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jek_recluse [69]
2 years ago
11

Which is the equation of the line that has a slope of 1/2​

Mathematics
2 answers:
Studentka2010 [4]2 years ago
6 0

y= 1/2x-2

hope that help!

aleksley [76]2 years ago
3 0

Answer:

y=1/2x-2

Step-by-step explanation:

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Consider the points A(5, 3t+2, 2), B(1, 3t, 2), and C(1, 4t, 3). Find the angle ∠ABC given that the dot product of the vectors B
Vilka [71]

Answer:

66.42°

Step-by-step explanation:

<u>Given:</u>

A(5, 3t+2, 2)

B(1, 3t, 2)

C(1, 4t, 3)

BA • BC = 4

Step 1: Find t.

First we have to find vectors BA and BC. We do that by subtracting the coordinates of the initial point from the coordinates of the terminal point.

In vector BA B is the initial point and A is the terminal point.

BA = OA - OB = (5-1, 3t+2-3t, 2-2) = (4, 2, 0)

BC = OC - OB = (1-1, 4t-3t, 3-2) = (0, t, 1)

Now we can find t because we know that BA • BC = 4

BA • BC = 4

To find dot product we calculate the sum of the produts of the corresponding components.

BA • BC = (4)(0) + (2)(t) + (0)(1)

4 = (4)(0) + (2)(t) + (0)(1)

4 = 0 + 2t + 0

4 = 2t

2 = t

t = 2

Now we know that:

BA = (4, 2, 0)

BC = (0, 2, 1)

Step 2: Find the angle ∠ABC.

Dot product: a • b = |a| |b| cos(angle)

BA • BC = 4

|BA| |BC| cos(angle) = 4

To get magnitudes we square each compoment of the vector and sum them together. Then square root.

|BA| = \sqrt{4^2 + 2^2 + 0^2} = \sqrt{20} = 2\sqrt{5}

|BC| = \sqrt{0^2 + 2^2 + 1^2} = \sqrt{5}

2\sqrt{5}\sqrt{5}\cos{(m\angle{ABC})} = 4

10\cos{(m\angle{ABC})} = 4

\cos(m\angle{ABC}) = \frac{4}{10}=\frac{2}{5}

m\angle{ABC} = cos^{-1}{(\frac{2}{5})}

m\angle{ABC} = 66.4218^{\circ}

Rounded to two decimal places:

m\angle{ABC} = 66.42^\circ

3 0
1 year ago
Which greater 9.28 or 9.3
saul85 [17]
9.3 is greater than 9.28 :)
5 0
3 years ago
Read 2 more answers
A set of data included the numbers 19, 81, 75, 42, 33 57, and 60. What number could be added to the data to cause the range to b
dsp73

Answer:

109

Step-by-step explanation:

81-19 is 62. if you add 109 then you could do 109-19 is 90

6 0
3 years ago
Could somebody please help me find the answers for 'x' for these pictures?
djyliett [7]

Answer:

(in order) #1

for the first one you have a vertical angle. Vertical angle is basically any 2 lines who intersect each other. The opposite sides will be congruent.

So in this case

2x+8 and 110 are oppostie sides.

2x+8=110

Which is x= 51

#2

For the second one you have supplementray angles

Now for supplementary angles its basically 2 angles added up that form a straight line And 180 degress is always the measure of a straight line. SO in this case we do

9x+12x+75=180

Which is x=5

#3

This is also a vertical angle pair and their congruent just like #1

So 5x+5=65

x=12

4 0
2 years ago
Read 2 more answers
Change 2x-y=-4 into slope-intercept form with steps
Art [367]

Answer:

Y=2x+4

Step-by-step explanation:

2x-y=-4

subtract 2x

-y=-2x-4

divide by -1

y=2x+4

3 0
3 years ago
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