Answers
Answer:
Given that,
[tex]\sum ^{30}_{n\mathop=2}(3n-1)[/tex]Simplifying we get,
[tex]\sum ^{30}_{n\mathop{=}2}(3n-1)=\sum ^{30}_{n\mathop{=}2}3n+\sum ^{30}_{n\mathop{=}2}1[/tex][tex]=3\sum ^{30}_{n\mathop{=}2}n+\sum ^{30}_{n\mathop{=}2}1[/tex]we have that,
[tex]\sum ^n_{n\mathop=1}1=n[/tex]If n is from 2 to n we get,
[tex]\sum ^n_{n\mathop{=}2}1=n-1[/tex]Also,
[tex]\sum ^k_{n\mathop=1}n=\frac{k(k+1)}{2}[/tex]If n is from 2 to n we get,
[tex]\sum ^k_{n\mathop=2}n=\frac{k(k+1)}{2}-1[/tex]Using this and substituting in the required expression we get,
[tex]=3\lbrack\frac{30\times31}{2}-1\rbrack+30-1[/tex][tex]=3(464)+29[/tex][tex]=1421[/tex]Answer is: 1421
Related Questions
INT. ALGEBRA: Write an equation that passes through (-10,-30) and is perpendicular to 12y-4x=8
Thank you for your help, and please do show work! I will be looking to give the Brainliest answer to someone!
Answers
The equation of the perpendicular line is y = -3x - 60
How to determine the line equation?The equation is given as
12y - 4x = 8
Make y the subject
12y= 4x + 8
y = 1/3x + 2/3
The point is also given as
Point = (-10, -30)
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = 1/3
This means that the slope of 12y - 4x = 8 is 1/3
So, we have
m = 1/3
The slopes of perpendicular lines are opposite reciprocals
This means that the slope of the other line is -3
The equation of the perpendicular lines is then calculated as
y = m(x - x₁) +y₁
Where
m = -3
(x₁, y₁) = (-10, -30)
So, we have
y = -3(x + 10) - 30
Evaluate
y = -3x - 30 - 30
y = -3x - 60
Hence, the perpendicular line has an equation of y = -3x - 60
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I need help with a math assignment. i linked it below
Answers
Since Edson take t minutes in each exercise set
Since he does 6 push-ups sets
Then he will take time = 6 x t = 6t minutes
Since he does 3 pull-ups sets
Then he will take time = 3 x t = 3t minutes
Since he does 4 sit-ups sets
Then he will take time = 4 x t = 4t minutes
To find the total time add the 3 times above
Total time = 6t + 3t + 4t
Total time = 13t minutes
The time it takes Edison to exercise is 13t minutes
I need help with my pre-calculus homework, please show me how to solve them step by step if possible. The image of the problem is attached. These are 2 parts of the same question.
Answers
We are given the following triangle:
We need to determine the area of the triangle. To do that we need to determine sides "a" and "b". We will use the sine law to determine the side "b":
[tex]\frac{b}{sin107}=\frac{98}{sin48}[/tex]Now, we multiply both sides by "sin107":
[tex]b=sin(107)\frac{98ft}{sin(48)}[/tex]Solving the operations:
[tex]b=126.11ft[/tex]Now, before determining side "a" we will determine the angle "x" that is opposed to "a". To do that we will use the fact that the sum of the interior angles of a triangle is 180, therefore:
[tex]107+48+x=180[/tex]Adding the values:
[tex]155+x=180[/tex]Now, we subtract 155 from both sides:
[tex]\begin{gathered} x=180-155 \\ x=25 \end{gathered}[/tex]Therefore, the angle opposite to "a" is 25 degrees. Now, we apply the sine law:
[tex]\frac{a}{sin(25)}=\frac{98}{sin(48)}[/tex]Now, we multiply both sides by "sin(25)":
[tex]a=sin(25)\frac{98}{sin(48)}[/tex]Solving the operations:
[tex]a=55.73ft[/tex]Now, we determine the area using the following formula:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]Where:
[tex]s=\frac{a+b+c}{2}[/tex]Now, we determine the value of "s":
[tex]s=\frac{55.73ft+126.11ft+98ft}{2}[/tex]Solving the operation:
[tex]s=139.92ft[/tex]Now, we substitute the value in the formula for the area:
[tex]A=\sqrt{(139.92ft)(139.92ft-55.73ft)(139.92ft-126.11ft)(139.92ft-98ft)}[/tex]Solving the operations:
[tex]A=2611.43ft^2[/tex]Now, since the search party can cover 300 ft^2/h we can use a rule of 3 to determine the number of hours it takes them to cover 2611.43 ft^2:
[tex]\begin{gathered} 300ft^2\rightarrow1h \\ 2611.43ft^2\rightarrow x \end{gathered}[/tex]Now, we cross multiply:
[tex](300ft^2)(x)=(1h)(2611.43ft^2)[/tex]Now, we divide both sides by 300ft^2:
[tex]x=\frac{(1h)(2611.43ft^2)}{(300ft^2)}[/tex]Solving the operations:
[tex]x=8.7h[/tex]Therefore, it takes 8.7 hours to cover the area. Therefore, the search party won't be able to conclude before the sun goes down.
Express the function y=5(x−6)² as a composition y=f(g(x)) of two simpler functions y=f(u) and u=g(x).
Answers
Answer:
y = 5u², u=x-6
Explanation:
Given the function:
[tex]y=5(x-6)^2[/tex]We want to express f(x) as a composition of two functions.
Let u = x-6
[tex]\implies y=5u^2[/tex]Therefore, the function y=5(x−6)² as a composition y=f(g(x)) of two simpler functions y=f(u) and u=g(x)
[tex]\begin{gathered} y=5u^2\text{ where:} \\ f(u)=5u^2 \\ u=g(x)=x-6 \end{gathered}[/tex]GWhich inequalities have no solution? Check all of the boxes that apply.XX-3x -3x–4 + x>-2 + xX-2
Answers
For every number x, x = x, not x < x. So, the inequality x < x has no solution.
Since -3x = -3x for every real number, the inequality
[tex]-3x\leq-3x[/tex]holds for every real number, that is, every number is a solution.
Consider the inequality
[tex]-4+x>-2+x[/tex]Subtract x on both sides gives -4 > -2, which is not possible.
Hence the inequality - 4 + x > - 2 + x has no solution.
Consider the inequality
[tex]x-2Subtract x on both sides gives -2 < 3, which is true.Every real number is a solution of the inequality. Hence the inequality has solution.
Thus the inequalities with no solution are: x < x and -4+x>-2+x
Find the first four terms of the sequence given by the following
Answers
1) In this question, we need to resort to that Explicit formula, with the first term so that we can find the terms:
[tex]\begin{gathered} a_n=54+8(n-1) \\ a_1=54+8(1-1) \\ a_1=54 \\ \\ a_2=54+8(2-1) \\ a_2=54+8 \\ a_2=62 \\ \\ a_3=54+8(3-1) \\ a_3=54+8(2) \\ a_3=54+16 \\ a_3=70 \\ \\ a_4=54+8(4-1) \\ a_4=54+8(3) \\ a_4=78 \\ \end{gathered}[/tex]2) As we can see, this is an Arithmetic sequence. And the answer is:
[tex]54,62,70,78[/tex]Two different telephone carriers offer the following plans that a person is considering. Company A has a monthly fee of $20 and charges of $.05/min for calls. Company B has a monthly fee of $5 and charges $.10min for calls. Find the model of the total cost of company a's plan. using m for minutes.
Answers
Based on the monthly fee charged by Company A and the charges per minute for calls, the model for the total cost of Company A's plan is Total cost = 20 + 0.05m.
How to find the model?The model to find the total cost of Company A's plan will incorporate the monthly fee paid as well as the amount paid for each minute of calls.
The model for the cost is therefore:
Total cost = Fixed monthly fee + (Variable fee per minute x Number of minutes)
Fixed monthly fee = $20
Variable fee per minute = $0.05
Number of minutes = m
The model for the total cost of Company A's plan is:
Total cost = 20 + 0.05m
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The required equation that represents the total cost of Company a's plan is x = 20 + 0.5m.
As of the given data, Company A has a monthly fee of $20 and charges $.05/min for calls. An equation that represents the total cost of Company a's plan is to be determined.
Here,
Let x be the total cost of the company and m be the number of minutes on a call.
According to the question,
Total charges per minute on call = 0.5m
And a monthly fee = $20
So the total cost of company a is given by the arithmetic sum of the sub-charges,
X = 20 + 0.5m
Thus, the required equation that represents the total cost of Company a's plan is x = 20 + 0.5m.
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For each quadratic expression below, drag an equivalent expression to its match
Answers
1. Given the expression:
[tex]\mleft(x+2\mright)\mleft(x-4\mright)[/tex]You can use the FOIL method to multiply the binomials. Remember that the FOIL method is:
[tex](a+b)\mleft(c+d\mright)=ac+ad+bc+bd[/tex]Then, you get:
[tex]\begin{gathered} =(x)(x)-(x)(4)+(2)(x)-(2)(4) \\ =x^2-4x+2x^{}-8 \end{gathered}[/tex]Adding the like terms, you get:
[tex]=x^2-2x-8[/tex]2. Given:
[tex]x^2-6x+5[/tex]You have to complete the square:
- Identify the coefficient of the x-term". In this case, this is -6.
- Divide -6 by 2 and square the result:
[tex](\frac{-6}{2})^2=(-3)^2=9[/tex]- Now add 9 to the polynomial and also subtract 9 from the polynomial:
[tex]=x^2-6x+(9)+5-(9)[/tex]- Finally, simplifying and completing the square, you get:
[tex]=(x-3)^2-4[/tex]3. Given the expression:
[tex]\mleft(x+3\mright)^2-7[/tex]You can simplify it as follows:
- Apply:
[tex](a+b)^2=a^2+2ab+b^2[/tex]In this case:
[tex]\begin{gathered} a=x \\ b=3 \end{gathered}[/tex]Then:
[tex]\begin{gathered} =\lbrack(x)^2+(2)(x)(3)+(3)^2\rbrack-7 \\ =\lbrack x^2+6x+9\rbrack-7 \end{gathered}[/tex]- Adding the like terms, you get:
[tex]=x^2+6x+2[/tex]4. Given:
[tex]x^2-8x+15[/tex]You need to complete the square by following the procedure used in expression 2.
In this case, the coefficient of the x-term is:
[tex]b=-8[/tex]Then:
[tex](\frac{-8}{2})^2=(-4)^2=16[/tex]By Completing the square, you get:
[tex]\begin{gathered} =x^2-8x+(16)+15-(16) \\ =(x-4)^2-1 \end{gathered}[/tex]Therefore, the answer is:
The distance d (in inches) that a ladybug travels over time t(in seconds) is given by the function d (1) = t^3 - 2t + 2. Findthe average speed of the ladybug from t1 = 1 second tot2 = 3 seconds.inches/second
Answers
The Solution:
Given that the distance is defined by the function below:
[tex]d(t)=t^3-2t+2[/tex]We are required to find the average speed of the ladybug from t=1 second to t=3 seconds in inches/second.
Step 1:
For t=1 second, the distance in inches is
[tex]d(1)=1^3-2(1)+2=1-2+2=1\text{ inch}[/tex]For t=3 seconds, the distance in inches is
[tex]d(3)=3^3-2(3)+2=27-6+2=21+2=23\text{ inches}[/tex]By formula,
[tex]\text{ Average Speed=}\frac{\text{ distance covered}}{\text{ time taken}}[/tex]In this case,
Distance covered = change in distance, which is
[tex]\text{ change in distance=d(3)-d(1)=23-1=22 inches}[/tex]Time taken = change in time, which is:
[tex]\text{ Change in time=t}_2-t_1=3-1=2\text{ seconds}[/tex]Substituting these values in the formula, we get
[tex]\text{ Average Speed=}\frac{22}{2}=11\text{ inches/second}[/tex]Therefore, the correct answer is 11 inches/second.
A gumball machine contains 5 blue gumballs and 4 red gumballs. Two gumballs are purchased, one after the other, without replacement.
Find the probability that the second gumball is red.
Answers
===================================================
Work Shown:
5 blue + 4 red = 9 total
A = P(1st is red, 2nd is red)
A = P(1st is red)*P(2nd is red, given 1st is red)
A = (4/9)*(3/8)
A = 12/72
B = P(1st is blue, 2nd is red)
B = P(1st is blue)*P(2nd is red, given 1st is blue)
B = (5/9)*(4/8)
B = 20/72
C = P(2nd is red)
C = A+B
C = 12/72 + 20/72
C = 32/72
C = 4/9
Madison is in the business of manufacturing phones. She must pay a daily fixed cost of $400 to rent the building and equipment, and also pays a cost of $125 per phone produced for materials and labor. Make a table of values and then write an equation for C,C, in terms of p,p, representing total cost, in dollars, of producing pp phones in a given day.
I need the equation
Answers
Here is the completed table:
Number of phones manufactured Total cost of Manufactured phones
0 $400
1 $525
2 $650
3 $775
The equation that represents the total cost is C = $400 + $125p .
What is the total cost?The equation that represents the total cost is a function of the fixed cost and the variable cost. The fixed cost remains constant regardless of the level of output. The variable cost changes with the level of output.
Total cost = fixed cost + total variable cost
Total cost = fixed cost + (variable cost x total output)
C = $400 + ($125 x p)
C = $400 + $125p
Total cost when 0 phones are made = $400 + $125(0) = $400
Total cost when 1 phone are made = $400 + $125(1) = $525
Total cost when 2 phones are made = $400 + $125(2) = $650
Total cost when 3 phones are made = $400 + $125(3) = $775
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Simplify. -(-6w + x - 3y)
Answers
Answer: 6w - x + 3y
Step-by-step explanation:
i have questions on a math problem. i can send when the chats open
Answers
The random sample is determined as the simplest forms of collecting data from the total population.
Under random sampling, each member of the subset carries an equal opportunity of being chosen as a part of the sampling process.
So according to the question given
Assign each person of the population a number. Put all the numbers into bowl and choose ten numbers.
is the random sample because every person carries an equal opportunity of being chosen from the total population.
Hence the correct option is A.
I am asked to graph f(x) = (- 1/x-2) -1
Answers
Answer
[tex]f(x)=-\frac{1}{x-2}-1[/tex]Point (7, 2) is translated up 2 units and left 5 units. Where is the new point located?(12, 4)(9, -3)(2,0)(2, 4)
Answers
The new point is located at (2,4)
Here, we want to get the result of a translation
2 units up simply mean, we are adding 2 to the y-axis value
5 units left mean we are subtracting 5 from the x-axis value
We can represent the translation as;
[tex]\begin{gathered} (x,y)\rightarrow\text{ (x-5 , y+2)} \\ =\text{ (7-5,2+2) = (2,4)} \end{gathered}[/tex]A number cube labelled 1 to 6 is rolled 276 times. Predict how many times a 5 will show.
Answers
All the outcomes of the cube are equally probable, therefore, it is expected to have all the outcomes after 6 rolls. To find the amount of times we're supposed to get one of the outcomes, we multiply the amount of rolls by the probability of this outcome.
The theoretical probability is defined as the ratio of the number of favourable outcomes to the number of possible outcomes. We have one number five out of six possible numbers, therefore, the probability of getting a 5 is:
[tex]P(5)=\frac{1}{6}[/tex]Therefore, in 276 rolls we're going to get the following amount of 5's:
[tex]276\times P(5)=\frac{276}{6}=46[/tex]5 will show 46 times.
Which statement is the converse of the conditional statement:
If point B bisects line segment AC into two congruent segments, then point B is the midpoint.
• If point B is the midpoint, then point B bisects line segment AC into two congruent segments.
O If point 8 is not the midpoint, then point B does not bisect line segment AC into two congruent segments.
Point B bisects line segment AC into two congruent segments if, and only if, point B is the midpoint.
O if point B
does not bisect line segment AC into two congruent segments, then point B is not the midpoint.
Answers
Point B is the midpoint if it divides line segment AC into two congruent segmentsIf point B is not the midpoint, then point B does not divide the line segment AC into two congruent segments, which is the statement opposite to the one that has been made.
Which statement is the converse of the conditional statement ?
A point that separates a segment into two congruent segments is the segment's midpoint.The segment is bisected by a point (or segment, ray, or line) that separates it into two congruent segments.Trisecting is the process of dividing a segment into three congruent segments using two points (segments, rays, or lines). A perpendicular bisector is a segment, ray, line, or plane that is perpendicular to another segment at its halfway. The x-coordinate of the midpoint M of the line segment AB is, as we can see from the formula, equal to the arithmetic mean of the x-coordinates of the segment's two endpoints.The midpoint's y-coordinate is also equal to the mean of the endpoints' y-coordinates. Even a unique postulate just for midpoints exists.Midpoint of a Segment Hypothesis.Any line segment will only have one midpoint, neither more nor less. Any line segment with equal measure is referred to as a congruent line segment.Congruent line segments, for instance, refer to the sides of an equilateral triangle since they all have the same length. Line segments that are congruent have the same length.There is a point in a line segment that will divide it into two congruent line segments.The middle is where you are now. A segment bisector runs through the middle of a line segment and divides it into two congruent portions.A segment bisector that intersects the segment at a right angle is called a perpendicular bisector.AB B C A C D E By applying algebraic techniques to solve the midpoint formula for one endpoint, the endpoint formula can be discovered.After performing the necessary algebra, (xa,ya)=((2xmxb),(2ymyb)) (x a, y a) = ((2 x m x b), (2 y m y b)) is the formula for the Endpoint A A of line AB A B.To learn more about mid point refer
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In a poll, students were asked to choose which of six colors was their favorite. The circle graph shows how the students answered. If 11,000 students participated in the poll, how many chose green?Orange 13%Pink 7%Blue 10%Red 24%Purple 10%Green 36%
Answers
Total of 11,000 students
Green 36%
how many chose green?
Chose green = 11000 * 36/100 = 3960
36% of 11,000 is 3960
Answer:
3,960 students chose green
with regard to promoting standards of excellence, lafasto and larson (2001) identified three rs that help improve performance: require results, review results, and ______.
Answers
With regard to promoting standards of excellence, Lafasto and Larson (2001) identified three Rs that help improve performance:
require results, review results, and Reward Results.What did the Larson and LaFasto 1989 study capture?
The LaFasto and Larson Model investigated team effectiveness. It is founded on the premise that, while individuals might be highly competent and talented, teams solve the most challenging issues.
It doesn't matter how skilled an individual is if they can't operate as part of a team.
They studied the traits of 75 highly successful teams. They discovered that high standards of excellence were a critical component in team performance.
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what is the conjugate of the denominator of the expression 9i/-2+7i
Answers
The answer is D.
One of the legs of a right triangle measures 13 cm and the other leg measures
2 cm. Find the measure of the hypotenuse. If necessary, round to the nearest
tenth.
Answers
Answer:
13.2 cm
Step-by-step explanation:
Use Pythagorean Theorem
Hypotenuse^2 = (leg1)^2 + (leg2)^2
H^2 = 13^2 + 2^2
= 169 + 4
H^2 = 173
H = sqrt (173) = 13.2 cm
The sign points at the smaller number. True or False. Example 2 < 100 True False
Answers
When working with inequalities you have to remember that:
The symbol "<" indicates that the number on the left is smaller than the number on the right, then, for example:
[tex]85<90[/tex]This indicates that 85 is less than 90.
The symbol ">" indicates that the number of the left is greater than the number on the right, for example:
[tex]70>54[/tex]This indicates that 70 is greater than 54.
Now for the given statement:
[tex]2<100[/tex]"The sign points at the smaller number"
The expression indicates that 2 is less than 100, so the statement is true.
the length of a rectangle is 2 inches more than the width. The area is 24 square inches. Find the dimensions
Answers
Given:
length(l) = width(w) + 2
[tex]\text{Area}=24[/tex][tex]l\times w=24[/tex][tex](w+2)w=24[/tex][tex]w^2+2w-24=0[/tex][tex](w+6)(w-4)=0[/tex][tex]w=4\text{ or -6}[/tex]Negative not possible.
[tex]\text{width(w)}=4\text{ inches}[/tex][tex]\text{length(l)}=w+2[/tex][tex]\text{length of the rectangle=4+2}[/tex][tex]\text{length of the rectangle=}6\operatorname{cm}[/tex]Over the next 10 years, town A is expecting to gain 1000 people each year. During the same time period, the population of town B is expected to increase by 5% each year. Both town A and town B currently have populations of 10,000 people. The table below shows the expected population of each town for the next three years.Which number of years is the best approximation of the time until town A and town B once again have the same population?
Answers
From the given figure we can see
The population in town A is increased by a constant rate because
[tex]\begin{gathered} 11000-10000=1000 \\ 12000-11000=1000 \\ 13000-12000=1000 \end{gathered}[/tex]Since the difference between every 2 consecutive terms is the same, then
The rate of increase of population is constant and = 1000 people per year
The form of the linear equation is
[tex]y=mx+b[/tex]m = the rate of change
b is the initial amount
Then from the information given in the table
m = 1000
b = 10,000
Then the equation of town A is
[tex]y=1000t+10000[/tex]Fro town B
[tex]\begin{gathered} R=\frac{10500}{10000}=1.05 \\ R=\frac{11025}{10500}=1.05 \\ R=\frac{11576}{11025}=1.05 \end{gathered}[/tex]Then the rate of increase of town by is exponentially
The form of the exponential equation is
[tex]y=a(R)^t[/tex]a is the initial amount
R is the factor of growth
t is the time
Since R = 1.05
Since a = 10000, then
The equation of the population of town B is
[tex]y=10000(1.05)^t[/tex]We need to find t which makes the population equal in A and B
Then we will equate the right sides of both equations
[tex]10000+1000t=10000(1.05)^t[/tex]Let us use t = 4, 5, 6, .... until the 2 sides become equal
[tex]\begin{gathered} 10000+1000(4)=14000 \\ 10000(1.05)^4=12155 \end{gathered}[/tex][tex]\begin{gathered} 10000+1000(5)=15000 \\ 10000(1.05)^5=12763 \end{gathered}[/tex][tex]\begin{gathered} 10000+1000(6)=16000 \\ 1000(1.05)^6=13400 \end{gathered}[/tex][tex]\begin{gathered} 10000+1000(30)=40000 \\ 10000(1.05)^{30}=43219 \end{gathered}[/tex]Since 43219 approximated to ten thousand will be 40000, then
A and B will have the same amount of population in the year 30
The answer is year 30
e22. Which expressions have values less than 1 whenx = 47 Select all that apply.(32)xo3x4
Answers
To know the expression that is less than 1 when x=4
we will need to check each expression
As for the first one;
[tex](\frac{3}{x^2})^0[/tex]anything raise to the power of zero will give 1, since the o affects all that is in the bracket, then the expression is 1
Hence it is not less than 1
For the second expression;
[tex]\frac{x^0}{3^2}=\frac{4^0}{9}=\frac{1}{9}[/tex]The value is less than 1
For the third expression;
[tex]\frac{1}{6^{-x}}[/tex]substituting x=4 in the above expression
[tex]\frac{1}{6^{-4}}[/tex]The above is the same as;
[tex]undefined[/tex]An air plane can cruise at 640mph. How far can it fly in 3/2 Ths of an hour?
Answers
Answer: 960 miles
3/2 of an hour would be 1 hour and 30 min or an hour and a half
640mph (mph = miles per hour)
1/2 of an hour is 30 minutes so its 640 miles in half so 320
now all you gotta do is add it
so 640 + 320 = 960
Graph the exponential function.f(x)=4(5/4)^xPlot five points on the graph of the function,
Answers
We are required to graph the exponential function:
[tex]f(x)=4(\frac{5}{4})^x[/tex]First, we determine the five points which we plot on the graph.
[tex]\begin{gathered} \text{When x=-1, }f(-1)=4(\frac{5}{4})^{-1}=3.2\text{ }\implies(-1,3.2) \\ \text{When x=0, }f(0)=4(\frac{5}{4})^0=4\text{ }\implies(0,4) \\ \text{When x=1, }f(1)=4(\frac{5}{4})^1=5\implies(1,5) \\ \text{When x=2, }f(2)=4(\frac{5}{4})^2=6.25\implies(2,6.25) \\ \text{When x=3, }f(3)=4(\frac{5}{4})^3=7.8125\text{ }\implies(3,7.8125) \end{gathered}[/tex]Next, we plot the points on the graph.
This is the graph of the given exponential function.
The functions f(x) and g(x) are shown on the graph.f(x)=x^2What is g(x)?A. g(x)=(x+3)^2B. g(x)=(x-3)^2C. g(x)=(1/3x)^2D. g(x)=3x^2
Answers
Given:
[tex]f(x)=x^2[/tex]Let's find g(x).
From the given graph, we can see the graph of g(x) is compressed horizontally from f(x).
Thus, to find g(x) aply the transformation rules for function.
We have:
Horizontal compression of b units ==> f(bx)
Given the point on g(x):
(x, y) ==> (2, 12)
Let's solve for the value of the compressed factor.
We have:
[tex]\begin{gathered} 12=b(2)^2 \\ \\ 12=b4 \\ \\ \text{Divide both sides by 4:} \\ \frac{12}{4}=\frac{b4}{4} \\ \\ 3=b \\ \\ b=3 \end{gathered}[/tex]This means the graph of f(x) was compressed horizontally by a factor of 3 to get g(x).
Thus, to write the function for g(x), we have:
[tex]g(x)=3x^2[/tex]ANSWER:
[tex]D\text{.}g(x)=3x^2[/tex]How do I simplify my answer of 42i^2+32i+6 when the original problem was (2-6i)(3-7i)
Answers
Given problem is
[tex](2-6i)(3-7i)[/tex]Now,
[tex]\begin{gathered} (2-6i)(3-7i)=42i^2-14i-18i+6 \\ =42i^2-32i+6 \end{gathered}[/tex]We know that
[tex]i^2=-1[/tex]Using this face,
[tex]\begin{gathered} 42i^2-32i+6=-42-32i+6 \\ =-32i-36 \end{gathered}[/tex]Hence, the simplified form is
[tex]-32i-36[/tex]although the actual amount varies by the season and time of the day the average volume of water that flows over the false each second is 2.9 x 10 to the 5th power gallons how much water flows over the falls in an hour write the result in scientific notation hint 1 hour equals 3600 second
Answers
We were told that volume of water that flows over the fall each second is 2.9 x 10^5 gallons.
Recall, 1 hour = 3600 seconds
If 1 second = 2.9 x 10^5 gallons, then
3600 seconds = 3600 x 2.9 x 10^5
= 1.044 x 10^9 gallons
Thus, 1.044 x 10^9 gallons of water will flow over the falls in an hour.