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2 years ago

What is the tangent ratio of angle y?

Mathematics

1 answer:

larisa [96]2 years ago

6 0

The answer should be b

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The hypotenuse of an isosceles right triangle is centimeters longer than either of its legs. Find the exact length of each side.

Varvara68 [4.7K]

Question

The hypotenuse of an isosceles right triangle is 11 centimeters longer than either of its legs. find the exact length of each side.

Answer:

$Hypotenuse:37.56$

$Other\ Legs: 26.56$

Step-by-step explanation:

Let the hypotenuse be y and the other legs be x.

So:

$y = 11 + x$

Required

Determine the exact dimension of the triangle

Using Pythagoras theorem;

$y^2 = x^2 + x^2$

$y^2 = 2x^2$

This gives:

$(11+x)^2 = 2x^2$

Open bracket

$121 + 22x + x^2= 2x^2$

Collect like terms

$2x^2 - x^2 -22x - 121 = 0$

$x^2 -22x - 121 = 0$

Using quadratic formula:

$x = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}$

$x = \frac{-(-22)\±\sqrt{(-22)^2 - 4*1*-121}}{2*1}$

$x = \frac{-(-22)\±\sqrt{968}}{2*1}$

$x = \frac{22\±31.11}{2}$

Split

$x = \frac{22+31.11}{2}\ or\ x = \frac{22-31.11}{2}\\$

$x = \frac{53.11}{2}\ or\ x = \frac{-9.11}{2}$

x can not be negative.

So:

$x = \frac{53.11}{2}$

$x = 26.56$

Recall that:

$y = 11 + x$

$y = 11 + 26.56$

$y = 37.56$

Hence, the dimensions are:

$Hypotenuse:37.56$

$Other\ Legs: 26.56$

6 0

2 years ago

Make t the subject of the formula. Please help.

Digiron [165]

Answer:

$t = \frac{2-3q}{q+4}$

Step-by-step explanation:

$q = \frac{2-4t}{t+3}\\\\$

Cross multiply,

q(t+3) = 2 - 4t

Use distributive property: a*(b + c) =(a*b) + (a*c)

qt + 3q = 2- 4t

qt + 4t + 3q = 2

qt + 4t = 2 - 3q

t(q + 4) = 2 -3q

$t = \frac{2-3q}{q+4}$

5 0

2 years ago

A random variable x is uniformly distributed between 45 and 150:

Ede4ka [16]

Answer:

67793993938383833837777773

6 0

2 years ago

Change the following expression to an equivalent expression in exponential form

Sever21 [200]

Answer:

12^4/5

Step-by-step explanation:

When doing this you put the number the base is raised to on top of the fraction and the root number on the bottom

8 0

2 years ago

What is the value of this expression if h = 8,j = -1, and k = -12

Rashid [163]

Answer:

Step-by-step explanation:

The given expression is :

$\dfrac{j^3k}{h^0}$

We need to find the value of this expression when h = 8, j = -1 and k = -12.

Put all the values in the given expression.

$\dfrac{j^3k}{h^0}\\\\=\dfrac{(-1)^3\times (-12)}{(8)^0}\\\\=\dfrac{-1\times -12}{1}\\\\=12$

So, the value of the given expression is 12.

7 0

2 years ago