Simplify: [(13 + 8) ÷ 3] − 4 =

Step-by-step explanation:

i¹ = i

i² = i×i = -1

i³ = -1 × i = -i

i⁴ = -i×i = - -1 = 1

i⁵ = 1×i = i

...

so, when the exponent of i modulo 4 (the remainder when dividing by 4) = 0, then the result is 1.

= 1, then the result is i

= 2, then the result is -1

= 3, then the result is -i

233 modulo 4 = 1 (233/4 = 58, remainder 1).

so, the result is i (the third answer option).

Work Shown:

[tex]a^2 + b^2 = c^2\\\\a^2 + 5^2 = 8^2\\\\a^2 + 25 = 64\\\\a^2 = 64-25\\\\a^2 = 39\\\\a = \sqrt{39}\\\\a \approx 6.244998\\\\a \approx 6.2[/tex]

Answer:

p=9

t20=516

Step-by-step explanation:

a

4p-60=2p-6-2p

6p=54

p=9

b

a=60.. d=24

t20=a+19d

=60+19×24

=516

c

Sn=12.5+12.3+12.1

=12n(6-n)

Answer: the answer is 150 :)

Step-by-step explanation: Volume of a cone is

V = 1/3 pi * r^2 *h

The volume of one cone is

pi = 3.14

r = d/2 = 6/2 =3

h=9

Substitute what we know

V = 1/3 * (3.14) * (3^2) * (9)

  = 27* 3.14

  = 84.78  cm^3

The water cooler has 12717 cm^3 water

Divide the water by the volume of the paper cup cone  and we will know how many paper cup cones we can fill, assuming we fill them completely.

12717/ 84.78 = 150

We can fill 150 paper cup cones. have a great day!

Step-by-step explanation:

so, the garden seems to be rectangular.

it has a length.

and width = length - 2

I assume the fence should go all around the rectangular garden.

that means it has to cover 2 lengths and 2 widths.

fence = 2×length + 2×(length - 2) =

= 2×length + 2×length - 4 = 4×length - 4 =

= 4×(length - 1)

length = 7.5 m

so, he will need

4×(7.5 - 1) = 4×6.5 = 26 meter of fencing.

Answer:

4, 4, 4, 4, and 4

Step-by-step explanation:

mode = 4

median = 4

so we know two of the five numbers are 4;

[tex](x+x+x+4+4)/5 =4[/tex]

[tex](3x+8x)/5 = 4[/tex]

multiply both sides by 5

[tex]3x+8=20\\3x=20-8\\3x=12\\x=4\\[/tex]

therefore; the numbers are all 4

Explanation:

On the die, the divisors or factors of 20 are: 1, 2, 4, 5

We have 4 faces we want out of 6 faces total

So 4/6 = 2/3 is the probability of getting a divisor of 20.

The cost of a full-length mirror when the cpi is 211 is $187.68. Then the correct option is C.

A ratio is an ordered couple of numbers a and b, written as a/b where b can not equal 0. A proportion is an equation in which two ratios are set equal to each other.

A full-length mirror cost $144.99 when the cpi was 163.

The cost of a full-length mirror when the cpi is 211, to the nearest cent will be

[tex]\dfrac{x }{211} = \dfrac{144.99}{163}\\\\x \ \ \ = \$187.68[/tex]

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762

Answer:

not similar

Step-by-step explanation:

4/3 = 1.3333...

10/8 = 1.25

The ratios are not equal, so the triangles are not similar.

The  two numbers are 8 and 13 and the system of equations are x + y = 21 and xy = 104

Let the two unknown numbers be x and y

If the sum of the numbers is 21, hence;

x + y = 21

x = 21 - y

If the product is 104, then;

xy = 104
(21-y)y = 104

21y - y^2 = 104
y^2-21y + 104 = 0

Factorize the result

y^2-8y - 13y+ 104 = 0
y(y-8) - 13()y-8) = 0
y = 13 and 8

Hence the two numbers are 8 and 13 and the system of equations are x + y = 21 and xy = 104

Learn more on system of equation here:  https://brainly.com/question/847634

Answer:

(5,3)

Step-by-step explanation:

Use desmos. I'll attach the graph below.

Solution is:

(5,3)

Answer:

4/3

Step-by-step explanation:

f(2) = (-2*2)^2 / (7(2))-4)

f(2) = (-4)^2 / 14-4

f(2) = 16 / 12

f(2) = 4 / 3

Answer:

Roy eat 4 sweets

Step-by-step explanation:

Roy =R

Mike= (R-2)

Leen= 3(R+ R-2)

R + (R-2) + 6R-6 = 24

8R-8=24

8R=32

R=4

     Mike  4-2 = 2

     Leen 3(4+2) = 18

4+2+18=24

Answer:

So there are 2 pi radians in one revolution and since there are also 360 degrees in one revolution, this gives us a way to convert from radians to degrees. 2 pi radians equals 360 degrees or you can divide both sides by 2 and use pi radians equals 180 degrees.

Answer:

1/52.

Step-by-step explanation:

The suit AND the number must be correct.

When you see AND in a probability question think 'multiply'.

That would be 13/52 * 4/52

= 52/(52)^2

= 1/52.

The height of the shot starts to increase when x is -5 feet, It continues to increase until x = 10 feet and then the height decreases until x = 25 feet

An equation is an expression that shows the relationship between two or more numbers and variables.

Let h(x) represent the height of the shot put, when the horizontal distance is x feet.

h(x)= -0.05x² + x + 6

From the graph of h(x):

The height of the shot starts to increase when x is -5 feet, It continues to increase until x = 10 feet and then the height decreases until x = 25 feet

Find out more on equation at: https://brainly.com/question/2972832

Answer:

x=4

y=1

Step-by-step explanation:

4x=7y+9

4x+y=17

7y+9+y=17

8y=17-9

8y=8

y=1

so

4x=7*1+9

4x=16

x=16/4

x=4

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: \sin(40 - x) = \cos(3x) [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cos\{90 - (40 - x ) \} = \cos(3x) [/tex]

[tex]\qquad \sf  \dashrightarrow \:90 - (40 - x) = 3x[/tex]

[tex]\qquad \sf  \dashrightarrow \:90 - 40 + x = 3x[/tex]

[tex]\qquad \sf  \dashrightarrow \:3x - x = 50[/tex]

[tex]\qquad \sf  \dashrightarrow \:2x = 50[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 25 \degree[/tex]

Answer: c = -28

Step-by-step explanation:

substitue x for 2

2(2^2) + 10(2) + c = 0

8 + 20 + c = 0

28 + c = 0

c = -28

The value of coefficient c of the quadratic equation 2x^2+10x+c=0  is -28.

One of the roots of the quadratic equation 2x^2+10x+c=0 is equal to 2.

The roots of a quadratic equation are the values of the variable that satisfy the equation.

They are also known as the solutions or zeros

The equation is 2x^2+10x+c=0.

a=2, b=10 and c=?

To substitute x for 2

2(2^2) + 10(2) + c = 0

8 + 20 + c = 0

28 + c = 0

c = -28

To learn more about the quadratic equation visit:

https://brainly.com/question/1214333

Answer:

 A)  1

Step-by-step explanation:

We want to find G such that ...

 (G-F)/(D-G) = 8/5

 5(G-F) = 8(D-G)

 5G -5F = 8D-8G . . . . eliminate parentheses

 13G = 8D +5F . . . . . . add 5F +8G to both sides

 G = (8D +5F)/13 . . . . divide by the coefficient of G

 G = (8(-4) +5(9))/13 = (-32 +45)/13 = 13/13

 G = 1 . . . . . . matches choice A

Answer:

A

Step-by-step explanation:

EDGE 22

Answer:

3.

Step-by-step explanation:

remember, when we multiply the same basic term, we add the exponents.

so,

x⁴×x² = x⁶

now, when there are other factors, we need to multiply them in too.

so,

(6x⁴)(3x²) = 6×3×x⁴×x² = 18x⁶ or simply (6×3)x^(4+2)

1)

[tex]x = 25 - \frac{2}{3} y[/tex]

[tex]y = 37.5 - 1 \frac{1}{2} x[/tex]

2)

[tex]x = 1 + 2y[/tex]

[tex] y = \frac{1}{2} - \frac{1}{2} x[/tex]

Work Shown:

[tex](x-5)^2+2=11\\\\(x-5)^2=11-2\\\\(x-5)^2=9\\\\x-5=\pm\sqrt{9}\\\\x-5=\pm3\\\\x=5\pm3\\\\x=5+3 \text{ or } x = 5-3\\\\x=8 \text{ or } x = 2\\\\[/tex]

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's solve ~

Total Mini - Easter eggs = 1345

Number of students = 26

So, let's find how many eggs will each student get through division ~

[tex]\qquad \tt  \dashrightarrow \: \dfrac{1345}{26} = 51 +remainder= 19[/tex]

So, each student will get 51 mini - Easter egg each.

And there would be 19 remaining eggs in there ~

Answer:

8x+5

Step-by-step explanation:

8x + 8 + (-3) = 8x+8 - 3 = 8x + 5.

Hope this helps!

Also, please mark as brainliest!

Answer:

The answer is 8x+5

Step-by-step explanation:

1. Combine like terms so it will be 8 and -3

2. this will leave you with 8x+5 which you cannot do anything further.

Here is how it is graphed:

Answer:

The circumference of a circle with diameter 4 is 12.57.