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3 years ago

Look at the sequence in the table.

Mathematics

1 answer:

malfutka [58]3 years ago

7 0

Answer:

Step-by-step explanation:

The consecutive values of $a_{n}$ have a common difference d, that is

d = 8 - 3 = 13 - 8 = 18 - 13 = 23 - 18 = 5

This indicates that the sequence is arithmetic.

The recursive formula allows the next term in the sequence to be found from the previous term by adding 5, thus

$a_{n}$ = $a_{n-1}$ + 5 → A

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What is the value of t in the equation 3(2t + 5) = 5t + 25? (4 points)

SSSSS [86.1K]

3 ( 2t + 5 ) = 5 t + 25

3 * 2 t + 3 * 5 = 5 t + 25

6 t + 15 = 5 t + 25

6t - 5t = 25 - 15

t = 10

Hope this helps!

5 0

3 years ago

Read 2 more answers

Simplify expression √18x4y3

Ierofanga [76]

$3x {}^{2} y \sqrt{2y}$

6 0

3 years ago

A new phone costs $230 and the sales tax rate is 7%. What is the total cost of the camera after tax?

rosijanka [135]

That's a question about percentage.

One way to represent percentage is using decimal number. In this way, 1 is equivalent to 100% and the other less percentages using numbers between 0 and 1.

Examples:

90% is equivalent to 0,90.
5% is equivalent to 0.05. It's not 0.5 because 0.5 is equivalent to 50%.
13.17% is equivalent to 0.1317.
245% is equivalent to 2.45.

If we want to know the percentage of a number, we should multiplacate the number by the porcentage in the decimal number form.

Examples:

55.90% of 200 is equal to: $200 \times 0.5590 = 111.8$

360% of 88 is equal to: $88\times 3.6 = 316.8$

In our problem, we have a phone with a increase of 7%. To solve that, it's important to perceive that $230 is equal to 100% and with a increase of 7%, we will pay 107%.

107% in the decimal number form is 1.07. With that information, we should multiplicate 1.07 by the original value and we will find the answer.

We know that $230\times 1.07 = 246.1$ , therefore, the total cost of the phone after tax is $246.1.

I hope I've helped. :D

Enjoy your studies. \o/

4 0

3 years ago

Sarah found that the product of 49 and 805 is 3,165. How would finding an estimate help her know that the answer is NOT reasonab

Dovator [93]

Answer:

49 +805=3,165

Step-by-step explanation:

answer

she will have to count

6 0

3 years ago

Question in picture A) 16/63 B)-16/63 C) 63/16 D) -63/16

Orlov [11]

ANSWER
$\tan(x + y) = - \frac{63}{16}$

EXPLANATION

We were given that,

$\csc(x) = \frac{5}{3}$

This implies that,

$\sin(x) = \frac{3}{5}$

We use the Pythagorean identity

$\sin^{2} (x) + \cos^{2} (x)= 1$
to get,

$\cos(x) = \sqrt{1 - ( { \frac{3}{5} })^{2}} = \frac{4}{5}$

We were also given that,

$\cos(y) = \frac{5}{13}$

This means that,

$\sin(y) = \sqrt{1 - {( \frac{5}{13}) }^{2} } = \frac{12}{13}$

This is because,

$0 < \: x \: < \frac{\pi}{2}$

$0 < \: y \: < \frac{\pi}{2}$

This angles are in the first quadrant so we pick the positive values.

$\tan(x + y) = \frac{ \sin(x + y) }{ \cos(x + y) }$

$\tan(x + y) = \frac{ \sin(x ) \cos(y) + \sin(y) \cos(x) }{ \cos(x) \cos(y) - \sin(x) \sin(y) }$

$\tan(x + y) = \frac{ \frac{3}{5} \times \frac{5}{13} + \frac{12}{13} \times \frac{4}{5} }{ \frac{4}{5} \times \frac{5}{13} - \frac{3}{5} \times \frac{12}{13} }$

$\tan(x + y) = - \frac{63}{16}$

The correct answer is D

4 0

3 years ago