The magnitude of the vector is √(7^2+12^2)=√(49+144)=√193

The direction is α=arctan(y/x)=arctan(12/-7)≈-59.74 however this is relative to the negative x-axis so we add 180° to get the standard angle...180-59.74=120.26°

So the vector is √193 @ 120.26°

5 0

3 years ago

At one store, Julia saved $10 with a coupon for 40% off her total purchase. At another store, the $29 she spent on books is

barxatty [35]

Let "a" and "b" represent the values of the first and second purchases, respectively.
0.40*(original price of "a") = $10
(original price of "a") = $10/0.40 = $25.00 . . . . divide by 0.40 and evaluate
a = (original price of "a") - $10 . . . . . . Julia paid the price after the discount
a = $25.00 -10.00 = $15.00

At the other store,
$29 = 0.58b
$29/0.58 = b = $50 . . . . . . . divide by the coefficient of b and evaluate

Then Julia's total spending is
a + b = $15.00 +50.00 = $65.00

Julia spent $65 in all at the two stores.

6 0

3 years ago

On a test, wrong answers are worth -5.25 points and right answers are worth 3.5 points. So far, Marshall has one right answer an

Over [174]

Answer:

Marshall's current score is - 1.75 points

Step-by-step explanation:

From the question,

Wrong answers are worth -5.25 points and right answers are worth 3.5 points.

Currently, Marshall has one right answer and one wrong answer.

To determine Marshall's current score, we will multiply the number of right answers has by 3.5 points and multiply the number of wrong answers by -3.5 points and then add the results.

Number of right answers = 1

Number of wrong answers = 1

For the right answer, he has

1 × 3.5 points = 3.5 points

For the wrong answer, he has

1 × - 5.25 points = -5.25 points

Hence, Marshall's current score is

3.5 points + ( -5.25 points) = 3.5 points - 5.25 points

= - 1.75 points.

Hence, Marshall's current score is - 1.75 points.

8 0

2 years ago