Calculus

2.5

X=27

x - y = -2

Get the y alone on the left.

- y = -2 - x

y = 2 + x

y = x + 2

This is the slope-intercept form. y=mx+b m=slope=1 and b=intercept=2

This means that the graph has a slope of 1, so goes up one unit for each unit it goes right, and crosses the y-axis at y=2. ■

2x + 3y = 12

x = 1.45, so

2 * 1.45 + 3y = 12

2.9 + 3y = 12

3y = 12 - 2.9 = 9.1

y = 9.1/3 = 3.0333... or 91/30 or 3 1/30.

x[x+1] squared

Simplified is, to my knowledge,

x squared plus ( x + 1) squared

2X + 50 = 5X - 10

subtract 2X from each side

50 = 3X - 10

add 10 to each side

60 = 3X

divide each side by 3

20 = X

check

2(20) + 50 = 5(20) - 10

40 + 50 = 100 - 10

90 = 90

checks

x equals (-5)

The graph of y = x - 8 is a straight line. The slope of the line is 1, and it intersects the y-axis at the point y = -8.

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I'm not sure what u mean by solving an identity. An identity is an equation that is always true, i.e., true for all values of the variable(s), in this case x. The only thing u can do with an identity is to prove that it is an identity. The problem here is that it is not an identity. Since sec x = 1 / cos x, the left side of the equation, when defined, is always = 1 (it is not defined when cos x = 0, because u cannot divide by 0). The right side, since tan x = sin x / cos x, is = sin2 x / cos x. When x = 0, the right side = 0 / 1 = 0. So it is not an identity.

Perhaps u meant how do u solve the equation. That is a completely different question, which means find what values of x makes the equation true. In this case, we need to find when the right side is = 1, so sin2 x = cos x (but not 0). Since sin2 x = 1 - cos2 x, this amounts to 1 - cos2 x = cos x, or 1 - cos2 x - cos x = 0. This is a quadratic equation in cos x, whose solutions are cos x = 0.61803398874989484820458683436564 and cos x = -1.6180339887498948482045868343656. The latter never happens (for real x), because cos x is always between -1 and 1. The other happens when x = 51.82729237298775250653169866715 degrees. This turns out to be, I believe, the arc cosine of the golden ratio.

Correction: 0.61803398874989484820458683436564 is actually the reciprocal of the golden ratio, so the answer I gave above is the arc sine of the golden ratio. Also, it is not the only solution. Subtracting it from 360 degrees gives 308.17270762701224749346830133285 degrees, which is another solution. Adding or subtracting any multiple of 360 degrees to or from either of those solutions will also work, since all trig functions are periodic with period 2 pi radians, or 360 degrees.

"Dingbot suspects that this answer contains gibberish". Dingbot is wrong - it looks fine to me.

My only reservation is the excess of precision. Surely four to six significant figures are enough (!). It's probably time to stop slavishly copying answers from Windows Calculator.

You're right. That's where I got the numbers from. I just thought that since this is not a physical measurement but a number that is the solution to a pure math equation, all the digits it gives me (except maybe the last one) are correct, so I might as well use what I have, rather than try to decide how many digits of precision to round to. I'll keep that in mind for future reference.

The graph of the first form passes through the origin while the second does not - unless c = 0.

If it took you, on average, 5 seconds to say each number, it would take you 27 * 5 million seconds, or 135 million seconds. Divide that by 86400 to get 1562.5 days. Divide that by 365.25 to get 4.28 years. And that not counting time to sleep, eat, and go to the bathroom.

0.5X - 1.5 - X = 5X

Combine terms: -1.5 - 0.5X = 5X

Add 0.5X to both sides: -1.5 = 5.5X

Didvide both sides by 5.5: X = -1.5/5.5 = -0.2727...

You want to move all like numbers and variables to the same side. You have 6x+13=2x+7. Subtract 2x from each side to have 6x-2x+13=7. Now subtract 13 from each side to have 6x-2x=7-13. Now work out each side to have 4x= -6. Divide each side by 4 to get x alone. Your answer should be x= -6/4. Reduce to -3/2. If you cannot have improper fractions, the mixed number would be -1 and 1/2. If you must answer in decimals, remember that 1/2=0.5, so your answer is -1.5.

10 since 10/5 = 2

7.446 is rounded to 7.45.

Look at the number to the right of the second decimal place (or the hundredth place), if:

x>= 5 then round up,

x<5 then round down.

Since 6 is >= 5 we round 4 up to 5.

The second equation works out as y = -1/2x+6 therefore it is perpendicular

You use the "vertical line test". If anywhere you can draw a vertical line that goes through two points of the graph, the relation is not a function; otherwise, it is a function. This is just another way of saying that in a function for every x value (input) there is AT MOST one y value (output).

8

If X = 5, then 5X = 5 x 5 = 25

4x+5=7x-8

the ansewr is 3.25

9000000 cubic centimetres = 9 cubic metres