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1 year ago

What is the answer for -6d < 24

Mathematics

1 answer:

hjlf1 year ago

5 0

9514 1404 393

Answer:

d > -4

Step-by-step explanation:

Divide both sides of the inequality by -6. That requires the sense of the comparison to be reversed.

(-6d)/(-6) > (24)/(-6)

d > -4

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You have 42,784 grams of a radioactive kind of curium. If its half-life is 18 years, how much will be left after 72 years?

s344n2d4d5 [400]

Answer:

2,674.14 g

Step-by-step explanation:

Recall that the formula for radioactive decay is

N = N₀ e^(-λt)

where,

N is the amount left at time t

N₀ is the initial amount when t=0, (given as 42,784 g)

λ = coefficient of radioactive decay

= 0.693 ÷ Half Life

= 0.693 ÷ 18

= 0.0385

t = time elapsed (given as 72 years)

e = exponential constant ( approx 2.7183)

If we substitute these into our equation:

N = N₀ e^(-λt)

= (42,787) (2.7183)^[(-0.0385)(72)]

= (42,787) (2.7183)^(-2.7726)

= (42,787) (0.0625)

= 2,674.14 g

6 0

2 years ago

Use substitution to solve the following system of linear equations and fill in the following blanks:

marissa [1.9K]

Answer:

$x=-4$

$y=3$

$z=-5$

Step-by-step explanation:

Given:

$x+y+z=-6$

$x-6y-7z=-29$

$-7y-5z=4$

Solve for $x$ in the 1st equation:

$x+y+z=-6$

$x+y=-z-6$

$x=-y-z-6$

Substitute the value of $x$ into the 2nd equation and solve for $z$ :

$x-6y-7z=-29$

$(-y-z-6)-6y-7=-29$

$-7y-z-13=-29$

$-7y-z=-16$

$-z=-16+7y$

$z=16-7y$

Substitute the value of $z$ into the 3rd equation and solve for $y$ :

$-7y-5z=4$

$-7y-5(16-7y)=4$

$-7y-80+35y=4$

$28y-80=4$

$28y=84$

$y=3$

Plug $y=3$ into the solved expression for $z$ and evaluate to solve for $z$ :

$z=16-7(3)$

$z=16-21$

$z=-5$

Plug $z=-5$ into the solved expression for $x$ and evaluate to solve for $x$ :

$x=-(3)-(-5)-6$

$x=-3+5-6$

$x=2-6$

$x=-4$

Therefore:

$x=-4$

$y=3$

$z=-5$

6 0

2 years ago

avery's water bottle holds 300 milliliters. dashawn'scontainer holds 3/4 as much water. how many milliliters of water does dasha

anastassius [24]

You could make this really simple by dividing 300 by 4 to see how much 1/4 of that is and then subtracting 1/4 from 300 to see how much dashawn's water bottle holds.

300/4 =75 so 1/4 is equal to 75 mL

300-75=225mL

Dashawn's water bottle holds 225mL

6 0

2 years ago

The 1997 value of an object was $9500. In 2012, it was worth $5000. The annual percent of decay has been constant. What is the a

vova2212 [387]

Hello,

Here is your answer:

The proper answer to this question is option D "4.19%".

Your answer is D.

If you need anymore help feel free to ask me!

Hope this helps!

5 0

2 years ago

Read 2 more answers

3. Which value of x makes the equation 3.5(2x - 4) = 21 true

Grace [21]

Answer:

Step-by-step explanation:

7 0

2 years ago