We cannot conclude that rectangle LMNO has side lengths of 3 cm and 4 cm solely based on its area being 12 cm², as the side lengths are not confirmed by the second statement, thus not properly applying the Law of Detachment.
Explanation:The question involves the use of the Law of Detachment in deductive reasoning within mathematics. The Law of Detachment, also known as modus ponens, is a logical form that states if the following two statements are true: 'If p, then q' and 'p is true', then we can conclude 'q is true'. In the given scenario, the first statement is 'If a rectangle has side lengths 3 cm and 4 cm, then it has an area of 12 cm2'. The second statement is 'Rectangle LMNO has area 12 cm2'.
To use the Law of Detachment, we need the second statement to confirm that rectangle LMNO has side lengths of 3 cm and 4 cm. However, we are only told the area of rectangle LMNO, not its side lengths. Therefore, based on the information given, we cannot properly apply the Law of Detachment because there is no direct statement verifying the specific side lengths of rectangle LMNO. For the Law of Detachment to be used correctly, the second statement must directly assert that LMNO has the side lengths in question.
Incorrect Conclusion using Law of DetachmentGiven the information provided, we cannot conclude that rectangle LMNO has side lengths of 3 cm and 4 cm just because its area is 12 cm2.
If Juan paid $21.30 for 7.1 pounds of salmon, what was the price of 1 pound of salmon?
The graph of a piecewise-defined function is shown below.
On the interval (x≤0, x≤1, x<1, x<0) the function is given by the rule (x= - 1, y= - 1, y=1, x=1), and on the interval (x≥0, x>1, x≥1, x>0) the function is given by the rule (y= - 1, x= - 1, y= 1, x= 1).
Answer:
one of these is wrong cause i got a three out of four but thats better than nothing i guess.
Step-by-step explanation:
x≤0, y=1, x≥1, this one is the one i think is wrong but y=-1
find the sum of the first 30 terms of the equation below: an=4n+1
Answer:
1,890 is the sum of the first 30 terms of the equation .
Step-by-step explanation:
[tex]a_n=4n+1[/tex]
if , n = 1
[tex]a_1=4\times 1+1=5[/tex]
If, n = 2
[tex]a_2=4\times 2+1=9[/tex]
If, n = 3
[tex]a_3=4\times 3+1=13[/tex]
The arithmetic sequence comes out to be:
5, 9, 13........
a = 5
d = [tex]a_2=a_1=9-5=4[/tex]
The sum of first 30 terms is given by:
[tex]S_n=\frac{n}{2}\times (2a+(n-1)d)[/tex]
[tex]S_{30}=\frac{30}{2}\times (2\times 5+(30-1)\times 4)[/tex]
[tex]S_{30}=1,890[/tex]
1,890 is the sum of the first 30 terms of the equation .
The hexagon GIKMPR and FJN are regular. The dashed line segments form 30 degree angles.
What is? (attached)
The dashed line segments form 30-degree angles in the given diagram of a regular hexagon and triangle.
In the given diagram, hexagon GIKMPR and triangle FJN are regular. The dashed line segments form 30-degree angles.
Since hexagon GIKMPR is regular, all its interior angles are equal. Each angle of a regular hexagon is 120 degrees, so angle GIK is 120 degrees.
The angle at GIK can be split into two equal angles by the dashed line segment, so each of these angles measures 60 degrees.
Similarly, since triangle FJN is regular, each of its angles measures 60 degrees.
Therefore, the dashed line segments form two 30-degree angles each side of the regular hexagon and triangle.
The correct answer is option d. The image of [tex]\overline{OQ}[/tex] after a rotation of 300 degrees about point O is [tex]\overline{OF}[/tex].
To find the image of line segment [tex]\( \overline{OQ} \)[/tex] after a rotation of [tex]\( 300^\circ \)[/tex] about point O, we need to understand that a rotation of [tex]\( 300^\circ \)[/tex] is equivalent to rotating [tex]\( 60^\circ \)[/tex] clockwise. This is because rotating [tex]\( 360^\circ \)[/tex] would bring us back to the original position, so a rotation of [tex]\( 300^\circ \)[/tex] is the same as rotating [tex]\( 360^\circ - 60^\circ = 300^\circ \)[/tex].
Given that line segment [tex]\( \overline{OQ} \)[/tex] forms a [tex]\( 30^\circ \)[/tex] angle with the dashed lines, after a rotation of [tex]\( 300^\circ \)[/tex], it will form a [tex]\( 30^\circ \)[/tex] angle with the new position of the dashed lines.
Therefore, the image of line segment [tex]\( \overline{OQ} \)[/tex] after the rotation is [tex]\( \overline{OF} \)[/tex].
The complete question
The hexagon GIKMPR and FJN are regular. The dashed line segments form 30 degree angles.
Find the image of [tex]\overline{OQ}[/tex] after a rotation of 300 degree about point O.
a. [tex]\overline{OJ}[/tex]
b. [tex]\overline{OH}[/tex]
c. [tex]\overline{OQ}[/tex]
d. [tex]\overline{OF}[/tex]
How can the pythagorean theorem be used to classify acute, right, and obtuse triangles?
Which shows the correct substitution of the values a, b, and c from the equation 0 = – 3x2 – 2x + 6 into the quadratic formula? Quadratic formula: x =
Answer:
[tex]x_{1,2}=\frac{-(-2)\pm\sqrt{(-2)^2-4\cdot (-3)\cdot 6} }{2(-3)}[/tex] shows correct substitution of the values a, b, and c from the given quadratic equation [tex]-3x^2-2x+6=0[/tex] into quadratic formula.
Step-by-step explanation:
Given: The quadratic equation [tex]-3x^2-2x+6=0[/tex]
We have to show the correct substitution of the values a, b, and c from the given quadratic equation [tex]-3x^2-2x+6=0[/tex] into quadratic formula.
The standard form of quadratic equation is [tex]ax^2+bx+c=0[/tex] then the solution of quadratic equation using quadratic formula is given as [tex]x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
Consider the given quadratic equation [tex]-3x^2-2x+6=0[/tex]
Comparing with general quadratic equation, we have
a = -3 , b = -2 , c = 6
Substitute in quadratic formula, we get,
[tex]x_{1,2}=\frac{-(-2)\pm\sqrt{(-2)^2-4\cdot (-3)\cdot 6} }{2(-3)}[/tex]
Simplify, we have,
[tex]x_{1,2}=\frac{2\pm\sqrt{76} }{-6}[/tex]
Thus, [tex]x_{1}=\frac{2+\sqrt{76} }{-6}[/tex] and x_{2}=\frac{2-\sqrt{76} }{-6}
Simplify, we get,
[tex]x_1=-\frac{1+\sqrt{19}}{3},\:x_2=\frac{\sqrt{19}-1}{3}[/tex]
Thus, [tex]x_{1,2}=\frac{-(-2)\pm\sqrt{(-2)^2-4\cdot (-3)\cdot 6} }{2(-3)}[/tex] shows correct substitution of the values a, b, and c from the given quadratic equation [tex]-3x^2-2x+6=0[/tex] into quadratic formula.
You can use the standard form of quadratic equation to find the correct substitution of the values a, b and c.
The correct substitution of the value a,b and c from the given quadratic equations into the solution form is [tex]x = \dfrac{-(-2) \pm \sqrt{(-2)^2 - 4 \times -3 \times 6}}{2 \times (-3)}[/tex]
What is the standard form of quadratic equations?The standard form of quadratic equations is [tex]ax^2 + bx + c = 0[/tex]
What are the solutions of standard quadratic equation?[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
From given equation [tex]0 = -3x^2 -2x + 6[/tex], we deduce that a = -3, b = -2 and c = 6.
Thus, substituting these values in the solutions' equation:
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\ \\ x = \dfrac{2 \pm \sqrt{4 + 72}}{-6} = \dfrac{2\pm 2\sqrt{19}}{-6} = \dfrac{-1 \mp 2\sqrt{19}}{3}[/tex]
Thus, the correct substitution of the value a,b and c from the given quadratic equations into the solution form is [tex]x = \dfrac{-(-2) \pm \sqrt{(-2)^2 - 4 \times -3 \times 6}}{2 \times (-3)}[/tex]
Learn more about solutions of quadratic equations here:
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Explain two ways to find the volume of a plastic cube.
V=a^3 and volume=Length × Width × Height are the two ways to calculate the volume of cube.
What is three dimensional geometry?Three-dimensional space is a geometric setting in which three values are required to determine the position of an element.
A cube is a three-dimensional figure with 6 faces, 8 vertices and 12 edges.
In a cube all the sides are equal like a square.
So the volume of cube can be measured by
V=a^3
where a is the measure of a side.
And the volume of cube can also be found by
volume=Length × Width × Height
Hence V=a^3 and volume=Length × Width × Height are the two ways to calculate the volume of cube.
To learn more on three dimensional Geometry click:
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the proportion of the perimeter of two similar polygons is blank the proportion of any pair of corresponding side lengths
A. greater than
B. equal to
C. less than
D. variable to
Which of the following is the linear parent function
Answer: The answer is C.
A Linear parent function is a function of the form f(x) = x
or y = x. This is the simplest of the linear functions, where the slope is 1 and the function pases for the point (0,0) (which is the same of saying that the intercept is 0).
a) isnt a linear function.
b) is a quadratic function.
d) is also a linear function, but it has a slope = 2, so it isn't the linear parent function.
simplify 1/5 b - 5 (2/5 a - 1/10 b) +4 a
simplify
A 2a - 3/10 b
B 2a + 7/10 b
C 2a - 7/10 b
D 2a +3/10 b
Which is a property of an angle?
has two sides that each extend forever in both directions
has two endpoints
has two center points
has two rays that share a common endpoint
Answer:
has two rays that share a common endpoint
Step-by-step explanation:
An angle is formed by a two rays that share a common endpoint. The distance between the two rays is what makes the measure of the angle wider or smaller. Each ray extends in one direction forever; however since they share an endpoint, the rays do not extend in both directions forever. There is only one endpoint, not two, and there is only one center point (vertex), not two.
How to Graph y=4/5x-7
To graph the equation y = 4/5x - 7, plot the y-intercept at -7 and use the slope to find a second point before drawing a line through the two points.
Explanation:To graph the equation y = 4/5x - 7, follow these steps:
Start by plotting the y-intercept at -7 on the y-axis.Use the slope 4/5 to find a second point by moving up 4 units and to the right 5 units. Plot this point.Draw a straight line through these two points to represent the graph of y = 4/5x - 7.On an average day, 38 customers buy a bag of grapes at Jerry's Market. There are an average of 47 grapes in each bag. Round to the nearest ten and then multiply to estimate the number of grapes Jerry's customers buy every day.
Answer:
40 x 50 = 2,000
Step-by-step explanation:
When we round a number, first identify the digit to round. Then proceed with the following two rules:
(a) If the number to the right of the digit to round is 0, 1, 2, 3, or 4 (that is, less than 5), then keep the digit to round and change the rest of the digits to the right of the digit to round to zero.
(b) If the number to the right of the digit to be rounded is 5, 6, 7, 8, or 9 (that is, greater than or equal to 5), then add one to the digit to round and change the rest of the digits to the right of the digit to round to zero.
In our case, we apply the two rules, rounding to the nearest ten, as follows:
For 38 = 40
Apply rule (b) since 8 is greater than or equal to 5, then add 1 to 3 to get 4, then change 8 to zero. The result is 40.
For 47 = 50
Apply rule (b) since 7 is greater than or equal to 5, then add 1 to 4 to get 5, then change 7 to zero. The result is 50.
Now, multiply to estimate the amount of grapes that Jerry customers buy every day.
40 x 50 = 2,000
Hope this helps!
How many numbers are divisible by 100 between 1 and 6296?
If you subtract twelve from twice a number, the result is eight. what is the number?
Perform the indicated operation. square root of 8 + square root of 50
3y - 5z = -23
4x +2y +3z = 7
-2x - y - z = -3
In your answer, can you please show work so that I can understand it myself
A pair of shoes costs $25 to make. This means that you need to charge a price of at least ___ just to cover your cost.
Answer: $25
Step-by-step explanation: you are not trying to make a profit. You are just trying to cover your cost and they cost $25 to make.
A symmetrical binomial distribution with large sample size can be approximated by a __________
Give the name of a quadrilateral that is formed when you have two bisected diagonals.
Which type of statement has the form " if A, then B"?
Answer: Conditional statement
Step-by-step explanation:
In discrete mathematics, a conditional statement denoted by "if R then S " is an if-then statement where R represents a hypothesis and S represents a conclusion.
For example : If a number is divisible by 6 ,then it must be divisible by 2 ."
Here, Hypothesis R: " number is divisible by 6"
Conclusion S: "it must be divisible by 2"
Hence, an conditional statement has the form " if A, then B" .
Factor this polynomial expression. 2x2 + 12x + 18
Answer: 2(x+3)(x+3)
i just took the test
Which expression is equal to (-12-2i)+(2+2i)
a) 10
b) -10
c) 10-4i
d)-10-4i
Square GHIJ shares a common center with regular hexagon ABCDEF on a coordinate plane. AB¯¯¯¯¯ is parallel to GH¯¯¯¯¯. If the combined figure rotates clockwise about its center, at which angle of rotation will the image coincide with the preimage?
60°
180°
90°
240°
a square needs to rotate 90 to coincide with itself
but the hexagon would need to rotate 180
the answer is 180 degrees
Answer:
Option B 180° is the right answer.
Step-by-step explanation:
Given is : GHIJ is a square and ABCDEF is a regular hexagon having common centre O.
We know that a square is symmetric at a rotational angle of 90°.
A regular hexagon is symmetric at a rotational angle of 60°.
We will find the LCM of 90 and 60, to know how much to rotate, to get a preimage.
Moreover, a hexagon needs to rotate 180 degrees to coincide with itself.
LCM(60°,90°)=180°.
So, the correct option is B. 180°.
what percent is the fraction 2/10 equal to
A ship is carrying 10,250 pounds of individually boxed TV sets. If each box weighs 20.5 pounds, how many boxes are on the ship?
divide total weight by weight of each box
10250 / 20.5 = 500 boxes total
round 4,719,429 to the nearest 10,000
Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 3 inches, and the larger gear has a radius of 7 inches.
Part 1: What is the angle measure, in degrees and rounded to the nearest tenth, through which the larger gear has rotated when the smaller gear has made one complete rotation?
Part 2: How many rotations will the smaller gear make during one complete rotation of the larger gear?
Show all work.
If the area of a square is 49 square inches, how long must each side be?
Car insurance that pays for your injuries when you're in an accident in your car is _______ insurance.
A. collision B. liability C. comprehensive D. medical