there are several different models for geometries in which the points are ordered pairs (x, y) of real numbers; we plot these points in the usual way in the x y-plane.
A circle having radius 5 and centre at (0,0) has equation x² + y² = 25.
What is the equation of circle?
A circle is a closed curve that extends outward from a set point known as the centre, with each point on the curve being equally spaced from the centre. A circle with a (h, k) centre and a radius of r has the equation:
(x-h)² + (y-k)² = r²
Let (x,y) be any point on the circle.
Given that centre of the circle is origin (0,0).
Now, we know that the distance from any point on the circle to the centre is equal to the radius of the circle.
So, distance between point (x,y) and centre (0,0) is equal to radius of the circle which is given 5 units.
Now, using the distance formula -
√[(x - 0)² + (y - 0)²] = 5
Squaring on both the sides of the equation -
(x - 0)² + (y - 0)² = 25
So, the equation of the circle with radius 5, centred at the origin is x² + y² = 25.
Therefore, the equation is x² + y² = 25.
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Kaia says the graph does not represent a function. Is Kaia correct? Explain your reasoning.
Answer: Kaia is not correct
Step-by-step explanation: A function works as long as there is only one 'output' for every 'input', or for every x value, only one y value works. (There can be multiple x values for any y value). If you do the verticle line test on this graph, the line won't pass through two points at the same time anywhere. Therefore, Kaia is incorrect.
Solve with a = 5.
20÷8
Answer:I.65
Step-by-step explanation:
An investment of $1200.00 is growing at the rate of 2.6% per year. What is the growth in balance from year 20 to year 25?
1) None of the answers are correct
2)16.52
3) 2655.89
4)265.59
5)156.00
6)274.57
Answer:
6
Step-by-step explanation:
The growth in balance from year 20 to year 25 is $274.57.
Marissa uses 64 feet of fence to make a border around a rectangular flower garden. The length of the garden is 20 feet. What is the width of the garden?
Answer: 12 feet
Step-by-step explanation: If the length of the garden is 20 feet then that means 40 feet of fence was used to make both lengths of the garden. So we subtract 40 from 64 which leaves us with 24 feet and then we divide 24 by 2 to get 12 because there are 2 widths.
Hope this helps!
grant is thinking of two numbers. He says one of the numbers is twice the other number and the sum of the numbers is 42. what are the numbers?
Answer:
Answer is in attached photo.
Step-by-step explanation:
SolutionThe solution is in the attached photo, do take note to solve this question, we can assign 2 variables to the 2 conditions stated in the question, and solve them simultaenously.
The top of a silo is a hemisphere with a radius of 12ft. The bottom of the silo is a cylinder with a height of 40 ft. How many cubic feet of grain can the silo hold?
Use 3.14 for pi.
The total number of cubic feet of grain or volume of the grain that the silo can hold is 28947.41 [tex]ft^3[/tex].
What is the volume of an object?
The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
Given that the top of a silo is a hemisphere
radius(r) = 12 ft.
Then,
the volume of a hemisphere = [tex]\frac{2}{3} \pi r^3[/tex] = [tex]\frac{2}{3} * 3.14* 12^3 = 10851.84[/tex] [tex]ft^3[/tex]
And, the bottom of the silo is a cylinder with
height (h) = 40ft.
the volume of a cylinder =[tex]\pi r^{2} h = 3.14*12^2*40=18095.57 ft^3[/tex]
So, the total volume is
V = 10851.84 + 18095.57 = 28947.41 [tex]ft^3[/tex]
Then, total volume = total number of cubic feet of grain
Hence, the required answer is 28947.41 [tex]ft^3[/tex].
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not a hard question!!!!
This is just a general how to! No example problems are attached, just explain how to do this, please!!!
1. given the graph of f(x) find f'(x)
2. find the piecewise for f(x)
To find the derivative of a piecewise function, you need to take the derivative of each individual piece and then combine them into one piecewise function.
How to explain the functionThe derivative of each piece can be found using the usual rules of differentiation (such as the power rule, sum rule, product rule, etc.).
Once you have the derivatives of each piece, you can write the overall derivative as a piecewise function, where the expression for each piece is limited to a specific range of x-values. The limits of each piece are defined by the breakpoints in the original function.
For example, if the original function is given as:
f(x) = {x^2 for x < 0,
x for 0 <= x < 1,
2x for x >= 1}
Then the derivative of f(x) can be found as:
f'(x) = {2x for x < 0,
1 for 0 <= x < 1,
2 for x >= 1}
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Find the slope of line
Slope; m=?
Answer:4/3
Step-by-step explanation: rise over run when finding slope, and the first point i can find (-3,-5) is 4 up and 3 right away from (0,-1)
50x+ 20 - 60(1/5y+60x) simplify the expression.
Answer:
-3550x - 12y + 20
Step-by-step explanation:
50x+ 20 - 60(1/5y+60x)
50x + 20 - 12y - 3600x
-3550x - 12y + 20
Which table shows a proportional relationship between x and y?
A. x 2.5 3 5 6
y 5 6 10 15
B. x 7 14 28 35
y 1 2 4 5
C. x 1 3 4 7
y 2 5 8 14
D. x 1 2 3 4
y 4 10 12 16
Answer:
D
Step-by-step explanation:The proportional relationship between x and y is;
x 7 14 28 35
y 1 2 4 5
The correct option is D.
Proportional relationships;
Proportional relationships between x and y satisfy the following equation;
Where k is some constant.
Rearranging the equation;
Then,
The proportional relationship between x and y is;
Hence, the proportional relationship between x and y is the correct option is D.
PLEASE HELP URGENT im using my last points for this
The publisher nedds to produce 2414 books and sell so that production cost will equal the money from sales.
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
A small publishing company is planning to publish a new book.
The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing).
The one-time fixed costs will amount to $27,160.
The variable costs will be $8.75 per book.
The publisher will sell the finished product to bookstores at a price of $20.00 per book.
Let x be the number of books.
Cost = 8.75x + 27160
Revenue = 20x
Revenue = cost
20x = 8.75x + 27160
11.25x = 27160
x = 2414.2
x ≈ 2414 books.
Therefore, the required number of books are 2414 books.
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Find the distance between the points on a number line. -8,9
Answer:
Below
Step-by-step explanation:
Start at -8... you have to go 8 units to reach 0
then you have to go another 9 to reach 9 total = 8 + 9 = 17
The smallest number such that when it is divided by 8 has a remainder of 6 and when it is divided by 9, has a remainder of 7
Using the Chinese Remainder Theorem, the smallest positive integer solution is x1 = 62.
How to Apply the Chinese Remainder Theorem?We can use the Chinese Remainder Theorem to find the smallest positive integer solution for this problem.
The Chinese Remainder Theorem states that if x ≡ a (mod m) and x ≡ b (mod n), then x is congruent to a unique value modulo mn. That is, there exists a unique solution x such that x is congruent to a modulo m and congruent to b modulo n, and the solution x is between 0 and mn - 1.
So, we want to find the smallest x such that:
x ≡ 6 (mod 8) and x ≡ 7 (mod 9)
We can start by finding a solution x1 such that x1 ≡ 6 (mod 8) and x1 ≡ 7 (mod 9). One such solution is:
x1 = 6 + 8k for some integer k
We can use the formula x1 = 6 + 8k to find a solution x1 that is also congruent to 7 (mod 9):
x1 = 6 + 8k = 7 + 9l (mod 9)
Expanding the right side of this equation, we get:
6 + 8k = 7 + 9l (mod 9)
6 - 7 = 9l - 8k (mod 9)
-1 = 9l - 8k (mod 9)
Since 9 and 8 are relatively prime, we can use the Extended Euclidean Algorithm to find integers r and s such that:
8r + 9s = gcd(8, 9) = 1
Using the Euclidean Algorithm, we can find r = -1 and s = 1. So,
-8 = 9(l - rk) (mod 9)
Since 9 is relatively prime to 8, l - rk is a multiple of 9. We can then rewrite the equation as:
-8 = 9j (mod 9)
Adding 9 to both sides of the equation, we get:
1 = 9j (mod 9)
So, j = 1.
Now, we have:
k = (1 - l) / r
Since r = -1, we can replace k with -l:
k = -l
So, we have:
x1 = 6 - 8l
And,
x1 = 7 + 9l (mod 9)
Combining these two equations, we get:
6 - 8l = 7 + 9l (mod 9)
Subtracting 9l from both sides, we get:
-2l = 13 (mod 9)
Dividing both sides by -2, we get:
l = -13 / -2 = 7 (mod 9)
So,
k = -l = -7 (mod 9)
And,
x1 = 6 - 8(-7) = 6 + 56 = 62 (mod 8)
So,
x1 = 62 (mod 8) and x1 = 7 (mod 9)
The smallest positive integer solution is x1 = 62
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Determine whether each fraction on the left is a proper or an
improper fraction. Options on the right may be used more than
once.
27
27
17
6100
21
5
Proper fraction
Improper fraction
Answer:
Improper, proper, proper, improper
Step-by-step explanation:
Step-by-step explanation:
To be a proper fraction the numerator (top number) must be less the the denominator (bottom number). Let’s start at the top.
27/27
This would be an improper fraction because the numerator is equal to the denominator, not less.
6/17
Because 6 is less then 17 this would make it a proper fraction
8/9
Same case as the last one, this is a proper fraction because the numerator is less then the denominator
21/5
21 is definitely more the 5 making this a improper fraction.
Hope this helped :)
On the grid, draw the graph of y+2x=6 for values of x from -2 to 4
The graph of the y+2x=6 is given in the attachment.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The standard equation of a line is expressed as y = mx + b, m is the slope
and b is the y-intercept.
Given the equation y = 2x - 2
If x = -2
y = 2(-2) - 2
y = -4-2
y = -6
If x = 4
y = 2(4) - 2
y = 8-2
y = 6
The point (-2, -6) and (4, 6 )must be on the line graph.
Hence, the graph of the y+2x=6 is given in the attachment.
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Your interest rate is compounded semi annually. If you have a annual interest rate of 7.5%, how much is the semi annual interest rate
Answer:
3.75%
Step-by-step explanation:
You want to know the semiannual interest rate if the annual rate is 7.5%.
Periodic rateThe rate of interest for a period is the annual rate divided by the number of periods in a year.
Interest compounded semiannually is compounded 2 times per year. The semiannual rate is ...
7.5%/2 = 3.75% . . . . semiannual rate
A model rocket is launched with an initial upward velocity of67m/s . The rocket's height h (in meters) aftert seconds is given by the following. h=67t-5t^(2)
Find all values of for which the rocket's height is 30 meters
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
Evaluate the expression 5+(-3x) for the given x-values. a) x=3 b) x=1/3 c( x= -3
Answer:
-4
4
14
Step-by-step explanation:
A:
5 + (-3)(3) = 5 -9 = -4
B:
5+ (-3)(1/3) = 5 - 1 - 4
C:
5 + (-3)(-3) = 5 + 9 = 14
15. ABC is
a. Congruent
b. Similar
c. Neither
to A'B'C'.
Answer:
Step-by-step explanation: 3
7
9
0
7
5
PLEASE HELP ASAP!!! FIND THE MULTIPLICITY AND ZEROS FOR THE GRAPH.
There are 4 zeros in the graph and the multiplicity is 5.
What are the zeros of a function?The zeros of a function are defined as the values of the variable of the function such that the function equals 0. Graphically, the zeros of a function are the points on the x-axis where the graph cuts the x-axis. In other words, we can say that the zeros of a function are the x-intercepts of its graph. The number of zeros of a polynomial function is equal to the degree of the polynomial.
In the given graph,
There are 4 turning points in the graph.
The 4 zeros from the graph are
(-3, 0), (-2, 0), (1, 0) and (1.5, 0)
The graph touches the x-axis and bounces off of the axis, it is a zero with multiplicity is 5.
Therefore, there are 4 zeros in the graph and the multiplicity is 5.
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Express each of the following numbers in standard scientific notation, rounding off each to three significant digits. a. 422.65 times 10^-3 b.71.246 times 10^5 c. 0.00044515 d. 22.9987 times 10^-5 e. 9.7222 times 10^5f. 0.0048545 times 10^5
In normal scientific notation, round off each integer to three significant digits:
a. 4.227 x 10⁻²
b. 7.125 x 10⁶
c. 4.452 x 10⁻⁴
d. 2.300 x 10⁻⁴
e. 9.722 x 10⁵
f. 4.855 x 10³
What is scientific notation?Scientific notation is a method of expressing numbers that are either too large or too little to be represented in decimal form. In the United Kingdom, it is known as scientific form, standard index form, or standard form. Scientific notation is a method of writing extremely big or extremely tiny integers. When a number between 1 and 10 is multiplied by a power of 10, it is expressed in scientific notation.
Here,
a. 422.65 times 10⁻³ = 4.227 x 10⁻²
b. 71.246 times 10⁵ = 7.125 x 10⁶
c. 0.00044515 = 4.452 x 10⁻⁴
d. 22.9987 times 10⁻⁵ = 2.300 x 10⁻⁴
e. 9.7222 times 10⁵ = 9.722 x 10⁵
f. 0.0048545 times 10⁵ = 4.855 x 10³
The following numbers in standard scientific notation, rounding off each to three significant digits:
a. 4.227 x 10⁻²
b. 7.125 x 10⁶
c. 4.452 x 10⁻⁴
d. 2.300 x 10⁻⁴
e. 9.722 x 10⁵
f. 4.855 x 10³
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Assume IJK ~ PQR with medians IM and PN
to sides JK and QR respectively, IJ = 15, and
PQ = 9. If IM is 2 greater than PN, find both
medians.
Step-by-step explanation:
Median IJK = IM = PN + 2
Median PQR = PN
Therefore, IM = PN + 2
IM = PN + 2
PN = IM - 2
IM = (15 + 9 + PN)/2
PN = (15 + 9 + IM - 2)/2
15 + 9 + PN = 2IM
15 + 9 + IM - 2 = 2PN
25 + PN = 2IM
25 + IM - 2 = 2PN
PN = 2IM - 25
PN = 2PN - 25
3PN = 25
PN = 25/3
IM = PN + 2
IM = 25/3 + 2
IM = 29/3
Therefore, IM = 29/3 and PN = 25/3.
Molly claims the animal listed in the table that weighs the most eats the most ahe also claims that the animal that weighs the least eats least
The animal listed in the table that weighs the most, eats the most,
and the animal that weighs the least, eats the least.
Molly's claim is correct.
What is the ratio?The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.
A table is given below:
Animals Weight of the animals, The weight of food packages
Cat 6 Kg 300 grams.
Dog 12 Kg 900 grams.
From the table:
The animal listed in the table that weighs the most, eats the most,
and the animal that weighs the least, eats the least.
Therefore, Molly's claim is correct.
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There are 7 roses and 9 daisies in a vase. What is the ratio of all flowers in the vase to daisies? and What is the ratio of roses to all flowers in the vase? Thanks
In a particular game of dice, you roll a single fair 6-sided die. You win 50 points for rolling a 1 or a 6, but you lose 5 points anytime you roll any other number. If you rolled the die 100 times, how many points would you expect to gain
or lose?
A. a gain of about 1,333 points
B. a gain of about 4,500 points
C. a loss of about 500 points
D. a gain of about 2,000 points
Answer: The expected value for rolling a 1 or 6 is 50 points, and the expected value for rolling any other number is -5 points. The chance of rolling a 1 or 6 is 2/6, or 1/3. The chance of rolling any other number is 4/6, or 2/3. The expected value for rolling the die once is:
(1/3 * 50) + (2/3 * -5) = 16.67
So, if you rolled the die 100 times, you would expect to gain or lose:
100 * 16.67 = 1667 points
The answer is: a gain of about 1,667 points.
Step-by-step explanation:
in an experiment to study the dependence of hypertension on smoking habits, the following data were collected on 180 individuals:
Smoking Status
Nonsmoker Moderate Smoker Heavy Smoker
Hypertension Status Hypertension 21 36 30
No Hypertension 48 26 19
What is the probability that a randomly selected individual is experiencing hypertension? Given that a heavy smoker is selected at random from this group, what is the probability that the person is experiencing hypertension? Are the events "hypertension" and "heavy smoker" independent? Give supporting calculations.
Answer: The probability that a randomly selected individual is experiencing hypertension can be calculated by taking the ratio of the number of individuals with hypertension to the total number of individuals:
P(hypertension) = (21 + 36 + 30) / 180 = 87 / 180 = 0.4833
Given that a heavy smoker is selected at random, the probability that the person is experiencing hypertension can be calculated by taking the ratio of the number of heavy smokers with hypertension to the total number of heavy smokers:
P(hypertension | heavy smoker) = 30 / (30 + 19) = 30 / 49 = 0.6122
To determine if the events "hypertension" and "heavy smoker" are independent, we can compare the joint probability of both events happening to the product of their individual probabilities:
P(hypertension and heavy smoker) = 30 / 180 = 0.1667
P(hypertension) * P(heavy smoker) = 0.4833 * (30 / 180) = 0.1083
Since P(hypertension and heavy smoker) ≠ P(hypertension) * P(heavy smoker), we can conclude that the events "hypertension" and "heavy smoker" are not independent.
Step-by-step explanation:
if is found that out of 53 cars,41 had clocks,30 had radios and 6 had neither. how many had a clock but no radio?
The number of 17 cars have clocks but no radios.
What is subtraction?Subtraction is a mathematic operation. Which is used to remove terms or objects in the expression.
Given:
Out of 53 cars,41 had clocks,30 had radios and 6 had neither.
That means,
53-6 = 47 cars have either clocks or radios or both.
47 - 30 = 17 cars have no radio.
47 - 41 = 6 cars have no clocks.
Hence, 17 cars have clocks but no radios.
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How do I find the solution
Answer: maybe look up the answer and ask ur teacher what to do
Step-by-step explanation:
Equation that represents the graph below:
The linear equation on the graph is:
y = x + 3
How to write the equation of the line?Here we have a linear equation.
Remember that the general one is y = a*x + b where b is the y-intercept, here we can see that the line intercepts the y-axis at y = 3
y = a*x + 3
And it passes through the point (-3, 0), replacing these values we get:
0 = a*-3 + 3
3a = 3
a = 3/3 = 1
The linear equation is:
y = x + 3
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