An expression is shown

I am stuck, please help

ASHA 777 [7]

Answer:

2323

Step-by-step explanation:

Mental math means to find a way to do this problem in your head without using paper, pencil or a calculator.

The question says there are 23 classes and each class is to collect 101 items.

The equation would be 23 x 101.

To do this in your head real quick, make the numbers easier to multiply.

Make the 101 items 100. That means you are telling each class to collect 1 less item or 23 less items total.

You can do this in your head real quick. 23 classes collecting 100 items is 2300 items.

You had each class collect 100 items instead of 101. That mean you didn't collect 23 items. So if you add those back in, you will get

2323 items.

3 0

3 years ago

The vertices of a parallelogram are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). Which of the following must be true if paral

Iteru [2.4K]

The answer is really none of the above, because all of these have divisions by difference in x, and there are perfectly fine rectangles where those will mean dividing by zero.

To do the problem the way they want us to, we note segments with the same slope are parallel (or collinear); segments with slopes which multiply to -1 are perpendicular.

Let's figure out what each choice is trying to tell us by translating it into parallel and perpendicular. Remember A is point 1, ...

A. ((y_4-y_3)/(x_4-x_3)= (y_3-y_2)/(x_3-x_2)) and ((y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2))=-1

translated, that's CD║BC and CD⊥BC - contradictory; second half right

B. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and ((y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1))=-1

CD ║ AB and CD ⊥ AB - only the parallelogram half is right

C. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and (y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2)=-1

CD║AB and CD⊥BC - that's TRUE

D. (y_4-y_3)/(x_4-x_3)= (y_3-y_1)/(x_3-x_1) and (y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1)=-1

CD║AC and CD⊥AB - nope

Answer: C

The way I'd get the proper expression is with the dot product.

A parallelogram is a rectangle when adjacent sides are perpendicular. It only takes one right angle to make them all right.

Two sides are perpendicular when the dot product of their direction vectors is zero. All the answers have $y_4 - y_3$ so one side is CD. The other side must be BC or AD; AD would give $y_4 - y_1$ terms which don't appear among the answer, so let's go with BC.