Circle P has its center at (4, 6). What is the slope of the line tangent to the circle at the point (10, -2)
Answers
The slope of the tangent line is -4/3.
We must first get the equation of the tangent line in order to determine the slope of the line that is tangent to the circle at the coordinates (10, -2).
The tangent line's slope is the same as the slope of the line from the circle's center to its point of tangency (10, -2).
The line running between (4, 6) and (10, -2) has the following slope:
slope = (y - y')/(x - x'),
slope = (-2 - 6)/(10 - 4)
slope = -8 / 6 = -4 / 3.
Hence, the tangent line has a slope of -4/3.
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Related Questions
Write an equation that models the linear relationship in the table below.
Write an equation for each table in your answer and number them!
Answers
Answer:
Do you have the answers to the ones above that ???
Step-by-step explanation:
Find the fifth term in the sequence: 9, 13, 17,...
Answers
Which equation represents a line which is perpendicular to I = 0?
y = 2
-
3
O x = -4y
Submit Answer
2= 5
o
y = -6
PLS HELP ASAP
Answers
The flowchart represents a mathematical algorithm that takes two positive integers as the input and returns a positive integer as the output. Processes are indicated in the rectangular symbols in the flowchart. Each process is symbolized by an equation, such as T = T + a . In this particular process, the current values of the variables T and a are added together and the sum then becomes the value of T . For example, if the value of T is 3 and the value of a is 7 before the process T = T + a is completed, then the value of T is 10 and the value of a is 7 after the process is completed. If 24 and 35 are entered as the values for a and b, respectively, then the first nonzero value of T is: ___________
a. 24
b. 48
c. 96
d. 192
e. 384.
Answers
If the values of a and b are 24 and 35, respectively, and the algorithm follows the process T = T + a, the first non zero value of T would be 24.
According to the given flowchart, the process T = T + a indicates that the current value of T is updated by adding the value of a to it.
Given that the initial values of a and b are 24 and 35, respectively, we can follow the flowchart to determine the value of T. Since the process T = T + a is the only process shown in the flowchart, it will be repeated until T becomes non zero. Initially, T is zero, so the first execution of the process would yield T = 0 + 24, resulting in T being 24. Since this value is already non zero, it becomes the first nonzero value of T.
Therefore, the correct answer is option (a) 24, as it represents the first nonzero value of T obtained by executing the given algorithm with the values 24 and 35 for a and b, respectively
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The equation shows the average cost, y, in dollars, of
electricity per kilowatt hour (kWh) used, x, for homes in
the state of Missouri in 2011.
Based on the equation what would be the cost, in dollars,
for a home using O kWh of electricity in 2011?
1
y= X
10
Answers
After answering the presented question, we can conclude that As a equation result, in 2011, the cost of a residence utilising 0 kWh of power would be zero dollars.
What is equation?In mathematics, an equation is a proposition that states the equivalence of two expressions. An equation consists of two sides separated by a system of equations (=). For instance, the statement "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The goal of solving equations is to find the value or amounts of the variable in the model) that will permit the calculation to be accurate. Mathematics can be simple or complex, linear or nonlinear, and contain one or more parts. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the power of 2. Lines are used in many areas of mathematics, including algebra, arithmetic, and geometry.
y = x/10 is the provided equation.
If a residence uses 0 kWh of power (x=0), the cost of electricity is as follows:
y = x/10 = 0/10 = $0 per kWh.
As a result, in 2011, the cost of a residence utilising 0 kWh of power would be zero dollars.
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The function a(b) relates the area of a trapezoid with a given height of 10 and one base length of 7 with the length of its other base. It takes as input the other base value, and returns as output the area of the trapezoid. a(b) = 10. b+7 2 Which equation below represents the inverse function b(a), which takes the trapezoid's area as input and returns as output the length of the other base? O A. b(a) = 2 + 7 5 B. b(a)= O c. b(a) = a) = 2+5 D. b(a)= 7 1. 47
Answers
The function for the trapezoid area is:
A(x)=(B+b)*h/2
where B and b are the bases and h is the height.
With the given data: h=10 B and b =7 and x (it may vary which one is bigger)
So that function becomes:
A(x)=(7+x)*10/2
A(x)=(7+x)*5
So if you want the inverse function, you have to operate to find x:
A(x)/5=7+x
A(x)/5-7=x
So the new function is:
x(A)=A/5-7
Solve the following pair of simultaneous equations 3^y+1=1/9 and 5^y/125^x=125
Answers
Answer:
Step-by-step explanation:
\(3^{y}\) + 1 = 1/9
3^y = -8/9
5^y/125^x = 125
5^y/5^3x = 125
5^(y-3x) = 5^3
y-3x = 3
Your question is incorrect as 3^x can never be negative.
But, now you know y - 3x = 3, so, use this to get the values when you reconsider the correct question.
Thanks
Determine the degree measure of one angle of a 30-sided regular polygon. 5,400° 5,040° 180° 168°
Answers
To determine the degree measure of one angle of a 30-sided regular polygon.
The degree measure of one angle of a 30 sided regular polygon is 168°.
What is a regular polygon?
A two-dimensional geometric shape with a finite number of sides is called a polygon. A polygon's sides or edges are made up of segments of straight lines that are joined end to end to create a closed shape.
The intersection of two lines is referred to as a vertex or corner, and an angle is created as a result. Regular polygons are those that have sides that are congruent.
We will use the side-angle relation of a regular polygon with any no. of sides to find total sum of interior angles that is
(Side - 2) × 180°
(30 - 2) × 180°
= 5040°
Measure of each angle of 30-gon
= 5040°/30
= 168°
Thus, the degree measure of One angle of a 30 sided regular polygon is 168°
Hence the answer is, The degree measure of one angle of a 30 sided regular polygon is 168°.
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(Please help!!!) A landscaper is creating a bench for a pool deck. A model of the bench is shown in the image.
A rectangular prism with dimensions of 6.2 feet by 3 feet by 4 feet.
Part A: Find the total surface area of the bench. Show all work. (6 points)
Part B: The landscaper will cover the bench in ceramic tiles except for the bottom that is on the ground. If the tiles cost $0.83 per square foot, how much will it cost to cover the bench? Show all work. (6 points)
Answers
Answer:
The answer to your problem is ↓
Part A: 110.8 feet
Part B: $77
Step-by-step explanation:
Calculation: Part A.
6.2 x 4 = 24.8
24.8 x 2 = 49.6
4 x 3 = 12
12 x 2 = 24
6.2 x 3 = 18.6
18.6 x 2 = 37.2
49.6 + 24 + 37.2 = 110.8
Calculation: Part B.
Same as the beginning of Part A:
6.2 x 4 = 24.8
24.8 x 2 = 49.6
4 x 3 = 12
12 x 2 = 24
6.2 x 3 = 18.6
49.6 + 24 + 18.6 = 92.2
92.2 x .83 = 76.526
We then need to round ‘ 76.526 ‘
Rounded = 77
Thus the answer to your problem is ↓
Part A: 110.8 feet
Part B: $77
Answer:
$76.526
Step-by-step explanation:
Front and back: length = 6.2 feet, width = 4 feet
Left and right: length = 3 feet, width = 4 feet
Top and bottom: length = 6.2 feet, width = 3 feet
The area of each face is:
Front and back: A = lw = (6.2)(4) = 24.8 square feet
Left and right: A = lw = (3)(4) = 12 square feet
Top and bottom: A = lw = (6.2)(3) = 18.6 square feet
The total surface area is the sum of the areas of all six faces:
SA = 2(24.8) + 2(12) + 2(18.6) SA = 49.6 + 24 + 37.2 SA = 110.8 square feet
Part B: To find the cost of covering the bench in ceramic tiles, we need to find the surface area of the bench excluding the bottom face that is on the ground. This is the same as the total surface area minus the area of the bottom face:
SA’ = SA - A(bottom) SA’ = 110.8 - 18.6 SA’ = 92.2 square feet
The cost of covering one square foot of the bench is $0.83, so the total cost is:
C = SA’ x $0.83 C = 92.2 x $0.83 C = $76.526
Rounding to the nearest cent, the cost is $76.53.
Received message. Part A: To find the total surface area of the bench, we need to find the area of each face of the rectangular prism and add them up. The formula for the area of a rectangle is A = lw, where l is the length and w is the width. The dimensions of the bench are 6.2 feet by 3 feet by 4 feet, so we can label the faces as follows: - Front and back: length = 6.2 feet, width = 4 feet - Left and right: length = 3 feet, width = 4 feet - Top and bottom: length = 6.2 feet, width = 3 feet The area of each face is: - Front and back: A = lw = (6.2)(4) = 24.8 square feet - Left and right: A = lw = (3)(4) = 12 square feet - Top and bottom: A = lw = (6.2)(3) = 18.6 square feet The total surface area is the sum of the areas of all six faces: SA = 2(24.8) + 2(12) + 2(18.6) SA = 49.6 + 24 + 37.2 SA = 110.8 square feet Part B: To find the cost of covering the bench in ceramic tiles, we need to find the surface area of the bench excluding the bottom face that is on the ground. This is the same as the total surface area minus the area of the bottom face: SA' = SA - A(bottom) SA' = 110.8 - 18.6 SA' = 92.2 square feet The cost of covering one square foot of the bench is $0.83, so the total cost is: C = SA' x $0.83 C = 92.2 x $0.83 C = $76.526 Rounding to the nearest cent, the cost is $76.53.
If it's $5 for 4 pounds of apples, how much does 1 pound cost?
Answers
80 cents
you divide 4 and 5 and get .8 so 80 cents
Answer:
$1.25
Step-by-step explanation:
$5/4=$1.25
please solve for me thanks!
Answers
Answer: 5
Step-by-step explanation:
11. Noah left a $7 tip on a $46 restaurant bill. What percent tip is that? Give your answer to two decimal places if necessary.
Answers
Okay, here we have this:
We need to calculate the percent tip, so we obtain the following:
\(\begin{gathered} PercentTip=\frac{7}{46}\cdot100 \\ \approx15.22 \end{gathered}\)Finally we obtain that the percent tip is 15.22 rounded to two decimal places.
according to smith travel research, the average hotel price in the united states in 2009 was $97.00. assume the population standard deviation is $18.00 and that a random sample of 40 hotels was selected. what is the probability that a randomly selected sample mean will be more than $100?
Answers
The probability that a randomly selected sample mean will be more than $100 = 0.14082.
We are given that according to a research institution, the average hotel price in a certain year was $97.00.
Assume the population standard deviation is $18.00 and that a random sample of 40 hotels was selected.
Here, Mean = μ = $97.00 and Standard deviation = σ = $18 and n = 40
(a) Standard error of the mean = σ/\(\sqrt{n}\) = 18/\(\sqrt{40}\) = 2.74
(b) Let X bar = Sample Mean
The z score probability distribution for sample mean is ;
Z = Xbar-μ/ σ/\(\sqrt{n}\) ~ N(0,1)
So, Probability that the sample mean will be less than $102 = P(X bar < $102)
P(X bar < 102) = P(Xbar-μ/ σ/\(\sqrt{n}\) < 102 - 97.00/ 18/\(\sqrt{40}\)) = P(Z < 0.74) = 0.7704
(c) Probability that the sample mean will be more than $104 =P(X bar > $104)
= P(X bar > 104) = P(Xbar-μ/ σ/\(\sqrt{n}\) < 104 - 97.00/ 18/\(\sqrt{40}\)) = P(Z > 1.47) = 1 - P(Z <= 1.47)
= 1 - 0.92922 = 0.0708
(d) Probability that the sample mean will be between $99 and $100 is given by = P($99 < X bar < $100) = P(X bar < $100) - P(X bar <= $99)
= P(X bar < 100) = P(Xbar-μ/ σ/\(\sqrt{n}\) < 100 - 97.00/ 18/\(\sqrt{40}\)) = P(Z < 0.01) = 0.50399
= P(X bar <= 99) = P(Xbar-μ/ σ/\(\sqrt{n}\) <= 99 - 97.00/ 18/\(\sqrt{40}\)) = P(Z <= -0.35) = 1 - P(Z <= 0.35)
= 1 - 0.63683 = 0.36317
Therefore, P($99 < X bar < $100) = 0.50399 - 0.36317 = 0.14082 .
Hence the answer is the probability that a randomly selected sample mean will be more than $100 = 0.14082.
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can someone help me with this
Answers
Answer:
1. 40 members
2. 4 cheerleaders
3. 40 marbles
4. 2 marbles
5. 8
6. 24
Step-by-step explanation:
1. cross multiply 12/x=30/100
2. cross multiply 12/x=10/100
3. 18/x=45/100
4. x/40=5/100
5. we know 5% is 2 marbles. multiply by 4 to get 8 marbles.
6. 20%=8 marbles. 60/20= 3. 3 x 8= 24 marbles.
EASY BRAINLIEST PLEASE HELP!!
-if you answer correctly ill give you brainliest which will give you 35pts-
(if you put links or don't answer accordingly im reporting your account)
Answers
STEP BY STEP EXPLANATION
Answer:
A,B and C i think
...........................
Point charges q1=2.0μCq1=2.0μC and q1=4.0μCq1=4.0μC are located at r1=(4.0iˆ−2.0jˆ+2.0kˆ)mr1=(4.0i^−2.0j^+2.0k^)m and r2=(8.0iˆ+5.0jˆ−9.0kˆ)mr2=(8.0i^+5.0j^−9.0k^)m. What is the force of q2onq1?
Answers
The force of q2 on q1 is 3.74 x 10^-3 N, directed from q2 towards q1.
Using Coulomb's law, the force (in N) of q2 on q1 is given by:
F = k * q1 * q2 / r^2
where k is Coulomb's constant (9 x 10^9 N m^2/C^2), q1 and q2 are the magnitudes of the charges (in C), and r is the distance between the charges (in m).
First, we need to calculate the distance between the two charges:
r = |r2 - r1| = |(8.0i - 4.0i) + (5.0j - (-2.0j)) + (-9.0k - 2.0k)| = |4.0i + 7.0j - 11.0k| = sqrt(4.0^2 + 7.0^2 + (-11.0)^2) = 13.0 m
Now, we can calculate the force of q2 on q1:
F = k * q1 * q2 / r^2 = (9 x 10^9 N m^2/C^2) * (2.0 x 10^-6 C) * (4.0 x 10^-6 C) / (13.0 m)^2 = 3.74 x 10^-3 N
Therefore, by using Coulomb's law the force of q2 on q1 is 3.74 x 10^-3 N.
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Richard bought three peaches and one orange and spend $3.50. Peaches are 0 point $.85 each. If there are no sales tax on fruits how much did the orange cost
Answers
You want to take $0.85 and multiply it by 3 for the 3 peaches and you get $2.55 then you do $3.50-2.55= $0.95
Choose the fraction that is equivalent to 0.53?
A
13
23
B
11
20
C
9
17
D
8
15
Answers
Answer:
D. 8/15
Step-by-step explanation:
13/23 = .565217
11/20 = .55
9/17 = .52941176
8/15 = .53333333
Duri wants their backpack to weigh less than 45 pounds.
Use w to represent weights where Duri can carry their backpack.
Answers
This inequality represents that the weight of Duri's backpack is w < 45
How to represent the backpack as an expressionGiven that
Weight = Less than 45 pounds
We can use the inequality symbol to represent Duri's weight limit as follows:
w < 45
This inequality states that the weight of Duri's backpack, represented by w, must be less than 45 pounds.
Any weight value for w that satisfies this inequality is within Duri's weight limit and can be carried in their backpack.
For example, if Duri's backpack weighs 30 pounds, then w = 30 satisfies the inequality w < 45, so Duri can carry this weight.
However, if the backpack weighs 50 pounds, then w = 50 does not satisfy the inequality w < 45, so Duri cannot carry this weight.
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The study of statistics rests on what two major concepts? A) Data and Context B) Variation and Number C) Variation and Data D) Average and Variation.
Answers
The study of statistics rests on two major concepts:
Variation and Data.
Correct option is C.
What is statistics?Statistics is simply defined as the study and manipulation of data. Statistics deals with the analysis and computation of numerical data.
Given,
The study of statistics rests on what two major concepts:
Variance and Data
The basics of statistics include the measure of central tendency and the measure of variation. The central tendencies are mean, median and mode and variation, comprise variance and standard deviation.
Mean is the average of the observations. Median is the central value when observations are arranged in order. The mode determines the most frequent observations in a data set.
Hence, Variation and Data are two major concepts, on which study of statistics rely.
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I don't understand this question can someone help me with this please, please explain!! and thank you for the help!! If u dont know try your best. Please do it quick, please do all :D
Answers
Answer:
Step-by-step explanation:
#1 the second one is correct. 2 3/20 < 2 1/4 < 2 29/60
#2 80 seconds
#3 The second one is the correct answer
what is -1/3(y-x) expanded
Answers
If A=(7,9) and B=(3,12) what is the length of AB
Answers
The distance between two points A and B is 5 units.
OTTO makes deliveries for restaurant the data in the table represents a proportional relationship between the
Answers
OTTO makes deliveries for restaurant the data in the table represents a proportional relationship between the Distance and Time.
The concept of proportionality states that two variables are proportional to one another if they have a constant ratio.
This means that when one variable changes, the other changes in a way that maintains the same ratio between the two. In the case of OTTO's deliveries, the distance and time it takes to make a delivery have a proportional relationship, meaning that the ratio of distance to time is constant.
The table below represents the data for OTTO's deliveries.
Distance (in miles) Time (in minutes) 1048.5221175828187. 5100239412596.5232
To determine if the relationship between distance and time is proportional, we can check if the ratio of distance to time is constant.
We can use any two pairs of values from the table to test this.
Let's use the first and fourth pairs:
10 miles ÷ 48.5 minutes
= 0.2062 miles/minute
23 miles ÷ 96.5 minutes
= 0.2387 miles/minute
Therefore, we cannot use proportionality to predict how long it will take to make a delivery of a certain distance.
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if a cone has a volume that is 12 pie cubic inches and the height is 4 inches then what is the radius?
Answers
Answer:
1.6924
Step-by-step explanation:
V=πr^2h/3=
Select the slope-intercept form of an equation for a line with y-intercept –5 and slope 2. A. x = 2x + 5 B. y = 2x – 5 C. y = 5x – 2 D. y = –5x + 2
Answers
Answer:
y=2x-5
Step-by-step explanation:
slope intercept form is y=mx+b
m=slope
b=y-intercept
Answer: y = 2x - 5
slope-intercept form ⇒ y = mx + b
⇒ where mx is the slope,
⇒ b is the y-intercept
⇒According to the question;
mx which is the slope = 2
b the y-intercept = -5
∴ the equation is
Make up an equation for a Quadratic function whose graph satisfies the given condition. Use
whatever form is most convenient.
Has a y-intercept at (0,8)
Answers
Answer: The equation of the quadratic function is y = ax^2 + 8, where a is any non-zero constant.
Step-by-step explanation: The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants. To find the equation of a quadratic function with a y-intercept at (0,8), we substitute x = 0 and y = 8 into the general equation to obtain:
8 = a(0)^2 + b(0) + c 8 = c
Therefore, c = 8, and the quadratic function is y = ax^2 + bx + 8.
Since we don't have any other condition to determine the values of a and b, any non-zero value of a can be chosen to satisfy the given condition. If a positive value is chosen for a, the graph of the function will open upwards, while choosing a negative value will make it open downwards. The value of b will alter the position of the vertex of the graph.
Hope this helps, and have great day!
PLEASE HELP ILL GIVE !!!
Answers
Answer:
4) y = 10x
5) y = 13x
6) 2,1
4,2
6,3
y=0.5x
consider the quadratic function y equals short dash x squared plus 6 x minus 5. what do we know about the graph of this quadratic equation, based on its formula?
Answers
Based on the formula of the quadratic function y=-x^2+6x-5, we know that its graph is a downward-facing parabola that opens wide, with a vertex at (3,-14), and an axis of symmetry at x=3.
Based on the formula of the quadratic function y=-x^2+6x-5, we can determine several properties of its graph, including its shape, vertex, and axis of symmetry.
First, the negative coefficient of the x-squared term (-1) tells us that the graph will be a downward-facing parabola. The leading coefficient also tells us whether the parabola is narrow or wide. Since the coefficient is -1, the parabola will be wide.
Next, we can find the vertex using the formula:
Vertex = (-b/2a, f(-b/2a))
where a is the coefficient of the x-squared term, b is the coefficient of the x term, and f(x) is the quadratic function. Plugging in the values for our function, we get:
Vertex = (-b/2a, f(-b/2a))
= (-6/(2*-1), f(6/(2*-1)))
= (3, -14)
So the vertex of the parabola is at the point (3,-14).
Finally, we know that the axis of symmetry is a vertical line passing through the vertex. In this case, it is the line x=3.
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Help me please somebody
Answers
Answer: 68%
Step-by-step explanation:
From the table on the left-hand side, we observe that the total number of the surveyed seventh grade students is:
\(12+7+13+6=38\)
The number of seventh graders who do not play guitar is:
\(7+13+6=26\)
Hence, the probability that a randomly chosen seventh grader will play an instrument other than guitar is:
\(\frac{26}{38}\times 100\% = 68\%\)