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3 years ago

What is the area of a rectangle with vertices at (2, 3), (7, 3), (7, 10), and (2, 10)?

2 answers:

7 0

D 35 units squared. If you would graph it on a piece of graph paper or look at the points one side would be the difference between 10 and 3 and the other side would be the difference between 7 and 2. Then taking those totals multiple them together to get the area

aalyn [17]3 years ago

6 0

Answer: The correct option is (d) 35 units².

Step-by-step explanation: We are given to find the area of a rectangle with vertices at the points (2, 3), (7, 3), (7, 10), and (2, 10).

Let A(2, 3), B(7, 3), C(7, 10), and D(2, 10) represents the co-ordinates of the vertices of the given rectangle.

Then, the lengths of the sides AB, BC, CD and DA ca be calculated using distance formula as follows :

$AB=\sqrt{(7-2)^2+(3-3)^2}=\sqrt{25+0}=\sqrt{25}=5~\textup{units},\\\\BC=\sqrt{(7-7)^2+(10-3)^2}=\sqrt{0+49}=\sqrt{49}=7~\textup{units},\\\\CD=\sqrt{(2-7)^2+(10-10)^2}=\sqrt{25+0}=\sqrt{25}=5~\textup{units},\\\\DA=\sqrt{(2-2)^2+(3-10)^2}=\sqrt{0+49}=\sqrt{49}=7~\textup{units}.$

So, the area of the given rectangle will be

$Area=AB\timesBC=5\times7=35~\textup{units}^2.$

Thus, (d) is the correct option.

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Which of the following graphs is the solution set of -10 < 3x - 4 < 8?

sveticcg [70]

Answer:

The First Graph -2○ and 4○

Step-by-step explanation:

Because these numbers aren't included in the solution.

8 0

3 years ago

What's the next number? 0 , 1/3 , 1/2 , 3/5 , 2/3

madam [21]

Answer:

The next number of the series 0, 1/3, 1/2, 3/5, and 2/3 is 5/7

Step-by-step explanation:

The given numbers are;

0, 1/3, 1/2, 3/5, and 2/3

The number sequence is formed adding $\dfrac{1}{\left (\dfrac{n^2 + n}{2} \right ) }$ to each (n - 1)th term to get the nth term number in the sequence, with the first term equal to 0, as follows;

For the 2nd term, the (n - 1)th term is 0, and n = 2, gives;

The

$0 +\dfrac{1}{\left (\dfrac{2^2 + 2}{2} \right ) } = 0 + \dfrac{1}{3} = \dfrac{1}{3}$

For the 3rd term, the (n - 1)th term is 1/3, and n = 3, gives;

$\dfrac{1}{3} +\dfrac{1}{\left (\dfrac{3^2 + 3}{2} \right ) } = \dfrac{1}{3} + \dfrac{1}{6} = \dfrac{1}{2}$

For the 4th term, the (n - 1)th term is 1/2, and n = 4, gives;

$\dfrac{1}{2} +\dfrac{1}{\left (\dfrac{4^2 + 4}{2} \right ) } = \dfrac{1}{2} + \dfrac{1}{10} = \dfrac{3}{5}$

For the 5th term, the (n - 1)th term is 3/5, and n = 5, gives;

$\dfrac{3}{5} +\dfrac{1}{\left (\dfrac{5^2 + 5}{2} \right ) } = \dfrac{3}{5} + \dfrac{1}{15} = \dfrac{2}{3}$

For the next or 6th term, the (n - 1)th term is 2/3, and n = 6, gives;

$\dfrac{2}{3} +\dfrac{1}{\left (\dfrac{6^2 + 6}{2} \right ) } = \dfrac{2}{3} + \dfrac{1}{21} = \dfrac{15}{21} = \dfrac{5}{7}$

The next number of the series 0, 1/3, 1/2, 3/5, and 2/3 = 5/7.

6 0

3 years ago

A company manufactures 2,000 units of its flagship product in a day. The quality control department takes a random sample of 40

Kisachek [45]

It's 100

Because You multiply the sample proportion to 2000

6 0

3 years ago

Read 2 more answers

Find the distance between the points (11, 4) and (10, 5).

alexdok [17]

Answer:

square root of 2 or if needed simplified, 1.414213 to the nearest millionth.

Step-by-step explanation:

Start with the equation d= square root of (11-10)^2+(4-5)^2 where that is simplified to square root of (1)^2+(-1)^2 to square root of 1+1 to your final answer, square root of 2. Also simplified to 1.414213.

6 0

4 years ago

Factorise fully 6ac + 10ac

ikadub [295]

Step-by-step explanation:

6ac+10ac

2ac(6ac+10ac)

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4 0

3 years ago