The Pythagorean theorem, usually applied in right-angled triangles, states the square of the hypotenuse equals the sum of the squares of the other two sides. This can be summarized by the equation: a² + b² = c². It is a fundamental principle in geometry.
Explanation:The Pythagorean theorem is a mathematical principle that applies specifically to right-angled triangles. The theorem, credited to the ancient Greek philosopher Pythagoras, stipulates that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This relationship can be represented by the equation: a² + b² = c², where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
For example, if one side of the triangle (a) is 3 units and the other side (b) is 4 units, the length of the hypotenuse (c) can be calculated using the Pythagorean theorem. The calculation would be set as follows: 3² + 4² = c². When solved, it results in c = √(3² + 4²) = √(9 + 16) = √25 = 5 units. Therefore, the length of the hypotenuse in this case is 5 units.
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What’s equivalent to 4/7 X 5/9? 5/9X4/7, 4/7 X 5/9, 4/9 X 5/7, 4/7 X 9/5 X=times
can someone please help me with this question
What the answer to simplifying( 6 to the power of negative 2) by (3 to the power of negative 3) and (3•6) to the power of 4
how many times larger is 9x10(9) than 3x10 (-4)
Step-by-step explanation: Well you see here 9x10 isnt 9 its 90 and 3x10 isnt -4 its 30
Describe the composition of an atom.
The atom consists of a tiny nucleus surrounded by moving electrons. The nucleus contains protons, which have a positive charge equal in magnitude to the electron's negative charge.
The two-way table shows the number of students in a school who have rabbits and/or birds as pets:
Have Rabbits Do Not Have Rabbits Total
Have Birds 18 22 40
Do Not Have Birds 25 35 60
Total 43 57 100
How many more students have rabbits than birds?
3
7
22
25
Answer:
3
Step-by-step explanation:
There are a total of 18+22 = 40 people with birds. There are a total of 18+25 = 43 people with rabbits.
This is a difference of 43-40 = 3 people.
There are 3 more students have rabbits than birds
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Have Rabbits Do Not Have Rabbits Total
Have Birds 18 22 40
Do Not Have Birds 25 35 60
Total 43 57 100
There are a total of 18+22 = 40 people with birds.
So 40 people with birds.
There are a total of 18+25 = 43 people with rabbits.
So 43 people with rabbits.
This is a difference of 43-40 = 3 people.
Hence, there are 3 more students have rabbits than birds
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Jake bought the pizza shown above for lunch, which was cut into four equal slices. What percentage of the pizza did Jake eat if he had three slices?
A) 25%
B) 50%
C) 67%
D) 75%
the pic is below
What is the slope of a line that is parallel to y=5x+3
two triangles are similar, and the ratio of the lengths of each pair of corresponding sides is 2:1. which statement regarding the two triangles is NOT True?
A- Their corresponding angles have a ratio of 2:!
B- Their areas have a ratio of 4:1
C- Their perimeters have a ratio of 2:!
D- Their altitudes have a ratio of 2:!
All statements are true. Ratio of corresponding angles, areas, perimeters, and altitudes is 2:1. No false statement exists.
To determine which statement regarding the two triangles is NOT true, let's analyze each option step by step.
Given:
- Two triangles are similar.
- The ratio of the lengths of each pair of corresponding sides is 2:1.
Let's denote the lengths of corresponding sides in the first triangle as [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex], and in the second triangle as [tex]\( 2a \)[/tex], [tex]\( 2b \)[/tex], and [tex]\( 2c \),[/tex] respectively.
A. Their corresponding angles have a ratio of 2:1.
- This statement is true because corresponding angles in similar triangles are congruent, so their ratios would indeed be 2:1.
B. Their areas have a ratio of 4:1.
- The area of a triangle is proportional to the square of the length of its sides. So if the ratio of the lengths of corresponding sides is 2:1, the ratio of their areas would be [tex]\( (2:1)^2 = 4:1 \)[/tex]. Hence, this statement is also true.
C. Their perimeters have a ratio of 2:1.
- The perimeters of triangles are directly proportional to the lengths of their sides. Since the ratio of the lengths of corresponding sides is 2:1, the ratio of their perimeters would indeed be 2:1. So, this statement is also true.
D. Their altitudes have a ratio of 2:1.
- The ratio of the altitudes of two similar triangles is equal to the ratio of their corresponding sides. So, if the ratio of corresponding sides is 2:1, the ratio of their altitudes would also be 2:1. Therefore, this statement is true.
Since all the statements are true, the correct answer is NONE.
The circumstance of a circle is 9pie cm. What is the diameter?
a rectangular deck has a area of 320 ft squared. the length of the desk is 4 feet longer than the width. find the dimensions of the desk. Solve by completing the square.
How to make a box and whisker plot for 21,21,22,20,13,13,27,24
Please help me with this
Simplify this expression:
3 2/3x-4/5(x-3 3/4)
At 3 p.m., the outside temperature was 4 degrees F. The temperature then fell steadily by 2 degrees F every hour for the next four hours. What was the temperature at 7 p.m.?
Sally decided to look at new and used vans. Sally found a used van for $14000. A new van is $20000, so what percent of the price of a new van does Sally pay for a used van?
Final answer:
Sally pays 70% of the price of a new van for a used van, which is calculated by dividing the price of the used van by the price of the new van and multiplying by 100.
Explanation:
To determine what percent of the price of a new van Sally pays for a used van, we use the formula for percentage: (Part / Whole) × 100. In this case, the price of the used van ($14,000) is the part, and the price of the new van ($20,000) is the whole. Hence, the calculation will be ($14,000 / $20,000) × 100.
Performing the calculation, we get: (14,000 / 20,000) × 100 = 0.7 × 100 = 70%.Therefore, Sally pays 70% of the price of a new van for a used van.
What is the first step of rationalizing the denominator of 7√11√?
Final answer:
The first step of rationalizing the denominator of 7√11 is to multiply both the numerator and denominator by the conjugate of the denominator.
Explanation:
The first step of rationalizing the denominator of 7√11 is to multiply both the numerator and the denominator by the conjugate of the denominator. In this case, the conjugate of √11 is -√11. Therefore, we multiply both the numerator and denominator by -√11 to get:
7√11 * -√11 = -77
√11 * -√11 = -11
So, the rationalized denominator is -11. The denominator becomes -11, and the simplified expression is:
-77 / -11 = 7
find the circumference of a circle with an area of 530.93
Community center has an L shaped swimming pool that is 10 feet deep. What is the volume of the pool
1200
1040
640
880
The total volume of pool is:
1040 cubic ft.
Step-by-step explanation:We know that the total volume of the pool is the sum of the volume of two rectangular prism.
one is a rectangular prism with dimensions 20ft.×10ft.×4ft.and the other rectangular prism has dimensions: 6ft.×4ft.×10ft.Hence, the volume of first rectangular prism is:
20×10×4=800 cubic ft.
Volume of second rectangular prism is:
6×4×10=240 cubic ft.
Hence, total volume of pool is:
800+240=1040 cubic ft.
*20 Pts* What are two fractions with different denominators that each have the LCD of 36?
If a horses man grows 6/5 per month, how long will it take to grow 24/10 cm
what is the product? (x-5)(2x+3x-1)
Answer:
-18^x-45x on edge
Step-by-step explanation:
sorry if this is late just letting people know in the future
Can someone help me with this question?
I think the answer is C but I’m not sure. Plz help me out
puppys mass 4500 grams kittens is 450,000milligrams who has the greater mass
A mobile phone carrier charges an extra fee if a customer uses more than 500 minutes each month. Tom has already used 230 minutes this month. Which inequality can be used to determine how many more minutes Tom can use this month without going over the 500-minute limit?
Answer:
x + 230 ≤ 500
Step-by-step explanation:
Given,
The time for which Tom used the phone = 230 minutes,
Let he further used the mobile for x minutes,
So, the total time for which he used the phone = ( x + 230 ) minutes,
According to the question,
For the extra minutes more than 500 minutes, the mobile phone carrier charges an extra fee,
Thus, if he wants to use the phone, without going over the 500-minute limit,
Then, the total time used by him ≤ 500 minutes,
⇒ x + 230 ≤ 500
Which is the required inequality.
ABC is congruent to FGH, AB=8.3, BC=10.4, and CA=4.2. What is the measure of segment GH?
For a better understanding of the explanation provided here please go through the diagram in the attachment given below.
As we can see from the diagram of the congruent triangles ABC and FGH, the vertices A,B,C of [tex] \Delta ABC [/tex] correspond to the vertices F,G,H of [tex] \Delta FGH [/tex], so the corresponding sides must correspond too. Thus, AB corresponds to FG, BC corresponds to GH and CA corresponds to GF.
Now, we know that BC=10.4. Therefore, it's corresponding side GH must be 10.4 too because they are corresponding sides of a congruent triangle.
Thus, GH=10.4 is the correct answer.
A town doubles its size every 22 years. If the population is currently 4,500, what will the population be in 88 years?
What is -2(3x+12y-5-17x-16y+4) simplified?
Answer:
B. 28x + 8y + 2
Step-by-step explanation:
Find the required annual interest rate to the tenth of a percent for $5200 to grow to $6500 if interest is compounded quarterly for five years
Final answer:
After rearranging the formula and solving for the interest rate, the required rate is found to be approximately 4.7%.
Explanation:
The subject of this question is finding the required annual interest rate that will grow a principal amount of $5,200 to $6,500 when compounded quarterly over five years. To solve this, we shall use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for, in years.
We are given:
A = $6,500
P = $5,200
n = 4 (since interest is compounded quarterly)
t = 5 years
We need to solve for r. First, we rearrange the formula to isolate r:
(1 + r/n) = (A/P)[tex]^({1/(nt))}[/tex]
Then we can insert our known values and solve for r:
(1 + r/4) = ($6,500/$5,200)^(1/(4*5))
Calculate the right-hand side:
(1 + r/4) = (1.25)[tex]^({1/20)}[/tex]
Find the 20th root of 1.25:
(1 + r/4) ≈ 1.01168
Subtract 1 from both sides:
r/4 ≈ 0.01168
Multiply both sides by 4:
r ≈ 0.04672
Convert the decimal to a percentage:
r ≈ 4.672%
Round to the nearest tenth of a percent:
r ≈ 4.7%
Therefore, the required annual interest rate to the tenth of a percent for $5200 to grow to $6500 with interest compounded quarterly for five years is approximately 4.7%.
Glenn Andrews recently bought a new motorbike for $3,950. If he had to pay 6 percent sales tax on the bike, what was the total cost of the bike?