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wolverine [178]
3 years ago
11

3 x^2 +30 x +75 factored completely

Mathematics
1 answer:
Fofino [41]3 years ago
4 0

Answer:

3(x + 5)²

Step-by-step explanation:

3x² + 30x + 75

3[x² + 10x + 25]

3[x² + 5x + 5x + 25]

3[x(x + 5) + 5(x + 5)]

3[(x + 5)(x + 5)]

3(x + 5)²

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Simplify? can you please help me understand this? I need some help! thanks so much!
jeyben [28]
Yo just reduve the fraction by dividing it into 2 or 3
and you kepp going
6 0
3 years ago
The initial size of the population is 300. After 1 day the population has grown to 800. Estimate the population after 6 days. (R
Cloud [144]

Solution :

Given initial population = 300

Final population after 1 day = 800

Number of days = 6

∴ $\frac{dP}{dt} =kt^{1/2} $

P(0) = 300    P(1) = 300

We need to find P(8).

$dP = kt^{1/2} dt$

$ \int 1 dP = \int kt^{1/2} dt$

$P(t) = k \left(\frac{t^{3/2}}{3/2}\right)+c$

$P(t)= \frac{2k}{3}t^{3/2} + c$

When P(0) = 300

$300 = \frac{2k}{3} (0)^{3/2} + c$

∴ c = 300

∴ $P(t)= \frac{2k}{3}t^{3/2} + 300$

When P(1) = 800

$800 = \frac{2k}{3} (1)^{3/2} + 300$

$500 = \frac{2k}{3}$

∴ k = 750

$P(t)= 500t^{3/2} + 300$

So, P(8) is

$P(t)= 500(8)^{3/2} + 300$

        = 11,614

So the population becomes 11,614 after 8 days.

8 0
3 years ago
Find the area of the figure
Eduardwww [97]

Answer:

132cm²

Step-by-step explanation:

You can find the area of the entire shape by calculating the area of seperate smaller shapes.

You can split them up into 2 rectangles, one with a base of 7cm and height of 4cm, and another one with a base of 7cm and height of 8cm. You also have 2 triangles, with a base of 19cm - 7cm / 2 = 6cm since it is the entire bottom line subtracted by the top; they will have a height of 8cm each.

To calculate the rectangles areas, simply do length x width, which are:

4cm x 7cm = 28cm²

8cm x 7cm = 56cm²

Next, since the triangles are similar in measurements, instead of doing the normal calculation to find the area of a triangle, you can do base times height again, which is:

6cm x 8cm = 48cm²

Add all the answers together to get the final area, which is 132cm².

8 0
3 years ago
The value of a mountain bike Y(in dollars) can be approximated by the model Y=200(1-.0025) to the t power, where T is the number
tino4ka555 [31]

Answer:

It will take 554 years

Step-by-step explanation:

Here, we want to estimate the time when t will be $50

We can rewrite the exponential equation as;

y = 200(1-0.0025)^t

In this case, y = $50 and we want to calculate t

so, we simply proceed to substitute the value 50 for y

we have this as ;

50 = 200(1-0.0025)^t

50/200 = (1-0.0025)^t

1/4 = 0.9975^t

0.25 = 0.9975^t

Take the natural logarithm of both sides

ln 0.25 = ln 0.9975^t

ln 0.25 = t ln 0.9975

t = ln 0.25 / ln 0.9975

t = 553.8 = 554 years

The bike will be $50 in 554 years

5 0
3 years ago
John bought a car for $8,000. After one year the car depreciates in value
Bad White [126]

Your answer will be 7,040.

<em>HOW TO SOLVE: </em>We start out with the car's value of 8,000. You see that the value of the vehicle is going to <em>depreciate, </em>or lower. It will depreciate by 12%, so we need to find 12% of 8,000.

This will you get you 960. All we need to do now is subtract 960 from 8,000, so you will be left with 7040.

6 0
3 years ago
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