Using the equation of a circle, it is found that the value of y is -4.
Equation of the circle:
A circle is a closed curve that is drawn from the fixed point called the center, in which all the points on the curve are having the same distance from the center point of the center.
The equation of a circle with (h, k) center and r radius is given by:
(x-h)² + (y-k)² = r²
Given,
The points (0, 5) and (0, −5) are the endpoints of the diameter of a circle.
The point (3, y) is on the circle, in quadrant 4.
Here we need to find the value of y.
The center is the midpoint of them, thus:
[tex]x=\frac{0+0}{2}=0\\ y=\frac{5-5}{2}=0[/tex]
So, the midpoint is (0,0).
The diameter(twice the radius) is the distance between these two points, so:
[tex]2r=\sqrt{(0-0)^2+(5-(-5))^2}[/tex]
=> 2r = √0+100
=> 2r = √100
=> 2r = 10
=> r = 5
Thus, the equation of the circle is:
=> x² + y² = r²
Apply the values,
=> x² + y² = 5²
=> x² + y² = 25
The point (3,y) is on the circle, in quadrant 4. This means that:
Replacing x by 3, we can find the value of y.
Quadrant 4 means that y < 0.
Then:
=> 3² + y² = 25
=> y² = 25 - 9
=> y² = 16
=> y = ±√16
=> y = - 4
The value of y is -4.
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To enter an arcade, Linus has to pay a $5 fee. In addition, every arcade game costs an additional $0.25 to play one round. The relationship between the amount of Linus' money spent, or C, and the number of rounds of arcade games played, or r, can be modeled by the equation C=0.25r+5.
The amount of Linus's money spent on 200 rounds of arcade game is $55.
The given question is incomplete, so
Lets suppose that Linus has played 200 round of arcade game and now we will need to determine the amount of Linus's money spent on 200 rounds of arcade game.
Entrance fee of an arcade = $5
Additional cost to play one round = $0.25
With the help of given equation ( C=0.25r+5 ) we will determine the amount of Linus's money spent on 200 rounds of arcade game.
'C' = The relationship between the amount of Linus' money spent
'r' = The number of rounds of arcade games played
Let's solve the equation now,
As we know that r is number of rounds Linus has played which is 200 rounds.
So, C = 0.25r+5
C = 0.25 × 200 + 5
C = 50 + 5
C = $55
Hence, we got that Linus has spent total $55 on 200 rounds of arcade game.
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Initial Knowledge Check
Suppose Deon places $3000 in an account that pays 11% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year.
$
(b) Find the amount in the account at the end of 2 years.
(a) The amount in the account at the end of 1 year is $3330
(b) The amount in the account at the end of 2 year is $3696.3
Compound interest is interest calculated on the principal and the interest accrued in previous periods. General formula for the number of annual interest on the principal. If the interest is compounded annually, the amounts is given by [tex]A=P(1+\frac{R}{100} )^t[/tex] where "A" represents the new principal sum or the total amount of money after compounding period , "P" represents the original amount or initial amount , "r" is the annual interest rate , "t" represents the number of years .It is given that Deon deposit $3000 that pays 11% interest compounded each year .
(a) Putting P = $3000, R = 11% , T = 1 year in equation (1) , we get
[tex]A=3000(1+\frac{11}{100} )^1\\\\A=3000(1+0.11)\\A=3000(1.11)\\A=3330[/tex]
(b) Putting P = $3000, R = 11% , T = 2 year in equation (1) , we get
[tex]A=3000(1+\frac{11}{100} )^2\\\\A=3000(1+0.11)^2\\A=3000(1.11)^2\\A=3000\times1.23\\A=3696.3[/tex]
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Was lulu related to the cubs? cite three (3) pieces of specific evidence here to support your answer:
Yes, Lulu was associated to one of the cubs. Cub #711 because It was discovered it in data set 5 for her parentage.
Why is genetics needed for lion research?They discovered that there is evident genetic evidence of current population fragmentation, which occurs when teams of a species are isolated from each other, by trying to compare the DNA of lions presently to lions from 100 years ago.
This fragmentation could have a long-term effect on the iconic species' genetic health.
What were the advantages for Lulu (#630) in raising the cubs who were not hers?Raising the children together has an evolutionary advantage because it makes sure that Lulu's genetic data is passed down.
Because her cub is one of many, there is safety in numbers.
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an equilateral triangle has sides of equal length. determine whether the triangle with vertices 1-1, -12, 12, 32, 1-4, 32 is equilateral.
The triangle with the given vertices (-1, -1), (2, 3), and (-4, 3) is not an equilateral triangle.
What is an equilateral triangle?An equilateral triangle can be defined as a special type of triangle that has equal side lengths and all of its three (3) interior angles are equal.
In order to determine whether the triangle with the given vertices is an equilateral triangle, we would apply the distance formula to calculate the length of each side of this triangle as follows:
Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
For the vertices (-1, -1) and (2, 3), we have;
A = √[(2 - (-1))² + (3 - (-1))²]
A = √[(2 + 1)² + (3 + 1)²]
A = √[3² + 4²]
A = √[9 + 16]
A = √25
A = 5 units.
For the vertices (2, 3) and (-4, 3), we have;
B = √[(-4 - 2)² + (3 - 3)²]
B = √[-6² + 0²]
B = √[36 + 0]
B = √36
B = 6 units.
For the vertices (-1, -1) and (-4, 3), we have;
C = √[(-4 - (-1))² + (3 - (-1))²]
C = √[(-4 + 1)² + (3 + 1)²]
C = √[-3² + 4²]
C = √[9 + 16]
C = √25
C = 5 units.
Therefore, the triangle with the given vertices is not an equilateral triangle because C = A ≠ B.
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Complete Question:
An equilateral triangle has sides of equal length. Determine whether the triangle with vertices (-1, -1), (2, 3), (-4, 3) is equilateral.
Only 5/8 of the class completed 1/2 of their homework. What is the rate of the homework per class?
Based on the values in the table below, find the slope and y-intercept to write the equation of the line in the form y=mx+by=mx+b.
xx yy
11 1111
22 2222
33 3333
Answer:
gjj uijh
Step-by-step explanation:
Solve the rational equation:
7/(s + 8) = −2/(9s + 1)
Answer: s=?
Answer:
s = (-23/65)
Step-by-step explanation:
7 -2
------ = -------
(s + 8) (9s + 1)
7 (9s + 1) -2 (s + 8)
------ = -------
(s + 8) (9s + 1) (9s + 1) (s + 8)
7 (9s + 1) -2 (s + 8)
(------------------ = ---------------------) ((9s + 1) (s + 8))
(s + 8) (9s + 1) (9s + 1) (s + 8)
7 (9s + 1) = -2 (s + 8)
63s + 7 = -2s - 16
+2s +2s
65s + 7 = -16
-7 -7
65s = -23
÷65s ÷65s
s = (-23/65)
joey chestnut is trying to break his own record for eating the most whole hot dogs in 101010 minutes. he needs to eat more than 727272 hot dogs to break his record. after 111 minute, joey has eaten 11 \frac{1}{4}11 4 1 11, start fraction, 1, divided by, 4, end fraction hot dogs. let ddd represent the number of hot dogs joey eats per minute for the next 999 minutes. which inequality represents the number of hot dogs per minute joey could eat for the last 999 minutes to break his record? choose 1 answer: choose 1 answer: (choice a) a 11\frac{1}{4} 9d>7211 4 1 9d>7211, start fraction, 1, divided by, 4, end fraction, plus, 9, d, is greater than, 72 (choice b) b 11\frac{1}{4} 9d
An inequality that represents the number of hot dogs per minute joey could eat for the last 9 minutes to break his record is: 9d + [tex]11\frac{1}{4}[/tex] > 72
For given question,
Joey chestnut is trying to break his own record for eating the most whole hot dogs in 10 minutes.
He needs to eat more than 72 hot dogs to break his record.
After 1 minute, joey has eaten [tex]11\frac{1}{4}[/tex] hot dogs.
let d represent the number of hot dogs joey eats per minute for the next 9 minutes.
9d + [tex]11\frac{1}{4}[/tex] is the expression that shows how many hot dogs he will eat in total.
9d being how much he'll eat in the remaining 9 minutes, and [tex]11\frac{1}{4}[/tex] being the number of hot dogs he's already eaten in the first minute.
Since it has to beat his former record of 72, it has to be greater than 72. The inequality would be
9d + [tex]11\frac{1}{4}[/tex] > 72
Therefore, an inequality that represents the number of hot dogs per minute joey could eat for the last 9 minutes to break his record is:
9d + [tex]11\frac{1}{4}[/tex] > 72
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If F(x) = 5x-7 and G(x)=√x +13, what is F(G(x)) ?
Answer:
5x - 7 ( √ x + 13)
5x√x + 65x - 7√x -91
√3 (5x - 7) +13 (5x - 7)
(5x - 7) (√3 + 13)
5x(√3 + 13) -7
Harry buys 3 granola bars for $5. Sidney buys 9 granola bars for $15 what is the constant of proportionality
The constant of proportionality is 5/3.
What is the constant of proportionality?In mathematics, proportionality denotes a linear relationship between two quantities or variables. Both quantities increase in size when one double, and both decrease in size when one drops to a tenth of its original value.
The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. The constant of proportionality may also be referred to by the terms constant ratio, constant rate, unit rate, constant variation, or even change rate.
Let the constant of proportionality is k.
Harry buys 3 granola bars for $ 5. So, we can write it as
3 × k = 5
k = 5/3
To Check:
Sidney buys 9 granola bars for $ 15, we can write it as
9 × k = 15
Put k= 5/3 in the equation
9 × 5/3 = 15
3 × 5 = 15
15 =15
The Left and right-hand sides are equal. Hence, the constant of proportionality is k=5/3.
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in a study, the data you collect is number of walk buttons that work in new york city. what type of data is this? qualitative (categorical) quantitative - discrete quantitative - continuous
In a study, the data you collect is number of walk buttons that work in New York city, which is discrete type of data.
We know that,
The data which is in numeric form is called Quantitative data.
Example: Weight, Marks, etc.
The data which we can't count is known as Qualitative data.
Example: Smoking, Non- Smoking, etc.
Quantitative data can be divided into two parts:
- Continuous
- Discrete
The data which we can count is known as the Discrete data . It includes the natural numbers only.
Example: Number of apples, Number of senior citizens in a particular area, etc.
The data which we can't count is known as Continuous data . Example: Height, Weight, etc.
In this question, the data you collect is number of walk buttons that work in New York city. This is discrete type of date.
Therefore, in a study, the data you collect is number of walk buttons that work in New York city, which is discrete type of data.
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use the given values to complete the table create quantities proportional to each other and graph them what's the answer?
Answer:
u need to make a more cleat picture and make it straight please so i can answer
Step-by-step explanation:
Geologic time is divided into units based upon evidence from
Answer:
Fossils
Step-by-step explanation:
Hope this helps.
Use the equation below to answer correctly fill in the blanks.
y = 3x + 2
Since linear lines are represented by the equation y = mx + b, I know that the slope (m) is
. The b value is
. This means the line is
3 to each figure when the starting value is
.
Answer:
this is sure confusing to me
In 2016, a school started its own aquarium with n’2 fish. In 2021, there were n² fish in the same aquarium. There were 81 fish in 2021. How many fish were there in 2016?
Show your work
There were 9 fishes in 2016.
How to calculate the value?From the information, the school started its own aquarium with n fish and in 2021, there were n² fish in the same aquarium, there were 81 fish in 2021.
Therefore, the fish in 2016 will be:
n² = 18
Square root both sides
n = ✓81
n = 9
Therefore, there are 9 fishes in 2016.
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How do make a pbandj.
Answer:
Bread, Peanut Butter and jelly
Step-by-step explanation:
Take the bread lay it out grab a spoon and smooth the ingredients on the sandwich bread.
What is the value of the expression below when y=7 y^2 +4y+3
Answer:
I believe that the value of the exprexpression is 80.
Step-by-step explanation:
Substitute 7 for every y variable.
y^2 + 4y + 3=
7^2 + 4(7) + 3=
49 + 28 + 3=
80
the length of a rectangle is twice as long as he width. the perimetter of the rectangle is 72 in. what tare thte length and width of this rectangle
For the given rectangle, having perimeter = 72, the length of the rectangle will be 12 cm and breadth will be 24 cm
What is the perimeter of rectangle?The overall length of the outline determines a shape's perimeter in two dimensions. We sum the lengths of all four corners of a rectangle to determine its perimeter.
Since the opposing sides of a rectangle are always equal, we must determine the length and breadth of the rectangle in order to determine its perimeter. The rectangle's perimeter may be expressed as the product of its length and breadth times two. As a linear measurement, the perimeter can be expressed in meters, centimeters, inches, feet, etc.
Given,
perimeter = 72
let us assume length = x
The breadth will thus be = 2x.
Now that these numbers have been plugged in, we may solve the equation for x.
perimeter of rectangle = 2 (L + B)
72 = 2 (x + 2x)
72 = 2 (3x)
72 = 6x
x = 72/6
x = 12
2x = 24
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Kerry paid $8 for his admission ticket to the fair and bought 14 ride tickets.
He spent a total of $43 on admission and ride tickets. Write and solve an
equation to find the cost of one ride ticket. Put the cost of one ticket in the
answer space.
Answer: answer is 4 multiplied by eleven minus one is fourty three
Step-by-step explanation:
Evaluate ab 0.5b when a = 1 and b = 5.
Answer:
Step-by-step explanation:
Calculate the formula weights.
mass of
1
mole of
a
b
⋅
(
0.5
b
)
=
0
g
I need help with this
Answer:
7×7=7×(5+2)
=(5×7)+(7×2)
=35+14
=49
Answer:
Step-by-step explanation:
7x7=7(5+2)
=
Logan is a salesperson who sells computers at an electronic store. He paid a 1.25 commission for every sale he makes and he also make a guaranteed base pay of $80 each day. Write an equation for p in terms of x representing Longan’s total pay on a day on which he sells x computer
Answer: Here is ur answer
p=1.25x + 80
p is the pay and the 1.25 depends on how much computers he sells but he gets at least 80$ for his paycheck
Step-by-step explanation: i really really hope this helps lmk if im wrong tho have a good day (:
3x, 4x-2 solve for x
Answer: x=2
Step-by-step explanation:
3x=4x-2
3x-4x=4x-4x-2
-x=-2
x=2
Jean makes a 15% commission on any clothing that she sells. Jean sold $50.00 worth of clothes to a customer. How much was her commission?
Answer:
$7.50
Step-by-step explanation:
15% of $50 is 7.50, so she or he made $7.50 from that piece of clothing
Evaluate the expression [8(4)-4^2]+7(4)
Answer:
44
Step-by-step explanation:
big brain
Solve the following system of equations graphically. Select the graph that shows the correct solution of the system.
x + y = 2
x = 1
Answer:
First one
Step-by-step explanation:
rearrange x + y = 2 in the form y = mx + c
y = -1x + 2
means gradient is -1 and y-intercept is 2. such line is shown in the first graph
see where x = 1 and draw a straight line. Such line is also only shown in the first graph.
it should be the first graph
Ok Ik yall might see me again, but I really need help on this question
Answer:
-2/9
Step-by-step explanation:
[tex]-1/6(3-15(1/3)^2 )[/tex]
[tex]-1/6(3-15(1/9))[/tex]
[tex]-1/6(3- (15/9))[/tex]
[tex]-1/6(4/3)[/tex]
[tex]-4/18[/tex]
[tex]-2/9[/tex]
The given equation is,
→ -1/6 × [3 - 15(1/3)²]
Then the solution will be,
→ -1/6 × [3 - 15(1/3)²]
→ -1/6 × [3 - 15(1/9)]
→ -1/6 × [3 - 15/9]
→ -1/6 × (27 - 15)/9
→ (-1/6) × (12/9)
→ -12/54 = -2/9
Hence, the answer is -2/9.
Joseph had the following scores for a four-day tournament. day: 1, 2, 3, 4 score : -1 ,2, -2, -3 what was his total score for the tournament? write your answer as an integer.
The total score of Joseph for four days of the tournament is -4 .
Joseph had the following scores for a four-day tournament,
For the first day i.e., day 1 of the tournament the total score is -1 . For the second day i.e., day 2 of the tournament the total score is 2 . For the third day i.e., day 3 of the tournament the total score is -2 . For the fourth day i.e., day 2 of the tournament the total score is -3 .
To calculate the total score of four days of the tournament we need to add the score of first, second, third and fourth day.
The total score of four days of the tournament = ( -1 ) + ( 2 ) + ( -2 ) + ( -3 )
The total score of four days of the tournament = -4
The total score of Joseph for four days of the tournament is -4 .
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Is there any value(s) of the domain of 2 2=8 that passes the vertical line test?
The value of domain that will pass the vertical line test is ±2√2.
What is a domain?The collection of inputs a function can accept is referred to as the domain of the function in mathematics. [tex]dom(f)[/tex] is a common way to refer to it, with f standing for the function.
To be more specific, the domain of f is X when the function [tex]f:X--Y[/tex] is specified. The domain of a function is not a characteristic of it, but rather an element of the definition in contemporary mathematical terminology.
The function f can be represented as a graph in the Cartesian coordinate system in the particular case where X and Y are both subsets of. A projection of the function's graph onto the graph's x-axis in this instance serves as the domain's representation.
Explanation:
Finding the domain,
[tex]x^2+ y^2[/tex] = 8
[tex]\sqrt{x^2} + \sqrt{y^2}[/tex] = √8
x + y = ±2√2
So, the domain is ±2√2.
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yolanda spends 8 2⁄3 hours per month playing soccer. approximately how many hours does she play soccer in a year? (there are twelve months in a year.)
The total time she spends playing soccer in a year is 104 hours, which is calculated using the concept of fraction and arithmetic operations.
What is a fraction?
Any numerical number which does not represent the entire quantity is called a fraction. It depicts a part or portion of something. It is generally written in the form of numerator by denominator.
Calculation of the total time Yolanda spends playing soccer
Given that Yolanda plays soccer for 8 ⅔ hours in a month
Firstly, convert the hours in mixed fraction to improper fraction i.e. 8 ⅔ = (8 × 3 + 2) / 3
= 26 / 3
Now, we need to calculate the no. of hours she played in a year, which is done by multiplying the obtained improper fraction with 12
i.e. (26 / 3) × 12
= 104 hours
Hence, Yolanda spends 104 hours a year playing soccer.
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