we know that
the perimeter of a polygon is the sum of the length sides
in this problem we have five vertices
so
the polygon has five sides
Let
[tex]A(-1,3)\\B(-1,6)\\C(2,10)\\D(5,6)\\E(5,3)[/tex]
the perimeter is equal to
[tex]P=AB+BC+CD+DE+AE[/tex]
The formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Step 1
Find the distance AB
[tex]A(-1,3)\\B(-1,6)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(6-3)^{2}+(-1+1)^{2}}[/tex]
[tex]d=\sqrt{(3)^{2}+(0)^{2}}[/tex]
[tex]dAB=3\ units[/tex]
Step 2
Find the distance BC
[tex]B(-1,6)\\C(2,10)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(10-6)^{2}+(2+1)^{2}}[/tex]
[tex]d=\sqrt{(4)^{2}+(3)^{2}}[/tex]
[tex]dBC=5\ units[/tex]
Step 3
Find the distance CD
[tex]C(2,10)\\D(5,6)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(6-10)^{2}+(5-2)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(3)^{2}}[/tex]
[tex]dCD=5\ units[/tex]
Step 4
Find the distance DE
[tex]D(5,6)\\E(5,3)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(3-6)^{2}+(5-5)^{2}}[/tex]
[tex]d=\sqrt{(-3)^{2}+(0)^{2}}[/tex]
[tex]dDE=3\ units[/tex]
Step 5
Find the distance AE
[tex]A(-1,3)\\E(5,3)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(3-3)^{2}+(5+1)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(6)^{2}}[/tex]
[tex]dAE=6\ units[/tex]
Step 6
Find the perimeter
the perimeter is equal to
[tex]P=AB+BC+CD+DE+AE[/tex]
substitute the values
[tex]P=3+5+5+3+6=22\ units[/tex]
therefore
the answer is
the perimeter of the polygon is [tex]22\ units[/tex]
Cost of a comic book: $3.95
Markup: 20%
Which expressions are equivalent to 3(62)? Select each correct answer. 3(60 + 2) 3(6 + 2) 3(6 + 56) 3(60 + 20)
Mei is writing a coordinate proof involving a right isosceles triangle. Mei places her triangle on the coordinate plane such that one of the legs of the triangle lies along the x-axis and the other leg is parallel to the y-axis.
~ What coordinates should she assign to this third vertex of the right isosceles triangle?
Answer: (a,a)
Step-by-step explanation:
Given: A right isosceles triangle which is placed on the coordinate plane such that one of the legs of the triangle lies along the x-axis and the other leg is parallel to the y-axis.
From the given figure one vertex is on origin(0,0) and second on x -axis as (a,0) .ii.e. one side of the triangle is on the x axis with length 'a' and the side parallel to the y axis should perpendicular to the x axis with length 'a'.(∵ two sides are equal in a right isosceles triangle)
So the coordinates should she assign to the third vertex of the right isosceles triangle is (a,a).[as the point lie above the point (a,0), so its x abscissa should be same]
The third vertex of a right isosceles triangle where one leg lies on the x-axis and the second leg is parallel to the y-axis would have equal x and y coordinates, assuming the second vertex is at (a,0). Therefore, the third vertex would be at (a,a), for any real numerical value of 'a'. This makes use of key concepts in coordinate geometry.
Explanation:In the context of mathematics, specifically coordinate geometry, Mei can assign the third vertex of this right isosceles triangle to any point that is equally distant from both the x and y axes. Assuming the other two vertices of the triangle are at the origin (0,0) and on the x-axis (a,0), then the coordinates of the third vertex would be (a,a).
Right isosceles triangle is a special type of triangle where two sides are equal in length and the angle between them is 90 degrees. Since the legs of the triangle are along the x and y axes, this leads to the third vertex being on the line y=x.
A coordinate proof involves using the properties and definition of the geometric figures in the coordinate plane. It involves calculations with the coordinates of the vertices of the figures. In the case of coordinate geometry, it's essential to understand the placement of points on the x-y plane.
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A segment in the complex plane has a midpoint at −1 + 7i. If one endpoint of the segment is at
3 + 8i, what is the other endpoint?
__+__i
Answer:
-5, 6i
Step-by-step explanation:
You decide to play roulette 200 times each time betting the same amount on red. you will loe money if you win on fewer than 100 of the plays. what is the probability that you will lose money? ( check that the normal approximation is permissible and use it to find this probability) in general, if you bet the same.
The probability of losing money in this scenario is 23.89%.
Probability of Losing Money in Roulette (200 spins, red bet)
Step-by-Step Calculation:
1) Probability of winning on one spin:
Red covers 18 out of 38 numbers (European roulette).
P(win) = 18/38 ≈ 0.474.
2) Number of wins needed to break even:
Divide total spins by 2 due to 1:1 payout on red.
200 spins / 2 = 100 wins needed.
3) Binomial distribution:
200 trials (spins), each with 2 outcomes (win/loss).
Success probability = P(win) = 0.474.
Failure probability = P(loss) = 1 - P(win) = 0.526.
4) Normal approximation:
Check conditions for normal approximation:
np > 5 (200 × 0.474 ≈ 95 > 5)
nq > 5 (200 ×0.526 ≈ 105 > 5)
Both conditions met, so normal approximation is valid.
5) Calculate mean and standard deviation:
Mean (μ) = np = 200 × 0.474 ≈ 94.8.
Standard deviation (σ) = sqrt(npq) = sqrt(200 * 0.474 * 0.526) ≈ 7.4.
6) Find probability of losing money:
We need wins < 100, which translates to losses ≥ 100.
Convert losses to z-scores:
z = (x - μ) / σ = (100 - 94.8) / 7.4 ≈ 0.71.
Look up probability of z ≥ 0.71 in standard normal distribution table:
P(z ≥ 0.71) ≈ 0.2389.
7) Generalization:
For any number of spins (n) and break-even win threshold (k), the steps are similar. Use the binomial distribution or its normal approximation to calculate the probability of winning k or fewer times.
Find x- and y-intercepts. Write ordered pairs representing the points where the line crosses the axes 3x+6y−12=0
Write an equation that represents "the difference between a number and eight is twenty-two". 8 - N = 22 N - 8 = 22 8 - 22N = 22
Answer:
N - 8 = 22
Step-by-step explanation:
If the center of a circle is (1, 1), and it has a radius of 5, which is another point on the circle?
Answer:
Step-by-step explanation:
The equation of this circle is:
(x - 1)² + (y - 1)² = 5²
Just supposing we choose x = 2. What's the corresponding y-value?
Actually, there are two unique y-values for each x value.
Let x = 2 in (x - 1)² + (y - 1)² = 5². Then:
(2 - 1)² + (y - 1)² = 5², or
1² + (y - 1)² = 25
Solving for (y - 1)², we get (y - 1)² = 25 - 4, or 24.
Taking the square root of both sides:
y - 1 = ±√24, so that y = 1 ±√24,
This simplifies to y = 1 ± 2√6.
Therefore, if x = 2, y has two values:
(2, 1+2√6) and
(2, 1-2√6
Becca and alice are training for a race. becca runs 3 3/4 miles in 1/2 of an hour, and alice runs 5 1/4 miles in 3/4 of an hour. who runs faster and by how many miles per hour? justify your answer.200 words left
Given that
∠A≅∠B, Gavin conjectured that ∠A and ∠B are complementary angles.
Which statement is a counterexample to Gavin 's conjecture?
m∠A=45° and m∠B=45°
m∠A=25° and m∠B=25°
m∠A=10°and m∠B=15°
m∠A=30°and m∠B=60°
Answer: It's B
B) m∠A=25° and m∠B=25°
The width of a rectangle is 9 units less than it length L. Write an expression that shows how wide the rectangle is in terms of L.
John is calculating 6% tax on an item in a store. he means to multiply the price of the item by 0.06, but he accidentally divides by 0.06. his answer is
Answer:
His answer will have a very large value.
Step-by-step explanation:
Lets take an example:
Let the item price be = $50
John is calculating 6% tax on an item. This becomes:
[tex]0.06\times50=3[/tex] dollars
But he accidentally divides by 0.06. This becomes: [tex]\frac{50}{0.06}= 833.33[/tex] dollars
We can see that the answer is completely wrong and the value is very large.
Ammon and nakia volunteer at an animal shelter. nakia worked 3 more hours than ammon. they each worked a whole number of hours. together they worked more than 27 hours. what is the least number of hours each worked
Final answer:
The least number of hours Ammon could have worked is 13 hours, and Nakia worked 16 hours since Nakia worked 3 hours more than Ammon, and together they worked more than 27 hours.
Explanation:
Let's denote the number of hours that Ammon worked as A and the number of hours that Nakia worked as N. According to the question, Nakia worked 3 more hours than Ammon, which can be written as N = A + 3. It's also given that together they worked more than 27 hours, so we can write this as A + N > 27. Substituting the first equation into the second, we get A + (A + 3) > 27, which simplifies to 2A + 3 > 27. By subtracting 3 from both sides, we get 2A > 24. Dividing by 2 gives us A > 12. Since A must be a whole number, the smallest whole number greater than 12 is 13.
Now that we know A is at least 13, we can find the minimum number of hours Nakia worked, which is A + 3. That gives us N = 13 + 3 = 16. Therefore, the least number of hours Ammon worked is 13 hours and Nakia worked 16 hours.
PLZ HELP!!!! WILL GIVE BRAINLIEST ANSWER!!!
△E′F′G′ is the image of △EFG under a dilation through point C.
What scale factor was used in the dilation?
the correct answer is - 1/2
Answer: The value of the scale factor is [tex]-\frac{1}{2}[/tex].
Explanation:
It is given that the △E′F′G′ is the image of △EFG under a dilation through point C.
We know that the length of sides of image are in the proportion of length of sides of preimage. That proportion factor is also known as scale factor.
It is given that the length of FG is 8 cm and the length of F'G' is 4 cm.
[tex]k=\frac{F'G'}{FG} =\frac{4}{8} =\frac{1}{2}[/tex]
Therefore the side of image and preimage are in proportion of [tex]\frac{1}{2}[/tex].
Since the image and preimage are not on the same side of the center of dilation it means the factor must be negative. So,
[tex]k=-\frac{1}{2}[/tex].
Therefore, [tex]-\frac{1}{2}[/tex] is the scale factor of dilation.
What is another name for this ?
Find the derivative of 4/square root of x
Answer:
[tex]\displaystyle \frac{dy}{dx} = \frac{-2}{x^\Big{\frac{3}{2}}}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \frac{4}{\sqrt{x}}[/tex]
Step 2: Differentiate
Derivative Property [Multiplied Constant]: [tex]\displaystyle y' = 4 \frac{d}{dx} \bigg[ \frac{1}{\sqrt{x}} \bigg][/tex]Basic Power Rule: [tex]\displaystyle y' = 4 \Bigg( \frac{1}{x^\Big{\frac{3}{2}}} \Bigg)[/tex]Simplify: [tex]\displaystyle y' = \frac{4}{x^\Big{\frac{3}{2}}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
The slope m, of a linear equation can be found using the formula m= y2-y1/x2-x1, where the x-and y-values come from 2 ordered pairs, and (x1, y1) and (x2, y2).
One machine can make 138,800 small paper clips in one day.Another machine can make 84,250 large paper clips in one day.How many more small paper clips than large paper clips are made by two machines in one day
What is the number in standard form?
Drag the answer into the box to match the number.
5.708×10−8
A standard form or a scientific notation is known as the value of any number that can be expressed or written as a decimal, usually within the range of 1.0 - 10.0 multiplied by the power of 10.
It is an effective technique of expressing large numbers in a simpler form.
From the information given, we are not provided with any decimal number to be converted into a standard form but we have a number in its standard form already.
i.e.
5.708 × 10⁻⁸
The standard number from above can be converted back into its decimal form, which is:
= 0.00000005708
From the above explanation, we can conclude that we've understood how to approach and solve questions related to the Standard form.
Learn more about standard form here;
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)a class has 15 boys and 16 girls. what is the probability that a boy's name is drawn at random? 15 over 31 16 over 31 15 over 16 16 over 15
Answer: A. 15 over 31
I took a the test and got it right, thank you!
A spherical balloon is inflated so that its volume is increasing at the rate of 3.1 {\rm ft}^3{\rm /min}. how rapidly is the diameter of the balloon increasing when the diameter is 1.6 feet?
Chico is financing a car for $9,550 and an APR 8.9 percent for 3 years. What is his monthly payment if the monthly payment per $100 is $3.52?
A. $336.16
B. $352
C. $251.48
D. $235.24
(I divided 9550 by 100 and then multiplied that by 3.52 and got A but I don't know if that's the right way to do it)
Answer:
A. $336.16
Step-by-step explanation:
The payment per $100 can be set up as a ratio:
[tex]\frac{3.52}{100}[/tex]
Let the unknown payment be x. Now setting up the ratio over the full value:
[tex]\frac{x}{9550}[/tex]
Set them equal and solve for x:
[tex]\frac{3.52}{100}=\frac{x}{9550}[/tex]
1[tex]100x=33616[/tex]
This gives x = $336.16
Therefore, the answer is option A.
Marcus has $5.45. He pays $1.25 for a bus ticket. He will buy some snacks before getting on the bus. Each snack will cost $0.75.
a) Write an equation that can be used to find the maximum number of snacks (x) that Marcus can buy.
b) What is the maximum number of snacks Marcus can buy?
( I've already done it but I don't think I'm right, I just want to be sure. )
Anyone knows the answer
Rashawn read 25 pages of his book each day until he finished the book. His book was 400 pages long.
Which sketch represents this situation?
Zoe is taking the measurements of her lawn. her lawn is 64.15 feet long and 22.70 meters wide. one foot is equivalent to 0.3048 meters. which dimension of zoe's lawn is longer, and how many yards longer is it?
Answer:
width of the lawn is greater than the length of the lawn.Step-by-step explanation:
The length of her lawn=64.15 feet.
Width of her lawn=22.70 meters.
we are given that:
1 foot=0.3048 meters.
Hence,
64.15 feet=21.86232 meters.
Hence, length of lawn=21.86232 meters.
Hence, width of the lawn is greater than the length of the lawn.
( since 22.70 meters> 21.862332 meters)
Also 1 meter=1.0936 yards.
so, width of lawn in yards is:
22.70×1.0936=24.82472 yards.
length of lawn is: 23.9086462752 yards.
Hence, width of lawn is 0.9160737 yards more than the length of lawn.
what are the properties of an obtuse triangle
An obtuse triangle will have one and only one obtuse angle.
The other two angles are acute angles.
The sum of the two angles other than the obtuse angle is less than 90º.
The side opposite to the obtuse angle is the longest side of the triangle.
The points of concurrency, the Circumcenter and the Orthocenter lie outside of an obtuse triangle, while Centroid and Incenter lie inside the triangle.
How to solve negative exponents with a negative base?
What is the perimeter of the triangle shown on the coordinate plane, to the nearest tenth of a unit?
a.14.6
b.15.5
c.21.0
d.21.6
In a garden the heights of six sunflowers are 135.0 cm, 162.5 cm, 180.0 cm, 235.0 cm, 185.0 cm, and 167.5 cm. What is the average height of the sunflowers?
135 + 162.5 + 180 + 235 + 185 + 167.5 = 1065
1065/6 = 177.5
average height is 177.5 cm
Answer:
Average height of sunflowers is:
177.5 cm
Step-by-step explanation:
Average is calculated as sum of all observations divided by number of observations
The heights of six sunflowers are 135.0 cm, 162.5 cm, 180.0 cm, 235.0 cm, 185.0 cm, and 167.5 cm.
Average= [tex]\dfrac{135+162.5+180+235+185+167.5}{6}[/tex]
Average= [tex]\dfrac{1065}{6}[/tex]
Average= 177.5
Hence, Average height of sunflowers is:
177.5 cm