Answer:
There are three main ways to prove that two triangles are congruent using transformations:
1. Congruence by translation: If there is a translation that maps one triangle onto the other, then the triangles are congruent.
2. Congruence by reflection: If there is a line of reflection that maps one triangle onto the other, then the triangles are congruent.
3. Congruence by rotation: If there is a rotation that maps one triangle onto the other, then the triangles are congruent.
In order to use these transformations to prove congruence, you need to show that all corresponding parts (angles and sides) are congruent after the transformation is applied. This can be done either algebraically, using coordinate geometry, or by providing a clear visual representation of the transformations that are applied.
For example, if you want to prove that two triangles, ABC and DEF, are congruent by translation, you need to show that there is a vector that, when added to the coordinates of any point on triangle ABC, produces the coordinates of the corresponding point on triangle DEF. Once you have shown that all three sides and angles are congruent after the translation, you can conclude that the triangles are congruent.
Find the probability that a randomly
selected point within the circle falls in the
red-shaded triangle.
12
12
P = [?]
Enter as a decimal rounded to the nearest hundredth.
Enter
Answer:
Area of triangle = (1/2)(12²) = (1/2)(144) = 72
Area of circle = π(12²) = 144π
P(point falls in triangle) = 72/(144π)
= 1/(2π)
= about .16
= about 15.92%
so in the same Equation i have to do use the values x=-4,0,5 to verify my solution to the equation 5+x-12=x-7 in my final answer.
5+x-12=2x-7
x-7=2x-7
x-7+7=2x-7+7
x=2x
x-2x=2x-2x
-x=0
--- ---
-1 -1
x=0
--
-1
x=0
Answer:
Step-by-step explanation:
Let's revisit the equation and the solution using the values x = -4, 0, and 5.
The given equation is: 5 + x - 12 = x - 7
Let's go through the steps again to solve it:
5 + x - 12 = x - 7
Combine like terms:
x - 7 = x - 7
Now, subtract x from both sides:
x - x - 7 = x - x - 7
Simplify:
-7 = -7
The equation simplifies to -7 = -7, which is true.
Now, let's use the values x = -4, 0, and 5 to verify the solution.
For x = -4:
5 + (-4) - 12 = (-4) - 7
-11 = -11
The equation is satisfied for x = -4.
For x = 0:
5 + 0 - 12 = 0 - 7
-7 = -7
The equation is satisfied for x = 0.
For x = 5:
5 + 5 - 12 = 5 - 7
-2 = -2
The equation is satisfied for x = 5.
Therefore, the solution x = 0 is correct, and it satisfies the equation for the given values. My earlier statement that x = -4 and x = 5 do not satisfy the equation was incorrect. I apologize for the confusion caused.
please answer i am stuck
(a) To find the assets in 2011 using the given information: A. To find the assets in 2011, substitute 11 for x and evaluate to find A(x).
In 2011 the assets are about $669.6 billion
(b) To find the assets in 2016 using the given information: B. To find the assets in 2016, substitute 16 for x and evaluate to find A(x).
In 2016 the assets are about $931.5 billion.
(c) To find the assets in 2019 using the given information: B. To find the assets in 2019, substitute 19 for x and evaluate to find A(x).
In 2019 the assets are about $1135.4 billion.
How to estimate the cost of the assets in 2011?Based on the information provided, we can logically deduce that the assets for a financial firm can be approximately represented by the following exponential function:
[tex]A(x)=324e^{0.066x}[/tex]
where:
A(x) is in billions of dollars.x = 7 corresponds to the year 2007.For the year 2011, the cost (in billions of dollars) is given by;
x = (2011 - 2007) + 7
x = 4 + 7
x = 11 years.
Next, we would substitute 11 for x in the exponential function:
[tex]A(11)=324e^{0.066 \times 11}[/tex]
A(11) = $669.6 billions.
Part b.
For the year 2016, the cost (in billions of dollars) is given by;
x = (2016 - 2007) + 7
x = 9 + 7
x = 16 years.
Next, we would substitute 16 for x in the exponential function:
[tex]A(16)=324e^{0.066 \times 16}[/tex]
A(16) = $931.5 billions.
Part c.
For the year 2019, the cost (in billions of dollars) is given by;
x = (2019 - 2007) + 7
x = 12 + 7
x = 19 years.
Next, we would substitute 19 for x in the exponential function:
[tex]A(19)=324e^{0.066 \times 19}[/tex]
A(19) = $1135.4 billions.
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HELP THIS QUESTION IS HARD
Answer:
a)
[tex] \frac{1}{( - 7)^{4} } [/tex]
Answer:
[tex](-7)^-^4=\frac{1}{(-7)^4}[/tex]
Step-by-step explanation:
The user aswati already wrote the correct answer, but I wanted to help explain why their answer is correct so that you'll understand.
According to the negative exponent rule, when a base (let's call it m) is raised to a negative exponent (let's call it n), we rewrite it as a fraction where the numerator is 1 and the denominator is the base raised to the same exponent turned positive.
Thus, the negative exponent rule is given as:
[tex]b^-^n=\frac{1}{b^n}[/tex]
Thus, [tex](-7)^-^4[/tex] becomes [tex]\frac{1}{(-7)^4}[/tex]
The cost of capsaicin arthritis rub is $21 for a
physical therapist who works with chronic arthritis patients, you need to buy
42 ounces of capsaicin. How many tubes will you need to purchase?
You will need to purchase approximately 1/42 of a tube, which is less than a full tube. In practical terms, you would need to purchase at least one tube to meet your requirement of 42 ounces of capsaicin arthritis rub.
To determine the number of tubes of capsaicin arthritis rub you will need to purchase, we can divide the total required quantity by the quantity in each tube.
Given that the cost of capsaicin arthritis rub is $21 and you need to buy 42 ounces, we need to find out how many ounces are in each tube.
Let's assume that each tube contains x ounces of capsaicin arthritis rub.
Now we can set up a proportion to solve for x:
42 ounces / x tubes = 1 tube / x ounces
Cross-multiplying gives us:
42x = 1 * x
Simplifying the equation:
42x = x
Dividing both sides of the equation by x (since x cannot be zero):
42 = 1
Since this equation is not true, it means that there is an error in our assumption. We need to revise our assumption.
Let's assume that each tube contains 1 ounce of capsaicin arthritis rub.
Now we can set up a new proportion:
42 ounces / x tubes = 1 tube / 1 ounce
Cross-multiplying gives us:
42x = 1 * 1
Simplifying the equation:
42x = 1
Dividing both sides of the equation by 42:
x = 1/42
As a result, you will need to buy less than a full tube—roughly 1/42 of a tube. In order to get the 42 ounces of capsaicin arthritis rub you need, you would essentially need to buy at least one tube.
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Calc II Question
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x axis
x = 4y^2 - y^3
x = 0
Ex is tangent to circle O at point L, and IF is a secant line. If m_FLX = 104°, find
mLKF.
The angle m∠MHU between the intersection of the secant line HM and tangent line HU is equal to 54°
How to calculate for angle between the intersection of a secant and a tangent.To calculate for the angle between the intersection of a secant and a tangent we need to know the measure of the intercepted arc, and then divide it by 2 to get the angle.
If the measure of the arc HM is given to be equal to 108°, then the measure of angle MHU is calculated as:
angle MHU = 108°/2
m∠MHU = 54°
Therefore, the angle m∠MHU between the intersection of the secant line HM and tangent line HU is equal to 54°
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Qué porcentaje de 200 es 164
Based on the two data sets represented below, complete the following sentences. DATA SET K DATA SET K 0 0 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 DATA SET L DATA SET L 0 0 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 The center of Data Set K is than the center of Data Set L. The spread of Data Set K is than the spread of Data Set L.
Based on the provided data sets, it can be observed that both Data Set K and Data Set L have identical values. Therefore, their centers and spreads are also identical.
The center of a data set can be measured using various statistical measures such as the mean, median, or mode. Since the data sets have the same values, all these measures will yield the same result for both sets.
In this case, the center of Data Set K is equal to the center of Data Set L.
Similarly, the spread of a data set refers to the measure of variability or dispersion within the data. Common measures of spread include the range, variance, and standard deviation.
However, since the data sets are exactly the same, all these measures will yield identical results for both sets. Thus, the spread of Data Set K is the same as the spread of Data Set L.
In summary, both the center and the spread of Data Set K are the same as those of Data Set L. Therefore, there is no difference between the two data sets in terms of their central tendency or variability.
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what is (0.3)0 in binominal distribution
Answer:
When p, the probability of success, is zero in a binomial distribution, the probability of getting exactly k successes in n trials is also zero for all values of k except when k is zero (i.e., when there are no successes).
So, in the case of (0.3)^0, the result would be 1, because any number raised to the power of 0 is equal to 1. Therefore, the probability of getting zero successes in a binomial distribution when the probability of success is 0.3 is 1.
Darla, Ellie, and Fran ate a whole container of ice cream. Darla ate half as much as Ellie ate, and Fran ate 5 times as much as Darla ate. If the container of ice cream cost $4.00, how much, in dollars, should each person pay?
Please help me I don't understand what to do in order to solve this question
Find x, the angle inscribed in the circle
What number completes the sequence below? Enter your answer in the input
box at the bottom.
8————-4
16————8
24———-12
32———-?
Answer here
Answer:
The number is 16
Step-by-step explanation:
This follows a multiplication rule,
4 times 1 = 4
4 times 2 = 8
4 times 3 = 12
4 times 4 = 16
So, the number is 16
At what points is the function y=sinx/3x continuous?
Answer: [tex](-\infty, 0) \cup (0, \infty)[/tex]
Step-by-step explanation:
The graph of [tex]\frac{\sin x}{x}[/tex] is continuous for all real [tex]x[/tex] except [tex]x=0[/tex], and multiplying this by [tex]1/3[/tex] does not change this.
{y=4x−19.4
y=0.2x−4.2
Answer:The solution of the linear equations y = 4x − 19.4 and y = 0.2x − 4.2 will be (4, -3.4). Then the correct option is A.
What is the solution to the equation?
The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The equations are given below.
y = 4x − 19.4 ...1
y = 0.2x−4.2 ...2
From equations 1 and 2, then we have
4x - 19.4 = 0.2x - 4.2
3.8x = 15.2
x = 4
Then the value of the variable 'y' will be calculated as,
y = 4 (4) - 19.4
y = 16 - 19.4
y = - 3.4
The solution of the linear equations y = 4x − 19.4 and y = 0.2x − 4.2 will be (4, -3.4). Then the correct option is A.
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consider the graph function below
The equation of the red graph is g(x) = f(x) - 5
How to calculate the equation of the red graphFrom the question, we have the following parameters that can be used in our computation:
The functions f(x) and g(x)
Where, we have
f(x) = -x
i.e.. the parent equation of the function
From the graph, we can see that
The function is shifted down by 5 units
This means that
g(x) = f(x) - 5
This means that the equation of the red graph is g(x) = f(x) - 5
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Copy the axes below.
a) By completing the tables of values to help
you, plot the lines y = 2x + 1 and
y = 10x on your axes.
b) Use your diagram to find the solution to the
simultaneous equations y = 2x + 1 and
y = 10 - x.
y = 2x+1
x012
Y
y = 10-x
x012
Y
Y
-3 -2 -1
10
2987
65
6
-5
4
3
NW
21
1
-14
--2
73
1 2 3 4 5 6 7 8 9 10 x
The solution to the simultaneous equations is x = 3 and y = 7
Finding the solution to the simultaneous equationsFrom the question, we have the following parameters that can be used in our computation:
y = 2x + 1
y = 10 - x
Subtract the equations
So, we have
3x - 9 = 0
This gives
3x = 9
So, we have
x = 3
Next, we have
y = 10 - x
y = 10 - 3
Evaluate
y = 7
Hence, the solution is x = 3 and y = 7
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Find the value of each variable. Round your answers
to the nearest tenth.
12
X
25°
The value of 12 remains 12.
The value of X cannot be determined without additional information.
The value of 25° remains 25°.
To find the values of the variables in the given information, we have:
12: This is a given value and does not require calculation. Therefore, the value of 12 remains as it is.
X: Without additional information or an equation to solve, we cannot determine the value of X. It could represent any unknown quantity or variable, and its specific value would depend on the context or problem being solved.
25°: This is an angle measure in degrees. The value of 25° remains as it is.
To summarize:
The value of 12 remains 12.
The value of X cannot be determined without additional information.
The value of 25° remains 25°.
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In circle I, IJ = 9 and m/JIK = 140°. Find the length of JK. Express your answer as a fraction times pie.
The calculated length of the arc JK is 7π
Finding the length of the arc JKFrom the question, we have the following parameters that can be used in our computation:
Central angle = 140 degrees
Radius, IJ = 9 inches
Using the above as a guide, we have the following:
JK = Central angle/360 * 2 * π * Radius
Substitute the known values in the above equation, so, we have the following representation
JK = 140/360 * 2 * π * 9
Evaluate
JK = 7π
Hence, the length of the arc is 7π
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please answer ASAP I will brainlist
The correct answer choice is: A. The system has exactly one solution. The solution is (11, 7).
The correct answer choice is: A. all three countries had the same population of 7 thousand in the year 2011.
How to solve this system of equations and interpret the answer?Based on the information provided above, the population (y) in the year (x) of the countries listed are approximated by the following system of equations:
-x + 20y = 129
-x + 10y = 59
y = 7
where:
y is in thousands.x = 10 corresponds to 2010.By solving the system of equations simultaneously, we have the following solution:
-x + 20(7) = 129
x = 140 - 129
x = 11
-x + 10(7) = 59
x = 70 - 59
x = 11
Therefore, the system of equations has only one solution (11, 7).
For the year when the population are all the same for three countries, we have:
x = 2010 + (11 - 10)
x = 2011
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PLEASE HELP 100 POINTS
Select the correct answer.
The length, l, of a rectangle is modeled by the equation l = w + 4, where w is the width of the rectangle in centimeters.
Two equations have been determined that represent the area of the rectangle, A, in square centimeters:
The first equation was created using the formula for the area of a rectangle: A = w2 + 4w.
The second equation models the relationship between the rectangle's area and width: A = 4w + 45.
Which statement describes the solution(s) of the system?
A.
There are two solutions, and neither are viable.
B.
There are two solutions, but only one is viable.
C.
There are two solutions, and both are viable.
D.
There is only one solution, and it is viable.
Answer:
B) There are two solutions, but only one is viable.
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}A=w^2+4w\\A=4w+45\end{cases}[/tex]
To solve the system of equations, substitute the first equation into the second equation:
[tex]w^2+4w=4w+45[/tex]
Solve for w using algebraic operations:
[tex]\begin{aligned}w^2+4w&=4w+45\\w^2+4w-4w&=4w+45-4w\\w^2&=45\\\sqrt{w^2}&=\sqrt{45}\\w&=\pm \sqrt{45}\\w &\approx \pm 6.71\; \sf cm\end{aligned}[/tex]
Therefore, there are two solutions to the given system of equations.
However, as length cannot be negative, the only viable solution is w ≈ 6.71 cm.
Find all values of x are not in the domain of h
Answer:
x = -1, 1
Step-by-step explanation:
The function h(x) is given below:
[tex]\displaystyle{h(x)=\dfrac{x-9}{x^2-1}}[/tex]
The denominator must not equal to 0. Therefore,
[tex]\displaystyle{x^2-1\neq 0}[/tex]
Solve the inequality; factor the expression:
[tex]\displaystyle{(x-1)(x+1) \neq 0}[/tex]
Hence,
[tex]\displaystyle{x \neq 1,-1}[/tex]
Therefore, x = -1, 1 both are not in the domain of h.
Find the exact value of cos 105⁰.
a. √√√2-√6
4
b.
√2+√6
4
C.
4
d. √2+√6
4
Answer:
[tex]\dfrac{\sqrt{2}-\sqrt{6} }{4} }[/tex]
Step-by-step explanation:
Find the exact value of cos(105°).
The method I am about to show you will allow you to complete this problem without a calculator. Although, memorizing the trigonometric identities and the unit circle is required.
We have,
[tex]\cos(105\°)[/tex]
Using the angle sum identity for cosine.
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Angle Sum Identity for Cosine}}\\\\\cos(A+B)=\cos(A)\cos(B)-\sin(A)\sin(B)\end{array}\right}[/tex]
Split the given angle, in degrees, into two angles. Preferably two angles we can recognize on the unit circle.
[tex]105\textdegree=45\textdegree+60\textdegree\\\\\\\therefore \cos(105\textdegree)=\cos(45\textdegree+60\textdegree)[/tex]
Now applying the identity.
[tex]\cos(45\textdegree+60\textdegree)\\\\\\\Longrightarrow \cos(45\textdegree+60\textdegree)=\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)[/tex]
Now utilizing the unit circle.
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{From the Unit Circle:}}\\\\\cos(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\cos(60\textdegree)=\dfrac{1}{2}\\\\\sin(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\sin(60\textdegree)=\dfrac{\sqrt{3} }{2} \end{array}\right}[/tex]
[tex]\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)[/tex]
Now simplifying...
[tex]\Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{4} \Big)-\Big(\dfrac{\sqrt{6} }{4} \Big)\\\\\\\therefore \cos(105\textdegree)= \boxed{\boxed{\frac{\sqrt{2}-\sqrt{6} }{4} }}[/tex]
Angela lives in New York, which has a sales tax of 8.125%. She bought some word-processing software whose full price was $110, but she presented the retailer with a coupon for $30. What was the total amount that Angela paid?
Answer: 88.94
Step-by-step explanation:
First, l found what was 8.125 out of 110 which is 8.94
then added 8.125 and 8.94 which got 118.94
But Angela gave the retailer an $30 coupon so l subtracted 30 from 118.94 which got me 88.94
A circles radius is 1 1/3 yard whats the perimeter
Step-by-step explanation:
Perimeter = pi * diameter
radius = 1 1/3 yard then diameter = 2 2/3 yd
perimter = pi * 2 2/3 yds = 8.38 yds
 Ex is tangent to circle O at point L, and IF is a secant line. If m_FLX = 104°, find
mLKF.
Answer:
arc LKF = 208°
Step-by-step explanation:
the angle FLX between the tangent and the secant is half the measure of the intercepted arc LKF , then intercepted arc is twice angle FLX , so
arc LKF = 2 × 104° = 208°
Ms. Lee used two dozen Mud Bugs in her suit the recipe makes 20 cups of soup approximately how many Mud Bugs are in each cup of soup round off the answer to the nearest whole number
Answer:
1
Step-by-step explanation:
So, 1 dozen is 12. Two dozen is 24.
She used 24 Mud Bugs in this soup.
This soup makes 20 cups.
So, 24 Mud Bugs are in 20 cups of soup.
To find the amount of Mud Bugs in each cup of soup, you divide the amount of Mud Bugs by the number of cups.
24/20
Which equals 1.2
You asked for the nearest whole number, so there is 1 Mud Bug per sup of soup.
Ralph chase plans to sell a piece of property for $145000. He wants the money to be paid off in two ways-short term note at 10% interest and a long term note at 8% interest. Find the amount of each note if the total annual interest paid is $13100.
10%:
8%:
To solve this problem, we can set up a system of equations based on the given information.
Let's assume the amount of money Ralph Chase will receive through the short-term note is represented by "x" and the amount through the long-term note is represented by "y".
According to the problem, the total amount Ralph plans to sell the property for is $145,000. Therefore, we have the equation:
[tex]\displaystyle x+y=145000[/tex] ...(1)
Now let's consider the interest paid annually. The interest paid on the short-term note at 10% is calculated as [tex]\displaystyle 0.10x[/tex], and the interest paid on the long-term note at 8% is [tex]\displaystyle 0.08y[/tex]. The total annual interest paid is given as $13,100. Therefore, we have the equation:
[tex]\displaystyle 0.10x+0.08y=13100[/tex] ...(2)
We now have a system of two equations (1) and (2). We can solve this system to find the values of "x" and "y".
Multiplying equation (2) by 100 to eliminate decimals, we get:
[tex]\displaystyle 10x+8y=1310000[/tex] ...(3)
Now we can solve equations (1) and (3) simultaneously using any method such as substitution or elimination.
Multiplying equation (1) by 10, we get:
[tex]\displaystyle 10x+10y=1450000[/tex] ...(4)
Subtracting equation (3) from equation (4), we can eliminate "x" and solve for "y":
[tex]\displaystyle 2y=140000[/tex]
Dividing both sides by 2, we find:
[tex]\displaystyle y=70000[/tex]
Now substituting the value of "y" back into equation (1), we can solve for "x":
[tex]\displaystyle x+70000=145000[/tex]
Subtracting 70000 from both sides, we have:
[tex]\displaystyle x=75000[/tex]
Therefore, the amount of money Ralph Chase will receive through the short-term note is 75,000 and through the long-term note is $70,000.
please answer i am stuck
The correct answer choice is: A. The system has exactly one solution. The solution is (13, 5).
The correct answer choice is: A. all three countries had the same population of 5 thousand in the year 2013.
How to solve this system of equations and interpret the answer?Based on the information provided above, the population (y) in the year (x) of the counties listed are approximated by the following system of equations:
-x + 20y = 87
-x + 10y = 37
y = 5
where:
y is in thousands.x = 10 corresponds to 2010.By solving the system of equations simultaneously, we have the following solution:
-x + 20(5) = 87
x = 100 - 87
x = 13
-x + 10(5) = 37
x = 50 - 37
x = 13
Therefore, the system of equations has only one solution (13, 5).
For the year when the population are all the same for three countries, we have:
x = 2010 + (13 - 10)
x = 2013
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There are 12 containers containing various amounts of water, as shown below. ←+ 0 H ½ X X X X X X 1 X 1½ X X X 2 Cups If all of the water were dumped into one container, how many cups would be in the container?
Answer: it contains 12 containers
Step-by-step explanation: i dont know what the answer is but i know what i can help you with all you have to do is round the answer.
