What is the Pythagorean Thereom
Answers
Answer:
Step-by-step explanation:
The Pythagorean theorem states that for a right triangle, the sum of the square for each of the sides is equal to the square of the hypotenuse.
See attached for graphic and formula
Related Questions
If each cube represents 0.25 in3, what is the volume of the prism?
A) 6 in3
B) 12 in3
C) 48 in3
D) 75 in3
Answers
Answer:B
Step-by-step explanation:
Answer:
its B
Step-by-step explanation:
i did the test and got it right
You start at (4, 4). You move up 1 unit and left 6 units. Where do you end?
Answers
Answer: (10,5)
Step-by-step explanation:
add 6 do the x value
then add 1 to the y value
nd the 52nd term and the term named in the problem
40, 140, 240, 340, ...
Find a 32
Answers
Answer:
5140 and 3140
Step-by-step explanation:
Note there is a common difference d between consecutive terms in the sequence, that is
d = 140 - 40 = 240 - 140 = 340 - 240 = 100
This indicates the sequence is arithmetic with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 40 and d = 100, thus
[tex]a_{52}[/tex] = 40 + (51 × 100) = 40 + 5100 = 5140
[tex]a_{32}[/tex] = 40 + (31 × 100) = 40 + 3100 = 3140
√2
4
Suppose that $2000 is invested at a rate of 5.1%, compounded semiannually. Assuming that no withdrawals are made, find the total amount after 6 years.
Do not round any intermediate computations, and round your answer to the nearest cent.
Answers
Solution:
The formula for compound interest, including principal sum, is:
[tex]A = p( 1 + \frac{r}{n})^{nt}[/tex]
Where,
A = the future value of the investment/loan
P = the principal investment amount
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per unit t
t = the time the money is invested
From given,
p = 2000
[tex]r = 5.1 \% = \frac{5.1}{100} = 0.051[/tex]
t = 6 years
n = 2 ( compounded semiannually)
Substituting the values we get,
[tex]A = 2000( 1 + \frac{0.051}{2})^{ 2 \times 6}\\\\A = 2000( 1 + 0.0255)^{12}\\\\\A = 2000(1.0255)^{12}\\\\A = 2000 \times 1.35278\\\\A = 2705.5649[/tex]
Thus the total amount after 6 years is $ 2705.5649
Final answer:
Using the compound interest with an initial investment of $2000 at a 5.1% interest rate compounded semiannually, the total amount after 6 years is calculated to be $2710.34.
Explanation:
To calculate the total amount after 6 years when $2000 is invested at a rate of 5.1% compounded semiannually, we use the formula for compound interest, which is [tex]A = P(1 + r/n)^(nt).[/tex] Here, A represents the future value of the investment, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time the money is invested for in years.
We can plug the values into the formula:
P = $2000 (the initial investment)
r = 0.051 (5.1% interest rate expressed as a decimal)
n = 2 (since the interest is compounded semiannually)
t = 6 (the investment period in years)
Therefore, we calculate A using the following expression:
[tex]A = 2000(1 + 0.051/2)^(2*6)[/tex]
[tex]A = 2000(1 + 0.0255)^(12)[/tex]
[tex]A = 2000(1.0255)^12[/tex]
After calculating the above expression without rounding intermediate computations and rounding the final answer to the nearest cent, the total amount comes out to be:
A = $2710.34
Thus, the total amount after 6 years, with a 5.1% interest rate compounded semiannually, is $2710.34.
if the triangles are congruent, then X=?
Answers
Answer:
Hi there!
The correct answer to this question is: x=3
Step-by-step explanation:
because these two triangles are similar, that means the hypotenuse are similar. which means you can set the sides equal to each other like this:
13 = 4x + 1 minus one on both sides and you should get 4x = 12 and then divide 4 on both sides and you should finally get x = 3
What is the length of the unknown leg in the right triangle? A right triangle has a side with length 8 feet, hypotenuse with length StartRoot 73 EndRoot feet, and side labeled a. 3 ft StartRoot 57 EndRoot ft StartRoot 65 EndRoot ft 9 ft
Answers
Answer:
It’s A
Step-by-step explanation:
Right on edge
Write the equation of the line that passes through the point (-5,5) and has a slope of -8/5
A) y= -8/5 x - 3
B) y= -8/5x+3
C) 3x - 5y =0
D) 5x-3y=0
Answers
Answer:
The equation of the line that passes through the point (-5,5) and has a slope of -8/5 will be:
[tex]y=-\frac{8}{5}x-3[/tex]
Step-by-step explanation:
Given
[tex]\left(x_1,\:y_1\right)=\left(-5,5\right)[/tex][tex]m=\frac{-8}{5}[/tex]Point-Slope Form equation is
[tex]\left(y-y_1\right)=m\left(x-x_1\right)[/tex]
[tex]\left(y-5\right)=\frac{-8}{5}\left(x-\left(-5\right)\right)[/tex]
[tex]\mathrm{Apply\:rule}\:-\left(-a\right)=a[/tex]
[tex]y-5=\frac{-8}{5}\left(x+5\right)[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}[/tex]
[tex]y-5=-\frac{8}{5}\left(x+5\right)[/tex]
[tex]y-5+5=-\frac{8}{5}\left(x+5\right)+5[/tex]
[tex]y=-\frac{8}{5}x-3[/tex]
Therefore, the equation of the line that passes through the point (-5,5) and has a slope of -8/5 will be:
[tex]y=-\frac{8}{5}x-3[/tex]
order this
1/2 , 1/3 , -1/2 , -1/3
let's see who is right
Answers
For least to greatest, -1/2, -1/3, 1/2, 1/3
For greatest to least, 1/3, 1/2, -1/3, -1/2
The negative numbers will be less then the positive ones
let s ={1 2 3 4 5 6}
A= {2 4 6}
B={3 4 5}
C={1 6}
find A'
A' n B
B n C'
(AuB)
(C')
Answers
Answer:
PLEASE CHECK THE ATTACHMENT.
HOPE U UNDERSTOOD
THANKS
Two numbers are in the ratio of 3:4. If 9 is subtracted from their sum, the result is 40. What is the greater number?
F. 35
G.21
H.28
J.49
Answers
Answer:
H.28
Step-by-step explanation:
x : y = 3 : 4
=> 4x=3y => x=3y/4 -----(1)
(x+y)-9=40
=>x+y=49
using (1)
3y/4 +y= 49
y=28
substituting y in (1)
x=21
hence 28 is greater.
please someone help me !! :(
Answers
Answer: 27 times bigger.
Step-by-step explanation:
You need to use the following formula to find the volume of a Square pyramid:
[tex]V=\frac{1}{3}s^2h[/tex]
Where "s" is the edge of a side of the square base and "h" is the height of the pyramid.
Knowing that:
[tex]s_A=12\ in\\\\h_A=8\ in\\\\\\s_B=36\ in\\\\h_B=24\ in[/tex]
You can find the volume of the Pyramid A and the volume of the Pyramid B:
[tex]V_A=\frac{1}{3}(12\ in)^2(8\ in)\\\\V_A=384\ in^3\\\\\\V_B=\frac{1}{3}(36\ in)^2(24\ in)\\\\V_B=10,368\ in^3[/tex]
Finally divide the volume of the Pyramid B and the volume of the Pyramid A, in order to find how many times bigger than the Pyramid A is the Pyramid B.
You get:
[tex]\frac{10,368\ in^3}{384\ in^3}=27[/tex]
If a quadratic function has the vertex (-1,3), what is the equation of its axis of symmetry
Answers
Check the picture below.
If your company sells basketballs. You sell
123,000 basketballs at a price of $42.50 each.
You have bills for your business equal to
$575,000. What is your profit?
Answers
123,000 x 42.50 = 5227500
5227500-575,000=4652500
your profit is 4652500
Hope this helps
The major and minor axes of an ellipse are 25 inches and 4 inches in length. What is the area of the ellipse?
Answers
Answer:
Therefore, the area of the ellipse is:
Area = 78.5 inches
Step-by-step explanation:
The formula to find the area of the ellipse is
[tex]\:a\:\times \:b\:\times \:\pi[/tex]
The major axis of an ellipse = 25 inches
The minor axis of an ellipse = 4 inches
The value of a = major axis/2 = 25/2 = 12.5 inchesThe value of b = minor axis/2 = 4/2 = 2 inchesThus
The area of the ellipse:
Area = [tex]\:a\:\times \:b\:\times \:\pi[/tex]
[tex]=\:12.5\:\times\:2\:\times\:\pi[/tex]
[tex]=25\pi[/tex]
[tex]=78.5[/tex] inches ∵ [tex]\pi =3.14[/tex]
Therefore, the area of the ellipse is:
Area = 78.5 inches
What is the equivalent fraction of 24/126
Answers
Answer:4/21
Step-by-step explanation:divide 6 by both sides
The equivalent fraction of 24/126 is 4/21.
To find an equivalent fraction, one can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 24 and 126 is 6.
Dividing both the numerator and the denominator by 6, we get:
[tex]\[ \frac{24 \div 6}{126 \div 6} = \frac{4}{21} \][/tex]
Therefore, the fraction 4/21 is equivalent to 24/126.
find the unit rate 50 min?
20 calls?
Answers
Answer: 2.5 minutes per call
Step-by-step explanation:
This is a fraction equal to
50 minutes ÷ 20 calls
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 20
50 minutes ÷ 20
20 calls ÷ 20 = 2.5 minutes/ 1 call
The unit rate is 2.5 minutes per call
To find the unit rate of making phone calls, we divide the total number of minutes by the total number of calls. This gives us the average number of minutes spent on each call.
We have 50 minutes and 20 calls. Dividing these gives us the unit rate:
Unit Rate = Total Minutes ∕ Total Calls
Unit Rate = 50 minutes ∕ 20 calls = 2.5 minutes per call
Therefore, the unit rate is 2.5 minutes per call, indicating on average, each call lasts for 2.5 minutes.
Martin kept track of the number of times he had to flip a coin before it landed tails up.
Number of Flips to Land Tails Up
1
2
3
4
Which is a true statement about the dot plot?
*
Six times it took 4 flips of the coin to land tails up.
Twice it took 4 flips of the coin to land tails up.
It took 6 flips of the coin to land tails up more often than any other number of flips.
The greatest number of flips it took to land tails up was 6.
Answers
Answer:
The dot plot of flip times increased gradually between 1, 2 and 3. The dot plot grew sharply from 3 to 4 and then 6.
Step-by-step explanation:
There are only 5 probabilities. It took Martin 1,2,3,4 and 6 flips to land a tail up. That 1,2,3 times of flips to land a tail up happened once. 4 times of flips to land a tail up happened 8 times. The greatest number of flips took to land tails up was 6 but the question didn't give details how many times it happens.
Answer:
the answer is A just took a quiz.
Step-by-step explanation:
Josie and her brother, Sean both have a job after school. For every $5.50 that Josie earns, her brother earns $6.50. On Tuesday, they earned $30.00. How much money did Josie earn? How much did her brother earn?
Answers
Answer:
Josie will earn $13.75 and her brother Sean will earn $16.25
Step-by-step explanation:
Given that For every $5.50 that Josie earns, her brother earns $6.50.
Tuesday, they earned $30.00
Using the ratio and the proportional
Josie : Sean : Total
5.5 : 6.5 : 12
x : y : 30
So, x = 5.5 * 30/12 = 13.75
And y = 6.5 *30/12 = 16.25
So, Josie will earn $13.75 and her brother Sean will earn $16.25
Rope costs $0.65 per foot.How much do 10.8 feet of rope cost?
Answers
Answer:
$7.02
Step-by-step explanation:
So we know that one foot of rope costs $0.65, and we are trying to fin the cost of 10.8 feet of rope. To find the cost of 10.8 feet of rope, we would multiply the length of the rope (in feet) and multiply it by the cost of one foot of rope. The length of the rope is already given to us in feet, so now we just need to multiply it by the cost per foot ($0.65).
$0.65 × 10.8 = ($0.65 × 10) + ($0.65 × 0.8) = $6.5 + $0.52 = $7.02
The cost of 10.8 feet of rope would be $7.02.
I hope this helps. :)
The required, 10.8 feet of rope costs $7.02.
What is arithmetic?Arithmetic is a constituent of mathematics that deals with the study of numbers, their properties, and their operations, it involves the basic operations of addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, roots, logarithms, and trigonometric functions.
To find the cost of 10.8 feet of rope at $0.65 per foot, we can multiply the length of the rope by the cost per foot:
Cost of 10.8 feet of rope = 10.8 feet x $0.65/foot
= $7.02
Therefore, 10.8 feet of rope costs $7.02.
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On the field trip, there are 225 students loaded onto 5 buses. Select the answer that shows the ratio of students to buses in simplest form
Answers
Answer:
45:1
Step-by-step explanation:
Which of the following defines liquid measure?
A. The measure of how much space is filled by an object
B. Units used to measure the volume of liquids, such as water, gasoline, and
milk
C. The volume of space inside a container
D. How heavy an object is
Answers
Liquid measure refers to the units used for measuring the volume of liquids such as liters, milliliters, etc. It's closely tied to the concept of volume, which is the amount of space that an object, liquid or solid, occupies.
Explanation:Liquid measure is defined as B. Units used to measure the volume of liquids, such as water, gasoline, and milk. This concept is related to the broader idea of volume, which is the measure of the amount of space occupied by an object, regardless of its state of matter. Let's say we want to measure the volume of water we're pouring into a jug. The volume units we would use (liters, milliliters, etc.) are examples of a liquid measure. Similarly, if we are filling a car's gas tank, the liters or gallons dispensed would be a liquid measure too.
Another example is milk that is sold in containers of varying volumes, from small cartons to large gallons. Each of these volumes is a measure of liquid. So, when we talk of liquid measure, we're looking at how much space a certain quantity of liquid occupies which is generally determined in liters, milliliters or sometimes cubic meter (m³).
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Place a term into each box to complete the equation that converts 3 yards to inches.
Answers
Answer:
1 yard, 12 inches, 108 inches.
Step-by-step explanation:
there are 3 feet in a yard, 12 inches in a foot and because 12 times 3 (one yard) is equal to 36, then three yards are equal to 108 inches.
The table below shows the cost of different numbers of goldfish at a pet store.
5----$1.50
10---$3
15---$4.50
20---$6
Which statement describes the rate of change of this function?
A.
The cost increases $3.00 each time 5 goldfish are added.
B.
The cost increases $0.30 each time 1 goldfish is added.
C.
The cost increases $6.00 each time 5 goldfish are added.
D.
The cost increases $1.50 each time 1 goldfish is added.
Answers
What is the missing number in this pattern?
1, 4, 9, 16, 25, 36, 49, 64, 81,
Answers
Answer:
no numbers are missing
Step-by-step explanation:
Don't fool others
Which three length cannot be the length of the sides of a triangle
Answers
The missing choices are here
A. 23 m, 17 m, 14 m
B. 11 m, 11 m, 12 m
C. 5 m, 7 m, 8 m
D. 21 m, 6 m, 10 m
Answer:
21 m, 6 m, 10 m cannot be the length of the sides of a triangle ⇒ D
Step-by-step explanation:
There is a fact to form a triangle:
The sum of the lengths of the two smaller sides must be greater than the length of the third side
A.
∵ The smallest sides are 14 m and 17 m
∵ Their sum = 14 + 17 = 31 m
∵ The third side is 23 m
∵ 31 > 23
∴ 23 m, 17 m, 14 m can be the length of the sides of a triangle
B.
∵ The smallest sides are 11 m and 11 m
∵ Their sum = 11 + 11 = 22 m
∵ The third side is 12 m
∵ 22 > 12
∴ 11 m, 11 m, 12 m can be the length of the sides of a triangle
C.
∵ The smallest sides are 5 m and 7 m
∵ Their sum = 5 + 7 = 12 m
∵ The third side is 8 m
∵ 12 > 8
∴ 5 m, 7 m, 8 m can be the length of the sides of a triangle
D.
∵ The smallest sides are 6 m and 10 m
∵ Their sum = 6 + 10 = 16 m
∵ The third side is 21 m
∵ 16 < 21
∴ 21 m, 6 m, 10 m cannot be the length of the sides of a triangle
Aiden borrows a book a public library. He read a few pages on day one. One day two, he reads twice the number of pages than he reads on one day. On the third day, he reads six pages less than what he read on the first day. If he read the entire book that contains 458 pages how many pages did he read on day three
Answers
Answer:
110 pages
Step-by-step explanation:
Day 1 =x
Day 2 =2x
Day 3 =x-6
(x)+(2x)+(x-6)=458
Add likes together.
4x-6=458
4x=464. Divide both sides by 4 to get x. X=116
Day 3=116-6=110
What is 4.49 rounded to the nearest whole number ?
Answers
Answer:
4
Step-by-step explanation:
A delivery company pays its drivers a fixed fee for each delivery made that day. The company deducts a daily fee for the use of the company's delivery truck. The drivers net pay in dollars, p, for one day is given by the equation p = 11d − 55, where d is the number of delivers made in one day. What does the number 55 most likely represent?
Answers
Answer:
55 is probably the fixed fee that the delivery company charges before anything.
Answer:
The companies daily fee
Step-by-step explanation:
P = pay
D = deliveries
55 = the daily fee the company deducts for the use of their truck
Pay = deliveries - company deduction
Given the functions f(n) = 11 and g(n) = −2(n − 1), combine them to create an arithmetic sequence, an, and solve for the 31st term.
Answers
To create an arithmetic sequence using the given functions, we add the functions together and substitute the desired term. The 31st term of the arithmetic sequence is -49.
Explanation:To combine the functions f(n) = 11 and g(n) = -2(n - 1) into an arithmetic sequence, we need to find the common difference between the terms. The common difference between the terms in an arithmetic sequence is obtained by subtracting one term from the previous term. In this case, the common difference is g(n). So, the arithmetic sequence can be expressed as an = f(n) + g(n).
For the 31st term, we substitute n = 31 into the equation and calculate:
a31 = f(31) + g(31)
a31 = 11 + [-2(31 - 1)]
a31 = 11 + [-2(30)]
a31 = 11 + [-60]
a31 = -49
Therefore, the 31st term of the arithmetic sequence an is -49.
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Find the degree of the term 8x^4
Answers
Answer:
4
Step-by-step explanation:
The degree of any variable is its power/exponent/index/indices