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3 years ago

10

Ashleigh wants to double her money. She put $5,000 in a bank account that pays 4% compounded continuously. How long will it take

her to double her money? (Round to

1 answer:

pantera1 [17]3 years ago

8 0

Answer:

approximately 17.3 years

Step-by-step explanation:

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All points from which of the following patterns would be contained on the given graph?

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The next number in the linear pattern would be 18

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3.5 hours: $10 1/2 hour: $1.25. which is the better deal

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The rectangular screen of a high-definition television set is 71 cm wide and 40 cm high. What is it’s area

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Which is the midpoint of the segment joining (12, 2) and (-5, – 7)?

Rainbow [258]

Answer:

$m(x, y)=(\frac{7}{2} , -\frac{5}{2} )$

Step-by-step explanation:

Midpoint of line segment is calculated as

$m(x, y)=(\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )$ -----------(1)

Here

$(x_1, y_1) = (12,2) \ \ and \ \ (x_2, y_2) = (-5, -7)$

Substituting values in equation (1)

$m(x, y)=(\frac{12-5}{2} , \frac{2-7}{2} )$

$m(x, y)=(\frac{7}{2} , -\frac{5}{2} )$

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3 years ago

2. Given a quadrilateral with vertices (−1, 3), (1, 5), (5, 1), and (3,−1):

zlopas [31]

<h2>Explanation:</h2>

In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.

So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.

So let's name the vertices as:

$A(-1,3) \\ \\ B(1,5) \\ \\ C(5,1) \\ \\ D(3,-1)$

First pair of opposite sides:

<u>Slope:</u>

$\text{For AB}: \\ \\ m=\frac{5-3}{1-(-1)}=1 \\ \\ \\ \text{For CD}: \\ \\ m=\frac{1-(-1)}{5-3}=1 \\ \\ \\ \text{So AB and CD are parallel}$

Second pair of opposite sides:

<u>Slope:</u>

$\text{For BC}: \\ \\ m=\frac{1-5}{5-1}=-1 \\ \\ \\ \text{For AD}: \\ \\ m=\frac{-1-3}{3-(-1)}=-1 \\ \\ \\ \text{So BC and AD are parallel}$

So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:

$d=\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2} \\ \\ \\ Diagonal \ BD: \\ \\ d=\sqrt{(5-(-1))^2+(1-3)^2}=2\sqrt{10} \\ \\ \\ Diagonal \ AC: \\ \\ d=\sqrt{(3-1)^2+(-5-1)^2}=2\sqrt{10} \\ \\ \\$

So the diagonals measure the same, therefore this is a rectangle.

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3 years ago