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4 years ago

Which ordered pairs are solutions to the inequality 4x+y>−6?

Mathematics

1 answer:

Naddika [18.5K]4 years ago

8 0

Hey!

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Substitute with (−1, −1)

4x + y > −6

4(-1) + (-1) > -6

-5 + (-1) > -6

-6 > -6

TRUE

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Substitute with (0, -9)

4x + y > −6

4(0) + (-9) > -6

0 + (-9) > -6

-9 > -6

FALSE

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Substitute with (2, 0)

4x + y > −6

4(2) + 0 > -6

6 > -6

TRUE

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Substitute with (4, -20)

4x + y > −6

4(4) + (-20) > -6

16 + (-20) > -6

-4 > -6

TRUE

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Substitute with (-3, 6)

4x + y > −6

4(-3) + 6 > -6

-12 + 6 > -6

-6 > -6

FALSE

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Hence, the answers are (2, 0), (4, -20), and (-1, -1)!

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Hope This Helped! Good Luck!

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Trey had a cylindrical can with a radius of 4 inches and a height of 12 inches that was completely full of beet juice. He poured

Slav-nsk [51]

Answer:

$8\ glasses\ of\ juice$

Step-by-step explanation:

step 1

Find the volume of the cylindrical can

The volume of the cylinder is equal to

$V=\pi r^{2}h$

we have

$r=4\ in$

$h=12\ in$

substitute the values

$V=\pi (4)^{2}(12)=192\pi\ in^{3}$

step 2

Find the volume of the cylindrical glasses

The volume of the cylinder is equal to

$V=\pi r^{2}h$

we have

$r=2\ in$

$h=8\ in$

substitute the values

$V=\pi (2)^{2}(8)=32\pi\ in^{3}$

<em>Find the volume of 3/4 of the glass</em>

$32\pi (\frac{3}{4})=24\pi\ in^{3}$

step 3

Divide the total volume of cylindrical can by the 3/4 volume of the glass

$192\pi\ in^{3}/24\pi\ in^{3}=8\ glasses\ of\ juice$

5 0

3 years ago

Alice has a bag of marbles consisting of 9 green marbles, 7 red marbles, 3 white marbles, and 6 yellow marbles. If she picks 2 o

olga_2 [115]

1. When solving similar problems, a tree diagram is a very useful method. Check the picture below for the solution of A:

the first pick can be either of the colors g, r, w or y, with a chance of 9/25, 7/25, 3/25 and 6/25 respectively.

After the first marble is yellow, now the second can be either of g, r, w, or y with chances 9/24, 7/24, 3/24, and 5/24 respectively.

Notice that the total number for the second choice is 25-1=24, since one is gone. In our case, one yellow, (this is why we now have 5/24)

So the P( that 1st is yellow, second is white) = (6/25)*(3/24)=3/100

B. P(both red)= (7/25)*(7/24)=49/600

C. P(1st red)=7/25
P(green, after replacement)=9/25
P(1.red,2.green)=(7/25)*(9/25)=63/625