The correct function that can be used to model the monthly profit for x trinkets produced is f(x) = (x + 50)(x + 250).
Explanation:The correct function that can be used to model the monthly profit for x trinkets produced is f(x) = (x + 50)(x + 250).
To model the monthly profit, we need to consider the profit made for each trinket produced. The function f(x) = (x + 50)(x + 250) represents the profit made for x trinkets produced, where x is the number of trinkets produced. This function is a quadratic function with two factors that represent the difference between the production cost and the selling price of the trinkets.
For example, if we produce 100 trinkets, we can substitute x = 100 into the function to find the monthly profit. f(100) = (100 + 50)(100 + 250) = 150 * 350 = 52,500. So, the monthly profit for producing 100 trinkets would be $52,500.
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The quadratic function f(x) = –4(x – 50)(x – 250) accurately models the monthly profit for x trinkets produced, displaying a concave-downward parabola as expected in this context.
To determine the appropriate quadratic function to model the monthly profit for x trinkets produced, let's analyze the given options.
A quadratic function is generally represented as f(x) = ax^2 + bx + c. The given options are all factored forms of quadratic expressions. The correct form should represent a concave-downward parabola since the profit typically decreases as production increases.
Comparing the given options:
f(x) = –4(x – 50)(x – 250): This expression has a negative leading coefficient, indicating a concave-downward parabola.
f(x) = (x – 50)(x – 250): This expression also has a positive leading coefficient, which would create a concave-upward parabola. It does not match the expected behavior for profit in this context.
f(x) = 28(x + 50)(x + 250): This expression has a positive leading coefficient, indicating a concave-upward parabola. It does not align with the expected downward trend of profit.
f(x) = (x + 50)(x + 250): This expression has a positive leading coefficient, suggesting a concave-upward parabola. Similar to option 3, it does not represent the expected profit behavior.
Therefore, the correct quadratic function to model the monthly profit for x trinkets produced is f(x) = –4(x – 50)(x – 250).
The question probable may be:
All-Star Trinkets estimates its monthly profits using a quadratic function. The table shows the total profit as a function of the number of trinkets produced.
Which function can be used to model the monthly profit for x trinkets produced?
f(x) = –4(x – 50)(x – 250)
f(x) = (x – 50)(x – 250)
f(x) = 28(x + 50)(x + 250)
f(x) = (x + 50)(x + 250)
If the endpoints of the diameter of a circle are (8, 6) and (2,0), what is the standard form equation of the circle?
A)
(x + 5)2 + (y + 3)2 = 18
(x + 5)2 + (y + 3)2 = 3.72
(x - 5)2 + (y - 3)2 = 18
D)
(x - 5)2 + (y - 3)2 = 32
Answer:
It is C.
Step-by-step explanation:
The centre of the circle is at the midpoint of The diameter = (8+2)/2, (6+0)/2 = (5,3) so the left side of the equation is (x-5)^2+(Y-3)^2. Now we need to work out the radius:
The diameter = square root(8-2)^2+6^2) = square root of 72 = 6sqrt2.
So the radius = 3sqrt2 and r^2=18.
plz help its urgent
Lets use 500 minutes and solve for each company:
Plan A = 15 +0.05(500) = 15 + 25 = 40
Plan B = 5 + 0.15(500) = 5 + 75 = 80
Plan C = 10 + 0.10(500) = 10 + 50 = 60
Plan D = 20 + 0.20(500) = 20 + 100 =120
Plan A is the most cost effective.
Answer:
Plan a
Step-by-step explanation:
plan a costs $15, plus the amount that it would cost for 500 minutes, which is $25. (0.05*500=$25). $15+$25=$40.
If she chose plan b, it would cost $80, because $5+ (0.15*500)=$80.
Plan c would cost $60, by plugging in the numbers to the same function above.
Plan d would cost $120
Paula’s paycheck varies directly with the number of hours she works. If she earns $52.50 for 6h of work, how much will she earn for 11 h of work? Round your answer to the nearest cent
Answer:
$96.25
Step-by-step explanation:
Find the unit rate of pay:
$52.50
------------- = $8.75/hr
6 hours
Now multiply this rate by 11 hours:
($8.75/hr)(11 hrs) = $96.25
Answer: $ 96. 25
Step-by-step explanation:
It is said that two variables x and z vary directly if they meet the following relationship:
[tex]z = kx[/tex]
Where k is the constant of variation.
In this case z represents the gains and x represents the hours of work.
Now we must find the value of the constant k.
We know that for 6 hours of work the earnings are $ 52.50
So
[tex]x = 6[/tex]
[tex]z = \$\ 52.50[/tex]
[tex]52.50 = 6k[/tex]
[tex]k= \frac{52.50}{6}[/tex]
[tex]k= 8.75[/tex]
Then the equation is:
[tex]z = 8.75x[/tex]
Finally when x = 11, then:
[tex]z = 8.75*11\\\\z =\$\ 96.25[/tex]
What are the solutions of x2 - 2x + 26 = 0 ?
O
A. x = 5; or x = -5;
B. x = 1+5i or x = 1-5i
C. x = 2 +10; or x = 2 -10;
O
D. * = 2+5; or x = 2-5;
SUBMIT
Answer:
B
Step-by-step explanation:
Given
x² - 2x + 26 = 0 ← in standard form : ax² + bx + c = 0 : a ≠ 0
with a = 1, b = - 2, c = 26
Use the quadratic formula to solve for x
x = ( - (- 2) ± [tex]\sqrt{(-2)^2-(4(1)(26)}[/tex] ) / 2
= ( 2 ± [tex]\sqrt{4-104}[/tex] ) / 2
= ( 2 ± [tex]\sqrt{-100}[/tex] ) / 2
= ( 2 ± 10i ) / 2
= 1 ± 5i
Solutions are x = 1 + 5i or x = 1 - 5i → B
The equation x² - 2x + 26 = 0 has no real solutions. Thus, none of the given options are correct.
Explanation:To solve the equation x² - 2x + 26 = 0, we can use the quadratic formula.
For an equation of the form ax² + bx + c = 0, the quadratic formula is given by:
x = (-b ± √(b² - 4ac)) / (2a)
By substituting the values a = 1, b = -2, and c = 26 into the formula, we get:
x = (-(-2) ± √((-2)² - 4(1)(26))) / (2(1))
Simplifying further:
x = (2 ± √(-92)) / 2
Since taking the square root of a negative number results in a complex solution, we can conclude that there are no real solutions to the equation x² - 2x + 26 = 0.
What are the solutions to x^2 + 4x - 12 = 0?
Answer:
That can be factored:
(x +6) * (x -2)
Therefore, x = -6 and x =2
Step-by-step explanation:
For this case we have the following quadratic equation:
[tex]x ^ 2 + 4x-12 = 0[/tex]
We can factor the equation, for it, we must find two numbers that when multiplied give as result -12 and when summed give as result +4. These numbers are: +6 and -2.
Then, the factorization is given by:
[tex](x + 6) (x-2) = 0[/tex]
Thus, the solutions are:
[tex]x_ {1} = - 6\\x_ {2} = 2[/tex]
Answer:
[tex]x_ {1} = - 6\\x_ {2} = 2[/tex]
Each exterior angle of a regular decagon has a measure of (3x+6) what is the value of x
Answer: 10
Step-by-step explanation:
We know that a regular decagon has 10 sides.
The sum of all exterior angles of any regular polygon is [tex]360^{\circ}[/tex].
Given: Each exterior angle of a regular decagon has a measure of [tex](3x+6)[/tex].
Then the sum of all the exterior angle will be :-
[tex]10\times(3x+6)=360\\\\\Rightarrow\ 30x+60=360\\\\\Rightarrow 30x=300\\\\\Rightarrow x=\dfrac{300}{30}=10[/tex]
Hence, the value of x = 10
find three different ways to write the number 437,000 using powers of 10.
Answer:
4370*10^2
437*10^3
43.7*10^4
Step-by-step explanation:
The given number is
437000
Scientific notation can be used to write the number in different ways. We can use the powers of 10 to write the given number.
First way:
The first way is:
4370*10^2
Separating the hundred from the given number
The second way:
437*10^3
Separating the 1000 from the number in the form of power of 10
The third way:
43.7*10^4
Hence scientific notation can be used for writing the number in different ways..
Which of the following is a 3rd degree polynomial with roots i and 2?
Answer:
D
Step-by-step explanation:
Given the roots of a polynomial, say x = a, x = b, x = c, then
(x - a), (x - b) and (x - c) are the factors and the polynomial is the product of the factors.
Note complex roots occur in conjugate pairs, thus
x = i is a root ⇒ x = - i is also a root
given roots x = 2, x = i, x = - i are roots, then
(x - 2), (x - i) and (x + i) are the factors and
f(x) = (x - 2)(x - i)(x + i)
= (x - 2)(x² - i²)
= (x - 2)(x² + 1)
= x³ + x - 2x² - 2
= x³ - 2x² + x - 2 → D
The 3rd degree polynomial with roots i and 2 is P(x) = x^3 - 2x^2 + x - 2, which is found by multiplying the factors (x - i), (x + i), and (x - 2).
Explanation:A 3rd degree polynomial with roots i and 2 must also have the complex conjugate of i, which is -i, as a root because the coefficients of the polynomial are real numbers. Thus, the polynomial will have three roots: i, -i, and 2. To find the polynomial, we can use the fact that a polynomial equation is the product of its factors. Therefore, we start by writing down the factors that correspond to each root:
(x - i)(x + i)(x - 2)Multiplying these factors together will give us the desired 3rd degree polynomial:
Multiply the factors (x - i) and (x + i), which are conjugates, to get x^2 + 1 because (i)(-i) = -i^2 = 1.Now, multiply the quadratic polynomial x^2 + 1 by (x - 2) to get the 3rd degree polynomial.The full expansion gives us the polynomial P(x) = x^3 - 2x^2 + x - 2.
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Please help...........
Answer:
THE ANSWER IS D
Step-by-step explanation:
if you have multiple choice answers like these you can plug in all the numbers for each equation and the only one that works is d
becuase it ends up equaling 2=2
A painter rented a wallpaper steamer at 9 a.m. and returned it at 4 p.m. He paid a total of $28.84. What was the rental cost per hour?
Hello There!
We know that the painter had the steamer from 9 a.m in the morning to 4 p.m in the afternoon
he had it for a total of 7 hours. 28.84 divided by 7 equals 4.12 an hour
Divide $28.84 by 7 hours.
28.84/7 = 4.12
The rental cost per hour was $4.12.
Given f(x)=2x+3 find x=9 show your work
Answer:
f(9) =21
Step-by-step explanation:
I will assume you want to find f(9) when x=9
Let x=9
f(9) = 2(9) +3
= 18+3
=21
f(9) =21
Translate each sentence into an equation. Then find each number.
The difference between four times a number and six is –46.
Question 1 options:
Answer:
Equation: 4x - 6 = -46
Solution: x=10.
Step-by-step explanation:
The difference between four times a number and six translated into a equation is: 4x - 6 = -46.
Solving for 'x'we have:
4x = -46 + 6 ⇒ 4x = -40 ⇒ x = 10.
Then, the solution is: x=10
Answer:
4x - 6 = -46
x = -10
Step-by-step explanation:
We are given the following sentence equation into a mathematical equation and then solve it to find each number:
The difference between four times a number and six is –46.
Translating it in chunks to make it easier:
1) The difference between ---> means there is a subtraction sign
2) four times a number ---> assuming x to be the number ---> 4x
3) and six ---> 6
4) is -46 ---> = -46
Combining these to get:
[tex]4x - 6 = -46[/tex]
[tex]4x = -46 + 6[/tex]
[tex]4x = -40[/tex]
[tex]x=\frac{-40}{4}[/tex]
x = -10
Blake brought 2 magazines for $4.95 each. If the sales tax was 6.75%, what was the total amount that he paid for the magazines?
Answer:
$10.57
Step-by-step explanation:
Blake brought 2 magazines for = $4.95 each
Cost of 2 magazines = 4.95 × 2 = $9.90
Sales tax rate = 6.75%
Total amount that he paid for the magazines = 9.90 + (6.75% × 9.90)
= 9.90 + (0.0675 × 9.90)
= 9.90 + 0.66825
= $10.56825 ≈ $10.57
He paid $10.57 for the magazines.
HELP PLEASE!! VERY APPRECIATED
•In the triangle below what is the tangent of 30°?
Answer: D
Step-by-step explanation:
Tangent is...
other leg/ adjacent leg
Answer:
The correct answer is D. 1/√3
Step-by-step explanation:
The ratio of the opposite side and the adjacent side to the given angle is the tangent.
According to the image below formula is:
tangent(α)=a/b
a= oppositive side: the side in front of the given angle.
b= adjacent side: the side next to the given angle.
α= the given angle.
According to the image, the value of “a” is 1 and there is √3 for “b”.
So, the correct answer is D. 1/√3
Which of the following could represent consecutive even Integers?
x + 1, x + 2
Ox+1,x+3
2x, 2x + 1
Answer:
x+1,x+3
Step-by-step explanation:
Lets look at consecutive even integers
2,4
How do we get from 2 to 4
We add 2
Our first even integer is x
We add 2
x+2
x, x+2
Buts lets say x is an odd number, so add 1 to it
x+1, x+1 +2
x+1, x+3
a 12 ft ladder leans against the side of a house. The bottom of the ladder is 6 ft from the side of the house. how high is the top of the ladder from the ground?
Answer:
Approximately 10.39 ft.
Step-by-step explanation:
First, draw a short diagram to understand the sides of the right triangle.
The 12 foot ladder leaning against the building would be the hypotenuse and because the bottom of the ladder is 6 feet from the house, that would be the bottom leg. We are trying to figure out the leg to the left (the top of the ladder from the ground.
To solve this, we must use the converse of the Pythagorean Theorem. To do this, we can set up the following equation.
12^2 - 6^2
144 - 36 = 108
Then we must find the square root of 108, which is approximately 10.39 feet.
The diameter of a bicycle wheel is 29 in. How many revolutions
does the wheel make when the bicycle travels 200 ft?
Round your answer to the nearest whole number
The number of revolutions the wheel makes when the bicycle travels 200 ft will be 26.
What is the distance?Distance is a numerical representation of the distance between two objects or locations.
The circumference of the bicycle wheel is;
C= π × diameter
C=π × 29 in
C= 91.11 in
Distance traveled by bicycle wheel in 1 revolution is 91.11 in
Unit conversion;
1 feet = 12 inches
1 inch=1/12 feet
91.11 in=7.592 ft
In one revolution, a bicycle wheel travels 7.592 feet. For a distance of 200 feet, the number of revolutions done by a bicycle wheel is:
[tex]\rm n= \frac{200}{7.5 } \\\\ n= 26.34 \\\\ n= 26 \ rev[/tex]
Hence, the number of revolutions the wheel makes when the bicycle travels 200 ft will be 26.
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Solve the equation.
—10x + 1 + 7х = 37
Answer:
X=- 12
Step-by-step explanation:
Answer:
x = -12
Step-by-step explanation:
—10x + 1 + 7х = 37
Combine like terms
-3x +1 = 37
Subtract 1 from each side
-3x+1-1 = 37-1
-3x = 36
Divide each side by -3
-3x/-3 = 36/-3
x = -12
What is the approximate distance between the points (-3,-4)(-8,1) on a coordinate grid?
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-8-(-3)]^2+[1-(-4)]^2}\implies d=\sqrt{(-8+3)^2+(1+4)^2} \\\\\\ d=\sqrt{25+25}\implies d=\sqrt{50}\implies d\approx 7.071[/tex]
What is the surface area of the cone? (Use 3.14 for pi .)
794.42 in.2
483.56 in.2
822.68 in.2
414.48 in.2
Answer:
794.42 in² (since I used the pi = 3.14159 , the result is slightly different,
Step-by-step explanation:
Formula: Given radius and slant height calculate the height, volume, lateral surface area and total surface area.
Given r, s find h, V, L, A
h = √(s² - r²)
r = 11 in
h = 4.796 in
s = 12 in
V = 607.7 in³
L = 414.7 in²
B = 380.1 in²
A = 794.8 in
Agenda: r = radius
h = height
s = slant height
V = volume
L = lateral surface area
B = base surface area
A = total surface area
π = pi = 3.14159
√ = square root
Answer: the correct option is
(A) 794.42 in.²
Step-by-step explanation: We are given to find the surface area of the cone shown in the figure.
We know that
the SURFACE AREA of a cone with height h units and radius r units is given by
[tex]S=\pi r(r+\sqrt{h^2+r^2}).[/tex]
For the given cone, we have
r = 11 in. and
[tex]h=\sqrt{12^2-11^2}=\sqrt{144-121}=\sqrt{23}=4.8.[/tex]
Therefore, the surface area of the given cone is
[tex]S\\\\=\pi r(r+\sqrt{h^2+r^2})\\\\=3.14\times11(11+\sqrt{4.8^2+11^2})\\\\=34.54(11+12)\\\\=34.54\times23\\\\=794.42.[/tex]
Thus, the required surface area of the given cone is 794.42 in.²
Option (A) is CORRECT.
If the probability of an event happening is 3/8 . What is the probability that the event will not happen ?
a. 0
b. 3/8
c. 5/8
d. 3/4
e. 1
Answer: C is the answer.
Step-by-step explanation:
It is 5/8 because, there is 3 out of 8 chances of the event happening. The rest of the chances, that is 5 out of eight chances, that are not going to happen.
The cone in the diagram has the same height and base area as the prism. What is the ratio of the volume of the come to the volume of the prism?
base area=B
base area =B
volume of cone
volume of prism
1
2
volume of cone
volume of prism
1
3
volume of cone
volume of prism
2
3
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Answer:
[tex]\large\boxed{\dfrac{V_{cone}}{V_{prism}}=\dfrac{1}{3}}[/tex]
Step-by-step explanation:
[tex]\text{The formula of a volume of a cone:}\ V_{cone}=\dfrac{1}{3}B_cH_c\\\\B_c-base\ area\ of\ a\ cone\\H_c-height\ of\ a\ cone\\\\\text{The formula of a volume of a prism:}\ V_{prism}=B_pH_p\\\\B_p-base\ area\ of\ a\ prism\\H_p-height\ of\ a\ prism\\\\\text{The cone and the prism have the same base area and height.}\\\text{Therefore}\\\\V_{cone}=\dfrac{1}{3}BH\ \text{and}\ V_{prism}=BH\\\\\text{The ratio of the volume of the cone to the volume of the prism:}[/tex]
[tex]\dfrac{V_{cone}}{V_{prism}}=\dfrac{\frac{1}{3}BH}{BH}=\dfrac{1}{3}[/tex]
The solution is, 1:3 the ratio of the volume of the come to the volume of the prism.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
The cone in the diagram has the same height and base area as the prism.
now, we know that,
The formula of volume of a cone:
if 'B' is the base of the cone,
and 'h' is the height of the cone,
its volume is V = (1/3) (Bh) cubic units.
The formula of volume of a prism:
if 'B' is the base of the prism,
and 'h' is the height of the prism,
its volume is V = (Bh) cubic units.
The cone in the diagram has the same height and base area as the prism.
so, the ratio of the volume of the come to the volume of the prism:
The formula of volume of a cone: The formula of volume of a prism
= 1/3 *BH : BH
=1/3
=1:3
Hence, The solution is, 1:3 the ratio of the volume of the come to the volume of the prism.
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What is the value of x?
What is the probability of the drawing a blue card, replacing it, and then drawing a blue card?
3/5
6/25
9/25
The probability of drawing a blue card, replacing it, and then drawing a blue card is Option 3. 9/25
Number of blue cards = 3
Number of red cards =2
Total number of cards as given in the diagram = 2+ 3 = 5
How do you calculate probability?The probability of an event can be calculated by the probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes. The probability of drawing a blue card is 3/5 because there are 3 blue cards and 5 cards in total. Multiply 3/5 by 3/5 to get the probability of drawing a blue card twice in a row. Multiply the numerators to get 9 and multiply the denominators to get 25.
This gives you a final answer of 9/25.
What is probability in math?Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.
What is the simple formula of probability?P(A) = n(A)/n(S)
P(A) is the probability of an event “A” n(A) is the number of favourable outcomes. n(S) is the total number of events in the sample space.
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Choose the correct classification of 3x4 − 9x3 − 3x2 + 6.
5th degree polynomial
4th degree polynomial
9th degree polynomial
24th degree polynomial
Answer:
The correct option is 2.
Step-by-step explanation:
The given polynomial is
[tex]3x^4-9x^3-3x^2+6[/tex]
In a polynomial, the highest degrees of its individual terms with non-zero coefficients is called degree of a polynomial.
The degrees of [tex]3x^4,-9x^3, -3x^2,6[/tex] are 4, 3, 2, 0 respectively.
In the given polynomial, the highest degree of its monomial is 4.
We can say that the given polynomial is 4th degree polynomial.
Therefore the correct option is 2.
How does the value of b affect the graph of y=my+b?
Answer:
It translates the graph up or down the y-axis by b units.
Step-by-step explanation:
got it right on edge
the PE clasd has 12 boys and 8 girls what is the maximum number of teams that the teacher can divide the class into so that each team has an equal number of boys and girls the greatest common factor of the numbers of girls and boys
Answer:
4
Step-by-step explanation:
We are given that a PE class has 12 boys and 8 girls. The teacher needs to divide in maximum number of teams so that each team has an equal number of boys and girls.
For this, we will factors of 12 and 8 and their greatest common factor.
12 = 4 × 3 = 2 × 2 × 3
8 = 4 × 2 = 2 × 2 × 2
The greatest common factor is 4, therefore the maximum number of teams with equal number of boys and girls is 4.
What does mean, median, mode, and range means in mathematics?
Mean is dividing the sum of all the numbers by how many numbers there are
Median is the middle of the set of number ordered from least to greatest
Mode is the number that appears the most often in the data set
Range is subtracting the biggest number in the data set by the smallest number
Hope this helped!
~Just a girl in love with Shawn Mendes
Final answer:
The mean is the average of a data set, the median is the middle value, the mode is the most frequent value, and the range is the difference between the highest and lowest values. The median is preferred in skewed distributions.
Explanation:
Mean, Median, Mode, and Range in Mathematics
The mean is the average of a data set, calculated by adding up all the values and dividing the total by the number of values. The median is the middle value when the data set is ordered from least to greatest, or the average of two middle values if there is an even number of values in the data set. The mode is the value that appears most frequently in a data set. The range is the difference between the highest and lowest values in the data set. Each of these measures provides different information about the distribution of the data and can be affected by outliers or the overall shape of the data distribution.
For example, consider the data set: 4, 5, 6, 6, 7, 8, 9. The mean is (4+5+6+6+7+8+9)/7 = 6.43, the median is 6, and the mode is 6 (since it appears the most). The range is 9-4 = 5.
In cases where data sets include outliers or are skewed, the mean may not be representative of the data's center. For instance, if a data set is 4, 5, 6, 6, 7, 8, 100, the mean is significantly influenced by the outlier (100), while the median remains a better indicator of the center. In such distributions, the median is often preferred over the mean.
if city A is 32% less than city b what is city A population
Answer:
there is definitely missing context in this question but if we are going off of per say 100% then A is 68%
Step-by-step explanation:
classify the triangle by its sides
a(3,-3), b(1,4), c(-1,-1)
Answer:
The triangle is scalene Δ
Step-by-step explanation:
* Lets revise the types of the triangle according to its sides
- Equilateral triangle: its three sides are equal in lengths
- Isosceles triangle: two sides are equal in lengths
- Scalene triangle: its three sides have different lengths
- The length of a segment basses through two points (x1 , y1) and
(x2 , y2) is √[(x2 - x1)² + (y2 - y1)²]
* Lets solve the problem
∵ abc is a triangle with vertices a (3 , -3) , b (1 , 4) , c (-1 , -1)
- To classify the triangle by its side find the lengths of the 3 sides
∵ a = (3 , -3) and b = (1 , 4)
∴ ab = √[(1 - 3)² + (4 - -3)²] = √[(-2)² + (7)²] = √[4 + 49] = √53
∵ b = (1 , 4) and c = (-1 , -1)
∴ bc = √[(-1 - 1)² + (-1 - 4)²] = √[(-2)² + (-5)²] = √[4 + 25] = √29
∵ c = (-1 , -1) , a = (3 , -3)
∴ ca = √[(3 - -1)² + (-3 - -1)²] = √[(4)² + (-2)²] = √[16 + 4] = √20
∵ The lengths of the three sides of the triangle are √53 , √29 , √20
∴ The lengths of the three sides are different
∴ The triangle is scalene Δ