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2 years ago

Prove that the diagonals of a parallelogram bisect each other. The midpoints are the same point, so the diagonals _____

Mathematics

1 answer:

Molodets [167]2 years ago

8 0

Answer:

Below

Step-by-step explanation:

To prove that the diagonals bisect each other we should prove that they have a common point.

From the graph we notice that this point is E.

ABCD is a paralellogram, so E is the midpoint of both diagonals.

●●●●●●●●●●●●●●●●●●●●●●●●

Let's start with AC.

● A(0,0)

● C(2a+2b,2c)

● E( (2a+2b+0)/2 , (2c+0)/2)

● E ( a+b, c)

●●●●●●●●●●●●●●●●●●●●●●●●

BD:

● B(2b,2c)

● D(2a,0)

● E ( (2a+2b)/2 , 2c/2)

● E ( a+b ,c)

●●●●●●●●●●●●●●●●●●●●●●●●●

So we conclude that the diagonals bisect each others in E.

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Answer:

Option B

Step-by-step explanation:

Option A, C and D have x- values that repeat and you cannot have that.

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2 years ago

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xeze [42]

I believe the answer would be (1) because they are not directly related

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2 years ago

Cory's average score after 8 tests is 91%. If he gets a 78% on his 9th test what will his new average be?

Luda [366]

You should be able to multiply 91 by 8 to get the sum of the first 8 tests, then add the score on the 9th test. Then to get the average of the sum of the 9 tests you need to divide it by 9.
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3 years ago

The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 40 m

daser333 [38]

Answer:

$\dfrac{dV}{dt}=502.65\ mm^3/s$

Step-by-step explanation:

The volume of a sphere is given by :

$V=\dfrac{4}{3}\pi r^3$

The rate of change of volume means,

$\dfrac{dV}{dt}=\dfrac{d}{dt}(\dfrac{4}{3}\pi r^3)\\\\\dfrac{dV}{dt}=\dfrac{4}{3}\pi \times 3r\times \dfrac{dr}{dt}$

We have, $\dfrac{dr}{dt}=2\ mm/s\ and\ r=40\ mm$

So,

$\dfrac{dV}{dt}=\dfrac{4}{3}\pi \times 3\times 20\times 2\\\\=502.65\ mm^3/s$

So, the volume is increasing at the rate of $502.65\ mm^3/s$ .

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2 years ago

Johnny has a bag with 84 coins in it. If the ratio of dimes to nickels to pennies is 3 to 2 to 1, how many

omeli [17]

Answer:

Step-by-step explanation:

Number of coins in the bag ⇒ 84

Give that,

Dimes : Nickels : Pennies

3 : 2 : 1

You can see that, there are 6 parts . ( 3 + 2 + 1 = 6 )

And now let us write the types of coins in fractions.

Dimes ⇒ $\frac{3}{6}$

Nickels ⇒ $\frac{2}{6}$

Pennies ⇒ $\frac{1}{6}$

And now they're asking for the number of nickels.

To find that, you can multiply 84 ( number of coins) by it's fraction ( 2/6).

Let us solve.

84 × $\frac{2}{6}$

$\frac{84*2}{6}$

$\frac{168}{6}$

Therfore, there are 28 nickels.

8 0

1 year ago