Answer:
The area of a cover that will fit on the larger tank is 6 square inches
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its Volumes is equal to the scale factor cubed
Let
z ---> the scale factor
so
[tex]z^3=\frac{64}{8}=8[/tex]
[tex]z=2[/tex]
step 2
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z ---> the scale factor
x ---> the area of a cover that will fit on the larger tank
y ---> the area of a cover that will fit on the smaller tank
so
[tex]z^2=\frac{x}{y}[/tex]
we have
[tex]z=2\\y=1.5\ ft^2[/tex]
substitute the given values
[tex]2^2=\frac{x}{1.5}[/tex]
solve for x
[tex]x=4(1.5)=6\ ft^2[/tex]
The area of the cover that will fit on the larger aquarium is approximately 12 square feet, calculated by multiplying the area of the smaller cover by the square of the scaling factor for linear dimensions (≈ 2.83) due to the difference in volume.
Explanation:Understanding Area Scaling in Rectangular PrismsTo find the area of a cover that will fit on the larger aquarium, we begin by understanding that the area scales by the square of the linear dimensions.
Since the volume of the larger aquarium is 64 gallons and the smaller one is 8 gallons, the volume scales by a factor of 64/8 = 8. Taking the square root of 8 gives us the scaling factor for the linear dimensions, which is sqrt(8) ≈ 2.83. The larger tank's cover will therefore need to increase by this scaling factor squared for its area.
To calculate the area of the larger tank's cover, we multiply the area of the smaller cover by this scaling factor squared: 1.5 ft2 * 2.832 ≈ 12 ft2. Thus, the cover for the larger tank should be approximately 12 ft2 in area. This demonstrates the concept that area is proportional to the square of the linear dimensions when scaling similar shapes.
2/3 inches x 5 inches
Answer:
10/3
Step-by-step explanation:
2/3 x 5 is really
2 x 5
3 1
when you multiply them separately you will get 10 as your numerator and 3 as your denominator.
hope this helps!
In magic squares, each row,
column, and diagonal adds up
to the same number. Complete
the magic square. Use each
number 1-9 only once.
Answer:
middle square top row =9 middle row left square= 7 middle row right square=3 bottom row left square =6 bottom row middle square 1
Step-by-step explanation:
every row = 15 so just start with the rows and columns that only need one square until you've filled it in enough that every row needs one and the solve from there
A magic square consists of a grid of numbers where each row, column, and diagonal add up to the same total. For a 3x3 magic square using numbers 1 through 9, this total is 15. Possible solutions include the rotations of the groupings 9, 5, 1 and 6, 2, 7.
A magic square is a grid of numbers where the values in each row, column, and diagonal add up to the same total. The key to solving such a puzzle is understanding that total. Since we are using the numbers 1 through 9, the total sum of these numbers is 45; because there are 3 rows (or columns or diagonals) in a 3x3 grid, each must add up to 15.
The only way to get 15 with three numbers in the 1-9 range is to either group 9, 5, and 1 or their rotations (such as 5, 1, 9 or 1, 9, 5) or use 6, 2, and 7 or their rotations. This leads to the following magic square:
8 1 6
3 5 7
4 9 2
Learn more about Magic Square here:https://brainly.com/question/33345513
#SPJ2
a bag contains 6 white marbles and 4 black marbles. a marble is drawn without replacing the first one. what is the probability of drawing a white marble on the first draw, followed by a white marble on the second?
Answer:
6 = white marbles
4 = black marbles
10 = total marbles
6/10 - Pulling white marbles
4/10 - Pulling black marbles
10 - 4 = 6
2/6 - Pulling two white marbles
2/6 = 1/3 = 0.33 or 33%I hope this helped!
The probability of drawing a white marble on the first draw after following the second draw of white marble should be 0.33.
Given that
There are 6 white marbles.There are 4 black marbles.The total marbles are 10.Now based on the above information
Put white marbles be [tex]\frac{6}{10}[/tex]
And, black marbles be [tex]\frac{4}{10}[/tex]
So,
= 10 - 4
= 6
Now pull two white marbles i.e.
[tex]= \frac{2}{6} \\\\= \frac{1}{3}\\\\= 33\%\ or\ 0.33[/tex]
Therefore we can conclude that The probability of drawing a white marble on the first draw after following the second draw of white marble should be 0.33.
Learn more about the probability here: brainly.com/question/11234923
Complete the expressions to find the perimeter P of a rectangle that is 9 inches long by 4 inches wide. P=2l+2w =2⋅9+2⋅ ( ) =( )+( ) =( )in. AKA. ( ) = blank
Answer:
[tex]P= 26\text{ inches}[/tex]
Step-by-step explanation:
We are given the following in the question:
Dimensions of rectangle:
Length of rectangle,l = 9 inches
Width of rectangle, w = 4 inches
Perimeter of rectangle =
[tex]P= 2l + 2w[/tex]
Putting values, we get,
[tex]P= 2(9) + 2(4)\\P= (18) + (8)\\P= 26\text{ inches}[/tex]
Thus, the perimeter of rectangle is 26 inches.
Beth needs to fertilize her flowerbed, which is in the shape of a regular pentagon. A bag of fertilizer states that it can fertilize up to 150 square feet, but Beth is not sure how many bags of fertilizer she should buy. Each side of the pentagon is 15 feet long
Answer: he should buy 3 bags
Step-by-step explanation:
In order to determine the area of the flower bed which has the shape of a Pentagon, we would apply the formula for determining the area of a polygon which is expressed as
Area = (perimeter × apotherm)/2
The apotherm is the perpendicular distance from the center of the polygon. The formula for determining the apotherm is
Apotherm = S/2tan(180/n)
Where
S = side length of the polygon
n = number of sides of the polygon.
From the information given,
S = 15 feet
n = 5
Apotherm = 15/2tan(180/5) = 10.3 ft
Perimeter = side length × number of sides
Perimeter = 15 × 5 = 75 ft
Therefore,
Area of the Pentagon = 75 × 10.3/2 = 386.25 ft²
A bag of fertilizer states that it can fertilize up to 150 square feet. Therefore, the number of bags that he can buy is
386.25/150 = 2.575 bags
He should buy approximately 3 bags
At 7am you drink a 12-ounce cup of coffee which has 140mg of caffeine. The liver metabolizes caffeine at a rate of 12.9% per hour. How many milligrams of caffeine is in your body after 2 hours? Group of answer choices 136.4 106.2 178.4 33.8
Answer:
B. 106.2
Step-by-step explanation:
We have been given that at 7 am you drink a 12-ounce cup of coffee which has 140 mg of caffeine. The liver metabolizes caffeine at a rate of 12.9% per hour. We are asked to find the milligrams of caffeine left in your body after 2 hours.
We will use exponential decay formula to solve our given problem.
[tex]y=a\cdot (1-r)^x[/tex], where,
y = Final value,
a = Initial value,
r = Decay rate in decimal form,
x = Time.
Let us convert 12.9% in decimal form.
[tex]12.9\%=\frac{12.9}{100}=0.129[/tex]
Initial value is 140 mg.
[tex]y=140\cdot (1-0.129)^x[/tex]
[tex]y=140\cdot (0.871)^x[/tex]
Now we will substitute [tex]x=2[/tex] in our equation as:
[tex]y=140\cdot (0.871)^2[/tex]
[tex]y=140\cdot (0.758641)[/tex]
[tex]y=106.20974\approx 106.2[/tex]
Therefore, approximately 106.2 milligrams of caffeine will be in your body after 2 hours.
Click on the number until you find the right quotient. 36m5n5 ÷ (12m3)
9mn^2
7m^4n^2
3m^2n^5
So the answer is 3m^2n^5
Final answer:
To find the quotient of ([tex]36m^5n^5 \div 12m^3[/tex]), divide the numerical coefficients and subtract the exponents for each variable base. The correct quotient is [tex]3m^2n^5[/tex], which corresponds to option 3.
Explanation:
Divide the numerical coefficients: 36 ÷ 12 = 3.
Subtract the exponents of the variables with the same base (m): 5 - 3 = 2.
Subtract the exponents of the variables with the same base (n): 5 - 0 = 5.
Therefore, the quotient is 3m2n5, which matches option 3: [tex]3m^2n^5[/tex].
the length of a rectangle with area 54 square centimeters is 9 centimeters. what is the perimeter of the rectangle, in centimeters?
Answer:
30 cm
Step-by-step explanation:
To find the perimeter of the rectangle, you first need to find the width and length of the rectangle:
54/9 = 6
L = 9
W = 6
The perimeter is 2lw:
The answer is 30 cm
Answer:
C 30 it not it 34
Step-by-step explanation:
just did it
Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 9t + 9 cot(t/2), [π/4, 7π/4]
To find the absolute maximum and minimum values of a function, we find the critical points and endpoints. Evaluating the function at these points gives the maximum and minimum values.
Explanation:To find the absolute maximum and absolute minimum values of a function on a given interval, we need to find the critical points and endpoints of the interval.
To find the critical points of f, we need to find where the derivative of f is equal to zero or undefined. The derivative of f(t) = 9t + 9cot(t/2) is f'(t) = 9 - 9csc^2(t/2).
Setting f'(t) = 0, we have 9 - 9csc^2(t/2) = 0. Solving this equation, we get csc^2(t/2) = 1, which means sin^2(t/2) = 1. This gives us sin(t/2) = ±1. The critical points occur when t/2 = π/2 or t/2 = 3π/2. Solving for t, we get t = π or t = 3π as the critical points.
The endpoints of the interval are π/4 and 7π/4.
Now we evaluate the function f at the critical points and endpoints:
f(π/4) = 9(π/4) + 9cot(π/8) ≈ 6.566f(π) = 9π + 9cot(π/2) = 9πf(3π) = 9(3π) + 9cot(3π/2) = 27πf(7π/4) = 9(7π/4) + 9cot(7π/8) ≈ 46.607From these evaluations, we can see that the absolute maximum value occurs at t = 7π/4 and is approximately 46.607, while the absolute minimum value occurs at t = π/4 and is approximately 6.566.
Learn more about Finding absolute maximum and minimum values here:https://brainly.com/question/34340601
#SPJ11
RAMON SELLS CARS AND TRUCKS HE HAS ROOM ON HIS LOT FOR 521 VEHICLES. Ramon has 175 more more cars than trucks. How many of each vehicles should he have
Answer: he should have 348 cars and 173 trucks.
Step-by-step explanation:
Let x represent the number of cars that he should have.
Let y represent the number of trucks that he should have.
He has room on his lot for 521 vehicles. It means that
x + y = 521- - - - -- - - - -1
Ramon has 175 more more cars than trucks. It means that
x = y + 175
Substituting x = y + 175 into equation 1, it becomes
y + 175 + y = 521
2y = 521 - 175 = 346
y = 346/2
y = 173
x = y + 175 = 173 + 175
x = 348
To determine the number of cars and trucks on Ramon's lot, two equations were formed: T + C = 521 and C = T + 175. Solving these equations simultaneously, it was found that Ramon should have 173 trucks and 348 cars.
Explanation:Ramon's Car and Truck Problem
Let us define the number of trucks Ramon has as T and the number of cars as C. According to the problem, Ramon has room for 521 vehicles on his lot. The problem states that Ramon has 175 more cars than trucks, so we can express this as C = T + 175.
We know the total number of vehicles Ramon can have is 521, which leads us to the following equation: T + C = 521. Substituting the first equation into the second, we get T + (T + 175) = 521. Simplifying, 2T + 175 = 521. Subtracting 175 from both sides, 2T = 346. Dividing by 2, we find that T = 173. This means Ramon has 173 trucks on his lot.
Now, we substitute the value of T back into the equation for C: C = 173 + 175, which equals 348. So, Ramon should have 348 cars and 173 trucks on his lot.
a painter can paint 20 windows in one day. If he has to paint 50 pairs of windows how much time will he take to paint
The painter would take 25 days to paint 50 pairs of windows, given that he can paint 20 windows in 5 days.
To solve this problem, we first need to find out how many windows are in 50 pairs of windows.
Since each pair consists of 2 windows, 50 pairs would mean 50 x 2 = 100 windows.
Now, if the painter can paint 20 windows in 5 days, we can find out how many days it would take him to paint 100 windows using a proportion:
20 windows ------- 5 days
100 windows ------ x days
We can set up the proportion:
20/5 = 100/x
Now, cross multiply:
20x = 5 x 100
20x = 500
Now, divide both sides by 20 to solve for x:
x = 500 / 20
x = 25
So, it would take the painter 25 days to paint 50 pairs of windows.
Complete Question:
A painter can paint 20 windows in 5 days.If he has to paint 50 pair of windows,how many much time will he take to paint them?
In circle N, KL ≅ ML.
What is the measure of Arc J M?
77°
90°
132°
154°
Answer:
es 132°
Step-by-step explanation:
KL ≅ ML, entonces triángulo KNL y NLM son similares ah Angle side Angle Theorom .
Entonces,{LNK ≅ LNM}
7x+7=8x-3 8x-7=7+3,x=10
13x+2=13*10+2=130+2=132°
La respuesta es 132°
Based on the relationship of the intercepted arcs of congruent chords, the measure of arc JM is: C. 132°.
What is the Measure of Intercepted Arcs of Equal Chords?If two chords are congruent, then the corresponding arcs bounded by the chords will have equal measure too.
Thus, KL = LM, therefore:
7x + 7 = 8x - 3
Solve for x
7x - 8x = -7 - 3
-x = -10
x = 10
Arc JM = 13x + 2
Plug in the value of x
Arc JM = 13(10) + 2
Arc JM = 132°
Learn more about intercepted arcs of congruent chords on:
https://brainly.com/question/4244936
#SPJ5
What is the value of B Image below
You have one type of nut that sells for $3.00/lb and another type of nut that sells for $5.40/lb. You would like to have 7.2 lbs of a nut mixture that sells for $4.60/lb. How much of each nut will you need to obtain the desired mixture?
Answer: 2.4 pounds of the type of nut that sells for $3.00/lb and 4.8 pounds of the type of nut that sells for $5.40/lb would be needed.
Step-by-step explanation:
Let x represent the number of pounds of the type of nut that sells for $3.00/lb that you would need.
Let y represent the number of pounds of the type of nut that sells for $5.40/lb that you would need.
You would like to have 7.2 lbs of a nut mixture. It means that
x + y = 7.2
The mixture would sell for $4.60/lb. It means that the cost of the mixture would be
4.6 × 7.2 = $33.12
This means that
3x + 5.4y = 33.12- - - - - - - - - 1
Substituting x = 7.2 - y Intl equation 1, it becomes
3(7.2 - y) + 5.4y = 33.12
21.6 - 3y + 5.4y = 33.12
- 3y + 5.4y = 33.12 - 21.6
2.4y = 11.52
y = 11.52/2.4
y = 4.8
x = 7.2 - y = 7.2 - 4.8
x = 2.4
victor wants to buy fertilizer for his yard. the yard measures 45 feet by 50 feet. the directions on the bag of fertilizer says that one bag will cover 1,220 sq ft. how many bags of fertilizer should victor buy to be sure that he cover the entire yard
Answer:
He'll need 2 bags to cover his yard.
Step-by-step explanation:
To solve this problem we first need to calculate the area of Victor's yard. It seemes by the dimmensions given that his yard have a rectangular shape, it's area is given by:
yard area = length*width
yard area = 45*50 = 2250 square feet
Since each bag will cover 1220 square feet, to calculate how many bags are needed for his yeard we need to divide the yard's area by the area each bag can cover. This is shown below:
number of bags = yard area/ bag area = 2250/1220 =1.84
Since he can't buy 0.84 bags we will round the number of bags to 2.
Mr. Smith started his own business making sweatshirts. It costs him $15 for the sweatshirt, $3 for the designs, and $.50 for delivery. If he sells the sweatshirts for $26 in his store, what is the return on investment on each sweatshirt?
Answer:
$7.5 is the ROI on each sweatshirt
Step-by-step explanation:
In this question, we are asked to calculate ROI for a businessman who sells sweatshirts.
To calculate the profit we need to subtract the total cost incurred form manufacture to delivery and subtract bogus from the cost at which he sells the shirts.
Mathematically let’s calculate the cost from production to delivery.
That would be ;
$15 + $3 + $0.5 = $18.5
sales price is $26
His ROI will be $26 - $18.5 = $7.5
Hey ya'll don't scroll please, just look at the attachment and answer every single question please- thank you very much.
I need this done in 15 minutes so it would really really help. Also I have made my 11th account this week regarding this question so just please answer it for me- thanks girlie.
Answer:
a. is B b. is D
Step-by-step explanation:
I need help ! It’s due today
Answer:we have the same thing,
Step-by-step explanation:medium,from end to middle
Answer:
Please give Branliest
1. minimum = 3
maximum = 9
median = 7
2. minimum = 8
maximum = 24
median = 15
3. minimum = 21
maximum = 40
median = 28
lower quartile =26
upper quartile = 24
Step-by-step explanation:
minimum is the lowest number in the set
maximum the highest number
to find the median, line the numbers up in order, and find the number in the middle that is the median
quartiles are the medians or middles of the numbers above the median or bellow
for example 21 26 27 28 33 34 40
the quartiles are 26 and 34
Point R on the coordinate grid below shows the location of a car in a parking lot. A second car needs to park 5 units above R to leave room for a utility truck. What are the coordinates of the location of the second car? (1, −2) (1, 3) (−4, −2) (−4, 3)
Answer:
Step-by-step explanation:
1,3
Sophia creates a blog about food specialties and how to make them at home. In one session she shares a recipe from her grandmother in Italy about making genuine Neapolitan pizza. In the blog, she inserts various links to products she has for sale, like pizza peels, tomato sauce, etc. This is an example of effective _________.
Answer:
inbound marketing
Step-by-step explanation:
The case of Sophia inserting links to products she sells within her food blog is an example of affiliate marketing. With this strategy, Sophia can generate revenue each time a reader makes a purchase through a link on her blog.
Explanation:Sophia's action of incorporating links to products that she has for sale within her blog about food specialties is an example of effective affiliate marketing. In affiliate marketing, an individual recommends products to their audience, and earns a commission on any sales that come from their referrals. By integrating these product links in her blog post, Sophia can generate revenue each time a reader clicks on the link and purchases the product. This allows her to monetize her blog in an easy and effective way.
Learn more about Affiliate Marketing here:https://brainly.com/question/31820974
#SPJ2
urgent help! can someone answer these questions for me?
Answer:
she needs 600 g chocolate. He needs 150 g flour. his recipe is for 6 people
Find the indicated probability. In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. For a randomly selected home, find the probability that the September energy consumption level is between 1100 kWh and 1225 kWh.
Answer:
p=0.1971
Step-by-step explanation:
-Let X be the normally distributed random variable with mean=1050kWh and standard deviation=218kWh.
-We use the z-test to test for the probability of mean consumption being between 1100kWh and 1225kWh as:
[tex]P(1100<X<1225)=P(\frac{1100-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{1225-\mu}{\sigma})\\\\=P(\frac{1100-1050}{218}<Z<\frac{1225-1050}{218})\\\\=P(0.2294<Z<0.8028)\\\\=P(Z<0.8028)-P(Z<0.2994)\\\\=0.7881-0.5910\\\\=0.1971[/tex]
Hence, the probability of mean consumption being between 1100 and 1225kWh is 0.1971
Two dice are rolled, and the results are summed find the probabilty of rolling an odd sum less than 9
Answer:
You can have 11 outcomes:
2: 1/36
3: 2/36
4: 3/36
5: 4/36
6: 5/36
7: 6/36
8: 5/36
9: 4/36
10: 3/36
11: 2/36
12: 1/36
Odd numbers are 3,5,7,9,11 thus the probability is (2+4+6+4+2)/36
Step-by-step explanation:
try this i think this is the answer i looked it up
The monthly cost of a certain long distance service is given by the linear function y=0.08x+ 8.95 where Y is in dollars and X is the amount of time in minutes called in a month. Find and interpert the slope and y-intercept of the linear equation
Answer:3747
Step-by-step explanation:
The slope of the linear function y=0.08x+8.95 is 0.08, indicating the cost increases by $0.08 per minute. The y-intercept is 8.95, representing the monthly flat fee of $8.95 when no calls are made.
Explanation:The linear function given is y=0.08x+8.95, where y represents the monthly cost in dollars and x represents the number of minutes called in a month. In this equation, the slope is 0.08 and it represents the rate at which the cost increases per minute of call time. The y-intercept is 8.95, which is the base cost of the service when no minutes have been used.
The interpretation of the slope is as follows: for each additional minute of call time, the cost increases by $0.08. The interpretation of the y-intercept is that even if no calls are made in a month, the service will still cost $8.95, reflecting a flat monthly fee.
Learn more about Slope and y-intercept Interpretation here:
https://brainly.com/question/32033361
#SPJ11
Find the quotient. 2y/5x / y/6x
Well let us see,
[tex]\dfrac{\frac{2y}{5x}}{\frac{y}{6x}}=\dfrac{12xy}{5xy}=\color{blue}\boxed{\dfrac{12}{5}}[/tex].
Hope this helps.
Answer:
[tex] \huge \purple { \frac{12}{5} }[/tex]
Step-by-step explanation:
[tex] \huge \frac{ \frac{2y}{5x} }{ \frac{y}{6x} } \\ \\ \huge = \frac{2y}{5x} \times \frac{6x}{y} \\ \\ \huge = \frac{2}{5} \times \frac{6}{1} \\ \\ \huge \red{ = \frac{12}{5} }[/tex]
18 students are going on a field trip, the bus can fit 14 so 4 of them will have to ride in a car. In how many ways can we chose the 4 students who must ride in the car?
Answer:
4
Step-by-step explanation:
The 4 youngest, the 4 oldest, the 4 shortest, the 4 tallest. Hope this helps.
Answer:
6
Step-by-step explanation:
Last 4First 4Fifth, Sixth,Seventh, and eighth kids.Eighth, nineth, tenth, eleventh. Tweleveth, Thirteenth, fourteenth, fifteenth.last one, second last, first, and second.A rectangle with length 10 inches and width 5 inches. A triangle sits on top of the rectangle. The triangle has a base of 10 inches and height of 3 inches. What is the area of the figure shown?
Answer:
The Area is 65
Step-by-step explanation: Hope this helps!
Answer:
65
Step-by-step explanation:
got it
Identify the fallacies of relevance and weak induction committed by the following arguments. If no fallacy is committed, write "no fallacy." Todd Burpo, the best-selling author, argues in his book that heaven is real and that his son Colton met Jesus and John the Baptist in a near-death experience. But it’s clear that Burpo says these things only to sell lots of books. Therefore, his arguments have no merit.
The argument discrediting Todd Burpo uses an ad hominem fallacy and a fallacy of weak induction called circumstantial ad hominem, focusing on Burpo's potential financial gain instead of the validity of his claims.
The argument presented commits a couple of logical fallacies.
Firstly, it commits the ad hominem fallacy, which is a type of fallacy of relevance.
This fallacy occurs when the arguer attacks the person making the argument instead of the argument itself.
In this case, discrediting Todd Burpo because he has a financial motivation does not address the actual content of his claims about heaven.
Secondly, there's a fallacy of weak induction known as circumstantial ad hominem.
Here, the suggestion is that Burpo’s circumstances (wanting to sell books), rather than evidence, make his claims unworthy of consideration, which is an insufficient basis to deny the merits of his arguments.
While the argument does not prove the existence of a supernatural deity, dismissing it because of the author's potential financial gain uses inappropriate grounds that do not speak to the truth or falsity of the actual claim, thus making it an invalid critique.
The burden of proof demands that a claim be established through reason and evidence, and this fallacy does not appropriately engage with either.
PLEASE HELPPPP!!!!!!!
Rectangle QRST has points at these coordinates:
Q(-9,2), R (1,2), S (1,-2), and T (-9,-2).
What is the length of QT?
Answer:
the length between them is 4
Step-by-step explanation:
from Q - T
both are at -9 so its a straight line.
the difference between -2 and 2 is 4
-2 , -1, 0, 1, 2,
Answer:
4
Step-by-step explanation:
Q and T are on the same line.
-9 is the x value for both points.
All you are left with is the distance between -2 and 2.
Subtract and take absolute value if you come up with a negative answer.
2 - -2 = 4
A parabola intersects the xxx-axis at x=3x=3x, equals, 3 and x=9x=9x, equals, 9.
What is the xxx-coordinate of the parabola's vertex?
Answer:
x=6
Step-by-step explanation:
Given the x-intercepts of a parabola: [tex]x_1=3, x_2=9[/tex]
The equation of symmetry at the parabola's vertex is x=h
Where [tex]h=\dfrac{x_1+x_2}{2}[/tex]
In this case,
[tex]h=\dfrac{3+9}{2}=6[/tex]
Therefore, the line of symmetry of the parabola is x=6 and is also the x-coordinate of the parabola's vertex.
The vertex of a parabola is the minimum or maximum point of the parabola.
The x-coordinate of the vertex is 6
The intersection points are given as:
[tex]\mathbf{x_1 = 3,\ x_2 = 9}[/tex]
The x-coordinate of the parabola is calculated as:
[tex]\mathbf{x = \frac{1}{2}(x_1 + x_2)}[/tex]
So, we have:
[tex]\mathbf{x = \frac{1}{2}(3 + 9)}[/tex]
[tex]\mathbf{x = \frac{1}{2}(12)}[/tex]
Simplify
[tex]\mathbf{x = 6}[/tex]
Hence, the x-coordinate of the vertex is 6
Read more about vertex at:
https://brainly.com/question/20209326