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2 years ago

How to find the area of a right angle triangle with one side length given?

1 answer:

5 0

Step 1 Decide which two sides we are using - one we are trying to find and one we already know – out of Opposite, Adjacent and Hypotenuse.Step 2 Use SOHCAHTOA to decide which one of Sine, Cosine or Tangent to use in this question.Step 3 For Sine write down Opposite/Hypotenuse, for Cosine write down Adjacent/Hypotenuse or for Tangent write down Opposite/Adjacent. One of the values is the unknown length.Step 4 Solve using your calculator and your skills with Algebra

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Find the largest prime divisor of 76^2 − 1.

saveliy_v [14]

Answer:

Step-by-step explanation:

This is a difference of squares and therefore can be written as (76-1)(76+1)=(75)(77).

So lets look at the factors....

75=3(25)=3(5)(5)

77=7(11)

The biggest prime factor is therefore 11.

Identities used:

Difference of squares a^2-b^2=(a-b)(a+b)

3 0

2 years ago

If x^2+1/x^2=3 find the value of x^2/(x^2+1)^2 Express answer as a common fraction. Thanks!!

timama [110]

$x^2+\dfrac1{x^2}=3\implies x^4+1=3x^2\implies x^4-3x^2+1=0$

By the quadratic formula,

$x^2=\dfrac{3\pm\sqrt5}2\implies x^2+1=\dfrac{5\pm\sqrt5}2$

Then

$(x^2+1)^2=\dfrac{25\pm10\sqrt5+5}4=\dfrac{15\pm5\sqrt5}2$

$\implies\dfrac{x^2}{(x^2+1)^2}=\dfrac{\frac{3\pm\sqrt5}2}{\frac{15\pm5\sqrt5}2}=\dfrac{3\pm\sqrt5}{15\pm5\sqrt5}$

Multiply numerator and denominator by the denominator's conjugate:

$\dfrac{3\pm\sqrt5}{15\pm5\sqrt5}\cdot\dfrac{15\mp5\sqrt5}{15\mp5\sqrt5}=\dfrac{45\pm15\sqrt5\mp15\sqrt5-25}{15^2-(5\sqrt5)^2}=\dfrac{20}{100}=\dfrac15$

3 0

3 years ago

How do you solve for x a=2x+6xz

maksim [4K]

a = 2x + 6xz

a = x(2 + 6z) factored out "x" on right side

a/(2 + 6z) = x divided both sides by (2 + 6z)

Answer: x = $\frac{a}{2 + 6z}$

8 0

2 years ago

Please help me with this problem

Katen [24]

Sorry if this is messy but I hope it helps you

6 0

3 years ago

Last week, it rained x inches. This week, the amount of rain decreased by 5%. Which expressions represent the amount of rain tha

sineoko [7]

I think the answer would be A because 5% ×100=0.05 , and in the question they have been telling us that it decreased by 5 from the last week so the equation would be g of the last week - 0.05

7 0

2 years ago