Today only, a table is being sold at a 27% discount. The sale price is $438 . What was the price yesterday?

Bob’s employer covers 23% of his family’s annual health insurance premium. The balance of the premium is deducted in equal amoun

Phantasy [73]

The amount withheld from Bob's paycheck is equivalent to the amount he pays for his family's health insurance premium, and because his employer covers 23% of the premium, the amount Bob pays is equivalent to 77% of the premium. Amount paid by Bob = 26 * 185.3 = $4,817.80 We divide this amount by 77% in order to calculate the total amount, 4,817.8 / 0.77 = $6,256.88 is Bob's family's annual health insurance premium

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3 years ago

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Where do the following graphs intersect? Show how you can find the intersection point algebraically.

nlexa [21]

Solve equation (1) for y
y-2x = 3
y-2x+2x = 3+2x
y = 2x+3

Plug that into equation (2)
y - 3 = x^2
2x+3 - 3 = x^2
2x = x^2

Get everything to one side
2x = x^2
2x-2x = x^2-2x
0 = x^2-2x
x^2-2x = 0

Now factor and use the zero product property to find the solutions for x
x^2-2x = 0
x(x-2) = 0
x = 0 or x-2 = 0
x = 0 or x = 2

If x = 0, then y is...
y = 2x+3
y = 2(0)+3
y = 3
So (x,y) = (0,3) is one solution of the system. This is one point where the graphs intersect.

If x = 2, then y is...
y = 2x+3
y = 2(2)+3
y = 4+3
y = 7
So (x,y) = (2,7) is another solution to the system. This is another point where the graphs intersect.

See the attached image for a visual. The two curves cross at point A and point B
A = (0,3)
B = (2,7)