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3 years ago

What is the equation to solve this problem?

Mathematics

1 answer:

andrey2020 [161]3 years ago

5 0

$\displaystyle\bf\\x^2+x^2=10^2\\\\2x^2=19^2\\\\x^2=\frac{10^2}{2}\\\\ \sqrt{x^2}=\sqrt{\frac{10^2}{2}}\\\\x=\frac{10\sqrt{2}}{\sqrt{2}\times\sqrt{2}}\\\\x=\frac{10\sqrt{2}}{2}\\\\\boxed{\bf x=5\sqrt{2}~~~~~~Correct~ansver:~~D)}$

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Plot and connect the following points: P(1, −4), Q(5, −2), R(9, −4), S(7, −8), and T(3, −8). Give the best name for the polygon,

Citrus2011 [14]

Answer:

The area of the pentagon is = 31.5

Step-by-step explanation:

First, we determine the perimeter of the "Pentagon" drawn in the attachment:

$p=4+4+4+4.5+4.5=21$

Now, we'll check the formula for pentagons:

$a=\frac{perimeter x apothem}{2}$

we calculate the apothem by placing a 90° angle in one of the sides of the shape. It is equal to:

apothem=3

then, we can substitute the values in the formula

$a=\frac{21(perimeter) x 3(apothem)}{2} =\frac{63}{2} =31 \frac{1}{2} or 31.5$

Let me know if you have questions :D

7 0

3 years ago

How do you work the square root of 29

Zepler [3.9K]

Answer: 14.5

Step-by-step explanation:Divide the number (29) by 2 to get the first guess for the square root . 29/2 = 14.5

hope it helps thx for the points :)

4 0

3 years ago

What is the probability of selecting a black card or a red card from a standard 52-card deck of cards?

Cloud [144]

Answer:

7/13

Step-by-step explanation:

5 0

3 years ago

A rectangle has one side of 10cm. How fast is the area of the rectangle changing at the instant when the other side is 12 cm and

melomori [17]

10x12 = 120
10x15 = 150
10x18 = 180 and so on.
The answer is that the area of the rectangle increase by 30 cm every minute!

8 0

3 years ago

Let z1 = 2 − 2i and z2 = (1 − i) + √3(1 + i).

gtnhenbr [62]

Answer:

Step-by-step explanation:

z₁ = 2 − 2i

z₂ = (1 − i) + √3(1 + i) = (1 + √3) + (√3 - 1) i

a) We get the modulus of z₁ as follows

║z₁║ = √((2)²+(-2)²) = 2

now we find the argument

α = Arctan (-2/2) = Arctan (-1) = -45º ⇒ α = 360º + (-45º) = 315º

b) z₁ = 2 Cis 315º

Although the complex number is in binomic or polar form, its representation must be the same, since the complex number is the same, only that it is expressed in two different forms. The modulus represents the distance from the origin to the point. The degree of rotation is the angle from the x-axis. When the polar form is expanded, the result is the rectangular form of a complex number.

c) If z₀*z₁ = z₂ and z₀ = a + b i

we have

(a + b i)*(2 − 2i) = (1 + √3) + (√3 - 1) i

⇒ 2a + 2bi - 2ai - 2bi² = (1 + √3) + (√3 - 1) i

⇒ 2a + 2bi - 2ai - 2b(-1) = (1 + √3) + (√3 - 1) i

⇒ 2a + 2b + 2bi - 2ai = (1 + √3) + (√3 - 1) i

⇒ 2 (a + b) + 2 (b - a) i = (1 + √3) + (√3 - 1) i

Now we can apply

2 (a + b) = 1 + √3

2 (b - a) = √3 - 1

Solving the system we get

a = 1/2

b = √3 / 2

Finally

z₀ = (1/2) + (√3 / 2) i

d) ║z₀║ = √((1/2)²+(√3 / 2)²) = 1

α = Arctan ((√3 / 2)/(1/2)) = 60º

e) z₀ = Cis 60º

f) Since z₂ = z₀*z₁, then z₂ is the transformation of z₁ rotated counterclockwise by arg(w) which is 60º

8 0

3 years ago