The width of the rectangle is 10 cm more than the length. The
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Answer:
The angles are <u>155°</u> and <u>25°</u>.
Step-by-step explanation:
Given:
Two supplementary angles are in the ratio of 31:5.
Now, to find the angles.
The sum of two supplementary angles = 180°
Let the ratio of the angles be .
So, according to question:
<em>Dividing both sides by 36 we get:</em>
So,
And,
Therefore, the angles are 155° and 25°.
So there are 3 siblings: the first twin, the second twin, and their older sister.
Since the sister is older by 11 years, you can represent their relationship with the following equation;
age of twin = age of older sister - 11
t = s - 11
Representing this next part may be a little hard to show, but i'll do my best :)
Adding the ages together can be represented like this;
total age = t + t + s
If the product of their ages ( t * t * s ) is 1181 more than the sum, you can show it like this:
Now you substitute in (s - 11) for t because s = t - 11.
Factor:
Since it's a third-degree equation, I just entered it into a polynomial solver in my calculator. There was only one factor listed, x = 19. Using (s - 19) = 0 as a factor, the equation becomes the following:
Using the quadratic formula, you get:
Since you have a square root of a negative number, the answer will be imaginary. You cannot have an age that is imaginary, so the age of the older sister (s) is 19 years.
Because t = s - 11, that means that t = (19) - 11 = 8.
t is the age of the twins, so the twins are 8 years old.
Since the sister is older by 11 years, you can represent their relationship with the following equation;
age of twin = age of older sister - 11
t = s - 11
Representing this next part may be a little hard to show, but i'll do my best :)
Adding the ages together can be represented like this;
total age = t + t + s
If the product of their ages ( t * t * s ) is 1181 more than the sum, you can show it like this:
Now you substitute in (s - 11) for t because s = t - 11.
Factor:
Since it's a third-degree equation, I just entered it into a polynomial solver in my calculator. There was only one factor listed, x = 19. Using (s - 19) = 0 as a factor, the equation becomes the following:
Using the quadratic formula, you get:
Since you have a square root of a negative number, the answer will be imaginary. You cannot have an age that is imaginary, so the age of the older sister (s) is 19 years.
Because t = s - 11, that means that t = (19) - 11 = 8.
t is the age of the twins, so the twins are 8 years old.