Answer:
The side c needs to be 12.85 for the triangle to have greatest perimeter
Step-by-step explanation:
We are given;
b = 13
a = 15
Angle at b: B = 55°
Let's find side c.
Using the law of cosines,we have;
b² = a² + c² - 2ac•cos(B)
13² = 15² + c² - 2•15•c•cos(55)
169 = 225 + c² - 30c•cos(55)
c² - 30c•cos(55) + 225 - 169 = 0
c² - 30c•cos(55) + 56 = 0
c² - 30c•(0.5736) + 56 = 0
c² - 30c•(0.5736) + 56 = 0
c² - 17.208c + 56 = 0
Using quadratic formula;
c = [-(-17.208) ± √((-17.208)² - (4•1•56)]/2(1)
c = [17.208 ± √(296.115 - 224)]/2
c = 8.604 ± 4.246
To have the greater perimeter, we need the larger value of c, thus we will use the positive sign and ignore the negative one ;
Thus,
c = 8.604 + 4.246 = 12.85
If ABC and DEF are complementary, then the value of x will be,
90 - ABC = x
90 - 53 = x
x = 37°
7x³ = 28x is our equation. We want its solutions.
When you have x and different powers, set the whole thing equal to zero.
7x³ = 28x
7x³ - 28x = 0
Now notice there's a common x in both terms. Let's factor it out.
x (7x² - 28) = 0
As 7 is a factor of 7 and 28, it too can be factored out.
x (7) (x² - 4) = 0
We can further factor x² - 4. We want a pair of numbers that multiply to 4 and whose sum is zero. The pairs are 1 and 4, 2 and 2. If we add 2 and -2 we get zero.
x (7) (x - 2) (x + 2) = 0
Now we use the Zero Product Property - if some product multiplies to zero, so do its pieces.
x = 0 -----> so x = 0
7 = 0 -----> no solution
x - 2 = 0 ----> so x = 2 after adding 2 to both sides
x + 2 = 0 ---> so = x - 2 after subtracting 2 to both sides
Thus the solutions are x = 0, x = 2, x = -2.
first of all you add all of the ratios together so it would be 1+3+5
That equals 9 then divide 72 by 9 which gets you 8. Then you times 8 by all of the ratios to get the answer
8:24:40
Answer: B) 3+y+3
This can be simplified to y+6, but the current un-simplified expression has 3 terms.
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Explanation:
Terms are separated by a plus sign. If you had something like 10x-5y, then you would write that as 10x+(-5y) showing that 10x and -5y are the two terms.
Choices A and C, xy and 6y respectively, have one term each. They are considered monomials. Mono = one, nomial = name.
Choice D is the product of the constant 3 and the binomial y+3. Binomials have two terms.
Only choice B has three terms, though we can simplify it down to two terms. I have a feeling your teacher doesn't want you to simplify it.
