What is the value of x in the equation 3x-y = 30, when y = 15?

Explanation:

Okay so we can start by substituting in as we know what it is already:

Now at this stage we could use a calculator to figure out what of are though a bit of mental math is as easy:

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okay so now we have:

 add 10 to both sides to get rid of the

let's get rid of that fraction by multiplying by

 and there's the solution for x

We can check we got this right by substituting it back into the original equation with the known y:

now,  and we already know what out of is so :

that means

which is ✓

Therefore we know our solution is right.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

$450.00 for 6 weeks

or

$300

step-by-step explanation:

$200.00 for first week $50.00 x5 equals $250 plus $200 equals $450.00 for six weeks.

$200 for first week

$200 x 0.10 = $20

$20 x 5 = $100

$200 + $100 = $300