The equation in slope-intercept form represents a line that is parallel to y = 12x − 2 and passes through the point (−8,1) is y = 12x + 97
<em><u>Solution:</u></em>
Given that we have to write the equation in slope intercept form for line that is parallel to y = 12x − 2 and passes through the point (−8, 1)
<em><u>The slope intercept form is given as:</u></em>
y = mx + c ---- eqn 1
Where "m" is the slope of line and "c" is the y - intercept
Given equation of line is y = 12x - 2
On comparing the above equation with eqn 1,
m = 12
Thus slope of line is 12
We know that slopes of parallel lines are equal
Therefore, slope of line parallel to given line is also 12
Given point is (-8, 1)
We have to find the equation of line passing through (-8, 1) with slope m = 12
Substitute m = 12 and (x, y) = (-8, 1) in eqn 1
1 = 12(-8) + c
1 = -96 + c
c = 97
Substitute c = 97 and m = 12 in eqn 1
y = 12x + 97
Thus the required equation of line is found
The algebraic proof shows that the angles in an equilateral triangle must equal 60° each
<h3>Laws of cosines </h3>
From the question, we are to use the law of cosines to write an algebraic proof that shows that the angles in an equilateral triangle must equal 60°.
Given any triangle ABC, the measures of angles A, B, and C by the law of cosines are
cos A = (b^2 + c^2 - a^2)/2bc
cos B= (a^2 + c^2 - b^2)/2ac
cos C = (a^2 + b^2 - c^2)/2ab
Now, given that the triangle is equilateral, with each of the side lengths equal to s
That is, a = b = c = s
Then, we can write that
cos A = (s^2 + s^2 - s^2)/(2s×s)
cos A = (s^2 )/(2s^2)
cos A = 1/2
cos A = 0.5
∴ A = cos⁻¹(0.5)
A = 60°
Also
cos B = (s^2 + s^2 - s^2)/(2s×s)
cos B = (s^2 )/(2s^2)
cos B = 1/2
cos B = 0.5
∴ B = cos⁻¹(0.5)
B = 60°
and
cos C = (s^2 + s^2 - s^2)/(2s×s)
cos C = (s^2 )/(2s^2)
cos C = 1/2
cos C = 0.5
∴ C = cos⁻¹(0.5)
C = 60°
Thus,
A = 60°, B = 60° and C = 60°
Hence, the algebraic proof above shows that the angles in an equilateral triangle must equal 60° each.
Learn more on The law of cosines here: brainly.com/question/2866347
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Answer:
See explanation
Step-by-step explanation:
The given absolute value is
When we simplify this we get:
Any absolute value expression whose value is less than 0.14 is a solution.
For instance :
are all less than the 0.14
Since you haven't provided the options, we can't provide an exact answer.
Please remember to post a complete question next time.
Answer: Its A
Step-by-step explanation:
Its the most reasonable answer the others seem off
9514 1404 393
Answer:
∠KXN and ∠QXT
Step-by-step explanation:
The measure of each angle is the difference of the scale values that the rays intercept. (The same scale needs to be used for each ray.) Of course, complementary angles have a sum of 90°.
Here, we'll refer to angle aXb as "ab".
NP = 95 -35 = 60
PQ = 35 -20 = 15 . . . not complementary to NP
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KN = 165 -95 = 70
QT = 20 -0 = 20 . . . complementary to KN ⇒ your answer
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JK = 180 -165 = 15
PQ = 35 -20 = 15 . . . not complementary to JK
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JK = 15
NK = KN = 70 . . . not complementary to JK
