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Arturiano [62]
3 years ago
10

Miles had three sets of building blocks.His first sett had 491 pieces.His second sett had 624 pieces.Miles combined his three se

ts for a total 1374 pieces. How many pieces had been in his third?
Mathematics
1 answer:
qaws [65]3 years ago
7 0

Answer:

259

Step-by-step explanation:

491+624=1115. 1374-1115=259

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Verify that the points are the vertices of a parallelogram and find its area. (2,-1,1), (5, 1,4), (0,1,1), (3,3,4)
Gelneren [198K]

Answer:

Area = 13.15 square units

Step-by-step explanation:

Let the given vertices be represented as follows:

A(2, -1, 1) = 2i - j + k

B(5, 1, 4) = 5i + j + 4k

C(0, 1, 1) = 0i + j + k

D(3, 3, 4) = 3i + 3j + 4k

(i) Let's calculate the vectors of all the sides:

\\AB = B - A =  (5i + j + 4k) - (2i - j + k)

AB = 5i + j + 4k - 2i + j - k                 [Collect like terms]

AB = 3i + 2j + 3k

BC = C - B =  (0i + j + k) - (5i + j + 4k)

BC = 0i + j + k - 5i - j - 4k                 [Collect like terms]

BC = -5i + 0j - 3k

CD = D - C =  (3i + 3j + 4k) - (0i + j + k)

CD = 3i + 3j + 4k - 0i - j - k                [Collect like terms]

CD = 3i + 2j + 3k

DA = A - D =  (2i - j + k) - (3i + 3j + 4k)

DA = 2i - j + k - 3i - 3j - 4k                [Collect like terms]

DA = -i - 4j - 3k

AC = C - A =  (0i + j + k) - (2i - j + k)

AC = 0i + j + k - 2i + j - k                [Collect like terms]

AC = -2i + 2j

BD = D - B = (3i + 3j + 4k) - (5i + j + 4k)

BD = 3i + 3j + 4k - 5i - j - 4k                [Collect like terms]

BD = -2i + 2j

(ii) From the results in (i) above, we can deduce that;

AB = CD This implies that AB || CD  [AB is parallel to CD]

AC = BD This implies that AC || BD  [AC is parallel to BD]

(iii) Therefore, ABDC is a parallelogram since opposite sides (AB and CD) are parallel. Hence, the points are vertices of a parallelogram

<u>Now let's calculate the area</u>

To find the area of the parallelogram, we find the magnitude of the cross product of any two adjacent sides.

In this case, we'll choose AB and AC

Area = |AB X AC|

Where;

AB X AC = \left[\begin{array}{ccc}i&j&k\\3&2&3\\-2&2&0\end{array}\right]

<u></u>

AB X AC = i(0 - 6) - j(0 + 6) + k(6 + 4)

AB X AC = - 6i - 6j + 10k

|AB X AC| = \sqrt{(-6)^2 + (-6)^2 + (10)^2}

|AB X AC| = \sqrt{172}

|AB X AC| = 13.15

Area = 13.15 square units.

<u></u>

<u></u>

<u>PS: </u> ACBD is also a parallelogram. The diagram has also been attached to this response.

6 0
3 years ago
I need help answer 6 through 7 I can't figure them out
seropon [69]
6. the answer is 4. because u find the diameter by dividing by 2. 
7. answer = 8 , the radius is 4 . so u need to multiply 2 times 4. 2 times 4 =8.
6 0
3 years ago
A pair of shoes is on sail for 30% off. The original price is p. Which expression can be used to find the price of the shoes aft
Vladimir79 [104]

Answer:


Step-by-step explanation:

.30 x p = ___

p - ___ = price of shoes after the discount

5 0
3 years ago
There are 130 people in a sport centre. 73 people use the gym. 62 people use the swimming pool. 58 people use the track. 22 peop
Delvig [45]

Answer:

\frac{11}{87}

Step-by-step explanation:

Total number of people = 130

Number of people who use the gym = 73

Number of people who use the pool = 62

Number of people who use the track = 58

Number of people who use the gym and the pool = 22

Number of people who use the pool and the track = 29

Number of people who use the gym and the track = 25

Number of people who use all three facilities = 11

Total number of people who use at least two facilities = 22 + 29 + 25 + 11 = 87

The probability that the randomly selected person uses all three facilities = number of those who use all three facilities ÷ total number of people who use at least two facilities.

==> 11 ÷ 87

==> \frac{11}{87}

3 0
3 years ago
Find the area of the figure. Round your answer to the nearest hundredth, if necessary. (12cm)
Brilliant_brown [7]

Answer:

The answer is 56.52 square centimeters

Step-by-step explanation:

The area of a circle is Pi R^2 so that means the area of a semi circle is half of that which is Pi R^2/2

since diameter is 12, radius = 12/2 = 6

Area = (3.14 × 6^2)÷2 = 56.52

3 0
3 years ago
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