We are concern about the vector (x-x0, y-y0, z-z0)
equaling to 5.
This happens
when √(x-x0)^2 + (y-y0)^2 + (z-z0)^2 = 5
Square
both side:
(x-x0)^2
+ (y-y0)^2 + (z-z0)^2 = 25 , a sphere
Which you will
recognize as a circle of radius one centered at (x0, y0, z0)
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Ok. In order to do this set up 2/5 divided by 5/7. The way you divide with fractions is by multiplying them but flipping the second fraction into 7/5 <---this is known as the reciprocal. In other words do:
2/5 x 7/5 =
14/25
There you go.
Answer:
A. at least two congruent sides
Step-by-step explanation:
Since, we know that,
'An isosceles triangle is a triangle having two sides of equal length or at least two sides of equal length (special case is equilateral triangle)'.
Thus, from the options, we see that,
Options B, C and D are not correct.
<em>Since, congruent sides means that the lengths of the sides are equal.</em>
Thus, we get that,
'An isosceles triangle has at least two congruent sides'.
Hence, option A is correct.
Answer:
-3, 1, 4 are the x-intercepts
Step-by-step explanation:
The remainder theorem tells you that dividing a polynomial f(x) by (x-a) will result in a remainder that is the value of f(a). That remainder will be zero when (x-a) is a factor of f(x).
In terms of finding x-intercepts, this means we can reduce the degree of the polynomial by factoring out the factor (x-a) we found when we find a value of "a" that makes f(a) = 0.
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For the given polynomial, we notice that the sum of the coefficients is zero:
1 -2 -11 +12 = 0
This means that x=1 is a zero of the polynomial, and we have found the first x-intercept point we can plot on the given number line.
Using synthetic division to find the quotient (and remainder) from division by (x-1), we see that ...
f(x) = (x -1)(x² -x -12)
We know a couple of factors of 12 that differ by 1 are 3 and 4, so we suspect the quadratic factor above can be factored to give ...
f(x) = (x -1)(x -4)(x +3)
Synthetic division confirms that the remainder from division by (x -4) is zero, so x=4 is another x-intercept. The result of the synthetic division confirms that x=-3 is the remaining x-intercept.
The x-intercepts of f(x) are -3, 1, 4. These are the points you want to plot on your number line.