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3 years ago

The number 0.7777 repeats forever therefore it is irrational true or false?

Mathematics

1 answer:

DochEvi [55]3 years ago

4 0

Answer:

It's false, this number is a rational number.

Step-by-step explanation:

It's false, the kind of decimal where the same digits repeats forever are known as periodic decimals and they can be represented with fractions therefore they are a part of the rational numbers. To represent this number in a fraction form we need to first identify the part that repeats, in this case it's 7, since it's only one number we can insert it in the numerator and the denominator will have a 9, if it were two numbers the denominator would have a 99 and so on. So in this case:

7/9 = 0.7777...

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Solve the system of equations. −2x+5y =−35 7x+2y =25

Otrada [13]

Answer:

The equations have one solution at (5, -5).

Step-by-step explanation:

We are given a system of equations:

$\displaystyle{\left \{ {{-2x+5y=-35} \atop {7x+2y=25}} \right.}$

This system of equations can be solved in three different ways:

Graphing the equations (method used)
Substituting values into the equations
Eliminating variables from the equations

Graphing the Equations

We need to solve each equation and place it in slope-intercept form first. Slope-intercept form is $\text{y = mx + b}$ .

Equation 1 is $-2x+5y = -35$ . We need to isolate y.

$\displaystyle{-2x + 5y = -35}\\\\5y = 2x - 35\\\\\frac{5y}{5} = \frac{2x - 35}{5}\\\\y = \frac{2}{5}x - 7$

Equation 1 is now $y=\frac{2}{5}x-7$ .

Equation 2 also needs y to be isolated.

$\displaystyle{7x+2y=25}\\\\2y=-7x+25\\\\\frac{2y}{2}=\frac{-7x+25}{2}\\\\y = -\frac{7}{2}x + \frac{25}{2}$

Equation 2 is now $y=-\frac{7}{2}x+\frac{25}{2}$ .

Now, we can graph both of these using a data table and plotting points on the graph. If the two lines intersect at a point, this is a solution for the system of equations.

The table below has unsolved y-values - we need to insert the value of x and solve for y and input these values in the table.

$\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & a \\ \cline{1-2} 1 & b \\ \cline{1-2} 2 & c \\ \cline{1-2} 3 & d \\ \cline{1-2} 4 & e \\ \cline{1-2} 5 & f \\ \cline{1-2} \end{array}$

$\bullet \ \text{For x = 0,}$

$\displaystyle{y = \frac{2}{5}(0) - 7}\\\\y = 0 - 7\\\\y = -7$

$\bullet \ \text{For x = 1,}$

$\displaystyle{y=\frac{2}{5}(1)-7}\\\\y=\frac{2}{5}-7\\\\y = -\frac{33}{5}$

$\bullet \ \text{For x = 2,}$

$\displaystyle{y=\frac{2}{5}(2)-7}\\\\y = \frac{4}{5}-7\\\\y = -\frac{31}{5}$

$\bullet \ \text{For x = 3,}$

$\displaystyle{y=\frac{2}{5}(3)-7}\\\\y= \frac{6}{5}-7\\\\y=-\frac{29}{5}$

$\bullet \ \text{For x = 4,}$

$\displaystyle{y=\frac{2}{5}(4)-7}\\\\y = \frac{8}{5}-7\\\\y=-\frac{27}{5}$

$\bullet \ \text{For x = 5,}$

$\displaystyle{y=\frac{2}{5}(5)-7}\\\\y=2-7\\\\y=-5$

Now, we can place these values in our table.

As we can see in our table, the rate of decrease is $-\frac{2}{5}$ . In case we need to determine more values, we can easily either replace x with a new value in the equation or just subtract $-\frac{2}{5}$ from the previous value.

For Equation 2, we need to use the same process. Equation 2 has been resolved to be $y=-\frac{7}{2}x+\frac{25}{2}$ . Therefore, we just use the same process as before to solve for the values.

$\bullet \ \text{For x = 0,}$

$\displaystyle{y=-\frac{7}{2}(0)+\frac{25}{2}}\\\\y = 0 + \frac{25}{2}\\\\y = \frac{25}{2}$

$\bullet \ \text{For x = 1,}$

$\displaystyle{y=-\frac{7}{2}(1)+\frac{25}{2}}\\\\y = -\frac{7}{2} + \frac{25}{2}\\\\y = 9$

$\bullet \ \text{For x = 2,}$

$\displaystyle{y=-\frac{7}{2}(2)+\frac{25}{2}}\\\\y = -7+\frac{25}{2}\\\\y = \frac{11}{2}$

$\bullet \ \text{For x = 3,}$

$\displaystyle{y=-\frac{7}{2}(3)+\frac{25}{2}}\\\\y = -\frac{21}{2}+\frac{25}{2}\\\\y = 2$

$\bullet \ \text{For x = 4,}$

$\displaystyle{y=-\frac{7}{2}(4)+\frac{25}{2}}\\\\y=-14+\frac{25}{2}\\\\y = -\frac{3}{2}$

$\bullet \ \text{For x = 5,}$

$\displaystyle{y=-\frac{7}{2}(5)+\frac{25}{2}}\\\\y = -\frac{35}{2}+\frac{25}{2}\\\\y = -5$

And now, we place these values into the table.

$\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & 25/2 \\ \cline{1-2} 1 & 9 \\ \cline{1-2} 2 & 11/2 \\ \cline{1-2} 3 & 2 \\ \cline{1-2} 4 & -3/2 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}$

When we compare our two tables, we can see that we have one similarity - the points are the same at x = 5.

Equation 1 Equation 2

$\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & -7 \\ \cline{1-2} 1 & -33/5 \\ \cline{1-2} 2 & -31/5 \\ \cline{1-2} 3 & -29/5 \\ \cline{1-2} 4 & -27/5 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}$ $\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & 25/2 \\ \cline{1-2} 1 & 9 \\ \cline{1-2} 2 & 11/2 \\ \cline{1-2} 3 & 2 \\ \cline{1-2} 4 & -3/2 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}$

Therefore, using this data, we have one solution at (5, -5).

4 0

3 years ago

Each week Charlene uses 3/4 of a bag of cat food to feed her cats. She has 112 bags of cat food in stock. How long will her stoc

inessss [21]

The stock of cat food will last for 149 weeks.

Step-by-step explanation:

Given,

Bags of cat food in stock = 112

Bags used each week = $\frac{3}{4}\ of\ one\ bag$

Let,

x be the number of weeks.

Therefore,

$\frac{3}{4}x=112$

Multiplying both sides by 4/3

$\frac{4}{3}*\frac{3}{4}x=112*\frac{4}{3}\\x=\frac{448}{3}\\x=149.33$

Rounding off to nearest whole number;

x=149

The stock of cat food will last for 149 weeks.

Keywords: fraction, multiplication

Learn more about fractions at:

#LearnwithBrainly

4 0

3 years ago

Using the Distance Formula, calculate the distance between the three points: (3 points)

AlladinOne [14]

The distance formula between two points is d∧2=(x2-x1)∧2 + (y2-y1)∧2

The distance between Vista and Oceanside is

d1∧2=(-1-(-6))∧2+(6-2)∧2=(-1+6)∧2+4∧2=5∧2+16=25+16=41 => d=√41= 6.4

The distance between Oceanside and Alpena is

d2∧2=(0-(-1))∧2+(-1-6)∧2=1+(-7)∧2=1+49=50 => d2=√50=7.07

The distance between Vista and Alpena is

d3∧2=(0-(-6))∧2+(-1-2)∧2=36+9=45 => d3=√45= 6.7

Answer a) is Oceanside and Alpena

Answer b) is Vista and Oceanside

Good luck!!!

4 0

3 years ago

Read 2 more answers

One gallon of gasoline in buffalo, New York costs $2.29. In Toronto, Canada, one liter of gas costs $0.91. There are 3.8 liters

Solnce55 [7]

Answer:

The cost of one gallon of gas in Toronto, Canada is $3.458.

Solution:

Given, One gallon of gasoline in buffalo, New York costs $2.29.

In Toronto, Canada, one liter of gas costs $0.91.

There are 3.8 liters in one gallon.

We have to find how much does one gallon of gas cost in Toronto?

Now, cost of one gallon of gas in Toronto = cost of one litre of gas in Toronto x 3.8 liters for 1 gallon.

Cost of one gallon of gas = 0.91 x 3.8 = 3.458

Hence, the cost of one gallon of gas in Toronto, Canada is $3.458.

3 0

3 years ago

QUICKLY PLEASE!! 18POINTS! 6(3p – 2) = 24

Gekata [30.6K]

Answer:

p= 2

Step-by-step explanation:

So first you want to distribute the 6 to 3p-2 which basically means multiply

6(3p – 2) = 24

6 times 3p is 18 and 6 time -2 is -12

* remember a negative and a positive equal a negative*

18p-12=24

you want to get 18p by itself, so in order to do that you can add 12 to both sides because if you add 12 on the left side it cancels out -12 and whatever you do to one side you have to do it to the other so add 12 to 24 which is 36

18p = 36

since you want to get p by itself you divide p on both sides so it can cancel out 18 and 36/18 is 2

so p = 2

if you are wondering why i divide it and not subtract or add it is because 18 and p are stuck together so you have to divide but if it was like 18 + p you can subtract because 18 and p arent together

6 0

3 years ago