The given expression has a value of 2.5.
The BODMAS rule is named after the letters in the acronym: B - Brackets, O - Order of powers or roots, D - Division, M - Multiplication. A stands for addition, and S stands for subtraction. According to the BODMAS rule, mathematical statements having several operations must be solved from left to right in the BODMAS order.
Given expression 6 x (2/3 divided by 2) + 0.5
To solve this expression, we must employ the BODMAS rule.
First 2/3 divided by 2
(2/3)/2
= 1/3
Now multiply 1/3 with 6
= 1/3 x 6
= 2
Now add both 2 and 0.5
= 2 + 0.5
= 2.5
Therefore the value of the given expression is 2.5
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Use technology to obtain approximate solutions graphically. All solutions should be accurate to one decimal place. (Zoom in for improved accuracy.)
Find the intersection of the line through (0, 1) and (4.3, 2) and the line through (2.1, 3) and (5.4, 0).
(x, y) =
Answer:
(x, y) ≈ (3.4, 1.8)
Step-by-step explanation:
You want the point of intersection of the lines through (0, 1), (4.3, 2) and (2.1, 3), (5.4, 0).
GraphThe first attachment shows a graph of the lines and the coordinates of the point of intersection. The solution is ...
(x, y) ≈ (3.42, 1.8)
(x, y) = (3.4, 1.8) . . . . accurate to 1 decimal place
__
Additional comment
For each pair of points, the equation of the line can be written as ...
(y2 -y1)(x -x1) -(x2 -x1)(y -y1) = 0
(2 -1)(x -0) -(4.3 -0)(y -1) = 0 ⇒ x -4.3y +4.3 = 0
and
(0 -3)(x -2.1) -(5.4 -2.1)(y -3) = 0 ⇒ -3x -3.3y +16.2 = 0
The calculator result in the second attachment shows the exact solution to be ...
(x, y) = (3 229/540, 1 43/54) ≈ (3.42407, 1.79630)
NO LINKS!! Please help me with this one
Answer:
The letter a in an ellipse equation is:
Half of the major axis if a > b and the ellipse is horizontal, orHalf of the minor axis if b > a and the ellipse is vertical.Step-by-step explanation:
General equation of an ellipse
[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]
where:
center = (h, k)Vertices = (h±a, k) and (h, k±b)Foci = (h±c, k) or (h, k±c) where c²=a²−b²If a > b the ellipse is horizontal, a is the major radius, and b is the minor radius.
If b > a the ellipse is vertical, b is the major radius, and a is the minor radius.
The major axis is the longest diameter of an ellipse, so the major radius is one half of the major axis.
The minor axis is the shortest diameter of an ellipse, so the minor radius is one half of the minor axis.
Therefore the letter a in an ellipse equation is:
The major radius (half of the major axis) if a > b and the ellipse is horizontal, orThe minor radius (half of the minor axis) if b > a and the ellipse is vertical.line x is the perpendicular bisector of segment ZY
what does YT equal
Answer:
Step-by-step explanation:
ZT=YT
x+3=3x-11
x-3x=-11-3
-2x=-14
x=-14/-2=7
YT=3×7-11=21-11=10
YT=10
Ben starts walking along a path at 3 mi/h. One and a half hours after Ben leaves, his sister Amanda begins jogging along the same path at 6 mi/h. How long (in hours) will it be before Amanda catches up to Ben?
It would take Amanda 2.25 hours to catch up with Ben
Speed is the ratio of distance to time. It is given by:
Speed = distance/time
Given that Ben covers a distance d at time t, hence:
3 = d/t
d = 3t
Since Amanda leaves One and a half hours (1.5) after Ben leaves, hence Time = t - 1.5
5 = d/(t - 1.5)
d = 5t - 7.5
Since they catch up, hence:
3t = 5t - 7.5
2t = 7.5
t = 3.75 hours
Time for Amanda = t - 1.5 = 3.75 - 1.5 = 2.25 hours
Hence it would take Amanda 2.25 hours to catch up with Ben.
After arriving in Australia, Jason exchanged $750 of US currency for $1,041.67 Australian
dollars. Complete the two statements based on this currency exchange. Round to the
nearest hundredth.
9. What is the exchange rate of US dollars per Australian dollar?
What is the exchange rate of Australian dollars per US dollar?
The exchange rate of US dollars per Australian dollar is 0.72
The exchange rate of Australian dollars per US dollar is 1.39
Exchange rate
Exchange rate is the price of a country's money in relation to another country's money and it is “fixed” when countries use gold or another agreed-upon standard, and each currency is worth a specific measure of the metal or other standard.
Given,
After arriving in Australia, Jason exchanged $750 of US currency for $1,041.67 Australian dollars. Complete the two statements based on this currency exchange.
Here we need to find the exchange rate of US dollars per Australian dollar and Australian dollars per US dollar then round it to the nearest hundredth.
According to the given details,
Total amount in US dollars = $750
Converted amount in Australian dollar = $1,041.67
When we divide the US dollar by the Australian dollar then we get the value of one dollar rate,
=> 750/1041.67
=> 0.719
When we round off it to the nearest hundredth then we get the exchange rate of $1 is 0.72
Similarly, now we have to divide the Australian dollar by the US dollar then we get the value of one dollar rate,
=> 1041.67/750
=> 1.388
When we round off it to the nearest hundredth then we get the exchange rate of $1 is 1.39.
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what is 954 divided by 70 using long division and with a remainder
Answer:
13 Remainder 44
Step-by-step explanation:
The solution after divide is, 13 and remainder = 44
We have to given that;
954 divided by 70 by using long division and with a remainder.
Now, We can divide as,
⇒ 954 divided by 70
70 ) 954 ( 13
-70
----------
254
- 210
----------
44
Therefore, The solution is, 13 and remainder = 44
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Please help please and thanks ..
In the given triangle JKL , NO = 26 units and JK = (7x + 17) units, then the value of x is equal to 5 units.
As given in the question,
In the given triangle JKL,
M, N ,O are the mid-points of the side JK, JL, KL of the triangle respectively.
Measure of NO is equal to 26 units
Measure of JK is equal to (7x + 17) units
Using mid- point theorem we have,
In triangle JKL,
NO is half the measure of opposite side JK
NO = 1/2 ( JK)
⇒ 26 = 1/2 ( 7x + 17 )
⇒ 7x + 17 = 26 × 2
⇒ 7x + 17 = 52
⇒ 7x = 52 - 17
⇒ 7x = 35
⇒ x= 5 units
Therefore, for the given triangle JKL , NO = 26 units and JK = (7x + 17) units, then the value of x is equal to 5 units.
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what fraction of the numbers from 1 to 20 contain the digit 7
Milan has been given a list of bands and asked to place a vote. His vote must have the names of his favorite, second favorite, and third favorite bands from the list. How many different votes are possible?
The number of possible different votes for Milan, based on the list of bands is 60 different votes.
How to find the number of possible votes?There are 5 lists of bands that Milan has to choose from to place a vote and there are only 3 bands to be chosen out of the 5 lists.
The total number of different votes possible is therefore possible by performing a permutation:
= 5! / ( 5 - 3) !
= 5 ! / 2 !
= (5 x 4 x 3 x 2 x 1) / (2 x 1)
= 60 different votes
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4.
Consider the following amount of energy
used for three different activities:
. 1 minute of walking uses
25 kilojoules of energy
A (4
• 1 minute of jogging uses 84 kilojoules
of energy
1 minute of swimming uses
50 kilojoules of energy
a) How many more kilojoules of energy
would you use in an hour of jogging
than an hour of swimming?
b) To the nearest tenth, how many
minutes of walking would you have to
do to burn up the 1,130 kilojoules in a candy bar
In given word problem ,
a) 2040 more kilojoules of energy would you use in an hour of jogging than an hour of swimming .
b) 45 minutes 2 seconds of walking would you have to do to burn up the 1,130 kilojoules in a candy bar.
What is word problem ?
Our extensive collection of math word problems ranges from addition, subtraction, multiplication, and division to more specialised operations. Mathematical questions that are written as one or more sentences and ask students to use their mathematical understanding to solve problems from "real-life" situations are known as word problems. As a result, for kids to understand the word problem, they need to be familiar with the terminology that goes along with the mathematical symbols that they are already used to.
Here the given ,
=> 1 minute walking = 25 kilojoules
=> 1 minute jogging = 84 kilojoules
=> 1 minute swimming = 50 kilojoules.
a) 1 hour = 60 minutes.
1 hour jogging = 60*84 = 5040 kilojoules.
1 hour swimming = 60*50 = 3000
Then , => 5040-3000=2040 kilojoules.
Therefore 2040 more kilojoules of energy would you use in an hour of jogging than an hour of swimming .
b) x minute of walking = 1130 kilojoules.
=> 25*x=1130
=> x = 1130/25 = 45minutes 2 seconds.
Therefore 45 minutes 2 seconds of walking would you have to
do to burn up the 1,130 kilojoules in a candy bar.
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What is the answer?? 3(b-5)<-2b
Answer:
b < 3
Step-by-step explanation:
3 ( b - 5 ) < - 2b
3 ( b ) - 3 ( 5 ) < - 2b
3b - 15 < - 2b
3b + 2b < 15
5b < 15
b < 15/5
b < 3
absolute value -2i help me quick please
The absolute value of the expression given as -2i is 2i
How to determine the absolute value?From the question, we have the following parameters that can be used in our computation:
Expression = -2i
The absolute value of an expression is represented as
Absolute value = |Expression|
Substitute the known values in the above equation, so, we have the following representation
Absolute value = |-2i|
Evaluate the expression
Absolute value = 2i
Hence, the result of the expression is 2i
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Factor of 14a–35? Pls Ty
A bank found that 2.5% of its loans to new small businesses become delinquent. If 400 small businesses are selected randomly from the bank’s files, what is the probability that at least 12 of them are delinquent? Use a TI-83, TI-83 plus, or TI-84 calculator to find the probability.
.3155
The probability that at least 12 are delinquent is given as 0.3155
How to solve for the probabilityProbability can be defined as the likelihood of getting an outcome out of other outcomes.
We have the mean u = np
where n = 400
p = proportion = 2.5% = 0.025
= 400 x 0.025
= 10
we have to find the population standard deviation
= [tex]\sqrt{np(1-p)}[/tex]
= √400 x 0.025 (1 - 0.025)
= 3.1225
P (X ≥ 12)
= P(X ≥ 11.5)
= 11.5 - 10 / 3.1225
= 1 - P(z < 0.4804)
= 1 - 0.6845
= 0.3155
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Randy is 8 years old. His brother is twice as old as randy. Randys sister is three years younger than randy. Write a expression to represent the age of randys brother
The expression that represents the age of randy's brother is
2x.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Randy age = 8 years old
Randy's brother age = 2 x 8 = 16
Randy's sister age = 8 - 3 = 5
The expression that represents the age of randy's brother.
Let the age of Randy = x.
= 2x
= 2x
= 2 x 8
= 16 years old.
Thus,
The expression that represents the age of randy's brother is
2x.
Where x is the age of Randy.
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A math class has 3 girls and 7 boys in the seventh grade and 4 girls and 4 boys in the eighth grade. The teacher randomly selects a seventh grader and an eighth grader from the class for a competition. What is the probability that the students she selects are both boys? Write your answer as a fraction in simplest form.
The probability that the selections are both boys is 7/10
How to determine the probability that the selections are both boys?The given parameters in the question are
Seventh grade
Boys = 7
Girls = 3
Eight grade
Boys = 4
Girls = 4
The probability of selecting a boy is calculated as
P(Boy) = Number of boys/Number of students
So, we have
Seventh grade
Boys = 7
Girls = 3
P(boy) = 7/10
Eight grade
Boys = 4
Girls = 4
P(boy) = 4/8
The probability that the selections are both boys is
P = P(boy) * P(boy)
So, we have
P = 7/10 * 4/8
Evaluate
P = 7/20
Hence, the probability is 7/20
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Mr. Abbas has bought a Villa in Saar recently for 80,000 BD. He wants to sell it at a 40% profit. House prices are projected to rise on average by 7% a year.
i) How many years will Mr. Abbas have to wait before selling?
The 80,000 BD Villa in Saar Mr. Abbas plans to sell at a 40% profit , with the annual house price growth rate of 7% (compounded) gives the number of years Mr. Abbas has to wait as approximately 5 years
What is the growth rate on an value?The growth rate is the rate at which the value changes within a specified period.
The amount Mr. Abbas bought the Villar in Saar = 80,000 BD
The profit at which he intends to sell it = 40% = 0.4
The rate at which the house prices rise on average = 7 % per annum
The formula for future value, FV is presented as follows;
[tex]FV = PV\cdot \left(1+\dfrac{r}{100} \right)^n[/tex]
Where;
FV = The future value = 80,000 BD + 0.4 × 80,000 BD = 112,000 BD
PV = The present value = 80,000 BD
r = The rate at which the house prices increases annually
n = The number of years
Which gives;
[tex]112,000 = 80,000\cdot \left(1+\dfrac{7}{100} \right)^n[/tex]
[tex]n = \dfrac{ln\left(\dfrac{112,000 }{80,000}\right) }{ln\left(1+\dfrac{7}{100} \right) } \approx 5[/tex]
The number of years Mr. Abbas has to to wait, n ≈ 5 years
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A surveyor is determining the area of a triangle piece of land bordered by three stretts. In the coordinate plane,the vertices of the triangle are at 0,0 -100,-300,and 200 -200. One unit in the coordinate plane represents 1m.what is the area of piece of land
The area of the piece of land with coordinates (0, 0), (-100, 300) and (200, -200) is as measured by the surveyor is 4000 square meter
How to calculate the area of the piece of the landThe given coordinates being plotted as
A (0, 0)
B (-100, 300)
C (200, -200)
Area of triangle is solved by 0.5 * base * height
dimensions from attached plot, BC = 316.2, Aa = 253
= 0.5 * BC * Aa
= 0.5 * 253 * 316.2
= 39 999.3 approximately 40 000
The plot gave an area of 40 000 square units on paper converting using the given scale which is: One unit in the coordinate plane represents 1m
1 unit = 1 m
1 square unit = 1 square meter
4000 square units = ?
cross multiplying
? = 4000 square units
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Find the equation of the linear function represented by the table below in slope-intercept form. x y 1 2 2 0 3 -2 4 -4
The equation of the line is will be y = -2x + 4.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Calculate the slope of the line,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( -2 - 0) / ( 2 - 1) = -2
The y-intercept will be calculated as,
y = mx + c
0 = -2 x 2 + c
c = 4
The equation of the line will be,
y = mx + c
y = -2x + 4
Therefore, the equation of the line will be y = -2x + 4.
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What is Prince William's full name?
Answer:
Depends on the gravitational force. On Earth, one pound equals 4.41N.
Step-by-step explanation:
The formula for Newton's Second Law of Motion is F=ma, which is Force = mass × acceleration.
The SI unit of mass is the kilogram (kg), so we'll have to convert one pound to kilograms. For practical purposes, one pound equals 0.45kg.
The gravitational force of the Earth is 9.8m/s^2. It is worth noting that each planetary body has its own gravitational force in respect to its mass.
Force = mass × acceleration = 0.45kg × 9.8m/s^2 = 4.41N
This number is only applicable on Earth, and may and will change on a planetary body with a mass different from Earth's.
The table shows the outputs, y, for different inputs, x:
Input
(x) 5 6 7 8
Output
(y) 2 5 8 11
Part A: Do the data in this table represent a function? Justify your answer.
Part B: Compare the data in the table with the relation f(x) = 2x + 13. Which relation has a greater value when x = 7?
Part C: Using the relation in Part B, what is the value of x if f(x) = 75?
A. Yes, the data justifies a function because there is no repeating x values.
B. The relation f(x) = 2x + 13 has a greater value at x = 7
C. The value of x when f(x) = 75 is; 31
How to Interpret Function Tables?A) The general formula for equation of a line in slope intercept form is;
y = mx + b
where;
m is slope
b is y-intercept
Slope is;
m = (y₂ - y₁)/(x₂ - x₁)
m = (5 - 2)/(6 - 5)
m = 3
Let us test the first coordinate;
2 = 3(5) + b
2 = 15 + b
2 - 15 = b
-13 = b
so the equation is : y = 3x - 13
B) When x = 7, we have;
y = 3(7) - 13
y = 21 - 13
y = 8
Let us now test for when f(x) = 2x + 13 to get;
f(x) = 2x + 13, when x = 7
f(7) = 2(7) + 13
f(7) = 14 + 13
f(7) = 27
the function has a greater value for f(x) = 2x + 13
C. f(x) = 2x + 13
when f(x) = 75
Thus;
75 = 2x + 13
75 - 13 = 2x
62 = 2x
62/2 = x
31 = x
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Danielle cecils driver rating factor is 1.60 and her car is in age group d and insurance rating group d. She wants 100/300 bodily injury and $50000 property damage coverage a)anual base premium B) anual premmium
a. The annual base premium when Danielle cecils driver rating factor is 1.60 and her car is in age group is $709.
b. The annual premium is $1134.40
What is a premium?It should be noted that the annual premium simply refers to the amount of premium that's paid yearly by the entity. The insurance company has premium payment options for the clients.
The annual base premium will be:
= Liability premium + Collision premium + Comprehensive premium
= $383 + $240 + $86
= $709
The annual premium will be:
= Annual base premium × Driver rating factor
= $709 × 1.60
= $1134.40
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What is the explicit form of an arithmetic sequence if the
first term is 5 and the recursive formula is an an-1 + 8?
=
The explicit form of the arithmetic sequence is
5, 13, 21, 29, .....
What is arithmetic sequence?
A sequence of numbers is said to be in arithmetic progression if the difference between the consecutive terms of the series are same
If the first term is a, common difference is d, then nth term of the sequence is given by
[tex]a_n = a + (n-1)d[/tex]
The recursive form of the given arithmetic series is
[tex]a_n = a_{n-1} + 8[/tex]
First term [tex]a_1 = 5[/tex]
[tex]a_2 = a_1 + 8\\a_2 = 5 + 8\\a_2 = 13[/tex]
[tex]a_3 = a_2 + 8\\a_3 = 13 + 8\\a_3 = 21[/tex]
[tex]a_4 = a_3 + 8\\a_4 = 21+8\\a_4 = 29[/tex]
So the explicit form of the arithmetic sequence is
5, 13, 21, 29, .....
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Erik has 2 bags of bird seed. One bag has
10 pounds of seed, and the other bag has
8 pounds of seed. He fills
7 bird feeders
with 2 pounds each. Write and solve
an
equation to find how many
pounds of bird
seed are left.
Answer:
(10 + 8) - (7 * 2) = x, 4 pounds of birdseed left
Step-by-step explanation:
For the first part of our equation, we will find the total amount of pounds of seeds among the bags (addition).
For the next part, we will find out how much of the bird seed is used (subtraction).
Then, it will equal whatever is left.
(10 + 8) - (7 * 2) = x, x = pounds of bird seed left
Now, we will solve.
(10 + 8) - (7 * 2) = x
(18) - (14) = x
x = 4 pounds of birdseed left
NUMBER SENSE Your Spanish club wants to order 29 hooded sweatshirts that cost $31 each. Explain how you can use
the polynomial identity (a + b)(a - b) = a²-b² and mental math to find the total cost of the hooded sweatshirts.
The total cost of the hooded sweatshirts will be 29 × 31 = $899.
What is multiplication?Multiplication is the general procedure in mathematics in which we multiply two or more numbers by each other to find a new multiplied number.
Multiplication gives us a resultant number that will be very big as compared to the number which is going to be multiplied if and only if the number which is going to be multiplied is more than one.
As per the given,
Number of hooded sweatshirts = 29
Cost of one hooded sweatshirt = $31
Total cost = 29 × 31 = $899.
Hence "The total cost of the hooded sweatshirts will be 29 × 31 = $899".
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what is 1311 divided by 20=?
using long division and with a remainder
The value of the solution of division is 115 with the remainder 11.
We have to give that,
1311 divided by 20.
Now, using long division as,
1311 divided by 20.
20 ) 2311 ( 115
- 20
------------
31
- 20
------
111
- 100
--------
11
Hence, the solution of division is, 115 with the remainder 11
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Can I pleaseeeee get some help solving these problems I’m really struggling
Answer:
2. $19,547.04
3. $10,276.54
4. $16,758.38
Step-by-step explanation:
You have three problems in compound interest with different initial payments, interest rates, and compounding intervals. You want the relationship between the initial payment and the future value.
Future value multiplierThe multiplier of a single payment earning annual interest rate r compounded n times per year for t years is ...
k = (1 +r/n)^(nt)
2.For this problem, r=0.09, n=1, t=9. The multiplier of the payment is ...
k = (1 +0.09/1)^(1·9) = 1.09^9 = 2.17189328
Then the future value of $9000 will be ...
FV = $9000 × 2.17189328 ≈ $19,547.04
3.For this problem, r=0.10, n=12, t=4. The multiplier of the payment is ...
k = (1 +0.10/12)^(12·4) = 1.08333...^48 = 1.48935410
Then the future value of $6900 will be ...
FV = $6900 × 1.48935410 ≈ $10,276.54
4.For this problem, r=0.13, n=12, t=13. The multiplier of the payment is ...
k = (1 +0.13/12)^(12·13) = 1.0108333...^156 = 5.3704484
Then the payment that gives a future value of $90,000 will be ...
P = $90,000/5.3704484 = $16,758.38
__
Additional comment
For the spreadsheet calculation, we used the "Goal Seek" capability to adjust the value of cell F4 to 90000 by changing the value in cell B4.
We could have calculated the multiplier as above, then used it different ways for the different problems. Instead, we used one FV( ) function for all of the problems.
write the equation of the line perpendicular to y= 3/2x + 1/2 that passes through the point (-2,4)
The equation of the line is y = (-2/3)x + 8/3
What is a perpendicular line?
Two geometric objects are perpendicular in simple geometry if they intersect at a right angle. The perpendicular line can be used to graphically depict the condition of perpendicularity. It can be defined between any pair of lines, any pair of planes, or any pair of lines and planes.
The slope-intercept form of a line is written in the form:
y = mx + b
where:
y = y-coordinate
m = slope
x = x-coordinate
b = y-intercept
Here, We have
y= 3/2x + 1/2 that passes through the point (-2,4)
But we do not know the value of b.
We can do this by substituting the point(-2,4), into the equation and we get
y = mx + b
4 = (-2/3)(-2) + b
b = 8/3
Now that you know all your values, rewrite the equation in slope-intercept form:
y = (-2/3)x + 8/3
Hence, the equation of the line is y = (-2/3)x + 8/3
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Could you please help with this.
Answer:
[tex] \sqrt[2]{15} = 7.5[/tex]
Determine the axis of symmetry of the graph of the following parabola. f(x)=3(x−5)2+1 Give your answer in the form x=h.
The axis of symmetry of the parabola, having the equation, f(x) = 3·(x - 5)² + 1 is the line x = h = 5
What is a parabola?A parabola is the locus of a point that moves such that the distance of the point from a fixed point is the same as the distance of the moving point from a fixed line.
The graph of a parabola has the shape of an open umbrella
The given equation for the parabola is; f(x) = 3·(x - 5)² + 1
The equation is given in the vertex form, f(x) = a·(x - h)² + k, where;
(h, k) = The vertex of the parabola
The axis of symmetry of a parabola, which is the line that divides the parabola in two, passes through the vertex of the parabola
Comparing the equation, f(x) = 3·(x - 5)² + 1, to the vertex form of a parabola, gives;
a = 3
(h, k) = (5, 1) (The vertex of the parabola)
Which gives; h = 5
The equation of the axis of symmetry is therefore the line, x = h = 5
Learn more about the graph of a parabola here:
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