The polygons above are similar. Write a similarity statement and solve for x. The images are not drawn to scale.
Which of these four sets of side lengths will form a right triangle?
Set 1
4 cm, 5 cm, 6 cm
Set 2
8 in., 12 in., 20 in.
Set 3
10 mm, 20 mm, 30 mm
Set 4
12 ft, 16 ft, 20 ft
Set of sides that will make right triangle is
Set 4 : 12 ft, 16 ft, 20 ft
What is Pythagoras theorem?Pythagoras theorem states that in a right angled triangle square of the hypotenuse is equal to the sum of the square of perpendicular and square of base. The longest side is the hypotenuse.
Given measurements
Set 1:
4cm , 5cm , 6cm
By Pythagoras theorem
4² + 5² = 6²
16 + 25 = 36
41 ≠ 36
Pythagoras theorem is not satisfied,
this set of sides will not make right triangle
Set 2
8 in., 12 in., 20 in.
By Pythagoras theorem
8² + 12² = 20²
64 + 144 = 400
208 ≠ 400
Pythagoras theorem is not satisfied,
this set of sides will not make right triangle
Set 3
10 mm, 20 mm, 30 mm
By Pythagoras theorem
10² + 20² = 30²
100 + 400 = 900
500 ≠ 900
Pythagoras theorem is not satisfied
this set of sides will not make right triangle
Set 4
12 ft, 16 ft, 20 ft
By Pythagoras theorem
12² + 16² = 20²
144 + 256 = 400
400 = 400
Pythagoras theorem is satisfied
this set of sides will make right triangle.
Hence, Set 4 of sides 12 ft, 16 ft, 20 ft will form a right triangle.
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A rectangular mat has a length of 12 in. and a width of 4 in. Drawn on the mat are three circles. Each circle has a radius of 2 in. Some friends play a game throwing darts onto the mat to see who can land a dart in one of the circles.
Assuming that a dart always lands on the mat, what is the probability that a dart thrown at random will land inside one of the circles?
Use 3.14 to estimate Pi.
Enter your answer, as a decimal rounded to the nearest hundredth, in the box.
P(landing in a circle) =
[tex] |\Omega|=4\cdot12=48\\
|A|=3\cdot3.14\cdot2^2=37.68\\\\
P(A)=\dfrac{37.68}{48}\approx0.79 [/tex]
Answer: 77.9
Step-by-step explanation: .
A jar contains 5 blue marbles, 7 yellow marbles, and 8 green marbles. What is the probability of randomly choosing a blue marble, not replacing it, and then choosing a green marble?
The probability of randomly choosing a blue marble, not replacing it, and then choosing a green marble is,
⇒ 2 / 19
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Given that;
A jar contains 5 blue marbles, 7 yellow marbles, and 8 green marbles.
Hence, Number of marbles = 5 + 7 + 8 = 20
Thus, the probability of randomly choosing a blue marble is,
⇒ 5 / 20
⇒ 1 / 4
And, the probability of randomly choosing a green marble is,
⇒ 8 / 19
Thus, the probability of randomly choosing a blue marble, not replacing it, and then choosing a green marble is,
⇒ 1/4 × 8/19
⇒ 2 / 19
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what is the distance between 1st and 3rd base?
The distance between the first base and third base in the given problem is 127.28 feet.
Distance is a measure of how far apart two objects are. It's a scalar quantity, which means that it has magnitude but no direction. The distance between two points can be gauged in various ways, including using a ruler, a tape measure, or a laser rangefinder. The primary difference between the distance and the displacement is that the latter has the direction but not the former.
As evident from the figure,
the running track is a square.
So, all the sides are equal to each other in length.
So, the distance between the first base and the second base is equal to the distance between that of the second base and the third base which is equal to 90 feet.
Let us name the square ABCD.
Join vertex A and vertex D.
The triangle ABC is the right-angled isosceles triangle.
So, by Pythagorean Theorem,
[tex]\sqrt{AC^2}[/tex] = [tex]\sqrt{AB^2+BC^2}[/tex]
= [tex]\sqrt{90^2 + 90^2}[/tex]
= [tex]\sqrt{8100+8100}[/tex]
= [tex]\sqrt{16200}[/tex]
= 127.28 (approximately)
So, the first base and third base are 127.28 feet apart.
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help please someone this is really important
write
(6b)^2 without exponents
Help me with a Geometry problem! (10 points)
solve the inequality 1/2 y +6<0
I do not understand how to do this
a point locates at (-3 7) undergoes two transformations. its images is located at (3 -7). what were the transformations?
Mary collects dolls. She has 4 dolls more then her friend Penney. Mary says if she tripled the number of dolls she has, she would have 27 dolls. How many dolls does Penney have?
The coordinate of the vertices for square CDEF translated 3 units right and 4 units up if the vertices are C(-3,1), D(1,5), E(5,1), and F(1,-3) are. C’(0,5), D(4,6), E,(8,6) and F(4,-1). Is it true or false
Answer:
false
Step-by-step explanation:
fr ong
An equation is shown below: 9(3x-2)=1
Which of the following correctly shows the first two steps to solve this equation?
B the second one. It shows all the steps correctly
Which of the following shows that polynomials are closed under subtraction when polynomial x + 5 is subtracted from 3x2 + 2x − 6?
3x2 + x − 11 may or may not be a polynomial
3x2 + x − 11 will be a polynomial
3x2 + x − 1 will be a polynomial
3x2 + x − 1 may or may not be a polynomial
Given the function h(x) = 3(5)x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.
Part A: Find the average rate of change of each section. (4 points)
Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other. (6 points)
i really just need an answer for B mostly
Part A: The average rate of change of section A is 12 and that of B is 300.
Part B: The average rate of change of Section B is 25 times greater than that of Section A due to the exponential nature of the function h(x).
Explaining the average rate of change for two sections and comparing their values in an exponential function context,
Part A:One rate of change is greater than the other because of the exponential growth nature of the function. The function h(x) = 3 [tex](5)^x[/tex] is an exponential function, and the rate of change increases rapidly as x increases, leading to a much greater average rate of change for Section B than Section A.
The question is:
Given the function h(x) = 3 [tex](5)^x[/tex], Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.
Part A: Find the average rate of change of each section.
Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other.
If 2 inches = 25 miles how many inches are 60 miles
a dragonfly the fastest insect, can fly a distance of 50 feet at a speed of 25 feet per second. find the time in seconds. write the equation in form d=
Using the equation 't = d/v', where 'd' is distance and 'v' is velocity, the time 't' for a dragonfly to fly 50 feet at 25 feet per second is calculated to be 2 seconds.
To find the time it takes for a dragonfly to fly a distance of 50 feet at a speed of 25 feet per second, we can use the formula d = vt, where d is the distance, v is the velocity (speed), and t is the time. To solve for time (t), we rearrange the formula to t = d/v.
So, plugging in the values:
Distance (d) = 50 feetSpeed (v) = 25 feet/secondWe get:
t = d/v = 50 feet / 25 feet/second = 2 seconds
The dragonfly takes 2 seconds to fly 50 feet at a speed of 25 feet per second.
7.Mrs. Deaton’s 6th grade class is creating a mural for the school entryway. Each student is creating a square with a side length of 10 inches that will be joined together to form this mural. The mural itself will be in the shape of a square with five of the student’s squares along each side. What is the total area of the mural?
Final answer:
To determine the total area of the mural, we calculate the area of one student's square, which is 100 square inches, and multiply by the total number of squares in the mural, resulting in 2500 square inches for the total area.
Explanation:
Mrs. Deaton's 6th grade class is working on a mural where each student contributes a square with a side length of 10 inches. The mural will be arranged in a larger square with five student squares along each side. To determine the total area of the mural, we will calculate the area of one student's square and then multiply by the total number of squares.
First, the area of one student's square is found by squaring the side length:
Area of one square = side length × side length = 10 inches × 10 inches = 100 square inches.
Since the mural is a square consisting of 5 student squares on each side:
Total number of student squares = 5 × 5 = 25 squares.
Finally, to find the total area of the mural, we multiply the area of one square by the total number of squares:
Total area of mural = area of one square × total number of squares = 100 square inches × 25 = 2500 square inches.
The total area of the mural is 2500 square inches.
Find the perimeter of right triangle WXY if the radius of the circle is 4 units and WY = 20 units.
The perimeter of the right triangle WXY is 60 units.
Explanation:To find the perimeter of a right triangle WXY, we need to know the lengths of the two legs. Given that the radius of the circle is 4 units and WY is 20 units, we can determine that the hypotenuse, XY, is equal to 20 units. So the perimeter of the triangle is the sum of the lengths of its three sides: 20 + 20 + 20 = 60 units.
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We calculate the perimeter of the right triangle by first finding the lengths of the legs using the Pythagorean theorem and the given radius, then summing these lengths with the hypotenuse.
Explanation:The subject of this question is Geometry, specifically involving the calculation of the perimeter of a right triangle. In a right triangle, the lengths of the three sides follow the Pythagorean theorem, written as [tex]a^2 + b^2 = c^2[/tex], where c is the hypotenuse and a and b are the lengths of the other two sides.
Here, the length of the hypotenuse WY is given as 20 units. In a right-angled triangle, where a circle is inscribed, the radius of the circle is equal to half the sum of the two legs of the triangle (radius = (a+b)/2). In this case, the radius is given as 4 units. Thus, the total of the two legs a and b is 8 units.
The Pythagorean theorem can now be used to solve for a and b, knowing that [tex]a^2 + b^2 = 20^2[/tex] and a + b = 8; then to find the perimeter, sum the hypotenuse and the lengths of the legs, i.e. Perimeter = a + b + c.
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What is the volume of the box if it is scaled down by a factor of $1/10$?
The volume of the box if it is scaled down by a factor of 1/10 is 27 cubic inches.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Given that, Length: 9 in, Width: 3 in and Height: 10 in
We know that, the volume of a cuboid is Length×Width×Height
Here, the volume of a box = 9×3×10
= 270 cubic inches
It is scaled down by a factor of 1/10
Now, 1/10 ×270
= 27 cubic inches
Therefore, the volume of the box if it is scaled down by a factor of 1/10 is 27 cubic inches.
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"Your question is incomplete, probably the complete question/missing part is:"
What is the volume of the box if it is scaled down by a factor of 1/10? Length: 9 in, Width: 3 in and Height: 10 in
A candy store sells walnuts for $8 per pound, and pecans for $2 per pound. If the store wants to create a bag of mixed nuts that sells for $6 per pound, how many pounds of pecans must be mixed with two pounds of walnuts?
what ia the length of the hypotenuse triangle below?
Answer: 18 - apex
Step-by-step explanation:
Can someone please put this in numerical order? Will give 15 points to who does!!!!!!
85 points 91 points 76 points 80 points 83 points
89 points 94 points 75 points 84 points 94 points
Please help me on number 8 and explain ?
Solve the system of linear equations by substitution check your solution show work
Y-x=23
Y=3x+11
A) 3 ,20
B)6,29
C)24,47
D)4,27
2 x-y=30
2.5 +y=5
A)8,-22
B) 122.5, 92.5
C) 10 , -20
D)11, -22.5
Courtney had $55 to spend at the fair. She paid $22.50 for rides and $14.25 for lunch and snacks. Courtney says she has $18.25 left to play games at the fair. Which explanation explains whether Courtney is correct or not? A. Courtney is not correct. Estimation: 22.50 – 14.25 is about 8. $55 – $8 = $47 There was about $47 left for Courtney to spend on games. B. Courtney is correct. Estimation: 22.50 + 14.25 is about 37. $55 – $37 = $18 There was about $18 left for Courtney to spend on games. C. Courtney is not correct. Estimation: 22.50 + 14.25 is about 37. $55 + $37 = $92 There was about $92 left for Courtney to spend on games. Question Resources
Find the value of x. If your answer is not an integer express it in simplest radical form.
Answer:
4to5 and 3to7
Step-by-step explanation:
:)hope this helped
Can people help me please to find the volume about question number 10 please and tell me the answer step by step please I need help
which of the following are examples of exponential decay? select all that apply.
a) the population of Florida is increasing by 43% each year
b) the pesticide DDT has a half-life of 15 years
c)march madness has 64 teams in the bracket. each round, half of the teams are eliminated
d)after an antibiotic is added to a culture of bacteria, the number of bacteria is reduced by half every three hours
e) a tree frog population doubles every three weeks