what's the domain of the function?

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The product of the complex numbers 65(cos(14°)+ i sin(14°)) and 8(cos(4°)+ i sin(4°)) is 520[cos(18) + isin(18)]

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

Complex number is in the form z = a + bi, where a and b are real numbers.

The product of the complex numbers 65(cos(14°)+ i sin(14°)) and 8(cos(4°)+ i sin(4°)) is:

z = 65 * 8 [cos(14 + 4) + isin(14 + 4)] = 520[cos(18) + isin(18)]

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The rectangle with:

Factorize the volume expression

If a > 4, then:

Since the longest dimension is the length, it is

The breadth is the middle dimension,  it is

The height is the smallest dimension, it is

The area of the floor is:

Answer:

i)  length > 9 ft

   breadth > 5 ft

   height > 3 ft

ii)  Area of floor > 45 ft²

Step-by-step explanation:

Volume of a rectangular prism

[tex]\textsf{V}=lbh[/tex]

where:

Given:

Part (i)

To find expressions for the 3 dimensions of the tank, factor the expression for Volume.

Using the Factor Theorem, if V(x) = 0 then (a - p) is a factor:

[tex]\implies \sf V(1)=2(1)^3+(1)^2-2(1)-1=0[/tex]

[tex]\implies \sf V(-1)=2(-1)^3+(-1)^2-2(-1)-1=0[/tex]

Therefore  (a - 1)  and  (a + 1)  are factors:

[tex]\implies \sf 2a^3+a^2-2a-1=(a-1)(a+1)(2a+p)[/tex]

(where p is a constant to be found)

To find the value of p, expand:

[tex]\implies \sf 2a^3+a^2-2a-1=2a^3+pa^2-2a-1[/tex]

and compare coefficients:

[tex]\implies \sf a^2=pa^2 \implies p=1[/tex]

Therefore:

[tex]\implies \sf 2a^3+a^2-2a-1=(a-1)(a+1)(2a+1)[/tex]

If  l > b  and  b > h  then:

If a > 4 ft then:

Part (ii)

The area of the floor can be found by multiplying the found expressions for breadth and length:

[tex]\begin{aligned}\implies \sf Area\:of\:floor & =(a+1)(2a+1)\\& = 2a^2+3a+1\end{aligned}[/tex]

If a > 4 ft then Area of floor > 45 ft²

Answer:

A triangle is equal to 540° so you do 112 add 37 which equals 149° then take it away from 540 which gives you 391° as your answer

Step-by-step explanation:

Your Welcome

The value of x and y in the right angle triangle are 6 units and 10.4 units.

The sides of a right triangle can be found as follows:

using trigonometric ratio,

sin 60 = opposite / hypotenuse

sin 60 = y / 12

cross multiply

y = 12 sin 60

y = 10.3923048454

y = 10.4 units

Therefore,

cos 60 = adjacent / hypotenuse

cos 60 = x / 12

x = 12 cos 60

x = 6 units

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So we conclude that x measures 6 units and y measures 10.39 units.

Here we have a right triangle.

x is the adjacent cathetus to the shown angle, and y is the opposite cathetus. We can see that the hypotenuse measures 12.

Then using trigonometric relations we get:

So we conclude that x measures 6 units and y measures 10.39 units.

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The value of x from the figures are 18 and 26 respectively

13) From the diagram, the angles at the corner is 90 degrees. This shows that the sum of the angles is complementary (sum is 90 degrees)

3x + 2x = 90

5x = 90

x = 90/5

x = 18

15) Since the sum of angles on a straight line is supplementary, hence;

6x + x - 2 = 180

7x = 182

x = 182/7

x = 26

Hence the value of x from the figures are 18 and 26 respectively

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The perimeter of the triangle is 16 feet

The perimeter of a triangle refers to the calculation of the total distance bounded by the triangle or around the triangle.

Perimeter of a triangle = (3x - 4) + (x² - 1) + (2x - 15)

Perimeter of a triangle = 5x + x² - 20

Perimeter of a triangle =  5(4) + (4)² - 20

Perimeter of a triangle = 16

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Work Shown:

12x+10

2*6x+2*5

2(6x+5)

Effectively, we use the distributive property in reverse when it comes to factoring expressions like this.

The distributive property in general is a*(b+c) = a*b+a*c

1) Find the Greatest Common Factor (GCF).

1 What is the largest number that divides evenly into 12 and 10?

It is 2.

2 What is the highest degree of  that divides evenly into 12and 10?

It is 1, since x is not in every term.

3 Multiplying the results above,

The GCF is 22.

2) Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

[tex]2(\frac{12x}{2}+\frac{10}{2})[/tex]

3) Simplify each term in parentheses.

2(6x+5)

Answer:

126

Step-by-step explanation:

The difference between the first two terms of this sequence is 5 (16 - 11 = 5). The difference between the second and third terms of this sequence is also 5 (21 - 16 = 5).

So, we can assume that the difference between each term in this sequence is 5. To get from the first term (11) to the second term (16) we had to add 5 once. (or, add 5  x 1 [time])

To get from the first term (11) to third (21), we had to add 5 twice

(or, add 5 x2)

*repeated addition, such as 5+5+5 is the same thing as multiplication. If we are adding 5 three times, we will get the same outcome as 5 x 3.

So, to get from the first term (11) to the 24th term, we will have to add 5 23 times, or 5 x 23

5 x 23 = 115

11 + 115 = 126

Making 126 the 24th term of the sequence

Answer: The answer is 22

Step-by-step explanation: you divide the 36 and the 9 to get 4 then you add the 18 and the 4 to get 22

Answer:

22

Step-by-step explanation:

[tex]18+(\frac{36}{9})=?\\ 18+4=?\\22=?[/tex]

The value of z is 7 when y = 7 and x = 14.

If x varies directly as y and inversely as z and when y = 16 and z = 14,  x = 16. Enter the value of z when y = 7 and x = 14.

The variation involves a direct and inverse variation from x to y and z.

This is represented as:

[tex]x = \frac{ky}{z}[/tex]

Where k is the constant of variation

For the first set of values, we have:

[tex]16 = \frac{k * 16}{14}[/tex]

Solve for k

k = 14

For the second set of values, we have:

[tex]14 = \frac{k * 7}{z}[/tex]

Substitute 14 for k

[tex]14 = \frac{14 * 7}{z}[/tex]

Solve for z

z = 7

Hence, the value of z is 7

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I think it's 28 units²

Answer:

-16.

Step-by-step explanation:

2/3 * (-3) * (4*5 + 6 - 2(-3)^2)

= -2(20 + 6 - 18)

= -2 * 8

= -16.

How much is $100 in ZA rands.

Let the unknown be "x"

[tex]\frac{1}{17}×\frac{100}{x}[/tex]

We'll have to do cross multiplication.

So we'll have to multiply 100 and 17.

[tex]100×17[/tex]

[tex]\huge\boxed{= 1700 \: ZA \: rands}[/tex]

Therefore, $100 is 1700 ZA rands.

0.75 + 1.25 = $2 everyday

Since there are 5 weekdays:

5 x 2 = $10 a week

Since there are 52 weeks in a year:

10 x 52 = $520 a year!

Answer: 18 kilograms

Step-by-step explanation:

If each pumpkin weighs 3 kilograms and the farmer has 6 pumpkins the equation would be 6x3=18 in order to find the mass of the farmer's pumpkins.

Answer:

[tex]3\ln 4 + 3 \ln a[/tex]

Step-by-step explanation:

[tex]\ln(4a)^3\\\\=3\ln (4a)~~~~~~~~~~~~~~~~~~~~~~~~~~~~;[\log_b m^n = n \log_b m]\\\\=3(\ln 4 + \ln a)~~~~~~~~~~~~~~~~~~~~;[\log_b (mn) = \log_b m + \log_b n]\\\\=3\ln 4 + 3 \ln a[/tex]

Answer:

Step-by-step explanation:

The numbers of zebrafish and neon tetras can be found by writing an equation relating the numbers of each to their total cost.

__

Let z represent the number of zebrafish Ernesto bought. Then the number of neon tetras is (13 -z), and the total cost of the purchase was ...

  2.10z +1.95(13 -z) = 26.70

  0.15z +25.35 = 26.70 . . . . . . simplify

  0.15z = 1.35 . . . . . . . . . . . . subtract 25.35

  z = 9 . . . . . . . . . . . . . . . divide by 0.15

Ernesto bought 9 zebrafish and 4 neon tetras.

Answer:

Step-by-step explanation:

Answer:

there's no picture dude

Answer:

d

Step-by-step explanation:

the fitness grows into bodyness from good

Answer:

3x+(4x-1)+90°=180°{sum of angles in a triangle}

3x+4x-1+90°=180°

7x+89°=180°

7x=180°-89°

7x=91°

divide both sides by 7

x=13

Answer:

The answer is x=13

The stems that have the same number of leaves are (c) 4 and 5 each have 3 leaves

The table of values is given as:

Week 1: 12 15 25 45 52 30 31

Week 2: 22 25 46 51 10 19 33

Week 3: 44 21 30 20 10 24 52

Remove the week tags:

12 15 25 45 52 30 31

22 25 46 51 10 19 33

44 21 30 20 10 24 52

Sort the data values in tens

10 10 12 15 19

20 21 22 24 25 25

30 30 31 33

44 45 46

51 52 52

Now, we can now plot the stem-and-leaf graph.

This is represented as follows:

Stem  |   Leaves

1               0 0 2 5 9

2              0 1 2 4 5 5

3              0 0 1 3

4              4 5 6

5              1 2 2

In the above plot, we can see that stems 4 and 5 have 3 leaves each

Hence, the stems that have the same number of leaves are (c)

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Using the distance formula, the length of WX is approximately: 8.5.

Distance formula is, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].

Given the endpoints:

W(5,-3) = (x1, y1)

X(-1,-9) = (x2, y2)

Plug in the values:

WX = √[(−1−5)² + (−9−(−3))²

WX = √[(−6)² + (−6)²]

WX = √72

WX ≈ 8.5

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Answer:

6 2 with the little check mark line in the midddle

Step-by-step explanation:

The probability of 3 successes is 0.0384

The given parameters are:

The binomial probability is represented as:

[tex]P(x) = ^nC_x * p^x * (1 - p)^{n-x[/tex]

So, the probability of three successes is:

[tex]P(3) = ^4C_3 * 0.4^3 * (1 - 0.4)^{4 -3[/tex]

Evaluate the factors in the expression

[tex]P(3) = ^4C_3 * 0.0384[/tex]

Evaluate the combination expression

P(3) = 1 * 0.0384

Evaluate the product

P(3) = 0.0384

Hence, the probability of 3 successes is 0.0384

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Answer:

0.1536

Step-by-step explanation:

Answer:

27 I think just divide 81 by 3

Answer:

6

Step-by-step explanation:

The constant is the number that's all by itself with no variable.

x is the variable. It can vary (change) as you use different values for x.

There are four terms here in the expression in your question they are separated by the plus or minus signs.

2 and 4 are exponents. 3 and 5 are coefficients.

x^4 is a fourth degree term. 3x^2 is a second degree term. 5x is a first degree term. The whole expression is 4th degree because the highest exponent is 4.

But the 6 is all by itself. 6 is the constant.

Answer:

[tex]x > \frac{5}{2} > 2\frac{1}{2}[/tex]

Step-by-step explanation:

group

[tex]4x-7 > 3\\4x-7+7 > 3+7\\4x > 3+7\\4x > 10[/tex]

isolate "x"

[tex]4x > 10\\=\frac{4x}{4} > \frac{10}{4}\\x > \frac{10}{4}\\x > \left(\frac{5\cdot 2}{2\cdot 2}\right)\\x > \frac{5}{2}[/tex]

Answer:

x > 2.5 or in fraction form x > 2 1/2

Step-by-step explanation:

4x - 7 > 3

     +7  +7         Add seven to both sides.

4x > 10

÷4     ÷4            Divide both sides by 4.

x > 2.5

Hope this helps!