How to I get 25ft to centimeters?

Problem page the longer leg of a right triangle is 1ft longer than the shorter leg. the hypotenuse is 9ft longer than the shorte

LenKa [72]

Hello,

To solve this problem we want to use the Pythagorean Theorem.
The pythagorean theorem states that for a 90° triangle,

$a^{2} + b^{2} = c^{2}$

where a and b represent the two legs of the triangle, and c represents the hypotenuse.

Let a = the longer leg and b = the shorter leg.
If the longer leg of the triangle is 1 foot longer than the shorter leg, then
a = b +1.

If the hypotenuse is 9 feet longer than the shorter leg, then c = b + 9.
Using the equations we created, we can plug them into the Pythagorean Theorem to solve for a, b, and c.

Doing this, we have:
$a^{2} + b^{2} = c^{2}$
$(b+1)^{2} + b = (b+9)^{2}$

Expanding this, we get $b^{2} + 2b + 1 + b^{2} = b^{2} + 18b + 81

 2b^{2} + 2b + 1 = b^{2} + 18b + 81

 b^{2} + 1 = 16b + 81

 b^{2} = 16b + 80
 
b^{2} - 16b - 80 = 0

$

Solving for b, we get b = 20, and b = -4.
The length of the side of a triangle cannot be negative, so we know that b = 20.

However, we should check this with the original question to make sure it checks out.

a = b + 1
a = 20 + 1 = 21

c = b + 9
c = 20 + 9 = 29

So, we have a = 21, b = 20, and c = 29. (Also, 20-21-29 is a well known Pythagorean triple)
Using the Pythagorean Theorem, we have:

$21^{2} + 20^{2} = 29^{2}$
441 + 400 = 841
841 = 841, checks out.

So, the shorter leg is 20 feet, the longer leg is 21 feet, and the hypotenuse is 29 feet.

Hope this helps!

7 0

3 years ago

What is the probability that a student failed the test GIVEN that they studied

puteri [66]

Answer:

1/12

Step-by-step explanation:

You are close but 1/27 includes people who did not study but still passed. If you want a singular value you should look at the value for the for only the people who studied even if they passed.

5 0

3 years ago

Help needed on this composition math problem

Marrrta [24]

Given that f(x) = x/(x - 3) and g(x) = 1/x and the application of function operators, f ° g (x) = 1/(1 - 3 · x) and the domain of the resulting function is any real number except x = 1/3.

<h3>How to analyze a composed function</h3>

Let be f and g functions. Composition is a binary function operation where the variable of the former function (f) is substituted by the latter function (g). If we know that f(x) = x/(x - 3) and g(x) = 1/x, then the composed function is:

$f\,\circ\,g \,(x) = \frac{\frac{1}{x} }{\frac{1}{x}-3}$

$f\,\circ\,g\,(x) = \frac{\frac{1}{x} }{\frac{1-3\cdot x}{x} }$

$f\,\circ\,g\,(x) = \frac{1}{1-3\cdot x}$

The domain of the function is the set of x-values such that f ° g (x) exists. In the case of rational functions of the form p(x)/q(x), the domain is the set of x-values such that q(x) ≠ 0. Thus, the domain of f ° g (x) is $\mathbb{R} - \{\frac{1}{3} \}$ .

To learn more on composed functions: brainly.com/question/12158468

#SPJ1

3 0

1 year ago

If u(x) = x5 – x4 + x2 and v(x) = –x2, which expression is equivalent to (u/v)(x)

choli [55]

Answer:

c) -x^3 + x^2 - 1

Step-by-step explanation:

Given: u (x) = x^5 - x^4 +x^2 and v(x) = -x^2

(u/v)(x) = u(x)/v(x)

Now plug in the given functions in the above formula, we get

= (x^5 - x^4 + x^2) / -x^2

We can factorize the numerator.

In x^5 - x^4 + x^2. the common factor is x^2, so we can take it out and write the remaining terms in the parenthesis.

= x^2 (x^3 - x^2 + 1) / - x^2

Now we gave x^2 both in the numerator and in the denominator, we can cancel it out.

(u/v)(x) = (x^3 - x^2 + 1) / -1

When we dividing the numerator by -1, we get

(u/v)(x) = -x^3 + x^2 - 1

Answer: c) -x^3 + x^2 - 1

Hope you will understand the concept.

Thank you.

6 0

3 years ago

Read 2 more answers

Tan (angle B) using an exact expression in trigonometric ratios in right triangles

goblinko [34]

The value of the tangent of an angle is the ratio (opposite side) / (adjacent side).

Here you see that the opposite side (opposite to Angle B) is of length 5 and the adj. side has length 12.

Thus, the tan of Angle B is 5/12. (answer)

4 0

3 years ago