Answer:
To solve this problem, we can use the equations of motion for a vertically launched object. First, we need to find the initial velocity of the snowball when it is kicked off the ground. We know that its speed is 24 feet per second, but we also need to take into account the angle at which it is kicked. Let's assume that Max kicks the snowball at a 45-degree angle. Using trigonometry, we can find that the horizontal velocity of the snowball is also 24 feet per second, and the vertical velocity is 24 feet per second times the sine of 45 degrees, which is approximately 16.97 feet per second. Now we can use the following equation to find the time it takes for the snowball to hit the ground: h = vi*t + 0.5*a*t^2 where h is the maximum height, vi
The graph shows f(x). The absolute value function g(x) is described in the table. The graph shows a v-shaped graph, labeled f of x, with a vertex at 0 comma 2, a point at negative 1 comma 3, and a point at 1 comma 3. x g(x) −1 5 0 4 1 3 2 2 3 3 If g(x) = f(x + k), what is the value of k? k = −2 k is equal to negative one half k is equal to one half k = 2
k is equal to 2, and the function g(x) is obtained by shifting the graph of f(x) two units to the left.
What is function?A function in mathematics is a relationship between a set of inputs (also known as the domain) and a set of outputs (also known as the range), where each input is connected to each output inexactly.
It can be compared to a machine that processes inputs and outputs in accordance with predetermined rules or algorithms.
In order to model real-world scenarios, carry out calculations, and examine mathematical relationships, functions are used.
They are frequently depicted through graphs or algebraic equations.
Since g(x) = f(x + k), we need to find the value of k that will shift the graph of f(x) to the graph of g(x). To do this, we can use the fact that g(x) = f(x + k) and the values in the table to determine the value of k.
When x = -1, g(x) = 5 = f(-1 + k). Since f has a point at (-1, 3), we know that f(-1) = 3.
Therefore, we have:
5 = f(-1 + k) = f(-1) + k = 3 + k
Solving for k, we get:
k = 5 - 3 = 2
To know more about graph visit:
https://brainly.com/question/25974513
#SPJ1
I have a question on this math problem, and I have to find the mean mode and range of the dot plot
With these steps, you can successfully find the mean, mode, and range of the data represented in the dot plot.
To find the mean, mode, and range of the dot plot, follow these steps:
Step 1: Count the total number of data points (dots) in the dot plot.
Step 2: Add up the values represented by the data points.
Step 3: Divide the sum from Step 2 by the total number of data points from Step 1 to calculate the mean.
Step 4: Identify the mode by finding the value(s) that appears most frequently in the dot plot (i.e., the value with the highest number of dots).
Step 5: Determine the range by finding the difference between the highest and lowest values in the dot plot.
For similar question on plot.
https://brainly.com/question/30408163
#SPJ11
according to financial experts, a renter should allow no more than 25% of their gross income for rent
true or false
Solve the system of equations
Answer:
(-1, 2)
Step-by-step explanation:
1.) The way to use elimination is to add or subtract both of the equations together to eliminate a variable. If we add the two equations together, the -6x and 6x cancel out. Since we added the equations together, -12y and 10y would add up to -2y, and -18 and 14 would add up to -4
2.) Now, we have the equation -2y = -4. By dividing by -2 on both sides, we get y=2.
3.) Next, we need to substitute y back in to get the x value. If you use the first equation, we get -6x - 12 * 2 = -18.
4.) By simplifying, you get that -6x - 24 = -18. If you add 24 on both sides, you get -6x = 6, and by dividing by -6 on both sides, you get x = -1.
5.) Finally, you have to put the answer in form of a point. -1 would be the x-coordinate and 2 would be the y-coordinate. Therefore, the point is (-1, 2)
f(x)= a (x - h)² + k
vertex axis of symmetry
h(x) = (x + 2)²
g(x) = (x-3)²
j(x)=(x-3)² + 2
y-intercept
Vertex of h(x) is (-2, 0), and the axis of symmetry is the line x = -2, vertex of g(x) is (3, 0), and the axis of symmetry is the line x = 3, vertex of j(x) is (3, 2), and the axis of symmetry is the line x = 3.
What is axis of symmetry?
In mathematics, the axis of symmetry is a line that divides a given shape into two symmetrical parts, such that each part is a mirror image of the other.
We can use the standard form of a quadratic function, which is given by:
[tex]F(x) = a(x - h)^2 + k[/tex]
where (h, k) is the vertex of the parabola and the axis of symmetry is the line x = h.
For [tex]h(x) = (x + 2)^2[/tex], we have:
h = -2 (since x + 2 = 0 when x = -2)
k = 0 (since the square of any real number is non-negative)
Therefore, the vertex of h(x) is (-2, 0), and the axis of symmetry is the line x = -2.
For [tex]g(x) = (x - 3)^2[/tex], we have:
h = 3
k = 0
Therefore, the vertex of g(x) is (3, 0), and the axis of symmetry is the line x = 3.
For [tex]j(x) = (x - 3)^2 + 2[/tex], we have:
h = 3
k = 2
Therefore, the vertex of j(x) is (3, 2), and the axis of symmetry is the line x = 3.
To find the y-intercept of each function, we can simply plug in x = 0:
For h(x):
[tex]h(0) = (0 + 2)^2 = 4[/tex]
Therefore, the y-intercept of h(x) is 4.
For g(x):
[tex]g(0) = (0 - 3)^2 = 9[/tex]
Therefore, the y-intercept of g(x) is 9.
For j(x):
[tex]j(0) = (0 - 3)^2 + 2 = 11[/tex]
Therefore, the y-intercept of j(x) is 11.
To learn more about axis of symmetry visit:
https://brainly.com/question/29723003
#SPJ1
Fill out the x-y chart. 11. y = log_2 x – 1 X -2 -1 O 1 2 Y C
ASAP!!!!
Answer:
[tex]\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12}x&y\\\cline{1-2}\vphantom{\dfrac12}-2&\rm DNE\\\cline{1-2}\vphantom{\dfrac12}-1&\rm DNE\\\cline{1-2}\vphantom{\dfrac12}0&\rm DNE\\\cline{1-2}\vphantom{\dfrac12}1&-1\\\cline{1-2}\vphantom{\dfrac12}2&0\\\cline{1-2}\end{array}[/tex]
Step-by-step explanation:
Given equation:
[tex]y=\log_2x-1[/tex]
To fill out the given x-y chart, substitute each given value of x into the given log equation.
The argument of a log function can only take positive arguments, so when x = -2, x = -1 and x = 0, the y-values are undefined.
The values of y for x = 1 and x = 2 are:
[tex]\begin{aligned}x=1 \implies y&=\log_21-1\\&=0-1\\&=-1\end{aligned}[/tex]
[tex]\begin{aligned}x=2 \implies y&=\log_22-1\\&=1-1\\&=0\end{aligned}[/tex]
Therefore, the completed x-y chart for the equation y = log₂x - 1 is:
[tex]\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12}x&y\\\cline{1-2}\vphantom{\dfrac12}-2&\rm DNE\\\cline{1-2}\vphantom{\dfrac12}-1&\rm DNE\\\cline{1-2}\vphantom{\dfrac12}0&\rm DNE\\\cline{1-2}\vphantom{\dfrac12}1&-1\\\cline{1-2}\vphantom{\dfrac12}2&0\\\cline{1-2}\end{array}[/tex]
Note: I have used DNE for does not exist.
a cereal comes in three different package sizes. what is the ratio of the cost of an 8-ounce box to a 16-ounce box of cereal? show your work on the sketchpad or explain in the text box.
As per the given scenario, a cereal comes in three different package sizes.
The ratio of the cost of an 8-ounce box to a 16-ounce box of cereal can be calculated as follows :Ratio of 8-ounce box to 16-ounce box= 8 : 16Here, the ratio of 8 and 16 can be simplified by dividing both the terms by [tex]8.8 : 16 = 1 : 2[/tex]
Therefore, the ratio of the cost of an 8-ounce box to a 16-ounce box of cereal is 1 : 2.
Note: The answer should be represented in the simplest form possible.
for such more questions on Ratios
https://brainly.com/question/12024093
#SPJ11
A cylindrical container holds 4.4 litres of water when full. If the height of the container is 14 cm, what is it's radius? (Take
[tex]\pi \binom{22}{7} [/tex]
Radius of cylindrical container is 10 cm, if cylindrical container holds 4.4 litres of water when full and If the height of the container is 14 cm.
How to measure radius of the cylinder?
To solve this problem, we can use the cylinder volume formula:
Volume of cylinder =
π × radius^2 × height
We know that the volume of water that the cylinder can hold is 4.4 litres. We can convert this to cubic centimeters (cm^3) by multiplying by 1000, since there are 1000 cm^3 in a liter:
4.4 litres =
4.4 × 1000 = 4400 cm^3
We also know the height of the cylinder is 14 cm. So we can plug in these values and solve for the radius:
4400 = π × radius^2 × 14
Dividing both sides by 14π, we get:
radius^2 = 4400 / (14 × π) = 100
Taking the square root of the both sides yields:
radius = √100 = 10 cm
As a result, the cylindrical container's radius is 10 cm.
To learn more about Radius, visit: https://brainly.com/question/30402082
#SPJ9
Calc Prep question involving Cramer's Rule:
Using Cramer’s Rule, what is the value of x in the solution to the system of linear equations below?
2/5X + 1/4Y = 9/20
2/3X + 5/12 = 3/4
A )X = 0
B) X = 1
C) There are no solutions to the system.
D) There are infinite solutions to the system.
For the given linear equations, x = 63/4 i.e. None of the above options.
What is a linear equation, exactly?
Each term in a linear equation is either a constant or the product of a constant and a single variable raised to the first power. A linear equation in one variable has the general form: axe + b = 0, where a and b are constants and x is the variable. This equation's answer is a single value of x that solves the problem.
Now,
To use Cramer's Rule to solve this system of linear equations, we need to set up the following matrices:
A = 2/5 1/4
2/3 5/12
B = 9/20
3/4
The determinant of A is given by:
|A| = (2/5)(5/12) - (1/4)(2/3) = 1/30 - 1/18 = -1/90
The determinant of the matrix obtained by replacing the first column of A with B is given by:
|A1| = (9/20)(5/12) - (3/4)(2/3) = 9/80 - 1/4 = -7/40
The determinant of the matrix obtained by replacing the second column of A with B is given by:
|A2| = (2/5)(3/4) - (1/4)(9/20) = 3/10 - 9/80 = 3/40
Now, we can use Cramer's Rule to find the value of x:
x = |A1|/|A| = (-7/40)/(-1/90) = 63/4
Therefore, the value of x
x = 63/4
So the answer is not any of the given options.
To know about linear equations visit the link
brainly.com/question/29739212
#SPJ1
A box has dimensions of 3ft by 4ft by 2ft. How long is the diagonal of the box?
Step-by-step explanation:
This is kinda like the Pythagorean Theorem with THREE dimensions instead of two
diagonal^2 = 3^2 + 4^2 + 2^2
diagonal = sqrt ( 29) = 5.39 ft
fossils found in deeper layers of sediment are
Answer:
older than those found in shallower layers of sediment. This is because sedimentary rock layers form over time, with the oldest layers at the bottom and the newest layers at the top. As sedimentary rocks form, they often trap the remains of plants and animals, which then become fossils. The deeper layers have been buried for a longer period of time, so they contain older fossils. This principle is known as the law of superposition and is an important tool for dating fossils and determining the relative ages of different rock layers.
On the graph of a quadratic function, the x-intercepts are (4, 0) and (8, 0), and the vertex is (6, −4). Which equation represents the function?
Answer:
A
Step-by-step explanation:
given the x- intercepts x = a and x = b then the corresponding factors are
(x - a) and (x - b)
the equation of the quadratic is then the product of the factors , that is
y = a(x - a)(x - b) ← a is a multiplier
here the x- intercepts are x = 4 and x = 8 , then factors are
(x - 4) and (x - 8 ) , so
y = a(x - 4)(x - 8)
to find a substitute any other point on the graph into the equation
given vertex = (6, - 4 ) , then
- 4 = a(6 - 4)(6 - 8)
- 4 = a(2)(- 2) = - 4a ( divide both sides by - 4 )
1 = a , then
y = (x - 4)(x - 8) ← expand using FOIL
y = x² - 12x + 32
how do you think the use of quantitative methods relates to these advantages and disadvantages? new york times
Using quantitative techniques in the context of The New York Times has both advantages and disadvantages.
The advantages are:
accuracy:
Quantitative techniques can provide more precise and accurate data, which can lead to more accurate reporting and analysis of news articles.
Data-Driven Insights:
Quantitative techniques help identify trends and patterns in data and help journalists make informed decisions about what to report on.
Objectivity:
Quantitative techniques help reduce bias and subjectivity in reporting by relying on data rather than personal opinions or interpretations.
The disadvantages include:
Lack of context:
Quantitative methods can oversimplify complex issues, resulting in misleading or inaccurate reporting.
Data limit:
Quantitative methods are data-dependent and results may not be reliable if data are incomplete or inaccurate.
Overall, it is very useful for the journalists in the New York Times to use quantitative techniques
learn more about quantitative techniques
brainly.com/question/8054076
#SPJ4
How would the shape of the distribution change if the salesman decides to also deal in cars priced under $5,000 and in cars priced from $45,000 to $50,000 and projects sales of 200 cars in each category?
The distribution will exhibit symmetry. The solution has been obtained by using the histogram.
What is a histogram?
A graph known as a histogram uses rectangles to show the frequency of numerical values. The vertical axis of a rectangle's height (which represents the distribution frequency of a variable) (the amount, or how often that variable appears).
The given histogram's form demonstrates that the distribution's shape exhibits symmetry (i.e. the shorter bars are to the left and to the right while the longer bars are in the middle).
Sales of vehicles under $5,000 and those between $45,000 and $50,000, with expected sales of 200 vehicles each, will be added, resulting in bars at both ends of the histogram that are the same size as the shortest bar.
Due to the distribution's continued symmetry, this won't change the histogram's initial shape of the distribution.
Hence, the first option is the correct answer.
Learn more about histogram from the given link
https://brainly.com/question/28164315
#SPJ1
The complete question and the figure is attached below.
Question: A salesman sells cars with prices ranging from $5,000 to $45,000. the histogram shows the distribution of the numbers of cars he expects to sell over the next 10 years.
How would the shape of the distribution change if the salesman decides to also deal in cars priced under $5,000 and in cars priced from $45,000 to $50,000 and projects sales of 200 cars in each category?
a. the distribution will exhibit symmetry.
b. the distribution will exhibit a positive skew.
c. the distribution will exhibit a negative skew.
d. the distribution will uniform throughout.
Please help me find X and Y.
2x - 4y = 36
4x + 3y = -5
A: (-7, 4)
B: (7, -4)
C: (-4, 7)
D: (4, -7)
Answer: B: (7, -4)
Step-by-step explanation:
To solve for x and y, we can use either substitution or elimination method. Here, we'll use the elimination method to solve for x and y:
2x - 4y = 36 (Equation 1)
4x + 3y = -5 (Equation 2)
To eliminate y, we can multiply Equation 1 by 3 and Equation 2 by 2, and then add the two resulting equations:
6(2x - 4y) = 6(36) (Multiplying Equation 1 by 3)
2(4x + 3y) = 2(-5) (Multiplying Equation 2 by 2)
Simplifying, we get:
12x - 24y = 216
8x + 6y = -10
Adding the two equations, we get:
20x = 206
Dividing both sides by 20, we get:
x = 10.3
Now, substituting x = 10.3 into Equation 1 or Equation 2, we can solve for y. Let's use Equation 1:
2x - 4y = 36
2(10.3) - 4y = 36
20.6 - 4y = 36
-4y = 15.4
y = -3.85
Therefore, the solution to the system of equations is (x,y) = (10.3,-3.85).
Rounded to the nearest integer, the solution is approximately (x,y) = (10,-4).
So, the answer is option B: (7, -4).
Answer:
D. (4, 7)
Step-by-step explanation:
2x - 4y = 36
4x + 3y = -5
2(4) - 4(-7) = 36
4(4) + 3(-7) = -5
Problem:
3/x^2 = x-4/3x^2 +2/x^2
Sοlving the equatiοn we get x=7
What is equatiοn?In mathematics an equatiοn is a mathematical statement which is built by twο expressiοns cοnnected by an equal ('=')sign. Fοr example, 3x – 8 = 16 is an equatiοn. Sοlving this equatiοn, we get the x = 8.
Given that,
3/x²= x-4/3x² +2/x²
Tο sοlve the given equation at first we will take LCM of the denominator of RHS
⇒ [tex]\frac{3}{x^{2} }[/tex]=[tex]\frac{x-4+6}{3x^{2} }[/tex]
⇒[tex]\frac{3}{x^{2} }[/tex] = [tex]\frac{x+2}{3x^{2} }[/tex]
By crο ss multiplicatiοn we get,
x+2= 9
Subtracting 2 frοm both sides of equation we get
x= 9-2
x=7
Hence sοlving the equation we get x=7
To knοw more about equation
https://brainly.com/question/2972832 from the link.
#SPJ9
Michale has a loan with a balance of 200$ at 14% simple interest.If he pays the loan back in 12 equal payments,how much will be each payment?
do eight-digit numbers with no digits 9 in their decimal representations constitute more than half of all eight-digit numbers?
Answer:
No.
Step-by-step explanation:
To determine whether eight-digit numbers with no digits 9 in their decimal representations constitute more than half of all eight-digit numbers, we need to calculate the total number of eight-digit numbers and the number of eight-digit numbers with no digit 9.There are 10 possible digits for each position in an eight-digit number, so there are 10^8 (or 100,000,000) total eight-digit numbers.
To count the number of eight-digit numbers with no digit 9, we can note that each digit in the number has 9 possible choices (0, 1, 2, 3, 4, 5, 6, 7, or 8), and since there are eight digits in the number, there are 9^8 (or 43,046,721) eight-digit numbers with no digit 9.Therefore, the proportion of eight-digit numbers with no digit 9 is:
9^8 / 10^8 = 0.43046721
This is less than half, so we can conclude that eight-digit numbers with no digits 9 in their decimal representations do not constitute more than half of all eight-digit numbers.
No, eight-digit numbers with no digit 9 in their decimal representations do not constitute more than half of all eight-digit numbers.
There are a total of 9 digits (0-9) in the decimal system, and an eight-digit number can have any of these digits in each of its eight places.
So, the total number of eight-digit numbers that can be formed is:
9 × 9 × 9 × 9 × 9 × 9 × 9 × 9 = 43,046,721
Out of these, there are 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 = 16,777,216 numbers that can have digits other than 9 in each of the eight places.
Therefore, the remaining numbers (43,046,721 - 16,777,216 = 26,269,505) will have at least one 9 in their decimal representations.
So, the eight-digit numbers with no digit 9 in their decimal representations constitute:16,777,216 / 43,046,721 = 0.3906 or approximately 39.06%of all eight-digit numbers. Therefore, they do not constitute more than half of all eight-digit numbers.
No, eight-digit numbers with no digit 9 in their decimal representations do not constitute more than half of all eight-digit numbers.
To learn more about the decimal system visit:
https://brainly.com/question/28222265?
#SPJ11
What is the measure of ∠EKY in this figure?
A. 104º
B. 1115º
C. 129º
D.I don't know.
Answer:
104
Step-by-step explanation:
You add 65+ 39 and that gives you 104
Write in standard notation 6.15x10^2
Marci performed a division.
175
was the dividend,
5
was the divisor, and
35
was the quotient. Which is a correct representation of this problem?
Answer:
35
Step-by-step explanation:
Question
What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
cm²
The area of the given triangle in the question is 48cm².
Area = (1/2) x base x height
where the base is 8cm and the height is 12cm, as given in the question.
Substituting these values, we get:
Area = (1/2) x 8cm x 12cm
Area = 48cm²
Therefore, the area of the triangle with a base of 8cm, a height of 12cm, and an angle of 59° is 48cm². A triangle is a 2-dimensional geometric shape that consists of three line segments or sides and three angles. The sum of the interior angles of a triangle is always 180 degrees. The area of a triangle is the amount of space inside the triangle and is calculated using the formula A = (1/2) x b x h, where A is the area, b is the base of the triangle, and h is the height of the triangle. The base of a triangle is any one of its sides and the height is the perpendicular distance from the base to the opposite vertex. The area of a triangle can be used to solve various real-world problems, such as calculating the amount of material needed to construct a roof or a sail.
To learn more about triangle click here
brainly.com/question/2773823
#SPJ1
jane is 3 times as old as kate. in 5 years jane's age will be 2 less than twice kate's. how old are the girls now
Answer:
Kate is 3 years old, Jane is 9 years old
Step-by-step explanation:
1.) First, assign variables to all of their ages. If we say Kate's age is x, Jane's age is 3 times this, which can be written as j, is 3x.
2.) Jane's age is also 2 less than twice of Kate's in 5 years. This means that her age is also 2(x+5) - 2 = j + 5. With a little simplification, you get that 2x + 8 = j + 5.
3.) Since j, Jane's age, is also 3x, we can substitute 3x in for j in the second equation. If you do this, you get 2x + 8 = 3x + 5.
4.) By moving the x onto one side and the numbers onto another, you get x = 3. X was Kate's age, meaning that Kate is 3 years old.
5.) Finally, since Jane's age is 3 times Kate's age, Jane's age is 3 * 3, which is 9. Jane is 9 years old.
Jane is 9 years old and Kate is 3 years old.To solve the problem, let's first establish variables for Jane and Kate's ages.
Let J represent Jane's age and K represent Kate's age.
According to the student question, Jane is 3 times as old as Kate, which can be represented as:
J = 3K
In 5 years, Jane's age will be 2 less than twice Kate's age, which can be represented as:
J + 5 = 2(K + 5) - 2
Now we can solve the equations step by step:
Substitute the first equation into the second equation to eliminate one of the variables:
3K + 5 = 2(K + 5) - 2
Distribute the 2 on the right side of the equation:
3K + 5 = 2K + 10 - 2
Simplify the equation by combining like terms:
3K + 5 = 2K + 8
Move the 2K term to the left side of the equation:
K = 3
now we know that Kate is currently 3 years old.
Substitute K's value back into the first equation to find Jane's age:
J = 3K
J = 3(3)
Simplify to find Jane's age:
J = 9
So, Jane is currently 9 years old.
Jane is 9 years old and Kate is 3 years old.
for more questions on variables
https://brainly.com/question/9302141
#SPJ11
Write log146−log14 3 2 as a single logarithm. log subscript 14 baseline 4 log subscript 14 baseline one-fourth log subscript 14 baseline 9
we have expressed log146 - log14 3 2 as a single logarithm in terms of natural logarithms, which is ln (2/3) / ln 14.
Using the properties of logarithms, we can simplify the given expression as follows:
[tex]log_{14}[/tex](6) = [tex]log_{14}[/tex](4) - [tex]log_{14}[/tex]([tex]3^{2}[/tex])
= 1 - 2[tex]log_{14}[/tex](3)
So the expression log146 − log1432 can be written as [tex]log_{14}[/tex](6) = 1 - 2[tex]log_{14}[/tex](3).
The first step used the property [tex]log_{a}[/tex] (b/c) = [tex]log_{a}[/tex](b) - [tex]log_{a}[/tex](c), and the second step used the property [tex]log_{a}[/tex](b^c) = c [tex]log_{a}[/tex](b).
In simpler terms, we can say that the given expression is equivalent to subtracting the logarithm of [tex]3^{2}[/tex] from the logarithm of 4, both to the base 14. We can then use the rules of logarithms to simplify the expression into a single logarithm of 6 to the base 14, with a coefficient of -2 in front of the logarithm of 3 to the base 14.
To learn more about logarithm:
https://brainly.com/question/30085872
#SPJ4
In this lesson, you learned how a compass and straightedge are used to create constructions related to circles. In this assignment, you will use those tools to complete those constructions on your own.
As you complete the assignment, keep this question in mind:
How do you perform constructions related to circles?
Directions
Complete each of the following constructions, reading the directions carefully as you go. Be sure to show all work and insert an image of each construction. If you are unable to take and insert screenshots of the constructions, print this activity sheet and create them by hand using a compass and straightedge.
Your teacher will give you further directions about how to submit your work. You may be asked to upload the document, e-mail it to your teacher, or print it and hand in a hard copy.
Now, let’s get started!
Step 1: Construct a circle through three points not on a line.
a) Construct a circle through three points not on a line using the construction tool. Insert a screenshot of the construction here. Alternatively, construct a circle through three points not on a line by hand using a compass and straightedge. Leave all circle and arc markings. (10 points)
Step 2: Construct regular polygons inscribed in a circle.
a) Construct an equilateral triangle inscribed in a circle using the construction tool. Insert a screenshot of the construction here. Alternatively, construct an equilateral triangle inscribed in a circle by hand using a compass and straightedge. Leave all circle and arc markings. (10 points)
b) Construct a regular hexagon inscribed in a circle using the construction tool. Insert a screenshot of the construction here. Alternatively, construct a regular hexagon inscribed in a circle by hand using a compass and straightedge. Leave all circle and arc markings. (10 points)
c) Construct a square inscribed in a circle using the construction tool. Insert a screenshot of the construction here. Alternatively, construct a square inscribed in a circle by hand using a compass and straightedge. Leave all circle and arc markings. (10 points)
Step 3: Construct tangent lines to a circle.
a) Construct a tangent to a circle through a point on the circle using the construction tool. Insert a screenshot of the construction here. Alternatively, a tangent to a circle through a point on the circle by hand using a compass and straightedge. Leave all circle and arc markings. (10 points)
b) Construct a tangent to a circle through a point outside the circle using the construction tool. Insert a screenshot of the construction here. Alternatively, construct a tangent to a circle through a point outside the circle by hand using a compass and straightedge. Leave all circle and arc markings. (10 points)
Use circumcenter to draw a circle through three non-collinear points.
a) Draw diameter, construct equilateral triangle with one vertex at center and other two on circle.
b) Draw diameter, construct regular hexagon with one vertex at center and other vertices on circle.
What is diameter?Step 1: To construct a circle through three points not on a line, we can use the circumcenter of a triangle. We first construct the perpendicular bisectors of any two sides of the triangle. The point where these two lines intersect is the circumcenter of the triangle. We can then draw a circle with this point as the center, which passes through all three vertices of the triangle.
Step 2:
a) To construct an equilateral triangle inscribed in a circle, we can draw a diameter of the circle and then construct an equilateral triangle with one of the endpoints at the center of the circle and the other two endpoints on the circle itself.
b) To construct a regular hexagon inscribed in a circle, we can draw a diameter of the circle and then construct a regular hexagon with one of the vertices at the center of the circle and the other vertices on the circle itself.
c) To construct a square inscribed in a circle, we can draw a diameter of the circle and then construct a square with one of the vertices at the center of the circle and the other vertices on the circle itself.
Step 3:
a) To construct a tangent to a circle through a point on the circle, we can draw a radius of the circle to the point of tangency, and then construct the perpendicular bisector of this radius. The line where the perpendicular bisector intersects the circle is the tangent line.
b) To construct a tangent to a circle through a point outside the circle, we can draw a line from the point to the center of the circle, and then construct the perpendicular to this line at the point of tangency. The line where the perpendicular intersects the circle is the tangent line.
To know more about diameter visit:
https://brainly.com/question/5501950
#SPJ1
A bag contains 3 red marbles, 4 white marbles, and 1 blue marble. You draw one marble. Without replacing it, you draw a second marble. What is the probability that the two marbles you draw are red, then white? Write your answer as a fraction in simplest form, using the / symbol for the fraction bar, and do not put spaces in your answer.
The probability of drawing a red marble on the first draw is 3/8 since there are 3 red marbles out of 8 total marbles.
After the first marble is drawn, 7 marbles are remaining, so the probability of drawing a white marble on the second draw is 4/7 since 4 white marbles are remaining out of 7 total marbles.
To find the probability of drawing a red marble followed by a white marble, we multiply the probabilities of each event:
P(red, then white) = (3/8) x (4/7) = 12/56
Simplifying this fraction by dividing both the numerator and denominator by their greatest common factor of 4, we get:
P(red, then white) = 3/14
Therefore, the probability of drawing a red marble followed by a white marble is 3/14.
Find out more about probability
brainly.com/question/30034780
#SPJ4
The diagram shows a trapezium All the measurements are in centimetres.
The area of the trapezium is 351 cm2.
Given that 2x*2+x-351=0
work out the value of x
The area οf the trapezium is 351 cm². Given that 2x² + x-351=0, sο the value οf x is 13 cm.
What is the quadratic equatiοn?The sοlutiοns tο the quadratic equatiοn are the values οf the unknοwn variable x, which satisfy the equatiοn. These sοlutiοns are called rοοts οr zerοs οf quadratic equatiοns. The rοοts οf any pοlynοmial are the sοlutiοns fοr the given equatiοn.
We have the equatiοn 2x² + x - 351 = 0.
We can sοlve fοr x by factοring οr using the quadratic fοrmula. Since the cοefficient οf x² is 2, it's easier tο use the quadratic fοrmula:
x = (-b ± √(b² - 4ac)) / 2a
Here, a = 2, b = 1, and c = -351. Plugging in these values, we get:
x = (-1 ± √(1² - 4(2)(-351))) / 2(2)
x = (-1 ± √(1 + 2808)) / 4
x = (-1 ± √(2809)) / 4
We can simplify [tex]\sqrt{(2809)[/tex] tο 53, since 53² = 2809. Sο we have:
x = (-1 ± 53) / 4
Taking the pοsitive sοlutiοn, we get:
x = (53 - 1) / 4
x = 52 / 4
x = 13
Therefοre, the value οf x is 13 cm.
To learn more about the quadratic equation visit:
brainly.com/question/28038123
#SPJ1
answer is 3-x/x-1 or (2/x-1)-1
HOW
Hence inverse of the function h is
h⁻¹ :x→ 2/(x-1) -1
Define inverse functionAn inverse function is a function that "undoes" the action of another function. In other words, if a function f(x) takes an input x and produces an output y, then its inverse function, denoted as f⁻¹(y) or sometimes as g(y), takes the output y and produces the input x such that f(x) = y.
Define functionA function is a rule that associates each element of a set (called the domain) with a unique element of another set (called the range or codomain).
Given function
f(x)=1+1/x for x>0
g(x)=(x+1)/2 for x>0
Given: h=fg
h=f(g(x))
h=1+1/(x+1)/2
Now, taking the inverse of the function h,
h=1+1/(x+1)/2
h-1=1/(x+1)/2
1/(h-1)=(x+1)/2
2/(h-1)=x+1
x=2/(h-1) -1
Hence inverse of the function h is
h⁻¹:x→ 2/(x-1) -1
To know more about range, visit:
https://brainly.com/question/28135761
#SPJ1
What if FC
F-2,0,0,8,2,1
C12,0,3/2,1,-6,7
The vector FC is (14, 0, 3/2, -7, -8, 6).
If you are given two vectors FC and F and C, with F represented as F(-2, 0, 0, 8, 2, 1) and C represented as C(12, 0, 3/2,
1, -6, 7), you can find the vector FC by subtracting the F vector from the C vector component-wise.
Step 1: Write down the F and C vectors.
F = (-2, 0, 0, 8, 2, 1)
C = (12, 0, 3/2, 1, -6, 7)
Step 2: Subtract the F vector from the C vector component-wise.
FC = C - F
FC = (12 - (-2), 0 - 0, 3/2 - 0, 1 - 8, -6 - 2, 7 - 1)
Step 3: Simplify the subtraction.
FC = (14, 0, 3/2, -7, -8, 6)
So, the vector FC is (14, 0, 3/2, -7, -8, 6).
for such more question on vector
https://brainly.com/question/17157624
#SPJ11
I NEED THIS ANSWER BY TONIGHT BY 9:00 PLEASE HELP!!
Which number sentence has exactly one solution A. x+5.4>8 B. 1/4 (x-5)=13 C. 3x+7.5<9 D. 1/2x-19>24
Answer:
B. 1/4(x-5) = 13
Step-by-step explanation:
You want to know which number sentence has one solution.
InequalityTypically, an inequality has an infinite set of solutions. The inequalities here are linear inequalities in one variable, so will have an infinite solution set consisting of numbers greater than, or less than, some boundary value.
EquationIf the equation can be arranged to be in general form, ax +b = 0, where a ≠ 0, then it will have exactly one solution: x = -b/a.
The set of number sentences contains exactly one equation. That is the number sentence that has exactly one solution:
B. 1/4(x-5) = 13