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3 years ago

What is the area of parallelogram ABCD

Mathematics

2 answers:

larisa86 [58]3 years ago

7 0

Answer:

20 square units

Step-by-step explanation:

You count how many across the parallelogram is (which is 4) and you count how high it is (which is 5). Then you multiply 5×4* which equals 20 square units.

*The reason you do this is because base×hieght=area

Dmitriy789 [7]3 years ago

6 0

Answer:

20 square units

Step-by-step explanation:

Area of a parallelogram formula = base times height

To find the length of the base we take end points of the base and use distance formula

$distance =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Two points are (1,0) and (5,0)

Distance = $\sqrt{(5-1)^2+(0-0)^2}$

$=\sqrt{4^2} =4$

Length of base = 4 units

Now we find out the height between B (1,0) and D (1,5)

Height = $\sqrt{(1-1)^2+(5-0)^2}=\sqrt{5^2}= 5$

Height = 5

Area of the parallelogram = base times height

= $4 \cdot 5= 20$

So area = 20 square units

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Step-by-step explanation:

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3 years ago

A bag had 7 orange rocks , 6 green rock , 1 white rock ,7 black rocks , and 2 yellow you randomly pull a rock from the bag ,keep

daser333 [38]

Answer:

$Probability = \frac{7}{253}$

Step-by-step explanation:

Given

$Orange = 7$

$Green = 6$

$White = 1$

$Black = 7$

$Yellow = 2$

Required

Probability of selecting a yellow then orange rock

From the question, we understand that the probability is that of without replacement.

Since the yellow, is first picked.

We need to determine the probability of picking a yellow rock, first.

$P(Yellow) = \frac{n(Yellow)}{Total}$

$P(Yellow) = \frac{2}{7 + 6 + 1 + 7 + 2}$

$P(Yellow) = \frac{2}{23}$

The rock has reduced by 1;

Next is to determine the probability of picking an orange rock

$P(Orange) = \frac{n(Orange)}{Total - 1}$

$P(Orange) = \frac{7}{7 + 6 + 1 + 7 + 2- 1}$

$P(Orange) = \frac{7}{22}$

The required probability is calculated as thus:

$Probability = P(Yellow) * P(Orange)$

$Probability = \frac{2}{23} * \frac{7}{22}$

$Probability = \frac{14}{506}$

$Probability = \frac{7}{253}$

4 0

3 years ago

The first term of a geometric sequence is equal to a and the common ratio of the sequence is r.

ololo11 [35]

Answer: (a) {a, ar, ar², ar³, ar⁴, ar⁵...}, (b) arⁿ⁻¹

For part (a), the question gives us the first term a, and then asks us to apply the common ratio r six times.

In order for ar = a, the nth term of r will have to equal 0 (this implies that n is an exponent; thus giving us the first term a, as r = 1).

Since we use this method on the first term, we must use it for the next five, in which r gains an additional exponent for every consecutive value (nth term) thereafter.

Ultimately getting: {a, ar, ar², ar³, ar⁴, ar⁵...}

For part (b), we first have to understand that the sequence does not start at 0, but at 1 for n. In order for ar = a, with n = 1, there needs to be subtraction of -1 within the exponent. So that arⁿ⁻¹

If we check and apply this, we can see that:

{ar¹⁻¹, ar²⁻¹, ar³⁻¹, ar⁴⁻¹, ar⁵⁻¹, ar⁶⁻¹...} = {a, ar, ar², ar³, ar⁴, ar⁵...} = arⁿ⁻¹ = Tn

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3 years ago