what is the graph of f(x) = 5(2)^x
Answers
The graph of the function f(x) = 5(2)^x is an upward-sloping exponential curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing the x-axis.
The function f(x) = 5(2)^x represents exponential growth. Let's analyze its graph.
As x increases, the value of 2^x grows exponentially. Multiplying it by 5 further amplifies the growth. Here are a few key points to consider:
When x = 0, 2^0 = 1, so f(0) = 5(1) = 5. This is the y-intercept of the graph, meaning the function passes through the point (0, 5).
As x increases, 2^x grows rapidly. For positive values of x, the function will increase quickly. As x approaches positive infinity, 2^x grows without bound, resulting in the function also growing without bound.
For negative values of x, 2^x approaches zero. However, the function is multiplied by 5, so it will not reach zero. Instead, it will approach y = 0, but the graph will never touch or cross the x-axis.
The function is always positive since 2^x is positive for any value of x, and multiplying by 5 does not change the sign.
Based on these observations, we can conclude that the graph of f(x) = 5(2)^x will be an exponential growth curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing or touching the x-axis.
The graph will have a smooth curve that rises steeply as x increases. The rate of growth will be determined by the base, in this case, 2. The larger the base, the steeper the curve. The function will approach but never reach the x-axis as x approaches negative infinity.
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Related Questions
Given the set of data
4
10
2
18
15
would finding the best predicted value for x = 20 be an example of interpolation or extrapolation?
a. Extrapolation since 20 is not within the range.
b. Extrapolation since 20 is within the range.
Answers
The correct answer is b. Extrapolation since 20 is within the range.
In this scenario, finding the best predicted value for x = 20 would be an example of extrapolation. Extrapolation involves estimating values outside the given range of data based on the trend or pattern observed within the existing data.
Given the data set: 4, 10, 2, 18, 15, we can see that the values provided are not in any particular order. To perform extrapolation, it is generally helpful to first examine the trend or pattern within the data. However, without additional information or context, it is difficult to determine the underlying trend in this case.
Since the given data set does not explicitly indicate any pattern or trend, any estimation made for x = 20 would be considered extrapolation. Extrapolation involves projecting or extending the existing trend or pattern beyond the known data points. In this case, the value of 20 falls outside the range of the given data set, so estimating its corresponding value would require extending the trend beyond the known data points.
Consequently, the appropriate response is b. Extrapolation since 20 is within the range.
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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
Answers
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
please answer ASAP I will brainlist
Answers
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.
Answers
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.
HELP THIS QUESTION IS HARD
Answers
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]
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.
Answers
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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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%:
Answers
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.
what is (0.3)0 in binominal distribution
Answers
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.
consider the graph function below
Answers
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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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
Answers
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%
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
Answers
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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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
Answers
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.
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?
Answers
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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Here is a unit circle with point P at (1, 0) Find the coordinates of P after the circle rotates the given amount counter clockwise around its center
1. 1/3 of a full rotation: ?
2 1/2 of a full rotation: ?
3. 2/3 of a full rotation: ?
Answers
1/3 of a full rotation: (-0.5, √3/2)
1/2 of a full rotation: (-1, 0)
2/3 of a full rotation: (0.5, -√3/2)
These are the coordinates of point P after the corresponding rotations around the unit circle's center.
To find the coordinates of point P after the unit circle rotates a certain amount counter-clockwise around its center, we can use the properties of the unit circle and the trigonometric functions.
1/3 of a full rotation:
A full rotation in the unit circle corresponds to 360 degrees or 2π radians. Therefore, 1/3 of a full rotation is equal to (1/3) * 360 degrees or (1/3) * 2π radians.
When the unit circle rotates 1/3 of a full rotation, point P will end up at an angle of (1/3) * 2π radians or 120 degrees from the positive x-axis.
In the unit circle, the x-coordinate of a point on the circle represents the cosine of the angle, and the y-coordinate represents the sine of the angle.
At an angle of 120 degrees or (1/3) * 2π radians, the cosine is -0.5 and the sine is √3/2.
Therefore, the coordinates of point P after rotating 1/3 of a full rotation are (-0.5, √3/2).
1/2 of a full rotation:
Similarly, 1/2 of a full rotation is equal to (1/2) * 360 degrees or (1/2) * 2π radians.
When the unit circle rotates 1/2 of a full rotation, point P will end up at an angle of (1/2) * 2π radians or 180 degrees from the positive x-axis.
At an angle of 180 degrees or (1/2) * 2π radians, the cosine is -1 and the sine is 0.
Therefore, the coordinates of point P after rotating 1/2 of a full rotation are (-1, 0).
2/3 of a full rotation:
Again, 2/3 of a full rotation is equal to (2/3) * 360 degrees or (2/3) * 2π radians.
When the unit circle rotates 2/3 of a full rotation, point P will end up at an angle of (2/3) * 2π radians or 240 degrees from the positive x-axis.
At an angle of 240 degrees or (2/3) * 2π radians, the cosine is 0.5 and the sine is -√3/2.
Therefore, the coordinates of point P after rotating 2/3 of a full rotation are (0.5, -√3/2).
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At what points is the function y=sinx/3x continuous?
Answers
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.
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
Answers
V = 2π ∫[0,1] y(4y^2 - y^3) dy
Simplifying the integrand, we get:
V = 2π ∫[0,1] (4y^3 - y^4) dy
Integrating, we get:
V = 2π [(y^4 - (1/5)y^5)]|[0,1]
V = 2π [(1 - (1/5))] = (8/5)π
Therefore, the volume of the solid is (8/5)π cubic units.
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
Answers
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.
Please help me I don't understand what to do in order to solve this question
Find x, the angle inscribed in the circle
Answers
87/2= 43.5
x=43.5
please answer i am stuck
Answers
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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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?
Answers
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
Find the exact value of cos 105⁰.
a. √√√2-√6
4
b.
√2+√6
4
C.
4
d. √2+√6
4
Answers
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]
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?
Answers
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.
Qué porcentaje de 200 es 164
Answers
Si hacemos una regla de tres
Se multiplica 164*100
Y después el resultado de divide entre 200
Espero que te sirva
{y=4x−19.4
y=0.2x−4.2
Answers
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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 Ex is tangent to circle O at point L, and IF is a secant line. If m_FLX = 104°, find
mLKF.
Answers
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°
Ex is tangent to circle O at point L, and IF is a secant line. If m_FLX = 104°, find
mLKF.
Answers
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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Find the value of each variable. Round your answers
to the nearest tenth.
12
X
25°
Answers
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.
Answers
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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Team A and Team B together won 50% more games than Team C did. Team A won 50% as many games as Team B did. The three teams won 60 games in all. How many games did each team win?
Answers
Let x be the number of games won by Team A.
Let y be the number of games won by Team B.
Let z be the number of games won by Team C.
From the given information, we can form the following equations:
Equation 1: x + y + z = 60 (The total number of games won by the three teams is 60.)
Equation 2: x = (1/2)y (Team A won 50% as many games as Team B.)
Equation 3: x + y = 1.5z (Team A and Team B together won 50% more games than Team C.)
Now, let's solve this system of equations:
Substituting Equation 2 into Equation 3, we get:
(1/2)y + y = 1.5z
(3/2)y = 1.5z
y = (1.5z) * (2/3)
y = z
Substituting y = z into Equation 1, we have:
x + y + z = 60
x + y + y = 60
x + 2y = 60
Substituting y = z into Equation 3, we have:
x + y = 1.5z
x + y = 1.5y
x = 0.5y
Now, we can substitute x = 0.5y and y = z into Equation 1:
0.5y + 2y = 60
2.5y = 60
y = 60 / 2.5
y = 24
Substituting y = 24 into x = 0.5y:
x = 0.5 * 24
x = 12
Substituting y = 24 into the equation y = z:
z = 24
Therefore, Team A won 12 games, Team B won 24 games, and Team C won 24 games as well.
Find all values of x are not in the domain of h
Answers
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.
