What coordinate below is a solution to the system of equations : 6x+7y =-9 and -4x-5y=5?

1 answer:

mote1985 [20]3 years ago

6 0

6x + 7y = -9

-4x - 5y = 5

We can use either substitution or elimination. I prefer substitution so I will explain it that way. You can use elimination as well.

We can solve for x first so we will need to substitute y in terms of x.

6x + 7y = -9
7y = -9 - 6x
y = (-9 - 6x)/7

Plugging this into the other equation:

-4x - 5[(-9 - 6x)/7] = 5
-4x + (45 + 30x)/7 = 5
-28x + 45 + 30x = 35
2x + 45 = 35
2x = - 10
x = -5

Insert this into the other equation to solve for y.

6(-5) + 7y = -9
-30 + 7y = -9
7y = 21
y = 3

Your answer should be (-5, 3). Hope this helps!

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A large washer has an outer radius of 10mm and a hole with a diameter of 14mm. What is the area of the top surface of the washer

choli [55]

<h2>Answer:</h2>

The area of the top surface of the washer is: 160.14 square mm.

<h2>Step-by-step explanation:</h2>

The top of the surface is in the shape of a annulus with a outer radius of 10 mm and a inner radius of 7 mm ( since the diameter of the hole is: 14 mm and we know that the radius is half of the diameter)

Now, we know that the area of the annulus region is given by:

$Area=\pi (R^2-r^2)$

where R is the outer radius and r is the inner radius.

Here we have:

$R=10\ mm\\\\and\\\\r=7\ mm$

Hence, we have:

$Area\ of\ top\ surface=\pi (10^2-7^2)\\\\i.e.\\\\Area\ of\ top\ surface=\pi (100-49)\\\\i.e.\\\\Area\ of\ top\ surface=\pi\cdot 51\\\\i.e.\\\\Area\ of\ top\ surface=160.14\ mm^2$