In a regular pentagon with equal sides and angles, the sum of the inside angles is 540 degrees. The third polygon P has 6 sides.
What is the Pentagon?In a regular pentagon with equal sides and angles, the sum of the inside angles is 540 degrees, and each angle is 108 degrees. Some actual items, including stars, soccer balls, and even street signs, contain pentagons.
Since P has a vertex at B, we can assume that its other sides emanate from B. Let's call the length of one of these sides x. Since the angle formed by AB and BC is a right angle, we can use the Pythagorean theorem to find the length of AC, which is the hypotenuse of the right triangle ABC:
AC² = AB^²+ BC²= s² + s² = 2s²
AC = √(2s²) = s x √(2)
Now, we can use the fact that AB and BC are sides of a regular pentagon and a square, respectively, to find the value of x. Since a regular pentagon has five sides of equal length, we know that AB is also a side of the Pentagon. Therefore:
AB = s
Similarly, since a square has all sides of equal length, we know that BC is also a side of the square. Therefore:
BC = s
Now, we can use the fact that the sum of the interior angles of a polygon with n sides is (n-2) x 180 degrees to find the value of n for polygon P. Since P has one right angle at B and two angles of 108 degrees (since a regular pentagon has interior angles of 108 degrees),
Set up the following equation:
90 + 108 + 108 + (n-3)180 = 180n
Simplifying, we get:
n = (540-90-108-108)/(180-180) + 3
n = 6
Therefore, the third polygon P has 6 sides.
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The average number of vehicles waiting in line to enter a sports arena parking lot is modeled by the function w(x)=x^2/2(1-x), where x is a number between 0 and 1 known as the traffic intensity. Find the average number of vehicles waiting if the traffic intensity is 0.92. ...?
To find the average number of vehicles waiting at a traffic intensity of 0.92, we substitute 0.92 into the function w(x) = x² / (2(1-x)) to arrive at the answer 5.29.
Explanation:The average number of vehicles waiting in line is modeled by the function w(x) = x^2 / (2(1-x)) where x represents traffic intensity. The question is asking us to calculate the average number of vehicles waiting when the traffic intensity is 0.92. By plugging this value into the function, we get w(0.92) = 0.92^2 / (2(1-0.92)), which simplifies to w(0.92) = 0.8464 / 0.16. The result is 5.29, so the average number of vehicles waiting would be 5.29 when the traffic intensity is 0.92. To find the average number of vehicles waiting when the traffic intensity is 0.92, we substitute the value of x into the given function w(x)=x^2/2(1-x). In this case, x=0.92. So, the average number of vehicles waiting can be found by evaluating w(0.92).
w(0.92) = (0.92)^2 / 2(1 - 0.92)
w(0.92) = 0.8464 / (2 * 0.08)
w(0.92) = 10.58
Therefore, when the traffic intensity is 0.92, the average number of vehicles waiting is approximately 10.58.
When the following expression is written in simplest form, what is the coefficient of the variable term?
-2.5y + 8y - 10.5y
Round to the nearest tenth 848.607
In a game of blackjack, a 2-card hand consisting of an ace and a face card or a 10 is called a blackjack. (Round your answers to four decimal places.)
(a) If a player is dealt 2 cards from a standard deck of 52 well-shuffled cards, what is the probability that the player will receive a blackjack?
(b) If a player is dealt 2 cards from 2 well shuffled standard decks, what is the probability that the player will receive a blackjack?
To calculate the probability of getting a blackjack from a single well-shuffled deck, you must consider the probability of drawing an Ace and then a 10-value card or vice versa, and add those probabilities together. The same process applies to two decks with adjusted numbers. You will then round the final probabilities to four decimal places.
Explanation:To answer the question of the probability of getting a blackjack in a single deck, consider that there are 4 aces in a deck and 16 cards that are either a face card or a 10 (each suit has 4 such cards - Jacks, Queens, Kings, and 10s). When one card is drawn, the remaining cards are one fewer, so we need to adjust our probability for the second card.
Calculate the probability of drawing an Ace first and then a card with a value of ten: P(Ace first, then 10) = (4/52) × (16/51).Calculate the probability of drawing a 10-value card first and then an Ace: P(10 first, then Ace) = (16/52) × (4/51).Add the two probabilities together for the final answer.For the probability of a blackjack from two decks, follow the same steps, but adjust the numbers for a 104-card deck.
P(Ace first, then 10) = (8/104) × (32/103).P(10 first, then Ace) = (32/104) × (8/103).Add the two probabilities together for the final answer.After doing the calculations, we round the probabilities to four decimal places as instructed.
Naomi draws a portion of a figure as shown. She wants to construct a line segment through R that makes the same angle with line segment QR as line segment PQ.
Answer:
In FLVS it is the third option
Step-by-step explanation:
Hope this helps :)
the sum of two numbers is s.if one of the numbers is n,the second number can be expressed as
1. s+n
2. s÷n
3. s-n
4. n-s
Given that two numbers sum to 's', and one of the numbers is 'n', the other number can be expressed as 's - n'. In essence, if you subtract 'n' from the sum 's', you obtain the second number.
Explanation:The student's question relates to expressing one number in terms of another when their sum is given. Given that the sum of the two numbers is s and one of the numbers is n, the second number can be expressed as s - n. This is because when two numbers add to give 's', subtracting one of the numbers (n, in this case) from 's' would give the other number.
For instance, if s = 10 and n = 3, then the second number would be 10 - 3 = 7. Hence, the correct answer from the options provided would be 3. s - n.
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PLEASE HELP PLEASE PLEASE
4 is equivalent to how hundreths
What is closer to 1/3 0.3 0.33 or 0.333
What is 0.853 to the nearest tenth?
The hypotenuse of a 45°-45°-90° triangle measures 128 cm.What is the length of one leg of the triangle?
Answer:
Since, a 45°-45°-90° triangle is a special type of isosceles right triangle, where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.
In 45°−45°−90° triangle
Sides are in the proportion [tex]1:1:\sqrt{2}[/tex]
then,
the measures of the sides are [tex]x , x ,\sqrt{2}x[/tex]
The length of hypotenuse= [tex]\sqrt{2}[/tex] times the length of the leg. ....[1]
Given: length of hypotenuse = 128 cm.
then,
from [1] we have;
128 = [tex]\sqrt{2}\cdot x[/tex]
or
[tex]x=\frac{128}{\sqrt{2}}[/tex] = [tex]\frac{128}{\sqrt{2} } \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{128\sqrt{2}}{\sqrt{2}\cdot \sqrt{2}}[/tex]
Simplify:
[tex]x =\frac{128 \cdot \sqrt{2}}{2} =64\sqrt{2}[/tex] cm.
Therefore, the length of one leg of the triangle is; [tex]64\sqrt{2}[/tex] cm.
If B=A, where on the number line will B appear?
A.to the right of A
B.in exactly the same location as A
C.to the left of A
the perimeter of a rectangle is twice the sum of its length and width. The perimeter is 34 meters and its length is 2 meters more than twice its width. What is its length? ...?
how to factor x3-x2-4x-4
Three-fourths of a number increased by one-fifth is no less than seven-eighths.
Which equation represents this problem?
Answer:
yea, most likely it´s 3/4 y + 1/5 ≥ 7/8
Step-by-step explanation:
Find the value of the coefficient of
1/x
in the expansion of (2x −
1/x )^5
. ...?
Final answer:
To find the coefficient of 1/x in the expansion of (2x - 1/x)^5, we use the binomial theorem, specifically the term where the exponent of x is -1. We find that the coefficient of 1/x is -80.
Explanation:
To find the coefficient of 1/x in the expansion of (2x - 1/x)^5, we can use the binomial theorem. The binomial theorem states that:
(a + b)^n = Σ (n choose k) a^(n-k) b^k
where 'n choose k' is the binomial coefficient, computed as:
n! / [(n-k)!k!]
In our case, a = 2x and b = -1/x, and we want the term where the power of x is -1, which occurs when k = 4:
(5 choose 4) (2x)^(5-4) (-1/x)^4 = 5 * 2 * 1 * 1/x^4 = 10/x^4
However, to get the term with 1/x, we need a positive power of 1 for x. We achieve this when k = 1:
(5 choose 1) (2x)^(5-1) (-1/x)^1 = 5 * 16x^4 * (-1/x) = -80
Therefore, the coefficient of 1/x in the expansion is -80.
State the postulate or theorem that proves that x||y.
A.converse of the consecutive interior angles theorem
B.converse of the alternate interior angles theorem
C.converse of the corresponding angles postulate
D.converse of the alternate exterior angles theorem
The theorem that proves x is parallel to y is the Converse of the Alternate Interior Angles Theorem, which states that if alternate interior angles are congruent, the lines are parallel. The correct answer to the question of which postulate or theorem proves that x is parallel to y is B. Converse of the Alternate Interior Angles Theorem.
Explanation:According to this theorem, if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel. The other options, such as the converse of the corresponding angles postulate or the converse of the consecutive interior angles theorem, are related but specifically address different sets of angles formed when two lines are cut by a transversal.
In geometry, it is crucial to apply the correct postulates or theorems to prove specific properties, like parallel lines. The reliability of these mathematical proofs, like those in trigonometry or physics, comes from the logical sequence of applying these fundamental principles accurately.
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(04.02 LC)
Triangle ABC is similar to triangle PQR, as shown below:
Two similar triangles ABC and PQR are shown. Triangle ABC has sides AB = c, BC = a, and AC = b. Triangle PQR has sides PQ = r,
Which ratio is equal to b:q? (1 point)
b:a
c:r
r:a
q:c
Answer:
The correct option is 2.
Step-by-step explanation:
It is given that triangle ABC is similar to triangle PQR.
In triangle ABC, AB=c, BC=a, and AC=b.
In triangle PQR, PQ=r, QR=p, PR=q.
The corresponding sides of similar triangles are proportional.
Since [tex]\triangle ABC\sim \triangle PQR[/tex], therefore their corresponding sides are proportional.
[tex]\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}[/tex]
[tex]\frac{c}{r}=\frac{a}{p}=\frac{b}{q}[/tex]
It meas the ratio c:r = a:p = b:q.
Therefore the correct option is 2.
the cost of a pencil is 25 cents more than the cost of an eraser. if the cost of 8 pencils and 10 erasers is 12.80 dollars, find the cost of each
Write the following in terms of sin(θ) and cos(θ); then simplify if possible.
cos(θ) + sin(θ)cot(θ) = ...?
The population of foxville is about 12 times 10 to the power of 3. which is another way to write this number
Answer:
The population of foxville is 12000.
Step-by-step explanation:
It is given that the population of foxville is about 12 times 10 to the power of 3.
Population of foxville = [tex]12\times 10^3[/tex]
[tex]12\times 10^3[/tex] is a scientific notation of a number.
We need to write this number in another way.
[tex]12\times 10^3=12\times 1000[/tex]
[tex]12\times 10^3=12000[/tex]
Therefore, the population of foxville is 12000.
What is 598% divided by 26%
At the halftime show, a marching band marched in formation. The lead drummer started at a point with coordinates (–2, –5) and moved 3 steps up and 1 step right.
a. Write a rule to describe the translation.
b. What were the coordinates of the drummer's final position? (3 points)
Answer:
a) The answer is: (x + a, y + b)
b) The answer is: (-1, -2)
The initial coordinates are:
(x, y) = (-2, -5)
should be the answer.
Let's find a and b.
a is a distance in x direction: a = 1
b is a distance in y direction: b = 3
The final position is:
(x + a, y + b) = (-2 + 1, -5 + 3) = (-1, -2)
Step-by-step explanation:
What is the answer to the riddle 20 30 x 0 1 the real answer..?
PEMDAS- [Parenthese, Exponents, Multiplication, Division, Addition, Subtraction.]
Since there is no Parentheses, nor Exponents, you have to go straight to multiplication. Then to addition
30+30×0+1
30×0=0
30+0+1=31.
I hope my answer has come to your help. God bless and have a nice day ahead!
The ratio of two numbers is 1 to 4, and the sum of the numbers is 45. What is the smaller number?
10
9
8
7
9 i think
what are the x and y intecepts of the graph of the equation 6x - 5y=3
Expressions cannot _____.
be evaluated
be solved
be simplified
have variables
Answer:
B. be solved
Step-by-step explanation:
the exterior angles of a triangle have measures of (x+10) degrees, (2x+20) and 3x degrees. what is the measure of the smallest interior angle of the triangle ...?
Answer: X= 55
Step-by-step explanation:
The sum of exterior angles of any polygon will always equal to 360 degrees. which means, we can write:
360 = (x+10) + (2x+20) + 3x
x = 55
The exterior angles have values of 65, 130 and 165. The exterior that will have the largest value will correspond to the smallest interior angle and therefore have a value of 15 degree!. ;)
Final answer:
By calculating the value of x and using the relationship that each exterior angle and its corresponding interior angle are supplementary, we find that the measure of the smallest interior angle of the triangle is 115 degrees.
Explanation:
To find the measure of the smallest interior angle of the triangle, we first need to use the fact that the sum of the exterior angles of a triangle is always 360 degrees. So, we set up the equation (x+10) + (2x+20) + 3x = 360 and solve for x. This gives us:
x + 10
2x + 20
3x
Combining like terms, we get 6x + 30 = 360. Subtracting 30 from both sides, we get 6x = 330. Dividing both sides by 6, we find that x = 55 degrees. Therefore, the exterior angles are 65 degrees, 130 degrees, and 165 degrees. To find the smallest interior angle, we take the smallest exterior angle, 65 degrees and subtract it from 180 degrees (since the exterior angle and interior angle at the same vertex are supplementary). Thus, the smallest interior angle is 180 degrees - 65 degrees = 115 degrees.
The average income, I, in dollars, of a lawyer with an age of x years is modeled with the following function:
What is the youngest age for which the average income of a lawyer is $450,000?
Round to the nearest year.
To find the youngest age for a lawyer to have an average income of $450,000, you solve the income function equation and round to the nearest year.
Explanation:The youngest age for which the average income of a lawyer is $450,000 can be found by solving the given function:
I(x) = 10000 + 2000x
Given I(x) = $450,000, the equation becomes:
450,000 = 10000 + 2000x2000x = 440,000x = 220Rounded to the nearest year, the youngest age would be 220 years old.
I need help on the back side