Drawn to scale
find the area of the figure

The 32° measure of A and the length of side a which is 17, and side B with length 11, using the law of sines, gives;

The law of sines can be stated as follows;

The ratio of the sine of an interior angle in an oblique triangle to the length of the side opposite the given angle, is a constant for the angles and their opposite sides of the triangle.

Mathematically, we have;

[tex] \frac{sin( A) }{a} = \frac{sin( B )}{b} =\frac{sin( C )}{c} [/tex]

Where;

Angle A is the angle opposite to side a

Angle B is the angle opposite to side b

Angle C is the angle opposite to side c

The given measure of angle A = 32°

The length of segment, a = 17

The length of segment, b = 11

Taking the given dimensions as the measurements of parts of a triangle, using sine rule, we have;

From the question, we have;

A = 32°

a = 17

b = 11

Which gives;

[tex] \frac{17}{sin( 32^{ \circ} ) } = \frac{11}{sin( B )} [/tex]

Therefore;

[tex] sin( B ) = \frac{11 \times sin( 32^{ \circ} ) }{17} [/tex]

Which gives;

[tex] \displaystyle{ B = arcsin \left( \frac{11 \times sin( 32^{ \circ} ) }{17} \right) \approx 20.1 ^{ \circ} }[/tex]

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Considering the definition of parallel line, the equation y= 1/3x - 2 is parallel to y=1/3x and it goes through (6,0).

A linear equation o line can be expressed in the form y = mx + b

where

Parallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.

Two lines are parallel if they have the same slope and different y-intercepts.

In this case, the line is y=1/3x

where:

If two lines are parallel if they have the same slope, the parallel line has a slope of 1/3 and has a form of: y= 1/3x + b

The line passes through the point (6, 0). Replacing in the expression for parallel line:

0= 1/3× 6 + b

0= 2 + b

0 -2 = b

-2= b

Finally, the equation of parallel line is y= 1/3x - 2.

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We will add 1 to 2/3 to make sum of [tex]1\frac{2}{3}\\[/tex] of an integer and a fraction.

What is integer?

What is fraction?

- [tex]1\frac{2}{3}[/tex]  = _ + (2/3)

we will add 1 to 2/3 to make sum of [tex]1\frac{2}{3}\\[/tex] of an integer and a fraction.

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The sale price of the magazine subscription is $11.55

From the question, the given parameters are:

Subscription = $35

Discount = 67% off

The sale price of the magazine subscription is then calculated as

Sales price = Subscription x (1 - Discount)

Substitute the known values in the above equation

So, we have the following equation

Sales price = 35 x (1 - 67%)

Evaluate the product

Sales price = 11.55

Hence, the sales price is $11.55

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(a) The probability distribution table is provided in the attachment.

(b) The probability distribution of X is discrete.

Let X = number of hours a service calls take.

(a)The probability of an event E is:

P(E)=n(E)/N

Here,

n (E) = number of favorable outcomes

N = total number of outcomes.

The probability distribution table is provided in the attachment.

(b)For a discrete probability distribution:

f(x) >= 0

summation f(x)= 1

Check that the probability distribution of X is discrete as follows:

The value of f (x) for all values of x is greater than 0.

The sum of all f (x) is 1.

Thus, the probability distribution of X is discrete.

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Answer:

The distance between the two cities is 360 miles.

Step-by-step explanation:

Let value "a" equal the airspeed of the plane in still air, and let value "d" be the distance between the two cities. Then:

d/a+30=1.5

d=1.5a+45

and

d/a-30=2

d=2a-60

So

2a-60=1.5a+45

.5a=105

a=210

d/210-30=2

d=360

The distance between the two cities is 360 miles.

If CA and CE are opposite rays, CH bisects ∠ GCD, and GC bisects ∠ BGD. If m ∠ BGC = (7x - 2)° and m ∠ CGF = (8x - 8)°, then the value of m ∠ BGF exists 80°.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The two rays are called the sides of an angle, and the common endpoint is called the vertex.

If CA and CE are opposite rays, CH bisects ∠ GCD, and GC bisects ∠ BGD.

Given: m ∠ BGC = (7x - 2)° and m ∠ CGF = (8x - 8)°,

m ∠ BGC = m ∠ CGF

7x - 8 = 8x - 8

substracting 2 from both sides of the equation, we get

7x - 8 = 8x - 8 - 8

7x - 8 = 8x

simplifying the above equation, we get

x = 6

Therefore, the value of x = 6.

⇒ m ∠ BGC = m ∠ C G F = 40°

Therefore, the value of m ∠ BGF = 2(40)° = 80°

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The population of the country in 1990 will be 274.7 million.

From the information given, the population of a country in 2015 was estimated to be 321.4 million people and this was an increase of 17% from the population in 1990.

Therefore,since let the population on 1990 be x. Therefore, this will be illustrated as:

x + (17% × x) = 321.4

x + 0.17x = 321.4

1.17x = 321.4

Divide

x = 321.4 / 1.17

x = 274.7

The population is 274.7 million.

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The equation of the line that contains the point P(-4,6) and has slope 4 is  y=4x+22 .

The equation of line passing through the point (x₁,y₁) with slope (m) is given by the formula

(y-y₁)=m(x-x₁)

In the question ,

it is given that

the required line passes through the point P(-4,6) and has slope 4

So, x₁= -4 , y₁=6 and m = 4

Substituting the values of x₁, y₁ and m in the equation of line formula , we get

y-6=4(x-(-4))

y-6=4(x+4)

y-6=4x+16

y=4x+16+6

y=4x+22

Therefore , the equation of the line that contains the point P(-4,6) and has slope 4 is  y=4x+22 .

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The question is testing knowledge on subsets. The application of combinations is used to sum up. Consider prime factors between 1 and 11. They are{1,2,3,4,5,6,7,8,9,10,11}.

The prime factors in the set are {2,3,5,7,11}. This set has 5 elements.

Apply combinations to obtain the total subsets.

The subsets with 1 element is 5C1 = 5 subsets

The subsets with 2 elements is 5C2= 10 subsets

The subsets with 3 elements is 5C3= 10 subsets

The subsets with 4 elements is 5C4= 5 subsets

The subsets with 5 elements is 5C5= 1 subset

The total non-empty subsets are 5+10+10+5+1 = 31 subsets.

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None of the given expressions are equivalent to 25.

What is an expression?

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers (operands), variable, operations, units, brackets, punctuation, and groups can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's sequence of operations and other features.

Many writers make a distinction between an expression and a formula, with the former designating a mathematical object and the latter a claim about such objects. However, in contemporary mathematics, and particularly in computer algebra, formulae are seen as expressions that, depending on the values supplied to the variables present in the expressions, can be evaluated to true or false.

The expressions are solved as follows

6-6-6-6-6-6 = -24

2-6 = -4

12-12 = 0

2-2-2-2-2-2 = -8

4-16 = -12

8-8 = 0

Hence, none of the expressions are equivalent to 25.

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Answer:

I'm sure it's 1.2506407mm

Step-by-step explanation:

The expressions that represent Bruce's score at the end of the game will be 5(10x) + 30(5) = 150 + 50x.

From the information, Bruce completed all 5 levels of his favorite video game, Extreme Treasure Hunter and in the game, you can earn points by collecting gemstones or finding pieces of the treasure map.

The expression to illustrate the number of points will be:

= 5(10x) + 30(5)

where c = number of points per gemstone

= 50x + 150

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we have the equation

Find out the first derivative

equate to zero the derivative, to find out the critical points

The value of cosine is zero when the angle is 90, 270 degrees (pi/2 and 3pi/2)

so

For x=pi/10

Find out the y-coordinate

Verify for x=3pi/10

[tex]5 {x}^{2} - 28x + 23 = 0 \\ \\ 5 {x}^{2} - 23x - 5x + 23 = 0 \\ (5 {x}^{2} - 23x) - (5x - 23) = 0 \\ x(5x - 23) - (5x - 23) = 0 \\ (x - 1)(5x - 23) = 0 \\ \\ x - 1 = 0 \\ \\ or \\ \\ 5x - 23 = 0 \\ \\ \\ x = 1 \\ \\ or \\ \\ x = \frac{23}{5} [/tex]

ATTACHED IS THE SOLUTION

Answer:

1. 6x+18 2. 5y-20 3. -7m+7

Step-by-step explanation:

1. 6(x+3) 2. 5(y-4) 3. -7(m-1)

6x+24. 5y-20. -7m+7 <--- - times - = +

With 19.5% annual interest on a daily basis, the finance charge due on October 14 will be $623.

So, the finance charge due:

Therefore, with 19.5% annual interest on a daily basis, the finance charge due on October 14 will be $623.

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Answer:

L'(0,-2)

K' (3, -2)

J' (0,3)

Step-by-step explanation:

Answer:

- 8n -4 +n+7

like terms (-8n, n) and (-4, 7)

so; -8n+n-4+7

    = -7n+3

Answer:

-7n + 3

Step-by-step explanation:

   Like terms are terms that have same variable with same power.

-8n and n are like terms.  subtract or add the coefficient of the like terms.

(-8) and 1. So, subtract and it is -7n

(-4) and 7 are like terms(constants).

-8n - 4 + n + 7 = -8n + n - 4 + 7

                        = -7n + 3

Answer:

y=4/3-5

Step-by-step explanation:

Y=mx+c

mx=gradient which is 4/3

c is y intercept which is -5

After thoroughly calculating we have come to find that, a number twice the sum of -17 and -14 is −62

To sum and complete mathematical operations, numerical values are needed. Numbers are used to represent numerical values, and they can also be used to represent them alphabetically. For instance, the number 22 can be expressed in writing or by using the alphabet 22. One more example is the number 3, which can be written as 3.

Numbers can take many different forms. Examples of opposites include odd and even, fraction and integer, rational and irrational, natural and whole, and many more. A few of the operations include arithmetic, algebra, and trigonometry.

Twice the sum of -17 and -14 is

2((-17) + (-14))

⇒ 2(-17 -14)

⇒ 2 × (-31)

⇒ −62

So, a number twice the sum of -17 and -14 is −62.

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Based on the calculations, the age of this person is equal to 25 years.

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

In order to solve this word problem, we would assign a variable to the age of this person and then translate the word problem into algebraic equation as follows:

Let x represent the age.

Translating the word problem into an algebraic equation, we have;

x + 65 = 6(x - 10)

Opening the bracket, we have:

x + 65 = 6x - 60

Re-arranging the equation, we have:

6x - x = 60 + 65

5x = 125

Dividing both sides by 5, we have:

x = 125/5

x = 25 years.

In conclusion, we can reasonably infer and logically state that this person's age was 25 years ten (10) years ago.

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Complete Question:

In 65 years I will be 6 times as old as I was 10 years ago. How old am I?

The value of x is 11.7.

The angles CAB, ACB, and ABC are 43.1°, 69°, and 68.2° respectively.

Given angles are:

A = (3x+8)°

B= (6x-2)°

C = 69°

Using the Angle sum property we get,

(3x+8)° + (6x-2)° + 69° = 180°

9x + 75° = 180°

9x = 180°- 75°

x = 11.7

CAB = (3 × 11.7 + 8)° = 43.1°

ACB = 69°

ABC = (6 ×11.7 - 2) = 68.2°

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The solution of the inequality will be;

⇒ x > 4 or x < -10/3

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is;

|3x - 1| > 11

Now, The inequality is solved as;

|3x - 1| > 11

⇒ 3x - 1 > 11 or 3x - 1 < -11

Solve the inequality as;

⇒ 3x - 1 > 11

Add 1 we get;

⇒ 3x - 1 + 1 > 11 + 1

⇒ 3x > 12

Divide by 3;

⇒ x > 4

And, Solve the inequality as;

⇒ 3x - 1 < - 11

Add 1 we get;

⇒ 3x - 1 + 1 < - 11 + 1

⇒ 3x < -10

Divide by 3;

⇒ x < -10/3

Thus, Solution of the inequality will be;

⇒ x > 4 or x < -10/3

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Answer:

y = -2x + 11

Step-by-step explanation:

When two lines are parallel, their gradients are the same. So the gradient of the line parallel to this equation will be -2 as well.

Now we substitute values from this point to find the rest of the equation :

y = -2x + c

3 = -2(4) + c

3 = -8 + c  

c = 11

So the equation of the line parallel will be y = -2x + 11

Hope this helped and have a good day

The expression that is equivalent to a fraction with nine raised to the negative third power in the numerator and the quantity three raised to the negative second power times nine squared end quantity in the denominator and the entire fraction is cubed is [tex]\frac{3^{6} }{9^{15} }[/tex]

Nine raised to the negative third power = [tex]9^{-3}[/tex]

Three raised to the negative second power times nine squared = [tex](3x^{-2})(9^{2} )[/tex]

The expression is [tex](\frac{9^{-3} }{(3^{-2})(9^{2} ) } )^{3}[/tex]

=[tex]\frac{9^{(-3)(3)} }{(3^{(-2)(3)})(9^{(2)(3)} }[/tex]

=[tex]\frac{9^{-9} }{(3^{-6})(9^{6}) }[/tex]

= [tex]\frac{3^{6} }{(9^{9})(9^{6}) }[/tex]

= [tex]\frac{3^{6} }{9^{15} }[/tex]

Hence, the expression that is equivalent to a fraction with nine raised to the negative third power in the numerator and the quantity three raised to the negative second power times nine squared end quantity in the denominator and the entire fraction is cubed is [tex]\frac{3^{6} }{9^{15} }[/tex]

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By using matrix operations, the resulting matrix is [tex]4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] - \left[\begin{array}{cc}1&2\\4&5\end{array}\right][/tex] is  [tex]\left[\begin{array}{cc}3&6\\12&15\end{array}\right][/tex].

In this problem we must simplify a combination of two matrices, this can be done by using properly the fundamental operations for matrices. Matrices are algebraic constructions characterized by a number of row and a number of columns. For instance, there is a matrix with two rows and three columns:

[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\end{array}\right][/tex]

There are two fundamental operations for matrices:

Sum - The respective elements of the same row and the same column of the matrix are summed:

[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] + \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] = \left[\begin{array}{ccc}2&4&6\\8&10&12\\14&16&18\end{array}\right][/tex]

Where C(i, j) = A(i, j) + B(i, j), i is the row index and j is the column index.

Scalar mutiplication - Every element of the matrix is multiplied by a scalar:

[tex]2 \cdot \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] = \left[\begin{array}{ccc}2&4&6\\8&10&12\\14&16&18\end{array}\right][/tex]

Where B(i, j) = k · A(i, j), k is the scalar.

Now we show the complete procedure to find the simplified expression:

[tex]4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] - \left[\begin{array}{cc}1&2\\4&5\end{array}\right][/tex]                         Given

[tex]4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] + (- 1) \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right][/tex]               Definition of subtraction

[tex]\left[\begin{array}{cc}4&8\\16&20\end{array}\right] + \left[\begin{array}{cc}- 1&- 2\\- 4&- 5\end{array}\right][/tex]                     Scalar multiplication

[tex]\left[\begin{array}{cc}3&6\\12&15\end{array}\right][/tex]                                             Sum of matrices / Result

The simplifed form of the matrix is [tex]4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] - \left[\begin{array}{cc}1&2\\4&5\end{array}\right][/tex] is  [tex]\left[\begin{array}{cc}3&6\\12&15\end{array}\right][/tex].

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The expression 63a–35 factored as a product with a whole number greater than 1 is 7(9a - 5)

Algebraic expressions are defined as expressions made up of variables, terms, coefficient, constants, and factors.

The are also made up of arithmetic or mathematical operations which includes;

Factorization can be defined as the mathematical method of breaking a number down into similar and smaller numbers which are the products of the original number.

Given the expression;

63a–35

To factor expression, we need to find a common product of the values

We have;

7(9a - 5)

This cannot be further factorized

Hence, the factored form is 7(9a - 5)

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