Write an equation of a parabola that has two x-intercepts and a minimum vertex.

Please help with this square problem, the picture is shown.

Galina-37 [17]

Area of the upper rectangle = x(16 - 6) = 10x yd²

Area of the bottom rectangle = 6(x + 6) = 6x + 36 yd²

Total area = 10x + 6x + 36 = 16x + 36 yd²

5 0

4 years ago

Compare these two functions. Which function shows a greater rate of change?

nata0808 [166]

Answer:

It's B

Step-by-step explanation:

"Brainlypatrol" is deleting my answers. >:(

5 0

2 years ago

Read 2 more answers

Yall help “How old am i if 200 is reduced by 2 times my age is 16?”

Nikitich [7]

Answer:

Two times of your age = 16 × 2 = 32

So, 200 reduced = 32 - 200 = - 163 years

<h3>PLEASE MARK ME BRAINLIEST</h3>

5 0

3 years ago

If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple ar

Oksana_A [137]

Answer:

$n + 4 {n \choose 2} + 6 {n \choose 3} + 4 {n \choose 4} + {n \choose 5}$

Step-by-step explanation:

Lets divide it in cases, then sum everything

Case (1): All 5 numbers are different

In this case, the problem is reduced to count the number of subsets of cardinality 5 from a set of cardinality n. The order doesnt matter because once we have two different sets, we can order them descendently, and we obtain two different 5-tuples in decreasing order.

The total cardinality of this case therefore is the Combinatorial number of n with 5, in other words, the total amount of possibilities to pick 5 elements from a set of n.

${n \choose 5 } = \frac{n!}{5!(n-5)!}$

Case (2): 4 numbers are different

We start this case similarly to the previous one, we count how many subsets of 4 elements we can form from a set of n elements. The answer is the combinatorial number of n with 4 ${n \choose 4} .$

We still have to localize the other element, that forcibly, is one of the four chosen. Therefore, the total amount of possibilities for this case is multiplied by those 4 options.

The total cardinality of this case is $4 * {n \choose 4} .$

Case (3): 3 numbers are different

As we did before, we pick 3 elements from a set of n. The amount of possibilities is ${n \choose 3} .$

Then, we need to define the other 2 numbers. They can be the same number, in which case we have 3 possibilities, or they can be 2 different ones, in which case we have ${3 \choose 2 } = 3$ possibilities. Therefore, we have a total of 6 possibilities to define the other 2 numbers. That multiplies by 6 the total of cases for this part, giving a total of $6 * {n \choose 3}$

Case (4): 2 numbers are different

We pick 2 numbers from a set of n, with a total of ${n \choose 2}$ possibilities. We have 4 options to define the other 3 numbers, they can all three of them be equal to the biggest number, there can be 2 equal to the biggest number and 1 to the smallest one, there can be 1 equal to the biggest number and 2 to the smallest one, and they can all three of them be equal to the smallest number.

The total amount of possibilities for this case is

$4 * {n \choose 2}$

Case (5): All numbers are the same

This is easy, he have as many possibilities as numbers the set has. In other words, n

Conclussion

By summing over all 5 cases, the total amount of possibilities to form 5-tuples of integers from 1 through n is

$n + 4 {n \choose 2} + 6 {n \choose 3} + 4 {n \choose 4} + {n \choose 5}$

I hope that works for you!

4 0

3 years ago

GUYS PLEASE HELP ME I REALLY DON'T UNDERSTAND THIS TASK!!!!!!! IT'S VERY IMPORTANT FOR ME!!!!! DISTANCE BETWEEN TWO TOWNSHIPS, E

Dimas [21]

For this problem, you know that the first walker will arrive 2 hours before the second, and increases his speed by 2 times the second walker. You also know there is a distance of 24 km. So up until some time x, the two walkers have to be going the same speed. If the first walker increases speed by two times the speed per hour, and arrives two hours earlier, then his initial speed will be 20 km/h, because after 2 hours, he will have an increase of 4 km/hr, and the second will have an increase of 2 km/h, thereby making the first arrive 2 hours earlier, if that makes sense.

5 0

3 years ago