Answers
Answer:
Part (a)Equation of a circle
\((x-a)^2+(y-b)^2=r^2\)
where:
(a, b) is the center r is the radiusGiven equation: \(x^2+y^2=6.25\)
Comparing the given equation with the general equation of a circle, the given equation is a circle with:
center = (0, 0)radius = \(\sqrt{6.25}=2.5\)To draw the circle, place the point of a compass on the origin. Make the width of the compass 2.5 units, then draw a circle about the origin.
Part (b)Given equation: \(x+y=1.5\)
Rearrange the given equation to make y the subject: \(y=-x+1.5\)
Find two points on the line:
\(x=-2 \implies -(-2)+1.5=3.5\implies (-2,3.5)\)
\(x=2 \implies -(2)+1.5\implies-0.5\implies (2,-0.5)\)
Plot the found points and draw a straight line through them.
The points of intersection of the circle and the straight line are the solutions to the equation.
To solve this algebraically, substitute \(y=-x+1.5\) into the equation of the circle to create a quadratic:
\(\implies x^2+(-x+1.5)^2=6.25\)
\(\implies x^2+x^2-3x+2.25=6.25\)
\(\implies 2x^2-3x-4=0\)
Now use the quadratic formula to solve for x:
\(x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0\)
\(\implies x=\dfrac{-(-3) \pm \sqrt{(-3)^2-4(2)(-4)}}{2(2)}\)
\(\implies x=\dfrac{3 \pm \sqrt{41}}{4}\)
To find the coordinates of the points of intersection, substitute the found values of x into \(y=-x+1.5\)
\(\implies y=-\left(\dfrac{3 + \sqrt{41}}{4}\right)+1.5=\dfrac{3-\sqrt{41}}{4}\)
\(\implies y=-\left(\dfrac{3 - \sqrt{41}}{4}\right)+1.5=\dfrac{3+\sqrt{41}}{4}\)
Therefore, the two points of intersection are:
\(\left(\dfrac{3 + \sqrt{41}}{4},\dfrac{3-\sqrt{41}}{4}\right) \textsf{ and }\left(\dfrac{3 - \sqrt{41}}{4},\dfrac{3+\sqrt{41}}{4}\right)\)
Or as decimals to 2 d.p.:
(2.35, -0.85) and (-0.85, 2.35)
Related Questions
What is the equation of the line that passes through (-3, 4) and (3, -2)?
y = - x - 1
y = x + 7
y = x - 1
y = - x + 1
Answers
Answer:
y = -x +1
Step-by-step explanation:
p1 (-3,4)
p2 ( 3, -2)
line equation y = mx + b
The slope m equals
\( \frac{y2 - 21}{x2 - x1} \)
\( \frac{ - 2 - 4}{3 - - 3} = \frac{ - 6}{6} = - 1\)
y = - x + b
from any point
-2 = -3 + b
b = 1
line equation = y = -x +1
Hope this helps
How many whole numbers are there
between 181 and 200
Answers
Answer:
19
Step-by-step explanation:
200−181 = 19
There are 19 whole numbers between 181 and 200.
Please answer this question!
Answers
Answer: 1/4
Step-by-step explanation: 1/2 turned into decimal form is 0.5 but halved equals 0.25 which in fraction form is 1/4
The graph shows the distance a skydiver falls over time once she reaches maximum speed.
Enter values to complete each statement below based on the graph.
A graph titled distance a skydiver falls has time (seconds) on the x-axis, and distance (feet) on the y-axis. A line goes through (0, 0) and (1.5, 300).
CLEAR CHECK
In one second, a skydiver falls
feet.
The unit rate is
feet per second
Answers
The unit rate for the skydiver falls is 200 feet per second.
What is speed?The distance that an object travels in relation to the amount of time it takes to do so can be used to define speed. In other words, it is a measurement of an object's motion's speed without direction Velocities are what we get when speed and direction are combined.
Given the graph shows the distance a skydiver falls over time,
and graph titled distance a skydiver falls has time (seconds) on the x-axis, and distance (feet) on the y-axis.
The line passes from (0, 0) and (1.5, 300)
the point (1.5, 300) says that a skydiver covers 300 feet in 1.5 seconds
to find the unit rate we need to calculate the speed,
speed = distance/time
distance covered = 300 feet
time taken = 1.5 seconds
speed = 300/1.5
speed = 200 feet per second
Hence the unit rate is 200 feet per second.
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If you use Desmos and know the answer to this question, please help me.
Answers
Answer:
Step-by-step explanation:
If you look at Desmos you will see that when you put in the (x,y) coordinates in the x,y positions in your inequality that lines your plot and the shaded areas are different. If you put in each of the coordinates in the inequality you will see all the differenences between the shaded and the lines. I would do that in Desmos and you should be able to figure it out. There is an example picture below.
I hope this helps!
If you have any questions or need any help, please ask.
Please someone help meeee
Answers
Answer:
2431.01
Step-by-step explanation:
Solve.
4x - 8x = 12 – 7x
Answers
Answer:
x = 4
Step-by-step explanation:
4x - 8x = 12 - 7x
4x - 8x + 7x = 12
-4x + 7x = 12
3x = 12
x = 12/3
x = 4
Answer:
Step-by-step explanation:
4x -8x = 12 - 7x
-4x = 12 - 7x
3x = 12
x = 4
Part F What is the mean absolute deviation for Doctor A’s data set on glasses? What is the mean absolute deviation for Doctor B’s data set on glasses? Write a sentence comparing the variation of the two data sets using their mean absolute deviations.
Doctor A Doctor B
Corrective Lenses Glasses Contacts Corrective Lenses Glasses Contacts
745 643 102 763 651 112
726 634 92 736 625 111
769 670 99 735 622 113
765 658 107 759 624 135
756 636 120 748 631 117
742 624 118 756 621 135
757 641 116 765 653 112
748 655 93 761 647 114
770 649 121 768 646 122
738 629 109 761 646 115
Answers
There is more variability on glasses of doctor B's dataset than the glasses of doctor A's dataset
The doctors' mean absolute deviation on glassesThe dataset of doctor A is given as:
643 634 670 658 636 624 641 655 649 629
The dataset of doctor B is given as:
651 625 622 624 631 621 653 647 646 646
Using a statistical calculator, we have:
Doctor A
Doctor A: Mean Absolute Deviation (MAD) = 11.28Doctor B: Mean Absolute Deviation (MAD) = 12Hence, the mean absolute deviation is 11.28 for Doctor A’s and 12 for Doctor B’s data set on glasses
The variation of the two dataIn a dataset, the larger the mean absolute deviations value, the larger the variation.
By comparison, 12 is greater than 11.28
Hence, there is more variability on glasses of doctor B's dataset than the glasses of doctor A's dataset
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What is the diameter of a circle with a radius of 9.5 cm ?
Answers
Answer:
9.5(2) = 19 is the diameter
Step-by-step explanation:
Answer:
19 cm
Step-by-step explanation:
Diameter is twice the radius, thus 2 x 9.5 cm = 19 cm
5.
A number n is such that when it is divided by 27, 30, or 45, the remainder is alway
smallest value of n
Answers
Answer:
it's 273 ..
Step-by-step explanation:
the LCM of 27, 30 and 45 is 270.
adding up a 3 to it will give the smallest value of n. so 270 + 3 = 273.
umm .. hope it helps ?! fanks -
What is a scientific hypothesis? Explain the difference between a guess and a hypothesis. Why do scientists need a hypothesis?
Are there any scientific hypotheses that can’t be tested? If yes, what are potential questions that cannot be answered by science?
Answers
A scientific hypothesis is a proposed explanation or prediction based on limited evidence or prior knowledge, which is subject to further investigation and testing.
A guess is a speculative, unsupported statement without any logical basis, whereas a hypothesis is an educated assumption derived from existing knowledge, observations, or theories. Unlike a guess, a hypothesis is testable and can be supported or refuted by evidence gathered through scientific methods.
Scientists need a hypothesis to provide a framework for their research and guide their investigations. It helps them define the specific question they want to answer and provides a starting point for designing experiments or making observations. By formulating a hypothesis, scientists can systematically evaluate and analyze data, ultimately leading to a deeper understanding of the phenomenon under investigation.
There are indeed scientific hypotheses that cannot be directly tested or proven due to practical or ethical constraints. For example, hypotheses related to historical events that occurred in the distant past may not have accessible evidence for direct testing. Additionally, some questions related to consciousness, subjective experiences, or philosophical concepts may lie beyond the scope of scientific inquiry, as they may not be objectively measurable or observable.
While science has its limitations, it is a powerful tool for investigating and understanding the natural world. However, there are questions that fall outside the realm of scientific inquiry and require other methods of investigation, such as philosophical or ethical considerations.
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What are the two decisions that you can make from performing a hypothesis test?
Answers
The two decision while performing hypothesis, these are -
Reject the null hypothesisFail to reject the null hypothesis.What is hypothesis?an assertion on a population's makeup. Frequently, a population parameter is used to express it. A statistical hypothesis that is to be tested is known as a null hypothesis.
Alternative hypothesis: A hypothesis that differs from the null hypothesis.
In the scientific process, the hypothesis is developed prior to the completion of any relevant study, other than a brief background review.
These claims list certain factors as well as their suggested outcomes. Cavities arise as a result of the variable in this case, which is the sugar intake.
The decisions are -
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The major axis of the following ellipse
(z-5)²
(y-2)2
16
36
is the
+
axis of length
and the minor axis is the
with length
(
Answers
The x axis is major axis with length of major axis = 8 and y axis is minor axis with length of minor axis = 12
How to interpret the equation of an Ellipse?We are given the equation of the major axis of an ellipse as;
(x - 5)²/16 + (y - 2)²/36
Now, the general form of equation of an ellipse is expressed as;
x²/a² + y²/b²
where;
2a = length of major axis
2b = length of minor axis
Now, our equation can be rewritten as;
(x - 5)²/4² + (y - 2)²/6²
Comparing to our general ellipse equation, we can say that;
a = 4 and b = 6
2a = 2 * 4 = 8
2b = 2 * 6 = 12
Thus, x axis is major axis with length of major axis = 8 and y axis is minor axis with length of minor axis = 12
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Given f(x) = x^2 − 36, which statement is true?
Answers
As a result, the statements regarding the function f(x) =\(x^{2} -36\) are all correct.
What is a function?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
The formula f(x) = \(x^{2} -36\) can be used to support a number of claims.
Because the function is cubic, its graph is a parabola.
The curve rises because the x2 term's coefficient is positive.
The graph crosses the y-axis at y = -36 because the constant factor is equal to -36.
Setting f(x) = 0 and figuring out the value of x will reveal the function's roots:
\(x^{2} -36\\x^{2} = 36\)
x = ±6
Consequently, x = -6 and x = 6 are the function's bases.
Filling in the rectangle will reveal the vertex of the parabola:
f(x) =\(x^{2} -36\)
= (\(x^{2}\) - 36 + 81) - 81
= \((x-9)^{2}\) - 81
Therefore, the parabola's apex is (-9, -81).
The function is symmetric about the vertical line that passes through its apex.
Since the function's minimum value is -81 and its maximum value rises without limit as x approaches infinity in either direction, the range of the function is all real numbers greater than or equal to -36.
Consequently, the function f(x) = \(x^{2} -36\) fulfills all of the aforementioned criteria.
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Solve the equation. Check your answers. |2 x-3|=-1
Answers
There are no solutions to the equation |2x - 3| = -1.
The absolute value equation given is:
|2x - 3| = -1
Absolute values are always non-negative, so it is not possible for the absolute value of an expression to equal -1. Therefore, there are no solutions to this equation.
If we assume that the absolute value expression is positive, we can set it equal to the positive value on the right-hand side:
2x - 3 = 1
Adding 3 to both sides:
2x = 4
Dividing both sides by 2:
x = 2
However, upon checking this solution, we find that it does not satisfy the original equation:
|2(2) - 3| = |-1| = 1 ≠ -1
Therefore, there are no solutions to the equation |2x - 3| = -1.
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mention about angles of a triangle
Answers
if there is 10in on one side of a square and 10 in on the other side of a square what would be the perimeter
Answers
The perimeter of a square is given by the formula:
\(P=4l\)Where l is the side length of the square. This is because the square has 4 sides of the same length. Substitute l=10in to find the perimeter:
\(\begin{gathered} P=4l \\ \Rightarrow P=4(10in) \\ =40in \end{gathered}\)Therefore, the perimeter of the square is:
\(40in\)One of Carla's friends suggests that she survey only eighth-graders because they are the
oldest and probably know more about the election than younger students. Do you think
this suggestion creates a random sample? Explain.
Answers
Answer:
This example is not a random example due to the fact that it is only questioning the eighth-graders. Random sample means that the sample is chosen simply randomly and everyone has an equal opportunity to be apart of the sampling.
Step-by-step explanation:
Martin recorded the low temperatures at his house for one week. the temperatures are shown below -
-7, -3, 4, 1, -2, -8. 7
Approximately what was the average low temperature of the week?
Answers
Answer:
The average temp was 4
Step-by-step explanation:
In Round Robin scheduling assume that time quantum $\mathrm{Tq}=12$ units, and there are 7 active processes. What is the maximum waiting time for a process to get the next quantum?
56
72
64
84
Answers
The maximum waiting time for a process to get the next quantum in Round Robin scheduling with a time quantum of 12 units and 7 active processes is 72 units.
In Round Robin scheduling, each process is given a fixed time quantum to execute before being preempted and allowing the next process to run. The time quantum determines the maximum amount of time a process can execute before it is interrupted. In this case, the time quantum is 12 units.
Assuming there are 7 active processes, the maximum waiting time for a process to get the next quantum can be calculated by considering the worst-case scenario. In this scenario, each process gets a turn to execute once, and then the cycle repeats. Therefore, the maximum waiting time for a process to get the next quantum is equal to the time taken for all other processes to complete their turn and for the cycle to repeat.
Since there are 7 processes, each process will have to wait for 6 other processes to complete their turn before it can get the next quantum. The total waiting time for a process is then given by (6 * time quantum). Substituting the value of the time quantum as 12 units, we have 6 * 12 = 72 units.
Therefore, the maximum waiting time for a process to get the next quantum in this scenario is 72 units.
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find an equation of the curve that passes through the point (0, 1) and whose slope at (x, y) is 5xy. (note: start your answer with y
Answers
The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.
To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:
We have:
Point: (0, 1)
Slope: 5xy
We can start by integrating the slope function to find the equation of the curve:
∫(dy/dx) dx = ∫(5xy) dx
Integrating both sides:
∫dy = ∫(5xy) dx
Integrating with respect to y on the left side gives us:
y = ∫(5xy) dx
To solve this integral, we treat y as a constant and integrate with respect to x:
y = 5∫(xy) dx
Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:
y = 5 * (1/2) * x^2y + C
Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:
1 = 5 * (1/2) * (0)^2 * 1 + C
1 = C
Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:
y = 5 * (1/2) * x^2y + 1
Simplifying further, we have:
y = (5/2) * x^2y + 1
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The two-way table represents data from a survey asking teachers whether they teach English, math, or both.
Answers
The joint relative frequency is 21%.
What is the joint relative frequency?Joint relative frequency can be described as the ratio of the frequency of data in a certain category to the total number of data points in that category.
The joint relative frequency for teachers who teach math and not English = number of teachers who teach maths and not English / total number of teachers
(22 / 104) x 100 = 21%
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What is 18/20 simplified
Answers
Answer:
9/10
Step-by-step explanation:
Answer:
0.4 or 2/5
Step-by-step explanation:
How do you write 533,000, 327.5, and 0.0034 in scientific notation
Answers
Answer:
A: 5.33 x 10∧5 and B.3.4 × 10-3
Step-by-step explanation:
Answer:
533,000,327.5 and o.oo34
If you hit a ball with 5,000 newtons of force, how many miles per hour would it travel?
Answers
Answer:
900.1
Step-by-step explanation:
hope this helps!
Verify the property a x (b+c) =(a x b)+(a x c) by taking: a = -7, b = (2/5), c = (-3/7)
Answers
= -14/5 + 3
=1/5
What is the average rate of change of f(x) = −x^2+ 3x + 6 over the interval −3 ≤ x ≤ 3?
Answers
Answer:
the answer is -2/7 i hope this helps n srry if it dont help
Step-by-step explanation:
Which of the following coordinates are exactly 5 units from (2, -1)? Select all that apply.
(3, 4)
(5, 3)
(-2, 2)
(-3, -1)
20 Brainly points!
Answers
Answer:
-3-1
Step-by-step explanation:
Write an expression for which subtracting 5 from an expression would isolate the variable
Answers
An expression for which subtracting 5 from an expression would isolate the variable is -9x + 5 = x + 2
What are algebraic expressions?Algebraic expressions are described as expressions that consists of coefficients, terms, variables, factors and constants.
These expressions are also known to consist of arithmetic operators, which includes;
Floor divisionDivisionExponentiationAdditionMultiplicationSubtraction, etcFrom the information given, we have to subtract five from an expression to isolate the variable
Now, let's us the algebraic expression;
-9x + 5 = x + 2
Let's subtract 5 from both sides of the equation, we get;
-9x + 5 - 5 = x + 2 - 5
add and subtract the like terms
-9x + x = -3
-8x = -3
x = 3/8
Hence, the expression is -9x + 5 = x + 2
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What is 3 + 2 HELP then after add 3456 then subtract 45 and then divid 20
Answers
The simplify value of numeric expression, 3 + 2, after adding 3456 then subtracting 45 and then dividing by 20 is equals the 17.8.
We have an expression of numbers, 3 + 2 we have to apply some arithematic operations on it and determine the final simplfy value. Let the expression be x = 3 + 2, add 3456 in it
=> x = 3 + 2 + 3456
Substracts 45 from above expression
=> x = 3 + 2 + 3456 - 45
Dividing the above expression of x by 20
=>
\(\frac{ x } {20} = \frac{ 3 + 2 + 3456 - 45}{20}\)
\(= \frac{3416}{20}\)
= 17.8
Hence, required simplify value is 17.8.
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