Solve the system by graphing. Write the solution as an ordered pair. y = 1/3x + 2 y = –x – 2Help me please....I need good grades

Answers

Answer 1

Answer: ANSWER

The solution is where the two graphs intersect, which is
$(-3,1).$

EXPLANATION

The given system of equations are
$y = (1)/(3) x + 2$
and

$y = - x - 2$

We need to graph the two equations.

Let us graph

$y = (1)/(3) x + 2$
first.

We need at least two points.

You can choose any appropriate value for x and solve for y. Choosing zero makes our working easier. So let us plot the intercepts.

When
$x = 0$

$\Rightarrow \: y = (1)/(3) (0) + 2$

$\Rightarrow y = 0 + 2$

$\Rightarrow y = 2$

So this gives us the ordered pair,

$(0,2)$

When
$y = 0$
we get,

$0= (1)/(3) x + 2$

$\Rightarrow \: - 2 = (1)/(3) x$

$\Rightarrow \: - 2 * 3= x$

$\Rightarrow \: -6= x$
This also gives the ordered pair

$(-6,0).$

We plot these two points and draw a straight line through them to obtain the blue graph in the attachment.

For the second line

We again find the intercepts and plot them.

When
$x = 0$

$y = - 0 - 2$

$\Rightarrow \: y = - 2$

This gives the ordered pair

$(0,-2)$

Also, when
$y = 0$

then we have,

$0 = - x - 2$

$2 = - x$

$x = - 2$

Then we again have the ordered pair,

$(-2,0)$

We plot these two points on the same graph sheet to obtain the red graph above.

The intersection of the two lines is
$(-3,1)$

You will get good grades so don't worry much.

Answer 2

Answer:

Answer:

jh24

Step-by-step explanation:

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How many times greater is 700,000 than 70,000

Answers

700,000 is x of 70,000
700,000=x times 70,000
divide both sides by 70,000
10=x

answer is 10 times

10 times greater, if u multiply 70,000 by 10, you 'insert a zero' at the end, making it 700,000, 10 moves the decimal left and right one, just depends on if u multiply or divide

A flagpole broke in a storm. 7 meters are still sticking straight out of the ground, where it snapped, but the remaining piece has hinged over and touches the ground at a point 24 meters away horizontally.How tall was the flagpole before it broke?

Answers

32 meters tall.
It would form a right triangle, in which the shorter leg is 7m and the longer leg is 24m. You're looking for the last side, the hypotenuse. So use the Pythagorean theorem. a^2 + b^2 = c^2 , in which a and b are the legs and c is the hypotenuse.
Therefore, you get 7^2 + 24^2 = c^2.
Which is, 49 + 576 = c^2
Add, 625 = c^2.
Take the square root of 625, which is 25. So, the length of the hypotenuse (last side) is 25m. Add the 7m that is sticking out of the ground, to get 32m.

The broken part forms the hypotenuse of a right angled triangle.

So we have a right angled triangle, the vertical part is 7m, and the horizontal is 24m.

From Pythagoras' Theorem:

x² = 24² + 7²

x² = 576 + 49

x² = 625

x = √625

x = 25

So the broken part is 25m long.

The length of the flagpole before it was broken = 25 + 7

= 32m.

Really beautiful question.

2 wires help support a tall pole. 1 wire forms an angle of 48 degrees with the ground and the other wire forms an angle of 72 degrees with the ground The wires are 20 meters apart. How tall is the pole?

Answers

the height of the pole is 24.48 m

What is the concept of heights and distances?

The concept of heights and distances is the use of right triangles in real-world examples and solving for missing components using trigonometric ratios in a right triangle.

The scenario is illustrated below :

let triangle form with wire of angle 48 degree be BCD and that with angle 72 degree is ACD,

with, distance AB equals to = 20 m

Let AD be = y

the height of the pole CD = x

y represents the distance from the foot of one stabilizing wire to the foot of the pole.

In solving the triangles, we would apply the tangent trigonometric ratio which is expressed as

Tan θ = opposite side/adjacent side.

Considering triangle ACD,

Tan 72 = x/y

x = ytan72° = y ×3.077

x = 3.077y- - - - - - - - -(1)

Considering triangle BCD,

Tan48 = x/(20 - y)

x = (20 - y)tan48 = 1.11(30 - y)

x = 33.31 - 1.11y- - - - - - - - -(2)

Substituting equation 1 into equation 2, it becomes

3.077y= 33.31 - 1.11y

3.077y+ 1.11y = 33.31

4.187y = 33.31

y = 7.95 m

x = 3.077y

x = 3.077 x 7.95

x = 24.48 m

Therefore, the height of the pole is 24.48 m.

Learn more about heights and distances :

brainly.com/question/16726384

#SPJ2

First you'll want to draw your triangles (2 right triangles with the pole running through the middle). The angles you know are 72 degrees on the bottom left corner and 48 degrees on the bottom right corner. With this, you can figure out what the remaining angles are.
Angles of a triangle add up to 180 degrees so the missing top angle for the first triangle is 18 degrees (180 - (90 + 72)) and the missing top angle for the second triangle is 42 degrees.

You can now set up a ratio since angles are directly proportional to their opposite side. You know that the bottom is 20 meters. This means that 18/(18+42) = x/20, which simplifies to x = 6. This means the bottom of the first triangle is 6 meters, and it follows that the bottom of the second triangle is 12 meters (although you don't really need this information).

Now comes the trig. You need to figure out the length of the hypotenuse of one of the triangles so that you can use the Pythagorean Theorem to figure out the height of the pole. You can set up tan(72) = (6/x) - tangent is opposite over adjacent - which simplifies to x = 6/tan(72). You can plug this into your calculator (make sure you're in degrees mode) and you'll get x = 5.4024. This is the length of your hypotenuse.

Now plug this value into the Pythagorean Theorem (a^2+b^2=c^2) to get 6^2 + b^2 = (5.4024)^2 = c^2, c^2 = 65.1862, and c is approximately 8.0738!

8.0738 meters tall.

Which expressions are equivalent to when x0? Check all that apply.

Answers

we have that

$((x+4))/(3) / (6)/(x) = (x*(x+4))/(3*6) \n \n = (( x^(2) +4x))/(18)$

therefore

case a)
$((x+4))/(3) * (x)/(6)$
Is equivalent

case b)
$(6)/(x) * ((x+4))/(3)$
Is not equivalent

case c)
$(x)/(6) * ((x+4))/(3)$
Is equivalent

case d)
$((2 x^(2) +4x))/(6)$
Is not equivalent

case e)
$((2 x^(2) +4x))/(18)$
Is equivalent

Hence

the answer is

$((x+4))/(3) * (x)/(6)$

$(x)/(6) * ((x+4))/(3)$

$((2 x^(2) +4x))/(18)$