Answer: [tex]x=20, m\angle 1=109^{\circ}, m\angle 2=71^{\circ}[/tex]
Step-by-step explanation:
Angles that form a linear pair add to 180 degrees, so:
[tex]5x+9+3x+11=180\\\\8x+20=180\\\\8x=160\\\\x=20\\\\\implies m\angle 1=5(20)+9=109^{\circ}\\\\\implies m\angle 2=180^{\circ}-109^{\circ}=71^{\circ}[/tex]
1/16 - ( -7/16)
Write your answer as a fraction in simplest form.
A bee flies at 12 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 16 minutes, and then flies directly back to the hive at 8 feet per second. It is away from the hive
for a total of 18 minutes.
a What equation can you use to find the distance of the flowerbed from the hive?
b. How far is the flowerbed from the hive?
In linear equation, 864 is distance the flowerbed from the hive .
What are a definition and an example of a linear equation?
A linear equation with one variable is one that includes just one variable. It has the formula Ax + B = 0, with A and B being any two actual values and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.a) The equation is so called "time equation"
D%2F12 + 16*60 + D%2F8 = 19*60 seconds
(b) To determine the distance D, solve the equation
D%2F12 + D%2F8 = 19*60 - 16*60 = 3*60,
multiply both sides by 24
2D + 3D = 3*60*24
5D = 4320
D = 4320/5 = 864
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Use the intersect method to solve the equation. x^2 - 3x = x^2 -1
The coordinate that represent the solution of the equation -
x² - 3x = x² - 1 is (0.333, -0.8889).
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given is the following equation -
x² - 3x = x² - 1
In order to solve it using intersect method, we will plot the graphs of both functions and find the point of intersection of graphs of both the equations.
Assume -
f(x) = x² - 3x
g(x) = x² - 1
Now, the point of intersection of both the graphs will be the solution to the equation given by -
f(x) = g(x)
It can be seen from the graph that, both the graphs intersect at the coordinate (0.333, -0.8889). This coordinate will be the solution set of the equation -
f(x) = g(x)
Therefore, the coordinate that represent the solution of the equation -
x² - 3x = x² - 1 is (0.333, -0.8889).
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Create three probability application problems of your own. Solve your problems. Explain your answers.
In the above question, we need to from 3 probability questions and then give solutions for them
Example 1 : A coin is tossed three times. What is the probability of getting at least one head?
Solution : A coin is tossed 3 times then
Sample space = [HHH, HHT, HTH, THH, TTH, THT, HTT, TTT]
Total number of ways = 2 × 2 × 2 = 8
Favorable Cases = 7
P (A) = 7/8
OR
Probability (of getting at least one head) = 1 – P (no head)⇒ 1 – (1/8) = 7/8
Example 2 : Three red and four black balls are contained in a bag. Randomly, one ball gets taken out of the bag. Determine the probability that the drawn ball is
(i) black
(ii) not black
Solution :
Total number of balls in the bag are = 3 + 4 = 7 balls
Number of favorable outcomes or number of black balls in the bag = 4
(i) Probability getting black balls = [tex]\frac{number of favorable outcomes}{number of total outcomes}[/tex]
P(black ball) = [tex]\frac{4}{7}[/tex]
(ii) Probability getting no black balls = 1 - P(black ball)
= 1 - [tex]\frac{4}{7}[/tex]
= [tex]\frac{3}{7}[/tex]
Example 3 : Given two dice, what is the likelihood of receiving the number 7?
Mathematical probability - There are 36 ways in all, or 6 times 6. Favorable scenarios are (1, 6) (6, 1) (2, 5) (5, 2) (3, 4) (4, 3), etc., in six different ways. P (A) = 6/36 = 1/6
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Just 5 and 6! Please!!✨
The three statement true about the the distance of a dog from a post are-
f(0) = 1.5f(60) = 4f(t) < 5What is termed as the function notations?Function notation is a method of representing a function utilizing symbols and signs.The most common function notation is f(x), which is read as "f" of "x." In this case, the letter x enclosed in parentheses, as well as the entire symbol f(x), represent the domain set as well as range set, respectively.For the given graph in the question,
Function f gives the distance of a dog from a post, in feet, as a function of time, t in seconds, since its owner left.
The time is denotes on the x axis and the distance covered by the dog on the y axis.
This can be described using the function as.
f(t) = d
Consider values from graph.
When, t = 0, d = 1.5 feet
Function notation ; f(0) = 1.5 ......statement 1
When t = 60, d = 4 feet
Function notation ; f(60) = 4 ......statement 2
Now, the maximum value is 5.
Thus, f(t) < 5 .....statement 3
Therefore, the three statement are formed.
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The correct question is -
Write three statement that are true about this situation. Use function notations.
Function f gives the distance of a dog from a post, in feet, as a function of time, t in seconds, since its owner left.
Use the = sign in at least one statement and < sign in another statement.
Reflect the given triangle over the y - axis [[3,6,3],[-3,3,3]]
By using a reflection over the y-axis, the coordinates of the image of the triangle are (- 3, - 3), (- 6, 3) and C'(x, y) = (- 3, 3).
How to determine the coordinates of the vertices of a triangle by rigid transformations
Rigid transformations are transformations applied on geometric loci such that the form of the construction is not altered. Reflections over the y-axis are examples of rigid transformations. In this problem we need to apply this kind of transformation on the three vertices of the triangle: A(x, y) = (3, - 3), B(x, y) = (6, 3), C(x, y) = (3, 3).
The reflection over the y-axis is described by the following formula:
P'(x, y) = P(x, y) + (- 2 · p, 0)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointp - x-Component of P(x, y).If we know that A(x, y) = (3, - 3), B(x, y) = (6, 3) and C(x, y) = (3, 3), then the image of the vertices of the triangle:
A'(x, y) = (3, - 3) + (- 6, 0)
A'(x, y) = (- 3, - 3)
B'(x, y) = (6, 3) + (- 12, 0)
B'(x, y) = (- 6, 3)
C'(x, y) = (3, 3) + (- 6, 0)
C'(x, y) = (- 3, 3)
Now we present the picture of the two triangles.
The coordinates of the image of the triangle are A'(x, y) = (- 3, - 3), B'(x, y) = (- 6, 3) and C'(x, y) = (- 3, 3).
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question is in the picture
If a fraction has a numerator of 2, then the fraction can be reduced. A counter example is ____ option below.
a) 10/15
b) 11/22
c) 1/10
d) 2/11
Answer:
The answer is d
Step-by-step explanation:
2/11 has a numerator of 2 but cant be reduced
Answer:
Step-by-step explanation:
I misunderstood the question. So, please disregard this answer. Thank you.
The product of -2 and a number is at most 10.
Find the possible numbers.
On<-5
Ons-5
Onz-5
On>-5
Answer:
n ≥ -5
Step-by-step explanation:
-2n ≤ 10
Divide both sides by -2. Remember to flip ≤ to ≥.
-2n/(-2) ≥ 10/(-2)
n ≥ -5
find the area of the circle. Use 3.14 for pie. Do not round your answer.
Answer: A = 452.16 ft²
Step-by-step explanation:
This gives us the formula to solve for the area.
A = πr²
The radius (r) is the same as the diameter divided by 2.
24 ft / 2 = 12 ft
We will input these given values and solve.
A = πr²
A = (3.14)(12)²
A = 452.16 ft²
Answer:
452.16 ft²
Step-by-step explanation:
To find the radius, you divide the diameter (24) by 2, which equals 12. The area of a circle formula is πr². To find area, you do 12² * 3.14. That equals 144 * 3.14, which equals 452.16.
please quickkkk :((((
According to given function the final value is [tex]$f=\frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}(x-i y)}{x^2+y^2} ; \quad x \neq-i y$[/tex]
[tex]$$f(x+i y)=\sum_{k=1}^{\infty} \frac{1}{k}(x+i y)$$[/tex]
[tex]$$f(x+i y)=\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}$$[/tex]
Divide both sides by [tex]$x+i y ; \quad x \neq-i y$[/tex]
[tex]\frac{f(x+i y)}{x+i y}=\frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}}{x+i y} ; \quad x \neq-i y$$[/tex]
Simplify
[tex]\frac{f(x+i y)}{x+i y}=\frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}}{x+i y}$$[/tex]
Simplify[tex]$\frac{f(x+i y)}{x+i y}: f$[/tex]
Simplify [tex]$\frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}}{x+i y}: \frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}(x-i y)}{x^2+y^2}$[/tex]
[tex]f=\frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}(x-i y)}{x^2+y^2} ; \quad x \neq-i y$$[/tex]
[tex]f=\frac{\sum_{k=1}^{\infty} \frac{1}{k^{x+i y}}(x-i y)}{x^2+y^2} ; \quad x \neq-i y$$[/tex]
The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x.
In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
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A summer camp is organizing a hike and needs to buy granola bars for the campers. The granola bars come in small boxes and large boxes. Each small box has 10 granola bars and each large box has 12 granola bars. The camp bought a total of 9 boxes that have 100 granola bars altogether. Write a system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased. Define the variables that you use to write the system.
The system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased is b + s = 9 and 10s + 12s = 100
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the small box be represented as s.
Let the big box be represented as b.
Each small box has 10 granola bars and each large box has 12 granola bars. The The camp bought a total of 9 boxes that have 100 granola bars altogether.
The equation will be:
b + s = 9
10s + 12s = 100
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Answer:
10x + 12y = 100
x + y = 9
Step-by-step explanation:
Define Variables:
Let x = the number of small boxes purchased
Let y = the number of large boxes purchased
Each small box has 10 granola bars, so small boxes have 10x granola bars.
Each large box has 12 granola bars, so large boxes have 12y granola bars. Therefore, the total number of granola bars 10x + 12y equals 100:
10x + 12y = 100
Since a total of 9 boxes were purchased, we know x + y must equal 9.
x + y = 9
Draw a polygon with vertices R(-4, 2), S(2, 2), T(2, -2), and U(-4, -2). What is the perimeter, in units, of polygon RSTU? Draw a polygon with vertices R(-4, 2), S(2, 2), T(2, -2), and U(-4, -2). What is the perimeter, in units, of polygon RSTU?
Answer:
The perimeter of rectangle RSTU is 20 unitsStep-by-step explanation:
Given Vertices R(-4, 2), S(2, 2), T(2, -2), and U(-4, -2).To find The perimeter of the RSTUSolutionPlot the points, we see it is a rectangle.
Side lengths are:
RS = TU = 2 - (-4) = 6, the difference of x-coordinates,ST = RT = 2 - (-2) = 4, the difference of y-coordinates.The perimeter is:
P = 2(l + w)P = 2(6 + 4) = 2(10) = 20 unitsThe perimeter of polygon RSTU is
How to find distance between straight line?A straight line connects any two places with the smallest distance possible. The distance formula can be used to get this distance. It is possible to define the distance between two positions (x 1, y 1) and (x 2, y 2) as d=√(x2-x1)² + (y2 - y1)².
Distance between R and S is;
√(2+4)² + (2 - 2)²= 6 units
Distance between S and T is;
√(2-2)² + (-2 - 2)²= 4 units
Distance between T and U is;
√(-4+-2)² + (2 - 2)²= 6 units
Distance between T and U is;
√(-4+4)² + (2 + 2)²= 4 units
The total perimeter is of polygon is:
6+4+6+4 = 20 units
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need answer asap please
The graph of the defined piece-wise function is sketched at the end of the answer.
What is a piecewise-defined function?A piecewise-defined function is a function that has different definitions, depending on the input of the function.
In the context of this problem, the function has three definitions, as follows:
To the left of x = -3. (x <= -3).Between x = -3 and x = 4. (-3 < x < 4).To the right of x = 4. (x >= 4)For the first definition, to the left of x = -3, the function assumes a constant value of 3, hence it is an horizontal line at y = 3.
For the second definition, between x = -3 and x = 4, the function is a increasing linear function, with intercept 1 and slope 2, due to the rule y = 2x + 1.
For the third definition, to the right of x = 4, the function assumes a constant value of -2, hence it is an horizontal line at y = -2.
With each of these definitions, the graph of the function is given at the end of the answer.
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A shirt that normally costs $30 is on sale for
$21.75. What percent of the regular price is
the sale price?
Answer:
72.5%
Step-by-step explanation:
Hello!
We can find the percentage by dividing the sale price by the original price, then multiplying that by 100.
Find the Percentage[tex]\frac{21.75}{30} * 100[/tex]0.725 * 10072.5The percentage is 72.5%.
Question 4 options:
Premises:
If I'm a student, then I go to school. If I go to school, then I learn.
Conclusion:
If I'm a student, then I learn.
This is an example of the Law of
The law of mathematical logic that was used to derive the given conclusion is; Law of Syllogism
What is the Law of Syllogism?The law of syllogism is defined as a type of logical argument using deductive reasoning.
Now, In mathematical logic, the Law of Syllogism states that if the following two statements are true:
(1) If a , then b .
(2) If b , then c .
Then we can derive a third true statement:
(3) If a , then c .
Now, applying that law to our question, we see that;
1) If I'm a student, then I go to school.
2) If I go to school, then I learn.
Then we can derive a third true statement:
3) If I'm a student, then I learn.
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Find the equation of the tangent at f(x) at x=0
Given:
The function
[tex]f(x)=\frac{2x}{x^2+1}[/tex]Required:
Find the equation of the tangent at f(x) at x=0.
Explanation:
The slope of f(x),
[tex]f^{\prime}(x)=\frac{2(-x^2+1)}{(x^2+1)^2}[/tex]Now, the slope of function at x = 0 is f'(x) = 2.
The line with slope m = 2 and passing through (0, 0).
[tex]f(x)=2x[/tex]Answer:
Equation of tangent of the function at x = 0, f(x) = 2x.
0.8 divided by 0.6 then round to nearst hundredth
Answer: 1.33
Step-by-step explanation:
0.8 divided by 0.6= 1.33333333333
3 is in the hundredths place and 3 is in the thousandths place.
Since the digit in the thousandths place (3) is less than 5, the digit in the hundredths place (3) does not change.
The digits to the right of the hundredths place are dropped.
1.33333333 rounded to the nearest hundredth (two decimal places) = 1.33.
Math
Show your solution please the question is in the picture
Answer: A) x^2+y^2 B) x^3+y^3 C) a^2b^2c^2 D) c^2/d^2
Step-by-step explanation:
For A, you add all the powers. This is because the bases are the same. Any number or letter without a visible power on top most likely means that is has a power of 1. Because this is a multiplication question, you have to add the powers. (Example n*n = n^2 or n^3*n^7 = n^10)
This is same for B.
For C, you multiply abc by abc so it's a*a, b*b, c*c. This is because they are inside a bracket. Anything inside the bracket that has a power outside the bracket is multiplied by itself.
For D, you multiply c and d so it's c*c, d*d. This is the same as C.
find the area under the standard normal distribution curve to the right of . use a ti-83 plus/ti-84 plus calculator and round the answer to at least four decimal places.
using calculator
Area right to the right of the 2=2.12
P(Z > 2.12)
• P(Z < -2.12)
= 0.0170
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Garth is baking cookies for his class! Once he
removes the cookies from the oven, the
temperature of the cookies (in °F) can be
modeled as a function of time (in minutes):
f(x) = 278(0.58)* + 72.
After 5 minutes, the cookies will be
°F (round to one decimal place).
Answer:
7358.84
Step-by-step explanation:
Choose two statements that are true for this expression
Find all of the numbers less than100 that have at least 2 and at least one 5 in their prime factorization
Answer: [tex]10, 20, 30, 40, 50, 60, 70, 80, 90[/tex]
Step-by-step explanation:
If the numbers have at least one 2 and at least one 5, then they are multiples of 10 (since [tex]10=2 \times 5[/tex]).
So, these numbers are [tex]10, 20, 30, 40, 50, 60, 70, 80, 90[/tex].
What are three pairs of corresponding angles?
Part 1
Tell whether the sequence is arithmetic. If it is, identify the common difference.
-1,4,9,14
PLEASE HURRY
Answer:
It is arithmetic, the common difference is 5
Step-by-step explanation:
What an arithmetic sequence has to have is a common difference meaning you are adding or subtracting the same number each time, in this case you are adding 5 every time so it is arithmetic
El valor de x que se cumple con 6x-10=2 es
Answer:
the answer is 2
Wilbur landed his plane.
The plane's elevation relative to the ground
(in meters) as a function of time (in seconds)
is graphed.
How high was the plane after 1000 seconds?
At 1000 seconds the graph shows the height of 3500 meter.
what is graph?The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.
Following the creation of a research question, data is continuously gathered through observation. The information is subsequently arranged, condensed, categorised, and visually portrayed.
In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.
Usually, data that varies over time is represented with a line graph.
Given:
The graph gives the relation between Elevation and Time.
As, if at 400 seconds the height is 6500 meters.
and, at 800 seconds the height is 4500 meters.
Thus, at 1000 seconds the graph shows the height of 3500 meter.
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Use the numbers 5, 6, and 7 and the operations of addition, subtraction, multiplication, and/or division to create three different number expressions with three different values. One of the expressions should have a value of 37.
The use the numbers 5, 6, and 7 and the operations of addition, subtraction, multiplication, and/or division to create three different number expressions with three different values will be:
1. 5 × 6 + 7 = 37
2. 5 + 6 - 7 = 4
3. 5 + 6 + 7 = 18
What is addition?Addition simply means the sum of the numbers that are given. It should be noted that addition is represented by the sign +.
In this case, we are told to use 5, 6 and 7 to create different values. These are represented above. The addition of 5, 6, and 7 gives 18.
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Find the values of a,b and c that would make the statements true.
1) (ax+2)(5x+b)=10x^2+bx+c
The values of a, b and c are a = 2, b = -10 and c = -20
How to determine the values of the variables?The equation is given as
(ax + 2)(5x + b) = 10x^2 + bx + c
Open the brackets
So, we have
5ax^2 + 10x + abx + 2b = 10x^2 + bx + c
By comparing the above equation.
We have the following set of equations
5a = 10
10 + ab = b
2b = c
By solving the equations, we have
a = 2
Substitute a = 2 in 10 + ab = b
10 + 2b = b
So, we have
b = -10
Substitute b = -10 in 2b = c
2(-10) = c
Evaluate
c = -20
Hence, the values of the variables are a = 2, b = -10 and c = -20
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write and solve a real world problem in which you find the commission
A car salesman earns a 3% commission on sales. If he sells a car for $27,990, how much commission will he earn?
($27,990)*(0.03) = $839.70
The Jones family will pay their insurance broker a commission of $1,750.00.
Commission is an amount of money paid to an employee or company as an incentive to sell more. A straight commission is a percentage of sales.
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