Consider the equation: x2 – 3x = 18A) First, use the "completing the square" process to write this equation in the form (x + D)² =or (2 – D)? = E. Enter the values of D and E as reduced fractions or integers.=z? - 3x = 18 is equivalent to:– 3rPreview left side of egn:B) Solve your equation and enter your answers below as a list of numbers, separated with a commawhere necessary.Answer(s):
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Part A.
The quadratic equation,
[tex]ax^2+bx+c=0[/tex]is equivalent to
[tex]a(x+\frac{b}{2a})^2=\frac{b^2}{4a}-c[/tex]In our case a=1, b=-3 and c=-18. Then, by substituting these value into the last result, we have
[tex](x+\frac{-3}{2(1)})^2=(\frac{-3}{2(1)})^2+18[/tex]which gives
[tex]\begin{gathered} (x-\frac{3}{2})^2=\frac{9}{4}+18 \\ (x-\frac{3}{2})^2=\frac{9}{4}+18 \\ (x-\frac{3}{2})^2=\frac{9+72}{4} \\ (x-\frac{3}{2})^2=\frac{81}{4} \end{gathered}[/tex]Therefore, the answer for part A is:
[tex](x-\frac{3}{2})^2=\frac{81}{4}[/tex]Part B.
Now, we need to solve the last result for x. Then, by applying square root to both sides, we have
[tex]x-\frac{3}{2}=\pm\sqrt[]{\frac{81}{4}}[/tex]which gives
[tex]x-\frac{3}{2}=\pm\frac{9}{2}[/tex]then, by adding 3/2 to both sides, we obtain
[tex]x=\frac{3}{2}\pm\frac{9}{2}[/tex]Then, we have 2 solutions,
[tex]\begin{gathered} x=\frac{3}{2}+\frac{9}{2}=\frac{12}{2}=6 \\ \text{and} \\ x=\frac{3}{2}-\frac{9}{2}=\frac{-6}{2}=-3 \end{gathered}[/tex]Therefore, the answer for part B is: -3, 6
Related Questions
You have quarters and dimes that total $2.80 your friend says it is possible that the number of quarters is 8 than the number of dimes. Is your friend correct? Let d represent the number of dimes. An equation that models this situation is ____ = 2.80
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If d is the amount of dimes and the number of quarters is 8 times the number of dimes, then, you have 8d number of quarters.
Moreover, due to the total amount of money is $2.80, then, you have the following expression:
d + 8d = 2.80 simplify like terms left side
9d = 2.80
Hence, the equation is 9d = 2.80
To determine if your friend is correct, solve the equation for d by dividing by 9 both sides:
d = 2.80/9 =
The domain of a quadratic function is all real numbers. The range of the quadratic function is determined by the vertex of the parabola. If the parabola has a minimum value than the range will be all outputs (less than or greater than) that maximum value. If the parabola has a maximum value then the range will be all outputs (equal to or less than) that maximum value.
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Answer:
If the parabola has a minimum value, the range will be all outputs greater than the maximum value. If the parabola has a maximum value then the range will be all outputs less than that maximum value.
Explanation:
The range of a function is the set of values that the y-variable can take. If the parabola has a minimum value, the y-variable can take values greater than or equal to the minimum.
In the same way, if the parabola has a maximum value, the y-variable can take values less than the maximum.
Therefore, the answers are:
If the parabola has a minimum value, the range will be all outputs greater than the maximum value. If the parabola has a maximum value then the range will be all outputs less than that maximum value.
a. Use the line of random numbers to obtain and report the resulting list of heads and tails. Use H for heads and T for tails.Q0000 00.000 0.0.000 00000
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Given -
An unbiased coin is tossed
To Find -
The list of heads and tails while tossing a coin
Assumption -
The coin is tossed twice
Explaination -
The following table lists some possible arrangements for the experiment
Solve for 3+y/2=-212
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You have the following equation:
[tex]3+\frac{y}{2}=-212[/tex]In order to solve the previous equation for y, proceed as follow:
3 + y/2 = -212 subtract 3 both sides
y/2 = -212 - 3 simplify right side
y/2 = -215 multiply by 2 both sides to cancel the denominator left side
y = -215(2)
y = -430
Hence, the solution for y in the given equation is y = -430
Consider the quadratic function y=2x2 – 12x + 20.Rewrite the equation in vertex format.
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The function:
[tex]y=2x^2-12x+20[/tex]has the form:
[tex]y=ax^2+bx+c[/tex]with a = 2, b = -12, and c = 20.
The vertex form of a quadratic function is:
[tex]y=a(x-h)^2+k[/tex]where (h,k) is the vertex.
The x-coordinate of the vertex, h, is computed as follows:
[tex]\begin{gathered} h=\frac{-b}{2a} \\ h=\frac{-(-12)}{2\cdot2} \\ h=\frac{12}{4} \\ h=3 \end{gathered}[/tex]The y-coordinate of the vertex, k, is found replacing h into the formula of the function, as follows:
[tex]\begin{gathered} k=2h^2-12h+20 \\ k=2\cdot3^2-12\cdot3+20 \\ k=18-36+20 \\ k=2 \end{gathered}[/tex]Finally, the quadratic function in vertex form is:
[tex]y=2(x-3)^2+2[/tex]Error Analysis .... Your friend knows that <1 and <2 are complementary and that <1and <3 are complementary. He concludes that <2 and <3 must becomplementary. What is his error in reasoning? *
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
We must analyze the problem to find the error.
Data
∠1 + ∠2 = 90
∠1 + ∠3 = 90
Step 02:
∠1 = 25
25 + ∠2 = 90
∠2 = 90 - 25
= 65
∠1 = 25
25 + ∠3 = 90
∠3 = 90 - 25
= 65
∠2 + ∠3 = 130
The answer is:
∠2 = ∠3
Angle 2 and angle 3 are equal, but they are not always complementary.
Which facts are true for the graph of the function below? Check all that apply.F(x) = log8x
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EXPLANATION
Given the function f(x) = log_8 x.
The facts that apply are:
B. The x-intercept is (1,0)
F. It is increasing.
Find the quotient. Write your answer in standard form. 3+ O A. + COLO O B.-1 O C. 1-1 OD. llo 011
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Option A is correct.
The given complex number is
[tex]\frac{3+i}{3-i}[/tex]Multiply the numerator and denominator by 3+i and solve as follows:
[tex]\begin{gathered} \frac{3+i}{3-1}\times\frac{3+i}{3-i}=\frac{(3+i)^2}{3^2-i^2} \\ =\frac{3^2+i^2+6i}{9+1} \\ =\frac{9-1+6i}{10} \\ =\frac{8+6i}{10} \\ =\frac{8}{10}+\frac{6}{10}i \\ =\frac{4}{5}+\frac{3}{5}i \end{gathered}[/tex]The international club at school has 125 members, many of whom speak multiple languages, the most commonly spoken languages in the club are English, Spanish and Chinese.55 students speak Spanish30 students speak Chinese89 students speak English15 students speak Spanish and Chinese20 students speak Chinese and English33 students speak Spanish and English8 students speak allCreate a Venn Diagram
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8 students speak all, so it is in the intersection of the three
15 speak Spanish and Chinese, but 15-8=7 do not speak English
20 speak Chinese and English, but 20-8=12 do not speak Spanish
33 speak Spanish and English, but 33-8=25 do not speak Chinese
55 speak Spanish, but 55-25-8-7=15, do not speak English or Chinese
30 speas chinese, but 30-12-8-7=3 do not speak English or Spanish
89 speak English, but 89-12-8-25=44 do not speak Spanish or Chinese
To end our diagram, we add
[tex]44+25+15+7+8+12+3=114[/tex]Then 125-114=11 students don't speak English, Spanish or Chinese
Show exact steps to solve and draw the construction!Don't mind the pink writing.
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Step by step:
1. Open the compass to a radius less than half the segment MN.
2. Usin point P as center draw two arcs that intersecs line MN on both sides of the point P (As you use the compass those arcs are in the same distance from point P)
3. Lavel the point of intersection of arcs with line MN (Use any other letter as A and B)
4. Use the points A and B as centers and using the compass draw two arcs (one with each point A and B) above the line that intersects each other.
5. Mark the point of intersection of arcs and link it with point P (as the line needs to go throught P corss point P and continue with the line) . That line is the perpendicular line to MN trought point P)
What would be and example of a point , a plane , and a line in a classroom setting?
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16.2-(3×4) + (14÷2) I have to tell how many terms the expression has.
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The expression we have is:
[tex]16.2-(3\times4)+(14\div2)[/tex]A term in an expression in every part of the said expression, for example, in the expression 10+3, 10 and 3 are terms.
For the case of our expression, each number is a term:
16.2, 3, 4, 14, and 2 are terms.
So in total, we have 5 terms.
Answer: 5 terms
I don't know how to shade for the 2nd one please help
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Answer: Your result (without simplifying) is actually 2/36, so you would shade two boxes out of the 36 shown.
NOTE: For problem #19, you have 6 boxes for shading, so each box represents 3 increments (3x6=18 boxes). For your result of 5/18, you should only shade the first box and 2/3 of the next box (the other four boxes should be unshaded).
Hope this helps!
Step-by-step explanation:
Hernando’s salary was $47,500 last year. This year his salary was cut to $38,475. Find the percent decrease
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To determine the percentage of decrease that Hernando's salary was cut, we first calculate the total value, then the ratio of this value to the initial one, then we multiplicate by 100, to get it in percent, as follows:
[tex]\begin{gathered} 47,500-38,475=9,025 \\ \frac{9,025}{47,500}=0.19 \\ 0.19\times100=19\text{ \%} \end{gathered}[/tex]From the solution we developed above, we are able to conclude that the salary of Hernando was cut by 19 %−6x−y=9−2x+10y=−28 please help me
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We have to solve the linear system:
-6x - y = 9
-2x + 10y = -28
Multiply both sides of the first equation by 10:
-60x - 10y = 90
-2x + 10y = -28
Now sum both equations, we get:
-60x - 2x -10y + 10y = 90 - 28
-62x + 0 = 62
-62x = 62
x = 62 / -62
x = -1
Now lets find y. I'm going to use the first equation since it is easier to do the math:
-6x - y = 9
-6(-1) - y = 9
6 - y = 9
-y = 9 - 6
-y = 3
y = -3
So the solution of the linear system is x = -1, y = -3 or simply (-1, -3).
Answer: x = -1 ; y = -3
4/8 =Express your answer as a whole number or fraction.
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Given the fraction:
[tex]\frac{4}{8}[/tex]Let's simplify the fraction.
To simplify, divide the denominator and the numerator by the Greatest Common Factor (GCF).
GCF of 4 and 8 = 4
Hence, we have:
[tex]\frac{4\div4}{8\div4}=\frac{1}{2}=0.5[/tex]Hence, the simplified fraction is:
[tex]\frac{1}{2}[/tex]As a decimal:
[tex]0.5[/tex]ANSWER:
[tex]\frac{1}{2}[/tex]The following data are the final exams scored on the 13th student in a small calculus class
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The following data set for the final exam score in a calculus class
(a) The data set represents a sample data
(b) Range
[tex]\begin{gathered} \text{Range = Highest mark - Lowest mark} \\ \text{Range = 98-60} \\ \text{Range = 38} \end{gathered}[/tex](c) Variance
[tex]\text{Variance = }\frac{\sum ^{}_{}(x-\bar{x})^2}{n}=\frac{2796.36}{13}=215.105[/tex](d) Standard Deviation
[tex]\begin{gathered} S\mathrm{}D\text{ = }\sqrt[]{variance} \\ S\mathrm{}D\text{ = }\sqrt[]{215.105} \\ S\mathrm{}D\text{ = }14.666 \end{gathered}[/tex]write the first three terms of sequence A(n+1)=1/2A(n) for n ≥ 1 and A(1)=4write your answer separated by commas, with no space for example 5,6,7
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For n= 1
[tex]A(1+1)=\frac{1}{2}A(1)[/tex]but A(1) = 4
[tex]A(2)\text{ = }\frac{1}{2}(4)\text{ = 2}[/tex]For n= 2
[tex]A(2+1)=\frac{1}{2}A(2)[/tex][tex]A(3)=\frac{1}{2}A(2)[/tex]But A(2) = 2
[tex]A(3)\text{ =}\frac{1}{2}(2)=\text{ 1}[/tex]Hence, the first three terms are;
4, 2, 1
Metropolis Elementary recommends a ratio of 2 adults for every 24 children on every field trip.
The school has 20 adults and 350 students.
If everyone goes on a field trip, would that meet the recommendation?
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If everyone goes on a field trip, then 29 adults are needed for 350 students, so the recommendation by Metropolis Elementary does not meet.
What is ratio?It is the comparison of one quantity with another. For example, if your weight is 30 kg and your father's weight is 90 kg, then the ratio of weight is 1:3.
Given:
The school has 20 adults and 350 students,
The Ratio of adults over children = 2 /24 = 1 / 12, which means for every 12 children there required one adult,
So to find the total adults needed = total students / 12
Total adults needed = 350 / 12 = 29 and 2 children come as a reminder.
Therefore, If everyone goes on a field trip then 29 adults are needed for 350 students, so the recommendation by Metropolis Elementary does not meet.
To know more about Ratios:
https://brainly.com/question/13419413
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In which quadrant or ok which axis does the point lie ?
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Explanation
We are given the following point:
[tex](-5,-3)[/tex]We are required to determine the quadrant, or the axis it lies on a coordinate plane.
We start by plotting the point thus:
Hence, the answer is:
[tex]III[/tex]The last option is correct.
1) What is the greatest common factor (GCF) of 9 and 27? 1 3 9 27
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GCF = 9
Explanations:To find the Greatest Common Factors of 9 and 27:
Step 1: Find the factors of 9 and 27
Factors of 9 = 1, 3, 9
Factors of 27 = 1, 3, 9, 27
Step 2: Find the Common Factors of 9 and 27
That is, the factors that are common to both 9 and 27
Common Factors of 9 and 27 = 1, 3, 9
Step 3: Find the Greatest Common Factor
The Greatest Common Factor (GCF) is the greatest of all the common factors in step 2
Greatest Common Factor = 9
find the sum of the first 6 terms of the following sequence. round to the nearest hundredth if necessary.35, 14, 28/5,...sum of a finite geometric series:Sn=a1-a1^r^n/1-r
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58.09
ExplanationTo find the sum of a finite geometric series, use the formula,
[tex]S_n=\frac{a(1-r^n)}{(1-r)}[/tex]where
[tex]\begin{gathered} a=\text{ first term} \\ r=\text{ common ratio} \\ n=\text{ number of terms} \\ S_n=sumo\text{f the firts n terms} \end{gathered}[/tex]so
Step 1
find the common ratio :
To calculate the common ratio in a geometric sequence, divide the n^th term by the (n - 1)^th term,in other words you can just divide each number from the number preceding it in the sequence
[tex]coomin\text{ ratio =}\frac{n\text{ term }}{(n-1)\text{ term}}[/tex]so
[tex]common\text{ ratio=}\frac{\frac{28}{5}}{\frac{14}{1}}=\frac{28}{70}=0.4[/tex]so r= 0.4
Step 2
Now we can use the formula
a)
let
[tex]\begin{gathered} r=0.4 \\ n=\text{ 6} \\ a=35 \end{gathered}[/tex]b) finally, replace in the formula
[tex]\begin{gathered} S_n=\frac{a(1-r^n)}{(1-r)} \\ S_n=\frac{35(1-0.4^6)}{(1-0.4)} \\ Sn=35*1.62984 \\ Sn=58.0944\text{ } \\ rounded \\ S_n=58.09 \end{gathered}[/tex]therefore, the answer is
58.09
I hope this helps you
Help me please . And have a good day :D
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Correct option is A, 0 to 0.25
and E, 15 to 20.
Given:
a data of f(x) and g(x) corresponding to the values of x is given.
Find:
we have to find the interval in ehich g(x) grows faster than f(x).
Explanation:
from the given data, it is clear that g(x) growing faster than f(
?In the table below, y is a linear function of x.X-214710y09182736What is the y intercept of the function
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y intercept : (0,6)
Explanation:
Use the formula:
. y = mx + b
Find m (the slope), using 2 random points of the graph: (-2,0) and (1,9)
. m = (y-y1) / (x-x1)
m = (0-9) / (-2-1)
m = -9 / -3
m = 3
Replace m in the equation:
. y = 3x + b
Find b by replacing y and x by a random point of the graph: (1,9)
. 9 = 3*1 + b
b = 9 - 3
b = 6
Replace b in the equation:
. y = 3x +6
To find the y-intercept replace x by 0 in the equation:
. y = 3*0 +6
y = 0+6
y = 6
=> y-intercept : (0,6)
calculate the difference quotient and use your results to find the slope of the tangent line
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Approximate Slope of a Function
We are given the function:
[tex]H(x)=8\ln x+3[/tex]We will find the approximate value of the slope at (e,11).
It's required to use 3 possible values of the approximation differential h.
Let's use h=0.1 and evaluate the function at x = e + 0.1 = 2.8182818
Compute:
[tex]H(e+0.1)=8\ln 2.8182818+3=11.2890193[/tex]Compute the difference quotient:
[tex]H^{\prime}=\frac{11.2890193-11}{0.1}=2.890193[/tex]Now we use h=0.01:
[tex]H(e+0.01)=8\ln 2.728281828+3=11.02937635[/tex]The difference quotient is:
[tex]H^{\prime}=\frac{11.02937635-11}{0.01}=2.9376353[/tex]Finally, use h=0.001:
[tex]H(e+0.001)=8\ln 2.719281828+3=11.00294249[/tex][tex]H^{\prime}=\frac{11.00294249-11}{0.001}=2.9424943[/tex]The last result is the most accurate, thus the slope of the tangent line is 2.94
I am going to attach a photo of the question. as you can tell the question has already been answered but my teacher wants me to show how she got the answer.
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Answer:
The ratio of their surface area is;
[tex]25\colon9[/tex]Explanation:
Given the length of the slant height of the cone as;
[tex]\begin{gathered} l_A=35\text{ in} \\ l_B=21\text{ in} \end{gathered}[/tex]since the cones are similar, the ratio of their sides is;
[tex]\begin{gathered} A\colon B \\ =35\colon21 \\ l^{}_A\colon l^{}_B=5\colon3 \end{gathered}[/tex]The ratio of the total surface area is the square of the ratio of the sides.
[tex]\begin{gathered} S_A\colon S_B=l^2_A\colon l^2_B \\ S_A\colon S_B=5^2_{}\colon3^2_{} \\ S_A\colon S_B=25\colon9 \end{gathered}[/tex]Therefore, the ratio of their surface area is;
[tex]25\colon9[/tex]Point P is located at (4, 8) on a coordinate plane. Point Pwill be reflected over the x − axis. What will be thecoordinates of the image of point P?
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SOLUTION:
Step 1:
In this question, we are given that:
Point P is located at (4, 8) on a coordinate plane.
Point P will be reflected over the x-axis.
What will be the coordinates of the image of point P?
Step 2:
How do you reflect a point over the x-axis?
When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse.
The reflection of point (x, y) across the x-axis is (x, -y).
CONCLUSION:
Point P ( 4, 8 ) reflected over the x-axis is ( 4, -8 ) -- OPTION C
Identify the independent and dependent variables for each relation below.1. "The more hours Maribel works at her job, the larger her paycheck becomes."Independent Variable =Dependent Variable =1. "Increasing the price of an itpunt of people willing to buy it."hours workedIndependent Variable =size of paycheckDependent Variable =
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First relation.
Independent variable: Hours worked.
Dependent variable: Size of paycheck
Second relation:
Independent variable: Price of an item
Dependent variable: Number of people willing to buy.
Now, this comes from the fact the the independent variable can be change witho
Find the improper fraction with a denominator of 8 that is equivalent to 3 and 1/2
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Given:
he improper fraction with a denominator of 8 that is equivalent to 3 and 1/2.
Required:
Find the improper fraction.
Explanation:
[tex]\begin{gathered} \text{ According to question} \\ \frac{x}{8}=3\frac{1}{2} \\ x=8\times3\frac{1}{2} \\ x=8\times\frac{7}{2} \\ x=28 \\ \text{ So, fraction is }\frac{28}{8}. \end{gathered}[/tex]Answer:
[tex]\text{ Improper fraction is }\frac{28}{8}.[/tex]An artist in Portland, Oregon, makes bronze sculptures of dogs. The ratio of the height of a sculpture to the actual height of the dog is 2:3. If the height of the sculpture is 14 inches, find the height of the dog.i need a step by step run through to understand
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Given,
The ratio of the height of a sculpture to the actual height of the dog is 2:3.
The height of the sculpture is 14 inch.
let the height of the dog be h.
Thus,
[tex]\begin{gathered} \frac{14}{h}=\frac{2}{3} \\ \Rightarrow h=14\times\frac{3}{2}=21inch \end{gathered}[/tex]The actual height of the dog is 21 inch.