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3 years ago

2(5v+3) - 4(7v+1) = -88 Show all work

Mathematics

1 answer:

Novosadov [1.4K]3 years ago

5 0

Answer:

Step-by-step explanation:

● 2(5v+3) - 4(7v+1) = -88

● 10v + 6 - 28v - 4 = -88

● (6-4) + (10v-28v) = -88

● 2 + -18 v = -88

● -18v = -90

● v = 90/18

● v = 5

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Rowan reads at a constant rate of 1.5 pages per minute and has already

saul85 [17]

Using linear functions, it is found that Rowan and Kennedy will have read the same number of pages in 10 minutes.

What is a linear function?

A linear function is modeled by:

$y = ax + b$

In which:

a is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0.

For Rowan, we have that:

He has already read 20 pages, hence the y-intercept is $b = 20$ .

He reads 1.5 pages per minute, hence the slope is $a = 1.5$

Then:

$y_R = 1.5x + 20$

For Kennedy, we have that:

He has already read 25 pages, hence the y-intercept is $b = 25$ .

He reads 1 page per minute, hence the slope is $a = 1$

Then:

$y_K = x + 25$

They will have read the same number of pages after x minutes, for which:

$y_R = y_K$

Then:

$1.5x + 20 = x + 25$

$0.5x = 5$

$x = \frac{5}{0.5}$

$x = 10$

To learn more about linear function, you can take a look at brainly.com/question/25823744

3 0

2 years ago

A given field mouse population satisfies the differential equation dp dt = 0.5p − 410 where p is the number of mice and t is the

ohaa [14]

Answer:

a) $t = 2 *ln(\frac{82}{5}) =5.595$

b) $t = 2 *ln(-\frac{820}{p_0 -820})$

c) $p_0 = 820-\frac{820}{e^6}$

Step-by-step explanation:

For this case we have the following differential equation:

$\frac{dp}{dt}=\frac{1}{2} (p-820)$

And if we rewrite the expression we got:

$\frac{dp}{p-820}= \frac{1}{2} dt$

If we integrate both sides we have:

$ln|P-820|= \frac{1}{2}t +c$

Using exponential on both sides we got:

$P= 820 + P_o e^{1/2t}$

Part a

For this case we know that p(0) = 770 so we have this:

$770 = 820 + P_o e^0$

$P_o = -50$

So then our model would be given by:

$P(t) = -50e^{1/2t} +820$

And if we want to find at which time the population would be extinct we have:

$0=-50 e^{1/2 t} +820$

$\frac{820}{50} = e^{1/2 t}$

Using natural log on both sides we got:

$ln(\frac{82}{5}) = \frac{1}{2}t$

And solving for t we got:

$t = 2 *ln(\frac{82}{5}) =5.595$

Part b

For this case we know that p(0) = p0 so we have this:

$p_0 = 820 + P_o e^0$

$P_o = p_0 -820$

So then our model would be given by:

$P(t) = (p_o -820)e^{1/2t} +820$

And if we want to find at which time the population would be extinct we have:

$0=(p_o -820)e^{1/2 t} +820$

$-\frac{820}{p_0 -820} = e^{1/2 t}$

Using natural log on both sides we got:

$ln(-\frac{820}{p_0 -820}) = \frac{1}{2}t$

And solving for t we got:

$t = 2 *ln(-\frac{820}{p_0 -820})$

Part c

For this case we want to find the initial population if we know that the population become extinct in 1 year = 12 months. Using the equation founded on part b we got:

$12 = 2 *ln(\frac{820}{820-p_0})$

$6 = ln (\frac{820}{820-p_0})$

Using exponentials we got:

$e^6 = \frac{820}{820-p_0}$

$(820-p_0) e^6 = 820$

$820-p_0 = \frac{820}{e^6}$

$p_0 = 820-\frac{820}{e^6}$

8 0

3 years ago

If the standard deviation of a data set was originally 6, and if each value in the

MakcuM [25]

Answer:

Step-by-step explanation:

answer is B

hope it helps you

please mark as brainliest

5 0

2 years ago

Can someone answer this for me? ty

Fiesta28 [93]

Answer:

The intercepts are the locations where the line touches the x-axis and y-axis.

This question is asking for the coordinates for each of those locations, which would be:

(3, 0) for x-intercept location

(0, -10) for y-intercept location

The easy way to remember how to find coordinates is that the x is 'running', and the y is 'jumping', so the x coordinate comes before the y coordinate when finding sets like the ones above.

4 0

3 years ago

Helpppppp asappppp pls <br><br> Show your work <br> I’ll give brainliest!!!!!!

sineoko [7]

Answer: 3360 ft squared

Step-by-step explanation:

Short side : 30 x 14 = 420

Long side 30 x 3 x 14 = 1260

420 + 420 + 1260 + 1260 = 3360

pls give brainliest

have a nice day

3 0

2 years ago