The length of a rectangle is increased by 20%. The width is decreased by 20%.

you order two tacos and a salad. The salad cost $2.50. You leave a three-dollar tip. Theres is no sales tax. How much does one t

Diano4ka-milaya [45]

Answer:

$5.50

Step-by-step explanation:

2.50+3.00=5.50

4 0

3 years ago

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Which linear equations have an infinite number of solutions? Check all that apply.

ladessa [460]

Answer:

a) (x – 3\7) = 2\3 (3\2x – 9\14 )

c) 12.3x – 18 = 3(–6 + 4.1x)

Step-by-step explanation:

A linear equation can be said to have an infinite number of solutions when the number of the right hand side is the same at the number on the left hand side of the equation.

For example:

2 = 2 or x = x or 0 = 0

Solving the question above:

Which linear equations have an infinite number of solutions? Check all that apply.

a) (x – 3\7) = 2\3 (3\2x – 9\14 )

x - 3/7 = 6x/6 - 18/42

x - 3/7 = x - 3/7

Collect like terms

x - x = -3/7 + 3/7

0 = 0

The linear equation in option a has an infinite number of solutions

b) 8(x + 2) = 5x – 14

8x + 16 = 5x - 14

Collect like terms

8x - 5x = -14 - 16

3x = -30

x = -30/3

x = -10.

The linear equation in Option b has a true solution.

c) 12.3x – 18 = 3(–6 + 4.1x)

12.3x - 18 = -18 + 12.3x

Collect like terms

12.3x - 12.3x = -18 + 18

0 = 0

The linear equation in Option c has infinite number of solutions

d) 1\2(6x + 10) = 7(3\7x – 2)

6x/2 + 5 = 21/7x - 14

3x + 5 = 3x - 14

Collect like terms

3x - 3x = -14 - 5

0 = -19

The linear equation Option d has no solution

e) 4.2x – 3.5 = 2.1 (5x + 8)

4.2x - 3.5 = 10.5x + 16.8

Collect like terms

4.2x - 10.5x = 16.8 + 3.5

-6.3x = 20.3

x = -20.3/6.3

x = -3.22

Hence, the linear equation in Option e has a true solution

Therefore, the linear equations have an infinite number of solutions are:

a) (x – 3\7) = 2\3 (3\2x – 9\14 )

c) 12.3x – 18 = 3(–6 + 4.1x)

8 0

3 years ago

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Zack wants to make a profit more than $300 for painting 4 identical rooms. The profit he makes is equal to the amount he is paid

crimeas [40]

Profit = paid - supplies

Plug in the given values. We are finding out how much money he needs per room, if he is doing 4 rooms, and subtracting the supplies: 300 = 4n - 4*32.50

Simplify: 300 = 4n - 130

Add 130 to each side. 430 = 4n

Divide by 4 on each side: 107.50= n

300 = 4(107.50) - 130? True

This tells us he must be paid $107.50 to make $300 exactly. Anything larger than $107.51 and up will make more than $300.

3 0

3 years ago

A set of equations is given below:

Gemiola [76]

2d+1=3d+5.
If both equations equal c, then both equations can be equal to each other.

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3 years ago

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Exercise 7.3.5 The following is a Markov (migration) matrix for three locations        1 5 1 5 2 5 2 5 2 5 1 5 2 5 2 5 2

fredd [130]

Answer:

Both get the same results that is,

$\left[\begin{array}{ccc}140\\160\\200\end{array}\right]$

Step-by-step explanation:

Given :

$\bf M=\left[\begin{array}{ccc}\frac{1}{5}&\frac{1}{5}&\frac{2}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{1}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{2}{5}\end{array}\right]$

and initial population,

$\bf P=\left[\begin{array}{ccc}130\\300\\70\end{array}\right]$

a) - After two times, we will find in each position.

$P_2=[P].[M]^2=[P].[M].[M]$

$M^2=\left[\begin{array}{ccc}\frac{1}{5}&\frac{1}{5}&\frac{2}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{1}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{2}{5}\end{array}\right]\times \left[\begin{array}{ccc}\frac{1}{5}&\frac{1}{5}&\frac{2}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{1}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{2}{5}\end{array}\right]$

$=\frac{1}{25} \left[\begin{array}{ccc}7&7&7\\8&8&8\\10&10&10\end{array}\right]$

$\therefore\;\;\;\;\;\;\;\;\;\;\;P_2=\left[\begin{array}{ccc}7&7&7\\8&8&8\\10&10&10\end{array}\right] \times\left[\begin{array}{ccc}130\\300\\70\end{array}\right] = \left[\begin{array}{ccc}140\\160\\200\end{array}\right]$

b) - With in migration process, 500 people are numbered. There will be after a long time,

$After\;inifinite\;period=[M]^n.[P]$

$Then,\;we\;get\;the\;same\;result\;if\;we\;measure [M]^n=\frac{1}{25} \left[\begin{array}{ccc}7&7&7\\8&8&8\\10&10&10\end{array}\right]$

$=\left[\begin{array}{ccc}140\\160\\200\end{array}\right]$

4 0

3 years ago