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#11 and #13 geometry help please help need work shown as well !!

Trava [24]

Answer: In diagram (11) X = 30 degrees and Y = 60 degrees

In diagram (13) X = 20.55 degrees and Y = 69.45 degrees

Step-by-step explanation: What we have are two right angled triangles with two sides given in each case, therefore we can calculate the two unknown angles (since the third angle equals 90 degrees).

For the second triangle (number 13) we shall use Y as the reference angle. That means we have an opposite (the side facing the reference angle) which is 24 and we have an adjacent (the side that lies between the right angle and the reference angle) which is 9. Hence,

Tan Y = opposite/adjacent

Tan Y = 24/9

Tan Y = 2.6667

Checking with your calculator or table of values, 2.6667 = 69.45

Having two angles, which are 90 and 69.45, the third angle X can be computed as

X = 180 - (90 + 69.45)

Sum of angles in a triangle equals 180

X = 180 - 159.45

X = 20.55 and Y = 69.45

For the first triangle (number 11) we shall use X as the reference angle. We have two sides, the opposite (the side facing the reference angle) which is 3, and the hypotenuse (side facing the right angle) which is 6. Hence,

Sin X = opposite/hypotenuse

Sin X = 3/6

Sin X = 0.5000

Checking with your calculator or table of values,

X = 30 degrees.

Also, now that we have two angles we can easily compute the third angle as follows

Y = 180 - (90 + 30)

Sum of angles in a triangle equals 180

Y = 180 - 120

Y = 60

X = 30 and Y = 60

4 0

3 years ago

Which equation shows the result of substituting and expression for y from the first equation into the second equation for the gi

krek1111 [17]

Answer:

x-2x = -3 and x = 3

Step-by-step explanation:

Given the expression

y=x+5.... 1

y-2x=2.... 2

Substituting the first equation into the second we will have;

From 2;

y -2x = 2

x+5-2x = 2

x-2x +5 = 2

x-2x = 2-5

x-2x = -3

-x =-3

x =3

Hence the required equation is x-2x = -3 and x = 3

7 0

2 years ago

Read 2 more answers

What is a point-slope equation of the line with slope -12 that goes through the point (5,3)

laila [671]

Answer:

y-3 = -12 (x-5)

Step-by-step explanation:

The point slope form of an equation is

y-y1 = m(x-x1) where m is the slope and (x1,y1) is the point

y-3 = -12 (x-5)

7 0

3 years ago

A small plane took 3 hours to fly 960 km from Ottawa to Halifax with a tail wind. On the return trip, flying into the wind, the

Rina8888 [55]

Answer:

Wind speed: $\rm 40\; km \cdot h^{-1}$ .
Speed of the plane in still air: $\rm 320\; km \cdot h^{-1}$ .

Step-by-step explanation:

This problem involves two unknowns:

wind speed, and
speed of the plane in still air.

Let the speed of the wind be $x \rm \; km \cdot h^{-1}$ , and the speed of the plane in still air be $y\rm \; km \cdot h^{-1}$ . It takes at least two equations to find the exact solutions to a system of two variables.

Information in this question gives two equations:

It takes the plane three hours to travel $\rm 960\; km$ from Ottawa to with a tail wind (that is: at a ground speed of $x + y$ .)
It takes the plane four hours to travel $\rm 960\; km$ from Halifax back to Ottawa while flying into the wind (that is: at a ground speed of $-x + y$ .)

Create a two-by-two system out of these two equations:

$\left\{ \begin{aligned}&3(x + y) = 960 && (1) \\ &4(-x + y) = 960 && (2) \end{aligned}\right.$ .

There can be many ways to solve this system. The approach below avoids multiplying large numbers as much as possible.

Note that this system is equivalent to

$\left\{ \begin{aligned}&4 \times 3 (x + y) = 4\times960 && 4 \times (1) \\ &3\times 4(-x + y) = 3\times 960 && 3 \times (2) \end{aligned}\right.$ .

$\left\{ \begin{aligned}&12 x + 12y = 4\times960 && 4 \times (1) \\ &- 12x + 12y = 3\times 960 && 3 \times (2) \end{aligned}\right.$ .

Either adding or subtracting the two equations will eliminate one of the variables. However, subtracting them gives only $1 \times 960$ on the right-hand side. In comparison, adding them will give $7 \times 960$ , which is much more complex to evaluate. Subtracting the second equation ( $3 \times (2)$ ) from the first ( $4 \times (1)$ ) will give the equation