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3 years ago

Allowance $10 Earn $18 Spend $3.28, $7.15, and $9.54 Save?

Mathematics

1 answer:

julsineya [31]3 years ago

4 0

Answer:

8.03

Step-by-step explanation:

10+18 = 28

28 - 3.28 - 7.15 - 9.54 = 8.03

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4x+8 less than or equal to 9x+3

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3 years ago

The line segment AB with endpoints A (-3, 6) and B (9, 12) is dilated with a scale

Gwar [14]

Answer:

C) (-2, 4), (6,8) is the correct answer.

Step-by-step explanation:

Given that line segment AB:

A (-3, 6) and B (9, 12) is dilated with a scale factor 2/3 about the origin.

First of all, let us calculate the distance AB using the distance formula:

$D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Here,

$x_2=9\\x_1=-3\\y_2=12\\y_1=6$

Putting all the values and finding AB:

$AB = \sqrt{(9-(-3))^2+(12-6)^2}\\\Rightarrow AB = \sqrt{(12)^2+(6)^2}\\\Rightarrow AB = \sqrt{144+36}\\\Rightarrow AB = \sqrt{180}\\\Rightarrow AB = 6\sqrt{5}\ units$

It is given that AB is dilated with a scale factor of $\frac{2}{3}$ .

$x_2'=\dfrac{2}{3}\times x_2=\dfrac{2}{3}\times9=6\\x_1'=\dfrac{2}{3}\times x_1=\dfrac{2}{3}\times-3=-2\\y_2'=\dfrac{2}{3}\times y_2=\dfrac{2}{3}\times 12=8\\y_1'=\dfrac{2}{3}\times y_1=\dfrac{2}{3}\times 6=4$

So, the new coordinates are A'(-2,4) and B'(6,8).

Verifying this by calculating the distance A'B':

$A'B' = \sqrt{(6-(-2))^2+(8-4)^2}\\\Rightarrow A'B' = \sqrt{(8)^2+(4)^2}\\\Rightarrow A'B' = \sqrt{64+16}\\\Rightarrow A'B' = \sqrt{80}\\\Rightarrow A'B' = 4\sqrt{5}\ units = \dfrac{2}{3}\times AB$

So, option C) (-2, 4), (6,8) is the correct answer.

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3 years ago

There are 28 total students in Mr. Flynn’s class. The ratio of his students who are in the play to those who are not in the play

PolarNik [594]

First, you calculate the total amount of parts : 2 + 5 = 7
Next, divide the number by the total amount of parts : 28 ÷ 7 = 4
After that, you multiply the answer by the amount of parts needed on both sides of the ratio : 4 × 2 = 8 and 4 × 5 = 20
Finally put these answers back into the ratio : 8:20
So there are 8 students in the play

To check, make sure both sides of the ratio add up to the original number : 8 + 20 = 28

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