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2 years ago

Is -2 + √3 rational or irrational?explain why.

Mathematics

1 answer:

andrey2020 [161]2 years ago

3 0

Answer:

It is irrational

Step-by-step explanation:

Let us assume that 2+√3 is a rational number.

A rational number can be written in the form of p/q.

2+√3=p/q

√3=p/q-2

√3=(p-2q)/q

p,q are integers then (p-2q)/q is a rational number.

But this contradicts the fact that √3 is an irrational number.

So, our assumption is false.

Therefore,2+√3 is an irrational number.

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What is the explicit formula for the sequence?

Aleksandr [31]

Answer:

$a_{n}$ = n - 2

Step-by-step explanation:

Note the difference between consecutive terms is constant, that is

0 - (- 1) = 0 + 1 = 1

1 - 0 = 1

2 - 1 = 1

3 - 2 = 1

This indicates the sequence is arithmetic with n th term

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 1 and d = 1, thus

$a_{n}$ = - 1 + n - 1 = n - 2

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2 years ago

How would i graph <br> y=− 5/2x-3<br> and<br> x−y=−4<br> (_,_)

SashulF [63]

Given:

The system of equations is

$y=-\dfrac{5}{2}x-3$

$x-y=-4$

To find:

The graph of the given system of equations and its solution.

Solution:

The table of values for $y=-\dfrac{5}{2}x-3$ is

x y

-4 7

-2 2

0 -3

Plot these points and connect them by a straight line.

The table of values for $x-y=-4$ is

x y

-4 0

-2 2

0 4

Plot these points and connect them by a straight line.

From the below graph it is clear that the lines intersect each other at point (-2,2).

Therefore, the solution of given system of equation is (-2,2).

6 0

3 years ago

FIRST TO ANSWER GETS BRAINLIEST!

scZoUnD [109]

Answer:

$\huge \boxed{ \red{ \boxed{c)78 \: units ^{2} }}}$

Step-by-step explanation:

<h3>to understand this</h3><h3>you need to know about:</h3>

circle
PEMDAS

<h3>tips and formulas:</h3>

$\rm \:A_{shaded}= \dfrac{\theta}{360} \times \pi {r}^{2}$

<h3>let's solve:</h3>

$\sf sustitute \: the \: value \: of \: \theta \: and \: r : \\ A_{shaded} = \frac{140}{360} \times \pi \times {8}^{2}$
$\sf simpify \: squre : \\ A_{shaded} = \frac{140}{360} \times \pi \times 64$
$\sf simpify \: fraction: \\ A_{shaded} = \frac{7}{18} \times \pi \times 64$
$\sf reduce \: 64: \\ A_{shaded} = \frac{7}{ \cancel{ \: 18} \: ^{9} } \times \pi \times \cancel{ 64} \: ^{32} \\ A_{shaded} = \frac{7}{9} \times \pi \times 32\\ A_{shaded} = \frac{224\pi}{9}$

$\large A_{shaded}\approx 78 \: square \: units$

8 0

2 years ago

Read 2 more answers

What is log25 with an exponent of 1/5?

Tomtit [17]

Log (25¹/⁵) = (1/5) log(25) = (1/5) (1.3979) = 0.2796

6 0

3 years ago

an initial deposit of $200 is made into an account that pays 4.2% annual interest. What is a model to represent the balance in t

Sholpan [36]

You would use the equation y = A(1+r)^t

A = Original amount = 200
r = interest rate = 0.042 (when converted from percent to decimal)
t = time = x

Plug them in and you get the model: y = 200(1+0.042)^x

or just simplify the parentheses to (1.042)

5 0

3 years ago