Answers
(2 + 3i)^2 = 4 + 12i + 9(-1)
= 4 + 12i - 9
= -5 + 12i
(2 - 3i)^2 = 4 - 12i - 9(-1)
= 4 - 12i + 9
= 13 - 12i
REsult
= -5 + 12i + 13 - 12i
= 8 - 0i
Then
a = 8 and b = 0
Related Questions
Review the proof. Which step contains an error? step 2 step 4step 6step 8
Answers
Answer
Option C is correct.
Step 6 contains the error.
Explanation
Looking through the steps, we can see easily that the mistake occurs at the 6th step, specifically when the process moves from step 5 to step 6
-1 + cos θ = -2 sin² (θ/2)
If one multiplies through by -1
1 - cos θ = 2 sin² (θ/2)
NOT 1 + cos θ = 2 sin² (θ/2)
Hope this Helps!!!
hours worked. pay2. 12.504. 25.006. 37.508. 50.00write a function rule for the table
Answers
The Function is the equation of a line
Step1: we pick any two-point in the of the table and substitute them into the formula below
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1_{}}{x_2-x_1}[/tex](y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)
Let us pick the point (4,25) and (8,50)
where
[tex]x_1=[/tex]Ava borrowed some money from her friend in order to help buy a new video game system. Ava agreed to pay back her friend $2 per week, and after 5 weeks, Ava still owed her friend $10. Write an equation for L, in terms of t, representing the amount Ava owes her friend after t weeks.
Answers
We know that Ava is paying $2 dollars per week so if L is the money that she owes and t is the number of weeks, and I is the initial debt so we can write an equation like:
[tex]L=I-2t[/tex]Now we can replace the info we have to find the value of I so:
[tex]10=I-2(5)[/tex]and we solve for I
[tex]\begin{gathered} I=10+10 \\ I=20 \end{gathered}[/tex]So the final equation will be:
[tex]L=20-2t[/tex]WITHOUT using a graphing device, find the x- and y-intercepts of the graph:y = 3x^3 - 9x^2
Answers
Given:
The function is,
[tex]y=3x^3-9x^2[/tex]To find the x intercept set y=0,
[tex]\begin{gathered} y=3x^3-9x^2 \\ 3x^3-9x^2=0 \\ x^2(3x-9)=0 \\ \Rightarrow x^2=0,3x-9=0 \\ x=0,3x=9 \\ x=0,x=\frac{9}{3} \\ x=0,x=3 \end{gathered}[/tex]So, x-intercepts are ( 0 , 0 ), ( 3, 0 ).
Now to find y-intercepts set x=0.
[tex]\begin{gathered} y=3x^3-9x^2 \\ y=3(0)-9(0) \\ y=0 \end{gathered}[/tex]y- intercept is ( 0 ,0 )
Answer: option e)
In 1906 Kennelly developed a simple formula for predicting an upper limit on the fastest time that humans could ever run distances from 100 yards to 10 miles. His formula is given by t= 0.0588s^(1.125) where s is the distance in meters and t is the time to run thatdistance in seconds.a. Find Kennelly's estimate for the fastest a human could possibly run 1609 meters.t= seconds (Round to the nearest thousandth as needed.)
Answers
For this problem, we are given a formula that predicts the fastest a human can run a certain distance. We need to determine the time a human can run 1609 meters.
The formula is:
[tex]t=0.0588s^{1.125}[/tex]We need to replace s with 1609 and solve for t.
[tex]\begin{gathered} t=0.0588(1609)^{1.125}\\ \\ t=0.0588\cdot4049.26\\ \\ t=238.096 \end{gathered}[/tex]The fastest a human can run 1609 meters is 238.096 seconds.
Instructions: Find the value of that completes the square and creates a perfect square trinomial.
Answers
Solution:
Given the expression;
[tex]x^2+18x+c[/tex]c is the half of square of coefficient of x. That is;
[tex]\begin{gathered} x^2+18x+c=x^2+18x+(\frac{1}{2}(18))^2 \\ \\ x^2+18x+c=x^2+18x+9^2 \\ \\ x^2+18x+c=x^2+18x+81 \\ \\ x^2+18x+81=(x+9)(x+9) \end{gathered}[/tex]Hence, the value of c is;
[tex]c=81[/tex]The selling price of a refrigerator, is $537.60. If the markup is 5% of the dealer's cost, what is the dealer's cost of the refrigerator?
Answers
The cost price of dealer is $512.
We have to find the dealer's cost of refrigerator.
We know that mark up is on dealer's cost.
We have been given the markup as 5%
Let the dealer's cost of refrigerator be x,
Now, we know that there is a markup on it
So, we will calculate the marked up price
Marked up price = (Cost price * Markup percent)/100 + cost price
Marked up price = x*5/100 + x
Marked up price = 5x/100 + x
Marked up price = x/20 + x = (x+20x)20
Marked up price = 21x/20
We know that marked up price is the selling price and we have been given the selling price of the refrigerator
537.60 = 21x/20
537.60*20 = 21x
10752 = 21x
x = 10752/21
x = 512
The dealer's cost price is $512.
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Enzo counted the number of sunny days each of his favorite towns had in the year 2013 and graphed theresults.Light LandBright VillagePlaceShiny TownSun City -050100150200250300Number of Sunny Days
Answers
From the graph, we can see that the town that had most sunny days was Shiny Twon.
So, between this town and Sun City, we have Bright Viallge, that had a number of sunny days between Sun City and Shiny Town.
So the answer is Bright Village.
Can someone help me with this math question?
pic of question below
Answers
The Cartesian equation of the polar equation r² = 5 represents a circle centered at the origin and with radius √5.
What is the Cartesian form of a polar equation?
In this problem we find a polar equation, that is, f(r, θ) = C, whose Cartesian form must be found by using the following substitutions:
x² + y² = r² (1)
x = r · cos θ (2)
y = r · sin θ (3)
Then, the Cartesian form of r² = 5 is:
x² + r² = 5
The polar equation represents a circle centered at the origin and with a radius of √5.
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The Cartesian equation of the polar equation r² = 5 represents a circle centered at the origin and with radius √5.
What is Coordinate System?A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points.
Given that r²=5
we find a polar equation,
x²+y²=r²
whose Cartesian form is found by substituting
x=rcosθ
y=rsinθ
as r²=5 then r=√5
So x²+y²=5.
This is equation of circle in polar form.
Hence it represents a circle with a radius of √5.
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A landscaper has built a U-shaped raised bed in a vegetable garden as shown in the figure. How many cubic yards of soil should be ordered to fill the bed to a depth of 30 inches?
Answers
First calculate the area of the shaded region by considering the U-shaped bed as formed by three rectangles, as follow:
where the lengths of the sides of the rectangles corresponds with the dimensions of the U-shaped bed.
Then, for the area of the figure, use the formula for the area of a rectangle, for all three rectangles, as follow:
A = 5*18 + 3*20 + 5*18
A = 90 + 60 + 90
A = 240
Then, the area is 240 in^2
Next, convert the previous result to yd^2. Use the equivalence 1 yd = 36 in:
[tex]240in^2\cdot\frac{(1yd)^2}{(36in)^2}=0.185yd^2[/tex]Now, to find the volume convert 30 in to yards:
[tex]30in\cdot\frac{1yd}{36in}=0.83yd[/tex]Finally, multiply the previous result by the area of the figure:
[tex]0.185yd^2\cdot0.83yd=0.154yd^3[/tex]if the equation, in which n, m, and r are constants, is true for all positive values of a, b, and c, what is the value of n?
Answers
since n, mand r are the constants for a, b,c n=6
1. On Monday, Mike's account balance shows $-135, on Tuesday, Mikequickly deposited $200. What is his new balance on Tuesday? Write anequation for the situation and find the answer. *
Answers
Ok we need to write an equation for the situation and find the answer. So, let's do it:
Balance on tuesday=previus balance+deposit
Replacing we get:
Balance on tuesday=-135+200=$65
The new balance on tuesday is $65.
Find the radius of a circle in which a 24 cm chord is 4 cm closer to the center than a 16 cm chord. Round your answer to the nearest tenth.
Answers
The diagram representing the scenario is shown below
A represents the center of the circle. It divided each chord equally. Thus, we have CB = 16/2 = 8 for the shorter chord and DE = 24/2 = 12 for the longer chord
Assuming the distance between the
A
Solve the system of two linear inequalities graphically. Graph the solution set of the first linear inequality? Type of boundary line? Two points on boundary line? Region to be shaded?
Answers
Answer:
Explanation:
Given the below system of linear inequality;
[tex]\begin{gathered} y<3 \\ y\ge-5 \end{gathered}[/tex]The graph of the linear inequality y < 3 will be a graph with a dashed line with a y-intercept of 3 since the inequality is not with an equal sign as seen below;
The graph of the 2nd linear inequality y >= -5 will be a graph with a solid line with a y-intercept of -5 since it has both the inequality sign and an equality sign as seen below;
The mean of a population is 100, with a standard deviation of 15. The mean of
a sample of size 100 was 95. Using an alpha of .01 and a two-tailed test, what do
you conclude?
O Accept the null hypothesis. The difference is not statistically significant.
Reject the null hypothesis. The difference is statistically significant.
Accept the null hypothesis. The difference is statistically significant.
Reject the null hypothesis. The difference is not statistically significant.
Answers
We conclude that Reject the null hypothesis. The difference is statistically significant.
Define integers.The symbol used to represent integers is the letter (Z). A positive integer can be 0 or a positive or negative number up to negative infinity. The three elements that make up an integer are zero, the natural numbers, and their additive inverse. It can be shown on a number line, but without the fractional portion. Z stands for it.
A number that contains both positive and negative integers, including zero, is called an integer. There are no fractional or decimal parts in it. Here are a few instances of integers: -5, 0, 1, 5, 8, 97, and 3,043
Given,
The mean of a population is 100, with a standard deviation of 15. The mean of a sample of size 100 was 95.
z = [tex]\frac{95-100}{15/10}[/tex]
z = 3.333
Using the p value technique, the value of p is 0.0009, and since p = 0.0009 0.01 the null hypothesis is rejected, the conclusion is made.
Reject the null hypothesis. The difference is statistically significant.
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If a car in 3 hours travels 156 miles, what is the speed of the car in miles per hour?
Answers
To calculate the speed a vehicle is traveling you have to use the following formula:
[tex]S=\frac{d}{t}[/tex]Where
S: speed
d: distance
t: time
The car traveled d=156miles in t=3hs
Its speed can be calculated as:
[tex]\begin{gathered} S=\frac{156}{3} \\ S=52 \end{gathered}[/tex]The car's speed was 52 miles per hour
The function h is defiend by the following rule. h(x)=5x+4.
Answers
we have the function
h(x)=5x+4.
Create a table
For x=-4
substitute the value of x in the function to obtain h(x)
so
h(-4)=5(-4)+4
h(-4)=-20+4
h(-4)=-16
For x=-3
h(-3)=5(-3)+4
h(-3)=-15+4
h(-3)=-11
For x=1
h(1)=5(1)+4
h(1)=9
For x=2
h(2)=5(2)+4
h(2)=14
For x=5
h(5)=5(5)+4
h(5)=29
What is the explicit rule for the nth term of the geometric sequence? Thanks
Answers
Solution.
Given the sequence
[tex]3,18,108,648,3888[/tex]Test which kind of sequence it is
[tex]\begin{gathered} \frac{18}{3}=6 \\ \frac{108}{18}=6 \\ The\text{ sequence has a common ratio which is 6. } \\ Thus,\text{ it is a geometric sequence} \\ \end{gathered}[/tex][tex]\begin{gathered} The\text{ nth term of a geometric sequence can be determined by the formula} \\ a_n=ar^{n-1} \\ where\text{ a = 1st term} \\ r=common\text{ ratio} \end{gathered}[/tex][tex]a_n=3(6^{n-1})[/tex][tex]The\text{ answer is a}_n=3(6^{n-1})[/tex]use the information provided to write the equation of each circle. center: (12,-13)point on circle: (18, -13)
Answers
Answer:
[tex](x-12)^2+(y+13)^2=36[/tex]Explanation:
Given:
• Center: (12,-13)
,• Point on circle: (18, -13)
First, we find the length of the radius.
[tex]\begin{gathered} r=\sqrt[]{(18-12)^2+(-13-(-13)_{})^2} \\ =\sqrt[]{(6)^2} \\ r=6\text{ units} \end{gathered}[/tex]The general equation of a circle is given as:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Substituting the centre, (h,k)=(12,-13) and r=6, we have:
[tex]\begin{gathered} (x-12)^2+(y-(-13))^2=6^2 \\ (x-12)^2+(y+13)^2=36 \end{gathered}[/tex]The equation of the circle is:
[tex](x-12)^2+(y+13)^2=36[/tex]20 quarts=_ 20_×(1 quart) =_20_×(1\4 gallon) =_20/4_gallons =_5_gallons
Answers
From the question, we are to convert 20 quartz to gallons.
Given
1 quartz = 1/4 gallons
20 quartz = x
Cross multiply and find x;
1 * x = 20 * 1/4
x = 20/4
x = 5
Hence 20 quartz is equivalent to 5 gallons
5+3x=5x-19 I need help solving Multi Step Equations with Variables on both sides.
Answers
The equation we have is:
[tex]5+3x=5x-19[/tex]when we have the variable on both sides of the equation, what we need to do is move all of the variables to one side of the equation.
For example, in this case, to have all of the variables on the same side, we substract 5x to both sides:
[tex]5+3x-5x=5x-19-5x[/tex]On the right side 5x and -5x cancel each other, and we are left with:
[tex]5+3x-5x=-19[/tex]Next, we add the like terms on the left side, 3x-5x is equal to -2x:
[tex]5-2x=-19[/tex]Since we need to solve for x, we substract 5 to both sides, to leave the variable term alone:
[tex]-2x=-19-5[/tex][tex]-2x=-24[/tex]And finally, we divide both sides by -2:
[tex]\begin{gathered} -\frac{2x}{-2}=\frac{-24}{-2} \\ \\ x=12 \end{gathered}[/tex]Answer: x=12
At Paul's Pet Palace, 3/16 of the animals are dogs and 5/24 of the animals are cats. What fraction of the animals are neither dogs nor cat?
Answers
You have that 3/16 of the animals are dogs and 5/24 of the animals are cat.
To determine the fraction of animals that are neither dogs nor cat, consider the following:
If 3/16 are dogs, then 13/16 are other animals, but from this fraction, 5/24 are cats. Then, the subtraction 13/16 - 5/24 results in the fraction of animals that are neither dogs nor cat:
[tex]\frac{13}{16}-\frac{5}{24}=\frac{312-80}{384}=\frac{232}{384}[/tex]simplify the last fraction:
[tex]\frac{232}{384}=\frac{116}{192}=\frac{58}{96}=\frac{29}{48}[/tex]Hence, 29/48 of the animal are neither dogs nor cats
The figure below shows a striaght line AB intersected by another straight line t: Write a paragraph to prove that the measure of angle 1 is equal to the measure of angle 3. (10 points)
Answers
Angles 1 and 3 are vertical angles, that is, are pairs of opposite angles made by intersecting lines. If 2 angles are vertical then they are congruent, in other words, they have the same measure.
On a number line, let point P represent the largest integer value that is less than V380.Let point Q represent the largest integer value less than 54.What is the distance between P and Q?A. 10B. 11C. 12D. 13
Answers
We have to find P and Q first.
P is the largest integer that is less than the square root of 380.
P is 19.
Q is the largest number that is less than the square of 54.
Q is 7.
Then the distance between P and Q is |19-7|=12.
Answer: C. 12
In AOPQ, 0 = 500 cm, p = 600 cm and q=380 cm. Find the measure of P to thenearest 10th of a degree.
Answers
Answer: Triangle has three sides, which are:
[tex]\begin{gathered} O=500\operatorname{cm} \\ P=600\operatorname{cm} \\ Q=380\operatorname{cm} \\ \end{gathered}[/tex]We need to find the angle p, that is right across the side P:
[tex]\angle A=\arccos (\frac{b^2+c^2+a^2}{2bc})=0.97895\text{rad}=56.09\text{degres}[/tex]This is the value of angle A
What is the value of 0 put a comma and space between answer sin61°=cos=0; cos17°=sin0;
Answers
For
[tex]\begin{gathered} \sin 61=\cos \theta \\ \theta=\cos ^{-1}(\sin 61) \\ \end{gathered}[/tex]For
[tex]\begin{gathered} \cos 17=\sin \theta \\ \theta=\sin ^{-1}(\cos 17) \\ \end{gathered}[/tex]The solution to the equation4(x + 2) =3(5-x) is:
Answers
ANSWER:
The value of x is 1, that is, the solution of the equation is 1
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]4\cdot(x+2)=3\cdot(5-x)[/tex]Solving for x:
[tex]\begin{gathered} 4x+8=15-3x \\ 4x+3x=15-8 \\ 7x=7 \\ x=\frac{7}{7} \\ x=1 \end{gathered}[/tex]The lengths of two sides of an isosceles triangle are 8 and 10. The length of the third side could beA. either 8 or 10B. 6, onlyC. 8, onlyD. 10, only
Answers
From Triangle Inequality Theorem
The sum of any 2 sides of a triangle must be greater than the measure of the third side.
The sum of 2 sides is less than (or equal to) the measure of a third side.
In an isosceles triangle, two sides are equal.
Then we have an option the third side= 8. Let's analyze!
c+a> b - for a and c =8
8+8 > 10
16> 10
The second option is the third side= 10. Let's analyze!
c+a> b - for a and c =10
10+10> 8
20> 8
Answer
A. either 8 or 10
The radius of a circle is 6 kilometers. What is the area of a sector bounded by a 126° arc?Give the exact answer in simplest form. ____ square kilometers.
Answers
It is given that the radius is 6 kilometers and the arc is 126 degrees.
The area of sector is given by:
[tex]\frac{126}{360}\times\pi\times6^2=39.5840\operatorname{km}^2[/tex]Therefore the area is 39.5840 square kilometers.
Suppose that the functions and g are defined for all real numbers x as follows. f(x) = x + 3; g(x) = 2x - 2 Write the expressions for (fg)(x) and (f - g)(x) and evaluate (f + g)(3)
Answers
Solution
Given
[tex]\begin{gathered} f(x)=x+3 \\ \\ g(x)=2x-2 \end{gathered}[/tex]Then
[tex](f\cdot g)(x)=f(x)\cdot g(x)=(x+3)(2x-2)=2x^2+4x-6[/tex][tex](f-g)(x)=f(x)-g(x)=(x+3)-(2x-2)=x-2x+3+2=5-x[/tex][tex](f+g)(3)=f(3)+g(3)=(3+3)+(2(3)-2)=6+4=10[/tex]