A woman is 10 times as old as her daughter. In 8 years she will be 4 times as old as her daughter. How old is the mother now?

Mathematics

2 answers:

mars1129 [50]2 years ago

4 0

Answer:

80 years

Step-by-step explanation:

Let daughter's age be x years.

Therefore, women's age = 10x years

8 years after:

Daughter's age = (x + 8) years

Women's age = 4(x + 8) years

$4(x + 8) = (x + 8) \\ 4x + 32 = x + 8 \\ 4x - x8 - 32 \\ 3x = - 24 \\ x = \frac{ - 24}{3} \\ x = - 8 \\ \because \: age \: of \: a \: person \: can \: not \: be \: negative \\ \therefore \: x = 8 \\ \therefore \: 10x = 10 \times 8 \\ \huge \red{ \boxed{\therefore \: 10x = 80 \: years}}$

jeka57 [31]2 years ago

3 0

Answer:

Mom is 40 and her daughter is 4; in eight years, mom will be 48 and her daughter will be 12.

Step-by-step explanation:

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In a triangle, two sides that measure 8 centimeters and 11 centimeters form an angle that measures 82°. to the nearest tenth of

Gwar [14]

We can use the Сosine formula to solve this problem.
First we must find the third side (АС) of the triangle:

$AC^2=AB^2+BC^2-2*AB*BC*cos82^o \\ AC^2=8^2+11^2-2*8*11*0.1392 \\ AC^2=64+121-24.4992= 160.508 \\ AC= \sqrt{160.508} \approx 12.67 \ cm$

The smallest angle of the triangle lies opposite the smallest side, so we need to find m∠C.

$cosC= \frac{AC^2+BC^2-AB^2}{2*AC*BC} \\ \\ cosC= \frac{12.67^2+11^2-8^2}{2*12.67*11}= \frac{160.53+121-64}{278.74} = \frac{217.53}{278.74} \approx 0.7804$

Now we can use Bradis's Table (I don't know the name in English, maybe Trigonometric Table?) to find m∠C:

m∠С = 38°42' = 38.7°

Answer: 38.7°

I hope this helps