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san4es73 [151]
2 years ago
12

[Maximum mark: 6]

Mathematics
1 answer:
DENIUS [597]2 years ago
3 0

The value of p is 0.6

<h3>What is a binomial expression?</h3>

A binomial expression is an algebraic expression that contains only two terms.

Binomial expansions are used to expand exponents of two terms

The expression is given as:

px^2(5 + px)^8

When the expression in bracket is expanded, one of its term is:

px^2(5 + px)^8 = px^2 (..........70 \times p^4 \times x^4...........)

So, we have:

px^2(5 + px)^8 = px^2 (..........70 \times 5^4 \times (px)^4...........)

px^2(5 + px)^8 = px^2 (..........70 \times 625 \times (px)^4...........)

px^2(5 + px)^8 = px^2 (..........43750 (px)^4...........)

px^2(5 + px)^8 = px^2 (..........43750 p^4x^4...........)

Expand the bracket, to get the coefficient of x^6

px^2(5 + px)^8 = px^2 (..........43750 p^5x^6...........)

The coefficient equals 3402.

So, we have:

43750p^5 = 3402

Divide both sides by 43750

p^5 = 0.07776

Take the 5th root of both sides

p = 0.6

Hence, the value of p is 0.6

Read more about binomial expansions at:

brainly.com/question/13602562

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In this problem, we need to use the concept of proportions. Proportion says that two ratios (or fractions) are equal. So, we have two numbers, namely:

x=8 \ and \ y=20

So, the given proportion is:

\frac{x}{y}=\frac{8}{20} \\ \\ \therefore \frac{x}{y}=\frac{2}{5}

That is, x-out-of-y is equal to 2-out-of-5

On the other hand, we know that x=42, so by using the previous proportion we have:

\frac{42}{y}=\frac{2}{5} \\ \\ Isolating \ y: \\ \\ y=\frac{42 \times 5}{2} \\ \\ y=\boxed{105}

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−2(x + 3) = −2(x + 1) − 4.
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Every x is a solution.

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<em>plz </em><em>mark</em><em> my</em><em> answer</em><em> as</em><em> brainlist</em><em> plzzzz</em><em>.</em>

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Answer:

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Step-by-step explanation:

The standard form:

Ax + By = C

So from the given form, arrange it to the standard form.

First, simplify the form by distribution.

y + 6 = -2/3(x - 11)

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Next, you make the fractions into whole by multiplying both sides by 3(this would eliminate all fractions).

(3)y + 3(6) = 3(-2/3x) + 3(22/3)

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Now, arrange the "Ax" and the "C's".

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Cheers!

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