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DochEvi [55]
3 years ago
6

I need help please. Thank you show your work please

Mathematics
2 answers:
Leni [432]3 years ago
5 0
3.5 because 5-1.5  =3.5
Effectus [21]3 years ago
4 0
Let, the number of hours, that Julia still can watch TV = x

Equation would be: 1.5 + x ≤ 5

Solving: 1.5 + x ≤ 5

Subtract 1.5 from both sides, 
1.5 - 1.5 + x ≤ 5 - 1.5
x ≤ 3.5

In short, She can watch 3.5 hours at maximum

Hope this helps!
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Show that a = −1 + √3i and b = 2 satisfy 1/a+b=1/a + 1/b
Zarrin [17]

Answer:

LHS = \frac{1 - \sqrt3i}{4} = RHS = \frac{1 - \sqrt3i}{4}

Step-by-step explanation:

Data provided in the question:

a = −1 + √3i and b = 2

to prove:

\frac{1}{a+b}=\frac{1}{a} + \frac{1}{b}

Considering the LHS

⇒ \frac{1}{a+b}

substituting the value of a and b, we get

⇒ \frac{1}{−1 + \sqrt3i+2}

or

⇒ \frac{1}{1 + \sqrt3i}

on multiplying and dividing by conjugate ( 1 - √3i )

we get

\frac{1}{1 + \sqrt3i}\times\frac{1 - \sqrt3i}{1 - \sqrt3i}

or

\frac{1 - \sqrt3i}{(1^2 - (\sqrt3i)^2}

or

\frac{1 - \sqrt3i}{1 + 3}              (as (√i)² = -1 )

or

\frac{1 - \sqrt3i}{4}

Now,

considering the RHS

\frac{1}{a} + \frac{1}{b}

substituting the value of a and b, we get

⇒ \frac{1}{-1 + \sqrt3i} + \frac{1}{2}

or

⇒ \frac{2\times1 + ( -1 + \sqrt3i)\times1}{(-1 + \sqrt3i)\times2}

or

⇒ \frac{2 + ( -1 + \sqrt3i)}{(-1 + \sqrt3i)\times2}

or

⇒ \frac{1 + \sqrt3i}{(-1 + \sqrt3i)\times2}

now,

on multiplying and dividing by conjugate ( -1 - √3i )

we get

\frac{1 + \sqrt3i}{(−1 + \sqrt3i)\times2}\times\frac{-1 - \sqrt3i}{-1 - \sqrt3i}

or

\frac{1 + \sqrt3i}{(−1 + \sqrt3i)\times2}\times\frac{-1( 1 + \sqrt3i)}{-1 - \sqrt3i}

or

\frac{(1 + \sqrt3i}^2\times(-1){((-1)^2 - (\sqrt3i)^2)\times2}

or

\frac{(1^2 + (\sqrt3i)^2+2(1)(\sqrt3i)\times(-1)}{(1 + 3)\times2}

or

\frac{(1 - 3 + 2\sqrt3i)\times(-1)}{(4)\times2}

or

\frac{(-2 + 2\sqrt3i)\times(-1)}{(4)\times2}

or

\frac{-2( 1 - 2\sqrt3i)\times(-1)}{(4)\times2}

or

\frac{( 1 - 2\sqrt3i)}{(4)}

Since, LHS = RHS

hence satisfied

3 0
3 years ago
1) Identify the slope in the equation y = 1/4 x + 2
igor_vitrenko [27]

Answer:  1/4

Step-by-step explanation:

y=mx+b

y=slope+y-intercept

mx=1/4

4 0
3 years ago
Read 2 more answers
Tell whether the statement is true or false. Tan20 degrees greater than cot20 degrees
Oxana [17]
True because tan(20)=2.1 and cot(20)=is o.44
8 0
3 years ago
Write the quadratic equation whose roots are −2 and 2, and whose leading coefficient is 3.
Elena L [17]

Answer:

3x^2-12=0

Step-by-step explanation:

<u>Quadratic Equation</u>

A quadratic equation also called a second-degree equation is a special polynomial whose highest degree is two.

The general form of the quadratic equation is

ax^2+bx+c=0

Where a is known as the leading coefficient. Another form to write the quadratic equation is

a(x-x_1)(x-x_2)=0

Where x1 and x2 are the roots or zeroes of the equation.

We have the roots of the given equation are -2 and 2, and the leading coefficient is 3.

Plugging in the given values we have

3(x+2)(x-2)=0

Operating

3(x^2-4)=0

\boxed{3x^2-12=0}

4 0
4 years ago
What is the expression 44 degrees equal to?
bekas [8.4K]
Sin44 is the same as Cos46. Hope this helped.
3 0
4 years ago
Read 2 more answers
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