Given a scalar number
and a vector
v, the product between
and
v is a vector, with
- magnitude given by the product between the absolute value of
and the magnitude of
v- direction given by the sign of
: if a is positive, the final vector has same direction of
v; if a is negative, the final vector has opposite direction to
v.
In our problem, the scalar number is
. This means that the product between the vector and this number:
- has magnitude equal to
times the magnitude of the vector
- has opposite direction with respect to the original vector (because the scalar
is negative)
Therefore, the correct answer is
<span>B.) The vector will change direction and decrease in magnitude.</span>
Answer:
- Yes it is a right triangle
- The side lengths satisfy the Pythagorean theorem equation
Step-by-step explanation:
We can test these numbers to see if they satisfy the Pythagorean theorem equation:
15² = 9² + 12²
225 = 81 + 144 . . . . true
Since the numbers satisy the Pythagorean theorem relation, they belong to a right triangle.
____
You can recognize that the ratio of side lengths is ...
9 : 12 : 15 = 3 : 4 : 5
Further, you can recognize that the side lengths 3, 4, 5 belong to the right triangle with the smallest integer side lengths that satisfy the Pythagorean theorem. Hence the 9 : 12 : 15 triangle is similar (by a scale factor of 3) to a right triangle, thus is a right triangle.
"If 5x+7=-13, then x=-4"
The contrapositive is the inverse and converse of a conditional statement. So, the contrapositive of this statement would be:
"If x does not equal -4, then 5x+7 does not equal -13."
Answer:
The principal he borrowed is $1500
Step-by-step explanation:
Let's assume principal he borrowed as P
now, we can use formula
where
SI is simple interest
r is interest rate
t is time in years
we are given
r=4%
SI=240
t=4
now, we can plug this value
now, we can solve for P
So,
The principal he borrowed is $1500. Hope this helps, and mark me as brainlest!
Lin's hourly rate is 15 dollars per hour.
The x represents the change that occurs per hour the 500 is the performance bonus which is a set constant amount.