All categories

2 years ago

Please help this is hard

Mathematics

1 answer:

olganol [36]2 years ago

7 0

'Consider the formula for the slope between two coordinate points; m, shown below.

m = y2 - y1/x2 - x1

Which of the following equations is equivalent to the slope formula?'

I think it would be C

You might be interested in

Solve x^2 + x - 12 = 0

bogdanovich [222]

Answer:

x₁ = -4

x₂ = 3

Step-by-step explanation:

x²+ x + 12 = 0

x = {-1±√((1²)-(4*1*-12))} / (2*1)

x = {-1±√(1+48)} / 2

x = {-1±√49} / 2

x = {-1±7} / 2

x₁ = {-1-7} / 2 = -8/2 = -4

x₂ = {-1+7} / 2 = 6/2 = 3

Check:

x₁

-4² + (-4) - 12 = 0

16 - 4 - 12 = 0

x₂

3² + 3 - 12 = 0

9 + 3 - 12 = 0

6 0

1 year ago

Which of the following is not one of the 8th roots of unity?

Anika [276]

Answer:

1+i

Step-by-step explanation:

To find the 8th roots of unity, you have to find the trigonometric form of unity.

1. Since $z=1=1+0\cdot i,$ then

$Rez=1,\\ \\Im z=0$

and

$|z|=\sqrt{1^2+0^2}=1,\\ \\\\\cos\varphi =\dfrac{Rez}{|z|}=\dfrac{1}{1}=1,\\ \\\sin\varphi =\dfrac{Imz}{|z|}=\dfrac{0}{1}=0.$

This gives you $\varphi=0.$

Thus,

$z=1\cdot(\cos 0+i\sin 0).$

2. The 8th roots can be calculated using following formula:

$\sqrt[8]{z}=\{\sqrt[8]{|z|} (\cos\dfrac{\varphi+2\pi k}{8}+i\sin \dfrac{\varphi+2\pi k}{8}), k=0,\ 1,\dots,7\}.$

Now

at k=0, $z_0=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 0}{8}+i\sin \dfrac{0+2\pi \cdot 0}{8})=1\cdot (1+0\cdot i)=1;$

at k=1, $z_1=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 1}{8}+i\sin \dfrac{0+2\pi \cdot 1}{8})=1\cdot (\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2})=\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2};$

at k=2, $z_2=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 2}{8}+i\sin \dfrac{0+2\pi \cdot 2}{8})=1\cdot (0+1\cdot i)=i;$

at k=3, $z_3=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 3}{8}+i\sin \dfrac{0+2\pi \cdot 3}{8})=1\cdot (-\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2})=-\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2};$

at k=4, $z_4=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 4}{8}+i\sin \dfrac{0+2\pi \cdot 4}{8})=1\cdot (-1+0\cdot i)=-1;$

at k=5, $z_5=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 5}{8}+i\sin \dfrac{0+2\pi \cdot 5}{8})=1\cdot (-\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2})=-\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2};$

at k=6, $z_6=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 6}{8}+i\sin \dfrac{0+2\pi \cdot 6}{8})=1\cdot (0-1\cdot i)=-i;$

at k=7, $z_7=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 7}{8}+i\sin \dfrac{0+2\pi \cdot 7}{8})=1\cdot (\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2})=\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2};$

The 8th roots are

$\{1,\ \dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2},\ i, -\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2},\ -1, -\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2},\ -i,\ \dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2}\}.$

Option C is icncorrect.

5 0

2 years ago

A triangular prism is 19 centimeters long. It has a triangular face with a height of 14 centimeters. The volume of the prism is

andreyandreev [35.5K]

The base of its triangular face of the triangular prism is found as 17.7 cm.

<h3>What is defined as the triangular prism?</h3>

A polyhedron with two triangular bases as well as three rectangular sides is known as a triangular prism.
It is a three-dimensional shape with three side faces but also two base faces that are connected by the edges.

The formula for the volume of triangular prism is;

Volume = base area x length

The base area of the triangular base.

The area of the triangle = 1/2 base×height

The given values are-

volume = 2,354. 1 cubic centimeters.
length = 19 cm
height = 14 cm.

Thus, volume = base area x length

volume = 1/2 base × height × length

base = 2v/(height × length)

Put the values;

base = 2×2,354.1/(14 × 19)

base = 4708.2/(14 × 19)

base = 17.7 cm

Thus, the base of the triangular prism is found as 17.7 cm.

To know more about the triangular prism, here

brainly.com/question/16128664

#SPJ9

7 0

8 months ago

Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below

Anastaziya [24]

Answer:

Nico

Step-by-step explanation:

In order to compare who had the best performance on the aptitude test, we can use Z score. Z score indicates how many standard deviation a result is over the mean. For this case the higher the result is, the best is the performance on the aptitude test.

Z score is expressed with the following formula:

Z=(X-μ)/σ

Where:

X is the test score

µ is the mean

σ is the standard deviation

Replacing in the formula we obtained

For Nico:

X = 88.3

µ = 66.2

σ = 13

Z=(88.3-66.2)/13=1.7

For Justin:

X = 226.2

µ = 216

σ = 17

Z=(226.2-216)/17=0.6

For Tera:

X = 7.97

µ = 7.2

σ = 0.7

Z=(7.97-7.2)/0.7=1.1

Nico had the higher Z score which means he had the better performance on the test and he should be offered the job.

3 0

2 years ago

Ann sleeps 8 hours per night. Write an expression for the number of hours Ann sleeps in n nights.

lord [1]

8n. 8 represents the number of hours she sleeps, and n represents the number of night she sleeps.

8 0

3 years ago