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OLEGan [10]
2 years ago
9

Solve the system of equations and choose the correct ordered pair.2x + 6y = 63x – 2y = 20

Mathematics
1 answer:
AnnyKZ [126]2 years ago
5 0

The first step I would do is split this into two functions so we can work with this system hand to hand. This is what it will look like:

2x + 6y = 20

63x - 2y = 20

It's easier to employ math strategies for system of equations when it is written like this.

Now, we are going to multiply every term in the second equation by 3. The reason for this is because we want to cancel either the x's or the y's, and if we multiply the bottom equation by 3, then the y becomes -6y, which we can combine with the +6y in the first equation to cancel out the y's. The first step looks like this:

2x + 6y = 20

189x - 6y = 60

(every number in the second equation was multiplied by 3)

Now, we can combine both of these equations into one, by combining each term seperately. In other words, the 189x and the 2x combine into 191x, the 6y and -6y cancel each other out, and the 60 and 20 on the right side of the equal sign combine into 80. This is what it looks like after combining:

191x = 80

Now, we just solve for x:

x =  \frac{80}{191}

Now that we have x, we can plug it in into one of the other equations to get y. It will be easier to plug x into the first equation, since 2 and 6 tend to be smaller numbers:

2 (\frac{80}{191})  + 6y = 20

Multiply the fraction by 2:

\frac{160}{191}  + 6y = 20

Subract the fraction on both sides:

6y = 20 -  \frac{160}{191}

Divide both sides by 6:

y =  \frac{20 -  \frac{160}{191} }{6}

Im going to use my calculator to simplify y. If you want to know how to simply this, let me know in the comments:

y =  \frac{610}{191}

So finally, our ordered pair, and the answer itself is:

( \frac{80}{191} \:  \frac{610}{191} )

(With a comma between both numbers)

Let me know if you have any questions or concerns in the comments ;)

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3 years ago
An 18 ft. tree casts a 15 ft. long shadow as shown in the following figure. Which of the following is the angle formed by the su
BabaBlast [244]

Answer:

The angle is 50.2°.

Step-by-step explanation:

The tree and its shadow from a right triangle with the tree being the perpendicular and the shadow being the base as shown in the figure attached.

Therefore the angle θ formed by the sun's rays and the ground is:

\theta = tan^-1(\frac{18}{15} )=\boxed{50.2^o}

8 0
2 years ago
PLS HELP!!<br><br> What values of u and v make triangle XYZ = Triangle GFH
Katarina [22]

Answers:

u = 18

v = 20

========================================================

Work Shown:

The leg YZ is congruent to the left FH

This means YZ = FH and that leads to u+v-18 = 10u-8v

The hypotenuse ZX is congruent to the hypotenuse HG

This means ZX = HG and we get the equation 14v-14u+32 = v+u+22

----------------------

The system of equations we have so far is

u+v-18 = 10u-8v

14v-14u+32 = v+u+22

Let's get the equations into standard form

Start with the first equation

u+v-18 = 10u-8v

u+v = 10u-8v+18

u+v-10u+8v = 18

-9u+9v = 18

-9(u-v) = 18

u-v = 18/(-9)

u-v = -2

Note how we can solve for the variable u to get

u = v-2

which we'll use later

----------------------

Let's get the other equation into standard form as well

14v-14u+32 = v+u+22

14v-14u-v-u = 22-32

-15u+13v = -10

Now plug in u = v-2 and solve for v

-15u+13v = -10

-15(v-2) + 13v = -10

-15v+30+13v = -10

-2v+30 = -10

-2v = -10-30

-2v = -40

v = -40/(-2)

v = 20

Which means,

u = v-2

u = 20-2

u = 18

3 0
2 years ago
How will you find the distance between these two points using Pythagorean theorem?
kow [346]
R represents radius or the distance between two points, the pythagorean expression will be
r² = Δx² + Δy²
Δ means the change, Δx means the change of x, Δy means the change of y

Given:
(x₁,y₁) = (-5,-1)
(x₂,y₂) = (0,2)

Input the numbers to the expression
r² = Δx² + Δy²
r² = (x₂ - x₁)² + (y₂ - y₁)²
r² = (0 + 5)² + (2 + 1)²
r² = 5² + 3²
r² = 25 + 9
r² = 34
r = √34

The distance is √34 unit length
3 0
2 years ago
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