A triangle has an area of 50cm its base is four times the height what is the height?

1 answer:

7 0

So area=1/2 base times height
50=1/2 base times height
multiply both sides by 2
100=base times height
base=4height
100=4height times height
100=4height^2
divide 4
25=height^2
squarer root
5=height

subisute
base=4(5)
base=20

height=5

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An instructor gives her class the choice to do 7 questions out of the 10 on an exam.

Maksim231197 [3]

Answer:

(a) 120 choices

(b) 110 choices

Step-by-step explanation:

The number of ways in which we can select k element from a group n elements is given by:

$nCk=\frac{n!}{k!(n-k)!}$

So, the number of ways in which a student can select the 7 questions from the 10 questions is calculated as:

$10C7=\frac{10!}{7!(10-7)!}=120$

Then each student have 120 possible choices.

On the other hand, if a student must answer at least 3 of the first 5 questions, we have the following cases:

1. A student select 3 questions from the first 5 questions and 4 questions from the last 5 questions. It means that the number of choices is given by:

$(5C3)(5C4)=\frac{5!}{3!(5-3)!}*\frac{5!}{4!(5-4)!}=50$

2. A student select 4 questions from the first 5 questions and 3 questions from the last 5 questions. It means that the number of choices is given by:

$(5C4)(5C3)=\frac{5!}{4!(5-4)!}*\frac{5!}{3!(5-3)!}=50$

3. A student select 5 questions from the first 5 questions and 2 questions from the last 5 questions. It means that the number of choices is given by:

$(5C5)(5C2)=\frac{5!}{5!(5-5)!}*\frac{5!}{2!(5-2)!}=10$

So, if a student must answer at least 3 of the first 5 questions, he/she have 110 choices. It is calculated as:

50 + 50 + 10 = 110

6 0

3 years ago

What are the zeros of the function f(x)=-x^2+13x-36

Galina-37 [17]

For this case we have the following function:

$f (x) = - x ^ 2 + 13x-36$

To find the zeros of the function we make $y = 0$ and solve for "x", then:

$0 = -x ^ 2 + 13x-36$

We multiply by -1 on both sides of the equation:

$0 = x ^ 2-13x + 36$

We factor the equation, for this we look for two numbers that, when multiplied, result in 36 and when added, result in -13. These numbers are -9 and -4.

$(-9) * (- 4) = 36\\-9-4 = -13$