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3 years ago

Solve the following two-step problems -5m - 4 = 4m

Mathematics

2 answers:

RSB [31]3 years ago

7 0

-2.25.
-5m-4=4m
+5m +5m
-4=9m
m= -2.25

Musya8 [376]3 years ago

3 0

Answer:

0.444

Step-by-step explanation:

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Leila works mowing lawns and babysitting. She earns $8.30 an hour for mowing and $7.30 an hour for babysitting. How much will sh

Mamont248 [21]

Answer:

$79 total earnings

Step-by-step explanation:

Here, earnings = (hourly rate)(number of hours):

= ($8.30/hr)(6 hrs) + ($7.30/hr)(4 hrs), or

Total earnings = $49.80 + $29.20

" " = $79.00

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3 years ago

5. Show that the following points are collinear. a) (1, 2), (4, 5), (8,9)

Irina-Kira [14]

Label the points A,B,C

A = (1,2)
B = (4,5)
C = (8,9)

Let's find the distance from A to B, aka find the length of segment AB.

We use the distance formula.

$A = (x_1,y_1) = (1,2) \text{ and } B = (x_2, y_2) = (4,5)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-4)^2 + (2-5)^2}\\\\d = \sqrt{(-3)^2 + (-3)^2}\\\\d = \sqrt{9 + 9}\\\\d = \sqrt{18}\\\\d = \sqrt{9*2}\\\\d = \sqrt{9}*\sqrt{2}\\\\d = 3\sqrt{2}\\\\$

Segment AB is exactly $3\sqrt{2}$ units long.

Now let's find the distance from B to C

$B = (x_1,y_1) = (4,5) \text{ and } C = (x_2, y_2) = (8,9)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(4-8)^2 + (5-9)^2}\\\\d = \sqrt{(-4)^2 + (-4)^2}\\\\d = \sqrt{16 + 16}\\\\d = \sqrt{32}\\\\d = \sqrt{16*2}\\\\d = \sqrt{16}*\sqrt{2}\\\\d = 4\sqrt{2}\\\\$

Segment BC is exactly $4\sqrt{2}$ units long.

Adding these segments gives

$AB+BC = 3\sqrt{2}+4\sqrt{2} = 7\sqrt{2}$

----------------------

Now if A,B,C are collinear then AB+BC should get the length of AC.

AB+BC = AC

Let's calculate the distance from A to C

$A = (x_1,y_1) = (1,2) \text{ and } C = (x_2, y_2) = (8,9)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-8)^2 + (2-9)^2}\\\\d = \sqrt{(-7)^2 + (-7)^2}\\\\d = \sqrt{49 + 49}\\\\d = \sqrt{98}\\\\d = \sqrt{49*2}\\\\d = \sqrt{49}*\sqrt{2}\\\\d = 7\sqrt{2}\\\\$

AC is exactly $7\sqrt{2}$ units long.

Therefore, we've shown that AB+BC = AC is a true equation.

This proves that A,B,C are collinear.

For more information, check out the segment addition postulate.

7 0

3 years ago

Three sticks of butter are needed for every 24 cookies.

NeX [460]

Answer:

40 cookies

Step-by-step explanation:

24÷3=8

8×5=40

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3 years ago

Leon is constructing the circumscribed circle for △PQR . He constructed the perpendicular bisectors of PR¯¯¯¯¯ and QR¯¯¯¯¯ .

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Answer: Last option:
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3 years ago

Harrison mows lawns and rakes leaves for his summer and fall weekend jobs. He gets $10 an hour to mow lawns and $8 an hour to ra

earnstyle [38]

Total money= 10m+8(12)

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3 years ago

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