Someone please help me with 13 and 14 I’m really struggling

Answer:

Step-by-step explanation:

[tex]Z_1=3+i\\Z_2=6\\Z_3=4+4i\\\\||Z_2\ Z_1||^2=||-3+i||^2=9+1=10\\\\||Z_1\ Z_3||^2=||1+3i||^2=10\\\\||Z_2\ Z_3||^2=||-2+4i||^2=20\\\\And\ 10+10=20[/tex]

Using the converse of the Pythagorean's theorem, the triangle is right.

Using Pythagorean theorem, the points 3 + i, 6, and 4 + 4i indeed form the vertices of a right triangle.

The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse).

Let's calculate the distances between the points and then check if the Pythagorean theorem holds for them.

Distance between points A (3 + i) and B (6):

Distance AB = |6 - (3 + i)|

                     = |6 - 3 - i|

                     = |3 - i|

                     = [tex]\sqrt{(3^2 + (-1)^2)[/tex]

                     = √10

Distance between points A (3 + i) and C (4 + 4i):

Distance AC = |4 + 4i - (3 + i)|

                     = |1 + 3i|

                     = [tex]\sqrt{(1^2 + 3^2)[/tex]

                     = √10

Distance between points B (6) and C (4 + 4i):

Distance BC = |4 + 4i - 6|

                     = |-2 + 4i|

                     = [tex]\sqrt{((-2)^2 + 4^2)[/tex]

                     = √20

Now let's check if the Pythagorean theorem holds for these distances:

Longest side: [tex]BC^2 = (\sqrt20)^2 = 20[/tex]

Sum of squares of shorter sides:

[tex]AB^2 + AC^2 = (\sqrt10)^2 + (\sqrt10)^2[/tex] = 10 + 10 = 20

Since the sum of the squares of the shorter sides is equal to the square of the longest side.

So, the points 3 + i, 6, and 4 + 4i are vertices of a right triangle.

Learn more about Pythagorean theorem here:

https://brainly.com/question/28361847

#SPJ3

Answer:

Answer is 2x^2 + 1x - 15

Step-by-step explanation:

12x because you multiply it

Answer:

Her younger brother is 11 years old

Step-by-step explanation:

35=3+2x

35-3=2x

32=2x

32÷2=2x÷2

11=x

9514 1404 393

Answer:

  (a)  2 + 2n

Step-by-step explanation:

If n represents the number, then "2 times a number" is 2n. Two more than that is ...

  2 + 2n

Answer:

1

because 1 times anything is that number!

Step-by-step explanation:

Answer: 9 or 3

Step-by-step explanation:

Step-by-step explanation:

[tex]3 {x}^{2} + 18x - 81 = 0 \\ \\ {x}^{2} + 6x - 27 = 0 \\ (x - 3)(x + 9) = 0 \\ x - 3 = 0 \: \: \: \: \: x + 9 = 0 \\ x = 3 \: \: \: \: x = - 9[/tex]

Answer:

10

Step-by-step explanation:

|5-9|+2*3

lets use the P.E.M.D.A.S order of operations rule

we have no parenthesis or exponents, so we skip to multiplication

2*3=6

then we do addition/subtraction

since the subtraction sign comes first in the equation, we evaluate

5-9=-4

since the subtraction part is in the absolution value signs, we change -4 to its absolute value.

|-4|=4

now we are left with 4+6

add

4+6=10

so, |5-9|+2*3=10

Answer:

81.64 cm

Step-by-step explanation:

c = 2(3.14) x 13

c = 6.28 x 13

c = 81.64

Step-by-step explanation:

1. m = (9-3)/(2-1) = 6/1 = 6 => B

2. m = (-7-5)/(2+1) = -12/3 = -4 => G

3. the horizontal line passes (0,4) => m = 0 =>I

4. m = (2-1)/(8-8) = 1/0 = oo => undefined => A

the answer would be

A. 53-53i !! :)

it was also the correct answer on the test ,, goodluck !!

Answer = B. -17 -53i

Answer:

1.) C. 32

2.) Stem-and-leaf plot

Step-by-step explanation:

    This is a stem-and-leaf plot. The stem represents tens and the leaves represent units. To make it easier to look at, it is equivalent to this:

    Now, to find the mean, add up all the numbers and divide the sum by the number of values.

(20 + 28 + 29 + 29 + 31 + 32 + 36 + 41 + 42)/9 = 288/9 = 32

[tex]\\ \sf\dashrightarrow \dfrac{x+20}{2}=3x[/tex]

[tex]\\ \sf\dashrightarrow x+20=2(3x)[/tex]

[tex]\\ \sf\dashrightarrow x+20=6x[/tex]

[tex]\\ \sf\dashrightarrow 20=6x-x[/tex]

[tex]\\ \sf\dashrightarrow 5x=20[/tex]

[tex]\\ \sf\dashrightarrow x=\dfrac{20}{5}[/tex]

[tex]\\ \sf\dashrightarrow x=4[/tex]

Answer:

69°

Step-by-step explanation:

4x3 = 12

81 - 12 = 69

69°

Answer:

[tex]12[/tex]

Step-by-step explanation:

[tex]3\times 7-3\times 3[/tex]

This term's numerical factors have been multiplied:-

[tex]=12[/tex]

OAmalOHopeO

Answer:

X= –10

[tex] \frac{1}{2} x - 5 = - 10 \\ \frac{1}{2} x = - 10 + 5 \\ \frac{1}{2} x = - 5 \\ x = - 5 \times 2 \\ x = - 10[/tex]

I hope I helped you^_^

Answer:

2, 4, 26, 142, 788

Step-by-step explanation:

Using the recursive rule and t₁ = 2, t₂ = 4 , then

t₃ = 5t₂ + 3t₁ = 5(4) + 3(2) = 20 + 6 = 26

t₄ = 5t₃ + 3t₂ = 5(26) + 3(4) = 130 + 12 = 142

t₅ = 5t₄ + 3t₃ = 5(142) + 3(26) = 710 + 78 = 788

First 5 terms are 2, 4, 26, 142, 788

a=65° d=75° b=25° c=25°

Answer:

a=65° d=75° b=25° c=25°

Step-by-step explanation:

Have a good day

-Bradi

Answer:

P) = 1/2 jawbreaker

simplified P) 3/6 = 1/2 jawbreaker

Which both mean the same, so show simplified if asked and either answer if not asked would be marked high.

as 2/6 + 1/3 = 3/6

1 - 3/6 = 3/6

= 1/2    are the workings.

Step-by-step explanation:

Jelly bean = 1/3 = 2/6

Gumdrop = 1/6

2/6 + 1/6 = 3/6 = the difference of 1

1-3/6 = 3/6

Therefore; P) = 3/6 jawbreaker

Answer:

7, 7, 6, 6

Step-by-step explanation:

Answer:

6.6.7.7

Step-by-step explanation:

that is we remove the subtract sign (negative sign)

Find the distance between A and B, AB,

[tex]AB=\sqrt{(3-3)^2+(-2-8)^2}=10[/tex]

Next, find the distance between B and C, BC,

[tex]BC=\sqrt{(t-3)^2+(1-2)^2}=\sqrt{(t-3)^2+1}[/tex]

The equation is,

[tex]10=2\sqrt{(t-3)^2+1}[/tex]

[tex]25=(t-3)^2+1[/tex]

[tex]t^2-3t+10=25[/tex]

[tex]t^2-3t-15=0[/tex]

Use quadratic formula to get possible values of t,

[tex]t_1=\frac{3+\sqrt{69}}{2}[/tex]

[tex]t_2=\frac{3-\sqrt{69}}{2}[/tex]

Hope this helps :)

Answer:

71.1 vreels on the farm

Step-by-step explanation:

Create a proportion where x is how many vreels are on the farm:

[tex]\frac{9}{8}[/tex] = [tex]\frac{80}{x}[/tex]

Cross multiply and solve for x:

9x = 640

x = 71.1

So, to the nearest tenth, there are 71.1 vreels on the farm.

Answer:

1-3-9+4-5

Step-by-step explanation:

Its 1

Doubled:-

[tex]\\ \rm\longmapsto 1\times 1=1=1^3[/tex]

[tex]\\ \rm\longmapsto 1\times 1\times 1=1=1^2[/tex]

Answer:

You have a 60% chance if obtaining tails

Step-by-step explanation:

30-12=18

30x60%=18

18 times of obtaining tails means you have a 60% chance of obtaining tails