Four consecutive integers... n, n+1, n+2, n+3.
The product of the 1st and 4th is four less than twice the 1st multiplied by the 4th.
n(n+3)=2n(n+3)-4 perform indicated multiplications...
n^2+3n=2n^2+6n-4 subtract n^2 from both sides
3n=n^2+6n-4 subtract 3n from both sides
n^2+3n-4=0 factor
n^2-n+4n-4=0
n(n-1)+4(n-1)=0
(n+4)(n-1)=0, and since n>0
n=1
So the four numbers are 1, 2, 3, 4
check...
1(4)=2(1)4-4
4=8-4
4=4
In completing the square, the first step is to factor out the first and second term so that the factor (x+a) is highlighted. This is seen in line 1. However, in line 2, the subtracted value should be 3 so as to compensate for the added value. This affects then line 3 as well. The answer is line 2.
The total number of common tangents that can be drawn to the circles is 2.
<h3>What is a tangent?</h3>
A tangent serves as line that touches the circle at a single point whereby the point where tangent meets the circle is the tangency.
A tangent to a circle can be described as the straight line that touches the circle at only one point.
Therefore, from the definition, The total number of common tangents that can be drawn to the circles is 2.
Read more on the tangent here:
brainly.com/question/12926708
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Answer:
-4
Step-by-step explanation:
The question is missing the figure. So, it is in the atachment.
Answer: MN = x
LN = 
Step-by-step explanation: The first figure in the attachment is the figure of the question. The second figure is a way to respond this question by tracing the altitude from M to LN as suggested. When an altitude is drawn, it forms a 90° angle with the base, as shown in the drawing. To determine the other angle, you have to remember that all internal angles of a triangle sums up to 180°.
For the triangle <u>on the left</u> of the altitude:
45+90+angle=180
angle = 45
For the triangle <u>on the right</u>:
30+90+angle=180
angle = 60
With the angles, use the Law of Sines, which is relates sides and angles, as follows:
For MN:
MN = 
MN = x
For LN:
LN = 
We can determine sin (105) as:
sin(105) = sin(45+60)
sin(105) = sin(45)cos(60) + cos(45)sin(60)
sin(105) = 
sin(105) = 
LN =
LN = 
LN =
The expressions for:
MN = x
LN =
