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2 years ago

All of the equations to –32 = k + –19

Mathematics

1 answer:

soldi70 [24.7K]2 years ago

8 0

Answer:

$k = - 13$

Step-by-step explanation:

$- 32 = k - 19 \\ -32 + 19 = k \\ - 13 = k$

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What term is 1/1024 in the geometric sequence,-1,1/4,-1/6..?

Trava [24]

Answer:

$\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}$

Step-by-step explanation:

The explicit formula for a geometric sequence:

$a_n=a_1r^{n-1}$

$a_n$ - n-th term

$a_1$ - first term

$r$ - common ratio

$r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}$

We have

$a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...$

The common ratio:

$r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}$

<h2>It's not a geometric sequence.</h2>

If $a_3=-\dfrac{1}{16}$ then the common ratio is $r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}$

Put to the explicit formula:

$a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}$

Put $a_n=\dfrac{1}{1024}$ and solve for <em>n </em>:

$-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1$

$\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6$

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3 years ago

An angle measures 44° less than the measure of its complementary angle. What is the measure of each angle?

Alchen [17]

Answer:

One angle is 46° and the other angle is 44°

Step-by-step explanation:

Complementary angle means the angles add up to 90 so:

90 - 44 = 46

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3 years ago

Identify the outlier in the data set 6, 9, 3, 2, 10, 138, 13. Then, find the mean with and without the outlier. If necessary, ro

Andrews [41]

138 is the outlier since it is more than 1.5 * IQR past the third quartile of the data set.

With this upper outlier, the mean will be significantly higher. Without it, it will lower back down, so B is your answer

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3 years ago

On Monday, three hundred ninety - two students went on a trip to the zoo. All nine buses were filled and five students had to tr

Vikki [24]

The answer to your question is 43

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3 years ago

What is the The range of y = square root X-5 – 1

Step2247 [10]

Answer:

[-1, infinity)

Step-by-step explanation:

I must assume that you meant y = √(x - 5) - 1.

The range of the square root function is [0, infinity.

If 1 is subtracted from the square root function, the range of the resulting function is [-1, infinity).

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3 years ago