Use the law of cosines to find the missing third side

Answer:

A. a = 16.23 and b = 17.99

Step-by-step explanation:

The addition of the three angles of the triangle is equal to 180°. So,

C + 64° + 85° = 180°

C =  180° - 64° - 85°

C = 31°

The law of sine states:

sin(A)/a = sin(B)/b = sin(C)/c

where c is the side opposite to angle C

Taking angles A and C, and sides a and c, we get

sin(A)/a = sin(C)/c

sin(64°)/a = sin(31°)/9.3

sin(64°)*9.3/sin(31°) = a

a = 16.23

Taking angles B and C, and sides b and c, we get

sin(B)/b = sin(C)/c

sin(85°)/b = sin(31°)/9.3

sin(85°)*9.3/sin(31°) = b

b = 17.99

warehouse location (24,-32)

airport location (-24,32)

 distance = sqrt((x2-x1)^2 +(y2-y1)^2)=

Sqrt(24--24)62 +(32--32)^2) =

sqrt(48^2 +64^2) =80

then distance from airport to the factory = -24 to 24 = 48

80+48 = 128 miles total

Answer:

4800 acres.

Step-by-step explanation:

We have been given an equation [tex]a=640s[/tex], which gives the relationship between s square miles and acres.

To find the number of acres Pam owns we will substitute [tex]s=7.5[/tex] in our given equation.

[tex]a=640\times 7.5[/tex]

[tex]a=4800[/tex]

Therefore, Pam owns 4800 acres.

Answer:

The difference of fifty-four and seven times a number is written as 54 - 7x.

Step-by-step explanation:

Given: expression “the difference of fifty-four and seven times a number”

We have to write the given algebraic expression represents “the difference of fifty-four and seven times a number”

Consider the given algebraic expression represents “the difference of fifty-four and seven times a number”

Let the number be x

Then, seven times a number is 7x

And the difference of fifty-four and seven times a number is written as 54 - 7x.

Thus, The difference of fifty-four and seven times a number is written as 54 - 7x.

Answer:

a

Step-by-step explanation:

1. Triangular, 2. Upwards, 3. (- ∞, 3),(3, ∞), 4. (-1, 0) and (-3, 0), and (0, 1),

5.  (-3, -1), 6. symmetry is along the x-axis.

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, A modulus function | x + 2 | - 1.

The shape of the graph is triangular.

The graph opens in the upwards direction positive y-axis.

The graph is decreasing at the interval (- ∞, 3) and it is increasing at an interval (3, ∞).

The x-intercepts of the graph is (-1, 0) and (-3, 0), and The y-intercepts of the graph is (0, 1).

The special point of the graph is (-3, -1) where the graph is increasing from decreasing.

Yes, the line of symmetry is along the x-axis.

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Final answer:

The height of an airplane during its descent to an airport runway is influenced by factors like approach angle, stall speed, and descent rate.

Explanation:

The height of an airplane as it descends to an airport runway is determined by various factors such as approach angle, stall speed, and glide slope.

During descent, the pilot manages corrections for side-winds, updrafts, and downdrafts to aim for a specific touchdown point on the runway.

Typically, the descent rate of an aircraft during landing is about 500 feet per minute, translating to approximately 8 mph.

Answer:

-10u^3

5u^3

15u^3

-5u^3

Step-by-step explanation:

Given tiles

-15u^3+5u^3

10u^3+(-5u^3)

10u^3+5u^3

5u^3+(-10u^3)

Monomial : that type of polynomial in which only one term .

coefficient of like terms means  same viable with same power  -15 and 5 .

Therefore, coefficient of these two terms added and no change in power of u^3

Answer:

Likely is the answer

Step-by-step explanation:

If you know the probability line you will know how to get the answer

Answer:

the next five terms are:

[tex]\frac{1}{ab} , \frac{1}{a^{3} } ,\frac{b}{a^{5} } ,\frac{b^{2} }{a^{7} } ,\frac{b^{3} }{a^{9} }[/tex]

Step-by-step explanation:

A geometric serie is a succession of terms on which every terms is the result of the last term multiply to a common ratio. for example, a geometric serie with inicial terms equal to 2 and the common ratio is 3, the four first numbers of the serie is given by

2, 6, 18, 54

Where every term is calculate as:

first term = 2

second term = first term x common ratio = 2 * 3 = 6

third term = second term x common ratio = 6 * 3 = 18

fourth term = third term x common ratio= 8 * 3 = 54

Then, with this exercise we have the same situation, the first term is [tex]\frac{a}{b^{2} }[/tex] and the common ratio is [tex]\frac{b}{a^{2} }[/tex], so we get:

first term = [tex]\frac{a}{b^{2} }[/tex]

second term = first term * common ratio = [tex]\frac{a}{b^{2} } *\frac{b}{a^{2} } = \frac{1}{ab}[/tex]

third term = second term * common ratio = [tex]\frac{1}{ab} *\frac{b}{a^{2} } =\frac{1}{a^{3} }[/tex]

fourth term = third term * common ratio = [tex]\frac{1}{a^{3} } *\frac{b}{a^{2} } = \frac{b}{a^{5} }[/tex]

fifth term = fourth term * common ratio= [tex]\frac{b}{a^{5} } *\frac{b}{a^{2} } = \frac{b^{2} }{a^{7} }[/tex]

sixth term = fifth term * common ratio= [tex]\frac{b^{2} }{a^{7} } *\frac{b}{a^{2} } = \frac{b^{3} }{a^{9} }[/tex]

so, the next five terms are:

[tex]\frac{1}{ab} , \frac{1}{a^{3} } ,\frac{b}{a^{5} } ,\frac{b^{2} }{a^{7} } ,\frac{b^{3} }{a^{9} }[/tex]

Answer:

March.

Step-by-step explanation:

We have been given that in March Tom had -£165 in his bank account. In April he had -£156.

We know that the a biggest negative number has least value as biggest negative numbers lie on the extreme left on the number line.

Since -£165 is more negative than -£156, so -£165 is the least amount.

Therefore, Tom had least amount of money in his account in March.

Answer:

398 ( did it on college bridge)

Step-by-step explanation:

The required value of the expression is 412 which is determined by substituting for x = 4 and y = 6.

Unknown variables, numbers, and arithmetic operators make up an algebraic expression. It contains no equality or inequality symbols.

The expression is given in the question as:

(4x−12)+(12xy−10)(4x-12)+(12xy-10)

To find the value of the expression for a given value of x and y, we can substitute the values of x and y into the expression and evaluate it.

(4x−12)+(12xy−10)(4x-12)+(12xy-10)

Substituting x=4 and y=6 into the expression, we get:

(4(4)−12)+(12(4)(6)−10)(4(4)−12)+(12(4)(6)−10)

This simplifies to:

(16−12)+(12(24)−10)(16−12)+(12(24)−10)

This further simplifies to:

4+(12(24)−10)(4)+(12(24)−10)

4+(12(24)−10)(4)+(12(24)−10)

4+288+120 = 412

Therefore, the value of the expression for x = 4 and y = 6 is 412.

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[tex] nPk=\dfrac{n!}{(n-k)!}\\\\
\dfrac{ 10P6}{10P4}=\dfrac{\dfrac{10!}{4!}}{\dfrac{10!}{6!}}=\dfrac{10!}{4!}\cdot\dfrac{6!}{10!}=5\cdot6=30 [/tex]

Answer:

[tex]\frac{5}{7}[/tex]

Step-by-step explanation:

Let

x------->the probability of its complement

we know that

The Complement Rule states that the sum of the probabilities of an event and its complement must equal [tex]1[/tex]

so

in this problem

[tex]\frac{2}{7}+x=1[/tex]

solve for x

Adds [tex]-\frac{2}{7}[/tex] both sides

[tex]x=1-\frac{2}{7}[/tex]

[tex]x=\frac{5}{7}[/tex]

The probability of its complement is 5/7

The complement of a probability event is the event that contains all of the universal elements of the event but is not found in the provided event.

From the given information:

The complement of an event is mathematically calculated as:

P(C') = 1 - (x)

P(C') = 1 - 2/7

P(C') = 5/7

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Answer:

60%

Step-by-step explanation:

Since the entire percentage is 100 than  40 plus 60 is a hundred