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3 years ago

Are the equations – 2x = 10 and -5x = 25 equivalent? Explain

2 answers:

8 0

Yes.
Explanation:
-2x=10
You’d divide both sides by -2 that would be
-5
Then -5x=25
You’d divide both sides by -5 that would be
-5

Dahasolnce [82]3 years ago

7 0

Answer:NO

Step-by-step explanation:

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A rhombus ABCD has AB = 10 and m∠A = 60°. Find the lengths of the diagonals of ABCD.

melisa1 [442]

Three important properties of the diagonals of a rhombus that we need for this problem are:
1. the diagonals of a rhombus bisect each other
2. the diagonals form two perpendicular lines
3. the diagonals bisect the angles of the rhombus

First, we can let O be the point where the two diagonals intersect (as shown in the attached image). Using the properties listed above, we can conclude that ∠AOB is equal to 90° and ∠BAO = 60/2 = 30°.

Since a triangle's interior angles have a sum of 180°, then we have ∠ABO = 180 - 90 - 30 = 60°. This shows that the ΔAOB is a 30-60-90 triangle.

For a 30-60-90 triangle, the ratio of the sides facing the corresponding anges is 1:√3:2. So, since we know that AB = 10, we can compute for the rest of the sides.

$\overline{OB}:\overline{AB} = 1:2$
$\overline {OB}:10 = 1:2$
$\overline{OB} = \frac{1}{2}(10) = 5$

Similarly, we have

$\overline{AO}:\overline{AB} = \sqrt{3}:2$
$\overline {AO}:10 = \sqrt{3}:2$
$\overline{AO} = \frac{\sqrt{3}}{2}(10) = 5\sqrt{3}$

Now, to find the lengths of the diagonals,

$\overline{AD} = 2(\overline{AO}) = 10\sqrt{3}$
$\overline{BC} = 2(\overline{OB}) = 10$

So, the lengths of the diagonals are 10 and 10√3.

Answer: 10 and 10√3 units

8 0

3 years ago

a wildlife manager determines that the function y=200x1.07* represents the deer population at a state park x years after the pop

Kobotan [32]

Answer:

Table:

0,200

4, 262

8,344

12, 450

Population after 12 years is 450 deer

Initial population is 200 deer.

Step-by-step explanation:

You take the x in the table and plug it in as an exponent so you will need a calculator or multiple the 1.07 by that many times so 1.07 12 times multipled by itself. and the initial is 0 years so anything to the exponent of 0 is 1 so that show i got 200 for the x=0

8 0

3 years ago

What are all the angle measures for right triangle ABC?

Alenkasestr [34]

Answer:

$\alpha = 60°,\:\beta = 30°, \: 90°$

Step-by-step explanation:

$Arccos( \frac{ \sqrt{3} }{2} ) = \beta \\ Arccos( \cos \: 30 \degree ) = \beta \\30 \degree = \beta \\ \therefore \: \alpha = 60 \degree \\ remaining \: angle = 90 \degree \\$

3 0

3 years ago

Bill Gates wrote a computer program that generates three random numbers

Allushta [10]

Answer:

1/1000

Step-by-step explanation:

The probability of two independent events A, B (independent = events that do not depend on each other) is given by the product of the individual probabilities of A and B:

$p(AB)=p(A)\cdot p(B)$ (1)

In this problem, the single event is "getting a 3" when extracting a random number between 1 and 10.

The total number of possible outcomes is

n = 10

While the number of succesfull outcomes (getting a 3) is only one:

$s=1$

So, the probability of drawing a 3 in 1 draw is

$p(3)=\frac{s}{n}=\frac{1}{10}$

Then, we want to find the probability of getting three "3" in 3 consecutive generations. These events are independent events, so we can use rule (1) to find the total probability, and we get:

$p(333)=p(3)p(3)p(3)=(\frac{1}{10})(\frac{1}{10})(\frac{1}{10})=\frac{1}{1000}$

7 0

3 years ago

Anyone know the answers

ExtremeBDS [4]

Answer:it’s going to be b

Step-by-step explanation:

3 0

3 years ago