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3 years ago

Choose the equation that represents the line that passes through the point (6, −3) and has a slope of one half

Mathematics

1 answer:

Tcecarenko [31]3 years ago

8 0

Answer:

y = 1/2x - 6

Step-by-step explanation:

slope = 1/2 = m

lets find your y-intercept using slope intercept form: y = mx + b using the points they gave us (6, -3)

y = mx + b; plug what we know to find b, which is our y-intercept.

-3 = 1/2(6) + b

-3 = 3 + b

-6 = b

Now you have all you need to write your equation

y = mx + b

y = 1/2x - 6

You might be interested in

Find an for the arithmetic series with s16 = -288 And a1 =-21

Maru [420]

If $d$ is the common difference between terms in the sequence $\{a_n\}$ , then

$a_1=-21$
$a_2=a_1+d=-21+d$
$a_3=a_2+d=-21+2d$
...
$a_n=a_{n-1}+d=\cdots=-21+(n-1)d$

You're told that $S_{16}=-288$ (the sum of the first 16 terms in the sequence, presumably). Well, we know that

$S_{16}=\displaystyle\sum_{n=1}^{16}a_n=\sum_{n=1}^{16}(-21+(n-1)d)$
$S_{16}=\displaystyle(-21-d)\sum_{n=1}^{16}1+d\sum_{n=1}^{16}n$

Recall that

$\displaystyle\sum_{n=1}^kn=\frac{k(k+1)}2$

so that we have

$-288=16(-21-d)+\dfrac{16(16+1)}2d\implies d=\dfrac25$

So we get

$\begin{cases}a_1=-21\\\\a_n=-21+\dfrac25(n-1)\end{cases}$

8 0

3 years ago

A particle is moving with the given acceleration function and initial conditions. Find the velocity function and the position fu

Lerok [7]

Answer:

The velocity function is the particle is $v(t)=-2\cos (t)-4\sin (t)-1$ .

Step-by-step explanation:

The acceleration function of a moving particle is

$a(t)=2\sin (t)-4\cos (t)$

The initial conditions are v(0) = −3, s(0) = 5.

Integrate the acceleration function with respect to time to find the velocity function.

$\int a(t)=\int (2\sin (t)-4\cos (t))dt$

$v(t)=-2\cos (t)-4\sin (t)+C_1$

Use the initial condition v(0) = −3 to find the value of C₁.

$-3=-2\cos (0)-4\sin (0)+C_1$

$-3=-2(1)-4(0)+C_1$

$-3=-2+C_1$

$-3+2=C_1$

$-1=C_1$

So the velocity function is the particle is

$v(t)=-2\cos (t)-4\sin (t)-1$

Integrate the acceleration function with respect to time to find the position function.

$\int v(t)=\int (-2\cos (t)-4\sin (t)-1)dt$

$s(t)=-2\sin (t)+4\cos (t)-t+C_2$

Use the initial condition s(0) = 5 to find the value of C₂.

$5=-2\sin (0)+4\cos (0)-(0)+C_2$

$5=-2(0)+4(1)+C_2$

$5=4+C_2$

$1=C_2$

So, the position function is the particle is $s(t)=-2\sin (t)+4\cos (t)-t+1$ .

5 0

3 years ago

An unbiased estimator is one for which: Group of answer choices its value always equals the value of the parameter it estimates.

m_a_m_a [10]

Answer:

its sampling distribution is centered exactly at the parameter it estimates.

Step-by-step explanation:

An unbiased estimator is an estimator that shows the correct statistic applied for the parameter of the population

Here correct represents that it should not be overestimated or underestimated. In the case when there is an underestimate or overestimate this means that there is a bias

So as per the given options the above option is correct

3 0

3 years ago

What does 1/3 equivalent to.

Finger [1]

Answer:

For a decimal 0.3333(it goes on forever)

Step-by-step explanation:

It is 0.3333 because that's the closest to a third you can get

4 0

3 years ago

Read 2 more answers