if PA=14 and PD=10 what is the length of PC

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

Answer:

The answer is 10 ft.  

Step-by-step explanation:

make a triangle 6ft tall, 8ft long (90 degrees to the other line) and draw a line to complete the triangle.  This is a type of 3,4,5 triangle, a 6,8,10.  The other way to do it is sqrt(6^2+8^2) = sqrt(36+64) = sqrt (100) = 10.

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]

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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[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:

(C)

Step-by-step explanation:

It is given that The steepest side of the model, AB, measures 4 inches, thus

From ΔABC, using the trigonometry, we have

[tex]\frac{AC}{AB}=sin45^{\circ}[/tex]

Substituting the given value, we have

⇒[tex]\frac{AC}{4}=sin45^{\circ}[/tex]

⇒[tex]AC=4{\times}\frac{1}{\sqrt{2}}[/tex]

⇒[tex]AC=2\sqrt{2}[/tex]

Now, from ΔACD, we have

[tex]\frac{AC}{AD}=sin30^{\circ}[/tex]

⇒[tex]\frac{2\sqrt{2}}{AD}=\frac{1}{2}[/tex]

⇒[tex]AD=4\sqrt{2}[/tex]

Therefore, the length of AD will be [tex]4\sqrt{2}[/tex]

thus, option C is correct.

Answer:

60%

Step-by-step explanation:

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

Answer:

Likely is the answer

Step-by-step explanation:

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

Answer:

D) EAC is equilateral triangle

Step-by-step explanation:

Given :

AEC is a triangle in which B∈ AC and D∈EC

Such that,

∠ABE = 90°,

∠ADE = 90°,

Also, BC = CD

We have to prove that :

Δ ABE is congruent to Δ EDA

Proof :

If EAC is an equilateral triangle,

By the property of equilateral triangle,

EA = AC = EC

If AC = EC

⇒ AB + BC = ED + CD

⇒ AB + CD = ED + CD

⇒ AB = ED

Also, AE = AE ( common segment )

Now, if in two right triangles hypotenuse are equal and any corresponding legs are equal,

Then, the other legs must be equal,

That is, BE = DA,

Hence, by SSS postulate of congruence,

Δ ABE ≅ Δ EDA

Therefore, option D is correct.

When x=7 , the first equation y = 200 + 350x has the greater value.

To determine which equation has the greater value when x=7, we need to evaluate both equations at x=7 and compare the resulting y values.

For the first equation [tex]\( y = 200 + 350x \):[/tex]

[tex]\[ y = 200 + 350 \times 7 \]\[ y = 200 + 2450 \]\[ y = 2650 \][/tex]

For the second equation y=3x

[tex]\[ y = 3 \times 7 \]\[ y = 21 \][/tex]

Comparing the values, we see that y=2650 for the first equation and y=21 for the second equation.

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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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:

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:

there are 6 sections and the sections are 4 x 4

 so the correct expression can be 6x4x4

Answer:

6 x 4 x 4

Step-by-step explanation:

IN order to calculate the total area or the cardboard you just have to make a simple multiplication, the carboard is divided in equal sized squares, 6 equal sizd squares, and each one of them has a 4 inches side, so to calculate the area of the cardboard you just calculate the area of one square and then multiply it by the number of squares.

Area of one square= 4x4

Number of squares=6

Total area of the carboard= 6x4x4