Which of the following complexe numbers is equal to (4 + 3i)(5 - 2i)?

20 + i

20+6i

26 + i^2

26 + 7i

Answer:

[tex]\textrm{Each side = 23.6893 cm}\\\\\\\textrm{Rounded to 2 decimal places = 23.69 cm}\\\\\textrm{Rounded to 1 decimal place = 23.7 cm}[/tex]

You can choose the level of precision as desired from the above

Step-by-step explanation:

The area of an equilateral triangle of side a

is
[tex]A = \dfrac{(a^2 \sqrt{3})}{4}[/tex]

We are given A = 243

Plugging in values we get

[tex]243 = \dfrac{a^2\sqrt{3}}{4}[/tex]

Switch sides so [tex]a^2[/tex] term is on the left

[tex]\dfrac{a^2\sqrt{3}}{4} = 243[/tex]

Multiply by 4 both sides to get rid of the denominator:
[tex]\dfrac{a^2\sqrt{3}}{4} \times 4 = 243 \times 4\\\\a^2\sqrt{3} = 972\\\\[/tex]

Divide by [tex]\sqrt{3}[/tex]  both sides:
[tex]a^2 = \dfrac{972}{\sqrt{3}}\\\\a^2 = 561.18446\\\\a = \pm \sqrt{561.18446}\\\\[/tex]

Taking only positive square root:
[tex]a = \sqrt{561.18446}\\\\a = 23.6893\\\\[/tex]

Step-by-step explanation:

It's a long answer. You have to find the area of the large triangle, the small triangle than subtract the two

A = 1/2(b)(h)

For the big triangle

A = 1/2(16)(4) = 1/2(64) = 32

For the small triangle

A = 1/2(8)(2)

We use 8 and 2 because that's half of 16 and 4, since at the bottom it says A and B are midpoints

A = 1/2(8)(2) = 1/2(16) = 8

Now we subtract

32-8 = 24 units

The relationship between the number of gallons of gas and the cost in dollars is: C. The cost of gas is $3.75 per gallon.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the relationship between the number of gallons of gas and the cost in dollars on this graph as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 7.5/2

Constant of proportionality, k = $3.75.

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The triangles given can be determined to be :

You can use the Pythagorean Theorem and its Converse to determine the type of triangle.

The Pythagorean Theorem and its Converse are basically :

c ² = a² + b ²   This is a right angled triangle

c ² > ( a² + b ² ) This is an obtuse triangle

c ² < ( a² + b ² )

The triangles are :

13 :

26 ² = 24 ² + 10 ²

676 = 676

Right - angled

14 :

20 ² = 13 ² + 6 ²

400 > 205

Obtuse triangle

15 :

17 ² = 16 ² + 3 ²

289 > 265

Obtuse triangle

16 :

32 ² = 29 ² + 24 ²

1, 024 < 1, 417

Acute triangle

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The reflection of point (-6, -5) across the x-axis will give (-6, 5)

A reflection point occurs when a figure is constructed around a single point, known as the point of reflection or center of the figure.

Given is a point (-6, -5), we need to find the coordinates of the point when it is reflected across the x-axis,

The rule for a reflection across the x-axis -:

The rule for reflecting over the x-axis is to negate the value of the y-coordinate of each point, but leave the x-value the same.

i.e, (x, y) → (x, -y)

Therefore,

(-6, -5) → (-6, 5)

Hence, the reflection of point (-6, -5) across the x-axis will give (-6, 5)

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The question is incomplete, the question is solved for:

Reflect point (-6, -5) across x-axis

Answer:B

Step-by-step explanation:

Answer:

Step-by-step explanation:

The solution to this problem involves calculating the monthly interest and reducing the balance accordingly each month until the balance reaches zero. Here are the steps:

Calculate the monthly interest: First, we need to calculate the monthly interest rate. We can do this by dividing the APR by 12. The monthly interest rate is 9.5% / 12 = 0.7917%.

Calculate the interest charge for the first month: The interest charge for the first month is the balance multiplied by the monthly interest rate. In this case, the interest charge is $1,367.90 x 0.7917% = $10.87.

Calculate the new balance: Next, we need to subtract the payment from the balance and add the interest charge to determine the new balance. The new balance after the first payment is $1,367.90 - $400.00 + $10.87 = $978.87.

Repeat the steps for subsequent months: Repeat the process of calculating the monthly interest charge and the new balance for each subsequent month until the balance reaches zero.

Keep track of the number of months: As we repeat the steps, keep track of the number of months it takes to pay off the card.

Here is a summary of the calculations:

Month Balance        Interest Payment    New Balance

1        $1,367.90 $10.87 $400.00       $978.87

2          $978.87          $7.74 $400.00       $586.61

3          $586.61          $4.62 $400.00        $191.23

4           $191.23          $1.50 $400.00      $-208.27

It takes 4 months to pay off the card, and the total amount paid including interest is $1,367.90 + $10.87 + $7.74 + $4.62 + $1.50 = $1392.73.

The information regarding the addition is explained below.

Adding 29 + 46:

Student 1: May use the traditional column addition method, lining up the digits in the ones, tens, and hundreds place and carrying over if necessary.

Student 2: May use the breaking apart method, where they break apart the numbers into smaller parts (e.g. 20 + 40) and then add the pieces together.

Student 3: May use a number line, counting up from 29 by the increments of 46 until they reach the sum.

Subtracting 54 - 28:

Student 4: May use the traditional column subtraction method, lining up the digits in the ones, tens, and hundreds place and borrowing if necessary.

Using bundled things to explain regrouping in the addition problem 167 + 59:

First, separate the numbers into bundles of ten.

Next, show how you can regroup the ones as ten ones to make a bundle of ten.

Then add the tens and hundreds place to get the answer 226.

Using bundled things to explain regrouping in the subtraction problem 231 - 67:

First, separate the numbers into bundles of ten.

Next, show how you can regroup the tens as ten tens to make a bundle of a hundred.

Then subtract the hundreds place and the tens place to get the answer 164.

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The mean of the sampling distribution is given as follows:

37.827 millimeters.

The mean of the sampling distribution is obtained using the Central Limit Theorem.

The mean of the sampling distribution is the same as the population mean, hence it is given as follows:

37.827 millimeters.

(on the problem, we are given the population mean).

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The amount of profit that the new coffee shop will make after 6 years is; 35.8 thousand dollars

The quadratic equation that represents the annual profit made by the new coffee shop in thousands of dollars is;

p(t) = 0.3t² + 5.5t - 8

where;

t is the number of years for which the profit is measured

Thus, after 6 years, we will substitute 6 for t in the quadratic equation to get;

p(6) = 0.3(6)² + 5.5(6) - 8

p(6) = 10.8 + 33 - 8

p(6) = 35.8 thousand dollars

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Answer:

Let's call the number of cubic yards of mix A that the farmer buys "x", and the number of cubic yards of mix B that the farmer buys "y".

We can write the following constraints based on the minimum monthly requirements:

20x + 10y >= 460 (for acid)

30x + 30y >= 939 (for nitrogen)

5x + 10y >= 200 (for potash)

We also want to minimize the cost, which is given by 25x + 49y.

This is a linear programming problem, which can be solved using simplex method or the graphical method.

By using the graphical method, we find that the optimal solution occurs at x = 11.75 and y = 4.5. This means that the farmer should buy 11.75 cubic yards of mix A and 4.5 cubic yards of mix B to meet the minimum monthly requirements at a minimum cost.

So, the answer to the question is: If mix A costs $25 per cubic yard and mix B costs $40 per cubic yard, the farmer should blend 11.75 yd of mix A & 4.5 yd of mix B to meet the minimum monthly requirements at a minimum cost.

Answer:

The 3rd and 6th equations

Step-by-step explanation:

Any equation that has a variable with an exponent is nonlinear and the 3rd and 6th equations follow this requirement.

The given triangles can be classified based on their sides and angles as:

1. Isosceles, acute triangle

2. Scalene, right triangle

3. Scalene, obtuse triangle

4 Equilateral

5. Isosceles, right triangle

6. Scalene, acute triangle

7. Equilateral, acute triangle

8. Isosceles, obtuse triangle

Triangles can be classified by both their sides and their angles.

Classification by sides:

Classification by angles:

Thus, using the sides or angles of the given triangles, they are classified as follows:

1. Isosceles, acute triangle

2. Scalene, right triangle

3. Scalene, obtuse triangle

4 Equilateral

5. Isosceles, right triangle

6. Scalene, acute triangle

7. Equilateral, acute triangle

8. Isosceles, obtuse triangle

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The Expression with coefficient 4 and -9 is 4j and -9j.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

We have to write the coefficient as 4 and -9.

As, coefficient is the number which is just before the variable like in 2x 'x' is the variable and '2' is the coefficient.

So, with coefficient 4 the expression is 4j

and, with coefficient  -9 the expression is -9j.

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if the second number is lower than that's the answer. so in this case kayla

Answer:

Step-by-step explanation:

To find the distance Tyler needs to swim, we can use the Pythagorean theorem. The theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side, which is the hypotenuse.

In this case, the two shorter sides of the triangle are 40 feet and 80 feet, and the hypotenuse is the distance Tyler needs to swim to reach Jason. So we can write the equation as follows:

40^2 + 80^2 = d^2

where d is the distance Tyler needs to swim.

Expanding the equation:

1600 + 6400 = d^2

8000 = d^2

Taking the square root of both sides:

d = sqrt(8000) = 80 * sqrt(2)

So, Tyler needs to swim a distance of 80 * sqrt(2) feet, or approximately 113.1 feet, to reach Jason.

Answer:

[tex]sin(P)=\frac{\sqrt{55}}{10}[/tex]

Step-by-step explanation:

The sine function is defined as a ratio of sides: [tex]sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]

where the "opposite" side is quite literally the opposite side, if you went straight from the angle, whatever side it's pointing towards is the opposite angle. The hypotenuse... is as the name implies, the hypotenuse. The symbol inside the parenthesis next to the sine is called theta and is just used to represent some angle.

We of course don't know the hypotenuse as it's not given, but we can use the Pythagorean Theorem to solve for the hypotenuse:

[tex]c^2=\sqrt{45}^2+\sqrt{55}^2\\c^2=45+55\\c^2=100\\c=10[/tex]

We do know the opposite side though, it's just the square root of 55, it's directly opposite of the angle P. Plugging in known values we get the following: [tex]sin(P)=\frac{\sqrt{55}}{10}[/tex] and we can't simplify this any further as 45 has no factors which are perfect squares.

Answer:

120°

Step-by-step explanation:

360 / 12

30 X (5-1)

30 X 4= 120°

There will be a total of 741 greetings at the mother-daughter tea.

Two or more expressions with an Equal sign is called as Equation.

Let's start by counting the number of greetings between the host mother-daughter pair and the other 19 mother-daughter pairs.

Since each pair only greets once, the host pair will make 19 greetings.

Now we need to count the number of greetings between the 19 guest mothers and the other 19 mother-daughter pairs

Each of the 19 guest mothers will greet 18 other mother-daughter pairs, for a total of 19 x 18 = 342 greetings.

Finally, we need to count the number of greetings between the 19 guest daughters and the 20 mothers

Each of the 19 guest daughters will greet 20 mothers

Total is 19 x 20 = 380 greetings.

By adding all we get 741 greetings

Therefore, there will be a total of 741 greetings at the mother-daughter tea.

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Tone is the feeling the author wants the reader to have when reading his or her work. Anaya employs tone to generate the texts "Take the Tortillas out of your poetry" and "Speaking Arabic."

Both authors explore regional cuisine and make use of terminology from various languages.

While Nye's tone is welcoming of mixed cultures, Anaya's tone is sincere towards culture and indignant towards suppression.

The funny tone of Anaya's writing reflects his intention to draw attention to the subject. The laid-back nature of Anaya's delivery is evident.

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The piecewise function for the given problem is;

C(x) = $61.29                           x ≥ 400

C(x) = $61.29 + 0.6(x - 400) if x ≥ 400

A piecewise function is defined as a function that has different definitions depending on which values of x are being used. Piecewise functions are called "piecewise" due to the fact that they are made of "pieces" with different function definitions. To evaluate a piecewise function for a given value of x, find which interval your value fits in, and then use that definition of the function to evaluate.

First, we will find the monthly cost if the 400-minute monthly limit is not exceeded. Then, the total cost would be;

47.35 + 13.94 = 61.29 with just the plan and taxes. So if x ≤ 400, then;

C(x) = 61.29

Now if the 400 minutes is exceeded, the bill will also include $0.60 per additional minute. To find the number of additional minutes, we can take the total number of minutes x and subtract 400. In general, the cost would be;

C(x) = $61.29 + 0.6(x - 400) if x ≥ 400

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Answer:

The answer

Step-by-step explanation:

Figure 1 figure

3/4

The steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.

Solution to the quadratic equation

The solution to the quadratic equation is determined as follows;

2x² + 12x - 3 = 0

2x² + 12x = 3

divide through by 2

x² + 6x = ³/₂

take half of coefficient of x, square it and add it both sides of the equation

(x + 3)² = ³/₂ + 3²

x² + 6x + 9 = 9 + ³/₂

2(x² + 6x + 9) = 18 + 3

Thus, the steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.

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The quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

A division is a process of splitting a specific amount into equal parts.

We have to find 3x³-2x²+7x+9 divided by x²-3x

3x³-2x²+7x+9 is the dividend and x²-3x is the divisor.

The steps to solve this are given below.

Step 1: Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor.

Step 2: Then divide it by the divisor and write the answer on top as the quotient.

Step 3: Subtract the result from the digit and write the difference below.

Step 4: Bring down the next digit of the dividend (if present).

Step 5: Repeat the same process.

Hence, the quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

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Answer:

x=-13

Step-by-step explanation:

Since the two angles given are equivalent, you set up the equation as 7x+205=114.

7x+205=114

7x=114-205

7x=-91

7x/7=-91/7

x=-13

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Using the equation of the arithmetic sequence given, the first four terms are 59, 52, 45 and 38 respectively

In the sequence given, the progression is an arithmetic progression since it increases by a common difference.

The first term of the sequence is 59 while the common difference is -7.

A = 59 - 7(n - 1)

n = 1

a = 59 - 7(1 - 1)

a = 59

n = 2

a = 59 - 7(2 - 1)

a = 52

n = 3

a = 59 - 7(3 - 1)

a = 45

n = 4

a = 59 - 7(4 - 1)

a = 38

The terms are 59, 52, 45 and 38

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Translation:  Find the first four terms of the sequence given the following

In the absence of trade between Glacier and Sequoia, Glacier would consume 8 million pairs of shorts and 48 million pounds of almonds, and Sequoia would consume 15 million pairs of shorts and 20 million pounds of almonds. However, if both countries decide to engage in trade, Glacier could specialize in producing shorts, using 1 million hours of labor per week, and Sequoia could specialize in producing almonds, using 1 million hours of labor per week. This specialization would result in Glacier producing 12 million pairs of shorts and Sequoia producing 24 million pounds of almonds. This would enable each country to consume more of both goods than they could produce in the absence of trade.

Answer:

The number of books sold were:

Math textbooks: 426
Sociology textbooks = 46

Step-by-step explanation:

Let us use the variable [tex]m[/tex]  to represent the number of math books sold

Let us use the variable [tex]s[/tex]  to represent the number of math books sold

Combined total of 426 math and sociology books were sold is represented by the equation:
[tex]m + s = 426\quad\quad\quad(1)[/tex]

Number of math books sold was 46 more than the number  of sociology textbooks sold is given by
[tex]m - s = 46\quad\quad\quad(2)[/tex]

Adding the equations (1) + (2):
[tex](m + s) + (m - s) = 426 + 46\\\\2m = 472\\\\m = \dfrac{472}{2}\\\\m = 236\\\\[/tex]

Using Equation (1): [tex]m + s = 426[/tex]  we get

[tex]236 + s = 426\\\\s = 426 - 236\\\\s = 190[/tex]

Answer: d. Triangle with angle measures: 8·, 17·, and 152·

Step-by-step explanation: i did the test

The triangle not possible is option

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

Let us find the sum of the angles for each triangle given.

(a) Triangle with angle measures: 26°, 19°, and 135°·

Sum = 26° + 19° + 135° = 180°

(b)Triangle with angle measures: 14°, 27°, and 139°·

Sum = 14° + 27° + 139° = 180°

(c) Triangle with angle measures: 9°, 18°, and 153°·

Sum = 9° + 18° + 153° = 180°

(d) Triangle with angle measures: 8°, 17°, and 152°·

Sum = 8° + 17° + 152° = 177°, which is not equal to 180°.

Hence the option (d) is not possible.

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Answer:

  1625

Step-by-step explanation:

You want the sum of the first 25 terms of the series 5 +10 +15 +....

The first term is 5, the common difference is 5, so the general term is ...

  an = a1 +d(n -1)

  an = 5 +5(n -1)

The last term of the sum is ...

  a25 = 5 +5(25 -1) = 125

The sum of the series is the average of the first and last terms, multiplied by the number of terms:

  S25 = (a1 +a25)/2 · 25 = (5 +125)/2 · 25 = 65·25 = 1625

The sum of 25 terms of the series is 1625.

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