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marshall27 [118]
2 years ago
15

The length of a rectangle is shown below: On a coordinate grid from negative 6 to positive 6 on the x-axis and on the y-axis two

points A and B are shown. The point A is on ordered pair 2, 1, and the point B is on ordered pair negative 1, 1. A straight line joins the points A and B. If the area of the rectangle to be drawn is 18 square units, where should points C and D be located, if they lie vertically below the line that connects B and A, to make this rectangle? (1 point) C(−1, −2), D(2, −2) C(−1, −8), D(2, −8) C(−1, −5), D(2, −5) C(−1, −6), D(2, −6)
Mathematics
1 answer:
Degger [83]2 years ago
5 0

9514 1404 393

Answer:

  3.  C(−1, −5), D(2, −5)

Step-by-step explanation:

The given points are 2 -(-1) = 3 units apart horizontally, so the remaining points will need to be 18/3 = 6 units below, vertically. Translating the given points down 6 gives ...

  D = A -(0, 6) = (2, 1) -(0, 6) = (2, -5)

  C = B -(0, 6) = (-1, 1) -(0, 6) = (-1, -5)

The two points required to make a rectangle with an area of 18 square units are ...

  C(-1, -5), D(2, -5)

_____

The area of a rectangle is the product of length and width. If the area is 18 square units, and the width is 3 units, then the length must be 6 units. 3×6=18.

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A wall is in the shape of a trapezium. The first level of the wall is made up of 50 bricks where as the top level has 14 bricks.
alukav5142 [94]

Answer:

i). 10 levels of the bricks

ii). 320 bricks

Step-by-step explanation:

First level contains number of bricks = 50

Second level will contain = 50 - 4 = 46 bricks

Similarly, 3rd level will contain number of bricks = 46 - 4 = 42

Therefore, sequence formed for the number of bricks in each level of the wall will be,

50, 46, 42........14

This sequence is an arithmetic sequence having,

First term 'a' = 50

Common difference 'd' = 46 - 50 = (-4)

Last term of the sequence T_{n}= 14

i). Expression representing last term will be,

  T_{n}=a+(n-1)d

  Here T_{n} = nth term

  a = first term

  n = number of term (Number of level of the wall)

  d = common difference

  By substituting these values in the formula,

  14 = 50 + (n - 1)(-4)

  14 - 50 = (-4)(n - 1)

  -36 = -4(n - 1)

  9 = (n - 1)  

  n = 9 + 1

  n = 10

ii). Number of bricks used in the wall = Sum of the sequence

   Expression for the sum of an arithmetic sequence is,

   S_n=\frac{n}{2}[2a+(n-1)d]

   S_n=\frac{10}{2}[2\times 50+(10-1)(-4)]

        = 5(100 - 36)

        = 320 bricks

4 0
2 years ago
Change the fraction to a decimal. a. 6⁄100 b. 43⁄100 c. 3⁄10 d. 4 23⁄1,000
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6/100 = 0.06

43/100 = 0.43

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Hope this helps!

3 0
3 years ago
Denise is making bean bags. She has 6.4 pounds of beans.
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Answer:

a) she be able to make 8 bags

b) she can make 16 bags.

Step-by-step explanation:

According to the exercise info Denise has 6.4 pounds of beans

<u>Solving question a </u>

 ⇒  if she makes each bean bag of 0.8 pounds and she has 6.4 pounds of beans, we can express this by using the three simply rule she needs to puts 6.4 pounds of beans in x quantity of bags of 0.8 pouns, so doing the division: 6. 4 pounds of beans / 0.8 pounds of beans per bag= 8 bags of 0.8 pounds of beans.

B- If she decides to make mini bean bags that are half as heave as the ohers bags, so now Denise is going to make bags of 0.8/2 = 0.4 pounds.

Doing the same procedure as question a, we can say that she has 6.4 pounds of beans and she needed to put these amount in a x quantity of 04 pounds bags. Doing the following division ⇒ 6.4 pounds of beans/ 0.4 pounds of beans per bag= 16 bags

 In conclusion she is going to make 16 bags of 0.4 pounds of beans.

 

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Answer:

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Step-by-step explanation:

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