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2 years ago

Because triangle XYZ is a right triangle, the side

Mathematics

1 answer:

Nitella [24]2 years ago

3 0

The final step is to determine the principal square root of both sides of the equation.

The triangle XYZ is a right triangle.
The sides "a" and "b" are the height and the base of the triangle.
The side "c" is the hypotenuse of the triangle.
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
The side lengths must satisfy the Pythagorean theorem, a² + b² = c².
It is also an isosceles triangle, so the equation becomes a² + a² = c².
By combining like terms, we get 2a² = c².
The final step is to take the square root of both sides.
√2a = c

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There are 84 boys in the 6th grade class. If boys make up 30% of the 6th graders, how many students are in this whole 6th grade

koban [17]

<h3>Answer: 280</h3>

Work Shown:

x = number of students in the 6th grade class

30% = 30/100 = 0.30

30% of x = 0.30x this is equal to 84 since "30% of the 6th graders are boys (and there are 84 boys in sixth grade)", so we say 0.30x = 84

Divide both sides by 0.30 to isolate x

0.30x = 84

0.30x/0.30 = 84/0.30

x = 280

So there are 280 students overall in the 6th grade class.

7 0

3 years ago

Read 2 more answers

2. The number of atoms of a particular chemical element is modelled by

____ [38]

9514 1404 393

Answer:

a) 600

b) see below

c) 1.26 hours

Step-by-step explanation:

a) The value of y when x=0 is the coefficient of the exponential term:

y = 600·3^(-0) = 600·1 = 600

There were 600 atoms to start.

b) see attached for a graph

c) The graph shows 150 atoms at t = 1.26, about 1.26 hours after the start of time counting.

If you want to find that value algebraically, substitute for y and solve for x. Logarithms are involved.

150 = 600·3^(-x)

150/600 = 3^(-x)

log(1/4) = -x·log(3)

x = -log(1/4)/log(3) = log(4)/log(3) ≈ 1.2618595

After about 1.26 hours, there were 150 atoms.

6 0

3 years ago

Use sigma notation to represent the following series for the first 12 terms. 2 +(-8) +32 + (-128) + .

Marysya12 [62]

$\displaystyle\sum_{i = 1}^{12} 2(-4)^{i-1}$

7 0

3 years ago

Read 2 more answers

Principal $4,700 Interest rate 4% time 10 months, what is the simple interest and maturity level?

Naddik [55]

The simple interest of $4,700 principal at 4% interest and 10 months is <u>$156.67</u> and its <u>maturity level</u> is <u>83%</u>.

<h3>What is simple interest?</h3>

Simple interest refers to the interest calculated only on the principal.

With the simple interest method, the borrower only pays interest on the principal without considering the previously-accumulated interests.

<h3>Data and Calculations:</h3>

Principal = $4,700

Interest rate = 4%

Period = 10 months

Simple interest = $156.67 ($4,700 x 4% x 10/12)

Thus, the simple interest of $4,700 principal at 4% interest and 10 months is <u>$156.67</u> and its <u>maturity level</u> is <u>83%</u>.

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6 0

2 years ago

If a coin is tossed and a number cube is rolled what is the probability of getting heads and the number cube shows 3?

Maurinko [17]

Answer:

1/12

Step-by-step explanation:

Since the probability of getting heads is 1/2 and the probability of the number cube getting three is 1/6, we multiply.

For every coin flip, there is a 1/6 chance of getting a three. But since there is another condition, we have to multiply. Multiplying both fractions make 1/12.

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3 years ago