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2 years ago

Given that NQ ll PR, find NP

Mathematics

1 answer:

kvasek [131]2 years ago

4 0

The parallel lines cuts the sides in equal proportion to give NP = 0.8

<h3>How can the length of NP be found?</h3>

The given diagram consists of a line parallel to one of the sides of the triangle.

According to the triangle proportionality theorem, the parallel line, NQ, proportionally divides the sides MR and MP, such that:

NQ || PR

By triangle proportionality theorem;

$\mathbf{ \frac{ MN }{ NP} } = \frac{ MQ }{ QR }$

Which gives;

$\mathbf{ \frac{ 5 }{ NP} } = \frac{ 8}{ 2 }$

2×5 = 8 × NP

<u>NP = 8 ÷ 10 = 0.8</u>

Learn more about the triangle proportionality theorem here:

brainly.com/question/8160153

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Dan and David are marking exam papers. Each set takes Dan 35 minutes and David 1 hour. Express the times Dan and David take as a

blagie [28]

Answer:

Step-by-step explanation:

1 hour =60 minutes

Ratio =35

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Answer=7

8 0

3 years ago

Which binomial is a factor of 8x^2y^3-18y

Musya8 [376]

Answer:

Please check the explanation.

Step-by-step explanation:

Given the expression

$8x^2y^3-18y$

Apply exponent rule: $a^{b+c}=a^ba^c$

$8x^2y^3-18y=8yy^2-18y$ ∵ $x^2y^3=yy^2$

$=4\cdot \:2yy^2+9\cdot \:2y$

Factor out common term 2y

$=2y\left(4x^2y^2-9\right)$

We know that the Binomial is an expression that consists of two terms. Thus,

(4x²y²- 9) represents the binomial factor of $8x^2y^3-18y$

We can further simplify by Factoring 4x²y² - 9: (2xy + 3) (2xy - 3)

$=2y\left(2xy+3\right)\left(2xy-3\right)$

Here:

(2xy + 3) and (2xy -3) are the binomial factors of $8x^2y^3-18y$ as each of them consists of two terms.

6 0

3 years ago

Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. x2+3/2x

denis23 [38]

Answer:

The added term needed for that expression to be a square is 9/16.

Step-by-step explanation:

We're provided with two terms, and asked to add an additional term to make this a perfect square. For this to work, the term needs to be a scalar value that is the square of half the coefficient of the second term.

That coefficient is 3/2, so half of that is 3/4, and its square is 9/16.

If we tack that on the end then, we get:

$x^2 + \frac{3x}{2} + \frac{9}{16}\\=(x + \frac{3}{4})^2$

To confirm the answer, let's expand it and see if we get the original expression:

$(x + \frac{3}{4})^2\\= (x + \frac{3}{4})(x + \frac{3}{4})\\= x^1 + \frac{3x}{4} + \frac{3x}{4} + \frac{9}{16}\\= x^2 + \frac{6x}{4} + \frac{9}{16}\\=x^2 + \frac{3x}{2} + \frac{9}{16}$