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3 years ago

Which best explains why the equation 7×+3=7×+3 has infinitely many solutions

Mathematics

1 answer:

madreJ [45]3 years ago

4 0

Left and right side are exactly same, therefore "the equation is true for any value of x."

Option B

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Carl solved 20 math problems in 55 minutes how many math problems will carl solve in 75mins

-BARSIC- [3]

You need to find out how many problems Carl can do in a minute (unit rate), which is 20/55 or .36363636363. If you multiply it by 75 mins, you get 27.27, so the answer would be 27.

5 0

3 years ago

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A teacher recorded the number of days her students went on vacation. Which statements describe the data? Select all that apply.

laiz [17]

Answer:

The students went on vacation for average 40 days.

The high school students went for more days than college students.

Step-by-step explanation:

The data shows number of students who went for vacation. The data class frequency shows that students who are in high school went for more days in vacation than college students. The students went for average of 40 days on vacation.

7 0

3 years ago

Find the complex fourth roots of 81(cos(3pi/8) + i sin(3pi/8))

BartSMP [9]

By using De Moivre's theorem:

If we have the complex number ⇒ z = a ( cos θ + i sin θ)
∴ $\sqrt[n]{z} = \sqrt[n]{a} \ (cos \ \frac{\theta + 360K}{n} + i \ sin \ \frac{\theta +360k}{n} )$
k= 0, 1 , 2, ..... , (n-1)

For The given complex number ⇒ z = 81(cos(3π/8) + i sin(3π/8))


Part (A) find the modulus for all of the fourth roots

∴ The modulus of the given complex number = l z l = 81

∴ The modulus of the fourth root = $\sqrt[4]{z} = \sqrt[4]{81} = 3$

Part (b) find the angle for each of the four roots

The angle of the given complex number = $\frac{3 \pi}{8}$
There is four roots and the angle between each root = $\frac{2 \pi}{4} = \frac{\pi}{2}$
The angle of the first root = $\frac{ \frac{3 \pi}{8} }{4} = \frac{3 \pi}{32}$
The angle of the second root = $\frac{3\pi}{32} + \frac{\pi}{2} = \frac{19\pi}{32}$
The angle of the third root = $\frac{19\pi}{32} + \frac{\pi}{2} = \frac{35\pi}{32}$
The angle of the fourth root = $\frac{35\pi}{32} + \frac{\pi}{2} = \frac{51\pi}{32}$

Part (C): find all of the fourth roots of this

The first root = $z_{1} = 3 ( cos \ \frac{3\pi}{32} + i \ sin \ \frac{3\pi}{32})$
The second root = $z_{2} = 3 ( cos \ \frac{19\pi}{32} + i \ sin \ \frac{19\pi}{32})$

The third root = $z_{3} = 3 ( cos \ \frac{35\pi}{32} + i \ sin \ \frac{35\pi}{32})$
The fourth root = $z_{4} = 3 ( cos \ \frac{51\pi}{32} + i \ sin \ \frac{51\pi}{32})$

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3 years ago

The following triangle. check all that apply

Amiraneli [1.4K]

Obtuse and isosceles

Isosceles means that at least two of the sides are congruent or equal.

Obtuse means that one angle of the triangle is greater than 90 degrees.

So, your answer is D and E

:)))

4 0

3 years ago

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Philip’s meal costs $12.82 at a local restaurant. The server did their job very well and Philip would like to leave a 20% tip. W

Elodia [21]

Answer:

$2.56

Step-by-step explanation:

If you multiply 12.82 by .20, you would get 2.564. Then you just round it up and the answer you get is $2.56. Hope this helps!

8 0

3 years ago