we know that
A method for calculating the area of a triangle when you know the lengths of all three sides is the Heron's Formula.
The Heron's Formula states that
[tex]A=\sqrt{p(p-a)(p-b)(p-c)}[/tex]
where
a,b.c are the length sides of the triangle
p is half the perimeter of the triangle
Let
[tex]A(-4,1)\\B(-7,5)\\C(0,1)[/tex]
Step 1
Find the distance AB
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]A(-4,1)\\B(-7,5)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(5-1)^{2}+(-7+4)^{2}}[/tex]
[tex]d=\sqrt{(4)^{2}+(-3)^{2}}[/tex]
[tex]d=\sqrt{25}[/tex]
[tex]dAB=5\ units[/tex]
Step 2
Find the distance BC
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]B(-7,5)\\C(0,1)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(1-5)^{2}+(0+7)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(7)^{2}}[/tex]
[tex]d=\sqrt{65}[/tex]
[tex]dBC=8.06\ units[/tex]
Step 3
Find the distance AC
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]A(-4,1)\\C(0,1)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(1-1)^{2}+(0+4)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(4)^{2}}[/tex]
[tex]d=\sqrt{16}[/tex]
[tex]dAC=4\ units[/tex]
Step 4
Find half the perimeter
[tex]p=\frac{1}{2}(AB+BC+AC)[/tex]
substitute the values
[tex]p=\frac{1}{2}(5+8.06+4)[/tex]
[tex]p=8.53\ units[/tex]
Step 5
Find the area
Applying the Heron's Formula
[tex]A=\sqrt{8.53(8.53-5)(8.53-8.06)(8.53-4)}[/tex]
[tex]A=\sqrt{8.53(3.53)(0.47)(4.53)}[/tex]
[tex]A=\sqrt{64.11}[/tex]
[tex]A=8\ units^{2}[/tex]
therefore
the answer is
the area of the triangle is [tex]8\ units^{2}[/tex]
The area of a shape is the amount of space it occupies.
The area of the triangle is 8 unit square.
The vertices are given as:
[tex]\mathbf{A = (-4,1)}[/tex]
[tex]\mathbf{B = (-7,5)}[/tex]
[tex]\mathbf{C = (0,1)}[/tex]
The area of the triangle is:
[tex]\mathbf{A= \frac{1}{2} \times |A_x(B_y - C_y) + B_x(C_y - A_y) + C_x(A_y - B_y)|}[/tex]
So, we have:
[tex]\mathbf{A= \frac{1}{2} \times |-4(5 - 1) -7(1 - 1) + 0(1 - 5)|}[/tex]
[tex]\mathbf{A= \frac{1}{2} \times |-4(4) -7(0) + 0|}[/tex]
[tex]\mathbf{A= \frac{1}{2} \times |-4(4) -0 + 0|}[/tex]
[tex]\mathbf{A= \frac{1}{2} \times |-16|}[/tex]
Remove absolute brackets
[tex]\mathbf{A= \frac{1}{2} \times 16}[/tex]
[tex]\mathbf{A= 8}[/tex]
Hence, the area of the triangle is 8 unit square.
Read more about areas at:
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A function is given. Determine the average rate of change of the function between the given values of the variable.
h(t) = t2^2+ 2t; t = −1, t = 4
What is the area of a rectangle with vertices at (−6, 3) , (−3, 6) , (1, 2) , and (−2, −1) ?
Find the slope of the line.
We can use the points (-4, -1) and (0, -2) to solve.
Slope formula: y2-y1/x2-x1
= -2-(-1)/0-(-4)
= -1/4
Best Regards,
Wolfyy :)
(10 pts) A plastic extruder can produce 3843 ft of plastic pipe in an 8 hour shift. If the plastic is cut into 7 ft long pipes, how many pipes are produced each shift ?
Do you just divide 3843 by 7?? It just seems to simple.
Answer:
8742
Step-by-step explanation:
838473
How many lines of symmetry are
found in a regular polygon with 40
A regular polygon has the same number of lines of symmetry as it has sides. Therefore, a regular polygon with 40 sides will have 40 lines of symmetry.
Explanation:In Mathematics, symmetry is a significant aspect when dealing with geometric figures, such as polygons. In a regular polygon, the number of lines of symmetry is equal to the number of sides. Therefore, a regular polygon with 40 sides will have 40 lines of symmetry.
This is because, in a regular polygon, all sides and angles are equal, meaning it can be reflected or folded over each of its sides and still remain the same shape. So, you can draw a line from each vertex to the opposite side (or vertex in some cases) and get a perfect fold or reflection.
Remember, this is only true for regular polygons, as irregular polygons won't have the same number of lines of symmetry because their sides and angles may not be equal.
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Which of the following measurements best describes the amount of water in a bucket? 3 gallons 30 fl. oz. 5 pints 10 cups
Solve this Multi-Step Equation
7p - (3p + 4) = -2(2p - 1) + 10
In a memory ad for dimms, you notice 256meg x 72 for one dimm and 256meg x 64 for another dimm. what does the 72 tell you about the first dimm?
A manufacturer is producing two types of shoes, types A and B. Type A cost $4 to produce and takes one hour. Type B costs $5 dollars to produce and takes 12 1 2 hour. Type A yields a profit of $10 and type B yields a profit of $12. The manufacturer has $40 and 7 production hours available. How many of each type of shoe should the manufacturer produce to maximize profit?\
If the top of a set of characters is chopped off, then line spacing may be set to ____.
Force equals mass times acceleration. If m represents mass and a represents acceleration, Which function f represents Force?
A. F=ma
B. F=m+a
C. F= m exponent a
D. F=m/a
What is the value of x in the equation 1/3x-2/3 =-18
Answer:52
Step-by-step explanation:
Hey Yo I needs some Help
Answer:
wow
Step-by-step explanation:
PLEASE HELP, BRAINLIEST William pays $32 per year for no-deductible comprehensive coverage of his new full sized car. A hailstorm causes $250 worth of damage to the paint on his car
How much will the insurance pay?
How much must Richard pay?
Answer:
The insurance company will pay $250.
Step-by-step explanation:
Deductible is the amount of the loss a policy holder pays when he files for an insurance claim, before the insurance company pays any money. And no deductible means that the person will not pay anything, The insurance company will pay.
So, here William pays for a no deductible insurance, which means he will not pay anything. His insurance company will pay the total amount of $250.
Help please! Reflection of a triangle on a graph. D:
The base angles of all trapezoids are congruent.
True or False
In a class of 20 students ,40% are boys.25% of theboys and 50% of the girls were glasses.how many students were glassses. show work
Ariel was told the x intercept and the y intercept of a line with a positive slope. Yet, it was impossible for Ariel to find the slope of the line. What can you conclude about this line?
Match the following items.
Am I right
1. 2x + x + 4 = -17
2
combine like terms
2. 3x + 4 = -17
3
subtraction
3. 3x = -21
4
division
4. x = -7
1
Given
A simple random sample is chosen in such a manner that
Find the slope of the line with the equation 2x+3y=6
How does a globe represent the fact that there are no parallel lines in elliptical geometry?
At 12:00 noon two Mississippi steamboats are 126 miles apart. At 6:00 p.m. they pass each other going in opposite directions. If one steamboat travels 9 miles per hour faster than the other, find the speed of both boats.
Final answer:
To determine the speed of two Mississippi steamboats, we use algebra to set up and solve a system of equations. The slower boat travels at 6 miles per hour, and the faster boat travels at 15 miles per hour.
Explanation:
To solve the problem of finding the speed of two Mississippi steamboats, we can set up a system of linear equations. The boats are 126 miles apart and travel towards each other until they pass at 6:00 p.m. This means they've been traveling for 6 hours. Let's define the speed of the slower boat as x miles per hour and the faster boat as x+9 miles per hour.
Since distance equals speed multiplied by time, the distance covered by the slower boat can be represented by 6x and by the faster boat as 6(x+9). The sum of these distances will be equal to 126 miles, the initial distance between the two boats.
Set up the equation: 6x + 6(x + 9) = 126.
Simplify the equation: 12x + 54 = 126.
Solve for x: x = 72 / 12 = 6 miles per hour.
Calculate the speed of the faster boat: x + 9 = 6 + 9 = 15 miles per hour.
Therefore, the speed of the slower steamboat is 6 miles per hour, and the speed of the faster steamboat is 15 miles per hour.
Whats the answer for solve the equation 6x + 3y = 15 for y. what does y equal if x = 2? if x = 5?
To solve the linear equation 6x + 3y = 15 for y, isolate y, which yields y = (15 - 6x) / 3. Substituting x as 2, we find y = 1, and when x is 5, y equals -5.
In order to solve the equation 6x + 3y = 15 for y, we must first isolate y on one side of the equation. This can be done by first subtracting 6x from both sides of the equation, resulting in 3y = 15 - 6x. To solve for y, we then divide both sides by 3, obtaining y = (15 - 6x) / 3.
When x = 2, we substitute it into the equation to find y:
y = (15 - 6(2)) / 3y = (15 - 12) / 3y = 3 / 3y = 1.
Similarly, when x = 5, we find y by substitution:
y = (15 - 6(5)) / 3y = (15 - 30) / 3y = -15 / 3y = -5.
GET 15 POINTS NOWWWWWWWWW!!!!
What is the point slope form of the line with slope [tex] \frac{2}{5} [/tex] that passes through the point (−4, −7) ?
BRAINLIESTTTTTTTTTTTTTTTTTT!''1. The function f(x) = 800(1.09)3x shows the growth due to interest that Jim earns on an investment.
The steps to calculate an equivalent function are shown below:
[Step 1] f(x) = 800(1.09)^3x
[Step 2] f(x) = 800(1.09^3)^x
[Step 3] f(x) = 800(1.09 ⋅ 3)^x
[Step 4] f(x) = 800(3.27)^x
Which of the following is the first incorrect step?
There is no mistake in the work.
Step 1
Step 2
Step 3
Step 4
Answer: The incorrect step is the second one or step 2
If ,f(x)= 1/4x+3, what is the equation for f–1(x)?
Final answer:
To find the equation for f–1(x), swap the roles of x and f(x) in the equation for f(x), solve for f(x), and replace it with x.
Explanation:
To find the equation for f–1(x), we need to swap the roles of x and f(x) in the equation for f(x) and solve for f(x). So, given that f(x) = 1/4x + 3, we can start by replacing f(x) with x in the equation:
x = 1/4f–1(x) + 3
Now we can solve for f–1(x). First, subtract 3 from both sides of the equation:
x - 3 = 1/4f–1(x)
Then, multiply both sides of the equation by 4:
4(x - 3) = f–1(x)
So, the equation for f–1(x) is f–1(x) = 4(x - 3).
Final answer:
To find the inverse of the function f(x) = 1/4x + 3, swap x and y and solve for y to get the inverse function f⁻¹(x) = 1/(4(x - 3)).
Explanation:
To find the equation for the inverse function f⁻¹(x) of the given function f(x) = 1/4x + 3, we need to swap the variables x and y and then solve for y.
Start with the original function, substituting y for f(x): y = 1/(4x) + 3.Swap x and y: x = 1/(4y) + 3.Solve for y. Subtract 3 from both sides: x - 3 = 1/(4y).Multiply both sides by 4y: 4y(x - 3) = 1.Divide both sides by (x - 3): y = 1/(4(x - 3)). Therefore, the inverse function is f⁻¹(x) = 1/(4(x - 3)).Therefore, the inverse function is f⁻¹(x) = 1/(4(x - 3)), showcasing the step-by-step process to derive the inverse relationship.
THE FUNCTION ARCSINE CAN ALSO BE DEFINED AS?
Erica sells magazine subscriptions and makes a flat rate of $5.35 for each subscription see cells if Erica man $42.80 on Monday $64.20 on Tuesday and $74.90 on Wednesday how many subscriptions did she sell in three days
C—34. Subscriptions
A girl delivering newspapers travels 2 blocks west, 5 blocks north, and then 6 blocks east.
What is her resultant displacement?
___blocks at
____ ° counterclockwise from east.