Answer:
the answer is 0.48
Step-by-step explanation:
your welcome
Let A={(x-3)/(x-2)ЄR : X<0}
be a subset of real numbers.
i) Define A's supremum and infimum.
The supremum of the set A does not exist (it is negative infinity), and the infimum of the set A is 1.
To define the supremum and infimum of the set A, we first need to determine the properties of the set.
The set A is defined as A = {(x-3)/(x-2) ∈ R : x < 0}.
To find the supremum (also known as the least upper bound) of A, we need to find the smallest value that is greater than or equal to all the elements of A. In other words, we are looking for the least upper bound of the set A.
Let's analyze the elements of A:
For x < 0, the expression (x-3)/(x-2) can take on different values depending on the value of x. We need to find the maximum value that this expression can reach for all x < 0.
As x approaches 0 from the left side, (x-3)/(x-2) approaches negative infinity. Therefore, there is no finite supremum for the set A.
Next, let's find the infimum (also known as the greatest lower bound) of A. We need to find the largest value that is less than or equal to all the elements of A. In other words, we are looking for the greatest lower bound of the set A.
Again, analyzing the elements of A:
As x approaches negative infinity, (x-3)/(x-2) approaches 1. Therefore, the infimum of the set A is 1.
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AC and BD bisect eachother prove AB || CD and BC ll AD
1) \(\overline{AC}\) and \(\overline{BD}\) bisect each other (given)
2) \(\overline{AE} \cong \overline{EC}\) (a bisector splits a segment into two congruent parts)
3) \(\overline{BE} \cong \overline{ED}\) (a bisector splits a segment into two congruent parts)
4) \(\angle BEA \cong \angle CED\) (vertical angles are congruent)
5) \(\triangle BEA \cong \triangle DEC\) (SAS)
6) \(\angle EBA \cong \angle EDC\) (CPCTC)
7) \(\overline{AB} \parallel \overline{CD}\) (converse of alternate interior angles theorem)
8) \(\angle DEA \cong \angle BEC\) (vertical angles are congruent)
9) \(\triangle AED \cong \triangle BEC\) (SAS)
10) \(\angle BCE \cong \angle EAD\) (CPCTC)
11) \(\overline{BC} \parallel \overline{AD}\) (converse of alternate interior angles theorem)
7y-4=17 what is the answer
Answer:
7y=21
y=21/7
y=3 answer
Answer:
y = 3
Step-by-step explanation:
Add 4 to each side, so it now looks like this: 7y = 21Divide each side by 7 to cancel out the 7 next to y. It should now look like this: y = 3I hope this helps!
A fourth-degree polynomial with a leading coefficient of 1 has gone through several transformations, including a vertical compression by a scale factor of 1/3 and a reflection across the x-axis. Two of the zero polynomials are -i and 3i.
Find a y-intercept of this polynomial, if it exists
The y-intercept of the resulting polynomial is equal to - 3.
How to derive a fourth-degree polynomial generated by rigid transformations
Herein we assume that the other two zeros of the polynomial are i and - i 3, otherwise the polynomial will have at least a complex number as coefficient of the expression. This is because we need to find values from a Cartesian plan, whose ordered pairs are real numbers.
Initially, we have the following expression by algebra properties:
f(x) = (x + i) · (x - i) · (x + i 3) · (x - i 3)
f(x) = (x² + 1) · (x² + 9)
f(x) = x⁴ + 10 · x² + 9
Then, we proceed to use the two rigid transformations described in the statement. Please notice that rigid transformations are transformations applied on polynomials such that Euclidean distance is conserved:
Vertical compression
f'(x) = (1 / 3) · f(x)
f'(x) = (1 / 3) · (x⁴ + 10 · x² + 9)
f'(x) = (1 / 3) · x⁴ + (10 / 3) · x² + 3
Reflection across the x-axis
g(x) = - f'(x)
g(x) = - (1 / 3) · x⁴ - (10 / 3) · x² - 3
The y-intercept is found for x = 0:
g(0) = - (1 / 3) · 0⁴ - (10 / 3) · 0² - 3
g(0) = - 3
The y-intercept of the resulting polynomial is equal to - 3.
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A line is perpendicular to y = -1/5x + 1 and intersects the point negative (-5,1) what is the equation of this perpendicular line?
Answer: y = 5x + 26
Step-by-step explanation:
To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.
We can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Substituting the values, we get:
y - 1 = 5(x - (-5))
Simplifying further:
y - 1 = 5(x + 5)
Expanding the brackets:
y - 1 = 5x + 25
Rearranging the equation to the slope-intercept form (y = mx + b):
y = 5x + 26
Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.
I shouldn't have watched that horror movie last night on TV. It gave me the strangest nightmare. I dreamed I was trapped on a planet of giant insects with Mega-Flies as big as elephants. I thought it was weird that the female Mega-Flies had 8 legs and the male Mega-Flies only had 3 legs. In my dream I was caught in the web of a Mega-Spider who would not let me go unless i could solve his problem: How many Mega-Flies would he need to catch if he eats exactly 140 Mega-Fly legs each day? He wants to know all the possibilities! What are they?
The possible combinations of the number of female and male Mega-Flies the Mega-Spider needs to catch are 17 female Mega-Flies and 3 male Mega-Flies.
This sounds like a math problem related to division. If the Mega-Spider needs to eat 140 Mega-Fly legs each day, and we know that each Mega-Fly has a certain number of legs, we can use division to figure out how many Mega-Flies the spider would need to catch in order to consume that many legs.
Let's call the number of legs per Mega-Fly "x".
If we assume that the female Mega-Flies have 8 legs and male Mega-Flies have 3 legs, we can use this information to set up the equation:
140 Mega-Fly legs = n × 8 legs + m × 3 legs
Where n is the number of Female Mega-Fly legs and m is the number of Male Mega-Fly legs.
To find all the possibilities, we can divide 140 by 8, and then divide the remainder by 3. We can also use the modulo operator which will give us the remainder in the division.
The number of Female Mega-Flies needed = 140/8 = 17.5
The number of Male Mega-Flies needed = (140%8) /3 = 3.73 (as this is a remainder this would not make sense)
So, the possible combinations of the number of female and male Mega-Flies the Mega-Spider needs to catch are 17 female Mega-Flies and 3 male Mega-Flies.
As Mega-Flies can not have fractional legs in reality so this dream problem doesn't make sense. It is a product of your mind during sleep and it is normal to have an unrealistic dream.
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A flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side is 19 feet more than the length of the shortest side. Find the dimensions if the perimeter is 167 feet.
PLS PLS HELP
student decides to investigate how effective washing with soap is in eliminating bacteria. to do this, she tested four different methods: washing with water only, washing with regular soap, washing with antibacterial soap, and spraying hands with an antibacterial spray (containing 65% ethanol as an active ingredient). she suspected that the number of bacterial on her hands before washing might vary considerably from day to day. to help even out the effects of those changes, she generated random numbers to determine the order of the four treatments. each morning she washed her hands according to the treatment randomly chosen. then she placed her right hand on a sterile media plate designed to encourage bacterial growth. she incubated each play for 2 days at 360c360c, after which she counted the number of bacteria colonies. she replicated this procedure 8 times for each of the four treatments. the data for the bacteria study is given in the file bacteria.csv on canvas. remember that higher bacteria count means dirtier hands after washin
The higher bacterial count means dirtier hands after washing.
Given data: A student decides to investigate how effective washing with soap is in eliminating bacteria. To do this, she tested four different methods: washing with water only, washing with regular soap, washing with antibacterial soap, and spraying hands with an antibacterial spray (containing 65% ethanol as an active ingredient). She suspected that the number of bacteria on her hands before washing might vary considerably from day to day. To help even out the effects of those changes, she generated random numbers to determine the order of the four treatments.
Each morning she washed her hands according to the treatment randomly chosen. Then she placed her right hand on a sterile media plate designed to encourage bacterial growth. She incubated each play for 2 days at 360C, after which she counted the number of bacteria colonies. She replicated this procedure 8 times for each of the four treatments. Remember that higher bacteria count means dirtier hands after washing.
Therefore, from the given data, a student conducted an experiment to investigate how effective washing with soap is in eliminating bacteria. For this, she used four different methods: washing with water only, washing with regular soap, washing with antibacterial soap, and spraying hands with an antibacterial spray (containing 65% ethanol as an active ingredient). The higher bacterial count means dirtier hands after washing.
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How do you know how many real solutions?
The number of real solutions of a quadratic equation depends on the sign of the discriminant.We can find discriminant by using discriminant formula.
What are real solutions of an equation?A real solution in algebra is simply a solution to an equation that is a real number. there can be 0, 1, or 2 solutions to a quadratic equation depending on whether the expression inside the square root sign (b2 - 4ac), is positive, negative, or zero.
How many real solutions does the discriminant have?When the discriminant value is positive we get two real solutions. When the discriminant value is zero we get one real solution. When the discriminant value is negative we get a pair of complex solutions.
So that we can find real solution of quadratic equation by finding discriminant of given equation.
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The measurement of the angle K is 3x - 42, and it is obtuse. Find the restriction(s) on the values of x.
Answer:
x = 44° and 74°: x cannot be less than 44°, x cannot be greater than 74°.
Step-by-step explanation:
Obtuse angles are greater than 90° but less than 180°.
We can first solve for the lower bound of x.
\(3x-42=90\)\(3x=132\\\)\(x=44\)°Thus the lower bound restriction of x is 44°
We can now solve for the upper bound of x.
\(3x-42=180\)\(3x=222\)\(x=74\)°Thus the upper bound restriction of x is 74°
Write the exponential equation for this scenario. Mike buys a car for $45,000.00. The cars value depreciates (loses value) at a rate of 18% per year.
Answer:
\(A=45000(0.82)^t\)
Step-by-step explanation:
Given data
P= 45,000
rate= 18%
Recall the expression for the compound interest
\(A=P(1+r)^t\)
Since we are talking of depreciation
\(A=P(1-r)^t\)
Substitute
\(A=45000(1-0.18)^t\\\\A=45000(0.82)^t\)
Hence the exponential function is
\(A=45000(0.82)^t\)
A tower that is 35 m tall is to have to support two wires and start out with stability both will be attached to the top of the tower it will be attached to the ground 12 m from the base of each wire wires in the show 5 m to complete each attachment how much wire is needed to make the support of the two wires
The 34 m of wire that is needed to support the two wires is the overall length.
Given, a tower that is 35 m tall and is to have to support two wires. Both the wires will be attached to the top of the tower and it will be attached to the ground 12 m from the base of each wire. Wires in the show 5 m to complete each attachment. We need to find how much wire is needed to make support the two wires.
Distance of ground from the tower = 12 lengths of wire used for attachment of wire = 5 mWire required to attach the wire to the top of the tower and to ground = 5 + 12 = 17 m
Wire required for both the wires = 2 × 17 = 34 m length of the tower = 35 therefore, the total length of wire required to make the support of the two wires is 34 m.
What we are given?
We are given the height of the tower and are asked to find the total length of wire required to make support the two wires.
What is the formula?
Wire required to attach the wire to the top of the tower and to ground = 5 + 12 = 17 mWire required for both the wires = 2 × 17 = 34 m
What is the solution?
The total length of wire required to make support the two wires is 34 m.
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f(3)=2x-5 evaluate function
Answer: HERES THE ANSWER
HOPE ITS HELPS :))
given the if/else statement: if (a < 5) b = 12; else d = 30; which of the following performs the same operation?
The equivalent operation is: b = (a < 5) ? 12 : (d = 30);
The original if/else statement is:
if (a < 5)
b = 12;
else
d = 30;
In this statement, the condition (a < 5) is evaluated. If the condition is true (i.e., if the value of a is less than 5), then the statement b = 12; is executed. Otherwise, if the condition is false (i.e., if the value of a is greater than or equal to 5), then the statement d = 30; is executed.
The equivalent operation using the conditional (ternary) operator is:
b = (a < 5) ? 12 : d = 30;
In this statement, the condition (a < 5) is evaluated. If the condition is true, the value 12 is assigned to b. This is indicated by ? in the statement. The : separates the true and false cases.
If the condition is false (i.e., if the value of a is greater than or equal to 5), the value 30 is assigned to d. This is the value assigned after the : in the statement.
The ternary operator statement (a < 5) ? 12 : d = 30; achieves the same outcome as the original if/else statement, providing an alternative way to write the logic based on the condition a < 5.
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factorise completely (x plus 2) Square - (x - 4) Square and hence find then value of 1000 Square minus 992 Square
Answer:
\(x^2+3x+8\)
\(15936\)
Step-by-step explanation:
\(\left(x+2\right)^2-\left(x-4\right)\)
\(\left(x+2\right)\left(x+2\right)-\left(x-4\right)\)
\(x^2+2x+2x+4-(x-4)\)
\(x^2+4x+4-\left(x-4\right)\)
\(x^2+4x+4-x+4\)
\(x^2+3x+8\)
\(1000^2-992^2\)
\(1000000-984064\)
\(15936\)
Probability: Discrete, Binomial, Normal
IB Math Applications SL
1. Jae Hee plays a game involving a
biased six-sided die. The score for
the game, X, is the number which
lands face up after the die is rolled.
The table shows the probability
distribution for X.
a. Find the exact value of p.
Score x
P(X=x)
Name: Somatar
Date:
-3
1
18
-1
P
Period:
0
3
18
1 point: Correct p-value
b. Jae Hee plays the game once. Calculate the expected score.
1
1
18
1 point: Correct substitution into formula
2 points: Correct substitution and answer
c. Jae Hee plays the game twice and adds the two scores together.
Find the probability Jae Hee has a total score of -3.
2
18
The precise value of p is 4/18. Jae Hee's expected score in the game is 1.833. Jae Hee has a 1/162 chance of receiving a total score of -3. The likelihood that something will happen is defined as probability.
How to calculate Probability ?Probability is calculated by dividing the number of possible outcomes by the total number of outcomes. Probability and odds are distinct concepts. Odds are the probability that something happens divided by the probability that it does not happen. Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or a statement being true.Therefore,
Value of p is,
∈p = 1
1/18 + p + 3/18 + 1/18 + 2/18 + 7/18 = 1
14/18 + p = 1
p = 4 / 18
So the exact value of p is 4/18
Expected score of the game :
∈(x) = ∈xi pi
= -3 (1/18) - 1 (4/18) + 0 (3/18) + 1 (1/18) + 2 (2/18) + 5 (7/18)
= 33/18
= 1.833
Expected score of the game Jae Hee plays is 1.833
Calculate Probability of Jae Hee getting total score of -3
p (total score -3 )
= p(x= -3) and p(x=0) + p(x=0) and p (x=3)
= 1/18 × 1/18 + 1/18 × 1/18
=1/162
Probability of Jae Hee getting total score of -3 is 1/162
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Answer:
Step-by-step explanation:
Which expression represents the prime factorization of 243?
A ) 3×3×3×3×2
B ) 3×3×3×3×3
C ) 3×3×3×3×2×2
D ) 3×3×3×3×3×3
Answer: B) 3 × 3 × 3 × 3 × 3
Concept:
In factorization, the easiest way is to divide the term multiple times by the least factor each time until the answer is not divisible. Then, multiply all the factors and the remainder together to get the factorization of a term.
Solve:
243 ÷ 3 = 81
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
Therefore, the prime factorization of 243 = 3 × 3 × 3 × 3 × 3
Hope this helps!! :)
Please let me know if you have any questions
Answer:
B
Step-by-step explanation:
how could it not be??
when describing quantitative data, an outlier group of answer choicesis a data point that does not fit the main pattern of the data.is always a data point with an unrealistic or even impossible value.is always a data entry error.is any point flagged by the 1.5 times iqr.
When describing quantitative data, an outlier a. is a data point that does not fit the main pattern of the data.
In statistics, an outlier is a data point that dramatically deviates from the overall pattern or trend of the data. It is an observation that, in a population-based random sampling, deviates unusually from the other values. Outliers can skew the overall analysis or interpretation of the data since they are either greater or lower than the bulk of the data points. As a data point that does not fit the predominant pattern of the data, an outlier is precisely defined as such.
Option (b) is not always accurate since outliers may have reasonable values, despite being rare. Option (c) is not always accurate, though, as data input mistakes may not always be the cause of outliers. Because not all probable outliers can be identified using the 1.5 times the interquartile range (IQR), which is a popular approach, option (d) is inaccurate.
Complete Question:
When describing quantitative data, an outlier
a. is a data point that does not fit the main pattern of the data.
b. is always a data point with an unrealistic or even impossible value.
c. is always a data entry error.
d. is any point flagged by the 1.5 times iqr.
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Find the quotient below. Write the answer as a fraction in simplest form.3/4 divided by 6 2/3
Answer:
6 x 3 = 18 + 2 = 20/3
3/4 X 3/20 =
3 X 3
-------- = 9/80 already simplified to lowest
4 X 20
find the radius, diameter, circumference, and area of this circle.
Answer:
Area of circle = 28.28 unit²
Radius of circle from center point = 3 units
Diameter of given circle = 6 units
Circumference of circle = 18.85 unit
Step-by-step explanation:
Given:
Circle in third quadrant
Radius of circle from center point = 3 units
Diameter of a circle = 2 x Radius of circle
Diameter of given circle = 2 x Radius of circle from center point
Diameter of given circle = 2 x 3 units
Diameter of given circle = 6 units
Circumference of circle = 2πr
Circumference of circle = 2(22/7)(3)
Circumference of circle = 18.85 unit
Area of circle = πr²
Area of circle = (22/7)(3)²
Area of circle = 28.28 unit²
WILL GIVE BRAINLIEST
Which expressions are difference of squares? Select all correct answers.
x2 + y2
x8 - 4
y2 - 25
x2 + 9
(the numbers next to the x's are exponents, i dont know how to write them on here)
Answer:
I think is x2-y2 cause the number have to be next to
PLz help will mark as brainlest
Answer:
B
Step-by-step explanation:
Not counting human error he should get exactly eight questions right using scicence, but since it is random there is margin of error that may disfigure the outcome.
Lock 4 (screen will be blank until you crack the code for lock #3) Awe-sum! You have reached the last lock. Use your equation solving skills to find the value of each variable. Use the values you calculate to help you move along in the puzzle and find all of the missing variables. When you have found all of the variables Imove to the next screen.
Problems:
4a +2= -10
a(2+ b) = -12
-5c+b= 22
7(c+d) = 14
d-c-e= 17
Answers:
a=
b=
c=
d=
e=
The values of the variables are:
a = -3
b = 2
c = -4
d = 6
e = -7
Given, the expressions are:
4a + 2 = -10
4a = -10-2
4a = -12
a = -3
substitute a value in the next expression.
a(2+b) = -12
-3(2+b) = -12
-6-3b = -12
-3b = -12+6
-3b = -6
b=6/3
b = 2
now substitute b value in the next expression.
-5c+b= 22
-5c+2 = 22
-5c = 22-2
-5c = 20
c = -20/5
c = -4
substitute c value in the next expression.
7(c+d) = 14
7(-4+d) = 14
-28+7d = 14
7d = 14+28
7d = 42
d=42/7
d=6
In the last expression substitute c and d values to find e.
d-c-e= 17
6-(-4)-e = 17
6+4-e = 17
10-e = 17
-e = 17-10
-e = 7
e = -7
hence we get the values of all the variables.
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Find an equation of rational function that has vertical asymptotes at x = 3 and x =
-5, horizontal asymptote at y = 0, and y intercept of 1.
The rational function that meets all the conditions is:
\(f(x) = \frac{-15}{(x - 3)*(x + 5)}\)
How to find the rational function?
A rational function is of the form:
\(f(x) = \frac{p(x)}{q(x)}\)
As the horizontal asymptote is at y = 0, we know that the numerator can't depend on x, so it is just a constant.
p(x) = a
And we want to have two vertical asymptotes at x = 3 and x = -5, then q(x) becomes zero at these values, so we have:
q(x) = (x -3)*(x + 5)
At this point, the function is:
\(f(x) = \frac{a}{(x - 3)*(x + 5)}\)
Finally, we know that the y-intercept is 1, then we need to solve:
\(f(0) = 1 = \frac{a}{(0 - 3)*(0 +5)} = \frac{a}{-15} \\\\-15 = a\)
Then we conclude that our function is:
\(f(x) = \frac{-15}{(x - 3)*(x + 5)}\)
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The equation for the graph of A is
.
The equation for the graph of B is
.
The equation for the graph of C is
.
The equation for the graph of D is
.
A: y = x²
B: y = -x
C: y = x
D: y = -x²
:)
PLEASE HELP it’s literally easy
Answer:
it would be 4 right (the last one)
Step-by-step explanation:
1. Find ſf Fin ds where F = = (xy2 + 3xz®, x2y + y3, 3x2z - zº) and S is the surface of the + - Z S = region that lies between the cylinders x2 + y2 = 4 and x² + y2 = 36 and between the planes z =
F · n = (xy² + 3xz) ∂f/∂x + (x²y + y³) ∂f/∂y + (3x²z - z²) ∂f/∂z dot product over the surface S
To find the surface integral of F over the given surface S, we need to evaluate the flux of F through the surface S.
First, we calculate the outward unit normal vector n to the surface S. Since S lies between the cylinders x² + y² = 4 and x² + y² = 36, and between the planes z = ±2, the normal vector n will have components that correspond to the direction perpendicular to the surface S.
Using the gradient operator ∇, we can find the normal vector:
n = ∇f/|∇f|
where f(x, y, z) is the equation of the surface S.
Next, we compute the dot product between F and n:
F · n = (xy² + 3xz) ∂f/∂x + (x²y + y³) ∂f/∂y + (3x²z - z²) ∂f/∂z
Finally, we integrate this dot product over the surface S using appropriate limits based on the given region.
Since the detailed equation for the surface S is not provided, it is difficult to proceed further without specific information about the surface S. Additional information is required to determine the limits of integration and evaluate the surface integral of F over S.
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Let p: x = 4
Let q: y = −2
Which represents "If x = 4, then y = -2"?
1.) pv q
2.) p^q
3.) p → q
4.) p<->q
Answer:
I think the answer is 2.) p^q
Step-by-step explanation:
hope this helps if it is wrong let me know have a blessed day
p → q represents “if p then q" represents "If x = 4, then y = −2”
Therefore, the correct representation is:
Thus Option 3 is correct. 3.) p → q
Given :Let p: x = 4 Let q: y = −2
To Find Which represents "If x = 4, then y = −2”?
we know that:
1. p ∧ q represents “p and q”
2.p ∨ q represents “p or q (or both)
3.p → q represents “if p then q”
4. p ↔ q represents “p if and only if q"
The statement "If x = 4, then y = -2" can be represented by the conditional statement "p → q" which reads "p implies q" or "if p, then q."
In the given representation:
p: x = 4
q: y = −2
The conditional statement "p → q" means that if x is equal to 4 (p is true), then y is equal to -2 (q is true).
So, we can see that p → q represents “if p then q" represents "If x = 4, then y = −2”
Therefore, the correct representation is:
Thus Option 3 is correct. 3.) p → q
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a square of area 36cm^2is cut to make two triangles,a and b
When a square with an area of 36 cm² is cut along its diagonal, it forms two congruent right triangles, labeled as triangle A and triangle B. Each triangle has a base and height of 3 cm.
To determine the characteristics of triangle A and triangle B, we need to understand how the square is cut. Since the square has an area of 36 cm², its side length can be calculated by taking the square root of the area: √36 = 6 cm. This means that each side of the square measures 6 cm.
To create the two triangles, we can cut the square along one of its diagonals, resulting in two congruent right triangles. Let's consider one of the resulting triangles, triangle A. Since the square is divided along the diagonal, triangle A will have a base and height that are half the length of the square's side, which is 3 cm. Therefore, triangle A has a base and height of 3 cm.
Similarly, triangle B will also have a base and height of 3 cm since it is congruent to triangle A. Both triangles A and B are right triangles with equal side lengths and angles.
In conclusion, when a square with an area of 36 cm² is cut along its diagonal, it forms two congruent right triangles, labeled as triangle A and triangle B. Each triangle has a base and height of 3 cm.
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Which part of the circle is labelled ? Thank you
Answer:
None of the following
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Answer:
Radius duh
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