Four tangents are drawn from E to two concentric circles A, B, C, and D are the points of tangency. 1. Name as many pairs of congruent triangles as possible 2. Tell how you can show each pair is congruent
Answers
1. Congruent triangles:
a) Triangle EAB and Triangle ECD
b) Triangle EAC and Triangle EBD
2. Triangle EAB ≅ Triangle ECD and Triangle EAC ≅ Triangle EBD by ASA Congruence Postulate.
In this scenario, we have two concentric circles and four tangents drawn from point E to these circles, creating points of tangency A, B, C, and D.
1. Pairs of congruent triangles:
a) Triangle EAB and Triangle ECD
b) Triangle EAC and Triangle EBD
2. Showing congruence for each pair:
a) To show that Triangle EAB and Triangle ECD are congruent, we can use the following information:
- EA and EC are both radii of the larger circle, so EA = EC (congruent radii).
- AB and CD are tangents to the smaller circle, so the segments are parallel and form corresponding angles at points A and C. Thus, Angle EAB and Angle ECD are congruent (alternate interior angles).
- EB and ED are both radii of the smaller circle, so EB = ED (congruent radii).
With this information, we can prove Triangle EAB ≅ Triangle ECD using the Angle-Side-Angle (ASA) Congruence Postulate.
b) To show that Triangle EAC and Triangle EBD are congruent, we can use the following information:
- EA and EB are both radii of the larger circle, so EA = EB (congruent radii).
- AC and BD are tangents to the larger circle, so the segments are parallel and form corresponding angles at points A and B. Thus, Angle EAC and Angle EBD are congruent (alternate interior angles).
- EC and ED are both radii of the smaller circle, so EC = ED (congruent radii).
With this information, we can prove Triangle EAC ≅ Triangle EBD using the Angle-Side-Angle (ASA) Congruence Postulate.
To know more about Congruence Postulate, refer to the link below:
https://brainly.com/question/7888063#
#SPJ11
Related Questions
What is 3x−2y=6 in slope-intercept form?
Answers
Answer:
Slope intercept form
y=mx=b
y=3/2x-3
Step-by-step explanation:
3x-2y=6
-3x -3x
=
-1 (-2y=-3x=6)
2y=3x-6
-- -- --
2 2 2
=
y=3/2x-3
Hope this helps
An architect is designing a new windmill with four sails. In his sketch, the sails' center of rotation is the origin, (0,0), and the tip of one of the sails, point Upper R,
has coordinates (2,-4).
He wants to make another sketch that shows the windmill after the sails have rotated 180 degrees about their center of rotation. What would be the coordinates of Upper R prime ?
The coordinates of Upper R prime would be ______?
Answers
The coordinates of upper R prime are (-2, 4).
Now, According to the question:
Rotation describes the circular motion of an object around its center. There are different ways things can rotate. Rotation of the Earthre. A very familiar kind of rotation is when a spherical, three-dimensional object turns around an invisible line inside its center.
The sails center of rotation is the origin (0,0)
The top of one sails point R(2, -4).
A 180 degree rotation make you turn (x, y) into (-x, -y),
So, the point turn (2,-4 ), into (-2, 4).
Therefore the coordinates of R are (-2, 4).
Learn more about the Coordinate after rotation at:
https://brainly.com/question/19527326
#SPJ4
Is the vertex of the graph a maximum or a minimum?
Answers
Answer:
maximum
Step-by-step explanation:
the vertex will give the maximum value for y, which is 3
if cotθ=1/\(\sqrt{x} 3\\\) , the value of \(sec^{2}\) θ + \(cosec^{2}\) θ is
a) 1
b) 40/9
c) 38/9
d) 5\(\frac{1}{3}\)
Answers
\(\text{Given that,}~\\\\\cot \theta = \dfrac 1{\sqrt 3} \\\\\\\text{So,}~~ \tan \theta = \dfrac 1{\cot \theta} = \sqrt 3\\\\\\\sec^2 \theta + \csc^2 \theta \\\\=(1+\tan^2 \theta) + (1 + \cot^2 \theta)\\\\=1 +\left (\sqrt 3 \right)^2 + 1 + \left(\dfrac 1{\sqrt 3} \right)^2\\\\=1 +3 + 1 + \dfrac 13 \\\\= 5 + \dfrac 13 \\\\= 5 \dfrac 13\)
Four pounds of apples cost $5 How much would 10 pounds o apples cost?
Answers
Answer:
Step-by-step explanation:
plus all of them 5times 10
What is (-11,,-27) reflected across the y-axis
Answers
Answer:
On the y- axis everything is postive so it would be (11,27)
The equation of the line that passes through the point (-2,7) and has a slope of Zero is
Answers
The equation of the line that passes through the point (-2,7) and has a slope of zero is y = 7
What is the slope of a straight line?Slope tells how vertical a line is.
The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.
To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.
Given that a point on the line is given which is (-2,7) and the slope of the line is zero.
To determine the equation of the line, the point-slope form of the equation of a straight line is convenient.
The point-slope form of the equation of a straight line;
y-y₁ = m(x-x₁)
Where m is the slope or gradient
From the question, m = 0, and (x₁, y₁ )= (-2,7)
Putting these into the equation, we get
y-y₁ = m(x-x₁)
y - 7 = 0(x+ 2)
y - 7 = 0
y = 7
Hence, the equation of the line that passes through the point (-2,7) and has a slope of zero is y = 7
Learn more about slope here:
https://brainly.com/question/2503591
#SPJ1
How do you step by step solve the equation n(n+2) = 0
Answers
Answer: n = 0 and -2
Step-by-step explanation:
Equate the expressions to zero
n(n+2) = 0
n = 0 and n+2 = 0
n = 0 and n = -2
According to the article, which strategy is ultimately the best option?
-The option that targets the smallest debt balance first.
-The option that gets you to pay off the total debt balance.
-The option that splits repayments based on the size of the debt balance owed.
-The option that targets the high-interest debt balance first.
Answers
The targeting the high-interest debt balance first is the best option for paying off debt because it can save money in interest payments and lead to a faster reduction in the overall debt balance.
The article discusses different strategies for paying off debt and concludes that the best option is to target the high-interest debt balance first.
This strategy, also known as the "avalanche method," can save the most money in the long run by minimizing interest payments.
Paying off the smallest debt balance first, known as the "snowball method," may provide a psychological boost by quickly eliminating one debt, but it may not be the most cost-effective strategy.
The article notes that by focusing on the high-interest debt balance, you can save money in interest payments and reduce the overall debt balance faster.
Similarly, splitting repayments based on the size of the debt balance may not be the best option because it does not prioritize the high-interest debt.
This can lead to higher interest payments over time and a longer time to pay off the debt.
Paying off the total debt balance, while an admirable goal, may not be feasible for everyone.
It may be more realistic to focus on paying off the high-interest debt first and then working on reducing the overall debt balance.
The targeting the high-interest debt balance first is the best option for paying off debt because it can save money in interest payments and lead to a faster reduction in the overall debt balance.
It may not provide an immediate psychological boost, but it can lead to long-term financial stability and freedom.
For similar question on interest payments:
https://brainly.com/question/13914148
#SPJ11
PLS HELP ASAP THANKS
Answers
Answer:
In general, the quadratic function f(x) = ax^2 + bx + c describes a parabola, which can open upwards or downwards depending on the sign of the coefficient a. In this case, since a = 5 is positive, the parabola opens upwards. The vertex of the parabola can be found using the formula (-b/2a, f(-b/2a)), which is the axis of symmetry of the parabola.
Step-by-step explanation:
either b or d i can't seem to remember how to find the width of the parent function im sorry but that narrows it down to two options
12. If the points A(4,3) and B(x,5)
are on the circles with centre
O(2,3), the value of 'x' is
(a) 2
(b) 4
(c) 6
(d) 8
Answers
Answer:
a) 2
Step-by-step explanation:
Just graph it
Find the volume of a cube that has the following dimensions:length=2x^2 width=x^3 height=x^2-6x+5 A) 4x^7-3x^6+8x^5 B) 2x^12-12x^7+10x^6 C) 2x^7+12x^6+10x^5 D) 2x^7-12x^6+10x^5
Answers
Answer:
Option D. 2x⁷ - 12x⁶ + 10x⁵
Step-by-step explanation:
From the question given:
Length (L) = 2x²
Width (w) = x³
Height (h) = x² - 6x + 5
Volume (V) =?
Volume (V) = length (L) x width (w) x height (h)
V = L x w x h
V = 2x² × x³ × x² - 6x + 5
V = (2x²) (x³) (x² - 6x + 5)
V = (2x⁵) (x² - 6x + 5)
Clear bracket
V = 2x⁷ - 12x⁶ + 10x⁵
Therefore, the volume of the cube is 2x⁷ - 12x⁶ + 10x⁵
A participant took 5. 2 hours to complete a marathon. How many minutes did the participant take to complete the marathon? use 1 hour = 60 minutes.
Answers
312 minutes the participant took to complete the marathon
Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding.
According to the question,
The time taken by participant to complete a marathon in hours = 5.2 hours
1 hour contains 60 minutes
so, to change hours into minutes , we have to multiple hours into 60
Time taken by participant to complete a marathon in minutes = 5.2 × 60
=> 312 minutes
To know more about Unit conversion here
https://brainly.com/question/12709593
#SPJ4
In a triangle, one acute angle is 33 degree. The adjacent side of angle 33 degree is 8 and opposite side is x. The largest side of the triangle is 15."/> find the value of x to the nearest tenth
Answers
The value of x, to the nearest tenth, is approximately 4.96. The steps involved using the tangent ratio and solving for the unknown side in a right triangle.
In a triangle, the angle opposite to the side x as angle A, and the side opposite to the angle 33° as side B, and the largest side as side C. So we have:
Angle A = 90° - 33° = 57° (since the sum of angles in a triangle is 180°)
Side B = 8
Side C = 15
Side x = ?
Write the formula for the tangent ratio in terms of the sides of the triangle. For angle A, we have:
tangent(A) = opposite/adjacent
Substitute the known values into the formula and solve for the unknown side. Substituting the values we have, we get
tangent(33°) = x/8
Multiplying both sides by 8, we get:
x = 8 * tangent(33°)
Use a calculator to find the value of the tangent of 33 degrees. We get:
tangent(33°) ≈ 0.6494
Substitute the value of the tangent into the formula we obtained in step 3 and solve for x. We get
x ≈ 8 * 0.6494
x ≈ 5.1952
Round the answer to the nearest tenth, since the question asks for the value of x to the nearest tenth. We get
x ≈ 4.96
Therefore, the value of x, to the nearest tenth, is approximately 4.96.
To know more about Trigonometric Ratio:
https://brainly.com/question/31511603
#SPJ1
Dan is Civil Engineer. He wants to create a small scale drawing of a city block. The block is a square with sides of length 100 m,
What would the dimensions of the scale drawing be if 1 unit represented 10 meters?
Answers
Find the first derivative for each of the following:
y = 3x2 + 5x + 10
y = 100200x + 7x
y = ln(9x4)
Answers
The first derivatives for the given functions are:
For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.
For \(y = 100200x + 7x,\) the first derivative is dy/dx = 100207.
For \(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.
To find the first derivative for each of the given functions, we'll use the power rule, constant rule, and chain rule as needed.
For the function\(y = 3x^2 + 5x + 10:\)
Taking the derivative term by term:
\(d/dx (3x^2) = 6x\)
d/dx (5x) = 5
d/dx (10) = 0
Therefore, the first derivative is:
dy/dx = 6x + 5
For the function y = 100200x + 7x:
Taking the derivative term by term:
d/dx (100200x) = 100200
d/dx (7x) = 7
Therefore, the first derivative is:
dy/dx = 100200 + 7 = 100207
For the function \(y = ln(9x^4):\)
Using the chain rule, the derivative of ln(u) is du/dx divided by u:
dy/dx = (1/u) \(\times\) du/dx
Let's differentiate the function using the chain rule:
\(u = 9x^4\)
\(du/dx = d/dx (9x^4) = 36x^3\)
Now, substitute the values back into the derivative formula:
\(dy/dx = (1/u) \times du/dx = (1/(9x^4)) \times (36x^3) = 36x^3 / (9x^4) = 4/x\)
Therefore, the first derivative is:
dy/dx = 4/x
To summarize:
For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.
For y = 100200x + 7x, the first derivative is dy/dx = 100207.
For\(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.
For similar question on derivatives.
https://brainly.com/question/31399608
#SPJ8
Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Select two options. y = –Three-fourthsx + 1 3x − 4y = −4 4x − 3y = −3 y – 2 = –Three-fourths(x – 4) y + 2 = Three-fourths(x + 4
Answers
Answer:
3x-3y=-4 and y+2=3/4x+4
Step-by-step explanation:
parallel line equations have the same slope. just find the equation that also has positive 3 in this problem
Answer:
B & D
Step-by-step explanation:
15) Suppose that Tony ordered 3 pizzas. Each pizza has 8 slices. Being shared with 5 people (3 pizzas - 8 slices in each
pie... total: 24 PIECES OF PIZZA)
Answers
Answer:
4.8 slices each
Step-by-step explanation:
8*3= 24
24/5= 4.8
The formula for the volume of a sphere is uppercase v = four-thirds pi r cubed. what is the formula solved for r?
Answers
Answer:
r = ∛(4v/3л)
Step-by-step explanation:
v = 3/4 л r³ (л = pi)
v/л = 3/4 r³
4v/3л = r³
∛(4v/3л) = ∛r³
r = ∛(4v/3л)
If a = 2 and b = 3, then the value of (a^b + b^a)-1 is :
Answers
Answer:
\(16\)
Step-by-step explanation:
Substituting \(a=2\) and \(b=3\) into \((a^{b}+b^{a})-1\) gives us:
\((a^{b}+b^{a})-1\)
\(=(2^{3} +3^{2})-1\) (Substitute given values into expression)
\(=(8+9)-1\) (Evaluate exponents)
\(=17-1\) (Evaluate expression in parentheses)
\(=16\) (Simplify)
Hope this helps!
Answer:
16
Step-by-step explanation:
Given
(\(a^{b}\) + \(b^{a}\) ) - 1 ← substitute a = 2, b = 3
= (2³ + 3²) - 1
= (8 + 9) - 1
= 17 - 1
= 16
Is it possible to draw a triangle has set of sides 9cm 7cm and 17cm give the reason?
Answers
It is not possible to construct a triangle whose sides are 9 cm 7 cm and 17 cm because the sum of two sides(9 cm and 7 cm) are smaller than third sides(17 cm).
In the given question, we have to check that it is possible to construct a triangle whose sides are 9 cm 7 cm and 17 cm.
To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always greater than the third side.
To check this we firstly add the 9 and 7
9 + 7 < 17
16 < 17
Now we add 17 and 7
17 + 7 > 9
24 > 9
Now we add 9 and 17
9 + 17 > 7
26 > 7
It is not possible to construct a triangle whose sides are 9 cm 7 cm and 17 cm because the sum of two sides(9 cm and 7 cm) are smaller than third sides(17 cm).
To learn more about construct a triangle link is here
brainly.com/question/14240187
#SPJ4
If f(-7)=14, what order pair does this represent?
Answers
Answer:
(-7, 14)
Step-by-step explanation:
The function f(x) is equal to the y-coordinate. The value inside of the parenthesis is the x-coordinate, so it would be -7 in this problem.
determine the taylor’s expansion of the following function: 2/(1+z)^3 on the region |z|<1.
Answers
The Taylor's expansion of 2/(1+z)^3 on the region |z|<1 is :
f(z) = 2 - 6z + 12z^2 - 20z^3 + ...
The Taylor's expansion of the function 2/(1+z)^3 on the region |z|<1 can be found using the formula:
f(z) = f(a) + f'(a)(z-a) + f''(a)(z-a)^2/2! + f'''(a)(z-a)^3/3! + ...
where a is the center of the expansion. In this case, we want to expand around a=0, since we are considering the region |z|<1.
First, let's find the derivatives of f(z):
f(z) = 2/(1+z)^3
f'(z) = -6/(1+z)^4
f''(z) = 24/(1+z)^5
f'''(z) = -120/(1+z)^6
Now we can plug these into the Taylor's expansion formula:
f(z) = f(0) + f'(0)z + f''(0)z^2/2! + f'''(0)z^3/3! + ...
f(0) = 2/(1+0)^3 = 2
f'(0) = -6/(1+0)^4 = -6
f''(0) = 24/(1+0)^5 = 24
f'''(0) = -120/(1+0)^6 = -120
Plugging these values in, we get:
f(z) = 2 - 6z + 12z^2 - 20z^3 + ...
This is the Taylor's expansion of 2/(1+z)^3 on the region |z|<1.
Note that this expansion is valid for all values of z inside the circle |z|<1.
To learn more about Taylor's expansion visit : https://brainly.com/question/28168045
#SPJ11
Which number is greatest?6. 23 times 10 superscript 126. 23 times 10 superscript 86. 23 times 10 superscript negative 66. 23 times 10 superscript 3.
Answers
From the given numbers, the greatest number is 23 × 10^126
The first number = 23 × 10^126
The second number = 23 × 10^86
The third number = 23 × 10^66
The fourth number = 23 × 10^3
The scientific notation is defined as the easiest method to represents the very smallest or the largest number. The scientific notation consist of a whole number multiplied by the power of ten
Here, the whole number is same in all cases, only the power of the 10 is different . To find the largest number we have to find the number with largest power of 10
The number with largest power of 10 = 23 × 10^126
Hence, the greatest number is 23 × 10^126
Learn more about scientific notation here
brainly.com/question/18073768
#SPJ4
what is 7(1 - 8n)???
Answers
Answer:
7-56n
Step-by-step explanation:
By using the distributive property you multiply the 7 to the 1 which equals 7. Then you distribute the 7 to the -8n which gives you -56n becaus emultiplying a negative and a possitive gives you a negative.
The required solution is -56n+7.
It is required to find the solution.
What is algebra?A part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.
Given:
Rearrange terms
7(1 - 8n)
=7(-8n+1)
Then distribute by multiplying 7 we get,
-56n+7
Therefore, the required solution is -56n+7.
Learn more about algebra here:
brainly.com/question/17516957
#SPJ6
She must determine height of the clock tower using a 1.5 m transit instrument (calculations are done 1.5 m above level ground) from a distance 100 m from the tower she found the angle of elevation to be 19 degrees. How high is the clock tower from 1 decimal place?
Answers
Step-by-step explanation:
We can use trigonometry to solve this problem. Let's draw a diagram:
```
A - observer (1.5 m above ground)
B - base of the clock tower
C - top of the clock tower
D - intersection of AB and the horizontal ground
E - point on the ground directly below C
C
|
|
|
|
| x
|
|
|
-------------
|
|
|
|
|
|
|
|
|
B
|
|
|
|
|
|
|
|
|
|
|
A
```
We want to find the height of the clock tower, which is CE. We have the angle of elevation ACD, which is 19 degrees, and the distance AB, which is 100 m. We can use tangent to find CE:
tan(ACD) = CE / AB
tan(19) = CE / 100
CE = 100 * tan(19)
CE ≈ 34.5 m (rounded to 1 decimal place)
Therefore, the height of the clock tower is approximately 34.5 m.
PLEASE HELP ME! I REALLY NEED SOME HELP!!
Answers
Answer:
a
Step-by-step explanation:
If the lines DE and BC were parallel then
Δ ADE and Δ ABC would be similar and the ratios of corresponding sides would be equal, that is
\(\frac{AD}{AB}\) = \(\frac{AE}{AC}\) , substituting values
\(\frac{4}{10}\) = \(\frac{6}{14}\)
but
\(\frac{4}{10}\) ≠ \(\frac{6}{14}\)
That is 4 : 10 ≠ 6 : 14 → a
you can compare two marginal distributions to see if the corresponding two variables are related. true/false
Answers
True. Comparing two marginal distributions can show if the corresponding two variables are related. This can be done by calculating the correlation coefficient of the two variables.
The correlation coefficient is a numerical measure of the degree of the linear relationship between two variables and can be calculated by dividing the covariance of the two variables by the product of their standard deviations. The correlation coefficient ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation and 1 indicates a perfect positive correlation.
If the correlation coefficient is close to zero, then the two variables are not significantly related. If the correlation coefficient is close to -1 or 1, then it can be inferred that the two variables are related.
Learn more about Marginal Distribution:
https://brainly.com/question/13127182
#SPJ4
The square of thrice a number a, number take away double a second number b
Answers
Answer:
3x^2 - 2b
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
what type of triangle is thiss
Answers
Answer:
This is a RIGHT TRIANGLE.
Sure there are two acute angles, but if it was an acute triangle, then there should be three acute angles. It is not an obtuse triangle because there are no obtuse angles. This is a right triangle because there are two acute angles and there is a right corner, 90º. This is why this is a right triangle. It's quite simple.