Point P(1,7) is located on circle C. The center of circle Cis (-2, 3). What is the radius of the circle?
A
5
B
3
С
D6
Answer:
5 units
Step-by-step explanation:
Hi there!
Equation of a circle: \((x-h)^2+(y-k)^2=r^2\) where the circle is centered at \((h,k)\) and r is the radius
1) Plug in the center (-2,3)
\((x-(-2))^2+(y-3)^2=r^2\\(x+2)^2+(y-3)^2=r^2\)
2) Plug in the given point P(1,7) and solve for r
\((1+2)^2+(7-3)^2=r^2\\(3)^2+(4)^2=r^2\\9+16=r^2\\25=r^2\)
Take the square root of both sides
\(\sqrt{25} =\sqrt{r^2} \\5=r\)
Therefore, the radius of the circle is 5 units.
I hope this helps!
felicias bill at the restaurant was $19.She left a tip of %20. what was the tip amount rounded to the nearest 10?What was the total bill?
Fans of the X-Men movies have been debating on an online forum regarding which of the films is the best. To see what the overall opinion is, visitors to the site can rank the four films in order of preference. The results are shown in the preference schedule below.
Fans of X-Men movies have been debating the best X-Men movie on an online forum. To see what the overall opinion is, visitors to the site were able to rank the four films in order of preference.
The result of the preference schedule is essential in finding the best movie according to the majority's opinion.
It is important to note that the preference schedule shows that the best X-Men movie can be determined through visitors ranking the four films in order of preference.
To determine the best X-Men film, you can start by looking at the film that received the most first-place rankings. This film is likely to be the favorite among the voters. If there is a tie for the most first-place rankings, you can consider the film that received the most second-place rankings, and so on.
By analyzing the preference schedule and considering the rankings for each film, you can identify the film that received the highest overall ranking and declare it as the best X-Men film according to the preferences of the voters.
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may you please answer this question
Answer:
Step-by-step explanation:
Vertically opposite angles are congruent.
∠A = ∠C
∠A + ∠C = 254
∠A + ∠A = 254
2∠A = 254
∠A = 254/2
∠A = 127
Linear Pair: In two adjacent angles, if the non common arms are opposite rays, then they are called linear and they add up to 180
∠A + ∠B = 180 {linear pair}
127 + ∠B = 180
∠B = 180- 127
∠B = 53°
the city of covington is placing a statue in a triangular grassy area bounded by sidewalks on all 3 sides. if the city wants the statue to be an equal distance from all 3 sides of the grassy area, where should they place it?
To place the statue an equal distance from all three sides of the grassy area, the city should position it at the intersection of the perpendicular bisectors of the three sides.
Here's a step-by-step process to determine the placement:
Identify the three sides of the grassy area and locate their midpoints.
Construct the perpendicular bisectors of each side. A perpendicular bisector is a line that cuts a line segment into two equal parts at a right angle.
The point where the three perpendicular bisectors intersect is the desired location to place the statue. This point is equidistant from all three sides.
By placing the statue at this intersection point, it ensures that the distance from the statue to each side of the grassy area is equal.
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Please Help!!! I'll mark the first person to get it right brainliest!
Answer:
x=8
Step-by-step explanation:
First we know that 14x +1 and 11x-21 are supplementary angles because they add to 180 degrees. That is the given. Now we need to make an equation.
(14x+1) + (11x-21) = 180
Simplify the equation
25x -20 =180
Addition property of equality
25x =200
Division property of equality
x =8
Use power series operations to find the Taylor series at x=0 for the following function. xcos 2
3πx
The Taylor series for cosx is a commonly known series. What is the Taylor series at x=0 for cosx ? ∑ n=0
[infinity]
(Type an exact answer.) Use power series operations and the Taylor series at x=0 for cosx to find the Taylor series at x=0 for the given function. ∑ n=0
[infinity]
(Type an exact answer.)
The Taylor series at x=0 for the given function x * cos²((3πx)/2) is:
∑(n=0 to infinity) ∑(m=0 to infinity) (-1)^(n+m) * (x²ⁿ⁺¹) * ((((3π)/2)^(2n+2m)) / ((2n)!(2m)!))
Here, we have,
The Taylor series at x=0 for cos(x) is given by:
cos(x) = ∑(n=0 to infinity) (-1)ⁿ * (x²ⁿ)) / (2n)!
Now, let's find the Taylor series at x=0 for the given function x * cos²((3πx)/2):
To find the Taylor series for the given function, we'll use power series operations.
We'll substitute the Taylor series expansion for cos(x) into the given function and then perform the necessary operations.
Let's start with cos²((3πx)/2):
cos²((3πx)/2) = (cos((3πx)/2))²
= (∑(n=0 to infinity) (-1)ⁿ * (((3πx)/2)²ⁿ) / (2n)!)²
Expanding the square of the series, we get:
cos²((3πx)/2)
= (∑(n=0 to infinity) (-1)ⁿ * (((3πx)/2)²ⁿ) / (2n)!) * (∑(m=0 to infinity) (-1)^m * (((3πx)/2)^(2m)) / (2m)!)
Now, we'll multiply the x term to obtain the Taylor series for the given function:
x * cos²((3πx)/2) = x * (∑(n=0 to infinity) (-1)ⁿ * (((3πx)/2)²ⁿ) / (2n)!) * (∑(m=0 to infinity) (-1)^m * (((3πx)/2)^(2m)) / (2m)!)
Expanding the multiplication and rearranging the terms, we have:
x * cos²((3πx)/2) = ∑(n=0 to infinity) ∑(m=0 to infinity) (-1)^(n+m) * (x²ⁿ⁺¹) * ((((3π)/2)^(2n+2m)) / ((2n)!(2m)!))
Therefore, the Taylor series at x=0 for the given function x * cos²((3πx)/2) is:
∑(n=0 to infinity) ∑(m=0 to infinity) (-1)^(n+m) * (x²ⁿ⁺¹) * ((((3π)/2)^(2n+2m)) / ((2n)!(2m)!))
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In a recent election, 63% of all registered voters participated in voting. In a survey of 275 retired voters, 162 participated in voting. Which is higher, the population proportion who participated or the sample proportion from this survey?
The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).
To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.
The population proportion who participated in voting is given as 63% of all registered voters.
This means that out of every 100 registered voters, 63 participated in voting.
In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.
Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .
Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).
Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.
It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.
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A student says that the x-intercept of the graph of × + 2y =5 is the point (0,5). Is the student correct or incorrect? Explain your answer and show your work.
Will give brainliest!!
The student is incorrect, the actual x-intercept is (5, 0).
Is the student correct or incorrect?
Here we have the equation:
x + 2y = 5
The student says that the x-intercept is the point (0, 5).
So if you look at the point you already can see that the student is incorrect, this is because the x-intercept always must have a y-value of 0. (the graph only intercepts the x-axis when y = 0).
So the point (0, 5) can't be an x-intercept.
For the given function:
x +2y = 5
The x-intercept is given by:
x + 2*0 = 5
x = 5
So it is (5 , 0).
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4. When triangle ABC is reflected across line AB, the
image is triangle ABD. Why are segment AD and
segment AC congruent?
D
A. Congruent parts of congruent figures are corresponding.
B. Corresponding parts of congruent figures are congruent.
C. An isosceles triangle has a pair of congruent sides.
D. Segment AB is a perpendicular bisector of segment DC.
(From Unit 2, Lesson 1.)
B
C
Corresponding parts of congruent triangles are congruent.
What do you mean by congruency?
In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. Formally speaking, two sets of points are said to be congruent if—and only if—they can be changed into one another by an isometry, which is a combination of rigid movements like translation, rotation, and reflection. This indicates that one item may be exactly aligned with the other object by moving and reflecting it, but not by resizing it. So if we can cut out and then perfectly match up two separate plane figures on a sheet of paper, they are congruent. The paper may be turned over.
Corresponding parts of congruent triangles are congruent.
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Dave owns 15 shares of ABC Mining stock. On Monday, the value of
each share rose $2, but on Tuesday the value fell $5. What is the
change in the value of Dave's shares?
To travol tho
Write an expression to represent.
Answer:
15(2) + 15 (-5) . #45 drop
Step-by-step explanation:
Unit 2 logic and proof homework 3 conditional statements
By engaging in these exercises, students can develop a deeper understanding of conditional statements and logical reasoning, which are essential skills for further studies in mathematics and logic.
In Unit 2 of a logic and proof course, homework 3 focuses on conditional statements.
Conditional statements are fundamental concepts in logic and mathematics, representing logical implications between two statements.
They are typically expressed in "if-then" format, where the "if" part is the hypothesis and the "then" part is the conclusion.
The homework may involve tasks such as:
Identifying conditional statements: Students are given a set of statements and asked to identify which ones are conditional statements.
They need to recognize the "if-then" structure and correctly identify the hypothesis and conclusion.
Analyzing the truth value of conditional statements:
Students may be given conditional statements and asked to determine whether they are true or false.
They need to evaluate the hypothesis and conclusion to determine if the implication holds in each case.
Writing converse, inverse, and contrapositive statements:
Students may be required to manipulate given conditional statements to form their converse, inverse, and contrapositive statements.
This involves switching the positions of the hypothesis and conclusion or negating both parts.
Applying the laws of logic:
Students may need to apply logical laws, such as the Law of Detachment or the Law of Modus Tollens, to deduce conclusions based on conditional statements.
Constructing counterexamples:
Students may be asked to provide counterexamples to disprove statements that are falsely claimed to be universally true based on a given conditional statement.
They also help students develop critical thinking and problem-solving abilities, as they have to analyze and manipulate logical structures.
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helphelphelp pls i am failing
Answer:
A
Step-by-step explanation:
27 = -3x - 9 plssss helppp
Answer:
x = 1-2
Step-by-step explanation:
27 = - 3x - 9
36 = -3x
-12 = x
x = -12
Step-by-step explanation:
27+9=-3x
36=-3x
36 divided by -3=x
-12=x
There are 1800 students in a school. 53.5% of them are male. How many are female?
Answer:
Step-by-step explanation:
837 are females as 52.5 percent of 1800 equals 837.
Answer:
Females = 100 - percent of males = 100 - 53.5 = 46.5%
Number of females = 46.5/100 × 1800 = 837
Sam and Bryan meet at the gym. Sam travels 6 miles farther to the gym than Bryan. Three times the distance Bryan travels is 12
miles. If x represents the distance traveled by Bryan to the gym, which statements are true when determining the distance traveled by
each?
Answer:
x+6=y and 3x=12
Step-by-step explanation:
Let x be the distance traveled by Bryan and let y be the distance traveled by Sam then the first equation would be:
x+6=y (x plus 6 is equal to y, Bryan's distance plus 6 is equal to Sam's distance) and the second one is:
3x=12 (3 times x is 12, 3 times the distance travelled by Bryan is 12)
So our statements/equations are:
x+6=y and
3x=12 (we dont write this as x=4 as it asks us to give the statements we got from the information given, we only start simplifying once it tells us to solve)
PO
What is the slope of a line that goes through the following 2 points?
(-12,-5) (0, -8)
Answer:
-1/4
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-8-(-5))/(0-(-12))
m=(-8+5)/(0+12)
m=-3/12
simplify
m=-1/4
Please mark me as Brainliest if you're satisfied with the answer.
sydney needs to make exactly 8 dozen items for a bake sale
Answer: If Sydney needs to make exactly 8 dozen items for a bake sale, that means she needs to make a total of 8 x 12 = 96 items
How do you get the surface area of a square pyramid?
Answer:
see below
Step-by-step explanation:
You need to know the base a and height h.
then use formula
Area = a²+2a+√(a²/4+h²)
1. What is the slope of the line that passes through the points (-2, -3), and (5, 4)?
-1
3
1
-3
60 points if you give me the answer with an explanation, please!
Hi!
I can help you with joy!
We are given 2 points: (-2, 3) and (5, 4), so we can easily calculate the slope of this line using this formula:
\(\displaystyle\frac{y2-y1}{x2-x1}\)
\(\displaystyle\frac{4-(-3)}{5-(-2)}\)
\(\displaystyle\frac{4+3}{5+2}\)
\(\displaystyle\frac{7}{7}\)
\(1\) (Answer)
I hope it helps!
Ask if you have any queries.
~Misty~
\(\bf{GracefulTeen\)
Enjoy your day!
Simplify this expression.
–6w + (–8.3) + 1.5+ (–7w)
The simplified form of the expression -6w + (–8.3) + 1.5+ (–7w) is -13w - 6.8.
What is the simplified form of the expression?Given the expression in the question;
-6w + (–8.3) + 1.5+ (–7w)
To simplify, first remove the parenthesis
Note that;
- × + = -- × - = ++ × + = +-6w + × - 8.3 + 1.5 + × - 7w
-6w - 8.3 + 1.5 - 7w
Next collect and add like terms
-6w - 7w - 8.3 + 1.5
Add -6w and -7w
-13w - 8.3 + 1.5
Add -8.3 and 1.5
-13w - 6.8
Therefore, -13w - 6.8 is the simplified form.
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Given; f(x)=9x+5, find f^-1(x) then state whether f^-1(x) is a function.
Answer:
(1/9)x-5/9=y
Step-by-step explanation:
Y=9x+5
You first swap/interchange x and y
x=9y+5
Then solve for y
x/9-5/9=9y/9
Final answer:(1/9)x-5/9=y
Simply and write the answer with positive integral index
\(27^{3}\) × \(3^{-6}\)
Pls answer
Answer:
3³
Step-by-step explanation:
Using the rules of exponents
\(a^{m}\) × \(a^{n}\) ⇔ \(a^{(m+n)}\)
\((a^{m}) ^{n}\) = \(a^{mn}\)
Given
27³ × \(3^{-6}\)
Note that 27 = 3³ , thus
= (3³)³ × \(3^{-6}\)
= \(3^{9}\) × \(3^{-6}\)
= \(3^{(9-6)}\)
= 3³
what is the percent of the total variance that can be explained by the regression equation? (cma adapted)
The size and nature of the dataset, the choice of independent variables, and the assumptions underlying the model, should also be considered when interpreting \(R^2\) values.
The percent of the total variance that can be explained by the regression equation is known as the coefficient of determination, denoted as\(R^2.\)
It represents the proportion of the total variation in the dependent variable (Y) that is accounted for by the independent variable(s) (X) included in the regression model.
To calculate\(R^2\), you can follow these steps:
Obtain the sum of the squared differences between the actual and predicted values of the dependent variable (also known as the residual sum of squares, or RSS).
Obtain the sum of the squared differences between the actual values of the dependent variable and their mean (also known as the total sum of squares, or TSS).
Divide the RSS by the TSS: \(R^2 = 1 - (RSS/TSS).\)
\(R^2\) ranges between 0 and 1, with higher values indicating a better fit of the regression model.
An\(R^2\) of 1 indicates that the regression equation perfectly explains the total variance, while an \(R^2\) of 0 indicates that the regression equation does not explain any of the total variance.
Keep in mind that while\(R^2\) is a useful measure of model fit, it should not be the only criterion used to evaluate the quality of a regression model.
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point (m, n) is transformed by the rule (m−3, n). what type of transformation occurred? a translation of 3 units up a translation of 3 units up a translation of 3 units to the right a translation of 3 units to the right a translation of 3 units down a translation of 3 units down a translation of 3 units to the left
The type of transformation that occurred is a translation of 3 units to the left.
The given rule states that the point (m, n) is transformed to the point (m - 3, n). This means that the x-coordinate of the point is shifted to the left by 3 units while the y-coordinate remains the same.
A translation is a type of transformation where each point of the original figure is moved a certain distance in a certain direction. In this case, the point (m, n) is moved to the left by 3 units, resulting in the new point (m - 3, n).
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How do I find the domain and range in this? Please help!!
Answer:
Step-by-step explanation:
p
A large automobile insurance company wants to test the null hypothesis that the mean age in its population of policyholders is 50, against the alternative hypothesis that it is different from 50. In a random sample of 361 policyholders, the average age is 47.2 years, and the variance is 121 (squared years). The significance level is 5%. What is the population? Letter (see multiple choices in the instructions)
tThe population in this scenario refers to the entire group of policyholders of the large automobile insurance company.
Set up the hypotheses ; Null hypothesis (H0): The mean age in the population of policyholders is 50. Alternative hypothesis (Ha): The mean age in the population of policyholders is different from 50. Determine the significance level: The significance level is given as 5%. Calculate the test statistic: The test statistic for a two-sample t-test is given by:
t = (sample mean - hypothesized mean) / (standard error)
In this case, the sample mean is 47.2, and the hypothesized mean is 50. The standard error can be calculated using the formula: standard error = sqrt(variance / sample size). In this case, the variance is 121 and the sample size is 361. Calculate the degrees of freedom: For a two-sample t-test, the degrees of freedom is calculated as the sum of the sample sizes minus 2. In this case, the sample size is 361. Determine the critical value: Since the alternative hypothesis is two-tailed (different from 50), we divide the significance level by 2 (5% / 2) to get the critical value for each tail.
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1.) Find and compare the population density for Arizona and New York. Round your answers to the nearest whole number.
State Population Land Area (square miles)
Arizona 6,828,065 113,594
New York 19,795,791 47,126
You need to explain your steps in detail.
Answer:
just round them at the end
Step-by-step explanation:
Arizona: 7,278,717
New York 8.419 milion
If these two shapes are similar, what is the measure of the missing length z?
z = ___ milimeters
Answer:
z = 10 mm
Step-by-step explanation:
\(\frac{z}{15} =\frac{40}{60\\}\)
\(z * 60 = 40 * 15\)
\(60z = 600\)
\(z = 10\\\)
Given log6^3=p. Express log1/9^(6)1/2 in terms of p
\(log1/9^{(6)}1/2\) can be expressed in terms of p as -6p.
Given \(log6^3=p\). Express\(log1/9^{(6)}1/2\) in terms of p
We can use the logarithmic identity that states:
\(loga(b^c) = c \times loga(b)\)
Using this identity, we can rewrite log6^3 as:
\(log6^3 = 3 \times log6\)
Since \(log1/9^{(6)}1/2\) can be rewritten as \(log(1/9^{(1/2))}^{6}\), we can apply the same identity to obtain:
\(log(1/9^{(1/2)})^6 = 6\times log(1/9^(1/2))\)
Now we need to express \(log(1/9^{(1/2)})\) in terms of p.
\(Since 1/9^{(1/2)} = 1/(3^2)^{(1/2)} = 1/3\), we can rewrite \(log(1/9^{(1/2)})\) as:
\(log(1/9^{(1/2)}) = log(1/3) = -log(3)\)
Therefore, we can express\(log(1/9^{(1/2)})^6\)in terms of p as:
\(log(1/9^{(1/2)})^6 = 6log(1/9^{(1/2)}) = 6(-log(3)) = -6 \times log(3)\)
Finally, substituting the value of p we obtained earlier, we have:
\(log(1/9^{(1/2)})^6 = -6log(3) = -6p\)
Therefore, \(log1/9^{(6)}1/2\) can be expressed in terms of p as -6p.
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