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Natalka [10]
3 years ago
6

5 times a number is 6 less than the square of that number

Mathematics
1 answer:
Fed [463]3 years ago
3 0

Answer:

5x = x^2 - 6

Step-by-step explanation:

<em>a number</em> can be represented by x,

<em>5</em><em> times a number</em> can be represented as the product of 5 and x, <em>6</em> <em>less than the square of that number</em> tells us that this is equal to a number squared minus 6. <em>is</em> tells us that these two expressions are equal.

If you want a working number, just solve by completing the square once this is in standard form. This is then converted to vertex form.

x^2-5x-6 = <u>(</u><u>x-5</u><u>/</u><u>2</u><u>)</u><u>^</u><u>2</u><u>-</u><u>4</u><u>9</u><u>/</u><u>4</u> = (x^2-5x+25/4) -49/4 = x^2-5x-6.

(x-5/2)^2-49/4=0

(x-5/2)^2=49/4

(x-5/2) = ±√49/4

(x-5/2) = ±7/2

x=5/2±7/2

x=(5±7)/2

x=12/2,-2/2

x=6,-1

Thus, the number can either be 6 or -1.

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Answer:

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Step-by-step explanation:

The equation of a line in slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.

Perpendicular lines have opposite reciprocal slopes.

Anyways we need to find the slope of the line going through (10,6) and (5,5).

To find the slope, we are going to line up the points vertically and subtract vertically, then put 2nd difference over 1st difference. Like so:

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So the slope of the line through (10,6) and (5,5) is 1/5.

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The line we are looking for is y=-5x+b where we need to find the y-intercept b.

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