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Lerok [7]
3 years ago
10

If you subtract 12 from my number and multiply the difference by-3 the result is -54 what is my number

Mathematics
1 answer:
Alla [95]3 years ago
4 0

first, make an equation:

- 54 =  - 3x - 12

then, add twelve to both sides to remove it from the right:

- 42 =  - 3x

then just divide by (-3) to get the value of x:

x = 14

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Vector v is shown in the graph.
Elis [28]

Question 4

<h3>Answer: Choice D</h3>

Explanation:

If the initial point is the origin, the coordinates of the terminal point form the vector itself in component form. We go from (-8,6) to <-8,6>. The notation change is from ordered pair to vector format.

We have a right triangle with legs of 8 and 6 units. The pythagorean theorem will help us determine the hypotenuse is 10. Therefore, the vector length is 10 units and we would say ||v|| = 10. We have a 6-8-10 right triangle.

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

Question 5

<h3>Answer: Choice B</h3>

Explanation:

Vector v starts at (2,5) and ends at (-3,-2).

The x component of the vector is x2-x1 = -3-2 = -5 meaning we move 5 units to the left when going from the start point to the endpoint.

At the same time we move 7 units down because y2-y1 = -2-5 = -7 which is the y component of the vector.

The component form of vector v is

v = <-5, -7>

it says "move 5 units left, 7 units down".

Apply the pythagorean theorem to find the length of the vector.

a^2+b^2 = c^2

c = sqrt(a^2 + b^2)

||v|| = sqrt( (-5)^2 + (-7)^2 )

||v|| = 8.602 which is approximate.

Now let's use the arctangent function to find the angle

theta = arctan(b/a)

theta = arctan(-7/(-5))

theta = 54.462 which is also approximate.

There's a problem however. This angle is in Q1 but the vector <-5,-7> is in Q3. An easy fix is to add on 180 to rotate to the proper quadrant.

54.462+180 = 234.462

which is the proper approximate angle for theta.

6 0
1 year ago
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3 years ago
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6 0
2 years ago
Evaluate each expression if r= −3, s=4, and t= −7.
saul85 [17]

Answer:

a. 5

b. -1

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Step-by-step explanation:

Given:

r =-3, s = 4 and r = -7

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