All categories

3 years ago

Determine whether each ordered pair is a solution to the inequality x+y<−1.

Mathematics

1 answer:

leva [86]3 years ago

6 0

Answer:

Step-by-step explanation:

coordinates pair (2,11) does not go with the inequality

You might be interested in

let sin(θ) =3/5 and tan(y) =12/5 both angels comes from 2 different right trianglesa)find the third side of the two tringles b)

statuscvo [17]

In a right triangle, we haev some trigonometric relationships between the sides and angles. Given an angle, the ratio between the opposite side to the angle by the hypotenuse is the sine of this angle, therefore, the following statement

$\sin (\theta)=\frac{3}{5}$

Describes the following triangle

To find the missing length x, we could use the Pythagorean Theorem. The sum of the squares of the legs is equal to the square of the hypotenuse. From this, we have the following equation

$x^2+3^2=5^2$

Solving for x, we have

$\begin{gathered} x^2+3^2=5^2 \\ x^2+9=25 \\ x^2=25-9 \\ x^2=16 \\ x=\sqrt[]{16} \\ x=4 \end{gathered}$

The missing length of the first triangle is equal to 4.

For the other triangle, instead of a sine we have a tangent relation. Given an angle in a right triangle, its tanget is equal to the ratio between the opposite side and adjacent side.The following expression

$\tan (y)=\frac{12}{5}$

Describes the following triangle

Using the Pythagorean Theorem again, we have

$5^2+12^2=h^2$

Solving for h, we have

$\begin{gathered} 5^2+12^2=h^2 \\ 25+144=h^2 \\ 169=h^2 \\ h=\sqrt[]{169} \\ h=13 \end{gathered}$

The missing side measure is equal to 13.

Now that we have all sides of both triangles, we can construct any trigonometric relation for those angles.

The sine is the ratio between the opposite side and the hypotenuse, and the cosine is the ratio between the adjacent side and the hypotenuse, therefore, we have the following relations for our angles

$\begin{gathered} \sin (\theta)=\frac{3}{5} \\ \cos (\theta)=\frac{4}{5} \\ \sin (y)=\frac{12}{13} \\ \cos (y)=\frac{5}{13} \end{gathered}$

To calculate the sine and cosine of the sum

$\begin{gathered} \sin (\theta+y) \\ \cos (\theta+y) \end{gathered}$

We can use the following identities

$\begin{gathered} \sin (A+B)=\sin A\cos B+\cos A\sin B \\ \cos (A+B)=\cos A\cos B-\sin A\sin B \end{gathered}$

Using those identities in our problem, we're going to have

$\begin{gathered} \sin (\theta+y)=\sin \theta\cos y+\cos \theta\sin y=\frac{3}{5}\cdot\frac{5}{13}+\frac{4}{5}\cdot\frac{12}{13}=\frac{63}{65} \\ \cos (\theta+y)=\cos \theta\cos y-\sin \theta\sin y=\frac{4}{5}\cdot\frac{5}{13}-\frac{3}{5}\cdot\frac{12}{13}=-\frac{16}{65} \end{gathered}$

4 0

1 year ago

Please help I need to get this done

hichkok12 [17]

Answer:

Step-by-step explanation:

So you take 7x-92+6x+12=180

And then you get x=20

Plug in 20 for x for <LOM

And you get and you get 48

Hope this helped!!

3 0

3 years ago

charmaine purchased a prepaid phone card for $25. Long distance calls cost 6 cents a minute using this card. Charmaine used her

neonofarm [45]

25-23.08=1.92

1.92/0.6=3.2

her call last 3.2minutes

7 0

4 years ago

The radius of a circle 6 cm what is the circles area?

dolphi86 [110]

Answer:

113.04 cm

Step-by-step explanation:

We know the formula to find the area of a circle is

$A= pi(r^{2})$

And we are told to use 3.14 instead of pi so what we have now is,

$A=3.14(r^{2})$

We are also told the radius, r, is 6. So our equation now looks like this,

$A=3.14(6^{2})\\\\6^{2}$ is the same as 36, because 6x6 is 36.

Now we have,

$A=3.14(36)$

Which equals 113.04 and that is the area!

Hope that helps and have a great day!

7 0

3 years ago

How to solve x=6y-11 and 3x-2y=-1 by substitution

vagabundo [1.1K]

Substitute x into the second equation:
3(6y-11)-2y=-1
18y-33-2y=-1
16y=32
y=2
Then put the y value into the first equation to get x:
x=6(2)-11
x=1
There you go!

Please mark brainliest

7 0

3 years ago