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jek_recluse [69]
2 years ago
10

Choose which set or sets the following number belongs to. Be sure to account for ALL sets. √19

Mathematics
1 answer:
Irina-Kira [14]2 years ago
6 0

√19 belongs to a set of irrational number

<h3>Irrational numbers</h3>

Numbers are irrational if they cannot be written as ratios or fractions of two numbers.

Examples of irrational numbers are √2, √3, √5, √11, √21, π, etc.

Since 19 is a prime number that can only be factored by 1 and itself, it is pairless and not in a power of 2.

Therefore, √19 belongs to the set of irrational numbers.

Learn more on irrational numbers here: brainly.com/question/20400557

#SPJ1

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The height of a triangle is 5 cm shorter than its base. If the area of the triangle is 25 cm2, find the height of the triangle.
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Answer:

h = 5\ cm

Step-by-step explanation:

Let's call B at the base of the triangle and call h at the height of the triangle. Then we know that:

The height of a triangle is 5 cm shorter than its base. This means that:

h = B-5.

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By definition the area of a triangle is:

A = 0.5Bh

For this triangle we know that A = 25\ cm^2 and h = B-5. We substitute these values in the equation and solve for B.

25 = 0.5B (B-5)

0.5B ^ 2-\frac{5}{2}B-25 = 0

Now we use the quadratic formula to solve the equation.

For an equation of the form ax ^ 2 + bx + c = 0 the quadratic formula is:

B=\frac{-b\±\sqrt{b^2-4ac}}{2a}

In this case note that:  a=0.5,\ \ b=-\frac{5}{2}\ \ c=-25

Then:

B=\frac{-(-\frac{5}{2})\±\sqrt{(-\frac{5}{2})^2-4(0.5)(-25)}}{2(0.5)}

B=\frac{\frac{5}{2}\±\sqrt{\frac{25}{4}+50}}{1}

B=\frac{5}{2}\±\frac{15}{2}

The solutions are:

B_1=\frac{5}{2}+\frac{15}{2}=10

B_2=\frac{5}{2}-\frac{15}{2}=-5

For this problem we take the positive solution.

B=10\ cm

Now we substitute the value of B in the equation to find the height h

h = 10-5

h = 5\ cm

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