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4 years ago

What is the solution to the system below 4x +y=1 and y=6x+1

Mathematics

2 answers:

ruslelena [56]4 years ago

8 0

Step-by-step explanation:

4x+y=1-(1)

-6x+y=1-(2)

solve simultaneously

10x =0

X=0/10

X=0

solve for X in (1)

4(0)+y=1

0+y=1

y=1-0

y=1

finlep [7]4 years ago

5 0

Answer:x = 0

y = 1

Step-by-step explanation:

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The side of each of the equilateral triangles in the figure is twice the side of the central regular hexagon. What fraction of t

lana [24]

Answer:

The fraction is 1/4

Step-by-step explanation:

we know that

The area of an equilateral triangle, using the law of sines is equal to

$A=\frac{1}{2}x^{2}sin(60^o)$

$A=\frac{1}{2}x^{2}(\frac{\sqrt{3}}{2})$

$A=x^{2}\frac{\sqrt{3}}{4}$

where

x is the length side of the triangle

In this problem

Let

b ----> the length side of the regular hexagon

2b ---> the length side of the equilateral triangle

step 1

Find the area of the six triangles

Multiply the area of one triangle by 6

$A=6[x^{2}\frac{\sqrt{3}}{4}]$

$A=3x^{2}\frac{\sqrt{3}}{2}$

we have

$x=2b\ units$

substitute

$A=3(2b)^{2}\frac{\sqrt{3}}{2}\\\\A=6b^{2}\sqrt{3}\ units^2$

step 2

Find the area of the regular hexagon

Remember that, a regular hexagon can be divided into 6 equilateral triangles

The area of the regular hexagon is the same that the area of 6 equilateral triangles

$A=3x^{2}\frac{\sqrt{3}}{2}$

we have

$x=b\ in$

substitute

$A=3(b)^{2}\frac{\sqrt{3}}{2}$

step 3

To find out what fraction of the total area of the six triangles is the area of the hexagon, divide the area of the hexagon by the total area of the six triangles

$3(b)^{2}\frac{\sqrt{3}}{2}:6b^{2}\sqrt{3}=\frac{3}{2} :6=\frac{3}{12}=\frac{1}{4}$

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4 years ago

What is the inverse of the given relation?<br> y=3x+12

daser333 [38]

We are asked in the problem to determine the inverse of the relation y = 3x + 12. first step is to express the equation in terms of y, that is y -12 = 3x, then exchange the places of x and y, that is x - 12 = 3y. This is the final answer

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What is the solution to the system below 4x +y=1 and y=6x+1​

What is the solution to the system below 4x +y=1 and y=6x+1