Answer:
b is correct
Step-by-step explanation:
Answer:
<h3>
![\frac{\sqrt{24}- \sqrt{54} }{\sqrt{6}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B24%7D-%20%5Csqrt%7B54%7D%20%7D%7B%5Csqrt%7B6%7D%7D)
= -1 </h3><h3>
![\sqrt{\frac{9}{20}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B9%7D%7B20%7D)
*
![\frac{10\sqrt{2} }{3\sqrt{5} }](https://tex.z-dn.net/?f=%5Cfrac%7B10%5Csqrt%7B2%7D%20%7D%7B3%5Csqrt%7B5%7D%20%7D)
= 1.4142</h3><h3>
![\frac{10\pi\sqrt{2}-8\pi\sqrt{2}}{2\sqrt{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B10%5Cpi%5Csqrt%7B2%7D-8%5Cpi%5Csqrt%7B2%7D%7D%7B2%5Csqrt%7B2%7D%7D)
= π =3.14159</h3><h3>
![\pi\sqrt{\frac{5}{3}}\cdot\pi\sqrt{\frac{3}{5}}](https://tex.z-dn.net/?f=%5Cpi%5Csqrt%7B%5Cfrac%7B5%7D%7B3%7D%7D%5Ccdot%5Cpi%5Csqrt%7B%5Cfrac%7B3%7D%7B5%7D%7D)
= π² = 9.8696</h3>
Explanation:
1.) Rewrite √24 =
Rewrite √54 =![\sqrt{9*6}= 3\sqrt{6}](https://tex.z-dn.net/?f=%5Csqrt%7B9%2A6%7D%3D%203%5Csqrt%7B6%7D)
Divide both terms by the denominator; √6 cancels. 2-3 = -1
2.) Rewrite as
×
The 3's cancel. 10/2 = 5√2 in the numerator.
√5 × √5 = 5 in the denominator. The 5's cancel.
That leaves √2 ≈1.4142
3.) Divide the terms in the numerator by the term in the denominator.
√2's cancel. 10π/2 = 5π 8π/2 = 4π
Subtract and we are left with π = 3.14159
4.)
The square roots are reciprocals. They multiply to 1
We are left with π × π = π² ≈ 9.8696
<h3>
</h3>
Answer:
12. Option A is correct
13. Option A is correct
14. Option C is correct
15. Option D is correct
16. Option A is correct
Step-by-step explanation:
12) Lowest Common Denominator of
![\frac{p+3}{p^2+7p+10} \,\, and \,\, \frac{p+5}{p^2+5p+6}](https://tex.z-dn.net/?f=%5Cfrac%7Bp%2B3%7D%7Bp%5E2%2B7p%2B10%7D%20%5C%2C%5C%2C%20and%20%5C%2C%5C%2C%20%5Cfrac%7Bp%2B5%7D%7Bp%5E2%2B5p%2B6%7D)
We should find the factors of denominators and then find the LCM of the denominators.Finding LCD is same as finding LCM.
Factors of p^2+7p+10 = p^2 +2p +5p+10 = p(p+2)+5(p+2) = (p+5)(p+2)
Factors of p^2+5p+6 = p^2+2p+3p+6 = p(p+2)+3(p+2) = (p+3) (p+2)
Now, rewriting the above equation with factors and finding the LCM
![\frac{p+3}{(p+5)(p+2)} \,\, and \,\, \frac{p+5}{(p+3)(p+2)}\\](https://tex.z-dn.net/?f=%5Cfrac%7Bp%2B3%7D%7B%28p%2B5%29%28p%2B2%29%7D%20%5C%2C%5C%2C%20and%20%5C%2C%5C%2C%20%5Cfrac%7Bp%2B5%7D%7B%28p%2B3%29%28p%2B2%29%7D%5C%5C)
LCM of (p+5)(p+2) and (p+3)(p+2) = (p+5)(p+3)(p+2)
The LCD is (p+5)(p+3)(p+2).
So, Option A is correct.
13. Divide
![\frac{40x}{64y} \,\,by\,\, \frac{5x}{8y}](https://tex.z-dn.net/?f=%5Cfrac%7B40x%7D%7B64y%7D%20%5C%2C%5C%2Cby%5C%2C%5C%2C%20%5Cfrac%7B5x%7D%7B8y%7D)
by stands for division. The equation can be written as:
![\frac{40x}{64y}\div\frac{5x}{8y}](https://tex.z-dn.net/?f=%5Cfrac%7B40x%7D%7B64y%7D%5Cdiv%5Cfrac%7B5x%7D%7B8y%7D)
Division sign changed into multiplication, we take reciprocal of second term i.e,
![\frac{40x}{64y}*\frac{8y}{5x}\\\\Solving\\\frac{40x*8y}{64y*5x}\\\\\frac{320xy}{320xy} \\\\1](https://tex.z-dn.net/?f=%5Cfrac%7B40x%7D%7B64y%7D%2A%5Cfrac%7B8y%7D%7B5x%7D%5C%5C%5C%5CSolving%5C%5C%5Cfrac%7B40x%2A8y%7D%7B64y%2A5x%7D%5C%5C%5C%5C%5Cfrac%7B320xy%7D%7B320xy%7D%20%5C%5C%5C%5C1)
So, Option A is correct.
14. Simplify:
![\frac{x+2}{x^2-6x-16} \div \frac{1}{9x} \\](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B2%7D%7Bx%5E2-6x-16%7D%20%5Cdiv%20%5Cfrac%7B1%7D%7B9x%7D%20%5C%5C)
Factors of x^2-6x-16= x^2 -8x +2x -16 = x(x-8)+2(x-8) = (x-8)(x+2)
Putting factors in the above equation and changing division sign with multiplication we get,
![\frac{x+2}{(x-8)(x+2)} * \frac{9x}{1}\\\frac{9x}{x-8}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B2%7D%7B%28x-8%29%28x%2B2%29%7D%20%2A%20%5Cfrac%7B9x%7D%7B1%7D%5C%5C%5Cfrac%7B9x%7D%7Bx-8%7D)
So, Option C is correct.
15. Simplify
![\frac{4}{\frac{1}{4}-\frac{5}{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B%5Cfrac%7B1%7D%7B4%7D-%5Cfrac%7B5%7D%7B2%7D%7D)
Solving denominator,
Taking LCM of 4 and 2 and subtracting we get
![\frac{4}{\frac{1-(5*2)}{4}}\\\frac{4}{\frac{1-10}{4}}\\\frac{4}{\frac{-9}{4}}\\\frac{4*4}{-9}\\\frac{16}{-9} \,\,or\,\,\\\frac{-16}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B%5Cfrac%7B1-%285%2A2%29%7D%7B4%7D%7D%5C%5C%5Cfrac%7B4%7D%7B%5Cfrac%7B1-10%7D%7B4%7D%7D%5C%5C%5Cfrac%7B4%7D%7B%5Cfrac%7B-9%7D%7B4%7D%7D%5C%5C%5Cfrac%7B4%2A4%7D%7B-9%7D%5C%5C%5Cfrac%7B16%7D%7B-9%7D%20%5C%2C%5C%2Cor%5C%2C%5C%2C%5C%5C%5Cfrac%7B-16%7D%7B9%7D)
Option D is correct.
16. Simplify:
![\frac{7x+42}{x^2+13x+42}](https://tex.z-dn.net/?f=%5Cfrac%7B7x%2B42%7D%7Bx%5E2%2B13x%2B42%7D)
Making factors of x^2+13x+42= x^2 +6x+7x+42 = x(x+6)+7(x+6) = (x+7)(x+6)
Taking 7 common from numerator and putting factors in denominator we get,
![\frac{7(x+6)}{(x+7)(x+6)}\\\\Cancelling\,\, x+6 \,\, from\,\, numerator \,\, and\,\, \\\\\frac{7}{(x+7)}](https://tex.z-dn.net/?f=%5Cfrac%7B7%28x%2B6%29%7D%7B%28x%2B7%29%28x%2B6%29%7D%5C%5C%5C%5CCancelling%5C%2C%5C%2C%20x%2B6%20%5C%2C%5C%2C%20from%5C%2C%5C%2C%20numerator%20%5C%2C%5C%2C%20and%5C%2C%5C%2C%20%5C%5C%5C%5C%5Cfrac%7B7%7D%7B%28x%2B7%29%7D)
Option A is correct.
Answer: One face is 16 square centimeters.
Step-by-step explanation: To find the area of a face, you need to know the length of the side. All the sides of the cube are the same, so take the cube root of 64.
cm is the length of the side
The area of one face is the side length squared 4² = 16
4cm × 4cm = 16 square centimeters.