Answer:
15 boys and 25 girls
Step-by-step explanation:
The sum of boys (b) and girls (g) is given as 40:
g + b = 40
The number of girls is 2 times the number of boys minus 5:
2b - 5 = g
First formula can be rewritten as g = 40 - b
Then you can substitute this for g in the second, and you get:
2b-5 = 40-b
Which simplifies to:
2b + b = 40 + 5
3b = 45
b = 15
g = 40-15 = 25
15 boys, 25 girls.
So if you're driving 25 miles per hour, it would take you 7 hours to drive 175 miles.
175 miles ÷ 25 miles = 7 hours.
Answer:
We draw line AB which is perpendicular to the 14 cm side
Since Angle C is 60 degrees that makes angle CAB = 30 degrees
Triangle CAB is a 30 60 90 triangle so line CB is half the hypotenuse or 5 cm
Line BD equals 9 cm
Line AB^2 = 10^2 - 5^2 = 75
Line AD^2 = AB^2 + BD^2
Line AD^2 = 75 + 81
Line AD^2 = 156
Line AD = 12.4899959968
Line AB = Sqr root (75) = 8.6602540378
Angle D = arc sine (8.6602540378 / 12.4899959968)
Angle D = 43.898 degrees
Angle A = 180 - 60 - 43.898 = 76.102 degrees
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Actually this could have been done a little easier by using the Law of Cosines and then the Law of Sines, but I just thought I'd show another way to solve this.
Step-by-step explanation:
Answer:
The answer is (d) ⇒ ![pq^{2}r\sqrt[3]{pr^{2}}](https://tex.z-dn.net/?f=pq%5E%7B2%7Dr%5Csqrt%5B3%5D%7Bpr%5E%7B2%7D%7D)
Step-by-step explanation:
* To simplify the cube roots:
If its number then the number must be written in the form x³
then we divide the power by 3 to cancel the radical
If its variable we divide its power by 3 to cancel the radical
∵ ![\sqrt[3]{p^{4}q^{6}r^{5}}=p^{\frac{4}{3}}q^{\frac{6}{3}}r^{\frac{5}{3}}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bp%5E%7B4%7Dq%5E%7B6%7Dr%5E%7B5%7D%7D%3Dp%5E%7B%5Cfrac%7B4%7D%7B3%7D%7Dq%5E%7B%5Cfrac%7B6%7D%7B3%7D%7Dr%5E%7B%5Cfrac%7B5%7D%7B3%7D%7D%7D)
∴ 
∵ ![p^{\frac{1}{3}}=\sqrt[3]{p}](https://tex.z-dn.net/?f=p%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D%5Csqrt%5B3%5D%7Bp%7D)
∵ ![r^{\frac{2}{3}}=\sqrt[3]{r^{2}}](https://tex.z-dn.net/?f=r%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%3D%5Csqrt%5B3%5D%7Br%5E%7B2%7D%7D)
∴ ![p(p)^{\frac{1}{3}}q^{2}r(r)^{\frac{2}{3}}=p(\sqrt[3]{p})q^{2}r(\sqrt[3]{r^{2}})](https://tex.z-dn.net/?f=p%28p%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7Dq%5E%7B2%7Dr%28r%29%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%3Dp%28%5Csqrt%5B3%5D%7Bp%7D%29q%5E%7B2%7Dr%28%5Csqrt%5B3%5D%7Br%5E%7B2%7D%7D%29)
∴ ![prq^{2}\sqrt[3]{pr^{2}}}](https://tex.z-dn.net/?f=prq%5E%7B2%7D%5Csqrt%5B3%5D%7Bpr%5E%7B2%7D%7D%7D)
∴ The answer is (d)
Answer:
Decimal point
Definition:
A <em>decimal point</em> is the symbol that is used to make the separation between the whole part and the fractional part of a number. Currently, not only is a point used to separate both parts, but the comma can also be used.
Example:
The number 39.847, in which 39 is the whole number, while 847 is the decimal part where 8 represent tenths, 4 hundredsths, and 7 thousandths.