Show how Aaliyah can finish her work using complexnumbers. As a reminder, her last step before requiringassistance is:(x- 3)2=1Be sure to show ALL steps that lead to your finalsolution set!
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aAs given by the question
There are given that the equation
[tex]x^2-6x+10=0[/tex]Now,
The solution of the Aaliyah is:
[tex](x-3)^2=-1[/tex]Then,
The next step of the given solution is:
[tex]\begin{gathered} (x-3)^2=-1 \\ x-3=\sqrt[]{-1} \end{gathered}[/tex]According to the concept of complex number
[tex]i=\sqrt[]{-1}[/tex]So,
[tex]\begin{gathered} x-3=\sqrt[]{-1} \\ x-3=i \\ x=i+3 \end{gathered}[/tex]Related Questions
Find all values of j for which the quadratic equation has no real solutions.7x^2+9x+j=0Write your answer as an equality or inequality in terms of j.
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The discriminant of a quadratic equation tells us whether there are two solutions, one solution or no real solutions and it is described as the part inside the root
[tex]D=b^2-4a\cdot c[/tex]the conditions are:
[tex]\begin{gathered} D>0;\text{ two real solutions } \\ D=0;\text{ one real solution} \\ D<0;\text{ no real solution} \end{gathered}[/tex]give values to a, b, and c, which are 7, 9, and j respectively.
using the third condition find the values for j that make the quadratic equation have no solution
[tex]\begin{gathered} 9^2-4\cdot7\cdot j<0 \\ \end{gathered}[/tex]solve the inequality
[tex]\begin{gathered} 81-28j<0 \\ -28j<-81 \\ 28j>81 \\ j>\frac{81}{28} \end{gathered}[/tex]Change to Ax+By=C form. y=-5x+9
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The function is:
[tex]y=5x+9[/tex]Now to put in the form Ax+By=c we hace to let the number that don't have x ot y in the left side of the equation anthe the rest of the term in the right side of the equation:
[tex]-5x+y=9[/tex]where:
[tex]\begin{gathered} A=-5 \\ B=1 \\ C=9 \end{gathered}[/tex]if like bc is parallel to line AD what is the measure of BAD
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D.
A bag is made with 1,350 green, blue, and white beads. Twice as many green beads as blue beads are used the number of white beads is half of the total number of green and blue beads. how many green beads are used?
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Write equations for each succeeding sentences. Use G for green, B for blue, and W for white beads.
[tex]\begin{gathered} G+B+W=1350 \\ G=2B \\ W=\frac{1}{2}(G+B) \\ G=\text{?} \end{gathered}[/tex]Solve for the value of G as follows.
Rewrite the equations in terms of B. Since the value of G is already written in terms of B, write the value of W in terms of B.
[tex]\begin{gathered} W=\frac{1}{2}(G+B)_{}_{} \\ =\frac{1}{2}(2B+B) \\ =\frac{1}{2}(3B) \end{gathered}[/tex]Substitute the values of G and W, in terms of B, into the first equation and then solve for B.
[tex]\begin{gathered} G+B+W=1350 \\ 2B+B+\frac{1}{2}(3B)=1350 \\ 4B+2B+3B=2700 \\ 9B=2700 \\ B=300 \end{gathered}[/tex]Note that we obtained the third equation by multiplying both sides of the equation by 2. This eliminates the denominator, 2, from the left side of the equation.
Substitute the obtained value of B in the second given equation to solve for G.
[tex]\begin{gathered} G=2B \\ =2(300) \\ =600 \end{gathered}[/tex]Substitute the obtained value of B into the obtained value of W and then simplify.
[tex]\begin{gathered} W=\frac{1}{2}(3B) \\ =\frac{1}{2}\lbrack3(300)\rbrack \\ =\frac{1}{2}(900) \\ =450 \end{gathered}[/tex]To check if the answer is correct, add all the number of beads per color and determine if the sum is the same as the given value.
[tex]\begin{gathered} G+B+W=1350 \\ 600+300+450=1350 \\ 1350=1350 \end{gathered}[/tex]Since the equation is true, the answers are correct.
Therefore, there must be 600 green beads that were used.
1.X: -2, -1, 0, 1, 2Y: -7, -2, 1, -2, -7Domain:Range:Function: Yes Or no?
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We have
X: -2, -1, 0, 1, 2
Y: -7, -2, 1, -2, -7
the domain is the set of all the possible values for x, in this case, we have
{-2, -1, 0, 1, 2}
the range is the set of all possible values of y in this case we have
{-7, -2, 1}
With this information, we can say it is a function,
Using the following images, name the intersection of line QS and line LC.
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The intersection between two non-parallel lines is a point, as we can see in the following diagram:
As we can see from the image, the intersection point between QS and LC is W.
Answer: Point W
When Ryan runs the 400 meter dash, his finishing times are normally distributedwith a mean of 65 seconds and a standard deviation of 2 seconds. If Ryan were to run.36 practice trials of the 400 meter dash, how many of those trials would be between63 and 65 seconds, to the nearest whole number?
Answers
Solution
Step 1
Dalvin's finishing time is normally distributed with a mean of 65 seconds and a standard deviation of 1 second.
[tex]\begin{gathered} \text{Mean }\mu\text{ = 65} \\ Standard\text{ deviation }\sigma\text{ = 1} \end{gathered}[/tex]Step 2
Under the empirical rule, 68% of the results will be within 1 standard deviation.
Step 3
Since the standard deviation is 1 second, 68% of Dalvin's finishing time will be between 63 and 65 seconds.
Final answer
68%
Given the area of triangle AEC=63cm^2, find the area of triangle ABC.
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We are given that the area of triangle AEC = 63 centimeters squared.
Since segment CD equals segment DB that means that triangle CDA and triangle BDA have the same area, and also triangle CDE and triangle BDE have the same area. This means mathematically the following:
[tex]A_{\text{ADC}}-A_{\text{AEC}}=A_{\text{ADB}}-A_{\text{AEB}},\text{ (1)}[/tex]Also
[tex]A_{\text{ADC}}=A_{\text{ADB}},\text{ (2)}[/tex]Replacing equation (1) in equation (2)
[tex]A_{\text{ADC}}-A_{\text{AEC}}=A_{\text{ADC}}-A_{\text{AEB}}[/tex]Simplifying
[tex]A_{\text{AEC}}=A_{\text{AEB}}[/tex]Therefore:
[tex]A_{\text{AEB}}=63\operatorname{cm}^2[/tex]Since segments DE and EA is the same, then:
[tex]A_{\text{CDE}}=A_{\text{AEC}}[/tex]Therefore:
[tex]A_{\text{CDE}}=63\operatorname{cm}^2[/tex]Since
[tex]A_{\text{CDE}}=A_{\text{BDE}}[/tex]We have:
[tex]A_{\text{BDE}}=63\operatorname{cm}^2[/tex]therefore, the area of the triangle is:
[tex]A_{\text{ABC}}=A_{\text{AEC}}+A_{\text{AEB}}+A_{\text{CDE}}+A_{\text{BDE}}[/tex]Replacing the known values:
[tex]\begin{gathered} A_{\text{ABC}}=68+68+68+68=4(68) \\ A_{\text{ABC}}=272\operatorname{cm}^2 \end{gathered}[/tex]Find the quotient. Express the final result using positive integer exponents only (72x^-1 y^4)^-1 / (8x^8y^3)
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ANSWER:
[tex]\frac{1}{576x^7y^7}[/tex]STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]\frac{\left(72x^{-1}y^4\right)^{-1}}{8x^8y^3}[/tex]We operate to simplify and we are left with the following:
[tex]\frac{72^{-1}x^{-1\cdot-1}y^{4\cdot-1}}{8x^8y^3}=\frac{\frac{1}{72}xy^{-4}}{8x^8y^3}=\frac{1}{72\cdot8\cdot x^8\cdot x^{-1}\cdot y^3\cdot y^4}=\frac{1}{576x^7y^7}[/tex]What value of x will make the following equation true? Log4(4^5x+1)=16•7/5•0•1/5•3(Picture for clarification)
Answers
Given:
There are given that expression:
[tex]log_4\left(4^{5x+1}\right?=16[/tex]Explanation:
From the given log function:
[tex]log_4(4^{5x+1})=16[/tex]According to the log rule:
[tex]5x+1=16[/tex]Then,
[tex]\begin{gathered} 5x+1=16 \\ 5x=16-1 \\ x=\frac{15}{5} \\ x=3 \end{gathered}[/tex]Final answer:
Hence, the correct option is D.
Which expression has the same value as sin(20∘)?A)cos(10∘)B)cos(20∘)C)cos(40∘)D)cos(70∘)
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sin 20 = y / r
cos 70 = y/ r
sin 20 = cos 70 = 0.342
Answer:
cos 70
60 is the LCM of witch of the following pair of numbers? 12 and 18 .....10 and 30.......15 and 20......20 and 25 witch on
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The correct pair is 15 and 20
Here, we want to select the pair of numbers which 60 is their LCM
What this mean is we want to select two numbers that 60 is the smallest multiple they have
For 12 and 18, the lcm is 36; so this is incorrect
For 10 and 30, the lcm is 30; so this is also incorrect
for 20 and 25, the lcm is 100; this is also incorrect
for 15 and 20, the lcm is 60 and this is our correct choice
the following ordered pairs give the entrance exam scores x and the grade-point averages y after 1 year of college for 10 students.interpret the slope of the line in a relationship of the problem.
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Find the slope
we take the points
(75,2.3) and (82,3)
so
m=(3-2.3)/(82-75)
m=0.7/7
m=0.1
the units of the slope are grade-point averages by entrance exam scores
The total volume of a tree increases
8% each year. What will its volume be
after 7 years if its volume is 5 cubic
meters now?
A) 5(1.08)^7
B) 5(7)(0.08)
C) 5(0.08)^7
D) 5(7)(1.08)
Answers
Answer:
A
Step-by-step explanation:
it all starts with 5 m³.
after one year this will be
5 × 1.08
as the original 5 m³ have increased by 8% (= multiplication by 1.08, as 8% = 0.08, and adding 8% means 100% + 8% = 1 + 0.08 = 1.08).
after the second year we will see another increase by 8% compared to the previous year.
so,
(5 × 1.08) × 1.08 = 5(1.08)²
...
and so, after the nth year, the volume is
5(1.08)^n
therefore, after 7 years means n = 7, and we get
5(1.08)⁷
Line A is perpendicular to Line B.If the slope of Line A is -5,what is the slope of Line B?391410
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Given:
Line A is perpendicular to Line B.
Required:
what is the slope of Line B?
Explanation:
Based on the given conditions, formulate.
[tex]m=\frac{-5}{3}[/tex]Find the slope of line that is perpendicular to
[tex]\frac{-5}{3}[/tex][tex]m=\frac{3}{5}[/tex]Required answer:
[tex]m=\frac{3}{5}[/tex]Rewrite the product (15y)(4x) using the Commutative Property of Multiplication.(15x)(4y)19xy(4x)(15y)(4y)(15x)
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Answer:
(4x)(15y)
Explanation:
The commutative property of multiplication says that
(a)(b) = (b)(a)
Where a and b are the factors. In this case, the factors are 15y and 4x, so
(15y)(4x) = (4x)(15y)
Therefore, the answer is
(4x)(15y)
It takes 3 1/3 spoons of chocolate syrup to make 3 1/2 į gallons of chocolate milk.How many spoons of syrup would it take to make 5 gallons of chocolate milk?
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Given:
[tex]3\frac{1}{3}spoons\text{ of chocolate syrup to make 3}\frac{1}{2}\text{ gallons of chocolate milk.}[/tex][tex]\begin{gathered} \text{Number of spoons required of syrup to make 5gallons of chocolate milk=}\frac{3\frac{1}{3}}{3\frac{1}{2}}\times5 \\ No\text{ of spoons required of syrup to make 5gallons of chocolate milk=}\frac{\frac{10}{3}}{\frac{7}{2}}\times5 \\ No\text{ of spoons required of syrup to make 5gallons of chocolate milk=}\frac{10}{3}\times\frac{2}{7}\times5 \\ No\text{ of spoons required of syrup to make 5gallons of chocolate milk=}\frac{100}{21} \\ No\text{ of spoons required of syrup to make 5gallons of chocolate milk=}4\frac{16}{21}\text{ } \end{gathered}[/tex]I need help with my math
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The Slope of a Line
Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]The graph provided suggests the use of the points (3,-3) and (5,-3). The slope is:
[tex]\displaystyle m=\frac{-3+3}{5-3}=\frac{0}{2}=0[/tex]The slope of the line is 0. It corresponds to a horizontal line
Suppose that a is an angle with seca alpha = - 11/10 and a is not in the third quadrant. Compute the exact value of sina. You do not have to rationalize the denominatorSin a =
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Given that
[tex]sec\text{ }\alpha=-\frac{11}{10}[/tex][tex]\alpha=sec^{-1}(-\frac{11}{10})=155.4^o[/tex]Now
[tex]\sin\alpha=\sin155.4=0.41628[/tex]Can anyone help me with this (there is a part two)
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Number of bottles: 6
Coupon discount on each bottle: $0.50
Final price: $5.10
If p is the regular price of each bottle, then 6p is the regular price of 6 bottles. This means that we have used 6 coupons of $0.50, so the total discount should be 6*0.50 dollars. We subtract this amount from the regular price (6p), leading to $5.10. The equation that represents this situation is:
[tex]\begin{gathered} 6p-6\cdot0.50=5.10 \\ \Rightarrow6(p-0.50)=5.10 \end{gathered}[/tex]What is anequation of the line that passes through the points (-7, -7) and(-7,4)?
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The line passes through (-7,-7) and (-7,4); thus the x-component remains fixed but the y-component is free
the y- component can take any value! thus the equation is
x=-7
There were 750 books sold last week at side bookstore. The table below summarizes these books by genre. This information is also presented as a circle graph. Find the central angle measure x, for self help slice in the circle graph. Do not round.
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we have that
total books sold=750
self help=117
the percentage of self-help books is equal to
117/750=0.156=15.6%
Remember that
in the complete circle, the angle of 360 degrees represents the 100%
so
Applying proportion
Find out the measure of angle x for a percentage equal to 15.6%
360/100=x/15.6
solve for x
x=(360/100)*15.6
x=56.16 degreesWhat are the coordinates of the first and last two points of his route?
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Answer:
Step-by-step explanation:
Wich function is used to find y,the remaining balance after x number of payments have been made?
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The slope of a line that passes through points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]The line of the picture passes through (0, 20000) and (40, 0) then its slope is:
[tex]m=\frac{0-20000}{40-0}=-500[/tex]The y-intercept of the line is (0, 20000)
Slope-intercept form of a line:
y = mx + b
where m is the slope and b is the y-coordinate of the y-intercept. Replacing with m = -500 and b = 20000, we get:
y = -500x + 20000
The value of an antique car is modeled by the function
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when we are modeling increments using functions the standard form should be
[tex]V(t)=A\cdot(1+r)^t[/tex]In which A represents the initial value and r represents the rate it is increasing per year.
In this case to find what is the increment per year we equal what is inside the parentheses
[tex]\begin{gathered} 1+r=1.004 \\ r=1-1.004 \\ r=0.004 \end{gathered}[/tex]now this decimal can be represented as a percentage if we multiply by 100
[tex]\begin{gathered} \text{\%r}=0.004\cdot100 \\ \text{\%r=0.4\%} \end{gathered}[/tex]It is increasing by 0.4% per year.
∣/8∣=3Group of answer choicesx = 2 and x = 4x = 16 and x = 4x = -24 and x = 24x = -6 and x = -8
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Given:
[tex]|\frac{x}{8}|=3[/tex]Applying absolute value property
[tex]\frac{x}{8}=-3\text{ and }\frac{x}{8}=3[/tex]Multiply both-side by 8.
That is;
[tex]\begin{gathered} \frac{x}{8}\times8=-3\times8 \\ \\ \text{and } \\ \\ \frac{x}{8}\times8=3\times8 \end{gathered}[/tex][tex]x=-24\text{ and x=24}[/tex]Hence, x=-24 and x=24
Chris rented a truck for one dah There was a base fee of 18.95$ and there was an additional charge of 83 cents for each mile driven. Chris had to pay 209.02 when he returned the truck. For how many miles did he drive the truck?
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Given:
Base fee $18.95
83 cents for each mile driven.
[tex]\text{Amount excluding the base fee=209.02-18.95}[/tex][tex]\text{Amount excluding the base fee= \$}190.07[/tex][tex]\text{Number of miles driven =}\frac{\text{19007}}{83}[/tex][tex]undefined[/tex]When a figure is translated its orientation (blank) and the measurements of its angles (blank).The options for both blanks are the same and the options are, remain the same or change
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First of all, remember that translation is a transformation which doesn't imply a change of size or shape, that is, the image will be congruent to its image.
Having said that, the complete paragraph would be
When a figure is translated its orientation remains the same and the measurements of its angles remain the same.
The orientation doesn't change because it's defined as the position of points of the figure, these points change its position where we rotate the figure, which is not the case here.
Consider the line . y=3/2x+3Find the equation of the line that is parallel to this line and passes through the point .(-8,3)Find the equation of the line that is perpendicular to this line and passes through the point . (-8,3)
Answers
Answer:
Equation of parallel line: y = 3x/2 + 15
Equation of perpendicular line: y = - 2x/3 - 7/3
Explanation:
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept
The equation of the given line is
y = 3x/2 + 3
By comparing with the slope intercept equation,
slope, m = 3/2
Recall, if two lines are parallel, it means that they have the same slope. Thus, the slope of the parallel line passing through the point, (- 8, 3) is 3/2. We would find the y intercept, c by substituting m = 3/2, x = - 8 and y = 3 into the slope intercept equation. We have
3 = 3/2 * - 8 + c
3 = - 12 + c
c = 3 + 12 = 15
By substituting m = 3/2 and c = 15 into the slope intercept equation, the equation of the parallel line passing through the point, (- 8, 3) is
y = 3x/2 + 15
Recall, if two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. Thus, the slope of the perpendicular line passing through the point, (- 8, 3) is - 2/3. We would find the y intercept, c by substituting m = - 2/3, x = - 8 and y = 3 into the slope intercept equation. We have
3 = - 2/3 * - 8 + c
3 = 16/3 + c
c = 3 - 16/3 = - 7/3
By substituting m = - 2/3 and c = - 7/3 into the slope intercept equation, the equation of the perpendicular line passing through the point, (- 8, 3) is
y = - 2x/3 - 7/3
A company sold garden hoses at a reduced price of $5.64 and took an end of season markdown of $13.35 what was the original selling price of each house? Use the formula M=S-N, where M is the markdown, S is the original selling price, and N is the reduced price. The original selling price of each hose is?
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From the details provided in the question, the formula;
[tex]M=S-N[/tex]Can be used to derive either of;
Markdown, Original selling price or Reduced price.
Having been given;
[tex]\begin{gathered} \text{Markdown}=13.35 \\ \text{ Reduced Price=5.64} \\ \text{Original selling price=?} \end{gathered}[/tex]We can now substitute the known values as follows;
[tex]\begin{gathered} M=S-N \\ 13.35=S-5.64 \\ \text{Add 5.64 to both sides;} \\ 13.35+5.64=S-5.64+5.64 \\ 18.99=S \end{gathered}[/tex]The original selling price, that is N, is now;
$18.99