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2 years ago

Find the equation of the line that passes through (3,1) and is parallel to y=2x+3

Mathematics

1 answer:

ICE Princess25 [194]2 years ago

7 0

Answer:

y -1 = 2(x -3)

Step-by-step explanation:

The given equation is in slope-intercept form:

y = mx +b . . . . line with slope m and y-intercept b

y = 2x +3 . . . . . line with slope 2 and y-intercept 3

A parallel line will have the same slope. Since you are given a point, it is convenient to use the point-slope form for the equation you want:

y -k = m(x -h) . . . . . line with slope m through point (h, k)

y -1 = 2(x -3) . . . . . . line with slope 2 through point (3, 1)

Additional comment

If you want the slope-intercept form you can solve for y:

y = 2(x -3) +1 = 2x -6 +1

y = 2x -5 . . . . . slope-intercept form of the parallel line

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Help me jim! geometry homework

Maksim231197 [3]

Question 1

The angles 52 degrees match up. So if the sides are in proportion, then the triangles are similar.

Notice how 8/12 = 18/27 is a true equation. So the sides are in proportion to one another.

Therefore, the triangles are similar. I used the SAS similarity theorem.

================================================================

Question 2

Let's find the missing angle of the triangle on the right. For now, make that missing angle to be x.

Rule: For any triangle, the three angles always add up to 180

x+70+32 = 180

x+102 = 180

x = 180-102

x = 78

The missing angle of the triangle on the left is 78 degrees

Repeat for the other triangle as well

y+78+32 = 180

y+110 = 180

y = 180-110

y = 70

Both triangles have the angles 32, 70, 78 in whatever order you wish.

Since the angles match up like this, the triangles are similar because of the AA Similarity theorem

Technically, we only need 2 pairs of congruent angles at minimum. But having 3 congruent pairs doesn't hurt either.

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Question 3

We have a pair of congruent 54 degree angles shown. There's another pair of angles at the very top that overlap (aka shared angles).

Since we have two pairs of congruent angles, the two triangles are similar.

This time we use the AA Similarity theorem

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Question 4

Let's divide the longest side of the bottom triangle by the longest side of the triangle on top

48/32 = 1.5

Now let's divide the shortest sides of each triangle in the same order

36/24 = 1.5

Repeat for the middle-most sides

45/30 = 1.5

We get the same linear scale factor 1.5 each time. Therefore, the triangles are similar due to the SSS Similarity theorem

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Question 5

Any angle is equal to itself due to the reflexive property. So that will go for reason number 2.

Reason 3 is SAS similarity because we have the sides in proportion (statement 1) and the angles are congruent (statement 2).

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2 years ago

in a first aid kit the ratio of large bandages to small bandages is 5 to 2. Based on this ratio, how many large bandages are in

Radda [10]

The best way to answer this question is to set up the first sentence as a ratio of large bandages to total bandages. You would write 5 large bandages to 7 total bandages to 7 total bandages. Then you would make this equivalent to x number of large bandages to 60 total. It would look like this 5:7 = x:60. You could use cross products to multiply 60 by 5 to get 300. 7 times x also should equal 300. Unfortunately, this example will not leave us with a whole number of bandages, but 300/7 is a repeating decimal or a mixed number (42 6/7 large bandages).

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3 years ago

Once again plesse help me

Molodets [167]

Number 10: 15
Work: Is up there