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Whitepunk [10]
2 years ago
12

The pie chart represents the proportions of how Henry spent the £720 he took on holiday.

Mathematics
1 answer:
Oksana_A [137]2 years ago
6 0

Answer:

£124

Step-by-step explanation:

first of all, you're meant to add all the figures given on the pie chart, which is 29+137+58+62+74 and that will give you a total of 360 degrees

so, you say 360 degrees is equal to the total amount of money he spent, which is £720, what about 62 degrees

therefore, you just do (62×720)÷360

that will give you £124

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256×7=1792 in expanded form it is 1000+700+90+2
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3 years ago
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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.

The direction vectors are

D-C = (x_4 - x_3, y_4 - y_3)

C-B = (x_3 - x_2, y_3 - y_2)

For perpendicularity we need a zero dot product:

0 = (D-C)\cdot(C-B) = (x_4 - x_3)(x_3 - x_2) + (y_4 - y_3)(y_3 - y_2)

- (x_4 - x_3)(x_3 - x_2) = (y_4 - y_3)(y_3 - y_2)

That's the correct expression, given it's a parallelogram, to demonstrate it's a rectangle. The divisions make it iffy.

8 0
3 years ago
Simplify the midpoint of PR.<br> Q (2b, 2c)<br> R (2a+2b, 2c)<br> Pl(0,0)<br> S (2a, 0)
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Answer:

The midpoint of PR is;

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Step-by-step explanation:

Here, we want to get the coordinates of the midpoint of PR

To get these, we make use of the midpoint formula

Mathematically, that will be;

(x,y) = (x1+y1)/2, (x2+y2)/2

(x1,y1) = (0,0)

(x2,y2) = (2a+2b, 2c)

The midpoint is thus;

(2a+2b)/2 , 2c/2

= (a + b, c )

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