Answer:
Step-by-step explanation:
So we need to find an equation of a line that crosses the point (6,-4) and is perpendicular to y = -2x -3.
First, let's find the slope of the line we want to write. The line we want is perpendicular to y = -2x -3. Recall that if two lines are perpendicular to each other, their slopes are negative reciprocals of each other. What this means is that:
Plug -2 for one of the slopes.
Divide by -2 to find the slope of our line.
Thus, our line needs to have a slope of 1/2.
Now, let's use the point-slope form. The point-slope form is given by:
Plug in 1/2 for the slope m and let's let our point (6,-4) be x₁ and y₁. Thus:
Simplify and distribute:
Subtract 4 from both sides:
The above is the equation that passes the point (6,-4) and is perpendicular to y = -2x -3.
Answer
B DID THE TEST
Step-by-step explanation:
YOU WILL DO YOU GOOD LUCK
Answer:
1) w₁=4 - i w₂= -4 + i
2) w₁= 3 - i w₂= -3 + i
3) w₁= 1 + 2i w₂= - 1 - 2i
4) w₁= 2- 3i w₂= -2 + 3i
5) w₁= 5 - 2i w₂= -5 + 2i
6) w₁= 5 - 3i w₂= -5 + 3i
Step-by-step explanation:
The root of a complex number is given by:
![\sqrt[n]{z}=\sqrt[n]{r}(Cos(\frac{\theta+2k\pi}{n}) + i Sin(\frac{\theta+2k\pi}{n}))](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bz%7D%3D%5Csqrt%5Bn%5D%7Br%7D%28Cos%28%5Cfrac%7B%5Ctheta%2B2k%5Cpi%7D%7Bn%7D%29%20%2B%20i%20Sin%28%5Cfrac%7B%5Ctheta%2B2k%5Cpi%7D%7Bn%7D%29%29)
where:
r: is the module of the complex number
θ: is the angle of the complex number to the positive axis x
n: index of the root
1) z = 15 − 8i ⇒ r=17 θ= -0.4899 rad
w₁=
=4-i
w₂=
=-1+i
2) z = 8 − 6i ⇒ r=10 θ= -0.6435 rad
w₁=
= 3 - i
w₂=
= -3 + i
3) z = −3 + 4i ⇒ r=5 θ= -0.9316 rad
w₁=
= 1 + 2i
w₂=
= -1 - 2i
4) z = −5 − 12i ⇒ r=13 θ= 0.4426 rad
w₁=
= 2- 3i
w₂=
= -2 + 3i
5) z = 21 − 20i ⇒ r=29 θ= -0.8098 rad
w₁=
= 5 - 2i
w₂=
= -5 + 2i
6) z = 16 − 30i ⇒ r=34 θ= -1.0808 rad
w₁=
= 5 - 3i
w₂=
= -5 + 3i
Answer:
If we define the random variable X ="time spend by the students doign homework"
And we want to tes t is students spend more than 1 hour doing homework per night, on average (alternative hypothesis), so then the system of hypothesis for this case are:
Null hypothesis: 
Alternative hypothesis: 
And they wnat to use a sample size of n = 100 and a significance level of 0.05
Step-by-step explanation:
Previous concepts
A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".
The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".
The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".
Solution to the problem
If we define the random variable X ="time spend by the students doign homework"
And we want to tes t is students spend more than 1 hour doing homework per night, on average (alternative hypothesis), so then the system of hypothesis for this case are:
Null hypothesis:
Alternative hypothesis:
And they wnat to use a sample size of n = 100 and a significance level of 0.05
