3-3(x-2)

simplify the expression

They don't need to be pure real or imaginary. Any "mixed" complex number works so long as [tex]z=z'[/tex].

Let [tex]z=z'=a+bi[/tex]. Then

[tex]|z+z'| = |2a+2bi| = 2 \sqrt{a^2+b^2}[/tex]

[tex]|z| + |z'| = 2|a+bi| = 2 \sqrt{a^2+b^2}[/tex]

so [tex]|z+z'|=|z|+|z'|[/tex].

The geometric interpretation is essentially identical. [tex]|z+z'|=2|z|[/tex] is a complex number twice the distance away from the origin in the complex plane as [tex]z[/tex], which is exactly [tex]|z|+|z|[/tex].

Answer: A

Step-by-step explanation:

The polynomial has roots at [tex]x=-4, -2, 4[/tex].

So, the equation should have factors of [tex](x+4), (x-2), (x-4)[/tex].

This eliminates everything except for A.

The trigonometric form of the complex number given in the task content is; 18(isin(π/2)).

If follows from the task content that the complex number whose trigonometric representation is to be determined is; 18i.

Hence, It follows that the trigonometric form is;

= 18(cos(π/2) + isin(π/2)). where; cos(π/2) = 0.

Hence, we have;

= 18(isin(π/2)).

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Answer:

triangle PQR is similar to triangle TSR because the measure of angle 3 is congruent to the measure of angle 4 and the measure of angle one is congruent to the measure of angle 5

Step-by-step explanation:

angle 3 and angle 4 are congruent because they are vertical pairs.

Angles 1 and five are congruent because they are alternate interior angles

Two ares are congruent if they have the same measure and lengths

The statement is given as:

Two ares are congruent if they have the same measure and ?

The conditions for congruent shapes in geometry are;

This means that the angle and the length must be equal

Hence, the term that completes the blank is length

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Since the function is h(t) = −5t² + 15t, the domain of the function h(t) is  0 ≤ t ≤ 3

The domain of a function is the range of input values that make the function have real values.

Now given the function h(t) = −5t² + 15t, it will have real values when

h(t) ≥ 0

So, h(t) ≥ 0

⇒  −5t² + 15t ≥ 0

Factorizing, we have

-5t(t - 3) ≥ 0

5t(t - 3) ≤ 0

t(t - 3) ≤ 0

t ≤ 0 and t - 3 ≤ 0

t ≤ 0 and t ≤ 3

For t ≤ 0, say -1, t(t - 3) = -1(-1 - 3) = -1(-4) = 4 ≥ 0

For 0 ≤ t ≤ 3, say 2, t(t - 3) = 2(2 - 3) = 2(-1) = -2 ≤ 0

For t ≥ 3, say 4, t(t - 3) = 4(4 - 3) = 4(1) = 4 ≥ 0

Since we require  t(t - 3) ≤ 0, the domain of t is thus 0 ≤ t ≤ 3

So, the domain of the function h(t) is  0 ≤ t ≤ 3

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The equation ln 5 = y as an exponential equation is [tex]e^y = 5[/tex]

The natural logarithm equation is given as:

ln 5 = y

Rewrite as:

ln(5) = y

Take the exponent of both sides

[tex]e^{ln(5)} = e^y[/tex]

Evaluate the expression

[tex]5 = e^y[/tex]

Rewrite as:

[tex]e^y = 5[/tex]

Hence, the equation ln 5 = y as an exponential equation is [tex]e^y = 5[/tex]

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The function P(x), for the price of the materials for the pen is 4.18(800/x + x) + 38.

Based on the information, the function P(x), for the price of the materials for the pen will be:

P(x) = 4.18 (2 × 400/x + x) + 38

= 4.18(800/x + x) + 38.

The dimensions will be:

We'll differentiate the function which will give 20✓2. Therefore, the value for x will be 20✓2 which is 28.28 feet and that of y will be 10✓2 which is 14.14 feet.

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Answer:

Brock or separate is located nearly Westside to centure in gives best direction from the central only

Factorization implies the obtaining of the common factors in an expression.

The term factorization implies the obtaining of the common factors in an expression.

The factors of the expressions are as follows;

1) (x−1)(x+7)

2) (x−2)(x−3)

3) (x+1)(x−7)

4) (x−1)(x+6)

5) (x−3)(x+4)

6) (x+2)(x−4)

7) (x+1)(x−5)

8) (x−1)(x+3)

9) (x+4)(x−4)

10) (x+3)(x−4)

11) (x−3)(x−6)

12) (x+2)(x−7)

13) (x−2)(x−5)

14) (x−3)(x−8)

15) (x+5)(x−6)

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Answer:

x = 15 & y = 35

Step-by-step explanation:

[tex]y = x + 20[/tex]

[tex]x + y = 50 \\ x + (x + 20) = 50 \\ 2x + 20 = 50 \\ 2x = 50 - 20 \\ 2x = 30 \\ x = \frac{30}{2} = 15[/tex]

[tex]y = x + 20 = (15) + 20 = 35[/tex]

Based on the information given about the equation, y will be 0.5x + 2.

From the information given, it should be noted that the equation of the line it represents was given and the y intercept is = (0, 2).

The function to represent y will be:

y = mx + b

y = (1/2)x + 2

y = 0.5x + 2

In conclusion, y = 0.5x + 2.

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Answer:

Step-by-step explanation:

Comment

The formula used to figure out the costs is

C(x) = 2885 + 30x

2885 is the total of the fixed costs -

Now the problem gets sort of complicated. If the company could print an unlimited amount of pages, the 2885 remains the same, no matter what.

But x gets larger and larger. and so C(x) gets larger and larger.

Answer

Therefore the average cost would approach infinity.

A

you need 628 square feet of sand.

Here we need to find the volume of the sand needed.

The volume filled with sand will be a cylinder of diameter of 20ft, and a height of 2 inches.

First, the radius is half of the diameter, then:

R = 20ft/2 =10ft

Remember that:

1ft= 12in

Then:

R = 10ft = 10*(12 in) = 120 in

And remember that the volume of a cylinder of radius R and height H is:

[tex]V = pi*R^2*H[/tex]

Where pi = 3.14

Then we have:

[tex]V = 3.14*(120 in)^2*2in = 90,432 in^2[/tex]

To get that in feets, we need to divide by 12 squared, then:

[tex]90,432 in^2 = 90,432ft^2/(12^2) = 628 ft^2[/tex]

So you need 628 square feet of sand.

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Answer:

watch oreimo..

The polynomial function is P(x) = x^3(x + 1)^3(x -1)

The zeros of the polynomial and the multiplicities are given as:

The degree is given as

Degree = 7

The polynomial is represented as:

P(x) = (x - zero)^multiplicity

Using the above format, we have

P(x) = (x + 1)^3(x - 0)^3(x -1)

This gives

P(x) = x^3(x + 1)^3(x -1)

Hence, the polynomial function is P(x) = x^3(x + 1)^3(x -1)

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Answer: 12/4

Step-by-step explanation: whole number = 3. given denominator = 4. 4/4 = 1. 1 times 3 = 3. 4 plus 4 plus 4 = 12. therefore answer is 12/4

The value of y in the triangle is B. 6✓3.

From the information given,

NU = 9

UM = 3

MN = 3 + 9 = 12

NT² = 9 × 12 = 108

NT = ✓108

NT = 6✓3

Therefore, y is 6✓3.

The value of y in the triangle is 6✓3.

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Answer:

B

Step-by-step explanation:

The distance between Ivy's house and the supermarket and the distance between the supermarket and the bank:
H&S = 1,014 M; and S&B = 854m. This is resolved using the Sine Theorem.

Notice that the Angles of a Triangle add up to 180° That is

∠A + ∠B  + ∠C = 180°

Thus,

∠C = 180° - 32° - 109°

= 39°

Recall the Sine Theorem which indicates;

a/SinA = b/SinB = c/SinC

thus given that

AC = 1,523m

We have

AC/SinB = BC/SinA

BC = AC/SinB * SinA

= 1523/Sin109° * Sin32°

BC =854m

Therefore

AC/SinB = AB/SinC
Thus,

AB = AC/SinB * SinC

= 1523/Sin109° * Sin39°
AB ≈ 1,014m

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Considering the hypothesis tested, the interpretation is that there is not enough evidence to conclude that the percentages are different at a significance level of 0.1.

We fail to reject the null hypothesis, hence the interpretation is that there is not enough evidence to conclude that the percentages are different at a significance level of 0.1.

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Answer:

95.7 cm by 126.5 cm

Step-by-step explanation:

To use the scale factor of 0.55, we multiply 174 and 230 by 0.55: 174*0.55 = 95.7,  230*0.55 = 126.5

The area of the circular manufactured good is given by:

[tex]A = 1.8146 \times 10^{16} \text{m}^2[/tex]

The area of a circle of radius r is:

[tex]A = \pi r^2[/tex].

In this problem, the radius in meters is:

[tex]r = 7.6 \times 10^7[/tex]

Hence the area in m² is:

[tex]A = \pi (7.6 \times 10^7)^2 = 181.46 \times 10^{14} = 1.8146 \times 10^{16} \text{m}^2[/tex]

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Answer:

Median

Explanation:

Real estate prices are virtually usually biased to the right. If we estimate the price of a typical home in a city at $500,000. We would have no trouble locating properties for $2 million and $3 million, and perhaps even some $5 or $6 million residences. However, you won't find houses for under $1.5 million. Because of this, the mean value is pulled toward the high end more than the median value.

Answer:

x = 70

Step-by-step explanation:

x and 2x - 30 are supplementary angles , sum to 180° , then

x + 2x - 30 = 180 ( add 30 to both sides )

3x = 210 ( divide both sides by 3 )

x = 70

Answer:

2x - 30 and x degrees should add up to 180 degrees

2x - 30 + x = 180

3x = 210

x = 70 degrees

The correct answer would be D

Answer:

C is 27 and d is 16

Step-by-step explanation:

count how many cubes are on the first level and multiple but how many it goes up too

Using it's concept, it is found that there is a 27.3% probability that someone throws the 11-sided die one time and rolls a number 9 or higher.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 11 numbers, 3 of which are 9 or higher, hence the probability is:

p = 3/11 = 0.273 = 27.3%.

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Answer:

10

Step-by-step explanation:

Answer:

10 apples

Step-by-step explanation:

20% of 50 = 10

10 apples

The area of the kite exists 48 sq. ft.

The area of a kite exists half the outcome of the lengths of its diagonals. The formula to define the area of a kite exists:

Area = ½ × p × q.

Given that a kite contain diagonals of lengths 12 ft and 8 ft.

We know that the area of a kite having diagonals of length 'p' units and 'q' units exists

Area of kite = ½ (p × q)

Here, p = 12 ft and q = 8 ft.

Area of kite = ½ (p × q)

= (12 × 8)/2

= 96/2 = 48

Therefore, the area of the kite will be 48 sq. ft.

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