Answer:
5
Step-by-step explanation:
Divide 30 by 6, since this will find the number of chairs she can paint in 1 minute:
30/6
= 5
So, the constant of proportionality is 5, since she can paint 5 chairs in a minute.
Answer:
"SAS" is when we know two sides and the angle between them. Then use the three angles add to 180° to find the last angle.
Step-by-step explanation:
The angle must be between the two sides
A. B. and C. are incorrect expressions for the slope.
m (slope) = rise/run = y2-y1/x2-x1 = change in the independent variable relative to the change in dependent variable
y is the independent variable and x is the dependent variable
For example, lets take
We need to first factor the numerator and denominator to find the common numbers which we can simplify it by.
If we divide by 5 x 5 on both the numerator and denominator because both of them have it in common, we will get the simplest form.
9514 1404 393
Answer:
y = 11.2 in
Step-by-step explanation:
The product of segment lengths to the near and far intersection points of the secant with the circle are the same for all secants from the same external point. Here, there are three, so we have the relations ...
9×9 = 5(5+y) = x(x+19)
Then the value of y can be found as ...
81/5 = 5+y
16.2 -5 = y = 11.2
__
The value of x is a little trickier, as a quadratic is involved.
81 = x² +19x
81 + 90.25 = x² +19x +90.25 . . . . complete the square
171.25 = (x +9.5)²
x = √171.25 - 9.5 ≈ 3.58625...
__
<em>Additional comment</em>
For the purpose here, the tangent can be considered to be a degenerate case of a secant in which the two points of intersection with the circle are the same point. For the purpose of this calculation, the length of the tangent is squared. (The distance to the points of intersection is the same.)
I find it easier to remember one rule, rather than a separate rule for tangents. With some imagination, the same rule can be applied when the "secants" meet <em>inside</em> the circle. In that case, they are called "chords".
We have shown the value for x because we suspect some versions of this question may ask for x instead of y. (Rounding may be required in that case.)
