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vagabundo [1.1K]
3 years ago
7

Rate of Change between August and October

Mathematics
2 answers:
nikdorinn [45]3 years ago
5 0

Answer:

15 students per month

Step-by-step explanation:

The rate of change is calculated as

\frac{f(b)-f(a)}{b-a}

f(b) = 95 ← number of students in October

f(a) = 65 ← number of students in August

b - a = 2 ← difference in months

Thus

rate of change = \frac{95-65}{2} = \frac{30}{2} = 15

MakcuM [25]3 years ago
5 0

The rate of change is the ratio between the change in the y and x coordinates. The students ranged from 65 to 95 in two months, so the rate is

\dfrac{95-65}{2}=\dfrac{30}{2}=15

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Suppose a triangle has 3 sides, 3, 4, 6 which of the following must be true
Inessa [10]

Answer:

  B. the triangle in question is not a right triangle

Step-by-step explanation:

A 3-4-5 triangle is a right triangle, so this one, with its longer longest side, is an obtuse triangle. It is not a right triangle.

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3, 4, 5 is one of the first Pythagorean triples that you learn:

  3² + 4² = 5²

These are the side lengths of the smallest right triangle with integer sides. It is worthwhile to remember. This triple is used not only in many math problems (such as this one), but also in real life when it is useful to lay out a right angle.

6 0
3 years ago
5a+5b=25 and -5a+5b=35
Alex_Xolod [135]

add the two equations together

5a+5b=25

-5a+5b=35

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

 0  + 10b =60

divide by 10

b=6

5a + 5b = 25

5a +5(6) = 25

5a +30 =25

subtract 30 from each side

5a =-5

divide by 5

a = -1

Answer (-1,6)

or a=-1 b=6

3 0
3 years ago
Find the slope of the line passing through the points (-9, -6) and (-4, 5)
Masja [62]

Answer:

11/5 slope

Step-by-step explanation:

5-(-6) -4-(-9)

11/ 5

4 0
3 years ago
Read 2 more answers
Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had decreased by 3%. If the rate of deca
Hitman42 [59]

Answer:

The half-life of the radioactive substance is 135.9 hours.

Step-by-step explanation:

The rate of decay is proportional to the amount of the substance present at time t

This means that the amount of the substance can be modeled by the following differential equation:

\frac{dQ}{dt} = -rt

Which has the following solution:

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

In which Q(t) is the amount after t hours, Q(0) is the initial amount and r is the decay rate.

After 6 hours the mass had decreased by 3%.

This means that Q(6) = (1-0.03)Q(0) = 0.97Q(0). We use this to find r.

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

0.97Q(0) = Q(0)e^{-6r}

e^{-6r} = 0.97

\ln{e^{-6r}} = \ln{0.97}

-6r = \ln{0.97}

r = -\frac{\ln{0.97}}{6}

r = 0.0051

So

Q(t) = Q(0)e^{-0.0051t}

Determine the half-life of the radioactive substance.

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

Q(t) = Q(0)e^{-0.0051t}

0.5Q(0) = Q(0)e^{-0.0051t}

e^{-0.0051t} = 0.5

\ln{e^{-0.0051t}} = \ln{0.5}

-0.0051t = \ln{0.5}

t = -\frac{\ln{0.5}}{0.0051}

t = 135.9

The half-life of the radioactive substance is 135.9 hours.

6 0
2 years ago
What is the equation of this trend line?<br> RE<br> Enter your answers b y filling in the boxes.
Deffense [45]

Answer:

K=-2J+28

Step-by-step explanation:

step 1

Find the slope of the line

The formula to calculate the slope between two points is equal to

m=\frac{k2-k1}{j2-j1}

we have the points

(2,24) and (6,16)

substitute in the formula

m=\frac{16-24}{6-2}

m=\frac{-8}{4}

m-2

step 2

Find the equation of the line in slope intercept form

K=mJ+b

we have

m=-2

b=28 ----> the k-intercept is the point (0,28)  see the graph

substitute

K=-2J+28

7 0
3 years ago
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