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3 years ago

Hannah says that 2.11 is a rational number. Gus says that 2.11 is a repeating decimal.

Mathematics

2 answers:

SVETLANKA909090 [29]3 years ago

8 0

Answer:

well does it have the repeating line on top? if it does then it's irrational if it doesn't it's rational

user100 [1]3 years ago

5 0

Answer:

Both Hannah and Gus are correct.

Step-by-step explanation:

We are given the following information in the question:

Hannah says that 2.11 is a rational number. Gus says that 2.11 is a repeating decimal.

Hannah is correct in the claim as 2.11 can be written in the form of a fraction, where,

$\displaystyle\frac{x}{y}, y \neq 0\\\\2.11 = \frac{211}{100}$

Hence, 2.11 is rational number.

2.11 is also a repeating decimal as it can be written as 2.110000...

A repeating or recurring decimal is decimal a number whose digits after point are periodic and repeats.
It can be shown that a number is rational if and only if its decimal expansion is repeating or terminating.

Hence, both Hannah and Gus are correct.

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Solve the following system of equations by substitution 2x – 3y = -1 y = x - 1

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Answer:

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Step-by-step explanation:

Plug in x - 1 where y is. The equation will turn in 2x - 3(x - 1) = -1. Distribute, and you'll have 2x -3x + 3 = -1. Combine like terms (2x and -3x) and you'll have -x + 3 = -1. Subtract 3 from both sides, and you'll have -x = -4. Divide by -x (or -1) on both sides, and you'll have x = 4. Since y = x - 1, y = 3, since 4 - 1 = 3. Sorry if this sounds repetitive btw. Good luck :D

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antoniya [11.8K]

-0.545 , -0.541 , -0.548

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3 years ago

Please help, will grant brainliest if correct, need now!!

Mama L [17]

Answer:

- 7

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

$\frac{f(b)-f(a)}{b-a}$

Here [ a, b ] = [ - 5, - 2 ]

f(b) = f(- 2) = (- 2)² - 4 = 4 - 4 = 0

f(a) = f(- 5) = (- 5)² - 4 = 25 - 4 = 21, thus

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<img src="https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7Bx%2By%3D1%7D%20%5Catop%20%7Bx-2y%3D4%7D%7D%20%5Cright.%20%5C%5C%5Clef

brilliants [131]

Answer:

(a) x=2, y=-1

(b) x=2, y=2

(c) $\displaystyle x=\frac{5}{2}, y=\frac{5}{4}$

(d) x=-2, y=-7

Step-by-step explanation:

Cramer's Rule

It's a predetermined sequence of steps to solve a system of equations. It's a preferred technique to be implemented in automatic digital solutions because it's easy to structure and generalize.

It uses the concept of determinants, as explained below. Suppose we have a 2x2 system of equations like:

$\displaystyle \left \{ {{ax+by=p} \atop {cx+dy=q}} \right.$

We call the determinant of the system

$\Delta=\begin{vmatrix}a &b \\c &d \end{vmatrix}$

We also define:

$\Delta_x=\begin{vmatrix}p &b \\q &d \end{vmatrix}$

And

$\Delta_y=\begin{vmatrix}a &p \\c &q \end{vmatrix}$

The solution for x and y is

$\displaystyle x=\frac{\Delta_x}{\Delta}$

$\displaystyle y=\frac{\Delta_y}{\Delta}$

(a) The system to solve is

$\displaystyle \left \{ {{x+y=1} \atop {x-2y=4}} \right.$

Calculating:

$\Delta=\begin{vmatrix}1 &1 \\1 &-2 \end{vmatrix}=-2-1=-3$

$\Delta_x=\begin{vmatrix}1 &1 \\4 &-2 \end{vmatrix}=-2-4=-6$

$\Delta_y=\begin{vmatrix}1 &1 \\1 &4 \end{vmatrix}=4-3=3$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-6}{-3}=2$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{3}{-3}=-1$

The solution is x=2, y=-1

(b) The system to solve is

$\displaystyle \left \{ {{4x-y=6} \atop {x-y=0}} \right.$

Calculating:

$\Delta=\begin{vmatrix}4 &-1 \\1 &-1 \end{vmatrix}=-4+1=-3$

$\Delta_x=\begin{vmatrix}6 &-1 \\0 &-1 \end{vmatrix}=-6-0=-6$

$\Delta_y=\begin{vmatrix}4 &6 \\1 &0 \end{vmatrix}=0-6=-6$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-6}{-3}=2$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{-6}{-3}=2$

The solution is x=2, y=2

$\displaystyle \left \{ {{-x+2y=0} \atop {x+2y=5}} \right.$

Calculating:

$\Delta=\begin{vmatrix}-1 &2 \\1 &2 \end{vmatrix}=-2-2=-4$

$\Delta_x=\begin{vmatrix}0 &2 \\5 &2 \end{vmatrix}=0-10=-10$

$\Delta_y=\begin{vmatrix}-1 &0 \\1 &5 \end{vmatrix}=-5-0=-5$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-10}{-4}=\frac{5}{2}$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{-5}{-4}=\frac{5}{4}$

The solution is

$\displaystyle x=\frac{5}{2}, y=\frac{5}{4}$

(d) The system to solve is

$\displaystyle \left \{ {{6x-y=-5} \atop {4x-2y=6}} \right.$

Calculating:

$\Delta=\begin{vmatrix}6 &-1 \\4 &-2 \end{vmatrix}=-12+4=-8$

$\Delta_x=\begin{vmatrix}-5 &-1 \\6 &-2 \end{vmatrix}=10+6=16$

$\Delta_y=\begin{vmatrix}6 &-5 \\4 &6 \end{vmatrix}=36+20=56$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{16}{-8}=-2$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{56}{-8}=-7$

The solution is x=-2, y=-7

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3 years ago