If the radius of a circle is multiplied by 3 what happens to the area of a circle
choose the correct conic section to fit the equation (x-8)^2+(y-12)^2=25
a. Circle
b. Eclipse
c. Parabola
d. Hyperbola
Answer: a. Circle
Step-by-step explanation:
Given equation: [tex](x-8)^2+(y-12)^2=25[/tex] which is equivalent to [tex](x-8)^2+(y-12)^2=5^2[/tex]
This equation is of the form [tex](x-h)^2+(y-k)^2=r^2[/tex] which is the standard equation of a circle centered at (h,k) with radius r.
On comparing given equation to the standard equation of circle we have, h=8 and k=12 and r =2.
Therefore, given equation represent a circle centered at (8,12) and radius=5 units.
Determine the slope of the line that contains the given points. t(6,3),v(8,8)
The slope of the line that contains the given points T(6, 3) and V(8, 8) will be 2.5.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
The points are given below.
T(6, 3) and V(8, 8)
The slope is given as,
m = (8 - 3) / (8 - 6)
m = 5 / 2
m = 2.5
The slope of the line will be 2.5.
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A LIST OF 300 NUMBERS START AT 1.AFTER THAT EVERY NUMBER IS TRIPLED THE NUMBER WHICH IT HAD PRECEDES IT.THE 200TH NUMBER ON THE LIST IS
A:600
B:900
C:3 to the 199 power
D:3 to the 200 power
What is the measure of a base angle of an isosceles triangle if its vertex angle measures 40°?
a) 70°
b) 65°
c) 140°
d) 75°
Answer:
The Answer Is A. edge 2020
Step-by-step explanation:
Marie worked 2 weeks during her college she earned $280 the first week and 245 the second week. If 1/2 of her total earnings went to taxes and 1/4 went to college tuition how much money did she have left
Marie's total earnings for the two weeks were $525. She paid $262.5 to taxes and $131.25 to college tuition, leaving her with a balance of $131.25.
Explanation:To find out the amount left, we need to first calculate Marie's total earnings for the two weeks by adding what she earned each week. $280 for the first week plus $245 for the second week gives her a total earnings of $525.
Marie gave half of her earnings to taxes, which is 0.5 * $525 = $262.5. After that, she spent one-fourth of her earnings on college tuition, which equals 0.25 * $525 = $131.25. Summing up both amounts, we find that she spent $262.5 + $131.25 = $393.75 on taxes and tuition.
To find out the amount Marie has left, we subtract the total expenses from her total earnings. Thus, $525 - $393.75 = $131.25 is the total amount she has left after paying her taxes and tuition.
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After calculating her total earnings, subtracting the amounts for taxes and tuition, Marie had $131.25 left. Her total earnings were $525. 1/2 went to taxes, and 1/4 went to tuition.
First, find her total earnings for the two weeks:
Total Earnings = $280 + $245 = $525
Next, calculate how much went to taxes. Since 1/2 of her total earnings went to taxes:
Taxes = 1/2 x $525 = $262.50
Then, calculate how much went to college tuition. Since 1/4 of her total earnings went to tuition:
College Tuition = 1/4 x $525 = $131.25
Finally, subtract the amounts for taxes and tuition from her total earnings to find out how much money she had left:
Money Left = $525 - $262.50 - $131.25 = $131.25
Marie had $131.25 left after paying taxes and college tuition.
Maria is making a candle in the shape of a cylinder. She wants the candle to have a height of 3 cm and a radius of 2 cm. How much wax does Maria need?
volume = PI x r^2 x h
using 3.14 for pi
volume = 3.14 x 2^2 x 3
volume = 37.7 cubic cm of wax needed
Round answer as needed
Answer:
12Pi cm3
Step-by-step explanation:
For how many positive integer values of N will the expression 18/N + 2 be an integer?
N can have 6 different positive integer values.
What is an Expression?An expression is a mathematical statement which consists of variables, constants and mathematical operators.
The expression is :
18/N +2
An integer is a whole number that includes all positive numbers, negative numbers and zero.
An integer cannot be a fraction.
The value of N has to be determined for the expression such that, the value of the expression is a positive integer.
For the expression to be positive integer, the 18/N should be an integer value, so the number N should completely divide 18.
The factors of 18 is 1,2,3,6,9,18.
If N is any value among these, it will divide 18 to give a integer and the value of the expression will be a positive integer value.
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Match the graph with the correct equation.
y – 1 = –4(x + 5)
y + 1 =-1/4 (x + 5)
y – 1 =-1/4 (x + 5)
y – 1 =-1/4 (x – 5)
The perimeter of the rectangle below is 86units . Find the length of side XY
A company manufactures and sells mini-recorders. A survey of office supply stores indicated that at a price of $82 each, the demand would be four hundred recorders, and at a price of $42 each, the demand would be nine hundred recorders. If a linear relationship between price and demand exists, which of the following equations models the price-demand relationship?
(Let x represent the price per mini-recorder and y represent the demand in hundreds.)
A. Y= -1/8x + 57/4
B. Y= -8x - 114
C. Y= -1/8x - 57/4
D. Y= -8x + 114
Final answer:
Using the two given points $(82, 4)$ and $(42, 9)$, the slope is calculated to be $-1/8$. Subsequently, by using the point-slope form of the line equation and simplifying, we find that the linear relationship between price and demand is described by $y = -1/8x + 57/4$, which corresponds to choice A.
Explanation:
To determine the linear equation that best models the price-demand relationship for the mini-recorders, we are given two points. At a price of $82, the demand is 400 recorders (4 hundred), and at a price of $42, the demand is 900 recorders (9 hundred). In the mathematical representation, these points are (82, 4) and (42, 9), where x is the price and y is the demand in hundreds.
To find the slope (m) of the line, we use the slope formula:
m = (y2 - y1) / (x2 - x1), which gives us m = (9 - 4) / (42 - 82) = 5 / (-40) = -1/8.
Now, we can use the point-slope form to find the equation of the line. Let's use the point (82, 4):
y - y1 = m(x - x1)
y - 4 = (-1/8)(x - 82)
Multiplying out the right-hand side of the equation, we have:
y - 4 = (-1/8)x + (82/8)
y - 4 = (-1/8)x + 10.25
Moving 4 to the other side to get 'y' by itself, the equation becomes: y = (-1/8)x + 10.25 + 4
This simplifies to:
y = (-1/8)x + 14.25
Converting 14.25 into quarters gives us 14.25 = 57/4. Hence the equation becomes:
y = (-1/8)x + 57/4 which matches choice A.
Final answer:
The correct equation that models the price-demand relationship is y = -1/8x + 57/4, where y is the demand in hundreds and x is the price per mini-recorder.
Explanation:
To find the equation that models the price-demand relationship, we need two points to determine the line: (x1, y1) = (82, 4) and (x2, y2) = (42, 9). The demand, y, is in hundreds of recorders and x represents the price per mini-recorder. The slope (m) of the line is given by the change in demand over the change in price: m = (y2 - y1) / (x2 - x1) = (9 - 4) / (42 - 82) = 5 / (-40) = -1/8. To find the y-intercept (b), we use one of the points and the slope in the linear equation formula y = mx + b. Using the point (82, 4), we have 4 = (-1/8)(82) + b. Solving this equation gives us b = 4 + (1/8)(82) = 4 + 10.25 = 14.25. Now the linear equation is y = -1/8x + 14.25. Since y needs to be in hundreds for the units to match the point given (400, 900), we must divide b by 100, resulting in b = 14.25 / 100 = 57/4. The final price-demand relationship is y = -1/8x + 57/4.
If the federal reserve decreases the reserve rate from 7% to 5%, how does this affect the amount of money that would result because of fractional-reserve banking from an initial deposit into a bank of $30,000?
Answer:
The total affect of the decrease in the interest rate = $29400
Step-by-step explanation:
The initial amount of money which has been deposited into the account = $30000
The rate at which the initial money was deposited = 7%
But it is given that the federal reserve decreases the reserve rate from 7% to 5%
Now, we need to find the affect of this decrease on the deposited money
The rate of change in the interest rate = 7 - 5 = 2%
So, The affect of this decrease = 2% of 30000
= $600
So, The money becomes = 30000 - 600
Therefore, The total affect of the decrease in the interest rate = $29400
The table below represents a linear function f(x) and the equation represents a function g(x):
x f(x)
−1 −5 g(x)
0 −1 g(x) = 4x + 3
1 3
Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x).
Part B: Which function has a greater y-intercept? Justify your answer.
what is the domain of the function on the graph?
a. all real numbers
b. all real numbers greater than or equal to - 2
c. all real numbers greater than or equal to - 5
d. all real numbers greater than or equal to 0
Answer:
Option a is correct.
Step-by-step explanation:
The given graph is of the function f(x)=|x|-2
Domain are the values that x will take in the given function x can take all the values whether fraction, integer the function will always be defined.
Hence, the domain of the function is all real numbers.
Therefore, Option a is correct.
Answer: Domain are all real number [a].
Step-by-step explanation:
Given : graph .
To find : what is the domain of the function on the graph.
Solution : We have given that a graph of function f(x) : |x| - 2.
Domain : The domain of a function is the set of its possible inputs,that is the set of input values where for which the function is defined.
Therefore, the domain are all real number [a].
PLEASE HELP!! IM REALLY CONFUSED
Can somebody please help me with this problem? Also please don't give me the final answer can you just like help me have an idea on how to do it. PLEASE AND THANK YOU
Is (-5, -1) a solution to y= -x + 4
Mrs. Patil bought 4 packs of pencils for her class. Then she bought 3 more packs of pencils. There are 12 pencils in a pack. How many pencils did she buy?
Solve for a:
3/5a = 1/4
About 145 out of 300 students prefer walking instead of riding the bus to school. About what percent of the students prefer walking?
Please help, I need the answer asap!
2 x 2 = 4 x 3 = 12
2 x 3 = 6 x 3 = 18
2 x 2 = 4 x 2 = 8 x 3 = 24 x 3 = 72
2x2 = 4 x 3 = 12 x 3 = 36
last one is the correct answer
Jason is a used-car salesman who sells domestic and foreign cars. He earns $7,000 for each domestic car sold and loses $3,500 for each foreign car sold. Due to certain business commitments, Jason has to sell at least 10 foreign cars each month. He needs to make at least $17,000 each month to cover his expenses. Which graph shows the number of cars he has to sell each month to at least cover his expenses?
What is the LCM of 24a^3b and 36ab^2?
Answer:
The LCM of given expressions is [tex]72a^3b^2[/tex].
Step-by-step explanation:
The given expressions are
[tex]24a^3b[/tex]
[tex]36ab^2[/tex]
Find factor form of each expression.
[tex]24a^3b=2\times 2\times 2\times 3\times a\times a\times a\times b[/tex]
[tex]36ab^2=2\times 2\times 3\times 3\times a\times b\times b[/tex]
LCM is the product of all factors where common factors are considered only once.
[tex]LCM(24a^3b,36ab^2)=2\times 2\times 2\times 3\times 3\times a\times a\times a\times b\times b[/tex]
[tex]LCM(24a^3b,36ab^2)=72a^3b^2[/tex]
Therefore the LCM of given expressions is [tex]72a^3b^2[/tex].
On Tuesday, Pizza Hut sold 60 plain pizzas at $5 each; 20 meatball pizzas at $8 each; 25 Sicilian pizzas at $9 each; and 33 large crust supremes at $10 each. What were the total dollar sales for Pizza Hut on Tuesday? A. $790 B. $1,015 C. $1,115 D. $1,511
What's the verbal expression for the algebraic expression 15+r ?
Which of the relations given by the following sets of ordered pairs is not a function?
a. {(5,2),(4,2),(3,2),(2,2),(1,2)}{(5,2),(4,2),(3,2),(2,2),(1,2)}
b. {(−4,−2),(−1,−1),(3,2),(3,5),(7,10)}{(−4,−2),(−1,−1),(3,2),(3,5),(7,10)}
c. {(−8,−3),(−6,−5),(−4,−2),(−2,−7),(−1,−4)}{(−8,−3),(−6,−5),(−4,−2),(−2,−7),(−1,−4)}
d. {(−6,4),(−3,−1),(0,5),(1,−1),(2,3)}
Answer:
The answer is the B)
Step-by-step explanation:
By the definition, in a function, a value in the first set of numbers only have a value in the second set of numbers, so for every pair of numbers, we have to review if the first number for this pair only appears one time in all the function.
All the set ot values agrees with this definition except the B, because the third and fourth pair have the same first value (3)
I need help with this question:
3c + 17, for c=5
The variable c = 5 meaning we can replace the value of c in the equation with 5. Solve the equation now as you normally would.
3 (5) + 17 = 15 + 17 = 32
The answer is 32 and if this helps please give brainliest to help me reach expert ;)
Help me with this plz
answer correctly for brainliest
Suppose you are standing 500 feet away from a tree and you see a hawk hovering directly above that tree. The angle of elevation from you to the hawk is 24°. To the nearest foot, at what height is the hawk hovering?