Answer:
Q4: 8; -2; Q5: {7;4;1}.
Step-by-step explanation:
for more details see the attached picture, the answers are marked with red and green colours.
Note, the suggested solutions are not the only way.
Answer:
Step-by-step explanation:
Angle 1 and Angle 2 are identified as vertical pairs
An angle is produced at the <u>point</u> where two or more lines<em> meet</em>. Thus the <u>value</u> of LP required in the question is approximately 14.
Two<em> lines</em> are said to be <em>perpendicular</em> when a <u>measure</u> of the angle <u>between</u> them is a <em>right angle</em>. While <u>parallel</u> lines are lines that do not meet even when <u>extended</u> to <em>infinity</em>.
From the question, let the <u>length</u> of LP be represented by x.
Thus, from the given question, it can be <u>deduced </u>that;
LM ≅ PN = 20
KP = KN - PN
= 30 - 20
KP = 10
LP = x
Also,
<MLP is a right angle, so that;
< KLP = < KLM - <PLM
= 126 - 90
<KLP = ![36^{o}](https://tex.z-dn.net/?f=36%5E%7Bo%7D)
So that applying the Pythagoras theorem to triangle KLP, we have;
Tan θ = ![\frac{opposite}{adjacent}](https://tex.z-dn.net/?f=%5Cfrac%7Bopposite%7D%7Badjacent%7D)
Tan 36 = ![\frac{10}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7Bx%7D)
x = ![\frac{10}{Tan 36}](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7BTan%2036%7D)
= ![\frac{10}{0.7265}](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B0.7265%7D)
x = 13.765
Therefore the <em>side</em> LP ≅ 14.
For more clarifications on segments and angles, visit: brainly.com/question/4976881
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Answer:
y = -4
Step-by-step explanation:
We can find the equation of a line that goes through two given points on the plane by finding 1) the slope of the segment that joints the two points, and using the coordinates of one of the given points, and use this information in the "point-slope" form of the line.
To find the slope of the segment that joins the two points, we use the general equation for the slope given two coordinate pair points
as: ![slope=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=slope%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
In our case, using the given (-3,-4) as
, and (1,-4) as
, we get the following slope:
![slope=\frac{y_2-y_1}{x_2-x_1}\\slope=\frac{-4-(-4)}{1-(-3)}\\\\slope=\frac{-4+4}{1+3}\\slope=\frac{0}{4}=0](https://tex.z-dn.net/?f=slope%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5Cslope%3D%5Cfrac%7B-4-%28-4%29%7D%7B1-%28-3%29%7D%5C%5C%5C%5Cslope%3D%5Cfrac%7B-4%2B4%7D%7B1%2B3%7D%5C%5Cslope%3D%5Cfrac%7B0%7D%7B4%7D%3D0)
Therefore, the slope is zero (this means we are dealing with a horizontal line.
Now we complete the work by using the point-slope form of a line which is:
Using one of the given points (let's say (1,-4) as
, and the slope (0) that we just obtained, we get the following equation for the line in question:
![y-y_0=m(x-x_0)\\y-(-4)=0(x-1)\\y+4=0\\y=-4](https://tex.z-dn.net/?f=y-y_0%3Dm%28x-x_0%29%5C%5Cy-%28-4%29%3D0%28x-1%29%5C%5Cy%2B4%3D0%5C%5Cy%3D-4)
So y = -4 is the expression for the line