Juan's age, x, is 4 times his age 15 years ago.

Answers

Answer 1

Answer: the answer to this question is 60 because 4 times 15 equals 60 so juans age is 60

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The shortest distance from a point to a straight line is

Answers

The shortest distance from a point to a straight line is the measurement of the line segment which connects the point to the straight line. This line segment should be perpendicular to the line and is thus called the perpendicular distance.

The center of a cricle ids (h,7) and the radius is 10. The circle passes through (3,-1). Find all possible values of h.

Answers

$center\ of\ a\ circle:(a;\ b)\n\nradius:r\n\n(x-a)^2+(y-b)^2=r^2\n\n========================\n\n(h;\ 7);\ r=10\n\n(x-h)^2+(y-7)^2=10^2\n\n========================$

$The\ circle\ passes\ throught\ (3;-1).\n\nSubstitute\ x=3\ and\ y=-1:\n\n(3-h)^2+(-1-7)^2=100\n\n(3-h)^2+(-8)^2=100\n\n(3-h)^2+64=100\ \ \ /-64\n\n(3-h)^2=36\iff3-h=\pm√(36)\n\n3-h=-6\ or\ 3-h=6\n-h=-6-3\ or\ -h=6-3\n-h=-9\ or\ -h=3\nh=9\ or\ h=-3\n\nAnswer:h=9\ or\ h=-3$

$equation\ of\ a\ circle:\n\n(x-h)^2+(y-7)^2=10^2\n\nif\ \ (x;y)=(3;-1),\ then\ \ (3-h)^2+(-1-7)^2=100\n\n(3-h)^2+64=100\n\n (3-h)^2=36\ \ \ \Leftrightarrow\ \ \ (3-h=6\ \ \ or\ \ \ 3-h=-6)\n\n3-h=6\ \ \ \ \ \Rightarrow\ \ \ h=-3\n3-h=-6\ \ \ \Rightarrow\ \ \ h=9\n\nAns.\ h=-3\ \ or\ \ h=9$

10+3(2xz+3y)2xz what's the answer.

Answers

$10+3(2xz+3y)\cdot 2xz=10+(6xz+9y)\cdot 2xz=\n \n=10+12x^2z^2+18xyz$

Three times a number s plus 4 times a number y is 1 more than 6 times the number s. solve for s

Answers

Three times a number s => 3s
4 times a number y => 4y
1 more than 6 times the number s => 6s + 1

The full equation would be:

3s + 4y = 6s + 1

Solve for s.
group same letter numbers and change its signs.
3s - 6s = -4y + 1
-3s = -4y + 1
solve for s. divide both sides by -3
-3s / -3 = (-4y + 1) / -3
s = (4y - 1) / 3

"Three times a number S" is 3s.
"Plus 4 times a number y" is + 4y
"is" =
"1 more than" is 1 +
"6 times the number S" is 6s.
The equation is:
3s+4y=1+6s
subtract 3s:
4y = 1 +3s
subtract 1:
4y - 1 = 3s
Divide everything by 3:
4y/3 - 1/3 = s

What is the value of the product (3 - 2i)(3 + 2i)