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erastovalidia [21]
3 years ago
11

Solve x2 + 4x + 8 = 0.

Mathematics
1 answer:
Novosadov [1.4K]3 years ago
5 0
X^2 + 4x + 8 = 0
( x + 2 ) ( x + 2 ) = 0

i am a mathematics teacher. if anything to ask please pm me
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Analyze the graph of the cube root function shown
Greeley [361]

The values of a, h, and k in the general equation is h=1, k=4 and a=2

<h3>What is parent function?</h3>

The function which can be transformed into different ways is the parent function.

On a coordinate plane, a cubic function approaches the x-axis in quadrant 2, crosses the y-axis at (0, 2), has an inflection point at (1, 4), and the goes through (2, 6).

The given function is

y =a³ √(x -h) + k

Put the coordinate (0,2) in the equation, we get

2 = a³ √(0 -h) + k..................(1)

Plug (1, 4), we have

4 =  a³ √(1 -h) + k..................(2)

Plug (2, 6), we have

6 =  a³ √(2 -h) + k..................(3)

On solving these three equations, we have

h=1

k=4

a=2

Thus, value of h is 1, k is 4 and a is 2.

Learn more about parent function

brainly.com/question/17939507

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7 0
1 year ago
Frank grows evergreen trees. He grew 535 trees for
TiliK225 [7]

Answer:

  1. Frank grows 535 trees during holiday season
  2. in November sold 215
  3. then dec sold 275
  4. 535 minus 490 which gives a total of 45 trees left
  5. then to find out how many trees he will have next season 650 plus 45 gives 695
3 0
2 years 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 hockey goalie got shot on 18 times . She saved 10 of the shots . Which ratio represents the amount of shots that went in to th
vredina [299]
<h3>Answer is   4:5</h3>

========================================================

Explanation:

She saved 10 shots out of 18 total, so that means 18-10 = 8 shots went in.

That forms the ratio 8:10 where we list the amount of shots that went in, followed by a colon, then the amount of shots that were saved. The order is important. From here, we divide both parts of the ratio by 2. The ratio 8:10 fully reduces to 4:5

Effectively, this means that for every 4 shots that went in, there were 5 shots that were blocked.

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3 years ago
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