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3 years ago

Simplify: (x+4)*(2x+5

Mathematics

1 answer:

s344n2d4d5 [400]3 years ago

7 0

Answer:

2x^2+13x+20 is the simplified answer

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What is the combined length of the 2 1/2 inch and 1 1/2 inch pieces of wire

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4 years ago

The formula used to convert Fahrenheit (°F ) to Celsius (°C

xeze [42]

Answer:

25°C

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3 years ago

Please help! <br>what is the answer to this question?<br>

tiny-mole [99]

Answer:

The clue to find 'x' is-

As both, the lines here are intersecting at a point to form VERTICALLY OPPOSITE ANGLES.

According to this theory (2x+20)=60

So, (2x+20)=60

= 2x=60-20

= 2x= 40

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3 years ago

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I really stuck on trying to prove this

Alisiya [41]

$\displaystyle\sum_{r=1}^nr(r+1)\cdots(r+p-1)$

When $n=1$ ,

$\displaystyle\sum_{r=1}^1r(r+1)\cdots(r+p-1)=1(1+1)(1+2)\cdots(1+p-2)(1+p-1)=p!$

Meanwhile, you have on the right

$\dfrac{(1)(1+1)(1+2)\cdots(1+p-2)(1+p-1)(1+p)}{p+1}=(1)(1+1)(1+2)\cdots(p-1)(p)=p!$

so the equality holds for $n=1$ .

Assume it holds for $n=k$ , i.e. that

$\displaystyle\sum_{r=1}^kr(r+1)\cdots(r+p-1)=\frac{k(k+1)(k+2)\cdots(k+p-1)(k+p)}{p+1}$

Now for $n=k+1$ , you have

$\displaystyle\sum_{r=1}^{k+1}r(r+1)\cdots(r+p-1)=\sum_{r=1}^kr(r+1)\cdots(r+p-1)+(k+1)(k+2)\cdots(k+1+p-1)$
$=\displaystyle\frac{k(k+1)(k+2)\cdots(k+p-1)(k+p)}{p+1}+(k+1)(k+2)\cdots(k+1+p-2)(k+1+p-1)$
$=\displaystyle\frac{k(k+1)(k+2)\cdots(k+p-1)(k+p)}{p+1}+(k+1)(k+2)\cdots(k+p-1)(k+p)$
$=\left(\dfrac k{p+1}+1\right)(k+1)(k+2)\cdots(k+p-1)(k+p)$
$=\dfrac{k+p+1}{p+1}(k+1)(k+2)\cdots(k+p-1)(k+p)$
$=\dfrac{(k+1)(k+2)\cdots(k+p-1)(k+p)(k+p+1)}{p+1}$

as required.

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3 years ago

A room contains 5 cats and 2 dogs. If the ratio is 5 to 2 the rate can be expressed as 5 cats __ 2 dogs

bezimeni [28]

5 cats : 2 dogs .......you usually use a

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3 years ago

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