
0 -58,000 -58,000 $0
1 34,000 21,200 $12,800
2 28,000 25,200 $2,800
3 20,000 30,000 -$10,000
4 13,600 25,200 -$11,600
using an excel spreadsheet and IRR function, the cross over rate = 14.85%
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if you flip 100 coins what is the probability of 50 being heads and 50 being tails
Answer:
1/2
Step-by-step explanation:
it is going to be 1/2 because you you have a 1 out of 2 chance of getting heads or
tails on any of them.
Answer:
if you
flipped a coin 100 times you saw the ratio of head and tails to be 50/50. They created a diagram of all the flips. There was a lot of flip-flopping between heads and tail.
Step-by-step explanation:
The legs of a right triangle are lengths 48cm and 55cm. What is the length of the hypotenuse?
The legs of a right triangle are lengths 48cm and 55cm. So, the length of the hypotenuse is 73 cm.
What is the Pythagoras theorem?The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
The legs of a right triangle are lengths 48cm and 55cm.
Let ABC be the right angle triangle and AB is the hypotenuse.
To find the length of the hypotenuse we will use the Pythagoras theorem,
[tex]AB^2 = BC^2 + AC^2\\\\AB^2 = 48^2 + 55^2\\\\AB^2 = 2304 +3025\\\\AB^2 = 5329\\\\AB = \sqrt{5329} \\\\AB = 73[/tex]
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PLEASEEE HELPP ME!!!!!!!!!!!
Answer: it’s all about the angle and length of it
Step-by-step explanation:
1st get sumthing that’s as long as that
2st do u see the point and what it’s touching use that follow alone with it
3
Answer:
they warned me and deleted my answer for no reason i think its because i sent a link to a calculator
Step-by-step explanation:
but the answer is the last one yes
helpppp!!!!!!!!!!! i’m so confused
Answer:
first thing: 1/2=2/4
then we change -3/4+1/2 to -3/4+2/4 (it's the same thing)
then it's gonna be -3+2/4
answer= -1/4
help me solve this problem please
Answer:
Step-by-step explanation:
If you put all the numbers on the number line it would be, -4/3, -4/5, -2/3, 7/10, 7/10, so the correct answer is letter A.
A parallelogram has a base that is 10.2 centimeters long and a height that measures 5 centimeters. What is the area of the parallelogram?
The area of the parallelogram is the product of length and height. Then the area of the parallelogram will be 51 square cm.
What is a parallelogram?It is a polygon with four sides. The total interior angle is 360 degrees. A parallelogram's opposite sides are parallel and equal.
A parallelogram has a base that is 10.2 centimeters long and a height that measures 5 centimeters.
Then the area of the parallelogram will be
Area = bh
Area = 10.2 x 5
Area = 51 square cm
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from the topic:areas and volumes
this question is unambiguous.
PLEASEEE HELP ITS WORTH 20 , the first 2 questions are yes or no !
by following the rule that the sum of two sides must exceed that of the last, a. is true and b. is false
A parallelogram in a coordinate plane is reflected over the line y=5 and translated 2 units left and 1 unit down.
Which statement is true?
The resulting parallelogram is not congruent to the original parallelogram regardless of the order of the transformations.
The resulting parallelogram is not congruent to the original parallelogram regardless of the order of the transformations.
The resulting parallelogram is congruent to the original parallelogram only if the reflection occurs first.
The resulting parallelogram is congruent to the original parallelogram only if the reflection occurs first.
The resulting parallelogram is congruent to the original parallelogram regardless of the order of the transformations.
The resulting parallelogram is congruent to the original parallelogram regardless of the order of the transformations.
The resulting parallelogram is congruent to the original parallelogram only if the translation occurs first.
The resulting parallelogram is congruent to the original parallelogram only if the translation occurs first.
Answer: The resulting parallelogram is congruent to the original parallelogram regardless of the order of the transformations.
Step-by-step explanation:
A reflection and a translation are both rigid motions, meaning both transformations preserve congruency.
Answer:
The resulting parallelogram is not congruent to the original parallelogram regardless of the order of the transformations.
Step-by-step explanation:
a. What can you conclude about LOBC? Justify your answer. b. Write and solve an equation to find the length of OE. c. Explain how you know your answer to part (b) is reasonable. d. How can you use the length you found in part (b) to find the length of one side of the red sail in the logo for the showroom display? What is that length?
The angle OBC is 90 degrees, the equation is 18r = 144, r = 8 feet, and the length of the AB is 16 feet which is the length of the red sail in the logo.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have the figure shown in the picture with dimensions.
a) As we can see, the AOB is the diameter of the circle which is perpendicular to the CBD
So the angle ∠OBC will be a right angle.
∠OBC = 90 degree.
b) Length OE is the radius of the circle.
Let's suppose OE = r
Then in a right angle triangle OBC where ∠OBC = 90 degrees.
Applying Pythagoras theorem:
OC² = CB² + OB²
(CE + OE)² = CB² + OB²
CE = 9 ft, OE = r, CB = 15 feet, and OB = r (radius of the circle)
(9 + r)² = 15² + r²
81 + 18r + r² = 15² + r²
18r = 144
r = 8 feet
OE = r = 8 feet
c)
As the angle ∠OBC = 90 degrees, that's why the triangle OBC becomes a right angle triangle and OB⊥CB.
d)
In the circle, there is a red triangle, we can find one of the lengths of the triangle which is AB.
AB is the diameter of the circle
r = 8
Diameter AB = double the radius = 2(8) = 16 feet
AB = 16 feet
Thus, the angle OBC is 90 degrees, the equation is 18r = 144, r = 8 feet, and the length of the AB is 16 feet which is the length of the red sail in the logo.
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What Is the solution for y?
3x-4=5y+3
Answer:
slope=1.200/2000=0.600
x-intercept =7/3=2.3333
y-intercept =7/-5--1.40000
Step-by-step explanation:
the x and y intercept and the aloe are called line of properties.
y tells us how far the line goes
x tells us how far it goes
m is the slope of gradient i.e. how steep the like is
bis y-intercept i.e. where the line line crosses the y
what has at least two pairs of consecutive sides are congruent,diagonals are perpendicular to one another,at least one pair of opposite sides are parallel to one another, and the quadrilateral cannot be inscribed in a circle
The quadrilateral that is described with the given properties is known as; Rhombus
How to identify quadrilaterals?
A quadrilateral is defined as a closed shape and a type of polygon that has four sides, four vertices and four angles.
Now, we are told that at least at least two pairs of consecutive sides are congruent, diagonals are perpendicular to one another.
The only quadrilaterals that fit into thus definition are square and rhombus.
Now, we are told that the quadrilateral cannot be inscribed in a circle. A square can be inscribed in a circle but not a rhombus and as such we can say that the quadrilateral with the given properties is a rhombus,
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Please help. What is this called.
Error Function of z {erf(z)}
Step-by-step explanation:
It is a much used function in statistics, fluid mechanics and thermodynamics.
It just tells the probability.
Find the area of a triangle with vertices A(0, 2), B(8, 2), and C(4, -3).
Answer:
20
Step-by-step explanation:
First, consider (0,2) and (8,2). The y-value is the same for both points. x ranges from 0 to 8, so the length of this horizontal side of the triangle is (8-0), or 8.
Again, this horiz. side has a y-value of 2.
The third point is (4,-3). Therefore the vertical distance from the horizontal line to the third point is 2 - (-3), or 5.
Thus, the "base" of the triangle is 8 and the "height" is 5.
The area is A = (bh)/2. Substitute the values 8 and 5. Simplify your result. Answer: 20 square units.
A distribution of scores on an aptitude test is Normally distributed with a mean of 80 and a standard deviation of 5. According to the Empirical Rule (68-95-99.7% Rule), approximately what percent of the values will be between 75 and 85
According to the Empirical Rule (68-95-99.7% Rule), approximately 68% percent of the values will be between 75 and 85.
What is empirical rule?According to the empirical rule, also known as 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95% and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.
[tex]P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) = 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) = 99.7\%[/tex]
Here, we had where mean of distribution of X is [tex]\mu[/tex] and standard deviation from mean of distribution of X is [tex]\sigma[/tex].
A distribution of scores on an aptitude test is Normally distributed with a mean of 80 and a standard deviation of 5.
[tex]\mu=80\\\sigma=5[/tex]
The percentage for the interval of values between 75 and 85 has to be found out. From the 68%, the interval is,
[tex]P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(80 - 5 < X < 80+ 5) = 68\%\\P(75 < X < 85) = 68\%[/tex]
Thus, according to the Empirical Rule (68-95-99.7% Rule), approximately 68% percent of the values will be between 75 and 85.
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What is the midpoint of AB?
Answer:
hence the midpoint of AB is 1/2,1
Step-by-step explanation:
A(-2,5)
B(3,-3)
now midpoint of AB is given by
[tex]mid \: point \: of \: ab = (\frac{ - 2 + 3}{2} ) \: ( \frac{5 - 3}{2} ) \\ = ( \frac{ 1}{2} ) \: (1)[/tex]
please help me with this question
Answer:
Step-by-step explanation:
lines cut by a transverse line which make angle x and y alternate exterior angles
Which function does the graph represent? What is the asymptote of the function?
5
5
5
On
4
النا
2
2
m
5
-1
-2
3
4
-5
The function is
B. Its asymptote is
e
Answer:
your new acc has not verify
plss try again!!
