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3 years ago

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 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

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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.

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

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

$e^{-6r} = 0.97$

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

$-6r = \ln{0.97}$

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

$r = 0.0051$

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

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

$m=-2$

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substitute

$K=-2J+28$

7 0

3 years ago