Answers
The proof for the above is given as follows:
∠A ≅ ∠C - Given
BD ⊥ ∠ABC - Given
AC ⊥ BD - Angle Bisector Theorem
According to the angle bisector theorem, a triangle's opposing side is split into two segments that are proportionate to its other two sides. A ray that splits a given angle into two equal angles is known as an angle bisector.
Thus, it is correct to state that AC ⊥ BD according to the angle bisector theorem.
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Related Questions
What is the area of the rectangle?
Answers
Answer:
55
Step-by-step explanation:
tell me if its wrong :)
sort the following list of functions in ascending order of growth rate and briefly explain why you put them in such order. for example, if f(n) appears before g(n) then f(n) = ___
Answers
The given list of functions can be arranged in ascending order of growth rate as follows: g1(n), g5(n), g3(n), g4(n), g2(n), g6(n), and g7(n).
The Big O notation describes the upper bound of a function's growth rate. In other words, it represents the maximum amount of time or space that a function requires to complete its operations.
Using this concept, we can arrange the given list of functions in ascending order of growth rate as follows:
g1(n) = √2 log n: This function has a growth rate of O(log n), which is less than the growth rates of all other functions in the list.
g5(n) = n log n: This function has a growth rate of O(n log n), which is greater than the growth rate of g1(n), but less than the growth rates of all other functions in the list.
g3(n) = n 4/3: This function has a growth rate of O(n 4/3), which is greater than the growth rates of g1(n) and g5(n), but less than the growth rates of all other functions in the list.
g4(n) = n(log n)3: This function has a growth rate of O(n(log n)3), which is greater than the growth rates of g1(n), g5(n), and g3(n), but less than the growth rates of all other functions in the list.
g2(n) = 2n: This function has a growth rate of O(2n), which is greater than the growth rates of g1(n), g5(n), g3(n), and g4(n), but less than the growth rates of g6(n) and g7(n).
g6(n) = 22 n: This function has a growth rate of O(2n), which is greater than the growth rates of g1(n), g5(n), g3(n), g4(n), and g2(n), but less than the growth rate of g7(n).
g7(n) = 2n2: This function has a growth rate of O(2n2), which is greater than the growth rates of all other functions in the list.
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Complete Question:
Arrange the following list of functions in ascending order of growth rate, i.e. if the function g(n) immediately follows f(n) in your list then, it should be the case that f(n) = O(g(n)).
g1(n) = √2 log n
g2(n) = 2n
g3(n) = n 4/3
g4(n) = n(log n)3
g5(n) = n log n
g6(n) = 22 n
g7(n) = 2n2
What arithmetic operations dose the the expression 12+8t
Answers
Answer:
- addition
- division
- multiplication
Answer:
addition 12+8t
multiplication 8*t
division 12+8t/25
Step-by-step explanation:
And the variable is t
pls say hard
very hard
Answers
Answer:
3
Step-by-step explanation:
In this arithmetic sequence 3, 8, 13, 18, ... which term has the the value 123?
25
24
617
613
Answers
Answer:
term 25
Step-by-step explanation:
a is the number added from 3 to 8 is 5(must be constant like 8 to 13 is also 5
b is the zero term so 3-a which is 3-5=-2
Statement: If yesterday is not Wednesday, then tomorrow is not Friday.
Converse:
Inverse:
Contrapositive:
Answers
Answer:
converse..............
a) In GeoGebra Links to an external site., construct a triangle (e.g. ABC), find the measure of all angles and all sides. Identify the type of your triangle (acute, right, obtuse/ scalene, isosceles, equilateral). Then construct a quadrilateral (e.g. DEFG), measure all angles and all sides. Identify the type of your quadrilateral (irregular, square, rectangle, etc.) Use the text command available in GeoGebra to describe the type.
b) Make a screenshot of your work in Geogebra and insert in the space provided below.
Answers
All angles are 90 degrees.Rhombus: All sides are of equal length.Square: All angles are 90 degrees and all sides are of equal length
a) To construct a triangle in GeoGebra, we can follow the steps below:
Step 1: Open GeoGebra and select the ‘Polygon’ tool.
Step 2: Select the ‘Triangle’ option.
Step 3: Click three points anywhere on the graph.
Step 4: Once you have drawn the triangle, you can use the ‘Angle’ tool to measure all the angles in the triangle. Similarly, use the ‘Length’ tool to measure the length of each side of the triangle.To identify the type of triangle, we can use the following properties:Acute Triangle: All angles of the triangle are less than 90 degrees.Right Triangle: One of the angles in the triangle is 90 degrees.Obtuse Triangle: One of the angles of the triangle is greater than 90 degrees.Scalene Triangle: All sides of the triangle are of different lengths.Isosceles Triangle: Two sides of the triangle are of the same length.Equilateral Triangle: All sides of the triangle are of the same length.To construct a quadrilateral in GeoGebra, we can follow the steps below:
Step 1: Open GeoGebra and select the ‘Polygon’ tool.
Step 2: Select the ‘Quadrilateral’ option.
Step 3: Click four points anywhere on the graph.
Step 4: Once you have drawn the quadrilateral, you can use the ‘Angle’ tool to measure all the angles in the quadrilateral. Similarly, use the ‘Length’ tool to measure the length of each side of the quadrilateral.To identify the type of quadrilateral, we can use the following properties:Irregular Quadrilateral: All sides and angles of the quadrilateral are of different lengths and measures.Trapezium: Only one pair of opposite sides is parallel.Parallelogram: Opposite sides are parallel.Rectangle:.b) Since we need to add a screenshot of the work done in GeoGebra, we cannot add it here. However, while you construct the triangle and the quadrilateral, you can keep adding the measure of angles and sides to find the properties of the figure. You can then use the Text command available in GeoGebra to describe the type of triangle or quadrilateral that you have constructed. To use the Text command in GeoGebra, follow the steps below:
Step 1: Select the ‘Text’ tool from the toolbar
.Step 2: Click anywhere on the graph to add the text box.
Step 3: Type the text in the text box.
Step 4: Customize the font, color, and size of the text as required.
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F(x)= 2ax^2 + bx + 3 has a relative extremum at the point (-1,2)
Answers
At the relative extremum
a = 1/2 and b = 2What is a relative extremum?
A relative extremum is a relative minimum or maximum of a function.
Since the function F(x) = 2ax² + bx + 3 has a relative extremum at the point (-1,2). This implies that dF(x)/dx = 0 at the extremum.
So, F(x) = 2ax² + bx + 3
dF(x)/dx = d(2ax² + bx + 3)/dx
= d2ax²/dx + dbx/dx + d3/dx
= 4ax + b
dF(x)/dx = 0
⇒ 4ax + b = 0
⇒b = -4ax at x = -1
b = -4a(-1)
= 4a
Since the function F(x) = 2ax² + bx + 3 has a relative extremum at the point (-1,2), we have that
F(-1) = 2a(-1)² + b(-1) + 3
= 2a - b + 3
F(-1) = 2
⇒2a - b + 3 = 2
⇒2a - b = 2 - 3
2a - b = -1
Now, b = 4a
So, substituting b into the equation, we have that
2a - b = -1
2a - 4a = -1
-2a = -1
a = -1/-2
a = 1/2
So, b = 4a
= 4(1/2)
= 2
So,
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Find the measure of angle A.
60x
O 60°
O 30°
O 23°
O 37°
30x
A
Answers
Answer:
Step-by-step explanation:
sum of angles in a triangle=180º
90+60x+30x=180
90+90x=180
90(1+x)=180
1+x=2
x=1
angle A=30º
URGENT *EASY 10 POINTS* : Show steps to get the expression ln(sqrt(2) +1) - ln(1/sqrt(2)) equal to -ln(1-(1/sqrt2))
Answers
Answer:
Step-by-step explanation:
To show that the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\), we can simplify both sides of the equation using the properties of logarithms. Here are the steps:
Step 1: Simplify the expression on the left side:
\(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\)
Step 2: Apply the logarithmic property \(\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)\) to combine the logarithms:
\(\ln\left(\frac{\sqrt{2} + 1}{\frac{1}{\sqrt{2}}}\right)\)
Step 3: Simplify the expression within the logarithm:
\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)}\right)\)
Step 4: Simplify the denominator by multiplying by the reciprocal:
\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)} \cdot \sqrt{2}\right)\)
\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{\left(\frac{1}{\sqrt{2}}\right) \cdot \sqrt{2}}\right)\)
\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)
Step 5: Simplify the numerator:
\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)
\(\ln\left(\sqrt{2}(\sqrt{2} + 1)\right)\)
\(\ln\left(2 + \sqrt{2}\right)\)
Now, let's simplify the right side of the equation:
Step 1: Simplify the expression on the right side:
\(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\)
Step 2: Simplify the expression within the logarithm:
\(-\ln\left(\frac{\sqrt{2} - 1}{\sqrt{2}}\right)\)
Step 3: Apply the logarithmic property \(\ln\left(\frac{a}{b}\right) = -\ln\left(\frac{b}{a}\right)\) to switch the numerator and denominator:
\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)
Step 4: Simplify the expression:
\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)
\(-\ln\left(\frac{\sqrt{2}(\sqrt{2} + 1)}{1}\right)\)
\(-\ln\left(2 + \sqrt{2}\right)\)
As we can see, the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) simplifies to \(\ln(2 + \sqrt{2})\), which is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\).
A triangle has lengths of 12 cm, 14 cm, and 18 cm. What is the perimeter of the triangle in inches? ( 1 cm = 0.4 in.)
Answers
Answer:
15.8 in
Step-by-step explanation:
12cm x .4 = 3 in
14 x .4 = 5.6
18 x .4 = 7.2
3 + 5.6 + 7.2 = 15.8 in
Hope that helps!
-Sabrina
I need help with both of these plss
Answers
Answer:
3. All you did was switch the numbers, so it will still equal the same :)
4. 8a and the other 8a cancel each other out, so since 8 has no variables, it ends up by itself.
ANSWER IT OR ELSE JAMES CHARLES
Answers
Answer:
Hiiiiii sisterrrrs!!!!
Step-by-step explanation:
Answer:
HI SisTErS!
Step-by-step explanation:
An item travels 70 feet in 10 seconds. What is the unit rate? Question 1 options: 7 ft/s 17 ft/s 70 ft/s 700 ft/s
Answers
Answer: 7ft/s
Step-by-step explanation: 7ft x 10 sec =70 seconds
Explain how you know that (3, 5) is not a solution to the given inequality by looking at the graph.
Answers
The reason that the point (3, 5) is not a solution to the given inequality is given below.
We are given that;
y > 2x + 1
Now,
The inequality y > 2x + 1 can be graphed by first graphing the boundary line y = 2x + 1. Since the inequality is strict (y >), we draw a dashed line to indicate that points on the line are not solutions to the inequality. Then, we shade the region above the line to indicate all points that satisfy the inequality.
If we have (3,5) as a point, we can see that it lies on the boundary line
y = 2x + 1.
Since the inequality is strict (y >), points on this line are not solutions to the inequality
Therefore, by the inequality the answer will be given above.
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PLEASE HELPPPP ITS A GRADE
Answers
Answer:
A. It is not a function because 0 outputs multiple items
B. the domain seems to be 0,1,2,3
c.The range seems to be -2,1,2,4
Step-by-step explanation:
Sammy finds satellite images of a school and a museum. They put the images on a coordinate grid (shown below). Compare the area of the school and the museum.
Answers
The area of the museum is given by:
\(\begin{gathered} A=\pi r^2 \\ \text{Where:} \\ r=30m \\ A=\pi(30^2)=900\pi\approx2827m^2 \end{gathered}\)The area of the school is:
\(\begin{gathered} A=w\cdot l \\ \text{where:} \\ w=\text{width} \\ l=\text{length} \\ w=\sqrt[]{30^2+10^2}=10\sqrt[]{10} \\ l=\sqrt[]{60^2+20^2}=20\sqrt[]{10} \\ A=(10\sqrt[]{10})(20\sqrt[]{10})=2000m^2 \end{gathered}\)\(2827m^2-2000m^2=827m^2\)The area of the school is about 827m² less than the area of the museum
What do you use to isolate a variable
Answers
Answer:
please specify
Step-by-step explanation:
what is ratio what is ratio what is ratio
Answers
The ratio or the proportion is solved
Given data ,
A ratio is a comparison of two quantities by division. It expresses the relative size or amount of one quantity in comparison to another.
Ratios are often written as a fraction, with a colon, or with the word "to".
For example, if we have a bowl of fruit that contains 6 apples and 2 oranges, the ratio of apples to oranges is 6:2, which can be simplified to 3:1. This means that for every 3 apples, there is 1 orange in the bowl.
Hence , the proportion is solved
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12. Find the Volume of the rectangular prism below. Write your final answer as a decimal by converting the fraction to decimal. Also write the units as cubic inches. * 13 in. 2 in. 3 in
Answers
Answer:
V = 9.75 cubic inches.
Step-by-step explanation:
Given the following data;
Length = 2 inches
Width = 3¼ inches
Height = 1½ inches
To find the volume of rectangular prism;
Volume of rectangular prism = length * width * height
V = 2 * 3¼ * 1½
V = 2 * 13/4 * 3/2
V = 2 * 39/8
V = 2 * 4.875
V = 9.75 cubic inches
QUOTIENT OF 84 AND 6
Answers
Answer:
Yo, 84/6 is 14
Step-by-step explanation:
The quotient is the answer you get from a division problem.
Answer:
84 ÷ 6 = 14, or 6 ÷ 84 = 0.07142857142857142857142857142857...
I assume that you meant 84 ÷ 6.
Hope that this helps!
The vertices of figure PQRS are translated to form figure P'Q'R'S'. Select all the statements that describe the two figures. Q S R P' S' Q' 'R
the anawer choices are : A. P Q R S is the preimage of PQRS, B. the two figures are congruent, C. the two figures are in different positions , but have the same orientation, D. the two figures are in different positions and have oppsoite orientation , E. corresponding angles and sides of the figures have the same measures.
Answers
The true statements are:
(B) Both figures are congurent.
(C) The two figures have the same orientation but different positions.
(E) Corresponding angles and sides have the same measures.
What is orientation?In geometry, how an item is positioned in the space it occupies—such as a line, plane, or rigid body—is described in terms of its orientation, angular position, attitude, bearing, and direction.
It refers more particularly to the fictitious rotation required to shift an object from a reference placement to its present location.
To get to the current positioning, a rotation might not be sufficient.
It could be required to include a fictitious translation known as the object's location (or position, or linear position).
Together, the position and orientation completely explain where the object is situated in space.
Therefore, the true statements are:
(B) Both figures are congurent.
(C) The two figures have the same orientation but different positions.
(E) Corresponding angles and sides have the same measures.
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Austin deposited $3000 into an account with a 4.6% annual interest rate, compounded quarterly. Assuming that no withdrawals are made, how long will it take
for the investment to grow to $4179?
Do not round any intermediate computations, and round your answer to the nearest hundredth.
Answers
The number of years for the compound interest to reach an amount of value $ 4179 is given by n = 7.25 years
Given data ,
Let the compound interest amount be represented as A
Now , the interest rate r = 4.6 %
The number of times the interest is applied = quarterly
The principal amount P = $ 3000
Let the number of years be represented as n
And , t = ln(A/P) / n[ln(1 + r/n)]
t = ln(4,179.00/3,000.00) / ( 4 × [ln(1 + 0.046/4)] )
t = ln(4,179.00/3,000.00) / ( 4 × [ln(1 + 0.0115)] )
t = 7.247 years
On simplifying , we get n = 7.25 years
Hence , time required to get a total amount of $4,179.00 with compounded interest on a principal of $3,000.00 at an interest rate of 4.6% per year and compounded 4 times per year is 7.25 years
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Unit 3, Lesson 10: What Are Percentages?
1.
Fill in the blank: The value of 8 dimes is
% of the value of a dollar.
Answers
Answer:
I believe it is 80%
Step-by-step explanation:
Tell me if its right
HELP ME OUT PLEASE!!!!!!!
Simplify
Answers
Answer:
I believe it is -2a⁶b¹² (the first option)
which is greater [-3.25] or [4.25]
Answers
Answer:
4.25
Step-by-step explanation:
The number is bigger in absolute form
Look at the expression below.
2h+y
40
917-y2
3h+y
Which of the following is the least common denominator for the expression?
O A. (3h + y)
ОВ.
(3h-y)(3h + y)
O C.
(3h+y)(3h + y)(3h - y)
OD. 3(h+y)(n-y
Answers
Answer:
B
Step-by-step explanation:
apply difference of two squares
NEED HELP ASAP!!!!!!!!!!!!!!!
Answers
Answer: c is the answer
Can someone please help me with this question, I have multiple of them and have no idea where to start. If you can help me with this please show how you got it because im clueless
Answers
Answer:
Step-by-step explanation:
( 3x - 7 )° + ( 9x - 2 )° + ( x + 7 )° = 180°
13x = 182
x = 14
m ∠ A = ( 3 × 14 - 7 )° = 35°
m ∠ B = ( 9 × 14 - 2 )° = 124°
m ∠ C = ( 14 + 7 )° = 21°
A bag of baseballs costs $12. There are 15 balls in the bag. Another bag of baseballs costs $15 for 20 balls. Which bag prices individual baseballs lower?
Answers
Answer:
Step-by-step explanation:
For the first bag:
Price of the bag = $12
Number of balls in the bag = 15
Price per ball = Price of the bag / Number of balls
Price per ball for the first bag = $12 / 15 = $0.8
For the second bag:
Price of the bag = $15
Number of balls in the bag = 20
Price per ball = Price of the bag / Number of balls
Price per ball for the second bag = $15 / 20 = $0.75
Comparing the prices per ball, we find that the second bag has a lower price per baseball. Therefore, the second bag offers a better price for individual baseballs compared to the first bag.
Answer:
Step-by-step explanation:
To find out which bag prices individual baseballs lower, we can divide the total cost of each bag by the number of balls in the bag. This will give us the price per ball for each bag.
For the first bag, the price per ball is $12 / 15 = $0.80.
For the second bag, the price per ball is $15 / 20 = $0.75.
Therefore, the second bag prices individual baseballs lower.