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Nookie1986 [14]

3 years ago

8

Roberta has $4.00 in dimes and quarters. She has 5 more dimes than quarters. Write a system of equations that you could use to f

ind how many dimes and quarters she has.

1 answer:

MakcuM [25]3 years ago

8 0

Answer:

$\left\{\begin{array}{l}25x+10y=400\\y=x+5\end{array}\right..$

Step-by-step explanation:

Let x be the number of quaters and y be the number of dimes Roberta has.

1. Quater is equal to 25 cents, then x quaters is equal to 25x cents. Dime is equal to 10 cents, then y dimes is equal to 10y cents. $4.00=400 cents, then

25x+10y=400.

2. Roberta has 5 more dimes than quarters, then

y=x+5.

3. The system of equations is

$\left\{\begin{array}{l}25x+10y=400\\y=x+5\end{array}\right..$

Substitute second equation into the first one:

$25x+10(x+5)=400,\\ \\25x+10x+50=400,\\ \\35x=350,\\ \\x=10,\ y=10+5=15.$

10 quaters and 15 dimes

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Correct responses:

$Slope \ of \ \overline{IJ} = \underline{-\dfrac{7}{6} }$ , Length of $\overline{IJ}$ = $\underline{\sqrt{85} }$

$Slope \ of \ \overline{JK} = \underline {-\dfrac{2}{9}}$ , Length of $\overline{JK}$ = $\underline{\sqrt{85} }$

$Slope \ of \ \overline{KL} = \underline{-\dfrac{7}{6} }$ , Length of $\overline{KL}$ = $\underline{\sqrt{85}}$

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<h3>Methods used to find the slope and length of a line</h3>

The given coordinates of the vertices are;

K(-7, 0), J(2, -2), I(8, -9), L(-1, -7)

$Slope = \mathbf{\dfrac{y_2 - y_1}{x_2 - x_1}}$

$Length \ of \ line = \mathbf{ \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}$

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$Slope \ of \ \mathbf{\overline{IJ}} = \dfrac{-2 - (-9)}{2 - 8} = \dfrac{7}{-6} = \underline{ -\dfrac{7}{6}}$

$Length \ of \ \mathbf{\overline{IJ}} = \sqrt{(2 - 8)^2 + (-2 - (-9))^2} = \underline{\sqrt{85}}$

$Slope \ of \ \mathbf{\overline{JK}} = \dfrac{0 - (-2)}{-7 - 2} = \dfrac{2}{-9} = \underline{-\dfrac{2}{9}}$

$Length \ of \ \mathbf{\overline{JK}} = \sqrt{(-7 - 2)^2 + (0 - (-2))^2} = \underline{ \sqrt{85}}$

$Slope \ of \ \mathbf{\overline{KL}} = \dfrac{0 - (-7)}{-7 - (-1)} = \dfrac{7}{-6} = \underline{ -\dfrac{7}{6}}$

$Length \ of \ \mathbf{\overline{KL} }= \sqrt{(-7 - (-1))^2 + (0 - (-7))^2} =\underline{ \sqrt{85}}$

$Slope \ of \ \mathbf{\overline{LI}} = \dfrac{(-9 - (-7))}{(8 - (-1))} = \dfrac{-2}{9} = \underline{-\dfrac{2}{9}}$

$Length \ of \ \mathbf{\overline{LI}} = \sqrt{(8 - (-1))^2 + (-9 - (-7))^2} = \underline{\sqrt{85}}$

Learn more about finding the slope and length of a line here:

brainly.com/question/11612395

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