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4 years ago

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Let f(x) = 4x - 3 and h(x) = -5x + 7 . F(-3) + h(2)

1 answer:

zheka24 [161]4 years ago

5 0

F(-3) = -12 - 3 = -15
h(2) = -10 + 7 = -3

-15 + (-3)

-18

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Write a rule for the nth term of the geometric sequence if r = 1/4 and a3 = 2.

GarryVolchara [31]

Answer:

$a_{n} = 32(\frac{1}{4})^{n-1}$

Step-by-step explanation:

The nth term of a geometric sequence is given by the following equation.

$a_{n+1} = ra_{n}$

In which r is the common ratio.

This can be expanded for the nth term in the following way:

$a_{n} = a_{1}r^{n-1}$

In which $a_{1}$ is the first term.

This means that for example:

$a_{3} = a_{1}r^{3-1}$

So

$a_{3} = a_{1}r^{2}$

$2 = a_{1}(\frac{1}{4})^{2}$

$2 = \frac{a_{1}}{16}$

$a_{1} = 32$

Then

$a_{n} = 32(\frac{1}{4})^{n-1}$

4 0

3 years ago

In the local frisbee league, teams have 7 members and each of the 4 teams takes turns hosting tournaments. At each tournament, e

mars1129 [50]

There are 4 teams in total and each team has 7 members. One of the team will be the host team.

Tournament committee will be made from 3 members from the host team and 2 members from each of the three remaining teams. Selecting the members for tournament committee is a combinations problem. We have to select 3 members out 7 for host team and 2 members out of 7 from each of the remaining 3 teams.

So total number of possible 9 member tournament committees will be equal to:

$7C3 \times 7C2 \times 7C2 \times 7C2\\ \\ = 324135$

This is the case when a host team is fixed. Since any team can be the host team, there are 4 possible ways to select a host team. So the total number of possible 9 member tournament committee will be:

$9 \times 324135\\ \\ =2917215$

Therefore, there are 2917215 possible 9 member tournament committees

8 0

3 years ago

2x^2 + 3x - 12 when x = 5 help pls

cluponka [151]

$\huge\textsf{Hey there!}$

$\mathsf{2x^2 + 3x - 12}$

$\mathsf{= 2(5)^2 + 3(5) - 12}$

$\mathsf{5^2}$

$\mathsf{= 5 \times 5}$

$\mathsf{\bf = 25}$

$\mathsf{2(25) + 3(5) - 12}$

$\mathsf{2(25)}$

$\mathsf{= \bf 50}$

$\mathsf{3(5)}$

$\mathsf{= \bf 15}$

$\mathsf{= 50 + 15 - 12}$

$\mathsf{50 + 15}$

$\mathsf{= \bf 65}$

65 - 12

$\mathsf{= \bf 53}$

$\boxed{\boxed{\huge\textsf{Answer: \bf 53}}}\huge\checkmark$

$\large\textsf{Good luck on your assignment and enjoy your day!}$

~ $\frak{Amphitrite1040:)}$

5 0

3 years ago

Read 2 more answers

What are the solutions to the quadratic equation 2x^2-8x-24=0

Vinvika [58]

2x^2 - 8x - 24

First, we can factor a 2 out of this expression to simplify it.

2(x^2 - 4x - 12)

Now, we can try factoring this two ways: by using the quadratic formula, or by using the AC method.

We're gonna try using the AC method first.

List factors of -12.

1 * -12

-1 * 12

2 * -6

-2 * 6 (these digits satisfy the criteria.)

Split the middle term.

2(x^2 - 2x + 6x - 12)

Factor by grouping.

2(x(x - 2) + 6(x - 2)

Rearrange terms.

<h3><u>(2)(x + 6)(x - 2) is the fully factored form of the given polynomial.</u></h3>

7 0

3 years ago

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3x + 1 = 7 What is the value of x?

Olin [163]

The value for X is 2

5 0

3 years ago