The height of a rocket a given number of seconds after it is released is modeled by h (t) = negative 16 t squared + 32 t + 10. W

Hi there!

While there are no answer choices provided, here's how you can solve a problem like this.

To find the average of two numbers, you simply sum them up and divide by two!

For instance, to find the midpoint between 1 and 3, you add 1 and 3 to get 4, then divide by 2 which results in 2!

For 100 and 580, adding gives you 680, and dividing by 2 results in 340!

The average between 0.57 and 0.69 involves adding to get 1.26, then dividing by 2 yields 0.63!

Now, with percentages, for 45% and 67%, the addition gives you 112%, and dividing that by 2 will result in 56%!

So, for your answer options, just calculate the total and divide by two to determine which one results in 76%!

I hope this information helps!

∠1 and ∠8 are alternate exterior angles while ∠3 and ∠6 are alternate interior angles.

step-by-step explanation:

When transversal l intersects lines m and n, the angles formed outside each line on the opposite side of the transversal constitute alternate angles (like ∠1 and ∠8). In contrast, alternate interior angles appear on opposite sides but are located between the two lines (like ∠3 and ∠6).

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Keywords: Transversal, angles

Response:

2/9 = 0.22

Clarification:

There are two ways to select the first number that is odd and less than 5: 1 and 3.

For each of these, the second number drawn can be any of the values from 1 to 9, giving us a total of 18 options.

Out of these, the only pairs that result in a sum less than 5 are (1,1), (1,2), (1,3), and (3,1). Thus we have 4 combinations from the total of 18:

4/18 = 2/9 = 0.22

Response:

Monomial

Trinomial

Monomial

Trinomial

Binomial

Explanation in detail:

A monomial consists of one distinct term

A binomial consists of two distinct terms

A trinomial consists of three distinct terms

In the first example, the -x^2 and +x^2 cancel each other, and since 2x and 4x are similar terms, combining gives you 6x, which is a monomial.

In the second example, after adding +3 and -2, you get three distinct terms that can't be combined, thus it's a trinomial

In the third example, all variables cancel out, resulting in just one term, 3, making it a monomial

In the fourth one, after combining like terms, you end up with:

x^3 + 3x^2 + 7x

This makes it a trinomial

In the last example, the 6x and -6x cancel, leaving two terms, qualifying it as a binomial.

Step-by-step explanation:

a) 7!

In absence of any restrictions, the answer is 7! as it represents the permutations of all animals.

b) 4! x 3!

Considering there are 6 cats and 5 dogs, the first and last slots must be occupied by cats to ensure alternate arrangements. The only options available then are based on the arrangement of the cats among themselves and the dogs among themselves, yielding 4! permutations for the cats and 3! for the dogs, thus leading to a total of 4! x 3! arrangements.

c) 3! x 5!

Here, the arrangement of the dogs among themselves can occur in 3! ways. Considering the dogs as a singular “object,” we can arrange this unit with the 4 cats, providing 5! total arrangements possible, leading to 3! · 5! arrangement possibilities.

d) 2 x 4! x 3!

In this scenario, both cats and dogs must be grouped together, allowing positions where all cats come before the dogs or vice versa. As there are two configurations, the resultant count is 2 multiplied by both arrangements, resulting in 2 x 4! x 3!