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3 years ago

At the market 5 light bulbs cost 9.85. How much do 7 light bulbs cost?

Mathematics

2 answers:

enyata [817]3 years ago

7 0

Cost = (9.85/5) * 7
=13.79

Leya [2.2K]3 years ago

5 0

The unit rate is $1.97 per lightbulb. Multiply $1.97 by 7 to get 13.79

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Factoer out the greatest common factor of 56^ - 49x + 14

babymother [125]

56x² - 49x + 14 = 7(8x² - 7x +2)

_____
The greatest common factor of 56, 49, and 14 is 7.

6 0

3 years ago

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

Now let's calculate the area

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;

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

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.

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

6 0

3 years ago

What your expect to gen.math subject

sveta [45]

Can you elaborate on ur question

6 0

3 years ago

Read 2 more answers

Plsss helpppp what’s the shape?

Alborosie

The shape shown here is a triangular pyramid, because it has a triangular base and a pointy tip.

4 0

3 years ago

Determine if the events A and B are independent. Show all steps.

zmey [24]

Answer:

$P(A U B ) = \frac{13}{25}$

Step-by-step explanation:

STEP:-1

Given that events A and B are independent then

P(A ∩B ) = P(A) P(B)

Given that P(A) = 2/5 and P(B) = 1/5

STEP:- 2

P(A ∩B ) = P(A) P(B)

$P(A U B) = P(A) +P(B) - P(A n B )$

$P(A U B ) = P(A) +P(B) - P(A) P(B)$

Step(iii):-

$P(A U B ) = \frac{2}{5} +\frac{1}{5} - \frac{2}{5} X \frac{1}{5}$

$P(A U B ) = \frac{3}{5} - \frac{2}{5} X \frac{1}{5}$

$P(A U B ) = \frac{3}{5} - \frac{2}{25}$

$P(A U B ) = \frac{15-2}{25} = \frac{13}{25}$

4 0

2 years ago