The squared pictured below has side lengths of 4 units. Questions are in the picture below-
A.
The length of the diagonal is given by the Pythagorean theorem therefore
[tex]d=\sqrt[]{4^2+4^2}=\sqrt[]{16+16}=\sqrt[]{32}[/tex]The length of the diagonal is ) units
B.
The area of the square is given by the next formula
[tex]A=s^2[/tex]where s is the side
s=4
[tex]A=(4)^2=16units^2[/tex]The area of the square is 16 units^2
C.
For the area of the triangle we will use the next formula
[tex]A=\frac{1}{2}b\times h[/tex]where b is the base and h is the height
b=4 units
h=4units
[tex]A=\frac{1}{2}(4)(4)=\frac{1}{2}(16)=8units^2[/tex]The area of the triangle formed by a diagonal and two of the sides is 8 units^2
D.
For the area of this triangle, we will use the same formula that we use in C. but in this case
b=sqrt(32)/2
h=sqrt(32)/2
We substitute the values
[tex]A=\frac{1}{2}(\frac{\sqrt[]{32}}{2})(\frac{\sqrt[]{32}}{2}))=4units^2[/tex]The area of one of these triangles is 4 units^2
ANSWER
A. sqrt(32) units
B.16 units^2
C. 8 units^2
D. 4 units^2
I need help!!!!!!!!!!!!!!!!!!!!!!!!!!
The absolute functions when matched to the respective vertex is as follows;
(-1, -3/7) → f(x) = (1/2)|x + 1| - (3/7)
(5, 2/3) → f(x) = (-3/5)|x - 5| + (2/3)
(0, -4/5) → f(x) = (1/2)|x| - (4/5)
(2/5, 5/3) → f(x) = (-3/2)|x - (2/5)| + (5/3)
What is the absolute value function of the Vertices?
We can solve all of them by writing the equations in a general form;
f(x) = a|x + b| + c
This is a function transformation of f(x) = |x|
where:
a = Factor of vertical stretch
b = Horizontal shift (- shifts right, + shifts left)
c = Vertical shift (+ shifts right, - shifts left)
The original function has its vertex in (0, 0) so the horizontal shift will be the new x coordinate in the new vertex and the vertical shift will be the new y in the new vertex like this:
f(x) = (1/2)|x + 1| - (3/7)
b = 1 horizontal shift of -1
c = -3/7 vertical shift of -3/7
Thus, (-1, -3/7)
f(x) = (-3/5)|x - 5| + (2/3)
b = -5 horizontal shift of 5
c = 2/3 vertical shift of 2/3
Thus, (5, 2/3)
f(x) = (1/2)|x| - (4/5)
b = 0 horizontal shift of 0
c = -4/5 vertical shift of -4/5
Thus, (0, -4/5)
f(x) = (-3/2)|x - (2/5)| + (5/3)
b = -2/5 horizontal shift of 2/5
c = 5/3 vertical shift of 5/3
Thus, (2/5, 5/3)
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Deepak wants to tile his bathroom using 1 m square tiles.
His bathroom measures 7 m x 7 m.
How many tiles will he need?
The bathroom must be tiled with 49 tiles, each of which has a surface area of 1 square meter and measures 7 meters by 7 meters.
How can I figure out how many tiles I need to tile the bathroom?
The bathroom's area is,
A= 7m x 7m
A= 49m^2
likewise the area of each tile = 1 square meter
The total amount of tiles needed to tile the bathroom is thus,
49/1 = 49
Therefore, the bathroom must be tiled with 49 tiles.
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Snow plowing plan , In the relationship between the amount of snowfall and the number of trucks proportional explain
Based on the number of trucks needed and the snowfall per inch, the relationship between snowfall and trucks is proportional.
When is a relationship proportional?A relationship is said to be proportional when the two variables increase at a set rate. In other words, proportional relationships will see variables increasing at the same rate.
The rate of snowfall per trucks for 6 inches of snowfall is:
= 15 / 6
= 2.5 trucks per inch of snowfall
The rate of snowfall per trucks for 12 inches of snowfall is:
= 30 / 12
= 2.5 trucks per inch of snowfall
The rate is therefore the same across the table so the relationship between snowfall and the number of trucks is proportional.
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5. If the standard error of the sampling distribution of the sample proportion is 0.0337 for samples of size 200, then the population proportion must be either:
The population proportion when the standard error of the sampling distribution of the sample proportion is 0.0337 for samples of size 200 must be D. 0.35 or 0.65.
How to illustrate the information?Based on the information, it should be noted that the formula for the standard error for the population will be:
✓p(1 - p)/n
where
p = population proportion
n = sample size
Therefore, this will be illustrated as:
✓p(1 - p)/n = 0.0337
Remove the square root
p( 1 - p)/200 = 0.00113569
Cross multiply
p(1 - p) = 0.227138
p - p² = 0.227138
Equate to 0
p² - p + 0.227138 = 0
Using almighty formula, P1 = 0.6512 and P2 = 0.3488
Therefore, the correct option is D.
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If the standard error of the sampling distribution of the sample proportion is .0337 for samples of size 200, then the population proportion must be:
A) 0.25
B) 0.75
C) 0.20 or 0.80
D) 0.35 or 0.65
Solve For X the picture of the problem will be provided
Answer:
x = 37
Step-by-step explanation:
∡CAE = 180°
Then:
∡ABC = 180° - (10+8X)
∡ABC = 180 - 10 -8X
∡ABC = 170 -8X
The sum of the internal angles of a triangle results im 180°:
70 + (6x+14) + (170-8x) = 180
70 + 14 + 170 + 6x - 8x = 180
254 - 2x = 180
254 - 180 = 2x
74 = 2x
x = 74/2
x = 37
Members of a softball team raised $1,186.50 to go to a tournament they rented a bus for $842.50 and budgeted $21.50 per player for Meals. write and solve an equation which can be used to determine x the number of players the team can bring to the tournament
If members of a softball team raised $1,186.50 to go to a tournament they rented a bus for $842.50 and budgeted $21.50 per player for Meals. The number of players the team can bring to the tournament is 16.
Number of playersLet x represent the number of players
Formulate an equation
$842.50 + $21.50 × x = $1,186.50
Using the formulated equation to determine the number of players
$842.50 + $21.50 × x = $1,186.50
$842.50 + $21.50 x = $1,186.50
Collect like terms
$21.50 x = $1,186.50 -$842.50
$21.50 x = $344
Divide both side by $21.50 x
x = $344 / $21.50
x = 16 players
Therefore the team can bring 16 players to the tournament.
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a tangent or contingent equation for the graph in the picture.......
The graph is about a tangent function.
[tex]y=a\tan (bx-c)+d[/tex]We have to find the parameters a and b.
The period formula is
[tex]P=\frac{\pi}{|b|}[/tex]If we find the period, we can find b.
Remember that the period is the distance between two consecutive asymptotes. In this case, the period is 2pi.
[tex]\begin{gathered} 2\pi=\frac{\pi}{b} \\ 2=\frac{1}{b} \\ b=\frac{1}{2} \end{gathered}[/tex]what is the sum of 1 1/2 plus 3 3/4 plus 5 1/8
Answer:
83/8 , decimal form 10.375, mixed number form 10 3/8
Step-by-step explanation:
What is 7.68 rounded to the nearest half's
The nearest half of 7.68 is 7.5
Given,
A number is given by:
7.68
and, to find the rounded to the nearest half
Now, The number 7.68 is between 7.5 and 8.
Let's find which of these two numbers 7.68 is closer too.
We can do this by subtracting 7.68 from each of those numbers:
8 - 7.68 = 0.32
7.5 - 7.68 = -0.18
So, 7.68 is 0.32 away from 8, but it's only 0.18 away from 7.5
Hence, The nearest half of 7.68 is 7.5
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A company has 15 employees with a salary of $21,900, 10 employees with a salary of $24,800, 3 employees with a salary of $31,200, 4 employees with a salary of $37,700 and 1 employee with a salary of $149, 600. Find the mean salary for the employees.The mean salary for the employees is $___.(Type a whole number. Round to the nearest hundred as needed.)
We need to find the mean salary for the employees:
There are
15 employees with a salary of $21,900, 10
10 employees with a salary of $24,800
3 employees with a salary of $31,200
4 employees with a salary of $37,700
1 employee with a salary of $149, 600
33 total of employees:
The mean formula is given by:
[tex]\text{Mean=}\frac{\text{add for all data}}{\text{total number of data}}[/tex]Replacing :
[tex]\text{Mean}=\frac{15(21,900)+10(24,800)+3(31,200)+4(37,700)+1(149,600)}{33}[/tex]Therefore:
[tex]\text{Mean = 70,209}.13[/tex]The result is rounded to the nearest hundred.
You create gift baskets to sell at the craft show. Small baskets sell for $12, and
large baskets sell for $20. Your goal is to sell $300 worth of baskets at the
upcoming craft show. Write an equation that represents the amounts of the
baskets you have to sell to reach your goal.
If you sell 7 large baskets, how many small baskets will you need to sell to meet or exceed your goal?.
You will need to sell 14 baskets to meet/exceed the goal
How to calculate the number of baskets needed to exceed the goal ?
Small baskets are sold at $12
Large baskets are sold at $20
The goal is to sell $300 worth of baskets at the upcoming craft show
Let x represent the small baskets and let y represent the large baskets
12x + 20y= 300
7 large baskets are sold, the equates to
7 × 20
= 140
The number of small baskets that must be sold to reach the goal can be calculated as follows
300-140
= 160
160/12
13.33
Hence 14 small basket needs to be sold to meet/exceed the goal
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Help IMMEDIATLY please I really need it
Based on the value of the angles in this triangle, the value of x can be found to be 82 degrees
How to find the missing angle?The interior angles of different polygons always add up to a certain number of degrees. For instance, the interior angles of a heptagon add up to 900 degrees.
In triangles, the the interior angles will always add up to 180 degrees. The value of x can then be found by the formula:
180 = 52 + 46 + x
x = 180 - 52 - 46
x = 82 degrees
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divide r by 8, then double the result
The expression divide r by 8 when doubled is r/4
What is an algebraic expression?An algebraic expression can be seen or described as a mathematical or arithmetic expressions that is composed of arithmetic terms, factors, constants, variables, and coefficients.
These expressions are also known to be composed of mathematical operations, such as;
SubtractionAdditionMultiplicationBracketDivision, etcFrom the information given, we have;
divide r by 8
This is expressed as;
r/8
In doubling the expression, we get;
2(r/8)
expand the bracket
2r/8
Simplify further
r/4
Hence, the expression is r/4
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The table below shows a runner's time t, in mintues, and distance traveled d, in miles.
Write an equation that shows a relationships between t and d.
The equation that shows a relationship between t (time in minutes) and d (distance in miles) is d = 0.075t
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
The standard form for linear equation is:
y = mx + b
Where m is the slope and b is the y intercept
Let d represent the runners distance after t minutes.
From the table, using the points (12, 0.9) and (16, 1.20):
d - 0.9 = [(1.2 - 0.9)/(16 - 12)](t - 12)
d - 0.9 = 0.075(t - 12)
d = 0.075t
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HELP PLEASEEEEE!!!!
( -4)¹⁹ = - 274877906944 is standard form of 4 to power -19.
What are power and exponent?
Exponents and powers are two techniques for simplification of extremely big or extremely small numbers. For instance, we can write 3 x 3 x 3 x 3 as 34, where 4 is the exponent and 3 is the base, to demonstrate 3 x 3 x 3 x 3 in a straightforward manner. There is a claim of power throughout the entire sentence 34.a) ( -8 )⁰ = 1 ( positive )
b) ( -4 )⁶ = - 4× -4 × -4 × -4 × -4 × -4 = 4096 ( Positive )
c) ( -5 )¹² = 244,1406,25 ( positive )
d) ( -4)¹⁹ = - 274877906944 ( Negative)
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Consider the function [tex]p(x)=\frac{cos^{2}x }{sin2x}[/tex]. Which of the following accurately describes the limit as x approaches 0 of the function?
a. as x approaches 0, the limit of p(x) approaches a large negative y-value
b. As x approaches 0, the limit of p(x) does not exist
c. As x approaches 0, the limit of p(x) approaches 0
d. As x approaches 0, the limit of p(x) approaches a large positive y-value
The function, [tex]\displaystyle { p(x) = \frac{ {cos}^{2}x }{sin(2 \cdot x)} }[/tex] has a limit that is undefined (does not exist) as x approaches 0. The correct option therefore option b;
b. As x approaches 0, the limit of p(x) does not exist
What is a function in mathematics?The given function is presented as follows;
[tex]\displaystyle { p(x) = \frac{ {cos}^{2}x }{sin(2 \cdot x)} }[/tex]
Required;
The limit of the function as x approaches (zero) 0
Solution;
The limit of a function at a given point within the domain of the function is the value of the function as the function's argument approaches a.
Therefore, the limit of the given function at the point x = 0 is given by the function's value as the argument of the function, x approaches 0.
cos²(0) = 1
sin(2×0) = sin(0) = 0
Therefore;
[tex]\displaystyle { p(x) = \frac{ {cos}^{2}0 }{sin(2 \times 0)} = \frac{ 1 }{0} = \infty}[/tex]
Therefore, the limit of the function does not exist as x approaches 0
The correct option is therefore, option b
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Set up a proportion and solve.
Find the cost of 3 scarves if 2 scarves cost $22.80.
[tex]\begin{array}{ccll} scarves&\$\\ \cline{1-2} 2 & 22.80\\ 3& x \end{array} \implies \cfrac{2}{3}~~=~~\cfrac{22.80}{x} \\\\\\ 2x=3(22.80)\implies x=\cfrac{3(22.80)}{2}\implies x=34.2[/tex]
Answer: $34.20
Step-by-step explanation:
2 scarves = $22.80
22.80 ÷ 2 = $11.40
11.40 x 3 = $34.20
To check your work you could do:
$22.80 + $11.40 = $34.20
or
$34.20 ÷ 3 = $11.40
The number of hours needed to paint a house, h, varies inversely with the number of painters, n. Four painters need 6 hours to paint a house. Find the equation represents this relationship.
The equation that represents this relationship is h*n = 24.
How do we solve linear equations?
First order equations include all linear equations as a subset. In the coordinate system, lines are defined as having linear equations. A linear equation in one variable is made up of one homogeneous variable of degree one (i.e., only one variable). A linear equation could contain multiple variables. When a linear equation comprises two variables, for instance, linear equations in two variables are utilized. A mathematical statement known as an equation contains an algebraic expression and the equal symbol (=). It is the equation for a straight line. The equation is shown to be valid when values are substituted for the unknown values in the solutions of linear equations. When there is just one variable, there is just one answer.
Given, number of hours needed to paint a house = h
Number of painters needed to paint the house = n
Also, the relation between h and n is inverse, thus:
h*n = k, where k is the proportionality constant.
Therefore, initial equation derived is h*n = k --(i)
Putting h = 6 and n =4 in (i), we can get the value of k as
k = h*n = 6*4 = 24 --(ii)
Comparing (i) and (ii), we get,
h*n = 24, which is the required equation.
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Combine like terms and simplify please
Simplifying the given term
What is Like Terms?
In algebra, equal terms are terms that have the same variables and powers. Coefficients do not have to match. Dissimilar terms are two or more terms that are not similar terms. That is, they do not have the same variable or exponentiation. The order of the variables does not matter unless there are exponentiations.
To simplify and combine the like terms of the given question
7) -4x^2 - y^2 - 6x^2 + 2xy - 4x^2 + 7xy - xy +4y^2-9xy - 4x^2 + xy
Now, arranging them with the like terms
= -4x^2- 4x^2- 4x^2- 6x^2- y^2 +4y^2+ 2xy- xy-9xy + xy
= -10x^2 + 3y^2 - 7xy
8) n+n^2-5n+40n-10+3n^2+1-5n+n^2+18n-2
Now, arranging them with the like terms
= n^2+n^2+3n^2+n-5n+40n-5n+18n-10+1-2
= 5n^2 + 49n - 11
9) 14y - y^2 + 9y^2 + 12 - 5y^2 + 25y - y +8y^2 - 9y +25y + y
Now, arranging them with the like terms
= 9y^2- y^2- 5y^2+8y^2+ 25y- y - 9y + y +25y + 14y +12
= 11y^2 + 45y + 12
10) 12b + 2b^2 + 6a^2 + a - 5b + 2a - ab + 4a^2 - b - ab + 10b
Now, arranging them with the like terms
= 2b^2+ 6a^2+ 4a^2 + a+ 2a + 12b - 5b - b+ 10b - ab- ab
= 10a^2 + 2b^2 + 3a + 16b - 2ab
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A My Drive ) CharlotteAnne Hill - Unit6 MYP Project.pdf . Cole thinks they would make the most money if their club supervisor, Mr. Alvarez, invests the $450 they already raised in the stock market. He suggests buying the stock shown in the graph since the value is currently increasing. Do you agree with Cole? Describe what you see in the graph to support your reasoning. 2 points
Looking at the graph
the value is currently increasing, because the slope of the line is positive
so
I agree with Mr. Alvarez reasoning
1) 65x12-92+13 =
2) 4/2+19-5x11 =
1.
[tex] = (65 \times 12) - 92 + 13 \\ =780 - 92 + 13 \\ = (780 - 92) + 13 \\ = 688 + 13 \\ = 701 [/tex]
2.
[tex] = \frac{4}{2} + 19 -(5 \times 11) \\ = (2 + 19 )- 55 \\ = 21 - 55 \\ = - 34[/tex]
ATTACHED ARE THE SOLUTIONS
The state department of transportation recorded the number of vehicles that passed through a toll booth between midnight and 5 am over a period of several months, and found that the average number of vehicles per night was 27. Find the probability that a randomly selected night has exactly 25 vehicles passing through the toll booth. Use Excel to find the probability.
Round your answer to three decimal places.
Provide your answer below:
$$
The probability would be 0.074 that a randomly selected night has exactly 25 vehicles passing through the toll booth.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes
Let X be the number of vehicles passing through the toll booth per night
X~Poisson(27)
The probability that exactly 25 vehicles passing through the toll booth is
⇒ P(X = 25) = (e⁻²⁷ × 27²⁵) / 25!
⇒ P(X = 25) = 0.074
Thus, Excel Command = POISSON.DIST(25,27,FALSE)
Therefore, the probability would be 0.074 that a randomly selected night has exactly 25 vehicles passing through the toll booth.
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help would be appreciated
We can define the translation of building from location C to location E by the following rule -
(x, y) → (x - 4 , y + 6)
What is translation of graph?
A translation is a movement of the graph either horizontally (parallel to the x -axis) or vertically (parallel to the y -axis) without changing its orientation.
Given is a Building C translated to Building E.
In order to translate the building from location C to location E, we will first shift the building near the x - axis vertically upwards. For this we will shift the y coordinate by -
- 7 + y[s] = - 1
y[s] = -1 + 7
y[s] = 6
So the y - coordinate of the translated graph will be -
(y + 6)
Now, we will shift the x coordinate -
1 + x[s] = -3
x[s] = -3 - 1
x[s] = -4
So the x - coordinate of the translated graph will be -
(x - 4)
Therefore, we can define the translation by the following rule -
(x, y) → (x - 4 , y + 6)
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Given (12, 8) and (X, -4 ) find all X such that the distance between these two points is 13separate multiple answers with a comma
Given:
(12, 8) and (X, -4 )
Required:
To calculate the value of x
Explanation:
Determine the parameter through distance formula
Required answer:
x=7 or x=17
HELP
In this unit, you will investigate some real-world scenarios which can be modeled through logarithmic functions. In particular, we'll investigate three phenomena using logarithmic models: magnitude of earthquakes, intensity of sound, and pH (or acidity) of substances. Research online and find an additional scenario not mentioned above that uses logarithmic functions, and explain why it is beneficial to your everyday life. Be sure to cite any sources you used in your response.
One example of real-world situation that uses logarithms is for amount of substance that are decaying over time.
Logarithms and amount of substancesAn amount of a decaying substance after t years is modeled by the following exponential equation:
[tex]P(t) = P(0)e^{-kt}[/tex]
In which:
P(0) is the initial amount.k is the exponential decay rate, as a decimal.The simplest example of the use of logarithms is to find the half-life of the substance, that is, the year t for which P(t) = 0.5P(0).
Then:
[tex]0.5P(0) = P(0)e^{-kt}[/tex]
[tex]e^{-kt} = 0.5[/tex]
The natural logarithm is used to find the half life, as it is the inverse of the exponential.
[tex]\ln{e^{-kt}} = \ln{0.5}[/tex]
[tex]-kt = \ln{0.5}[/tex]
[tex]t = -\frac{\ln{0.5}}{k}[/tex]
Hence we showed another application of logarithms in a real-word model.
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(LO11) The weight of adult male beagles is normally distributed with a mean of 25.0pounds and a standard deviation of 2.9 pounds. Find the probability that a randomlyselected beagle weighs more than 21.8 pounds.0.1280O 0.13490.86510.8720
A randomly chosen beagle has a 0.86508 probability of weighing more than 21.8 pounds.
How can probability be explained?A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be represented as percentage with values between 0 and 1.
What does the term "z-score" mean?The relationship between a value and the mean of a group of values is quantified by a Z-score.
Adult male beagle weight is normally distributed, with a mean of 25.0 pounds and a standard deviation of 2.9 pounds.
Given values are:
Mean(μ) = 25 pounds
Standard deviation(σ) = 2.9 pounds
Sample mean(x') = 21.8
We need to calculate z-score:
z = (x' - μ)/σ
z = (21.8 - 25)/2.9
z = 1.25
P-value from Z-Table:
P(x>21.8) = 1 - P(x<21.8) = 0.86508
As a result, the probability of a randomly selected beagle weighing more than 21.8 pounds is 0.86508.
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4. Identify all possible proper subset relationships that occur among the following sets.
Show work please.
The proper subset relationship of the given set A, B and C are in option;
Option A; C ⊂ AOption C: C ⊂ BOption D: B ⊂ AWhat is meant by the term proper subset?A subset is a subset of a larger set (someother set or same set). A B is the set notation used to symbolize a set A as a subset of a larger set B.A proper subset would be any subset of a set that is not the set itself. Every set, we know, is a subset of itself, but it is not a proper subset of it's own.The correct subset symbol is ⊂ . In other words, if A is a proper subset of B, after which:A ⊂ B andA ≠ BFor the given question;
The set are given as;
A = { x | x = 2n + 1, n ∈ R }
This, can be written as for the real number say, n = 0, 1, 2, 3....
A = {1, 5, 7, 9 , 11 ..}
B = { x | x = 4n + 1, n ∈ R }
This, can be written as for the real number say, n = 0, 1, 2, 3....
B = {1, 5, 9, ....}
C = { x | x = 8n + 1, n ∈ R }
This, can be written as for the real number say, n = 0, 1, 2, 3....
C = {1, 9, 17...}
Thus, it is clear from the above relation that,
C contain B and A while B contain some element of A.
Thus, C ⊂ A, C ⊂ B and B ⊂ A are the correct relationship of the proper subset.
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I will give brainliest, like and rating if u solve this right
2) TRUE OR FALSE?
Answer: True
Step-by-step explanation:
write a two-step equatipn that involves division and addition and has a solution of x=-25
The equation that involves division and addition and has a solution of x=-25 will be 3x - 40 = x + 90
How to illustrate the information?It should be noted that an equation is used to show the relationship between the variables that are given.
The equation that involves division and addition and has a solution of x = -25 will be:
3x - 40 = x - 90
Collect like terms
3x - x = -90 + 40
2x = -50
Divide
x = -50 / 2
x = -25
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