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valentinak56 [21]
3 years ago
6

Identify the equation in slope-intercept form for the line containing the point (2,1) and parallel to y=5/3x−1/3.

Mathematics
1 answer:
Gekata [30.6K]3 years ago
3 0

Answer:

y = 5/3x -7/3

Step-by-step explanation:

parallel lines will have the same slope

m = 5/3, point (2, 1)

use point-slope form to find the new equation for the parallel line

y - 1 = 5/3(x - 2)

y = 5/3x - 10/3 + 1

y = 5/3x -7/3

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find the length of the line segment with end points (7,2) and (-4,2) explain how you arrived at your solution
Inga [223]

Answer:

<h2>11 units</h2>

Step-by-step explanation:

Method 1:

The formula of a distance between two points:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

We have the points (7, 2) and (-4, 2). Substitute:

d=\sqrt{(2-2)^2+(-4-7)^2}=\sqrt{0^2+(-11)^2}=\sqrt{11^2}=11

Method 2:

Look at the picture. Mark points in the coordinate system.

Read the length of the segment.

6 0
3 years ago
Factor sec^2x-secx+tan^2x
marysya [2.9K]

Answer:

sec²(x) - sec(x) + tan²(x) = (sec(x) - 1)(2sec(x) + 1)

Step-by-step explanation:

sec²(x) - sec(x) + tan²(x) =

= sec²(x) - sec(x) + [sec²(x) - 1]

= sec²(x) - sec(x) + [(sec(x) + 1)(sec(x) - 1)]

= sec(x)[sec(x) - 1] + [(sec(x) + 1)(sec(x) - 1)]

= (sec(x) - 1)(sec(x) + sec(x) + 1)

= (sec(x) - 1)(2sec(x) + 1)

6 0
3 years ago
What is the measure of the vertex angle of an isosceles
pshichka [43]

Answer:

A) 96

Step-by-step explanation:

The 2 base angles are both 42* thus adding up to 84*. 180-84=96

You are welcome.

3 0
3 years ago
A bus makes a stop at 2:30, letting off 16 people and letting on 3. The bus makes another stop ten minutes later to let off 2 mo
liq [111]

Answer:

10 people lesser.

Step-by-step explanation:

Initially, it 15 people  get off but 9 people get picked up, hence losing 6 people.  If 4 more people get off, it has then lost 10 people total.

The original number of passengers on the bus decreased by 10 after the second stop

Assume that the total passengers on the bus before 2:30 was x

Now, at 2:30:

15 passengers got off and 9 got on.

This means that:

number of passengers = x - 15 + 9 

number of passengers = x -6

10 minutes later:

4 passengers got off the bus

This means that:

number of passengers = (x-6) - 4

number of passengers = x - 10

The original number of passengers on the bus decreased by 10 after the second stop.

3 0
3 years ago
Triangle TUV was dilated to create triangle T'U'V' using point A as the center of dilation. What is the scale factor of the dila
Tomtit [17]
A dilation is a transformation, with center O and a scale factor of k that is not zero, that maps O to itself and any other point P to P'. The center O is a fixed point, P' is the image of P, points O, P and P' are on the same line.

Thus, a dilation with centre O and a scale factor of k maps the original figure to the image in such a way that the<span> distances from O to the vertices of the image are k times the distances from O to the original figure. Also the size of the image are k times the size of the original figure.

In the dilation of triangle TUV</span>, It is obvious that the image <span>T'U'V' is smaller than the original triangle TUV and hence the scale factor is less than 1.

</span>The ratio of the distances from A to the vertices of the image T'U'V'  to the distances from A to the original triangle TUV is the scale factor.

The scale factor = 3.2 / 4.8 = 2/3
8 0
3 years ago
Read 2 more answers
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