Find the product of these complex numbers.(8 + 6i)(-5 + 7i) =A.-82 - 86iB.-82 + 26iC.2 + 26iD.2 - 86i
Answers
Solution
Step 1:
Write the expression:
(8 + 6i)(-5 + 7i)
Step 2:
[tex]\begin{gathered} \left(8+6i\right)\left(-5+7i\right) \\ \\ 8\times(-5)\text{ + 8 }\times7i\text{ + 6i }\times(-5)\text{ + 6i }\times\text{ 7i} \\ \\ =\text{ -40 + 56i - 30i + 42i}^2 \\ \\ =\text{ -40 + 26i - 42} \\ \\ =\text{ - 82 + 26i} \end{gathered}[/tex]Final answer
B.
-82 + 26i
Related Questions
Econ The area of a square is 36 square meters. What is the length (in meters) of one side of the square
Answers
We have the following equation of the area of a square:
[tex]A=s^2[/tex]where s is the length of the side.
In this case, we have that the area is 36 square meters, then:
[tex]\begin{gathered} A=36m^2=s^2 \\ \Rightarrow s^2=36 \end{gathered}[/tex]if we apply the square root on both sides we get:
[tex]\begin{gathered} \sqrt[]{s^2}=\sqrt[]{36}=6 \\ \Rightarrow s=6 \end{gathered}[/tex]therefore, the measure of the side of the square is 6 meters
Which of the terms cannot be combined with the others?ОЗху2x-5xОх
Answers
0x cannot be combined with other terms
Because when it is combined it always results in 0.
Question 12 of 19 What is the solution to the system of equations graphed below? -5 y= x + 2 N 5 5 y = -2x - 4 -5 y = -2x - 4 y = x+2
Answers
For finding the solutions, you need to match the equations
[tex]\begin{gathered} x+2=-2x-4 \\ x+2x=-4-2 \\ 3x=-6 \\ x=-2 \end{gathered}[/tex]For the next step, you should replace the value for x in any of the equations given
y=x+2
y=-2+2
y=0
(-2,0) Letter a
1) In 2014, the percentage of households that owned a 4K TV was found to be 18%. Using a sample of 300 households in which 60 of them owned a 4K TV, do we have sufficient evidence that the percentage of households with a 4K TV has increased? Use a level of significance of 0.10.
Answers
Hello there. To solve this question, we need to calculate the percentage of households that owns a 4K TV with the values given in the sample and compare with the other percentage to see if the value has increased.
Using that sample of 300 households, in which 60 of them owns a 4K TV, we get that the percentage will be calculated by the ratio:
60/300
Simplify the fraction by a factor of 60
1/5
Multiply it by 100%
20%, equal to 0.20
In 2014, we had that percentage being equal to 18%, which is equal to 0.18
So, we do have sufficient evidence that the percentage of households satifying this situation have increased with the time.
ASAP Please help and ThankyouThis graph shows how the total distance jack has walked depends on the number of trips he has made to school. What is the rate of change?
Answers
we will take two points on the line,
first is (0,2) and other is (1, 4)
the rate of change will be the slope of the line,
[tex]\begin{gathered} m=\frac{4-2}{1-0} \\ m=\frac{2}{1}=2 \end{gathered}[/tex]so the rate of the change is 2 km per trip
so the answer is 2
3x +5= 2x +7How will the equation look if you subtract 2xfrom both sides?Click on the correct answer.5x +5= 7x+5=73x +5=7
Answers
If you subtract 2x from both sides of the equation you have:
[tex]\begin{gathered} 3x+5=2x+7 \\ 3x+5-2x=2x+7-2x \\ \text{ Operate similar terms} \\ x+5=7 \end{gathered}[/tex]Therefore, if you subtract 2x both sides, the equation will look like
[tex]x+5=7[/tex]what is the polar form of -3+sqrt3i
Answers
Solution
For this case we have the following number given:
[tex]-3+\sqrt[]{3}i[/tex]We can see that x = -3 and y = - sqrt(3)
The angle is given by:
[tex]\arctan (\frac{-\sqrt[]{3}}{3})=-30=-\frac{\pi}{6}[/tex]The radius would be:
[tex]r=\sqrt[]{(3)^2+(-\sqrt[]{3})^2}=\sqrt[]{12}[/tex]And the polar form would be given by:
[tex]z=\sqrt[]{12}(\cos (-\frac{\pi}{6})+i\sin (-\frac{\pi}{6}))\text{ }[/tex]Answer:
The answer is D!!
Step-by-step explanation:
Right on edg 2022
to a certain meeting room a college charge a reservation fee of $37 and a ln additional fee of $9.40 per hour. the math club wants to spend less than $ 93.40 on renting the meeting room. what are the possible amounts of time for which they could rent the meeting room. use t for the number of hours the meeting room is rented and solve your inequality for t
Answers
For the information given in the statement, you have the inequality:
[tex]\text{ \$37+\$9.40t < \$93.40}[/tex]Now, to solve the inequality, subtract $37 from both sides of the inequality.
[tex]\begin{gathered} \text{ \$37+\$9.40t -\$37< \$93.40 - \$37} \\ \text{ \$9.40t < \$}56.4 \end{gathered}[/tex]Now, divide by $9.40 into both sides of the inequality
[tex]\begin{gathered} \text{ \$9.40t < \$}56.4 \\ \frac{\text{ \$9.40t }}{\text{ \$9.40}}\text{< }\frac{\text{\$}56.4}{\text{ \$9.40}} \\ t<6 \end{gathered}[/tex]Therefore, the math club could rent the meeting room for a maximum of 6 hours.
Tavon and Raven are feeling backpacks for Arlington woods elementary Schoolthey have 24 boxes of markers 56 coloring books and 72 packages of modeling claywhich of the following are possible answers for the greatest number of backpacks they can fill if the markers books and clay are equally distributed
Answers
we have that
they have 24 boxes of markers 56 coloring books and 72 packages of modeling clay
so
24=(2^3)(3)
56=(2^3)(7)
72=(2^3)(3^2)
24/8=3
56/8=7
72/8=9
the number of backpacks is 8
therefore
teh answer is option B
In the quadratic formula the expression b^2-4ac is called the _____1 maximum value 2 discriminant3 minimum value
Answers
ANSWER :
Discriminant
EXPLANATION :
b^2 - 4ac in quadratic formula determines if the roots are real or imaginary.
It is called discriminant.
5(y + 1) = 10 Submit Answer
Answers
5(y + 1) = 10 → 5y + 5 = 10
Now to subtract 5 on both sides:
5y + 5 = 10 → 5y = 5
Finally, we can divide by the coefficient:
5y = 5 → y = 1
Therefore, y = 1.
Please Help. I will mark you BRAINLIST
Answers
Answer:
(D). f(x) = [tex]-\frac{3}{2}[/tex] x² + [tex]\frac{17}{2}[/tex] x - 7
Step-by-step explanation:
( x , y )
ax² + bx + c = y ............ ( 1 )
~~~~~~~~~~~~~~
( 2 , 4 ) --------> ( 1 )
a(2)² + b(2) + c = 4
4a + 2b + c = 4 .............. (2)
( 3 , 5 ) ---------> ( 1 )
a(3)² + b(3) + c = 5
9a + 3b + c = 5 ............... (3)
( 4 , 3 ) ----------> ( 1 )
a(4)² + b(4) + c = 3
16a + 4b + c = 3 .............. (4)
[tex]delta[/tex] = Δ = [tex]\left[\begin{array}{ccc}4&2&1\\9&3&1\\16&4&1\end{array}\right][/tex] = - 2
[tex]delta_{a}[/tex] = [tex]\left[\begin{array}{ccc}4&2&1\\5&3&1\\3&4&1\end{array}\right][/tex] = 3
[tex]delta_{b}[/tex] = [tex]\left[\begin{array}{ccc}4&4&1\\9&5&1\\16&3&1\end{array}\right][/tex] = - 17
[tex]delta_{c}[/tex] = [tex]\left[\begin{array}{ccc}4&2&4\\9&3&5\\16&4&3\end{array}\right][/tex] = 14
a = [tex]delta_{a}[/tex] / [tex]delta[/tex] = [tex]-\frac{3}{2}[/tex]
b = [tex]delta_{b}[/tex] / [tex]delta[/tex] = [tex]\frac{-17}{-2}[/tex] = [tex]\frac{17}{2}[/tex]
c = [tex]delta_{c}[/tex] / [tex]delta[/tex] = [tex]\frac{14}{-2}[/tex] = - 7
f(x) = [tex]-\frac{3}{2}[/tex] x² + [tex]\frac{17}{2}[/tex] x - 7 (D)
Translate the sentences into an algebraic inequality.A tour bus can seat 55 passengers. A minimum of 15 people must register for the tour to book the bus.
Answers
ANSWER
[tex]\text{15 }\leq\text{ x }\leq55[/tex]EXPLANATION
The tour bus can seat 55 passengers.
A minimum of 15 people must register for the tour to book the bus.
This means that the number of people that must register for the tour must be greater than or equal to 15 and less than or equal to 55.
Let the number of people that must register be x.
Then we have that the inequality that represents the situation is:
[tex]\begin{gathered} x\ge\text{ 15 and x }\leq\text{ 55} \\ \Rightarrow\text{ 15 }\leq\text{ x }\leq55 \end{gathered}[/tex]That is the inequality.
Find the total value of the investment after the time given: $36,000 at 13.7% compounded semiannually for 2 years
Answers
A = P ( 1 + r/n ) ^ nt
P is the principle which is 36000
r is the rate which is 13.7 % or .137 in decimal form
n is the number of time per year, semi annual means 2 times per year
t is the time = 2
A = 36000( 1 + .137/2) ^ (2*2)
36000( 1 + .137/2) ^ (4)
I don't understand how to do this problem. Could you explain to me how to do this problem? The formula for the perimeter of a rectangle is P=2l + 2w, where l is the length and w is the width. A rectangle has a perimeter of 24 inches. Find it's dimensions if it's length is 3 inches greater than it's width.
Answers
Given:
• Perimeter of the rectangle = 24 inches
,• The length is 3 inches greater than it's width.
Let's find the dimensions of the rectangle.
To find the dimensions, apply the formula for perimeter of a rectangle:
P = 2l + 2w
Where l is the length and w is the width.
Given that the length is 3 inches greater than the width, the length can be expressed as:
l = (w + 3) inches
Substitute 24 for P and (w + 3) for l in the formula:
P = 2l + 2w
24 = 2(w + 3) + 2w
Let's solve the equation for w:
24 = 2(w + 3) + 2w
APply distributive property:
24 = 2(w) + 2(3) + 2w
24 = 2w + 6 + 2w
Combine like terms:
24 = 2w + 2w + 6
24 = 4w + 6
Subtract 6 from both sides:
24 -6 = 4w + 6 - 6
18 = 4w
Divide both sides by 4:
[tex]\begin{gathered} \frac{18}{4}=\frac{4w}{4} \\ \\ 4.5=w \\ \\ w=4.5\text{ } \end{gathered}[/tex]The width of the rectangle is 4.5 inches.
Since the lengh is 3 inches greater than the width, add 3 to 4.5 inches to get the length of the rectangle.
l = w + 3
l = 4.5 + 3
l = 7.5
The length of the rectangle is 7.5 inches.
Therefore, the dimensions of the rectangle are:
Length = 7.5 inches
Width = 4.5 inches
ANSWER:
Length = 7.5 inches
Width = 4.5 inches
Does the quadratic functionf(x) = 4x2 – 12x + 9 have one,two, or no real zeros? Utilize thequadratic formula to determinethe answer[?] real zero(s)-b Vb2 - 4acRemember the quadratic formula: x =
Answers
SOLUTION
Step1: Write out the equation
[tex]y=-2x^2-4x+2[/tex]Compare the equation with the general form of a quadratic equation
[tex]\begin{gathered} y=ax^2+bx+c \\ \text{then } \\ a=-2,b=-4,c=2 \end{gathered}[/tex]Step2 Write out the quadratic formula
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Step3: Substitute the parameters in step1
There is a rectangular garden with an area of 24 square leel. The garden is 2 feet longer than it is wide. Create an equation that can be used to determine the length and wath of the garden
Answers
The equation that can be used to determine the length and width of the garden is x² + 2x - 24 =0, the length is 6 feet and the width is 4 feet.
There is a rectangular garden with an area of 24 square feet
The garden is 2 feet longer than it is wide
Let the width of the garden be x
Then, the length of the garden is x + 2
The area of a rectangular garden = length of the garden x width of the garden
24 = x (x + 2)
x² + 2x - 24 =0
x² + 6x - 4x - 24 = 0
x(x + 6) -4(x + 6) = 0
(x - 4)(x + 6) = 0
x - 4 = 0
x = 4
Width of the rectangular garden is 4 feet
Length of the rectangular garden is (4 + 2) feet = 6feet
Therefore, the equation that can be used to determine the length and width of the garden is x² + 2x - 24 =0, the length is 6 feet and the width is 4 feet.
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Please help with this
Answers
Answer:
[tex]y = 100 - \frac{17}{3} x[/tex]
Here you go the visual explanation should be there for you, if your still confused i suggest asking your teacher for help on how to find the slope.
The hypotenuse of an isosceles right triangle is 6cm longer than either of its legs. Note that an Isosceles right triangle is a right triangle whose legs are the same length, find the exact length of its legs and it’s hypotenuse
Answers
We know by the pythagorean theorem that
We know that the length of the hypotenuse squared will be equal to the sum of the legs squared. The problem says that the legs have the exact same length and the hypotenuse is 6cm longer, so we can write
Where "a" is the leg length, see that we can apply the pythagorean theorem here, and it will be
[tex]a^2+a^2=(a+6)^2[/tex]See that now c = a + 6, and b = a.
We can simplify that expression
[tex]2a^2=(a+6)^2[/tex]We know that
[tex](a+6)^2=a^2+12a+36[/tex]Therefore our equation will be
[tex]2a^2=a^2+12a+36[/tex]Now we pass all the terms for one side and we will have a quadratic equation
[tex]-a^2+12a+36=0[/tex]We can use the formula for the quadratic equation and find out the solutions
[tex]\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Using it
[tex]\frac{-12\pm\sqrt[]{12^2-4\cdot(-1)\cdot36}}{2\cdot(-1)_{}}[/tex]Now we can just do all the calculus
[tex]\frac{-12\pm\sqrt[]{144^{}+144}}{-2_{}}=\frac{12\pm\sqrt[]{2\cdot12^2}}{2}=\frac{12\pm12\sqrt[]{2}}{2}[/tex]Then the solution are
[tex]\begin{cases}a_1=6+6\sqrt[]{2} \\ a_2=6-6\sqrt[]{6}\end{cases}[/tex]Even though we have two solution, see that the second one is negative, and we can't have negative length! Then the length of its legs will be
[tex]a=6+6\sqrt[]{6}[/tex]And the hypotenuse will be a + 6, then
[tex]h=6+6+6\sqrt[]{6}=12+\sqrt[]{6}[/tex]Therefore, the legs and the hypotenuse length is
[tex]\begin{gathered} l=6+\sqrt[]{6} \\ h=12+6\sqrt[]{6} \end{gathered}[/tex]We can write it approximately as
[tex]\begin{gathered} l=14.485\text{ cm} \\ h=20.485\text{ cm} \end{gathered}[/tex]If we want a more rough approximation we can say it's
[tex]\begin{gathered} l=14.5\text{ cm} \\ h=20.5\text{ cm} \end{gathered}[/tex]Which relations are functions?Select Function or Not a function for each graph. FunctionNot a functionGraph of a line on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A line passes through the origin and the points begin ordered pair negative 2 comma negative 4 end ordered pair and begin ordered pair 2 comma 4 end ordered pair.Function –Not a function –The graph of a parabola on a coordinate plane. The x axis ranges from negative 5 to 5 in increments of 1. The y axis ranges from negative 5 to 5 in increments of 1. The vertex is located at begin ordered pair 1 comma 0 end ordered pair. The parabola opens upward. It passes through the vertical axis at begin ordered pair 0 comma 1 end ordered pair. It passes through begin ordered pair 2 comma 1 end ordered pair.Function –Not a function –An absolute value function graphed on a coordinate plane. The x axis ranges from negative 5 to 5 in increments of 1. The y axis ranges from negative 5 to 5 in increments of 1. The vertex is at the origin. The V-shaped graph passes through the points begin ordered pair 1 comma 1 end ordered pair and begin ordered pair 1 comma negative 1 end ordered pair.Function –Not a function –A circle on a coordinate plane centered at the origin, begin ordered pair 0 comma 0 end ordered pair. The circle passes through points begin ordered pair negative 2 comma 0 end ordered pair, begin ordered pair 0 comma negative 2 end ordered pair, begin ordered pair 2 comma 0 end ordered pair, and begin ordered pair 0 comma 2 end ordered pair.Function –Not a function –
Answers
SOLUTION
To identify or determine which relation in the graph is a function, we use the vertical line test.
The vertical line test explains that If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because that x-value has more than one output. A function has only one output value for each input value.
Hence, from the explanation above, we cam see that
Graph 1 is a Function
Graph 2 is a Function
Using similar approach
Graph 3 is not a function
Graph 4 is not a function
Evaluate the function for the given value of x.p(x) = x2-9x, q(X) = VX-6,(p. q)(x) = ?
Answers
The functions are:
[tex]\begin{gathered} p(x)=x^2-9x \\ q(x)=\sqrt[]{x-6} \end{gathered}[/tex]So the product (p*q) is
[tex](p\cdot q)(x)=(x^2-9x)(\sqrt[]{x-6})[/tex]So the solution is is B)
9000 Employees 24 hours a day 365 days a week how many man hours a year
Answers
Answer: 2096 work hours per year
54. Foucault Pendulum
Foucault used a pendulum to demonstrate the Earth’s rotation. There are now over 30 Foucault pendulum displays in the United States. The Foucault pendulum at the Smithsonian Institution in Washington, DC, consists of a large brass ball suspended by a thin 52-ft cable. If the ball swings through an angle of 1°, how far does it travel?
Answers
The distance travelled by the ball is 0.9076 feet.
Foucault used a pendulum to demonstrate the earth’s rotation. There are now over 30 Foucault pendulum displays in the United States. The Foucault pendulum at the Smithsonian Institution in Washington, DC, consists of a large brass ball suspended by a thin 52-foot cable. The ball swings at an angle of 1°. We have to find the distance travelled by the ball.
The ball travels in a circular motion. The radius of the circle is equal to the length of the cable. The distance travelled by the ball is equal to the arc length traversed in circular motion. Let the radius, angle, and distance be denoted by the variables "r", "θ", and "d", respectively.
r = 52 feet
We need to convert the angle from degrees into radians.
θ = 1°
θ = 1°*(π/180°)
θ = π/180
The formula for arc length is used below to calculate the distance.
d = r*θ
d = 52*(π/180)
d = 0.9076
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In simplified radical form, the person can see how many miles?
Answers
We are given the equation:
[tex]d(x)=\sqrt{\frac{3x}{2}}[/tex]Where x is the height over the sea level, where d is in miles, and x in feet. We want to know the value of the function at x = 18 feet. Thus:
[tex]d(18)=\sqrt{\frac{3\cdot18}{2}}[/tex]We can now simplify by dividing 18 by 2:
[tex]d(18)=\sqrt{3\cdot9}[/tex]Now, using properties of radicals:
[tex]d(18)=\sqrt{3}\cdot\sqrt{9}=3\sqrt{3}[/tex]The answer in simplified radical form is:
[tex]d(18)=3\sqrt{3}\text{ }miles[/tex]Using the calculator, we can find the answer to the nearest tenth of a mile d(18)= 5.2 miles
Leann determines the volume of the cylinder shown using the formula V=Bh.
Answers
We have that the base of the cylinder is a circle, and the area of a circle can be calculated with the following equation:
[tex]B=\pi\cdot r^2[/tex]In this case, we have the following:
[tex]\begin{gathered} \pi=3.14 \\ r=\frac{d}{2}=\frac{6}{2}=3 \\ \Rightarrow B=(3.14)(3)^2=(3.14)(3)(3) \end{gathered}[/tex]therefore, the area of the base is B=(3.14)(3)(3) = 28.26 cm^2
2) y = -5 +4V7-2 A) Domain: { All real numbers. } Range: { All real numbers. } B) Domain: x 22 Range: y 2-5 + C) Domain: 'x z 2 Range: ys-5 D) Domain: x 2-2 Range: y z 5
Answers
Looking at the restrictions over the variable x, we know that the domain is:
[tex]x\ge2[/tex]To find the range, notice that:
[tex]\sqrt[]{x-2}\ge0[/tex]On the other hand, the function:
[tex]y=\sqrt[]{x-2}[/tex]is an increasing function (its value grows when x grows), and can get as large as we want provided a sufficiently large value for x. Then, the range of such a function would be:
[tex]y\ge0[/tex]Which does not get altered when we multiply the square root of (x-2) by 4.
Since the function:
[tex]y=-5+4\sqrt[]{x-2}[/tex]is a 5-units shift downwards, then the variable y can take any value from -5 onwards.
Then, the range of the function is:
[tex]y\ge-5[/tex]Another way to find the range is to isolate x from the equation:
[tex]\begin{gathered} y=-5+4\sqrt[]{x-2} \\ \Rightarrow y+5=4\sqrt[]{x-2} \\ \Rightarrow\frac{y+5}{4}=\sqrt[]{x-2} \\ \Rightarrow(\frac{y+5}{4})^2=x-2 \\ \Rightarrow x-2=(\frac{y+5}{4})^2 \\ \Rightarrow x=(\frac{y+5}{4})^2+2 \end{gathered}[/tex]Since we already know that x must be greater than 2, then:
[tex]\begin{gathered} 2\le x \\ \Rightarrow2\le(\frac{y+5}{4})^2+2 \\ \Rightarrow0\le(\frac{y+5}{4})^2 \\ \Rightarrow0\le|\frac{y+5}{4}| \\ \Rightarrow0\le|y+5| \end{gathered}[/tex]From here, there are two options:
[tex]\begin{gathered} 0\le y+5 \\ \Rightarrow-5\le y \\ \text{ Or} \\ 0\le-y-5 \\ \Rightarrow y\le-5 \end{gathered}[/tex]Since we know an equation for y, then:
[tex]\begin{gathered} -5\le-5+4\sqrt[]{x-2} \\ \Rightarrow0\le4\sqrt[]{x-2} \end{gathered}[/tex]Or:
[tex]\begin{gathered} -5+4\sqrt[]{x-2}\le-5 \\ \Rightarrow4\sqrt[]{x-2}\le0 \end{gathered}[/tex]The second case is not true for every x.
Therefore:
[tex]-5\le y[/tex]Therefore:
[tex]\begin{gathered} \text{Domain: }x\ge2 \\ \text{Range: }y\ge-5 \end{gathered}[/tex]35 06286 rounded to the nearest ten thousandth is
Answers
35. 06 286 = 35.0629
Solve the equation3x + 15 = 3(x + 5)
Answers
Given the following equation:
[tex]3x+15=3\mleft(x+5\mright)[/tex]You must solve for "x" as following:
1. Apply the Distributive property:
[tex]\begin{gathered} 3x+15=(3)(x)+(3)(5) \\ 3x+15=3x+15 \end{gathered}[/tex]2. Observe the equation. You can notice that left side is equal to right side. If you try to solve for "x", you get:
[tex]\begin{gathered} 3x-3x=15-15 \\ 0=0 \end{gathered}[/tex]55 pointsWhen the equation log. ( VnUn = 3 is solved for n in terms of a, where a > 0,a # 1, the resulting equation isn=adn = 03ооооn = 9n = 26Previous
Answers
please wait the question is downloading
the answer is
n=a^6What is 505 divided by 2, if there is a remainder, please say it in your answer or explanation.
Answers
Answer:
252,5 or 2,525 rounded.
Step-by-step explanation:
Rounding explanation:
2525_
You rounded to the nearest one's place. The 5 in the ones place rounds down to 5, or stays the same because the digit to the right in the tenth place is _.
2,525
When the digit to the right is less than 5 we round toward 0.2525 was rounded down toward zero to 2,525