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3 years ago

Simplify the product using the distributive property. (2h-3)(3h+4)

Mathematics

2 answers:

Charra [1.4K]3 years ago

8 0

Answer:

6h^2-h-12

Step-by-step explanation:

justt bc i said so jk

myrzilka [38]3 years ago

4 0

6h^2-h-12 apply the foil method : (a+b)(c+d)=ac+ad+bc+bd

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Rationalize the denominator of $\displaystyle \frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}$, and write your answer in the form\[

Butoxors [25]

9514 1404 393

Answer:

Step-by-step explanation:

Apparently, you want to simplify ...

$\displaystyle \frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}$

so the denominator is rational. It looks like the form you want is ...

$\dfrac{A\sqrt{2} + B\sqrt{3} + C\sqrt{7} + D\sqrt{E}}{F}$

And you want to know the sum A+B+C+D+E+F.

We can start by multiplying numerator and denominator by a conjugate of the denominator. Then we can multiply numerator and denominator by a conjugate of the resulting denominator.

$\displaystyle =\frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}\cdot\frac{\sqrt{2} + \sqrt{3} - \sqrt{7}}{\sqrt{2} + \sqrt{3} - \sqrt{7}}=\frac{\sqrt{2} + \sqrt{3} - \sqrt{7}}{2\sqrt{6}-2}\\\\=\frac{\sqrt{2} + \sqrt{3} - \sqrt{7}}{2\sqrt{6}-2}\cdot\frac{\sqrt{6}+1}{\sqrt{6}+1}=\frac{(1+\sqrt{6})(\sqrt{2}+\sqrt{3}-\sqrt{7})}{10}\\\\=\frac{\sqrt{2}+\sqrt{3}-\sqrt{7}+2\sqrt{3}+3\sqrt{2}-\sqrt{42}}{10}=\frac{4\sqrt{2}+3\sqrt{3}-\sqrt{7}-\sqrt{42}}{10}$

Comparing this to the desired form we have ...

A = 4, B = 3, C = -1, D = -1, E = 42, F = 10

Then the sum is ...

A +B +C +D +E +F = 4 + 3 -1 -1 +42 +10 = 59 -2 = 57

The sum of interest is 57.

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3 years ago

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kari74 [83]

Answer:

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Step-by-step explanation:

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3 years ago

The volume of this prism Is ___ cubic inches

hoa [83]

Answer:

The answer is 140 cubic in

Step-by-step explanation:

The formula for the volume of a prism is V=Bh, where B is the base area and h is the height. The base of the prism is a rectangle. The length of the rectangle is 9 cm and the width is 7 cm. The area A of a rectangle with length l and width w is A=lw. Hope this helped! :) (ps. I am sorry if it does not help.)

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2 years ago

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What is 791.483 rounded to the nearest whole number? please help me!!

sveticcg [70]

791 since it has no decimal places

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3 years ago

What is the absolute value of 2 and 1 therds

sleet_krkn [62]

Answer: 2 and 1 thirds is the answer

Step-by-step explanation: