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ra1l [238]
3 years ago
15

If 9x²+Px+25 is a perfect square, then find the value of P​

Mathematics
2 answers:
kvv77 [185]3 years ago
8 0
30 is the value of P
Steps:
A perfect square follows the pattern a^2+2ab+b^2\\\boxed{a=3,b=5}\\\boxed{2ab=30}
lorasvet [3.4K]3 years ago
6 0

Answer:

P = 30

Step-by-step explanation:

A perfect square of the form

(ax + b)² = a²x² + 2abx + b²

9x² = (3x)² ⇒ a = 3 and 25 = 5² ⇒ b = 5

2abx = 2 × 3 × 5x = 30x

9x² + 30x + 25 = (3x + 5)² ← a perfect square

P = 2ab = 30

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madreJ [45]

You multiply 3 times 3 which gives you 9. Then you multiply 9 times 5, which gives you 45.

3 0
3 years ago
Read 2 more answers
The population P of a small town, measured in hundreds, is modeled by the inverse of the function P−1(t) = 10ln(50t − 1000), whe
AleksandrR [38]

Using the inverse function, it is found that the equation is:

P(t) = \frac{e^{0.1t}}{50} + 20

It's initial value is 20.

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

We want to find the inverse of:

y = P^{-1}(t) = 10\ln{50t - 1000}

To do this, we <u>exchange y and t, and isolate y.</u>

Then:

10\ln{50y - 1000} = t

\ln{50y - 1000} = \frac{t}{10}

e^{\ln{50y - 1000}} = e^{0.1t}

50y - 1000 = e^{0.1t}

50y = e^{0.1t} + 1000

y = \frac{e^{0.1t} + 1000}{50}

y = \frac{e^{0.1t}}{50} + \frac{1000}{50}

P(t) = \frac{e^{0.1t}}{50} + 20

It's initial value is:

P(0) = \frac{e^{0.1(0)}}{50} + 20 = 0.02 + 20 = 20.02

Rounding, 20.

A similar problem is given at brainly.com/question/23950969

5 0
3 years ago
At a hockey game a vendor sold a combine total of 248 sodas and hot dogs. The number of sodas sold was three times the number of
8_murik_8 [283]

Answer:

total =248

sodas=3x

hot dogs=x

3x+x=248

4x =248

x=62

hot dogs =62

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5 0
3 years ago
I need help with this question??
salantis [7]
I believe it's four times as great : )
4 0
3 years ago
The area of an 11-cm-wide rectangle is 242cm2. What is it's length
VladimirAG [237]
22 centimeters

242 ( area ) divided by 11( width) =22 ( length)
3 0
3 years ago
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