Solve by completing the square:
x2 + 3x – 9 = 0

Answer:

1

Step-by-step explanation:

note that i² = - 1

Thus

[tex]i^{8}[/tex]

= i² × i² × i² × i²

= - 1 × - 1 × - 1 × - 1

= 1 × 1

= 1

The value of complex number is 1. Therefore, the option B is the correct answer.

A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z.

The given complex number is i⁸.

We know that, i²=-1

Now, i⁸ can be written as i²×i²×i²×i²

= -1×(-1)×(-1)×(-1)

= 1

Therefore, the option B is the correct answer.

To learn more about the complex numbers visit:

https://brainly.com/question/10251853.

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Answer:

3 * 5 ^ (n-1)

Step-by-step explanation:

3 is the first term and it multiplies by 5

The explicit formula for the geometric sequence is [tex]T_n = 3(5)^{n-1}[/tex]

The standard explicit formula for  a geometric sequence is expressed as:

[tex]T_n = ar^{n-1}\\[/tex]

a is the first term

r is the common ratio

n is the number of terms

Given the sequence of numbers 3, 15, 75, 375...

r = 15/3 = 75/15 = 5

a = 3

Substitute the given parameters into the formula to have:

[tex]T_n = ar^{n-1}\\T_n=3(5)^{n-1}[/tex]

Hence the explicit formula for the geometric sequence is [tex]T_n = 3(5)^{n-1}[/tex]

Learn more here: https://brainly.com/question/20548958

Answer:

(B)

Step-by-step explanation:

The value of 9 is more than the value than 4.

Therefore,

9 > 4.

4 is not greater than 9, and nine is not less than four.

Brainilest Appreciated!

Answer:

6 4/5

Step-by-step explanation:

-1 3/7 • (-3 2/5)

Let's turn them both into fractions with no whole numbers to make this easier:

-10/7 • -17/5

Now we can multiply straight across much easier!

170/35 (the negatives canceled each other out)

34/5 (simplified)

6 4/5 (answer)

Hope this helps! Please mark Brainliest :)

Step-by-step explanation:

First we will calculate the total amount spent on each website so

Website A = 49.95 + 4.39 = 54.34

Website B = 47.68 + 6.95 = 54. 63

So website A is cheaper by €0.29

Answer:

3.5

Step-by-step explanation:

0 1 1 3 3 3 4 5 7

median= 3

Q1= 1

Q3= 4.5

4.5-1= 3.5

Answer:3.5

0,1,1,3,3,3,4,5,7

Answer:

If a runner went around the track 3 times, he would have ran 3/4 of a kilometre. He would have to run around the track 8 times to run 2 kilometres.

Step-by-step explanation:

Answer:He would have to go around the track 8 times to get 2 kilometers

Step-by -step explanation:

Inverse operations are an operation that undoes each other. For example, addition and subtraction, multiplication and division, squares and square roots.

For example, we have the equation:

2 + 2 = 4

The inverse of this equation is:

4 - 2 = 2

Best of Luck!

Answer:

1. Arc angle

2. Angle at circumference

3. Base angle of an isosceles triangle

4. Sum interior of angles in a triangle

5. Sum interior of angles in a triangle

6. The sum of angles on a straight line

7. Sum interior of angles in a triangle

8. Sum interior of angles in a triangle

9. Angle from a tangent to the radius of a circle

10. Alternate angles of line crossing two parallel lines

Step-by-step explanation:

Here, we note that, the angles where derived as follows;

1. mBC = 90°, therefore, angle subtended by the arc BC at the center of the circle = 1 = 90°

2. 90° The angle at the center which is the straight line diameter with angle 180° = 2 × angle at the circumference

∴ The angle at the circumference, angle 2 = 180°/2 = 90°

3.  Angle subtended by the sum of arcs CD + DE at the center = 50°, therefore, ∡EOC = 50° and ∡EOA = 180° - 50° = 130° (the sum of angles on a straight line), since ΔAOE is an isosceles triangle, therefore, ∡OAE = ∡OEA = (180° - 130°)/2 = 25°

4. ∡A + ∡E + ∡C = 180° (Sum interior of angles in a triangle)

∴ 25° + 90° + ∡C = 180°

Hence ∡C = 180° - (90° + 25°) = 65°

5. From arc CD = 30°, ∡COD = 30°, ∴ ∡OBD = 30° = base angle of isosceles triangle with sides equal to the radius

Hence ∡8 = 30° from ∡8 + ∡1 + ∡OBD = 180° which gives

∡8 + 90° + 30° = 180°, hence;

∡8 = 180° - (90° + 30°) = 60°

∡8 = opposite ∡8 = 60°

Opposite ∡8 + ∡C + ∡5 = 180° (Sum interior of angles in a triangle)

Therefore ∡5  = 180° - (opposite ∡8 + ∡C) = 180° - (60° + 65°) = 55°

6. Angles 6 plus angle 5 = 180° (The sum of angles on a straight line)

Therefore, ∡6 = 180° - ∡5 = 180° - 55° = 125°

7. ∡7 + opposite ∡5 + ∡E = 180° (Sum interior of angles in a triangle)

∡E + ∡2 = 180° (The sum of angles on a straight line)

∴ ∡E = 180° - ∡2 = 180° - 90° = 90°

Hence, ∡7 + opposite ∡5 + ∡E = 180° = ∡7 + 55° + 90° = 180°

∴ ∡7 = 35°

8. ∡8 = 60° as found above

9. ∡9 = 90° (Angle from a tangent to the radius of a circle)

10. ∡10 = ∡8 = 60° (Alternate angles).

Answer:

To find the x-intercept of a given linear equation, plug in 0 for 'y' and solve for 'x'. To find the y-intercept, plug 0 in for 'x' and solve for 'y'.

Answer:

C

Step-by-step explanation:

A, B, and D don't make sense

Answer:ones

Step-by-step explanation:

Answer:

d, c and a

Step-by-step explanation:

O///O

Answer:

D

Step-by-step explanation:

A linear function has a constant slope. Meaning that for any equal change in x, there will be an equal change in y.

Answer:

C. 24 degrees

Step-by-step explanation:

All triangle must be 180 degrees in total. So you have to add all the known degrees together to find the missing degree.

120+36=156

Then subtract the sum of the known angles from 180 to find the degree of the unknown angle

180-156=24

Answer: C

Step-by-step explanation:

I'll explain why.

The sum of the angles in a triangle must be equal to 180º. We already know 2 of the 3 angles, therefore, we can make an equation to find x.

The sum of the angles (x+36+120) must be equal to 180 (=180)

x+36+120=180

Combine like terms

x+156=180

Subtract 156 to isolate x

x=180-156

x=24

Answer:

See explanation

Step-by-step explanation:

[tex] In\: \triangle ABC \:\&\: \triangle EDC\\

\angle ABC \cong \angle EDC... (Right \: \angle s) \\

\angle ACB \cong \angle ECD... (Vertical \: \angle s) \\\therefore \triangle ABC \sim \triangle EDC... (By\: AA\: Postulate) \\[/tex]

Answer: Bristol's heart rate reaches a maximum of 120

bpm

Step-by-step explanation:

Answer:

Bristol's heart rate reaches a maximum of 120 bpm

At the end of yoga class, Bristol's heart rate returned to her resting heart rate

The graph that models Bristol's heart rate is a parabola

Step-by-step explanation:

Answer:

Value of x = 25

Step-by-Step Explanation:

~ Knowing that, in a right triangle ~

sin(40-x)=cos(3x) ⇒

sin(40-x)=sin(90-3x) ⇒

40 - x = 90 - 3x ⇒

40 - x  +3x=90 - 3x  +3x =>

40+2x=90 =>

2x=50 =>

x = 25

Now it is proven to be that,

x = 25

The rectangle is 28×34 and the two triangles are (1/2) 11 (28) and (1/2) (9)(34)

A = 28(34) +  (1/2) 11 (28) + (1/2) (9)(34)

A = 1259

Answer: 1259 sq units

Step-by-step explanation:

answer of (ii) : perimeter = 66m

area = 272m^2

Answer:

12π

Step-by-step explanation:

Volume of the cone is πr^2 * h / 3

r = 3

h = 4

9π * 4 / 3 = 12π

Answer: 37.6991118

Step-by-step explanation:

Answer:825

Step-by-step explanation:

Answer:

p > 6

Step-by-step explanation:

Given

[tex]\frac{p}{3}[/tex] > 2 ( in fractional form )

Multiply both sides by 3 to clear the fraction

p > 6

Answer:

honestly idk

Step-by-step explanation:

it may be p (1/3)

hope this is right:000

Answer:

v-19

Step-by-step explanation:

Answer:

It depends on what you mean.

Step-by-step explanation:

If its to separate questions,

1-2= 1

V-18= -13

If its one whole question then

1-2 - V-18= 14

1-2 / V-18= -0.07692307692

1-2 * V-18= -13

1-2 + V-18= -12

Hope this helps! :D

Answer:

The difference between the number of expected outcomes and the number of actual outcomes = 5

Step-by-step explanation:

She tosses a two sided counter and spins a spinner with six equal sized sections numbered 1 to 6.

Probability of the counter landing on either of the two sides is exactly = (1/2)

Probability of the counter landing on the red side = (1/2)

Probability of the spinner landing in a region greater than 3 = Probability of the spinner landing in a region of 4, 5 or 6. = (3/6) = (1/2)

In one toss and spin, the probability of a toss landing on red and the spinner landing on a number greater than 3 = p = (1/2)×(1/2)

p = (1/4)

Expected number of times that a toss will land on a red and a spinner will land on a number greater than 3 in 80 trials

= np = 80 × (1/4) = 20

Number of actual times that the toss lands on a red and a spinner lands on a number greater than 3 in 80 trials = 25

The difference between the number of expected outcomes and the number of actual outcomes = 25 - 20 = 5

Hope this Helps!!!

Answer:

3.5

Step-by-step explanation:

26, 31, 32, and 39

First we need to find the mean

(26+ 31+ 32+ 39) /4

128/4 = 32

The mean absolute deviation is sum of   the positive difference between the number and the mean  divided by the number of terms

((32-26)+ (32-31)+ (32-32)+ (39-32)) /4

14/4

3.5

Answer:

R = 152

Step-by-step explanation:

what i did was if it is talking about more than 48 something plus 48 is 200 so

200 - 48 = 152

r = 152

so 200 is 152 more than 48

Answer:

A) Dilation  C)Reflections or B) Rotations

Step-by-step explanation:

Answer:

story 1

Step-by-step explanation:

because it says 2 higher than -2 so -2+2 is 0

Answer:

The simple interest rate on the student loan is 6%.

Step-by-step explanation:

To solve for the simple interest rate, use the formula for total simple interest:

[tex]I = Prt[/tex]

[tex]I[/tex] = total interest paid

P = principal, or starting value

r = interest rate in decimal form

t = time in years

State known values

P = 12,000

t = 5

[tex]I[/tex] = 3,600

Substitute known values and isolate "r"

[tex]I = Prt[/tex]

3,600 = (12,000) (r) (5)

3,600 = (60,000) r

r = 0.06

Since "r" is given as a decimal, convert this to a percentage by multiplying by 100.

0.06 = 6%

∴ The simple interest rate on the student loan is 6%.

Answer=6%

Step-by-step explanation:

Principal(P)=12000

Time(T)=5  yrs

Interest(I)=3600

We have,

I=PTR/100

3600=(12000*5*R)/100

3600*100=60000*R

R=360000/60000

R=6%