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2 years ago

Solve the system of equations 3x + y = 3 and 7x + 2y = 1.

Mathematics

1 answer:

vodka [1.7K]2 years ago

4 0

Answer:

(x, y) = (-5, 18)

Step-by-step explanation:

You have done the first two steps.

7x +2(3 -3x) = 1 . . . . . equation with y substituted

7x +6 -6x = 1 . . . . . . . eliminate parentheses using the distributive property

x = -5 . . . . . . . . . . . . . subtract 6 from both sides, collect terms

y = 3 -3(-5) . . . . . . . . use the substitution equation to find y

y = 18

The solution is (x, y) = (-5, 18).

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A 10-year annuity pays $1,850 per month, and payments are made at the end of each month. If the APR is 12 percent compounded mon

Fittoniya [83]

Based on the amount the annuity pays per month and the APR, the value of the annuity today is $133,349.85.

<h3>What is the present value of the annuity?</h3>

First, find the present value of the annuity at 5 years:

= 1,850 x present value interest factor of annuity, 60 months, 8/12%

= 1,850 x 49.32

= $91,242

Then find the present value of the annuity from 5 years till date:

= (1,850 x present value interest factor of annuity, 60 months, 12/12%) + ( 91,242) / (1 + 1%)⁶⁰)

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1 year ago

Derive the equation of the parabola with a focus at (_5, 5) and a directrix of y = -1.

mars1129 [50]

Answer: Option D is correct.

Step-by-step explanation:

Since we have given that

focus = (-5,5)

and a directrix y= -1

Since, equation of parabola in this case will be

$(x-h)^2=4.a(y-k)$

Now, here

$y=k-a=-1\\\\\text { focus =(h,k+a)}\\\\\text{So,} k+a=5\\\\\text{ by solving these two equation , we get }\\\\a=3\text{ and } k=2$

So equation will be

$(x+5)^2=4\times 3(y-2)\\\\(x+5)^2=12(y-3)\\\\y=\frac{1}{12}(x+5)^2+2$

So, option D is correct .

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