To determine the number of edges in a polyhedron with seven faces, two being pentagons and five being rectangles, you apply Euler's formula, resulting in a total of 15 edges.
To find the number of edges in a polyhedron with seven faces using Euler's formula, which is V - E + F = 2, we first need to determine the number of vertices (V) and faces (F) of the polyhedron.
Given that the polyhedron has two pentagons and five rectangles, we can calculate the total number of vertices. Each pentagon has 5 vertices and each rectangle has 4, but since rectangles share sides, some vertices will be counted twice.
Therefore, for the rectangles, we should calculate the vertices as if there were four distinct ones and then subtract the overlaps. Assuming all rectangles share exactly one side with its adjacent, we would have 4 vertices for each rectangle minus 2 for each shared side, resulting in 2 vertices per rectangle.
With five rectangles, that's 10 vertices, plus the 10 from the two pentagons, we get 20 vertices in total. Now, we apply Euler's formula: V - E + F = 2, substituting the values:
E = V - F + 2
E = 20 - 7 + 2
E = 15
Therefore, the polyhedron has 15 edges. .
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What is the equation of a circle with its center at(10,−4) and a radius of 4?
(x−10)2+(y+4)2=4
(x+10)2+(y−4)2=16
(x−10)2+(y+4)2=16
(x+10)2+(y−4)2=2
(x−10)2+(y+4)2=2
(x−10)2+(y+4)2=8
(x+10)2+(y−4)2=8
(x+10)2+(y−4)2=4
In this triangle, side AT = 24. Please give the value for the sine, cosine, and tangent for this diagram (Which is the marked angle?). Give the value as a ratio ONLY. Make sure all ratios are in the lowest form.
Be sure to explain IN WRITING how you find sine, cosine, and tangent! If you are not sure, check the directions in this problem!
Question 1 options:
Find the surface area of the cylinder in terms of π.
See picture
a) 1008π in.2
b) 522π in.2
c) 360π in.2
d) 396π in.2
A feed bucket holds 12 quarts. How many cups of feed does the bucket hold?
what is the surface area of this triangular pyramid
Equilateral Triangle Height = side * square root (3) / 2 =
12 * 0.8660254038 = 10.3923048454
Triangle Area = 12 * 10.3923048454 * .5
WILL GIVE BRAINLIEST PLZ HURRY!!!!!!!!Woodland High School recently won the state Academic Bowl Championship. The medal counts for the 7 members of the team are listed in the table. Which statement is true about the data shown in the table?
A) The range is less than the mode.
B) The mode is greater than the median.
C) The mean is greater than the median.
D) The median is greater than the mode.
Answer: B = The range is greater than the mean.
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
The mean is greater than the median
Solve each of the following right triangles. Round angle measures to the nearest degree and segment lengths to the nearest tenth. Angle C is the right angle of the triangle
Which of the following is an undefined term?
Angle
Circle
Plane
Ray
Answer:
Plane is an undefined plane
Step-by-step explanation:
Hi, there are three undefined terms in geometry: point, line, and plane.
Point: has no size, only location . It can be named with a capital letter.
Plane: a flat surface that has no thickness, that extends infinitely n every direction. Is named by a single letter or by three coplanar, but non-collinear, points.
Line: Set of points extending in either direction infinitely.
Angle, circle, and ray are not undefined terms. are not Plane.
A license plate has 3 letters and 3 digits in that order. a witness to a hit-and-run accident saw the first 2 letters and the last digit. if the letters and digits can be repeated, how many license plates must be checked by the police to find the culprit?
The police must check 2600 possible license plates, calculated by multiplying 26 possibilities for the third letter not seen by the witness with 100 possibilities for the two digits also not seen.
To determine how many license plates the police must check to find the culprit, we consider the information that the witness saw the first two letters and the last digit. Since letters can be repeated, there are 26 possibilities for each of the two letters the witness saw. For the last digit, which the witness also saw, there are 10 possibilities (0 through 9). The third letter and the other two digits, which the witness did not see, each have the following number of possibilities: 26 for the third letter, and 10 for each of the two remaining digits.
Calculating the number of possible combinations:
First two letters (seen by the witness): 26 * 26 = 676 possibilitiesLast digit (seen by the witness): 10 possibilitiesThird letter (not seen by the witness): 26 possibilitiesThe two remaining digits (not seen by the witness): 10 * 10 = 100 possibilitiesTherefore, the total number of license plates the police must check is the product of the possibilities for the parts the witness did not see:
26 (third letter) * 100 (two remaining digits) = 2600 possible license plates.
Find the inverse function of h(x) = - 2/3x + 6.
h -1(x) = -3/2x + 9
h -1(x) = -3/2x - 6
h -1(x) = -2/3x + 9
h -1(x) = -2/3x - 6
What is 3 to the 100th power?
3 to the 100th power is a very large number with over 47 digits, symbolizing the potential of exponential growth.
Explanation:The question is asking for the computation of the number 3 raised to the 100th power. In mathematics, exponents are used in expressions such as 'a to the power of n', written as an. Here, 'a' is the base and 'n' is the exponent, indicating how many times 'a' is multiplied by itself.
In our case, we have '3' as the base and '100' as the exponent. However, calculating 3100 directly is quite impractical due to the vast result it produces. However, we do know that it's a very large (over 47 digits!) number which could be useful for illustrating the power of exponential growth in mathematical or scientific contexts.
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Helllllppppp MEEEEEEE
To find the distance the player runs, we have to use pythagorean formula, which is
[tex] a^2 + b^2 = c^2 [/tex]
In the question , value of a is 64 meters and value of b is 100 meters .
Substituting the values of a and b , we will get'
[tex] 64^2 +100^2=c^2
\\
c^2 = 14096
\\
c = 119meters [/tex]
Factor the trinomial below.
9x2 + 6x + 1
A. (3x + 1)(3x – 1)
B. (9x + 1)(x – 1)
C. (9x + 1)(x + 1)
D. (3x + 1)(3x + 1)
Answer: D. (3x + 1)(3x+1)
Step-by-step explanation:
9x² + 6x + 1
find two factor of 9 such that its product gives 9 and its sum gives 6 (3 and 3, 3×3 = 9 , also 3+ 3=6)
we are going to replace 6x by 3x + 3x
9x² + 6x + 1
9x² + 3x +3x + 1
3x(3x + 1) + 1(3x+ 1)
(3x + 1)(3x+1)
The correct factorization of the trinomial 9x² + 6x + 1 is (3x + 1)(3x + 1) or (3x + 1)². option D.
How do we identify the correct option when the trinomial is factorized?The trinomial 9x² + 6x + 1 is a perfect square trinomial, which can be factored as the square of a binomial.
Let's find the correct answer from your options:
(A) (3x + 1)(3x - 1): The difference of squares isn't the correct form for our trinomial.
(B) (9x + 1)(x - 1): Expanding this will not give us the original trinomial.
(C) (9x + 1)(x + 1): Expanding this will not give us the original trinomial.
(D) (3x + 1)(3x + 1): When expanded, this gives us 9x^2 + 3x + 3x + 1, which simplifies to 9x² + 6x + 1.
Therefore option D (3x + 1)(3x + 1) is correct
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A rectangle has a length of 4 feet and a perimeter of 14 feet. what is the perimeter of a similar rectangle with a width of 9 feet?
a. 36 ft
b. 108 ft
c. 42 ft
d. 126 ft
The frequency of F3 is 174.61 Hz. What is the frequency of the note that is a perfect fifth below f3?
A) 43.6525 Hz
B) 87.305 Hz
C) 116.407 Hz
D) 261.915 Hz
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The population of a town is 20,000 and is decreasing at a rate of 5% per year. What is the population after 23 years?
There are five red marbles eight blue marbles and 12 Green marbles in a bag. What is the theoretical probability of randomly drawing a red marble and then a green marble
What is the value of b?
If 7 is subtracted from the product of 3 and a number, the result is 5 more than the number.
Please help me I’m about to cry
Use complete sentences to explain how the coordinate plane is a useful tool for geometric proofs.
The coordinate plane is an essential tool in geometry, allowing for a visual representation of shapes and aiding in geometric proofs, such as the Pythagorean Theorem. It allows abstract geometric concepts to be more concrete and easier to understand.
Explanation:The coordinate plane is a pivotal instrument in the field of Mathematics for conducting geometric proofs. The coordinate plane enables us to visually represent geometric shapes and articulate the different points, distances, and areas which helps us in proving geometric theorems and statements.
For instance, the Pythagorean Theorem, a fundamental theorem in Geometry can be illustrated efficiently and proven right on the coordinate plane. By placing a right-angled triangle on the coordinate plane, the lengths of the sides can be calculated using the coordinates of the vertices. Then, by applying the theorem, we can demonstrate that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Overall, the coordinate plane provides a graphical representation of the geometric shapes, making the abstract ideas more concrete and easier to understand, thus aiding in geometric proofs.
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Which of the following types of equations have you learned to solve using algebraic methods?
[]Quadratic[]Exponential[]Radical[]Linear[]Rational
The following types of equations have you learned to solve using algebraic methods is Linear.
Quadratic equations involve a variable raised to the power of 2, and algebraic methods like factoring or using the quadratic formula are used for solving.
Exponential equations involve variables in the exponent, and logarithmic methods are employed to solve them.
Radical equations involve roots, and solving them often involves isolating the radical and squaring both sides or other methods based on the root's degree.
Linear equations involve variables raised to the power of 1, and solving them uses standard algebraic techniques like isolating the variable.
Rational equations involve ratios of polynomials and are solved by methods such as clearing denominators and factoring.
which transformation can verify congruence by flipping a triangle over the y-axis?
A. Dilation
B. Translation
C. Reflection
D. Rotation
Answer: C. Reflection
Step-by-step explanation:
There are three rigid transformations which create congruent figures :
a)reflections, b) rotations, c) translations
A reflection is a transformation that flips a figure on the coordinate plane across a given line without changing the shape or size of the figure.
A translation moves a shapes by a particular distance.
A rotation rotates a shape around a fix point by an angle .
Therefore, the transformation can verify congruence by flipping a triangle over the y-axis is reflection.
Four golf balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 4cm.
What is the volume of the cylinder rounded to the nearest cubic centimeter?
What is the total volume of the four balls rounded to the nearest cubic centimeter?
What percent of the volume of the container is occupied by the four balls?
Circle J has center J (4,-3) and radius 5 What is the measure, in degrees, of the arc with endpoints A (9,-3) and B (4,2)?
Explain the process you used (in words) and include the work you did to find this answer.
Twenty different statistics students are randomly selected. for each of them, their body temperature ( degrees °c) is measured and their head circumference (cm) is measured. if it is found that r=0, does that indicate that there is no association between these two variables?
The letter r represents the sample correlation coefficient .The Pearson product-moment correlation coefficient, also known as r, R, or Pearson's r, is a measure of the strength and direction of the linear relationship between two variables that is defined as the covariance of the variables divided by the product of their standard deviations.
The sample correlation coefficient value r is 0 given,so there is no linear relationship between the 2 variables that is the body temperature and head circumference.
A train travels at a constant speed. What is the train's speed between checkpoints, expressed as a unit rate? Use the information given in the picture to help you.
Please help me, if you'd be so kind.
A right rectangular prism is shown.
What is the length of DH¯¯¯¯¯¯ to the nearest tenth of an inch?
Drag and drop the answer into the box.