Answer:
Center: (-3, 2)
Radius: 4
Step-by-step explanation:
x2 + 6x + y2 - 4y = 3
x² + 6x + 9 + y² - 4y + 4 = 3 + 9 + 4
(x + 3)² + (y - 2)² = 16
(x + 3)² + (y - 2)² = 4²
Center: (-3, 2)
Radius: 4
Use the figure to answer the following.
a. What is the surface area of the cylinder? Leave your answer in terms of x.
b. Suppose the diameter and the height of the cylinder are cut in half. How does this affect the surface area of the cylinder? Explain
The diameter of the cylinder is 8 and the height is 11
a. The surface area of the cylinder is 120π square units.
b. Assuming the diameter and the height of the cylinder are cut in half, the surface area of the cylinder would be reduced by a scale factor of 1/4.
How to calculate surface area of a cylinder?In Mathematics and Geometry, the surface area (SA) of a cylinder can be calculated by using this mathematical equation (formula):
SA = 2πrh + 2πr²
Where:
h represents the height.r represents the radius.Note: Radius = diameter/2 = 8/2 = 4 m.
By substituting the side lengths into the formula for the surface area (SA) of a cylinder, we have the following;
Surface area = 2πrh + 2πr²
Surface area = 2(π)(4)(11) + 2(π)(4²)
Surface area = 120π square units.
Part b.
Assuming the diameter and the height of the cylinder are cut in half, we have:
Surface area = 2(π)(4/2)(11/2) + 2(π)((4/2)²)
Surface area = 2(π)(2)(5.5) + 2(π)(2²)
Surface area = (π)(2)(11) + 2(π)(4)
Surface area = 22π + 8π
Surface area = 30π square units.
Scale factor = 30π/120π
Scale factor = 1/4.
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Note: "The diameter of the cylinder is 8 and the height is 11"
Angel works at a small shop that sells candy
bars. She oversees ordering more boxes of
candy bars. A box of candy bars (p) costs
$64 and Angel has no more than $230 to
spend on the order. What inequality
represents her situation?
Op 64 >= 230
Op 64 <= 230
O p/64 <= 230
O p/64 >= 230
Answer:
p/64 <= 230
Step-by-step explanation:
The inequality that represents Angel's situation is:
p/64 <= 230
This inequality states that the number of boxes of candy bars, represented by p, divided by 64 (the cost of each box), is less than or equal to 230 (the maximum amount Angel has to spend on the order).
If Shawn rides his bike ¾ mile every ½ hour, how many miles does he bike per hour?
Answer:
1 1/2 miles per hour
Step-by-step explanation:
We can use a ratio to solve
3/4 mile
--------------
1/2 hour
Double the top and the bottom to get to 1 hour
3/4 * 2 miles
--------------
1/2 *2 hours
1 1/2 miles
-------------------
1 hours
1 1/2 miles per hour
Answer:1 1/2 mile or 6/4 mile
Step-by-step explanation:
Every half hour he rides 3/4Just multiply 3/4 by 2 which equals 6/4 or 1 1/2.
Maxine's credit card has an APR of 27.99%. If her current monthly balance, before interest, is $1,834.50, what will her monthly interest charge be? (4 points) $42.78 $42.79 $51.67 $65.54
Answer:
(b) $42.79
Step-by-step explanation:
You want the monthly interest charge on a balance of $1834.50 when the annual rate is 27.99%.
Monthly rateThe monthly interest rate is the annual rate divided by 12. This means the interest charge is ...
I = Prt . . . . . interest on P at annual rate r for t years
I = $1834.50 × 0.2799 × 1/12 ≈ $42.79
Her monthly interest charge will be $42.79.
What is the domain of f(x)? {x | 1 < x < 5} {x | 1 < x < 5} {y | −4 < y < 1} {y | −4 < y < 1}
The domain of function f(x) is given as follows:
{x | 1 ≤ x < 5}.
How to define the domain and range of a function?The domain of a function is defined as the set containing all possible input values of the function, that is, all the values assumed by the independent variable x in the context of the function.The range of a function is defined as the set containing all possible output values of the function, that is, all the values assumed by the dependent variable y in the context of the function.The values of x of the function given at the end of the answer are as follows:
Starts at x = 1(closed interval).Ends at x = 5 (open interval).Hence the domain is given as follows:
{x | 1 ≤ x < 5}.
Missing InformationThe function is given by the image presented at the end of the answer.
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Answer:
A - {x | 1 < x < 5}
Step-by-step explanation:
took the Quiz
Help pleaseeeee guys
On performing , the "row-operation" 2R₁ + R₂ → R₂ on the matrix "M", the resulting new-matrix is [tex]\left[\begin{array}{ccc}5&1&-5\\10&0&-8\end{array}\right][/tex] .
The matrix "M" is given as : [tex]\left[\begin{array}{ccc}5&1&-5\\0&-2&2\end{array}\right][/tex],
We have to apply the Row-Operation : 2R₁ + R₂ → R₂, on the matrix "M",
Performing the row-operation "2R₁ + R₂ → R₂" on a matrix "M" means multiplying the first-row of "M" by 2, and then adding the resulting values to the second-row of "M" to produce a new value for each element in the second row.
This operation does not affect the first row of "M" and changes the values in the second row of "M".
⇒ [tex]\left[\begin{array}{ccc}5&1&-5\\2\times5+0&2\times 1-2&2\times(-5)+2\end{array}\right][/tex],
⇒ [tex]\left[\begin{array}{ccc}5&1&-5\\10+0&2-2&-10+2\end{array}\right][/tex],
⇒ [tex]\left[\begin{array}{ccc}5&1&-5\\10&0&-8\end{array}\right][/tex].
Therefore, the new-matrix is [tex]\left[\begin{array}{ccc}5&1&-5\\10&0&-8\end{array}\right][/tex].
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please help me with this!
4 glue sticks cost $7.76.
which equation would help determine the cost of 13 glue sticks
choose 1 answer
A x/13 = 4/$7.76
B 13/x = $7.76/4
C 4/$7.76 = 13/x
D 13/4 = $7.76/x
E None of the above
Answer:
13 glue sticks cost $25.22.
Step-by-step explanation:
4 blue sticks cost $7.76, this means that one glue stick costs
$7.76/4 = $1.94.
Let be the cost of the glue sticks, and be the number of glue sticks; then
We can use this equation to find the cost of 13 glue sticks; we just put into our equation and it gives:
So 13 glue sticks cost $25.22.
Part A: Jan INCORRECTLY finds the surface area of the cone using the following work. Explain Jan's error and find the
correct volume AND surface area of the cone.
Therefore, Jan has taken the wrong slant height, he has taken height, h is a place of slant height, l. That's why he has got the wrong answer.
How to solveGiven:,
r= d/2
22/2= 11m
Using the Pythagorean theorem, we can find the length:
l =[tex]11\sqrt{5}\\ = 24.6m[/tex]
Therefore, to find the surface area:
SA= 3.14(270.56 + 121)
=[tex]1229.5m^2[/tex]
Therefore, to find the volume:
V= [tex]1/3 \pi.r^2h[/tex]
V= [tex]2786.23m^3[/tex]
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The Complete Question
Jan INCORRECTLY finds the surface area of the cone using the following work. Explain Jan's error and find the correct volume AND surface area of the cone. 22 m SA = = url + ar?
What is the surface area of a cone with radius 8 in. and slant height 9 in.?
The total surface area of the cone is 427.04 square inches.
What is the surface area of the cone?For a cone of radius R and slant height L, the total surface area is given by the formula:
S = π*R*L + π*R²
Where π = 3.14
In this case, we know that the radius of the cone is 8 inches, and the slant height of the cone is 9 inches.
Then the total surface area of the cone is:
S = 3.14*8in*9in + 3.14*(8in)²
S = 427.04 in²
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Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:
In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.
The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.
Which of these could be a step to prove that BC2 = AB2 + AC2?
possible answers -
By the cross product property, AB2 = BC multiplied by BD.
By the cross product property, AC2 = BC multiplied by BD.
By the cross product property, AC2 = BC multiplied by AD.
By the cross product property, AB2 = BC multiplied by AD.
The correct step to prove that [tex]BC^2 = AB^2 + AC^2[/tex] is:
By the cross product property, [tex]AC^2 = BC \cdot AD[/tex].
To prove that [tex]BC^2 = AB^2 + AC^2[/tex], we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:
Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.
By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).
Using the proportionality of similar triangles, we can write the following ratio:
[tex]$\frac{AB}{BC} = \frac{AD}{AB}$[/tex]
Cross-multiplying, we get:
[tex]$AB^2 = BC \cdot AD$[/tex]
Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:
[tex]$\frac{AC}{BC} = \frac{AD}{AC}$[/tex]
Cross-multiplying, we have:
[tex]$AC^2 = BC \cdot AD$[/tex]
Now, we can substitute the derived expressions into the original equation:
[tex]$BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$[/tex]
It was made possible by cross-product property.
Therefore, the correct step to prove that [tex]BC^2 = AB^2 + AC^2[/tex] is:
By the cross product property, [tex]AC^2 = BC \cdot AD[/tex].
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When Grace opens and lays a shipping box out flat, she sees that the top and the bottom of the box
both measure 10 inches by 14 Inches, the sides of the box both measure 14 inches by 8 inches, and
the front and back of the box both measure 8 inches by 10 inches. What is the surface area of Grace's
strooing box?
The surface area of Grace's shipping box is 664 square inches.
We have,
The box can be divided into six rectangles, each of which represents the face of the box.
To find the surface area of the box, we need to find the area of each face and then add them all up.
The top and bottom of the box are both 10 inches by 14 inches, so the area of each of these faces is:
= 10 x 14
= 140 square inches
The sides of the box are both 14 inches by 8 inches, so the area of each of these faces is:
= 14 x 8
= 112 square inches
The front and back of the box are both 8 inches by 10 inches, so the area of each of these faces is:
8 x 10
= 80 square inches
To find the surface area of the whole box, we add up the areas of all six faces:
= 2(140) + 2(112) + 2(80)
= 280 + 224 + 160
= 664 square inches
Therefore,
The surface area of Grace's shipping box is 664 square inches.
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We mixed 5l of 45% alcohol, 4l of 82% and 1l of 92% alcohol. How many percent alcohol does the resulting mixture contain? I got 58.6% and im wondering IF that's correct.
The resulting mixture contains approximately 64.5% alcohol, not 58.6% as you mentioned.
To solve this problemWe can calculate the weighted average of the alcohol percentages based on the volumes of each component.
Let's figure out how much alcohol there is overall in the mixture:
Total alcohol is calculated as follows: (Volume of 45% alcohol) * (Property of 45% alcohol) + (Volume of 82% alcohol) * (Property of 82% alcohol) + (Volume of 92% alcohol) * (Property of 92% alcohol).
Total alcohol = (5 liters) * (45%) + (4 liters) * (82%) + (1 liter) * (92%)
Total alcohol = 2.25 liters + 3.28 liters + 0.92 liters
Total alcohol = 6.45 liters
Let's now determine the amount of alcohol included in the final mixture:
Alcohol content is calculated as (total alcohol / total mixture volume) * 100.
The mixture's total volume is = 5 liters + 4 liters + 1 liter = 10 liters
Alcohol content: (6.45 liters / 10 liters) x 100 = 64.5%
Therefore, the resulting mixture contains approximately 64.5% alcohol, not 58.6% as you mentioned.
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Si 10 obreros construyen un consultorio médico en 12 dias.¿Con cuántos obreros se hará la misma obra en 15 dias?
A total of 8 workers are required for a building time of 15 days.
How many workers are needed to complete a building?
In this problem we find a case of inverse relationship, in which the number of workers (n) is inversely proportional to building time (t), in hours. The situation is represented by following formulas:
n ∝ 1 / t
n = k / t
Where k is the proportionality ratio, which can be eliminated by building the following formula:
n₁ · t₁ = n₂ · t₂
If we know that n₁ = 10, t₁ = 12 and t₂ = 15, then the required number of workers is:
n₂ = n₁ · (t₁ / t₂)
n₂ = 10 · (12 / 15)
n₂ = 10 · (4 / 5)
n₂ = 8
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A researcher at a major clinic wishes to estimate the proportion of the adult population of the United States that has sleep deprivation. What size sample should be obtained in order to be 99 % confident that the sample proportion will not differ from the true proportion by more than 4%? Round up to the nearest whole number.
The sample size needed to be 99% confident that the sample proportion will not differ from the true proportion by more than 4% is given as follows:
n = 1037.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The margin of error is given as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
As we have no estimate, the parameter is given as follows:
[tex]\pi = 0.5[/tex]
Then the sample size for M = 0.04 is obtained as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.04\sqrt{n} = 2.575 \times 0.5[/tex]
[tex]\sqrt{n} = \frac{2.575 \times 0.5}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2[/tex]
n = 1037.
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evaluate xy-y when x = 2 and y = 5
Answer:
5
Step-by-step explanation:
Just do as the problem says:
xy-y = (2)(5)-(5) = 10-5 = 5
Answer: 5
Step-by-step explanation: All you have to do is substitute x & y for their respective numbers. In this case, change x for 2 & y for 5, So xy-y becomes 2(5)-5, which equals 10-5, which is 5.
Shirley Garcia is a restaurant supplies salesperson and receives 8% of her total sales as commission. Her sales totalled $15,000 during a given week. Find her commission.
Answer:
8% of $15,000 = .08 × $15,000 = $1,200
the third term of an arithmetic sequence is 7 and the twelfth term in 106. what is the one hundredth term of the sequence
Answer:
a₁₀₀ = 1074
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
given a₃ = 7 and a₁₂ = 106 , then
a₁ + 2d = 7 → (1)
a₁ + 11d = 106 → (2)
solve the equations simultaneously to find a₁ and d
subtract (1) from (2) term by term to eliminate a₁
(a₁ - a₁) + (11d - 2d) = 106 - 7
0 + 9d = 99
9d = 99 ( divide both sides by 9 )
d = 11
substitute d = 11 into (1) and solve for a₁
a₁ + 2(11) = 7
a₁ + 22 = 7 ( subtract 22 from both sides )
a₁ = - 15
Then
a₁₀₀ = - 15 + (99 × 11) = - 15 + 1089 = 1074
Groups 1 and 3 In a class of 42 students, 12 boys and 15 girls know how to read three-letter words in English. 19 boys and 17 girls know how to identify all letters of the alphabet. None of the students in the class can write a sentence of five words if dictated to them. There are 22 boys and 20 girls in the class.
•Using a Venn diagram, show how many boys and girls cannot read a letter or a three-letter word.
•If all students should know how to write a sentence of five words by the end of the academic year, how many groups will you need to form to focus on remedial/tutor support (to teach at the right level)?
• If by the end of the academic year, all students are able to identify all letters, read three-letter words, and write a five-word sentence, what would this Venn diagram look like?
There are 23 boys and 20 girls in the class who cannot read a letter or a three-letter word.
How to solveThe Venn diagram is drawn as shown in the attached image, and it shows that the number of boys and girls who cannot read a letter or a three-letter word is marked as (c+d) which represents 13 boys and 8 girls.
Given:
The class has 42 students.
12 boys and 15 girls are said to know how to read three-letter words in English.
19 boys and 17 girls are said to know how to identify all letters of the alphabet.
None of the students in the class is able to write a sentence of five words if dictated to them.
There are in total 22 boys and 20 girls in the class.
Read three-letter words |
|____________|______________|
| | |
| Boys (12) | Girls (15) | Can read three-letter words
|____________|______________|
| | |
| Boys (10) | Girls (13) | Cannot read three-letter words
_______|____________|______________|
| | |
| Boys (9) | Girls (13) | Can identify all letters
|____________|______________|
| | |
| Boys (13) | Girls (7) | Cannot identify all letters
|____________|______________|
To find the number of boys and girls who cannot read a letter or a three-letter word, we need to add up the numbers in the two bottom circles:
Boys who cannot read a letter or a three-letter word: 10 + 13 = 23
Girls who cannot read a letter or a three-letter word: 13 + 7 = 20
Therefore, there are 23 boys and 20 girls in the class who cannot read a letter or a three-letter word.
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can u give an answer
Answer: 0
Step-by-step explanation:
Put 0 in the front box.
this is because you cant divide 11 apples equally into 6 people; 11 isn't a multiple of 6
100 Points! Algebra question. Photo attached. Solve the equation. Please show as much work as possible. Thank you!
Answer:
[tex]3 {cos}^{2} x - {sin}^{2} x = 0[/tex]
[tex]3 - 3 {sin}^{2} x - {sin}^{2} x = 0[/tex]
[tex]3 - 4 {sin}^{2} x = 0[/tex]
[tex]4 {sin}^{2} x = 3[/tex]
[tex] {sin}^{2} x = \frac{3}{4} [/tex]
sin(x) = +(1/2)√3
x = π/3 + 2kπ or x = 2π/3 + 2kπ
x = -π/3 + 2kπ or x = -2π/3 + 2kπ
(k is an integer)
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
A
Step-by-step explanation:
i do this all the time math is my thing
Find the distance from point X to line p.
Answer:
[tex]\sf 2\sqrt{17}[/tex]
Step-by-step explanation:
To find the distance of a line using distance formula:
The line from point X intersect the line p at (0 , -3).
( -2 , 5) ⇒ x₁ = -2 & y₁ = 5
(0 , -3) ⇒ x₂ = 0 & y₂ = -3
[tex]\boxed{\bf Distance = \sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}}[/tex]
[tex]\sf = \sqrt{-2-0)^2+(5-[-3])^2}\\\\=\sqrt{(-2-0)^2 + (5+3)^2}\\\\=\sqrt{(-2)^2+(8)^2}\\\\=\sqrt{4+64}\\\\=\sqrt{68}\\\\=\sqrt{2*2*17}\\\\=2\sqrt{17}[/tex]
Please help with that question
The value of function f (α + β) is determined as (3√3 + 1)/3, (2√2 - 3)/3.
What is the value of function f (α + β)?The value of f (α + β) is calculated by applying the following formula as follows;
The given functions;
for α: x² + y² = 4
y is given as -1, the value of x is calculated as;
x² + (-1)² = 4
x² + 1 = 4
x² = 3
x = √3
α = (√3, - 1)
for β: x² + y² = 1
x is given as ¹/₃, the value of y is calculated as;
(¹/₃)² + y² = 1
¹/₉ + y² = 1
y² = 1 - ¹/₉
y² = ⁸/₉
y = √ (8/9)
y = 2√2/3
β = (¹/₃, 2√2/3)
The value of function f (α + β) is calculated as;
f(α + β) = (√3, - 1) + (¹/₃, 2√2/3)
f(α + β) = (3√3 + 1)/3, (2√2 - 3)/3
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How many 1/3 inch cubes does it take to fill a box with a width of 2 2/3 inches, length of 3 1/3 inches with a height 2 1/3
The number of 1/3 inch cubes required to fill the box is 62.
Volume of boxVolume = length × width × height
Height = 7/3
Length = 10/3
width = 8/3
Hence ,
Volume = 7/3 × 10/3 × 8/3 = 560/27
Size of cube = 1/3
Number of cubes required = Volume of box / size of cube
Number of cubes = 560/27 × 3/1
Number of cubes = 1680/27 = 62.22
Therefore, it will take 62 1/3 cubes to fill the box
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D
(x+2)(x+6)=0
In the problem shown, to conclude that x+2=0 orx+6=0, one must use the:
O zero product property
O division property
O transitive property
O multiplication property
H
OI
The property used to calculate x in (x + 2)(x + 6) = 0 is (a) the zero product property
How to determine the property used to calculate xFrom the question, we have the following parameters that can be used in our computation:
(x + 2)(x + 6) = 0
The equation when expanded becomes
x + 2 = 0 or x + 6 = 0
In algebra, the zero product property states that
if ab = 0, then a = 0 or b = 0
using the above as a guide, we have the following:
The property used to calculate x is (a) the zero product property
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I NEED YOUR HELP WITH STATISTICS
For a probability distribution to be represented, it is needed that P(X = 0) + P(X = 1) = 0.44. Hence one possible example is:
P(X = 0) = 0.40.
P(X = 1) = 0.04.
Discrete random variable to represent a probability distribution =
The sum of all the probabilities must be of 1, hence:
P(X = 0) + P(X = 1) + P(X = 3) + P(X = 4) + P(X = 5) = 1.
Then, considering the table:
P(X = 0) + P(X = 1) + 0.15 + 0.17 + 0.24 = 1
P(X = 0) + P(X = 1) + 0.56 = 1
P(X = 0) + P(X = 1) = 0.44.
Hence one possible value is:
P(X = 0) = 0.40.
P(X = 1) = 0.04.
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What do they mean and why please
NO LINKS!!! URGENT HELP PLEASE!!!
The distance between Miami, Florida and Bermuda is about 1042 miles. The distance from Bermuda to San Juan. Puerto Rico is about 965 miles, and the distance from San Juan to Miami is about 1038 miles. Find the area of the triangle formed by the three locations.
Answer:
444523.45 square miles
Step-by-step explanation:
By using Heron's formula, we can easily find the area of the triangle formed by Miami, Bermuda, and San Juan, we need to use the lengths of the three sides of the triangle.
Let,
Side a: Distance from Miami to Bermuda = 1042 miles
Side b: Distance from Bermuda to San Juan = 965 miles
Side c: Distance from San Juan to Miami = 1038 miles
Now we can use Heron's formula to find the area of the triangle:
s =[tex]\frac{a+b+c}{2}[/tex]
s = [tex]\frac{1042 + 965 + 1038}{2}=1522.5[/tex] miles
A = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
A = [tex]\sqrt{1522.5(1522.5-1042)(1522.5-965)(1522.5-1038)}=444523.45[/tex]
Therefore, the area of the triangle formed by Miami, Bermuda, and San Juan is approximately 444523.45 square miles.
Answer:
444,523.45 square miles (2 d.p.)
Step-by-step explanation:
To find the area of a triangle formed by the locations of Miami, Bermuda, and San Juan, use Heron's formula.
[tex]\boxed{\begin{minipage}{8 cm}\underline{Heron's Formula}\\\\$A=\sqrt{s(s-a)(s-b)(s-c)}$\\\\where:\\ \phantom{ww}$\bullet$ $A$ is the area of the triangle. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the side lengths of the triangle. \\ \phantom{ww}$\bullet$ $s$ is half the perimeter.\\\end{minipage}}[/tex]
Label the three sides of the triangle as 'a', 'b', and 'c', where 'a' is the distance from Miami to Bermuda (1042 miles), 'b' is the distance from Bermuda to San Juan (965 miles), and 'c' is the distance from San Juan to Miami (1038 miles):
a = 1042 milesb = 965 milesc = 1038 milesTo find the half perimeter, s, half the sum of the three side lengths:
[tex]\implies s=\dfrac{a+b+c}{2}=\dfrac{1042+965+1038}{2}=1522.5[/tex]
Substitute the values of a, b, c and s into Heron's formula and solve for area, A:
[tex]\begin{aligned}A&=\sqrt{s(s-a)(s-b)(s-c)}\\&=\sqrt{1522.5(1522.5-1042)(1522.5-965)(1522.5-1038)}\\&=\sqrt{1522.5(480.5)(557.5)(484.5)}\\&=444523.4468348...\\&=444523.45\; \sf miles^2\;(2\;d.p.)\end{aligned}[/tex]
Therefore, the area of the triangle formed by the three locations is 444,523.45 square miles, to two decimal places.
18. Multiply, then check your work by switching factors.
a. 693 x 83
b. 910 x 45
c. 38 x 84
d. 409 x 89
The requried, Multiplies(with switching factors.) area given below,
a.
693 x 83 = 57489
83 x 693 = 57489
The answer is 57489.
b.
910 x 45 = 40950
45 x 910 = 40950
The answer is 40950.
c.
38 x 84 = 3192
84 x 38 = 3192
The answer is 3192.
d.
409 x 89 = 36401
89 x 409 = 36401
The answer is 36401.
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Show that the points (2, 5), (5 , 2) and (6,6) are composites of a triangle
The slopes of the lines connecting all the points are distinct. Hence, they form a triangle.
Proof that 3 points form a triangleTo show that the points (2, 5), (5, 2), and (6, 6) form a triangle, we can calculate the slopes of the lines connecting these points. If the slopes are all distinct, then the points form a triangle.
Let's calculate the slopes:
The slope between (2, 5) and (5, 2):
m₁ = (y₂ - y₁) / (x₂ - x₁)
= (2 - 5) / (5 - 2)
= -3/3
= -1
The slope between (2, 5) and (6, 6):
m₂ = (y₂ - y₁) / (x₂ - x₁)
= (6 - 5) / (6 - 2)
= 1/4
The slope between (5, 2) and (6, 6):
m₃ = (y₂ - y₁) / (x₂ - x₁)
= (6 - 2) / (6 - 5)
= 4/1
= 4
Since the slopes of the lines connecting these points are all distinct (-1, 1/4, and 4), the points (2, 5), (5, 2), and (6, 6) form a triangle.
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