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Andreas93 [3]
2 years ago
8

On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (negative 2, 3) an

d (0, negative 1). Everything to the left of the line is shaded. The second dashed line has a negative slope and goes through (0, 2) and (1, 0). Everything to the right of the line is shaded.
Which inequality pairs with y≤−2x−1 to complete the system of linear inequalities represented by the graph?

y<−2x+2
y>−2x+2
y<2x−2
y>2x−2
Mathematics
1 answer:
alina1380 [7]2 years ago
5 0

Answer:

y > -2x + 2

Step-by-step explanation:

The dashed line tells us the answer doesNOT have the "or=to" under the inequality symbol. Then the y-intercept is positive 2. So it must be

y > -2x + 2

see image

Look at the y-intercept and think of up/down instead of left/right on the shading and then you can see whether its < or >

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A fluid ounce is a customary unit for measuring liquid capacity.
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Suppose an unknown radioactive substance produces 8000 counts per minute on a Geiger counter at a certain time, and only 500 cou
mariarad [96]

Answer:

The half-life of the radioactive substance is of 3.25 days.

Step-by-step explanation:

The amount of radioactive substance is proportional to the number of counts per minute:

This means that the amount is given by the following differential equation:

\frac{dQ}{dt} = -kQ

In which k is the decay rate.

The solution is:

Q(t) = Q(0)e^{-kt}

In which Q(0) is the initial amount:

8000 counts per minute on a Geiger counter at a certain time

This means that Q(0) = 8000

500 counts per minute 13 days later.

This means that Q(13) = 500. We use this to find k.

Q(t) = Q(0)e^{-kt}

500 = 8000e^{-13k}

e^{-13k} = \frac{500}{8000}

\ln{e^{-13k}} = \ln{\frac{500}{8000}}

-13k = \ln{\frac{500}{8000}}

k = -\frac{\ln{\frac{500}{8000}}}{13}

k = 0.2133

So

Q(t) = Q(0)e^{-0.2133t}

Determine the half-life of the radioactive substance.

This is t for which Q(t) = 0.5Q(0). So

Q(t) = Q(0)e^{-0.2133t}

0.5Q(0) = Q(0)e^{-0.2133t}

e^{-0.2133t} = 0.5

\ln{e^{-0.2133t}} = \ln{0.5}

-0.2133t = \ln{0.5}

t = -\frac{\ln{0.5}}{0.2133}

t = 3.25

The half-life of the radioactive substance is of 3.25 days.

7 0
3 years ago
Alaska's Wrangell St Elias National Park is the largest national Park in the United States with an area of 13,005 squar miles.Th
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The correct algebraic expression will be the area of Alaska's Wrangell St Elias minus Gates park so the expression is:

13005-g

5 0
2 years ago
If f(x)=x^2+2x-3 and g(x)=x^2-9, find (f/g)(4) and (f+g)(4)
Likurg_2 [28]

Answer:

<u>Part 1:</u> Find (f/g)(4) = 3

<u>Part 2:</u> Find (f+g)(4) = 28

Step-by-step explanation:

<u>Part 1:</u> Find (f/g)(4):

(f/g)(4) means <em>divide f function by g function and simplify it. Then plug in 4 into x of that simplified function.</em>

Let's do this:

\frac{x^2+2x-3}{x^2-9}\\=\frac{(x+3)(x-1)}{(x-3)(x+3)}\\=\frac{x-1}{x-3}

Plugging in 4 into x gives us:

\frac{x-1}{x-3}\\=\frac{4-1}{4-3}\\=\frac{3}{1}\\=3

The answer is 3

<u></u>

<u>Part 2:</u> Find (f+g)(4):

(f+g)(4) <em>means add f function and g function and simplify it. Then plug in 4 into x of that simplified function.</em>

Let's do this:

(x^2+2x-3)+(x^2-9)\\=2x^2+2x-12

Plugging in 4 into x gives us:

2x^2+2x-12\\=2(4)^2+2(4)-12\\=28

The answer is 28

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