The circle's radius is the same as the radius of the circle whose equation is x2 + y2 = 9.
What is the equation of circle?A circle's standard equation is written as:
x² + y² + 2gx + 2fy + C = 0
The radius of the center is (-g, -f) and radius = √g² + √f² - C
Given a circle with the equation,
x² + y² - 2x - 8 = 0
Find the circle's center.
2gx = -2x
2g = -2
g = -1
Likewise, 2fy = 0.
f = 0
(-(-1), 0) = Centre (1, 0)
This demonstrates that the circle's center is on the x-axis.
r = radius
= √g² + √f² - C
By substituting,
radius = √1² + 0² - (-8)
=√9
= 3 units radius
The circle's radius is three units.
The radius of the circle x² + y² = 9 is written as:
r² = 9
radius = 3 units
As a result, the radius of this circle equals the radius of the circle whose equation is x² + y² = 9.
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A diver starts out at 426 feet below the surface (or -426 feet). She then swims upward 212 feet. Use a signed number to represent the diver's current depth
Step-by-step explanation:
this is a college question ?
oh, my dear ...
we start at -426 ft.
swimming upwards reduces depth by adding hight.
so,
-426 + 212 = -214 ft
basically the same method is used as if we would subtract 212 from 426.
so, the diver is currently at -214 ft (214 ft below the surface).
Jane's family divided up their garden so that 2/3 of garden will have vegetables. Jane and her sister will plant2/3 of the vegetable portion of the garden. How much will the sisters plant?
3/2 part of the garden is planted by both the sisters.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given,
Jane's family divided up their garden so that 2/3 of garden will have vegetables.
Jane and her sister will plant2/3 of the vegetable portion of the garden
2/3 is the vegetable portion
In this vegetable portion 2/3 part is of the vegetable portion of the garden
3/2/2/3
3/2×3/2
6/4
3/2
Hence, 3/2 part of the garden is planted by both the sisters.
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fill in the blank so that the equation is a prefect square trinomial
John drew a triangle with side lengths of 5, 12 and 13. His friend, Bryan, looked at it and asked John if it is a right triangle. John’s response was yes. Explain or show how John can prove to Bryan that the triangle is a right triangle
It's a right angle as 13² is the addition of 5² and 12².
How to prove the right angle?A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly known as a rectangled triangle, is a triangle with one right angle, i.e. two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.
In this case, the values given are 5, 12 and 13. This will be illustrated thus:
5² + 12² = 13²
25 + 144 = 169
169 = 169
This was done based on Pythagoras theorem.
Therefore, it's a right angle.
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Please help ASAP I don;t understand it
Answer:
the points that will fall on a line where the constant of proportionality is k are A) (6,8) and B) (3,2).
Step-by-step explanation:
A point (x,y) falls on a line where the constant of proportionality is k if y is equal to k times x. In other words, the equation for the line is y = kx.
Given this, we can determine which of the given points fall on a line where the constant of proportionality is k by evaluating whether the y-coordinate of each point is equal to k times the x-coordinate.
For example, if k = 2, then the point (6,8) falls on the line y = 2x because 8 is equal to 2 times 6. Similarly, the point (3,2) falls on the line y = 2x because 2 is equal to 2 times 3.
On the other hand, the point (6,4) does not fall on the line y = 2x because 4 is not equal to 2 times 6.
Therefore, the points that will fall on a line where the constant of proportionality is k are A) (6,8) and B) (3,2).
Note that if k is not specified, then any of the given points could potentially fall on a line where the constant of proportionality is k, depending on the value of k.
Please help me on math very easy graphing! thank you!! due soon
Linear regression is a system of plotted points which shows a relationship between two given variables. The required linear equation is: y = 4x.
A graph is a plotted coordinate on a Cartesian plane which shows the relationship between two variables. A system of plotted points in relations to variables that shows a linear relationship is termed linear regression.
In a linear regression, the plotted points can be described by an equation:
y = bx + c
where: y is the dependent variable
x is the independent variable
b is the slope of the graph
c is the intercept
Therefore, considering the given question;
the slope of the graph = [tex]\frac{change in y}{change in x}[/tex]
= [tex]\frac{12 - 4}{3 - 1}[/tex]
= [tex]\frac{8}{2}[/tex]
slope of the graph = 4
While there is no intercept, thus intercept is zero.
Therefore, the required equation that shows the relationship between liters of water and number of minutes is:
y = 4x
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b) On the grid draw the graph of x + y = 6
for values of x between -2 and 3.
Answer:
x=1 y=6
Step-by-step explanation:
???
Directions: construct equations for the following and evaluate for X .
The value of x is 13 and value of x in second question is 28, in the angle of line. The angle between a line's inclination and the x-axis's positive direction is known as the inclination.
How do you calculate inclination?The angle between a line's inclination and the x-positive axis's direction is known as the inclination. This angle's value ranges from 0° to 180°. It is measured counterclockwise around the positive x-axis direction. The slope of a line is the tangent of the angle of inclination if the inclination angle is known. Take the tangent of the angle produced between the line and the x-axis to get the degree of inclination.Angle B, which is the opposite of angle A and measures 100 degrees, will also be 100 degrees. This indicates that the sum of the two angles is 200 degrees.From first fig :
26° = 2x °
x = 26 / 2 = 13
Second fig :
134° = 4x + 22
x = 134 - 22 / 4 = 28
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HELPPPP!!! 30 POINTSSSSSS!!!!!!
Find the line of best fit for the set of data:
x y
-2 2.9
-3.5 2
1.4 4.8
-4.2 1.5
0 4
2.8 6
-1.5 3.5
A. y = .613x + 4.142
B. y = -.613x - 4.142
C. y = -.613x + 4.142
D. y = .613x - 4.142
Answer:
[tex]\boxed{\tt A. \;y = .613x + 4.142}[/tex]
Step-by-step explanation:
Equation: (y-y_1)=y_2-y_1/x_2-x_1 (x-x_1)
Here,
[tex]\tt (x_1,y_1):(-2,2.9)[/tex]
[tex]\tt (x_2,y_2): (-3.5,2)[/tex]
[tex]\tt y-2.9=\cfrac{(2-2.9)}{(-3-5-(-2))} (x-(-2))[/tex]
[tex]\tt y-2.9=\cfrac{-0.9}{-1.5} (x+2)[/tex]
[tex]\tt y-2.9=0.6(x+2)[/tex]
[tex]\tt y-2.9=0.6x+1.2[/tex]
[tex]\tt y=.613x+4.142[/tex]
___________________
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Have a nice day!
- 4y + 11 = -3(2y + 1)
Answer: y=-7
Step-by-step explanation:
Answer: y=-7
Step-by-step explanation:
K
Problem Solving
X 4.3.PS-7
Simplify the expression.
-2.6f+0.2f-15-9
-2.6f+0.2f-15-9=
(Simplify your answer. Use integers or decimals for any numbers in the
Answer:
(23x+4.2)
Step-by-step explanation:
Andrea's record label released her new album. Andrea wants to know when she has sales of at least $20,000 per week. She uses the related equation below to determine when sales will be at least this amount, where t represents time in weeks.
please finish the other half
Answer:
10 ≤ t ≤ 20 or t ∈ [10; 20]----------------------------
The other half is:
t - 15 ≥ - 5t ≥ - 5 + 15t ≥ 10The answer, considering both halves, is:
10 ≤ t ≤ 20or
t ∈ [10; 20]Answer:
[tex]10 \leq t \leq 20[/tex]
Step-by-step explanation:
Given absolute value inequality:
[tex]1000(-2|t-15|+30) \geq 20000[/tex]
Isolate the absolute value on one side of the equation:
[tex]\implies \dfrac{1000-2|t-15|+30)}{1000} \geq \dfrac{20000}{1000}[/tex]
[tex]\implies -2|t-15|+30 \geq 20[/tex]
[tex]\implies -2|t-15|+30-30 \geq 20-30[/tex]
[tex]\implies -2|t-15|\geq -10[/tex]
[tex]\implies \dfrac{-2|t-15|}{-2}\geq \dfrac{-10}{-2}[/tex]
[tex]\implies |t-15|\leq 5[/tex]
[tex]\textsf{Apply absolute rule:\quad {If} $|u| \leq a, \;a > 0$ \;then\; $-a \leq u \leq a$}[/tex]
[tex]\implies -5 \leq t-15\leq 5[/tex]
Solve both equations:
[tex]\begin{aligned}\underline{\sf Equation\;1} && \underline{\sf Equation\;2}\\t-15 &\geq -5 \quad & t-15& \leq 5\\t-15+15& \geq-5+15 &\qquad t-15+15& \leq 5+15\\t&\geq10 & t &\leq20\end{aligned}[/tex]
Merge the overlapping intervals:
[tex]10 \leq t \leq 20[/tex]
What is the solution to the division problem below? (You can use long division or synthetic division.)
(2x2 + 7x-15) - (x+ 5)
A cookie recipe calls for 4 cups of flour for every 1 cup of sugar. If you want to make multiple batches of the cookies and you use 8 cups of sugar, how much flour will you use?
Answer:
8x4=32
Step-by-step explanation:
I hope I helped you
Write the following equation in slope-intercept form and identify the slope and y-intercept.
6x - 4y = 11
Answer:
Step-by-step explanation:
This in standard form (Ax + By = C.) In order to make this slope-intercept form, you need to isolate y.
y = -1.5x + 2.75
y=mx + b is slope intercept, where m is the slope and b is the y-intercept.
In this case, -1.5 is the slope and 2.75 is the y-intercept.
Hope this helps!!
Can somebody help asap I need the steps as well !!!
The total addition of numbers is, 53975687481.
What is addition of numbers?
The other three fundamental arithmetic operations are subtraction, multiplication, and division. Addition is one of these four operations. The total sum or value obtained by adding two whole numbers is the result of the addition.
For the given addition first add the digits on 1st place.
7 + 7 + 7 + 7 + 2 + 2 + 2 + 1 + 8 + 7 + 1 = 51
Take 1 as it is and add 5 on the 10th place numbers.
Now add 10th place numbers,
6 + 6 + 8 + 8 + 2 + 3 + 4 + 4 + 6 + 6 + 5 = 58
Take 8 as it is and add 5 to the 100th place numbers.
Now, 9 + 9 + 9 + 1 + 2 + 4 + 4 + 0 + 7 + 4 + 5= 54
Take 4 as it is and add 5 to the 1000th place numbers.
Now, 4 + 4 + 4 + 7 + 6 + 7 + 7 + 0 + 1 + 2 + 5 = 47
Take 7 as it is and add 4 to the next addition.
Now, 9 + 6 + 7 + 4 + 8 + 3 + 1 + 2 + 4 + 4 = 48
Take 8 as it is and add 4 to the next addition.
Now, 8 + 7 + 7 + 9 + 7 + 2 + 2 + 4 = 46
Take 6 as it is and add 4 to the next addition.
Now, 7 + 6 + 6 + 2 + 6 + 1 + 3 + 4 = 35
Take 5 as it is and add 3 to the next addition.
Now, 4 + 9 + 4 + 3 + 4+ 3 = 27
Take 7 as it is and add 2 to the next addition.
Now, 7 + 4 + 2 + 4 + 2= 19
Take 9 as it is and add 1 to the next addition.
Now, 9 + 3 + 1 = 13
Take 3 as it is and add 1 to the next number.
4 + 1 = 5.
Now take the last numbers one by one from step by step.
⇒ 53975687481
Hence, the total addition of numbers is, 53975687481.
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What is the value of x in the figure
shown?
37°
y
(3x + 1)
Answer:
x=4
Step-by-step explanation:
x=4 because when you have 3x+2=14 Subtract 2 from both sides. Then 3x+2−2=14−23x=12. Divide both sides by 3.3x3=123
The value of x in the figure having 3 angles on a line as shown in the image attached below is 28.
The angle is formed by two rays and a common point.
To calculate the value of x using the diagram attached below:
∠AOC+∠COD+∠BOD = 180° because the sum of all the angles on a line is 180°
On substituting the values from the figure,
∠AOC=3x-7
∠COD=55
∠BOD=x+20
∠AOC+∠COD+∠BOD =3x-7+55+x+20
3x-7+55+x+20=180
4x+68=180
4x=112
x=28
Thus, the value of x is 28 for the figure attached below.
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A contractor bought 6.4ft^2 of sheet metal. has used 2.1ft^2 so far and has $129 worth of sheet metal remaining. The equation 6.4x - 2.1x = 129 represents how much sheet metal is remaining and the cost of the remaining amount. How much does sheet metal cost per square foot?
Answer:
30$ per ft^2
Step-by-step explanation:
6.4x-2.1x=129
4.3x=129
x=30
:]
A family buys a studio apartment for $200,000 . They pay a down payment of $20,000.
a. Their down payment is what percent of the purchase price?
b. What percent of the purchase price would an $80,000 down payment be?
Answer:hope i helped A. 20% B.45%
A= 40,000/40,000/200000=.2 Or 20%b. 90,000/200000=.45
Step-by-step explanation:
CAN SOMEONE HELP WITH THIS QUESTION?✨
a) The exponential function that models the population in t years after 2000 is of: P(t) = 14300(1.06)^t.
b) The estimate for the population in 2008 is of: 22792.
How to define the exponential function?Considering it's standard format, the increasing exponential function is defined as follows:
P(t) = P(0)(1 + r)^t.
In which the parameters of the function are defined as follows:
P(0) is the population in the reference year of 2000.r is the growth rate, as a decimal.Hence the values of these parameters are given as follows:
P(0) = 14300, r = 0.06.
Thus the function is given by:
P(t) = 14300(1.06)^t.
2008 is eight years after 2000, thus the estimate is P(8), which is obtained as follows:
P(8) = 14300 x (1.06)^8 = 22792.
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PLEASE HELP ASAP!!! Will IMMEDIATELY give Brainliest to the correct answer!! 100 pt question!!
The function f(x)=∣x−3∣ can be used to determine how far a number x is away from the number 3 on the number line. Find and interpret the given function values and determine an appropriate domain for the function.
Answer:
The function f(x) = |x - 3| can be used to determine how far a number x is away from the number 3 on the number line. To find the function value for a given x, we first need to subtract 3 from x and then take the absolute value of the result. For example, if x = 5, then the function value would be f(5) = |5 - 3| = |2| = 2.
The domain of the function is the set of all possible values of x that we can plug into the function to get a real number result. In this case, the function will work for any real number value of x, so the domain of the function is the set of all real numbers, which can be written as:
Domain: (-∞, ∞)
In other words, the function f(x) = |x - 3| can be used to determine how far any real number x is away from the number 3 on the number line.
Where, if anywhere, does h(x) = m(x) when h(x) = (x+2)^2-9 and m(x) = x-10
Answer:
Where, if anywhere, does h(x) = m(x) when h(x) = (x+2)^2-9 and m(x) = x-10
wut do i have to find
Step-by-step explanation:
Is the following statement linear or exponential?
Lalo's hair is also known to grow rapidly. It began at a length of 6 in and grew at a constant rate of 1 in per month. HELP PLEASE Nobody is helping me :(
Answer:
Step-by-step explanation:
exponential
What are the zeros of this function?
Answer:
B. x = 0 and x = 5
Step-by-step explanation:
The zeros of this function are x = 0 and x=5
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Use the information to answer questions 8-10.
The time in minutes a factory needs to make a cell phone parts in a single day is modeled by th
inequality y-0.0005² ++20, for the domain 0 ≤ ≤ 1000.
8. What does the ordered pair (200, 100) represent?
Type a response
4
the longest it will take the factory to make 600 cell phone parts?
Since y<-0.0005x^2+x+20 and y represents the time in minutes needed to make x cell phone parts, the longest it will take the factory to make 600 cell phone parts will be y=-0.0005(600)^2+600+20
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.
A number is a solution to an inequality in x if it can be used to replace x with a statement that is true. Therefore, while 8 is not a solution for example 1, 4, it is. The collection of all solutions makes up the solution set for an inequality.
Wealth inequality, treatment and responsibility disparity, political inequality, life inequality, and membership inequality are the five systems or sorts of social inequality.
In mathematics, larger than symbol (>), less than symbol (), less than or equal to symbol (), and not equal to symbol () are the five inequality symbols.
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a researcher obtained a random sample of 100 smokers and a random sample of 100 non smokers. after interviewing all 200 participants in the study, the researcher compared the rate of depression among the smokers with the rate of depression among nonsmokers
observational study
Based on the study, the researcher may develop a hypothesis that smoking is associated with an increased risk of depression.
What is Hypothesis?An explanation that is put up for a phenomena or a group of facts is called a hypothesis. It is a speculative explanation that needs more testing and improvement because it is supported only by a small body of data. A hypothesis is not a tested theory, but rather a point of departure for more research. A hypothesis is examined in scientific study by testing and observationit. The purpose of hypothesis testing is to evaluate the likelihood that the suggested explanation is accurate and to spot any discrepancies or holes in the available data. The act of testing and improving hypotheses is a crucial component of the scientific method since it ensures that scientific ideas are supported by reliable data.
How to solve?
This hypothesis can then be tested through further research, such as conducting a larger study with more participants, or conducting experiments to evaluate the potential mechanisms by which smoking may affect the development of depression.
The researcher may also use statistical methods to analyze the data collected from the study, in order to determine the significance of the relationship between smoking and depression.
If the hypothesis is supported by the evidence, the researcher may conclude that smoking is a risk factor for depression, and may recommend interventions or preventative measures to reduce the risk of depression among smokers.
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to create a pivottable layout, you can drag fields from the field list to an area box in the pivottable fields pane
a. true
b. false
Yes , we can drag fields from the field list to an area box in the pivot table fields pane in order to create a pivot table. Hence , true.
The four sections of the pivot table
Report FilterColumn LabelsRow LabelsValuesare located at the bottom of the PivotTable Field List window.
The fields will appear in the corresponding region of the worksheet's pivot table layout when you drag them into these locations.
Only the fields included in the PivotTable Field List can be moved in Excel 2007. If you try to drag the Promo field onto the pivot table in the screen photo below, the cursor displays an X. The drag-and-drop function is broken.
You can alter a setting in the pivot table options if you'd like to drag the pivot fields onto the worksheet layout.
To access the PivotTable Options menu, right-click a cell in the pivot table.Put a checkmark next to Classic PivotTable Layout on the Display tab.PivotDrag02To close the PivotTable Options dialogue box, click OK.To learn more about pivot table
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The population of Greenville was 4,870 people. Six years later, the population had
grown to 5,080 people. What was the average rate of change in Greenville's
population for this six-year period?
The average rate of change in Greenville's population for this six-year period is 35 person per year
What's the math rate?
A rate is a unique ratio where the two words are expressed in several units. For instance, the price is 69 for 12 ounces if a 12-ounce can of maize costs 69. This is not a proportion of two comparable units, like shirts. Cents and ounces are the two dissimilar units in this ratio.
Given that:
Greenville population = 4,870
Greenville population after 6 years = 5,080
Difference of population = 5080 - 4870 = 210
Average rate = Population / Years = 210/6 = 35 person per year
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Find the degrees of freedom if N is 12.
The degrees of freedom is [tex]12N[/tex]
What is degrees of freedom?
Degrees of freedom refers to the maximum number of logically independent values, which are values that have the freedom to vary, in the data sample. Degrees of freedom is calculated by subtracting one from the number of items within the data sample.
[tex]\text { Least Common Multiplier of } N, 12: 12 N[/tex]
Find Least Common Multiplier of [tex]$N, 12$[/tex]
Lowest Common Multiplier [tex](LCM)[/tex]
The LCM of [tex]$a, b$[/tex] is the smallest multiplier that is divisible by both [tex]$a$[/tex] and[tex]$b$[/tex]
Factor 12
[tex]$2^2 \cdot 3$[/tex]
Multiply each factor with the highest power:
[tex]12 \mathrm{~N}[/tex]
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Find all angles, 0°≤θ≤360° that solve the following equation.
sin θ=-1
The solution for the given equation is, θ = 270°.
What is solving an equation?
Finding an equation's solutions, or the values that satisfy the condition stated by the equation, is known as solving an equation in mathematics. Solutions typically consist of two expressions connected by an equals sign. One or more variables are marked as unknowns in order to find a solution.
Consider, the given inequality
sinθ = -1
The general solution for sinθ = -1 is
θ = 270° + 360°n
But the condition is, 0° ≤ θ ≤ 360°
Hence, the solution for the given equation is, θ = 270°.
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