Answer:
15
Step-by-step explanation:
Given equation of the Circle is ,
And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,
Here we can say that ,
• <u>Radius</u> = 5 units
• <u>Centre </u> = (0,0)
<u>Finding</u><u> </u><u>distance</u><u> between</u><u> </u><u>the </u><u>two </u><u>points</u><u> </u><u>:</u><u>-</u><u> </u>
- Here we can see that the distance of point from centre is less than the radius.
<u>Hence </u><u>the</u><u> </u><u>point</u><u> </u><u>lies </u><u>within</u><u> </u><u>the </u><u>circle</u><u> </u><u>.</u>
<span>You are told that the two angles are supplementary. That means that when you add the measure
of angle A (call it mA) and the measure of angle B (call it mB) the resulting sum is 180 degrees.
This relationship can be written in equation form as:
.
mA + mB = 180
.
You are also told that the two angles are congruent. This means that their measures
are equal. You can write this relationship as the equation:
.
mA = mB
.
From this second equation you can see that wherever you have mA you can substitute mB
in its place because they are equals. So go back to the equation:
.
mA + mB = 180
.
In place of mA substitute mB. This makes the equation become:
.
mB + mB = 180
.
On the left side you can see that the sum is 2 times mB or 2*mB. Make this simplification
to get:
.
2*mB = 180
.
To solve for mB divide both sides of this equation by 2. When you do that division the
equation reduces to:
.
mB = 180/2 = 90
.
This tells you that the measure of angle B is 90 degrees, and that means that the measure
of angle A is also equal to 90 degrees because the two angles are congruent.
I hope this helps!</span>
Answer: D) 85
Step-by-step explanation:
The area of a rectangular prism is length * width * height(5*3.4*5)
5 * 3.4 * 5 = 85
Answer:
x = 6
Step-by-step explanation:
Since, ∠1 ≅ ∠2
By angle bisector theorem,

By substituting the measures of each side in the given ratio of the sides,

12 = x(x - 4)
12 = x² - 4x
x² - 4x - 12 = 0
x² - 6x + 2x - 12 = 0
x( x - 6) + 2(x - 6) = 0
(x + 2)(x - 6) = 0
x = -2, 6
Since, measure of the sides can't be negative, x can not be negative.
Therefore, x = 6 will be the answer.