Identify the binomial that is a factor of the polynomial P(x) = 2x^3 + 12x^2 − 26x − 84.
A. x+7
B. x-7
C. 2x-4
D. x+3

Answer:

b. 1,2,3,4,5,6

bc a dice has 6 sides

The remainder when 2 is divided by 1000 is 2

Let O be the center of the circle, R be the length of the radius, and let the chord be AB with midpoint M. Let x be the distance from O to M, then the length of the radius OM is R/2 and the length of the chord AB is 2x.

Since the chord is perpendicular to the radius at the midpoint, we know that the radius bisects the chord. Therefore, the two segments MO and MB are congruent and have length x.

The area of the larger region is the area of the sector OMB, which is (1/4) of the area of the circle. The area of the smaller region is the area of the triangle OMA, which is (1/2) of the area of the sector OMA.

The ratio of the larger region to the smaller region is (1/4) : (1/2) = 2 : 1.

So, the area of the larger region is twice the area of the smaller region.

We can see that abcdef = 21111*1 = 2, the remainder when 2 is divided by 1000 is 2. Thus, the answer is \boxed{002}.

To know more about Circle Cord Ratio visit :

https://brainly.com/question/11013575?referrer=searchResults

#SPJ4

Answer:

71

Step-by-step explanation:

I found the area by spliting the figure into the triangle, square, and rectangle

triangle = .5(14*5)=35

square = 2*2=4

rectangle = 8*4=32

35+4+32=71

hope this is right:)

if n is a positive integer: 1²+ 2² + 3² + ... +n² = 1/6n(n+1)(2n+1)​ IS 1

P(n) :

1²+ 2² + 3² + … +n² = 1/6n(n+1)(2n+1)​

P(1) :

[tex]1^2=\frac{1(1+1)(2(1)+1)}{6}[/tex]

[tex]1=\frac{6}{6}=1[/tex]

∴ LHS = RHS

Assume P(k) is true

P(k):

To learn more about integer, refer to:

https://brainly.com/question/929808

#SPJ1

Identification if a polynomial is a sum or difference of two cubes can be done by factorizing the provided polynomial.

A polynomial is a mathematical expression that is a sum of one or more terms. Each term is a constant or a variable raised to a non-negative integer power and multiplied by a coefficient. The degree of a polynomial is the highest degree of the terms in the expression. A polynomial with one variable is called a univariate polynomial, and a polynomial with more than one variable is called a multivariate polynomial. Polynomials are used in various areas of mathematics, physics, engineering, computer science, and other fields. They can be used to model a wide range of phenomena and to solve problems that involve polynomial equations or inequalities.

Factorization, also known as factoring, is the process of breaking down a mathematical expression into a product of simpler factors. The goal is to express a given expression as a product of simpler expressions, which can be useful in solving equations and understanding the structure of the expression.

Factor the polynomial completely into its irreducible factors.

Look for terms that are of the form (x - a)^3 or (x + a)^3, where a is a constant. These are the cubes that you are looking for.

If there are two such terms, check if they can be combined into a single term by adding or subtracting them. If they can, then the polynomial is a sum or difference of two cubes.

If there are more than two such terms, check if any two of them can be combined in the same way. If they can, then the polynomial is a sum or difference of two cubes.

To learn more about polynomials visit:

https://brainly.com/question/11536910

#SPJ4

Answer:

22 by 26

Step-by-step explanation:

10+10+14+14=48 (the perimeter)

48×2=96

10+12=22

14+12=26

22+22+26+26=96

Slope of the line AB is 7/6.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

From the given graph the coordinates of A are (4, 3) and B is (-2, -4)

Slope AB=-4-3/-2-4

=-7/-6

Slope=7/6

Hence, slope of the line AB is 7/6.

To learn more on slope of line click:

https://brainly.com/question/14511992

#SPJ1

Answer:

1.) 15

2.) 12.5

Step-by-step explanation:

h = 7 is the solution to the equation 1/ (h - 5) + 2/ (h + 5) = 16 / (h² - 25)

The meaning of such an equations in algebra is just a mathematical expression stating the equality between two mathematical terms. For instance, 6x + 5 = 11 is an equation where 6x + 5 and 11 are two expressions separated by the 'equal' sign.

Identity equations and conditional equations are the two types of equations. For just any value of both the variables, an equality remains true. Only such variables have values that make a condition expression true. Two expressions joined by an equals sign ("=") form an equation.

The equation given that,

1/ (h - 5) + 2/ (h + 5) = 16 / (h² - 25)

The least common multiple of the denominators is:

h² - 25 = (h - 5) (h + 5)

We multiply through with the LCM to obtain:

= [(h - 5) × (h + 5)] × [1 / (h - 5)] + [(h - 5) × (h + 5)] × [2 / (h - 5)]

= 16 / (h² - 25) × [(h - 5) × (h + 5)]

We cancel out common factors to obtain:

= 1 (h + 5) + 2 (h - 5)

= 16

We expand the brackets to obtain

= h + 5 +2h - 10

We group like terms to get:

h + 2h = 16 - 5 + 10

This simplifies to:

3h = 21

We now divide through by 3 to obtain:

h = 7

To know more about equation refer to:

brainly.com/question/22688504

#SPJ4

Answer:

D

Step-by-step explanation:

Earth's rotation and revolution are both very slow motions, so slow that we don't feel them. The rate of Earth's rotation is about 1,000 miles per hour, and the speed of its revolution is about 67,000 miles per hour, but both of those speeds are so slow that we don't feel any movement or acceleration.

Earth's rotation and revolution are both very slow motions, so slow that we don't feel them. The rate of Earth's rotation is about 1,000 miles per hour and its revolution is about 67,000 miles per hour, but both of these speeds are too slow to be felt.Earth's rotation and revolution are both very slow motions, so slow that we don't feel them. The speed of Earth's rotation is about 1,000 miles per hour, and the speed of its revolution is about 67,000 miles per hour, but both of those speeds are so slow that we don't feel any movement or acceleration.

Learn more about rate here

https://brainly.com/question/13481529

#SPJ4

The ratio of blue shirts to red shirts is 2:5, so for every five red shirts, there are two blue shirts.

Ratio is a mathematical term used to compare two different values. It is a way of expressing one quantity in relation to another. Ratios can be written as fractions, decimals, or percentages. Ratios are used in many different areas, such as finance, economics, science, and engineering. Ratios are also used to compare the size, speed, or cost of different items. Ratios can be used to compare parts of a whole, or to compare different items within a group.

Since there are 100 red shirts in the store, there are 40 blue shirts in the store (100 / 5 x 2 = 40).

To know more about ratio click-
https://brainly.com/question/25927869
#SPJ1

Using the provided equations, Applying the addition method in the system of equations, The answer is x=-2 and y =-6.

An equation is a statement of equality between two expressions, usually containing one or more variables. Equations can be used to express mathematical relationships and can be solved to find the value of the variables. Equations can take many forms, such as linear equations, quadratic equations, and differential equations. They can also be represented graphically.

The addition method to solve a system of equations is a way to solve a system of two linear equations by adding them together. The goal is to eliminate one variable by adding or subtracting the equations. We can eliminate one variable by adding the equations together. To do this, we'll add the left-hand side of the first equation to the left-hand side of the second equation and add the right-hand side of the first equation to the right-hand side of the second equation. It is important to note that the addition method works only when the coefficients of the variable you want to eliminate are opposite in sign.

4x-5y=22

3x+2y=-18

multiplying first equation with 3 and second equation with 4 and subtracting them , we eliminate x and solve for y,

y=-6

put y=-6 in first equation , we get x,

x=-2

To learn more about equations visit:

https://brainly.com/question/29657983

#SPJ1

Answer:

2x^2-6x^4-2

Step-by-step explanation:

Answer:

Remove parentheses.

−7x²−3[tex]x^{4}[/tex]−5−3[tex]x^{4}[/tex]+3+9x²

Add −7x² and 9x² .

2x²−3[tex]x^{4}[/tex]−5−3[tex]x^{4}[/tex]+3

Subtract 3[tex]x^{4}[/tex] from −3[tex]x^{4}[/tex].

2x²−6[tex]x^{4}[/tex]−5+3

Add −5 and 3.

2x²−6[tex]x^{4}[/tex]−2

Step-by-step explanation:

The equation of the line that passes through the points (−8, −10) and (6, 3)in slope-intercept form is y = (13/14) x - 18/7.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The slope-intercept form of the equation of a line is given by the formula:

y = mx + b

where m is the slope of the line

b is the y- intercept

Given the two points, (−8, −10) and (6, 3), get the slope of the line using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

m = (3 - -10) / (6 - -8)

m = 13 / 14

Using the slope-intercept form, plug in the value of the slope and one point to determine the y-intercept, b.

y = mx+ b

-10 = (13/14)(-8) + b

b = -18/7

Substitute the value of the slope and y-intercept in the slope-intercept form.

y = mx + b

y = (13/14) x - 18/7

Hence, the equation of the line in slope-intercept form is y = (13/14) x - 18/7.

To learn more about equation of the line in slope-intercept form: brainly.com/question/1884491

#SPJ4

Using percentage and equations, Greg has 734 songs, Raj has 426 songs and Mark has 720 songs

Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the percent symbol, "%". For example, 45% (read as "forty-five percent") is equal to 45/100, or 0.45. Percentages have no dimension, which it's why they are dimensionless number. for example 60% of a number, then it means 60 per cent of its whole.

In this problem, we can write an equations and solve to determine the number of songs Greg has on his computer.

Let;

Since Mark has 720 songs in his computer;

x = 14 + 720

x = 734

Greg has 734 songs

We can calculate the number of songs Raj has by;

y = 60%(720) - 6

y = [(0.6) * 720] - 6

y = 426

Learn more on percentage here;

https://brainly.com/question/843074

#SPJ1

Supposing the value of x to be an integer, the values of k that donot

satisfy the given equation 3x = k mod 6 are 1,2,4,5.

An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion.

Integers are a set of numbers that include both positive and negative numbers, as well as zero. Whole numbers, on the other hand, only include the set of non-negative numbers starting from 0 (i.e., 0, 1, 2, 3, 4, ...). In other words, whole numbers are a subset of integers.

If 3x = k mod 6 has no solutions in x, then k must not be divisible by 3. The positive integers less than 6 that are not divisible by 3 are 1, 2, 4, and 5. Therefore, k can take on 4 values: 1, 2, 4, and 5.

To learn more about solving equations visit:

https://brainly.com/question/29657983?

#SPJ4

Answer:

No, it is AAS.

Step-by-step explanation:

By vertical angle theorem ∠KLJ≅∠MLN.

And the given congruent sides are not between the two congruent angles, therefore it cannot be ASA.

Triangle KLJ ≅ Triangle MLN

Using the Pythagoras Theorem the third side c of the right-angled triangle is obtained as 6.5 units.

What is Pythagoras Theorem?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

The data given is -

Assume a, b and c are sides of right-angled triangle.

Then, two adjacent sides of right-angled triangle are -

a^2=29.25 squared units

b^2=13 squared units

The unknown side c is taken to be x.

Find the length of c using Pythagoras Theorem -

c^2=a^2+b^2

where, c is the hypotenuse, a is the perpendicular and b is the base.

Plugging the values in the equation -

x^2=29.25+13

x=√(29.25+13)

x=√42.25

x=6.5

Therefore, the third side measures x=6.5 units.

To learn more about Pythagoras Theorem from the given link

https://brainly.com/question/21332040

#SPJ4

Answer:

Well everyone does

Step-by-step explanation:

Answer:

A.) x + 3 and x + 2

Step-by-step explanation:

The trinomial which is factored as described is; x² + x - 6.

According to the question;

(x -1 -1)

x + 1 + 1 + 1

x²-2x +3x -6

Hence, the product of the factors is therefore;

From the description of the previous factors; the trinomial which is factored is; x² + x - 6.

Read more on trinomial factorisation;

https://brainly.com/question/25824273

Answer:

$2.31

Step-by-step explanation :

$16.17 divided by 7

The number of points is simply 5 times this random variable, and E(C*Y) = C*E(Y), where C is a constant and Y is a random variable, according to expected value principles. As a result, E(X) = 5*2 = 10.

The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Here,

The number of dice that are showing an even number is a binomial random variable with n = 4, and p = 1/2 (because half the faces on the die are even and half are odd).

The expected value of this random variable is n*p = 4*1/2 = 2.

The number of points is simply 5 times this random variable, and by the rules of expected value, E(C*Y) = C*E(Y), where C is a constant and Y is a random variable. Thus E(X) = 5*2 = 10.

To know more about probability,

https://brainly.com/question/30034780

#SPJ4

Answer:

B

Step-by-step explanation:

14.50 / 1.75 = 8.3

26.25 / 2.5 = 10.5

3/8 * 2 = 0.75 .... 5.5 * 2 = 11 (no need to continue)

Answer:

A farmer has enough food to feed 20 animals in his cattle for 6 days. How long would the food last if there were 10 more animals in his cattle? Here the number of animals and the number of days are in inverse proportion. Hence the food will last 4 days.

Jane should land 1.5 mi down the shoreline and walk the remaining 4.5 mi to the village to minimize her travel time.

Let x = distance travelled along the shore over water.

Then, 6 − x = distance travelled along the shore over land.

Let T = the total time taken to reach the destination.

T = distance/velocity = √(4 + x²)/3 + (6-x)/5 on [0, 6].

Note that T must be non negative and that x = 6 means the destination

is reached solely by rowing and without the benefit of faster land

travel. In actual fact, T is valid over [0, ∞) but [0, 6] is reasonable here.

T' = x/3√(4 + x²) - 1/5 = 5x - 3√(4 + x²) = 0

⇒5x = 3√(4 + x²)

⇒25x² = 9(4 + x²)

⇒16x² = 36

⇒x = ±6/4 = ±1.5

The negative x value is discarded since it does not belong to [0,6].

T(0) = 28/15 = 1.8667

T(1.5) = 1.733

T(6) = 2.1082

Therefore, Jane should land 1.5 mi down the shoreline and walk the

remaining 4.5 mi to the village to minimize her travel time.

Her minimum travel time will be T(1.5) = 1.733 hrs. or 1hr 44 min.

--The given question is incomplete, the correct question is

"Jane is 2 mi, offshore in a boat and wishes to reach a coastal village 6 mi, down a straight shoreline from the point nearest the boat. She can row at 3mph and can walk at 5 mph. Where should she land her boat to reach the village in the least amount of time?"--

To know more about destination, here

https://brainly.com/question/14693696

#SPJ4

Answer:

5 + 2q = 15

Step-by-step explanation:

The perimeter is 4 + 2 + q + (q - 1) = 15.

Add 4 + 2 then subtract the sum from both sides.

q + (q - 1) = 9

This can be simplified further by adding the "q" variables together.

2q - 1 = 9

Add 1 to both sides.

2q = 10

Divide both sides by 2 to isolate q.

q = 5