To find the zeros and poles of a function, you can use the following steps:
Write the function in standard form, with the independent variable (usually x) in the denominator.Find the zeros by setting the numerator equal to zero and solving for x. In the example above, the zeros are the solutions to the equation x^2 + 3x + 2 = 0. You can solve this equation using the quadratic formula or by factoring.Find the poles by setting the denominator equal to zero and solving for x. In the example above, the poles are the solutions to the equation x - 1 = 0, which means that the pole is x = 1.Plot the zeros and poles on the complex plane. The zeros correspond to points where the function is equal to zero, and the poles correspond to points where the function is undefined.How do you find the zeros and poles of a function?Generally, It's also important to note that a function can have multiple zeros and poles, and they can be complex numbers as well as real numbers. In that case, you can use the same steps above to find all of the zeros and poles.
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CQ
How do you find the zeros and poles of a function?
Solve and graph by using systems of inequalities.
A 24 hour radio station plays only classical music, jazz music, talk programs, and news. It plays at most 12 hours of music per day, of which at least 4 hours is classical. Jazz music gets 25% as much time as classical. Write and graph a system of inequalities.
PLEASE HELP!!!
The inequality that represents the most no. of music played is,
C ≤ 4, J ≤ 1 and 4C + 0.25C ≤ 12
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.
Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, the radio station plays at most 12 hours of music per day. Let C denotes classical music, J denotes jazz music, and 25% of 4 hours be 1 hour.
The inequality representing this situation is
C ≤ 4 and J ≤ 1.
4C + 0.25C ≤ 12. (less than or equal to is at most)
4.25C ≤ 12.
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What is the greatest common of 45?
Answer:
Step-by-step explanation:
If it is the greatest common factor then it would be 5 I think.
How do you work out 2x 3y 12?
The resultant answer after solving the given equation by taking x as the subject is x = (12 + 3y)/2.
What is an equation?The concept of an equation in algebra is a mathematical statement that shows the equality of two mathematical equations.
For example, the equation 3x + 5 = 14 comprises the two equations 3x + 5 and 14, which are divided by the 'equal' sign.
So, we have the equation:
2x - 3y = 12
Now, solve the equation by taking x as the subject as follows:
2x - 3y = 12
2x = 12 + 3y
x = (12 + 3y)/2
Therefore, the resultant answer after solving the given equation by taking x as the subject is x = (12 + 3y)/2.
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Correct question:
How do you work out 2x - 3y = 12?
How do you tell if a linear equation is consistent or inconsistent?
An inconsistent system of equations has no solution, whereas a consistent system has at least one solution.
How can a linear equation be determined to be consistent or inconsistent? An inconsistent system of equations has no solution, whereas a consistent system has at least one solution.If there is only one solution or an unlimited number of solutions, a system of linear equations is said to be consistent.If there is no solution to a set of linear equations, the equations are said to be inconsistent.In a rectangular array known as a matrix, a system can be compactly recorded.The two linear equations have a singular solution if and only if both lines meet at that point.In this situation, it is argued that the pair of linear equations is consistent.If a set of equations has at least one solution, it is said to be consistent.If a system cannot be solved, it is inconsistent.To learn more about inconsistent system refer
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The points scored per game by a professional basketball player are represented by the box plot below. A number line plots points per game by the basketball player. The plots are 16 through 21 and 21 through 24. If the player scores 9 points and 35 points in the next two games, how is the median of the data set affected? A. The median points per game increases. B. The effect on the median points per game cannot be determined. C. The median points per game decreases. D. The median points per game is not affected.
The median of the data set would be affected as the median points per game decreases. That is option C.
What is a median of a data set?The median of a data set is defined as the value of a data set the is found in the middle of a data after it has been arranged in an ascending order.
The first number line plots points per game;
= 16, 17 ,18 ,19 ,20 ,21 = 18+19 = 37/2 = 18.5
The second number line plots points per game;
= 21, 22, 23, 24 = 22 + 23 = 45/2 = 22.5
The third number line plots points per game:
= 9 points through 35 points
= 22 as the median.
Therefore, the scores of the next two games led to a decrease in the median determined per game point.
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[tex]14-4 \sqrt{ 6 \phantom{\tiny{!}}} = { \left( \sqrt{ x \phantom{\tiny{!}}} -2 \sqrt{ y \phantom{\tiny{!}}} \right) }^{ 2 }[/tex]
Answer:
(x=2, y=3) and (x=12, y=1/2)
Step-by-step explanation:
14 - 4[tex]\sqrt{6}[/tex] = ([tex]\sqrt{x}[/tex] - 2[tex]\sqrt{y}[/tex])^2
14 - 4[tex]\sqrt{6}[/tex] = ([tex]\sqrt{x}[/tex] - 2[tex]\sqrt{y}[/tex])([tex]\sqrt{x}[/tex] - 2[tex]\sqrt{y}[/tex])
14 - 4[tex]\sqrt{6}[/tex] = [tex]\sqrt{x}[/tex]([tex]\sqrt{x}[/tex] - 2[tex]\sqrt{y}[/tex]) - 2[tex]\sqrt{y}[/tex]([tex]\sqrt{x}[/tex] - 2[tex]\sqrt{y}[/tex]) ==> distribute ([tex]\sqrt{x}[/tex] - 2[tex]\sqrt{y}[/tex]) to [tex]\sqrt{x}[/tex] and
2[tex]\sqrt{y}[/tex]
14 - 4[tex]\sqrt{6}[/tex] = ([tex]\sqrt{x}[/tex] * [tex]\sqrt{x}[/tex]) - ([tex]\sqrt{x}[/tex] * 2[tex]\sqrt{y}[/tex]) - (2[tex]\sqrt{y}[/tex] * [tex]\sqrt{x}[/tex]) - (2[tex]\sqrt{y}[/tex] * (-2[tex]\sqrt{y}[/tex])) ==> use
distribution property
14 - 4[tex]\sqrt{6}[/tex] = (x) - (2[tex]\sqrt{xy}[/tex]) - (2[tex]\sqrt{xy}[/tex]) - (-4[tex]\sqrt{y}[/tex] *[tex]\sqrt{y}[/tex]) ==> simplify
14 - 4[tex]\sqrt{6}[/tex] = (x) - (4[tex]\sqrt{xy}[/tex]) - (-4y)
14 - 4[tex]\sqrt{6}[/tex] = (x) - (4[tex]\sqrt{xy}[/tex]) + 4y ==> subtracting by a negative number is
equivalent to adding by a positive number
14 - 4[tex]\sqrt{6}[/tex] = x + 4y - 4[tex]\sqrt{xy}[/tex] ==> notice any similarities?
x + 4y = 14
[tex]\sqrt{xy}[/tex] = [tex]\sqrt{6}[/tex]
xy=6 ==> solve for x
x = 6/y ==> isolate x by dividing by y on both sides
6/y + 4y = 14 ==> plugin 6/y for x in x + 4y = 14
(6/y + 4y = 14) * y ==> multiply the equation by y to remove fractions
6 + 4y^2 = 14y
4y^2 - 14y + 6 = 14y-14y
4y^2 - 14y + 6 = 0
2y^2 - 7y + 3 = 0 ==> divide both sides by 2 to simplify the equation
2y^2 - 1y - 6y + 3 = 0 ==> -1y - 6y = -7y
y(2y - 1) - 3(2y - 1) = 0 ==> factor the equation
(y - 3)(2y - 1) = 0
y - 3 = 0 ==> y=3
2y - 1 = 0 ==> 2y = 1 ==> y = 1/2
y=3: 3x = 6 ==> plugin 3 for y in xy = 6
x = 2 ==> divide both sides by 3
y=1/2: x/2 = 6 ==> plugin 1/2 for y in xy = 6
x = 12 ==> multiply both sides by 2
When y=3, x=2. When y=1/2, x=12
Hence, the answers are (2, 3) and (12, 1/2).
The expression will be simplified as x + 4y + 4√x√y -14 + 4√6 = 0.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 14 - 4√6 = ( √x - 2√y)². The given expression will be simplified as below,
14 - 4√6 = ( √x - 2√y)²
14 - 4√6 = (√x )² + (4√x√y) + 4(√y)²
14 - 4√6 = x + 4√x√y + 4y
x + 4√x√y + 4y -14 + 4√6 = 0
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Which point atify thi linear-quadratic ytem of equation?
x y = 1
y = 4x − 3 − x2
The point that satisfy linear quadratic system of equation are (1,0) and (4,-3)
A linear equation is an algebraic equation in which each term has an exponent of 1, and which, when plotted on a graph, always yields a straight line. It is called a "linear equation" for this reason. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.
we have x + y = 1 ......... (i)
y=4x-3-x²...... (ii)
put y=4x-3-x² in equation (i)
x + y = 1
x + 4x - 3 - x^2 = 1
-x^2 + 5x - 4 = 0
(-x + 1)(x - 4) = 0
-x + 1 = 0
-x = -1
x = 1
To find the value of y put x=1 in equation ii
y = 4x - 3 - x^2
y = 4(1) - 3 - 1^2
y = 4 - 3 - 1 = 0
similarly.
x - 4 = 0 y = 4x - 3 - x^2
x = 4 y = 4(4) - 3 - 4^2
y = 16 - 3 - 16
y = -3
so the point that satisfy linear quadratic system of equation are (1,0) and (4,-3)
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we have x + y = 1 ......... (i)
y=4x-3-x²...... (ii)
put y=4x-3-x² in equation (i)
x + y = 1
x + 4x - 3 - x^2 = 1
-x^2 + 5x - 4 = 0
(-x + 1)(x - 4) = 0
-x + 1 = 0
-x = -1
x = 1
To find the value of y put x=1 in equation ii
y = 4x - 3 - x^2
y = 4(1) - 3 - 1^2
y = 4 - 3 - 1 = 0
similarly.
x - 4 = 0 y = 4x - 3 - x^2
x = 4 y = 4(4) - 3 - 4^2
y = 16 - 3 - 16
y = -3
so the point that satisfy linear quadratic system of equation are (1,0) and (4,-3)
What is the slope intercept form of the inequality 2x 3y 12?
The level of a line's slope indicates its steepness, y = (2/3)x - 4 is the slope intercept form of the inequality 2x - 3y = 12.
How do one find the slope of a graph?The slope is computed mathematically as "rise over run" (change in y divided by change in x).
In accordance with the slope equation, the slope of such a line may be determined by dividing the rise of the line between two positions by the run of the same line between the same two sites.
The above equation is a standard straight-line equation, and we are asked to change it to slope-intercept form, which is given as y = mx + c. "m" denotes the slope of the line and "c" denotes its intercept.
Now, it is given that,
2x - 3y = 12
or, - 3y = 12 - 2x
or, 3y = 2x - 12
or y = (2/3)x - 4
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The complete question is as follows:
What is the slope intercept form of the inequality 2x - 3y = 12.
What are the three methods of mean?
They are the three methods of mean - Direct Method. Assumed Mean Method. Step-deviation Method.
What does the mode mean?
By summing all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined.
A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently.
What are the mean, median, and example?
The most frequent number, or the one that happens the most frequently, is known as the mode.
Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.
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a large company is interested in opening an on-site gym for the employees and would like to know what hours the employees would prefer to have the gym open. which data collection method would provide an unbiased sample?
For unbiased sample by data collection, The method to be used is Survey method.
What do you mean by data collection?To answer specified research questions, test hypotheses, and assess results, data collection is the act of acquiring and measuring information on variables of interest in a systematic and defined manner. All academic disciplines, including the humanities, social sciences, business, and natural and applied sciences, share the data collection component of research. Although techniques differ depending on the profession, the importance of ensuring accurate and truthful collection does not change.
What are methods for data collection?The popular data collection methods are:
Direct Observation Experiments SurveysSurvey method of data collection is to be used for collection of unbiased sample. It is so because while planning for a on-site gym for the employees, Survey conducted on the employees working would be the best method for data collection which will increase the efficiency for selection of gym hours.
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What shape has 4 sides and 1 set of parallel?
The trapezoid has 4 sides and 1 set of parallel
What is trapezoid?In American and Canadian English, a quadrilateral with at least one pair of parallel sides is referred to as a trapezoid. It is referred to as a trapezium in British and other varieties of English. In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides. The top and bottom bases are parallel to one another. An isosceles trapezoid has opposite sides that are the same length. Angles next to one another add up to 180 degrees. Both bases are parallel to the median. Equal sides and parallel opposing sides make up a rhombus. In general, a trapezoid has uneven sides with two parallel sides. Only the trapezoid's legs can have equal lengths.To learn more about trapezoid refer to:
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What are the first 3 whole numbers?
Answer:
0,1,2
Step-by-step explanation:
you have to go in numerical order starting from zero and going forward with no fractions.
What is the vertical asymptote of the graph of f X?
The vertical asymptotes of the graph of f(x) = (2x² + 7x - 4)/(x² + 5x + 4) is x = -1
How to determine the vertical asymptote?The equation of the function is given as
f(x) = 2x² + 7x - 4/x² + 5x + 4
Introduce bracket, to differentiate the numerator and the denominator
So, we have
f(x) = (2x² + 7x - 4)/(x² + 5x + 4)
Next, we plot the graph of the function
The asymptotes are the points on the graph is a line that acts as the limit of another line or curve
From the graph, we have the asymptotes to be
x = -1 and y = 2
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Complete question
What is the vertical asymptote of the graph of f X?
f(x) = 2x² + 7x - 4/x² + 5x + 4
SOMEONE HELP PLEASE. if f(x) is an exponetial function where f(-0.5)=18 and f(1)=52 then find the value of f(0) round to nearest hundredth
Step-by-step explanation:
The form of a exponential function is
[tex]y = a \times {b}^{x} [/tex]
We know that
[tex]18 = a \times {b}^{ - 0.5} [/tex]
[tex]52 = a \times {b}^{1} [/tex]
If we divide these two we will get
[tex] \frac{26}{9} = b {}^{1.5} [/tex]
[tex] \frac{676}{81} = b {}^{3} [/tex]
[tex] \sqrt[3]{ \frac{676}{81} } = b[/tex]
Solving for a,
[tex]52 = a \times \sqrt[3]{ \frac{676}{81} } [/tex]
[tex]a = 25.64[/tex]
f(0)=a, so
f(0)=25.64
GIVING 70 POINTS AND I WILL MARK BRAINLIEST PLEASE HELP! :D sorry for the all caps im just rlly energetic right now
A square garden is expanded to a rectangle in which the width is 1.5 times the original side length and the length is 3.5 times the original side length. The area of the expanded garden can be modeled by the expression (1.5s)(3.5s).
Simplify the expression (1.5s)(3.5s).
(A)5s
(B)5s2
(C)5.25s2
(D)5.25s
Answer:
C) 5.25s^2
Step-by-step explanation:
1. Multiply 1.5s x 3.5s = 5.25.
2) Because 1.5 has one s, and 3.5 has another s, these 2 s combine (s+s)=s^2. Meaning there is 2 s in the equation. s^2 happens when you multiply two numbers that each have an s. Multiplication in this problem is brought by the use of parenthesizes surrounding these 2 numbers.
What is the area of an isosceles right triangle that has one leg that measures 4 cm?
The area of an isosceles right triangle that has one leg that measures 4 cm is 8 cm ^ 2.
One leg of the isosceles triangle is 4 cm.
Since the given isosceles triangle is also a right triangle, the base of the isosceles would also be equal to the height of the triangle which is 4 cm.
Area of a triangle = 1 / 2 × base × height
Therefore, the area of an isosceles right triangle that has one leg that measures 4 cm is:
1 / 2 × 4 cm × 4 cm = 8 cm ^ 2.
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FILL IN THE BLANK. the diaphragm creates a ________ section between the thoracic and abdominal body cavities.
The diaphragm creates a transverse section between the thoracic and abdominal body cavities.
The diaphragm is one of the important muscle involved in respiration, or breathing. It is a dome-shaped muscle is found just beneath the lungs and heart. It constantly contracts as you breathe in and out.
Thoracic diaphragm is the diaphragm which is present in the thorax and serves as an important anatomical landmark.
It acts as a separation between the thorax, or chest, from the abdomen.
It contracts to enlarge the thoracic cavity and reduce the intrathoracic pressure so that lungs may expand and fill their alveoli with air during respiration.
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Is the 3X 1 Problem solved?
Answer:
The 3x+1 problem, also known as the Collatz conjecture, is a problem in mathematics that remains unsolved. It involves taking a positive integer and repeatedly applying a simple rule to it: if the integer is even, divide it by 2, and if it is odd, multiply it by 3 and add 1. The problem is to determine whether this process will always eventually reach the number 1, regardless of which positive integer is chosen as the starting point. Despite much effort by mathematicians, the 3x+1 problem remains unsolved.
Step-by-step explanation:
How many terms are in the expression 3x2y xy2 2x 5?
The expression 3x²y + xy² + 2x + 5 has in its entirety 4 term.
First let's define what algebraic expressions are.
Algebraic expressionAn algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
The terms of an expression are identified by the fact that they are separated by means of an addition and subtraction operation:
x + y has two termsAs we can see the expression has addition operations so it has more than 1 term:
1 = 3x²y2 = xy²3 = 2x4 = 5this expression has 4 terms.
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Jessica drinks 5/6 cup of milk for breakfast every day.
How many cups of milk has Jessica drink after 8 days?
Answer:
20/3 cups of milk
Step-by-step explanation:
Take 5/6 time 8 = 40/6 = 20/3
So, Jessica drinks 20/3 cups of milk after 8 days
18 The three solids A, B and C are similar such that
and
the surface area of A: the surface area of B=4:9
the volume of B: the volume of C = 125:343
Work out the ratio
the height of A: the height of C
Give your ratio in its simplest form.
Answer:
1:1
Step-by-step explanation:
Since the surface area of A is 4 times the surface area of B, and the volume of B is 125 times the volume of C, we can write the following proportion:
(surface area of A) / (surface area of B) = (volume of B) / (volume of C)
(height of A)^2 / (height of B)^2 = (height of B)^3 / (height of C)^3
We can then cross-multiply and simplify to find the ratio of the heights:
(height of A)^2 / (height of C)^2 = (height of B)^3 / (height of B)^3
(height of A)^2 = (height of C)^2
Therefore, the ratio of the height of A to the height of C is 1:1, or simply 1.
Please help me with this question
Answer:
[tex]m=\frac{1}{2}[/tex]
Step-by-step explanation:
The average rate of change (m) for the given line segment can be found with
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Given the graph, the following values can be recorded:
[tex](x_1,y_1)=(-1,-5)\\(x_2,y_2)=(1,-4)[/tex]
So,
[tex]m=\frac{(-4)-(-5)}{(1)-(-1)}\\m=\frac{-4+5}{1+1}\\m=\frac{1}{2}[/tex]
This answer makes sense in both sign and scale with the given image.
pls answer need help[.
Answer:x=98
Step-by-step explanation:you add each corner
its a joke srry
Use the Pythagorean Theorem to find the missing length and then round the
result to the nearest tenth.
= 12, b = 12, C =
Answer:
17.0
Step-by-step explanation:
pythag theorem is a^2 + b^2 = c^2
12^2 + 12^2 = c^2
144+144=288=c^2
[tex]\sqrt{288}[/tex]= 16.97056275
round to nearest tenth, 17.0
How much can evan make and how many bagels will be leftover please help
Answer:
okay he can make 62 packages with 1 bagel left over
Step-by-step explanation:
Answer:
Step-by-step explanation:
381/6 = number of packages = 63 packages
63 * 6 = 378; 381-378 = 3 bagels left over
What is an example of a linear line?
An equation that depicts a straight line on a graph is said to be linear line.
What is linear line?
Linear refers to a straight line. Straight-line graphs called linear graphs are used to show the relationship between two values. The single straight lines on this graph assist to represent a result. The phrase "linear" refers to a straight line and excludes the usage of curves, dots, bars, etc.
A linear line can include more than one variable. Linear lines with two variables, for example, are those that have two variables in them.
2x - 3 = 0 and 2y = 8 are few examples of linear lines.
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The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $4, and each adult ticket sells for $8. There was a total of $640 in revenue from the sale of 100 total tickets. Graphically solve a system of equations in order to determine the number of student tickets sold, x, and the number of adult tickets sold, y.
The number of student tickets sold is 40 and the number of adult tickets sold is 60.
Define System of equations
A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given,
Each student ticket sells for = $4
Each adult ticket sells for = $8
Total tickets sale = 100
Revenue from the sale of 100 tickets = $640
Let, x = number of student tickets sold
and, y = number of adult tickets sold
so, let's form a equation
x + y = 100 ------(i)
4x + 8y = 640 -------(ii)
Rewrite eq(i),
x = 100 - y
Now, substitute x value in eq(ii)
4(100- y) + 8y = 640
400 - 4y + 8y = 640
4y = 640 - 400
y = 240 / 4
y = 60
Now, put y value in eq(i)
x + 60 = 100
x = 40
Hence, the number of student tickets sold is 40 and the number of adult tickets sold is 60.
Now, to solve graphically
Let's rewrite the eq(i) and eq(ii)
y = 100 - x
y = 80 - (1/2) x
Plot these lines on graph as mentioned below.
And, the solution is the point of intersection(40,60)
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*URGENT NEED TO PASS FOR GRADUATION*
built for the 1976 olympic games in montreal canada, the tower is 156 meters tall, measured vertically from the ground to the top. the tower makes a 45 degree angle with the ground. if you were to climb to the top and then accidentally drop your keys, where would you start looking for them?
Answer:
156 meters from the bottom of the tower--------------------------------
The height of the tower is the leg of the isosceles right triangle, since one of angles is 45 degrees.
The horizontal distance from the to the point where you dropped your keys is same as the vertical distance, 156 meters, because it is the other leg of the triangle.
LT 1.5 I can determine if a number is a factor of another number.
Directions: Is 6 a factor of 35? Explain how you know that it is or is not a factor. Yes or No,
then EXPLAIN!
No. The GCF of 6 and 35 is 1.
To determine the biggest factor that perfectly divides both 6 and 35, i.e. 1, we must factor each number separately (factors of 6 are 1, 2, 3, 6; while factors of 35 are 1, 5, 7, 35).
What is Factors of 35?
Factors of 35 are the list of integers that we can split evenly into 35. It has a total of 4 factors of which 35 is the biggest factor and the positive factors of 35 are 1, 5, 7 and 35. The Prime Factors of 35 are 1, 5, 7, 35 and its Factors in Pairs are (1, 35) and (5, 7).
Factors of 35: 1, 5, 7 and 35
Negative Factors of 35: -1, -5, -7 and -35
Prime Factors of 35: 5, 7
Prime Factorization of 35: 5 × 7 = 5 × 7
Sum of Factors of 35: 48
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The probability that the fourth marble amy picks is black is. If amy picks a black marble in the fourth attempt, the probability that in the fifth attempt she will pick a red or a black marble is.
The probability that the fourth marble Amy picks is black: This probability cannot be determined without knowing the total number of marbles and the number of black marbles.
The probability that, if Amy picks a black marble in the fourth attempt, she will pick a red or a black marble in the fifth attempt: This probability cannot be determined without knowing the total number of marbles and the number of red and black marbles.
Probability is a measure of the likelihood of an event occurring. To calculate the probability of an event, you need to know the total number of outcomes and the number of outcomes that are favorable to the event. For example, if there are 10 marbles in total and 4 of them are black, the probability that Amy will pick a black marble on the fourth attempt is:
Probability = Number of black marbles / Total number of marbles = 4/10 = 0.4
Similarly, if Amy picks a black marble in the fourth attempt and there are a total of 10 marbles, with 4 of them being black and 6 of them being red, the probability that she will pick a red or a black marble in the fifth attempt is:
Probability = (Number of red marbles + Number of black marbles) / Total number of marbles = (6 + 4) / 10 = 0.8
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