Carlos needs to build a fence for his chickens. The area he wants to build a fence around is 40 feet long and 20 feet wide. How many feet of fence does he need to buy? (Hint: 40x2 + 30x2)

For a polynomial, Leading coefficient is the coefficient of the term with the degree of polynomial. For [tex]a^{2}+bx+c[/tex] , The leading coefficient is 'a'.

Sums of terms with the form  kxⁿ, where K is any number and N is a positive integer, are known as polynomials.

The term with the greatest x power is the leading term in a polynomial function. The leading coefficient is the coefficient of the leading phrase.

Example of leading coefficient are:

[tex]2x^{2}+x+1[/tex], leading coefficient=2

[tex]8x^{3}+5x^{2}+3x+1[/tex], leading coefficient =8

[tex]3x^{5}+8x^{3}+7x+6[/tex], leading coefficient = 3

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Continuity of a function can be checked by examining the limits of the function as x approaches a certain value and ensuring the function's output is equal to the value of the function at that point.

Continuity of a function is an important concept in calculus and other branches of mathematics. In order to check the continuity of a function, the limits of the function must be examined as x approaches a certain value. This means that the left-hand limit and the right-hand limit must be equal. If the limits are equal, then the function is continuous at that point. If the limits are not equal, then the function is not continuous at that point. Additionally, the value of the function at that point must also be equal to the limits in order for the function to be continuous. If the function is discontinuous at any point, then it is not considered continuous. Continuity is necessary for certain properties of functions, such as derivatives and integrals, to be defined.

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The factors form of the given equation 3x²−6x is 3x(x−2)

Given that:

3x²−6x

To find : The factor form of 3x²−6x

The splitting or decomposition of an entity (such as a number, a matrix, or a polynomial) into the product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics. You will mostly learn this idea in your lower secondary studies, which run from grades 6 to 8.

=3×x×x−2×3×x, factor each monomial

=3x(x−2), factor out common factor 3x

The factors form of 3x²−6x is 3x(x−2)

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Answer:

Step-by-step explanation:

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes. Probability of event to happen P (E) = Number of favourable outcomes/Total Number of outcomes

As per the unitary method, the value of x for the expression 4x = 64 is written as, 16.

The term unitary method in math is defined as a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here we have to find the value of x if the given expression 4x = 64.

According to the unitary method, here we have given the expression,

=> 4x = 64

Here we need to find the value of x, so we have to move the other values instead of x to the other side, then we get the expression,

=> x = 64/4

Now, we have to divide the number 64 by 4, then we get the value,

=> x = 16

Therefore, the value of x is 16.

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Answer:

{ X = 5} {Y = 3} pls mark brainliest

Step-by-step explanation:

Add the two equations: 4x + 7y + (x-7y) = 41 + (-16)

Remove parentheses: 4x + 7y + x-7y = 41 + -16

Cancel one variable:4x + x + = 41 + -16

Combine like terms: 5x = 41 - 16

Calculate the sum or difference: 5x = 25

Divide both sides of the equation by the coefficient of variable: x = 25/5

Cross out the common factor: X = 5

Substitute into one of the equations: 5 - 7y = -16

Rearrange unknown terms to the left side of the equation:  5 - 7y = -16 - 5

Calculate the sum or difference: -7y = -21

Divide both sides of the equation by the coefficient of variable: -21/-7

Determine the sign for multiplication or division: y = 21/7

Cross out the common factor: y = 3

The solution of the system is: { X = 5} {Y = 3}

As per the given height of the wall, the approximate weight is 149kN

The term Hydrostatic refers to the force exerted by static water on the plate or object and its magnitude depends upon the positioning of the object inside the water.

Here we have given the following values,

Height = 2.76 upright

Width = 10 m

Here we have to consider the hydrostatic force acting on the wall about the pinned point say P then the expression is looks like,

=> F = ωAx

=> F =  9810(10 × 4) × 2

=> F = 784800 N = 785KN

Now, the weight is calculated as per the Hydrostatic method as,

=> W = (1.33/7) x 785

=> W = 149 kN

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Answer:

A = 3

B = 6

C = 4

D = 5

left rectangle = 4 x 6 = 24

mid = 5 x 6 = 30

right = 6 x 3 = 18

both triangles = 4 x 3 = 12

24 + 30 + 18 + 12

= 84 cm²

Answer: 84

Step-by-step explanation:

The rewritten expression using the summation notation is ∑ k = 1 1! + 2! + 3! + ... + (n+1)!

The summation notation is a way to represent the sum of a series of terms. In the summation notation, the series of terms is represented by an expression that is followed by a summation symbol (∑). The summation symbol is usually followed by an index of the summation (k in this case), an equal sign (=), the starting value of the index, and a colon (:). The series of terms is then written below the summation symbol, with the index replacing the variable in each term.

To rewrite the given expression using the summation notation, we can use the following steps:

Identify the series of terms: 1 + 2 + 3 + ... + n.

Write the series of terms below the summation symbol: ∑ k = 1

Replace the variable in each term with the index: 1! + 2! + 3! + ... + (n+1)!

The rewritten expression using the summation notation is ∑ k = 1 1! + 2! + 3! + ... + (n+1)!

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Answer:

Step-by-step explanation:

(5x )4 +(5x )3 = (10x)12

A corporate bond has a face value of p dollars. The interest each year is 6% of the face value.  the total interest /, in dollars, as a function of the age f, in years, of the bond is

a)I(f) = 0.06 * f * p

b) P(f) = I(f) + p

Generally, (a) The total interest, in dollars, as a function of the age f, in years, of the bond can be expressed as:

I(f) = 0.06 * f * p

This represents the total interest paid over f years, which is calculated by multiplying the annual interest rate (0.06), the number of years (f), and the face value of the bond (p).

(b) The payout P, in dollars, as a function of f can be expressed as:

P(f) = I(f) + p

This represents the total payout over f years, which is calculated by adding the total interest paid (I(f)) and the face value of the bond (p).

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When a person registers for SSS membership in any capacity, he/she becomes a member for life. Thus, withdrawal of membership is not possible.

Once you become a covered SSS member, you become a member for life. The contributions that you remit become savings for the future that will serve as the basis for the granting of social security benefits in times of contingencies. Membership cannot be withdrawn and contributions paid cannot refund.

Workers in the private sector are covered by social security under the Social Security System (SSS). In the event of a worker's passing, disability, illness, pregnancy, or old age, social security provides replacement income. The Social Security Act of 1954 went into effect on September 1st, 1957.

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The length of the line is 1712.12 miles if there were often long lines of cars waiting at gas stations. If there were a million cars in line, bumper to bumper.

Given :

What is average?

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

There were often long lines of cars waiting at gas stations. If there were a million cars in line, bumper to bumper.

The average length  = 9.04 feet

The length of the line can be found as follows:

= 9.04 * 1,000,000

The length of the line  = 9,040,000 feet/5280 feet (1 mile)

= 1712.12 miles

Thus, the length of the line is 1712.12 miles if there were often long lines of cars waiting at gas stations. If there were a million cars in line, bumper to bumper.

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The rational root theorem is the representation of the finding rational solution of the given polynomial function.

As given in the question,

Therefore, the rational root theorem is the representation of the finding rational solution of the given polynomial function.

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We are asked to find the first derivative of,

[tex]\longrightarrow g(x) = \sqrt{x^2+2x}[/tex]

Here we can write the term [tex]x^2+2x[/tex] by adding and subtracting 1 as,

[tex]x^2+2x = x^2+2x+1-1[/tex]

[tex]x^2+2x = (x+1)^2-1\quad[\because\, x^2+2x+1=(x+1)^2][/tex]

Thus,

[tex]\longrightarrow g(x) = \sqrt{(x+1)^2-1}\quad\dots(1)[/tex]

Now take,

[tex]x+1=\sec\theta\quad\dots(2)[/tex]

[tex]x=\sec\theta-1[/tex]

[tex]dx=\sec\theta\tan\theta\, d\theta[/tex]

[tex]\dfrac{d\theta}{dx}=\dfrac{1}{\sec\theta\tan\theta}\quad\dots(3)[/tex]

Then (1) becomes,

[tex]\longrightarrow g(x) = \sqrt{sec^2\theta-1}[/tex]

We have,

[tex]\sec^2\theta-1=\tan^2\theta[/tex]

So we get,

[tex]\longrightarrow g(x) = \tan\theta[/tex]

Now,

[tex]\longrightarrow g'(x) = \dfrac{d}{dx}\,[\tan\theta][/tex]

By chain rule,

[tex]\longrightarrow g'(x) = \dfrac{d}{d\theta}\,[\tan\theta]\cdot\dfrac{d\theta}{dx}[/tex]

[tex]\longrightarrow g'(x) = \sec^2\theta\cdot\dfrac{1}{\sec\theta\tan\theta}\quad\quad\textrm{[From (3)]}[/tex]

[tex]\longrightarrow g'(x) = \sec\theta\cdot\dfrac{1}{\tan\theta}[/tex]

[tex]\longrightarrow g'(x)=\dfrac{1}{\cos\theta}\cdot\dfrac{\cos\theta}{\sin\theta}[/tex]

[tex]\longrightarrow g'(x)=\dfrac{1}{\sin\theta}\quad\dots(4)[/tex]

But we have,

[tex]\sin^2\theta+\cos^2\theta=1[/tex]

[tex]\sin\theta=\sqrt{1-\cos^2\theta}[/tex]

[tex]\sin\theta=\sqrt{1-\dfrac{1}{\sec^2\theta}}[/tex]

[tex]\sin\theta=\dfrac{\sqrt{\sec^2\theta-1}}{\sec\theta}[/tex]

[tex]\sin\theta=\dfrac{\sqrt{(x+1)^2-1}}{x+1}\quad\quad\textrm{[From (2)]}[/tex]

[tex]\sin\theta=\dfrac{\sqrt{x^2+2x}}{x+1}[/tex]

Hence (4) becomes,

[tex]\longrightarrow\underline{\underline{g'(x)=\dfrac{x+1}{\sqrt{x^2+2x}}}}[/tex]

This is the first derivative of the given function.

Answer:

6/4

1 2/4

1 1/2

Step-by-step explanation:

3 x 2/4 = 3/2 or 1 1/2

6/4 reduces to 3/2 as factors of 2

1 2/4 simplifies to 1 1/2

1 1/2 is equal to 3/2

Answer:

Additional root of 7+√5 and 1/4 is:

D.5-√7

The business college wants to determine the proportion of business students who have extended time between classes. The p value for two tailored test was 0.0124

Let p represent the percentage of business students who own laptops.

As said, we must conduct the exam.

The test is a two-tailed test because the alternative hypothesis has two tails.

We presume that a normal distribution would apply in this situation.

We employ the z-test for proportion.

The two-tailed test's P-value is 2P(Z>|z|)=2P(Z>|2.5|).

=2P(Z>2.5)=2(1-P(Z<2.5)) P(Z>z)=1 - P(Zz)

=2(1-0.9938) Z-table, by

= 2(0.0062) (0.0062)

= 0.0124

Consequently, the two-tailed test's p-value was 0.0124.

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Answer:

316 milliliters of compound A

Step-by-step explanation:

We know for every 7milliliters, we have 4 milliliters of compound A and 3 milliliters of compound B

So, take 553 divided by 7 = 79

So, take 4 times 79 = 316 milliliters of Compound A

So, 316 milliliters of Compound A are needed!

Answer:m<1 = 111 degrees, m<2 = 69 degrees

Step-by-step explanation:The measure of angles 1 and 2 are supplementary, (two angles adding up to 180 degrees). Using this, set up the equation:

x + 88 + 3x = 180  

4x = 108

x=23 degrees

Next, substitute 23 into the given angles:

m<1 = (23 + 88) = 111 degrees

m<2 = 23 * 3 = 69 degrees

Thus, m<1 = 111 degrees, m<2 = 69 degrees.

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The 16% variability in weight can be explained by the relationship with height.

What is correlation?

In statistics, there are three different forms of correlation: positive, negative, and no correlation.

The link between two variables is said to be positive correlated when both variables move in the same direction. When one variable decline (or grows) while the other variable lowers (or increases), there is a positive perfect correlation, denoted by the number +1.

When two variables are correlated negatively, both of the variables are moving in the opposing direction. When one variable rises (or falls) while the other rises (or falls), there is a negative perfect correlation, which is symbolised by the number -1.

No correlation, which is represented by 0, means that there is no connection or reliance between the two variables.

On the basis of provided information, the correlation between the height and weight for adults is,

r = +0.4

So, the coefficient of determination is calculated as,

[tex]r^{2} = (0.40)^{2}[/tex] = 0.16 = 16%

Based on the provided information, the required answer is 16%.

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Answer: Yes, you will make it on time

Step-by-step explanation:

The distance from San Antonio to Dallas is 274 miles

We take 274 divided by 65 = 4.2 hours or 4 hours and 12 minutes to get there at the speed of 65 mph

We have 4 1/2 hours to get there

4 1/2 hours = 4 hours 30 minutes

So, you will make it on time!

If q ║ r, value of x is 17.

When a transversal connects two or more parallel lines at different locations, alternate exterior angles are created. The word exterior refers to something that is located outside. Whenever the transversal intersects two lines, alternate external angles are always outside of those two lines and are situated on the opposing sides of the transversal. As a result, the pair of alternate external angles—two outside angles—that arise at the opposing ends of transversals in the exterior section are always equal. When a transversal splits two parallel lines, we obtain two of these pairs of alternate exterior angles.

Given

q ║ r

Alternate exterior angle,

7x - 10 = 9x - 44

9x - 7x = 44 - 10

2x = 34

x = 17

If q ║ r, value of x is 17.

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In order to understand all properties of an equilateral triangles we will take a traingle ΔABC and let the side length be a,b,c and angle measures be α, β and Ф.

1. All 3 side of an equilateral triangles have same length .

   so as mentioned a=b=c.

2. All 3 angles of an equilateral triangles have same measure.

   so α=β=Ф , which shows that all angles measures same.

3. Each angles of an equilateral triangles is [tex]60^0[/tex].

4. Area of equilateral triangles = [tex]\frac{\sqrt{3} }{4}*a^2[/tex]

5 . Perimeter of an equilateral triangles = 3*a

6. Any two triangle sides can add up to a length that is longer than the third side.

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Answer:

1. y=x    2. x=4   3. y=3x-10   4. y=-2/5x-1/5    5. y=-8x-13    6. y=-x+3

Step-by-step explanation: