For numbers 15-17, we need to remember that two of a triangle's angles are always acute and the third angle will allow us to classify the triangle based on its angles. now that we know this, let's look at #15. the first two angles listed are acute, and the third is an obtuse angle, therefore it is an obtuse triangle. on #16 we have three acute angles, so it is an acute triangle. #17 has two acute angles and a right angle so it is a right triangle.
on numbers 21-23, we need to know that a triangle with all congruent sides is called equilateral, a triangle with two equal sides is isosceles, and a triangle with no equal sides is called scalene. #21 shows two equal sides so it is an isosceles triangle. #22 has three equal sides so it is an equilateral triangle. #23 has no equal sides so it is scalene. hope this helped! :)
Answer:
8.7 units
Step-by-step explanation:
Given is a right angled triangle (because the segment with 5 units length is tangent to circle. Tangent is perpendicular to RADIUS or diameter)
Let the length of the diameter be d units
By Pythagoras Theorem:
Notice that
(1 + <em>x</em>)(1 + <em>y</em>) = 1 + <em>x</em> + <em>y</em> + <em>x y</em>
So we can add 1 to both sides of both equations, and we use the property above to get
<em>a</em> + <em>b</em> + <em>a b</em> = 76 ==> (1 + <em>a</em>)(1 + <em>b</em>) = 77
and
<em>c</em> + <em>d</em> + <em>c d</em> = 54 ==> (1 + <em>c</em>)(1 + <em>d</em>) = 55
Now, 77 = 7*11 and 55 = 5*11, so we get
<em>a</em> + 1 = 7 ==> <em>a</em> = 6
<em>b</em> + 1 = 11 ==> <em>b</em> = 10
(or the other way around, since the given relations are symmetric)
and
<em>c</em> + 1 = 5 ==> <em>c</em> = 4
<em>d</em> + 1 = 11 ==> <em>d</em> = 10
Now substitute these values into the desired quantity:
(<em>a</em> + <em>b</em> + <em>c</em> + <em>d</em>) <em>a</em> <em>b</em> <em>c</em> <em>d</em> = 72,000
Though you did not list the points, I can tell you how to solve for the question.
One way to tell if a point lies on a given line is to take the point and plug it into the equation. If the equation remains true, then the point lies on the line. For example:
If we have the point (1,1), we can plug in 1 for x and 1 for y and see if the equation is true:
First we have to distribute the parentheses on the left side, 2*x is 2x and 2*-3 is -6, so now the equation is 4x+2x-6 = 8x+12
Then, we can add together the two x's on the left side,
so now we have 6x-6 = 8x+12 Subtract 12 from both sides and
you get 6x -18 = 8x Then you can subtract 6x from both the sides and get
-18 = 2x Now we can divide both sides by 2, and the final answer is -9 = x
Since they are not the same and the two sides aren't unequal, there is one solution(:
Hope this is helping you(:
