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2 years ago

Find the 59th term of the following arithmetic sequence. 15, 23, 31, 39

1 answer:

4 0

$15~~,~~\stackrel{15+8}{23}~~,~~\stackrel{23+8}{31}~~,~~\stackrel{31+8}{39}~~,~~...~\hspace{10em}\stackrel{common~difference}{d=8} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\stackrel{\textit{term position}}{59}\\ a_1=\stackrel{\textit{first term}}{15}\\ d=\stackrel{\textit{common difference}}{8} \end{cases} \\\\\\ a_{59}=15+(59-1)8\implies a_{59}=15+472-8\implies a_{59}=479$

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The following is a geometric sequence.<br> - 1/2 , 1/4, -1/8 , 1/16 <br> true <br> false

seraphim [82]

Answer:

True

Step-by-step explanation:

It has a common ratio of -1/2

Each term after the first is obtained by multiplying the previous one by -1/2:-

-1/2 * 1/2 = 1/4 ; 1/4 * -1/2 = -1/8 and so on.

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2 years ago

At the Souvenir Shop, gemstone souvenirs cost $11.60 for 5. Which proportion can be used to find the cost of just 1 gemstone?

Assoli18 [71]

$2.32

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3 years ago

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Gail baked some muffins. She sold 2/7 of the muffins on Monday. She sold 1/3 more of the muffins on Tuesdays than on Monday. Wha

baherus [9]

13/21 were sold on the two days

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3 years ago

A and B are supplementary angles. If A = 7x - 18 and B = 8x + 3, find x.

Mila [183]

Answer:

x=13

Step-by-step explanation:

Angle A and angle B are supplementary

Supplementary angles add to 180 degrees

<A + <B = 180

7x-18 + 8x+3 = 180

Combine like terms

15x -15 = 180

Add 15 to each side

15x-15 +15 = 180+15

15x = 195

Divide by 15

15x/15 =195/15

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3 years ago

A person standing close to the edge on top of a 24-foot building throws a ball vertically upward. The quadratic function h(t)=−1

Nutka1998 [239]

Answer:

a) maximum height is 156.25 ft

b) 6 seconds

Step-by-step explanation:

a) The maximum height can be found by finding the y-coordinate of the vertex. The vertex is the highest point in a parabola opened downward.

I start with by finding the t-coordinate of the vertex.

The t-coordinate of the vertex is $\frac{-b}{2a}$ where the expression $-16t^2+92t+24$ will need to be compared to $at^2+bt+c$ .

We see that $a=-16,b=92,c=24$ .

So the t-coordinate of the vertex is $\frac{-b}{2a}=\frac{-92}{2(-16)}=\frac{-92}{-32}=\frac{23}{8}$ .

We can find the h, the height, that corresponds to this t by using the equation $h=-16t^2+92t+24$ where $t=\frac{23}{8}$ .

So inserting 23/8 for $t$ .

$-16(23/8)^2+92(23/8)+24$

Plugging into calculator gives you 625/4.

So the maximum height is 625/4 or 156.25.

b) Let's find how long it takes the ball to hit the ground. If the ball is on the ground, then the distance between the ball and the ground is 0. So we are looking to solve h(t)=0 for t.

So this is equation we are solving for t:

$-16t^2+92t+24=0$