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3 years ago

Anna, Laura and David each earn the same monthly salary.

1 answer:

3 0

So convert them all to percentages

Anna: 19%
Laura: 17/20 then times by 5 to get 85%
therefore she saves 15%
David: 2:8 = 2/10 saved = 20%

so david saves the most

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19) Albert says that the two systems of equations shown have the same solutions.

k0ka [10]

Answer:

option A) Agree, because the solutions are the same is correct.

Step-by-step explanation:

FIRST SYSTEM

$6x + y= 2$

$-x-y=-3$

solving the system

$\begin{bmatrix}6x+y=2\\ -x-y=-3\end{bmatrix}$

$\mathrm{Multiply\:}-x-y=-3\mathrm{\:by\:}6\:\mathrm{:}\:\quad \:-6x-6y=-18$

$\begin{bmatrix}6x+y=2\\ -6x-6y=-18\end{bmatrix}$

adding the equation

$-6x-6y=-18$

$+$

$\underline{6x+y=2}$

$-5y=-16$

so the system becomes

$\begin{bmatrix}6x+y=2\\ -5y=-16\end{bmatrix}$

solve -5y for y

$-5y=-16$

Divide both sides by -5

$\frac{-5y}{-5}=\frac{-16}{-5}$

simplify

$y=\frac{16}{5}$

$\mathrm{For\:}6x+y=2\mathrm{\:plug\:in\:}y=\frac{16}{5}$

$6x+\frac{16}{5}=2$

subtract 16/5 from both sides

$6x+\frac{16}{5}-\frac{16}{5}=2-\frac{16}{5}$

$6x=-\frac{6}{5}$

Divide both sides by 6

$\frac{6x}{6}=\frac{-\frac{6}{5}}{6}$

$x=-\frac{1}{5}$

Therefore, the solution to the FIRST SYSTEM is:

$x=-\frac{1}{5},\:y=\frac{16}{5}$

SECOND SYSTEM

$2x-3y = -10$

$-x-y=-3$

solving the system

$\begin{bmatrix}2x-3y=-10\\ -x-y=-3\end{bmatrix}$

$\mathrm{Multiply\:}-x-y=-3\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-2x-2y=-6$

$\begin{bmatrix}2x-3y=-10\\ -2x-2y=-6\end{bmatrix}$

$-2x-2y=-6$

$+$

$\underline{2x-3y=-10}$

$-5y=-16$

so the system of equations becomes

$\begin{bmatrix}2x-3y=-10\\ -5y=-16\end{bmatrix}$

solve -5y for y

$-5y=-16$

Divide both sides by -5

$\frac{-5y}{-5}=\frac{-16}{-5}$

Simplify

$y=\frac{16}{5}$

$\mathrm{For\:}2x-3y=-10\mathrm{\:plug\:in\:}y=\frac{16}{5}$

$2x-3\cdot \frac{16}{5}=-10$

$2x=-\frac{2}{5}$

Divide both sides by 2

$\frac{2x}{2}=\frac{-\frac{2}{5}}{2}$

Simplify

$x=-\frac{1}{5}$

Therefore, the solution to the SECOND SYSTEM is:

$x=-\frac{1}{5},\:y=\frac{16}{5}$

Conclusion:

As both systems of equations have the same solution.

Therefore, we conclude that Albert is right when says that the two systems of equations shown have the same solutions.

Hence, option A) Agree, because the solutions are the same is correct.

8 0

3 years ago

PLEASE HELP AS SOON AS POSSIBLE

Elodia [21]

d = |150 - 20t|

70 = |150 = 20t|

70 = 150 - 20t -70 = 150 - 20t

-80 = -20t -220 = -20t

4 = t 11 = t

Answer: 4, 11 seconds

7 0

4 years ago

How do u solve 1.2= k over 4

salantis [7]

1.2 = k/4

multiply both sides by 4,

1.2*4 = k

k = 4.8

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3 years ago

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jaime makes a necklace with beads that are 0.08 meter long. her next necklace will have beads that are 1/10 the size of the bead

MatroZZZ [7]

It would be 0.008 meters long

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3 years ago

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A store sells both cold and hot beverages. Cold beverages, c, cost $1.50, while hot beverages, h, cost $2.00. On Saturday, drink

Marina86 [1]

2h + 4h (1.5c) = 360 so option b is correct.

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