Given: KL is a tangent to the circle.
LM is another tangent to the circle.
We can use the tangent meeting at an external point theorem.
<em>Theorem</em>: <em>The tangent segments to a circle from an external point are equal.
</em>
Thus, we can say KL = LM, as they lie on a common circle, and are tangents to such circle.
4x - 2 = 3x + 3
4x - 3x = 3 + 2
x = 5
Since LM is 3x + 3, we can substitute the value of x to LM to render:
3(5) + 3 = 18
Thus, LM = KL = 18 units.
Answer:
The value of g(−2) is smaller than the value of g(4).
Step-by-step explanation:
To solve this, simply plug in the values in the given equation g(x)=8x-2.
g(-2)=8(-2)-2 -----> -18
g(4)=8(4)-2 ------> 30
here it is obvious that -18 is smaller than 30, therefore the value of g(−2) is smaller than the value of g(4).
Answer:
associative property
Step-by-step explanation:
Grouping like this
a + (b + c) = (a + b) + c
or
a(bc) = (ab)c
is the associative property
Answer:
Step-by-step explanation:
The quadrilateral has 4 sides and only two of them are equal.
A) to find PR, we will consider the triangle, PRQ.
Using cosine rule
a^2 = b^2 + c^2 - 2abcos A
We are looking for PR
PR^2 = 8^2 + 7^2 - 2 ×8 × 7Cos70
PR^2 = 64 + 49 - 112 × 0.3420
PR^2 = 113 - 38.304 = 74.696
PR = √74.696 = 8.64
B) to find the perimeter of PQRS, we will consider the triangle, RSP. It is an isosceles triangle. Therefore, two sides and two base angles are equal. To determine the length of SP,
We will use the sine rule because only one side,PR is known
For sine rule,
a/sinA = b/sinB
SP/ sin 35 = 8.64/sin110
Cross multiplying
SPsin110 = 8.64sin35
SP = 8.64sin35/sin110
SP = (8.64 × 0.5736)/0.9397
SP = 5.27
SR = SP = 5.27
The perimeter of the quadrilateral PQRS is the sum of the sides. The perimeter = 8 + 7 + 5.27 + 5.27 = 25.54 cm
