The price of an item has been reduced by 30%. The original price was $30. What is the price of the item now ?

Mathematics

1 answer:

Anit [1.1K]2 years ago

6 0

Answer:

Step-by-step explanation:

30 multiply by 30 and divide by 100

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Determine the nth term for each of the following sequences: 2,5,8,11,14,..

Tanya [424]

To determine the nth term, we must create a function.

f(n) = 1st term + common difference (n - 1)

n = term you are looking for
1st term = 1st number in the sequence
common difference = the difference between two consecutive numbers in the sequence.

based on the above sequence, the 1st term is 2, its common difference is 3.

f(n) = 2 + 3(n-1)

Assuming we are looking for the 5th term
f(5) = 2 + 3(5-1)
= 2 + 3(4)
= 2 + 12
f(5) = 14 as you can see in the above sequence 14 is the 5th term.

For any other value of the nth term, simply substitute n by the number of the term and solve the equation.

8 0

2 years ago

the height of a triangle is 4 meters less than the base. if the area of the triangle is 6 m^2 what is the height of the triangle

inna [77]

Answer:

$2m$

Step-by-step explanation:

Alrighty let's do this.

We know that formula for the Area of a triangle is:

$A = \frac{1}{2}bh$

They give us the area as $6m^2$ , so let's include it in the equation.

$6 = \frac{1}{2}bh$

Now we reach a stage where we have 2 unknown variables! That means we can't solve it in its current state. So the idea you should have in cases like these where you have 2 or more unknown variables is, "Can I represent this one variable in terms of another variable?" In this case you can do exactly that. You can represent height in terms of length of the base. We are told the height of the triangle is 4 meters less than the base. That is telling us that $h = b-4$

So replace $h$ in the equation with $b-4$ .

You will now get:

$6 = \frac{1}{2}b(b-4)$

Now we can work towards solving. Let's get simplifying.

$12 = b(b-4)\\12 = b^2 - 4b\\$

bring everything to one side so we can make a quadratic and factor:

$0 = b^2 - 4b - 12\\0 = (b-6)(b+2)\\\\b = 6\\b\neq -2$

We get that $b=6$ .

Since we need the height of the triangle we'll need to call back on what h is. We found earlier that $h = b - 4$ , so to find h, we just sub in our b value into that.