The radius of a circle is 8 ft. Find its area in terms of pi

If a transversal intersects two lines such that a pair of alternate interior angles is equal , then the two lines are parallel.

What do you mean by traversal line?

A transversal is a line that, at two different locations in the geometry, cuts through two lines in the same plane. Various sorts of angles in pairs, including successive internal angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.

What do you mean by angle?

An angle is defined as the figure, in which two rays meet at a common point called the vertex. The angle is denoted using the symbol “∠”.

From the figure,

x + 1 = 180°

y + 2 = 180°

Adding above equations,

x + y + 1 + 2 = 360°

Given ,

x + y = 1 +2

x + y + x + y = 360°

2(x + y) = 360°

x + y = 180°

Angles made on same side of transversal is supplementary . So the lines are parallel.

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The partial fraction is proved.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

=3x²+8x+4/(x²-4)(3x-2)

=3x2+8x+4/(x2-4)(3x-2)

= 3x2+6x+2x+4/(x2-4)(3x-2)

=3x(x+2)+2(x+2)/(x2-4)(3x-2)

Hence proved, l.h.s = r.h.s

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The dividend is 35286 and the divisor is 7. The value of the division is $540.8571

When dividing, it's important to note that the number that is being divided in this case 35286 is the dividend.

On the other hand, the number that is being divided by which is in this case 7 is the dividend.

The division will be:

= $35286 ÷ 7

= $540.8571

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We can conclude that (C) Gibbons will live in a building that is similar to the Chimpanzee's rectangular house.

So, observe the given shapes on the graph:

Therefore, we can conclude that (C) Gibbons will live in a building that is similar to the Chimpanzee's rectangular house.

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Answer:

1/5

Step-by-step explanation:

equation: 3/5-2/5=x

we can multiply the whole equation by 5 so that we can easily subtract the numbers

3-2=1

now we divide it by 5 so that we get our number in a fraction

after we divide we get 1/5

Answer: the coefficient of the 6th term of (2x - 7)⁹ is -33882912

Step-by-step explanation:

[tex](2x-7)^9[/tex]

In this problem we use the following formula:

                              [tex](a+b)^n=\sum\limits _{k=0}^nC_n^ka^{n-k}b^k[/tex]

a=2x         b=-7        n=9

The 1th term of (2x-7)^9 is k=0

The 2th term of (2x-7)^9 is k=1

The 3th term of (2x-7)^9 is k=2

..........................................................

The 6th term of (2x-7)^9 is k=5

Hence,

[tex]\displaystyle\\C_9^5(2x)^{9-5}(-7)^5=\\\\\frac{9!}{(9-5)!*5!}(2x)^4(-7)^5 =\\\\\frac{9!}{4!*5!} 2^4x^4(-7)^5=\\\\126(16)(-16807)(x^4)=\\\\=-33889212x^4[/tex]

- 33889212x⁴ is the coefficient of the 6th term in  binomial theorem .

What is binomial theorem?

( 2x - 7 )⁹

compare with formula

a = 2x    b = - 7  n = 9

The 1th term of (2x-7)^9 is k=0

The 2th term of (2x-7)^9 is k=1

The 3th term of (2x-7)^9 is k=2

...................................................

The 6th term of (2x-7)^9 is k=5

hence

⁵C₉( 2x )⁹⁻⁵ ( - 7)⁵  = 9!/( 9-5)!* 5! (2x)⁴( -7)⁵

                            = 9!/4! * 5! 2⁴x⁴( -7)⁵

                              = 126(16) ( - 16807 )(x)⁴

                              =  - 33889212x⁴

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The area of any circle is directly proportional to the square of the radius thus there are proportional relationships between the area of a circle and to the radius of the circle.

The ratio is the division of the two numbers.

Proportion is the relation of a variable with another. It could be direct or inverse.

The area of a circle with radius "r" is given as,

A = πr²

Since,π = constant.

Removing constant by proportionality.

A ∝ r²

Hence "The area of any circle is directly proportional to the square of the radius thus there are proportional relationships between the area of a circle and to the radius of the circle".

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The expressions (5 + 9 - 2³) and (4² - 6) are not equal (≠) to each other. Then the correct option is B.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The numerical expressions are given below.

(5 + 9 - 2³) and (4² - 6)

Simplify the expression, then we have

(5 + 9 - 2³) = 5 + 9 - 8 = 6

(4² - 6) = 16 - 6 = 10

The expressions (5 + 9 - 2³) and (4² - 6) are not equal (≠) to each other. Then the correct option is B.

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The equation of the line representing the given situation is y = (3/4)x , the graph of the equation is shown below .

In the question ,

it is given that ,

a refreshment stand makes 3 large serving of frozen yogurt from 4 pints .

also given that number of pints is represented by x - axis .

the number of servings is represented by y - axis  .

the equation of the line is represented by y = mx + c .

we get c = 0, because at 0 pint there is no servings

hence , the  equation becomes y [tex]=[/tex] mx .

According to the question ,

3 = m*4

m = 3/4 .

Substituting the value of m in the equation , we get

y = (3/4)x

the graph of the equation is shown below .

Therefore , The equation of the line representing the given situation is y = (3/4)x .

The given question is incomplete , the complete question is

A refreshment stand makes 3 large servings of frozen yogurt from 4 pints. Graph the line and then write its equation. Let the x-axis represent the number of pints and the y-axis represent the number of servings. Use only fractional form, if necessary.

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The differentiation of [tex]e^x[/tex] is [tex]\frac{d}{dx}(e^x) =e^x[/tex]. Hence, proved,

Given that, [tex]\frac{d}{dx}(e^x) =e^x[/tex].

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

Differentiate using the Exponential Rule which states that [tex]\frac{d}{dx}(a^x)[/tex] is [tex]a^xln(a)[/tex] where [tex]a=e.e^x[/tex]

So, now [tex]\frac{d}{dx}(e^x) =e^x[/tex]

The differentiation of [tex]e^x[/tex] is [tex]\frac{d}{dx}(e^x) =e^x[/tex]. Hence, proved,

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The other names of AB in the given figure are

Collinear points refers to points that lies on the same plane and on the same straight line.

The figure shows two planes and point A, B and C are collinear points, while points Q and R are collinear

Points A, B and C are non colinear to points Q and R

Points AB are still part of line AC hence can be noted as part of line segment BC.

The line has arrow head and may also be called rays. In this case the are part of an arrow

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By using the concept of differentiation, it can be calculated that

value of P is -2 and value of Q is 1

What is differentiation?

Differentiation is the process where  the instantaneous rate of change of function can be calculated based on one variable. Differentiation is a very important tool in calculus

Here differentiation is used

f(x) = [tex]x^2y[/tex]

[tex]df = 2xydx+x^2dy[/tex]

Here P = 2xy, Q = [tex]x^2[/tex]

At x = 1, y = -1

P = 2(1)(-1) = -2

Q = [tex](-1)^2[/tex] = 1

So value of P is -2 and value of Q is 1

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Answer:

- 90

Step-by-step explanation:

substitute x = - 2 into f(x)

f(- 2) = 3[tex](-2)^{5}[/tex] - [tex](-2)^{4}[/tex] - 6(- 2) + 10

        = 3(- 32) - (16) + 12 + 10

        = - 96 - 16 + 22

        = - 112 + 22

        = - 90

[tex]{ \boxed{ \sf{f( - 2) = - 90}}}[/tex]

Step-by-step explanation:

[tex]{ \red{ \tt{f(x) = {3x}^{5} - {x}^{4} - 6x + 10}}}[/tex]

[tex]{ \red{ \tt{f( - 2) = 3( { - 2})^{5} - ( { - 2})^{4} - 6( - 2) + 10}}}[/tex]

[tex]{ \red{ \tt{f( - 2) = 3( - 32) - 16 + 12 + 10}}}[/tex]

[tex]{ \red{ \tt{f( - 2) = - 96 - 16 + 12 + 10}}}[/tex]

[tex]{ \red{ \tt{f( - 2) = - 112 + 22}}}[/tex]

[tex]{ \green{ \boxed{ \bold{f( - 2) = - 90}}}}[/tex]

The percentages to complete the table for the steaming time are 40 min, 20 min and 100 min respectively

A percentage is a number or ratio that can be expressed as a fraction of 100.

Given: Percentage: 100% of 40 min, 50% of 40 min and 250% of 40 min

100% of 40 min:

100% of 40 min = (100/100) × 40 min = 1 × 40 min = 40 min

50% of 40 min:

50% of 40 min = (50/100) × 40 min = 0.5 × 40 min = 20 min

250% of 40 min:

250% of 40 min = (250/100) × 40 min = 2.5 × 40 min = 100 min

Therefore, the value of the percentages to complete the table for the steaming time are 40 min, 20 min and 100 min for 100% of 40 min, 50% of 40 min and 250% of 40 min respectively.

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Answer:

7/12

Step-by-step explanation:

12/12 - 5/12 = 7/12

Answer:

(4 , 5)

Step-by-step explanation:

midpoint formula: (x1+x2/2 , y1+y2/2)

so

(1+7/2 , 4+6/2)

(8/2 , 10/2)

4 , 5

The percentage of the cupcakes that had sprinkles if 39 out of the 52 cupcakes had sprinkles on top is 75%.

A division by 100 results in a percentage, often known as a percent. A percentage denotes a component of a total sum and indicates "per 100". For example, 45% represents 45 out of 100. Calculating a percentage is the process of determining a whole's proportion in terms of 100.

Given:

The total no cupcakes = 52,

The no of sprinkled cupcakes = 39,

Percentage of sprinkled cupcakes = The no of sprinkled cupcakes / The total no cupcakes × 100

Percentage of sprinkled cupcakes = 39 / 52 × 100

Percentage of sprinkled cupcakes = 75%

Therefore, the percentage of the cupcakes that had sprinkles if 39 out of the 52 cupcakes had sprinkles on top is 75%.

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A' - (-1,4)

B' - (-1,8)

C' - (-5,4)

hope this helps

Using the information from the given diagram, the measure of angle x (m ∠x) is 52°

From the question, we are to determine the measure of angle x.

From the given diagram, we can write that

m ∠A + m ∠H + m ∠I = 180° (Sum of angle in a triangle)

Also,

m ∠K = m ∠I (Corresponding angles theorem)

∴ m ∠I = 62°

Thus,

x° + 66° + 62° = 180°

x° + 128° = 180°

x° = 180° - 128°

x° = 52°

Hence, the measure of ∠x 52°

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The solution to the given inequality 3 - x ≤ 19

or - x ≥ 24 is x ≥ -16 or x ≤ -24

An inequality is a statement that is of two quantities; one is specifically less than or greater than another. Inequality symbols are:

3 - x ≤ 19

or

- x ≥ 24

3 - x ≤ 19

-x ≤ 19 - 3

- x ≤ 16

divide both sides by -1

x ≤ 16/-1

x ≥ -16

or

- x ≥ 24

x ≥ 24/-1

x ≤ -24

In conclusion, the solution to the inequality is given by x ≥ -16 or x ≤ -24

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⇒ ∠AEC is the angle vertical opposite to ∠BEC

Answer:

9 days (round up)

Step-by-step explanation:

70 ÷ 8 = 8.75

           ≈ 9 (round up)

Answer:

If the coordinates of at least two points in the line are given, the slope (m) may be calculated by,                               m = (y2 - y1) / (x2 - x1

Answer:

99

Step-by-step explanation: 99

The interest she is pay total is $2340.822 when Angela's bank granted her a 6490 loan with a 5 year add-on interest period. 7.26% is the interest rate per year.

Given that,

For the purpose of buying new equipment for her business of antique restoration, Angela's bank granted her a 6490 loan with a 5 year add-on interest period. 7.26% is the interest rate per year.

We have to find will she pay interest at all.

We know that,

i=p×r×t

Here,

i is interest.

p is principal amount.

r is rate of interest

t is time.

So, p is $6490

r is 7.26%

t is 5 years

So,

i= 6490×0.0726×5

i= $2355.87

Therefore, the interest she is pay total is $2355.87 when Angela's bank granted her a 6490 loan with a 5 year add-on interest period. 7.26% is the interest rate per year.

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The probability that the proportion of Labradors in a sample of 694 pet dogs would differ from the population proportion by less than 3% is 0.9964

The probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean

The z score is given by the formula

z = (X - μ) / σ

Definition of variables

mean, μ  = p = 8% = 0.08

sample size, n = 694

standard deviation, σ

= √{(p(1 - p)) / n}

= √{(0.08(1 - 0.08)) / 694}

= √{(0.08 * 0.98) / 694}

= 0.0103

The probability

differ from the population proportion by less than 3%

|X - 0.08| < 0.03

X < 0.11 OR X > 0.05

0.05 < X < 0.11

P(z < 0.11) - P(z < 0.05 )

z score for z < 0.05

z = (0.05 - 0.08) / 0.0103

= -2.9126

p value for z < -2.9126 = 0.001792

z score for z < 0.12

z = (0.12 - 0.09) / 0.0102

=  2.9412

p value for z < 2.9412 = 0.9982

The probability required = 0.9982 - 0.0016 = 0.9964 or 99.64%

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We will need 7 quart package if we want 62 strawberries

What is division?

Division is one of the basic arithmetic computation which divide a value in equal sets of smaller values. The other basic arithmetic computations are addition, subtraction, multiplication. We use long division method to find the quotient and remainder.

We are given that there are 9 strawberries in a quart package

Also we want 62 strawberries

Then how many quart will be required

Now we perform division to find the number of quart

62/9 = we get a value of 8.88

Which is very close to nine

Hence we will need 9 quart packages if we want 62 strawberries

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