Answers
============================================================
Explanation:
We'll need to find the slope of the line through the two given points.
[tex](x_1,y_1) = (-3,17) \text{ and } (x_2,y_2) = (2,-3)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{-3 - 17}{2 - (-3)}\\\\m = \frac{-3 - 17}{2 + 3}\\\\m = \frac{-20}{5}\\\\m = -4\\\\[/tex]
The slope is -4.
Think of -4 as -4/1. The reciprocal is -1/4, and it flips in sign to +1/4 or simply 1/4.
The original slope -4 leads to the perpendicular slope 1/4. The two slopes multiply to -1. This is true of any perpendicular lines where neither is vertical nor horizontal.
------------------------
In short, the answer equation will involve a slope of 1/4. This points us directly to choices A and E as two answers so far.
Something like choice B is not an answer since it has slope 4. Choice C is ruled out because 4x+y = -8 solves to y = -4x-8. It has a slope of -4.
Choice D on the other hand has x-4y = 2 solve to y = (1/4)x - 1/2, and this has a slope of 1/4 that we want. This means choice D is another answer.
Choice F and choice G are ruled out because they involve slopes of 4 and -4 respectively.
------------------------
Summary: The 3 answers are choices A, D and E
Step-by-step explanation:
the slope of a line is the ratio
y coordinate change / x coordinate change
when going from one point on the line to another.
so for (-3, 17) and (2, -3) we get
x changes by +5 (from -3 to 2).
y changes by -20 (from 17 to -3).
the slope is
-20/+5 = -4/1 = -4
now, a perpendicular slope (90° to the original slope) is putting the slope fraction upside-down and flips the sign :
+1/4 or simply 1/4.
the slope in an equation of the form "y = ..." is always the factor of x.
y + 2 = (1/4)(x - 1)
yes, there are only some constant additions or subtractions to get to a or "y = ..." form, so 1/4 is indeed the factor of x and the slope of this line.
y = 4x + 12
4 <> 1/4, so, no, it is not.
4x + y = -8
y = -4x - 8
-4 <> 1/4, so, no, it is not.
x - 4y = 2
-4y = -x + 2
y = (1/4)x - 2/4
1/4 is indeed 1/4, so, yes, it is.
y = (1/4)x - 15
1/4 is indeed 1/4, so, yes, it is.
y + 3 = 4(x - 2)
similar to the first one, but 4 <> 1/4, so, no, it is not.
y = -4x + 3
-4 <> 1/4, so, no, it is not.
Related Questions
The vehicle's fuel efficiency is no less than 35 miles per gallon and I have fuel efficiency of eight new cars so what is the percentage of these cars? The fuel efficiency of the new cars is 42, 16, 54, 13, 31, 23, 13, 27
Answers
37.5% of the cars have a fuel efficiency of at least 35 miles per gallon.
What is the Percentage of Cars?To find the percentage of cars that have a fuel efficiency of at least 35 miles per gallon,
We first need to determine how many of the eight cars meet that threshold.
To do this, we can compare each car's fuel efficiency to 35 miles per gallon, and count the number that is greater than or equal to 35.
Identify the cars that have a fuel efficiency of at least 35 mpg: 42, 42, 54,
count the number of cars which is 3
divide it by 8 which is the total number of cars
Multiply the result by 100 to get the percentage, so:
3/8 * 100 = 37.5%
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write the missing digits to make this addition correct
_2_+_2=200
Answers
Answer:
128 + 72 = 200
Step-by-step explanation:
Start from the ones. And go next to tens and last find the hundreds.
see image.
1000(9x-10)=50(976+100x)
Answers
9,000x - 10,000 = 48800 + 5,000x
-5,000x - 5,000x
4,000x - 10,000= 48800
+10,000 +10,000
4,000x = 58800
—————————
4,000 4,000
x = 14.7
Jim purchased x iced teas and y soft pretzels at a cricket game. He spent a
total of $32. The equation below describes the relationship between the
number of iced teas and the number of soft pretzels purchased.
3x+2y=32
The ordered pair (4, 10) is a solution of the equation. What does the solution
(4, 10) represent?
HELPPPP
Answers
The solution that (4, 10) represents is that Jim purchased 4 iced teas and 10 soft pretzels at a cricket game.
How to solve linear equation word problems?The equation that describes the relationship between the
number of iced teas and the number of soft pretzels purchased is;
3x + 2y = 32
Where;
x represents the iced teas.
y represents soft pretzels at a cricket game
Now, we are told that the ordered pair (4, 10) is a solution of the equation. This means that;
x = 4 and y = 10 is a solution.
What it means is that Jim purchased 4 iced teas and 10 soft pretzels at a cricket game
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A company tests a new battery for an electric car. The distance the car travels, d km, and the charge left in the battery, C%, are measured. Some measurements are shown in the table. Find the C-axis intercept of the line. Pls help I would really appreciate it!
Answers
Based on the measurements shown in the table, the C-axis intercept of the line is equal to 100.
What is y-intercept?In Mathematics, the y-intercept of any graph such as a linear function, exponential function, polynomial function, quadratic function, etc., generally occur at the point where the value of "x" is equal to zero (x = 0).
What is the x-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of a linear function, exponential function, polynomial function, quadratic function, etc., crosses the x-coordinate and the value of "y" is equal to zero (y = 0).
In this scenario, the C-axis intercept of the line simply refers to x-intercept. Therefore, we can reasonably infer and logically deduce that the C-axis intercept of the line (x-intercept) is equal to 100 while the d-axis intercept of the line (y-intercept) is equal to 200.
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People at a local festival were asked if their favorite dessert was cake or pie. The probability of each result are as follows: • Probability of 0.42 that people liked pie • Probability of 0.90 that people liked cake or pie • Probability of 0.12 that people liked both cake and pie Use a Venn Diagram to support your calculations for the following questions:
a) Determine the probability that a person will like cake.
B) Determine the probability that a person at the festival does not like either of these two desserts.
C) Are the event liking cake and liking pie mutually exclusive or non-mutually exclusive? Justify your answer.
Answers
a) The probability that a person will like cake is given as follows: 0.6 = 60%.
b) The probability that a person does not like any of the two desserts is given as follows: 0.1 = 10%.
c) The events are non-mutually exclusive, as the probability of liking both is different of zero.
What is a Venn probability?In a Venn probability, two events are related with each other, as are their probabilities.
The "or probability" is given by:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
The events for this problem are given as follows:
Event A: person likes pie.Event B: person likes cake.The probabilities for this problem are given as follows:
P(A or B) = 0.9, P(A) = 0.42, P(A and B) = 0.12.
Hence the probability that a person likes cake is given as follows:
0.9 = 0.42 + P(B) - 0.12
0.3 + P(B) = 0.9
P(B) = 0.6.
Probability of 0.90 that people liked cake or pie, hence the probability that a person likes neither is of:
1 - 0.9 = 0.1 = 10%.
(or means at least one of them, and neither is complementary to at least one).
As P(A and B) = 0.12 is different of zero, the events are non-mutually exclusive.
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Consider the following problem:
The length s(t) of the side of the base of a square prism is decreasing at a rate of 7
kilometers per minute and the height h(t) of the prism is increasing at a rate of 10
kilometers per minute. At a certain instant to, the base's side is 4 kilometers and the
height is 9 kilometers. What is the rate of change of the surface area A(t) of the
prism at that instant?
Match each expression with its given value.
Answers
The rate of change of surface area is 524.02 square kilometers per minutes.
what is surface area of square prism?The total space occupied by a three-dimensional square prism is called surface area.
What is the rate of change of surface area of the prism?
Given, the decreasing rate of the base side with respect to time, ds/dt = 7 km/min
the increasing rate of height with respect to time, dh/dt = 10 km/min
At a time, t, base side, s = 4 km
and height, h = 9 km
we need to determine the rate of change of surface area with respect to time, d A/dt
from the differentiation chain rule, d A/ dt = d A /dt × ds /ds
d A /dt = d A/ ds × ds /dt ... equation 1
we know that the surface area for prism, A = 2s² + 4sh
if we differentiate with respect to s then we find d A /ds
d/ds (A) = d/ ds (2s² + 4sh)
d A /ds = 4s + 4h +4s dh/ds ...... equation 2
now dh /ds = dh /ds × dt /dt [ using differentiation chain rule]
dh/ds = dh/ dt× dt/ds
d h/ ds = dh/dt × 1/ ds/dt
it stated earlier that dh/ dt = 10 and ds /dt = 7
dh / ds = 10/7
putting this value in equation 2, we get
d A /ds = 4s +4h + 4s ×10/7
as we know at time t, s= 4 and h = 9
d A /ds = 4 × 4 + 4 ×9 +4×4 ×10 /7
d A /ds = 74.86
putting the value d A /ds in equation 1, we get
d A /dt = d A /ds × ds/ dt
d A/ dt = 74.86 × 7
d A /dt = 524.02 km² / min
hence, the rate of change of surface area = 524.02 square kilometers per minutes
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Write an equation that represents a discount of 18% on a retail price of $55. Let p represent the new price. f
Answers
p = 0.82 * 55
In this equation, p represents the new price after the discount has been applied, and 0.82 represents the percentage of the original price that remains after the discount has been applied (100% - 18% = 82%).
Solving this equation, we find that the new price, p, is equal to $45.90.
Note: This equation represents a discount, which means that the final price, p, will be less than the original price. If you want to represent a markdown (i.e., a price increase), you would use a value greater than 1 for the percentage factor (e.g., 1.18 for a markdown of 18%).
two angles add up to 180 if and only if they are supplementary
Answers
Answer:
True
Step-by-step explanation:
You want to know if it is true or false that "two angles add up to 180° if and only if they are supplementary."
Supplementary anglesTwo supplementary angles have a sum of 180°. That is the definition of supplementary angles. The offered statement is True.
Prove that if a, b, and c are real numbers such that A^2 + B^2 + C^2 = 0, then A = B = C = 0
Answers
The proof that if if a, b, and c are real numbers such that A^2 + B^2 + C^2 = 0, then A = B = C = 0 is made by contradiction in this problem.
What is a proof by contradiction?Proof by contradiction is different of traditional proof because it accepts a single example showing that a statement is false, instead of having the need to derive a general relationship for all input values.
For this problem, we must assume the case in which at least one of the terms is non-zero, hence we assume that A is non-zero, hence the expression would be given as follows:
A² + B² + C² = 0
A² = -(B² + C²)
This means that the square of A would be negative. However, the square of a number is always a non-negative number, hence this equation above is a contradiction.
This contradiction was used to prove that if a, b, and c are real numbers such that A^2 + B^2 + C^2 = 0, then A = B = C = 0.
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Please help me solve
Answers
Answer:
The number of shuttles completed successfully is recorded as the score of that runner. The score is recorded in Level. Shuttles format (e.g. 9.5). The maximum laps on the PACER test is 247, which former Central Middle School student Dennis Mejia achieved, the only person to ever reach such a level.
Step-by-step explanation:
The equation of a ellipse is given below.
Graph the ellipse find the center, vertices, foci, and equation of major axis.
(y+5)^2/9 + (x+5)^2/25 = 1
Answers
Therefore , the solution of the given problem of equation comes out to be Focii (-2,5 ± (2√5 x 1/√5) and vertex ( − 2,5 ± 2√√5).
Explain the equation.An equation is a mathematical representation of two identical variables, one on each side of a "equals" sign. Common difficulties can be solved using equations. We commonly seek pre algebra help to resolve problems in real life. Pre-algebra is the fundamental building block of mathematics.
Here,
[tex](x + 2)^{2}[/tex] / [tex]a^{2}[/tex] + [tex](y-5)^{2}[/tex] /[tex]b^{2}[/tex] -=1 is (h, k).
the ellipse's nucleus
The major axis is the larger of the two axes, which are 2a and 26.
(H, a, k) and (H, k, b) are the vertices. Vertices are those along the major axis in this case, and covertices are those along the minor axis.
[tex](x + 2)^{2}[/tex]/16 + [tex](y-5)^{2}[/tex] /20 =1
can be written as
[tex](x + 2)^{2}[/tex]/ [tex]4^{2}[/tex] + [tex](y-5)^{2}[/tex] /(2√/5)2
hence centre is (-2, 5), maor axis is 2 x 2√√5 = 4√√5 and minor axis
is 2 x 4 = 8
Vertices are ( 2,5 25), or ( 2,5 25) and ( 2,5 + 25), while covertices are ( 2 4, 5) and ( 6,5), respectively.
As a result of the presence of a vertical major axis, eccentricity e and focii are
(h, k ± be). e is given by the relation a2 = b2(1 − e2) i.e.
=> e = [tex]\sqrt{1 - \frac{a^{2} }{b^{2}} }[/tex]
a2= 16 and b2= 62
=> e = 1/√5
Focii (-2,5 ± (2√5 x 1/√5)
or (-2,5±2) i.e. (-2, 7) and (-2, 3).
Therefore , the solution of the given problem of equation comes out to be Focii (-2,5 ± (2√5 x 1/√5) and vertex ( − 2,5 ± 2√√5).
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If f(x) = 2x4 - 3x + 3, then what is the remainder when f(x) is divided by x - 1?
Answers
The remainder on dividing 2x⁴-3x+3 by x-1 is 2
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here: 2x⁴-3x+3 by x-1
The remainder theorem states that when a polynomial p(x) is divided by (x - a), then the remainder = f(a)
∴ The remainder would is f(1) = 2×1-3+3
=2
Hence, The remainder on dividing 2x⁴-3x+3 by x-1 is 2
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3 2/3 Divided by 1 2/7
Answers
Answer:
[tex]2 \frac{23}{27} [/tex]
I wish you luck in your assignments.
The price of a house was #2.3, 400,006 in 201 At the end of each year, the price was increases by 6% find the price of the house after 3 years Find the price of the house after 5 years
Answers
After 3 years, the price of the house would be $2,494,822.48. After 5 years, the price of the house would be $2,830,530.94.
What is price?Price is the value of a product or service that an individual or business is willing to accept in exchange for a good or service. It is typically determined by the market forces of supply and demand. Prices are usually expressed in monetary terms, but can also be expressed in terms of labor time or other resources. Prices can vary widely depending on the availability of a good or service, the amount of competition, and other factors.
To calculate the price of the house after 3 years, the formula is P x (1 + r)^t. P is the initial price of the house, which is $2,300,006. R is the rate of increase each year, which is 6%. T is the number of years, which is 3. Therefore, the price of the house after 3 years is P x (1 + 0.06)^3, which equals to $2,494,822.48.
To calculate the price of the house after 5 years, the formula is P x (1 + r)^t. P is the initial price of the house, which is $2,300,006. R is the rate of increase each year, which is 6%. T is the number of years, which is 5. Therefore, the price of the house after 5 years is P x (1 + 0.06)^5, which equals to $2,830,530.94.
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mr doyle shares 1 roll of bulletin board paper equally with 8 teacher.The total length of the roll is 72 meters. How
Answers
NTP2PS
Write 3 equivalent ratios.
For the given ratio.
12/14
Answers
Answer:
4 7
Step-by-step explanation:
-2(x+5)=4 math homework help
Answers
Answer:
-7
Step-by-step explanation:
-2(x+5)=4
First, distributive property,
-2x-10=4
Add 10 to both sides,
-2x=14
Divide both sides by -2
-7
what is schur polynomial in numerical analysis.
Answers
Schur polynomials, named after Issai Schur, are certain symmetric polynomials in n variables, indexed by partitions, that generalize the elementary symmetric polynomials and the complete homogeneous symmetric polynomials.
What is Schur polynomial?Issai Schur gave the name Schur to a class of symmetric polynomials in n variables that generalize both the complete homogeneous symmetric polynomials and the elementary symmetric polynomials. They are the features of polynomial irreducible representations of the generic linear groups in representation theory. For the space of all symmetric polynomials, the Schur polynomials provide a linear basis. Any Schur polynomial product can be expressed as a linear combination of Schur polynomials with non-negative integral coefficients; these coefficients' values are supplied combinatorially by the Littlewood-Richardson rule. More generally, skew Schur polynomials are connected to pairs of partitions and share Schur polynomials' characteristics.To learn more about Schur polynomial refer to:
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Input 8-2n
I’m getting confused
Thanks
Answers
Answer:
4,2,0
Step-by-step explanation:
the rule is subtract 2 so 0 and 8 , 1 and 6 , 2 and 4 , 3 and 2 , and then finally 4 and 0
Solve: 2x - 5 = 4x + 3
Important: No spaces in your answer
(any spaces within the answer can get the whole answer wrong)
Answers
The time t in seconds that it takes a car to accelerate to ask mph can be described by T=0.001×0.7 32X^2 +15.417X +603.738 how fast in miles per hour is the car going after 8.55 seconds
Answers
The miles per hour that the car is going after 8.55 seconds is 610.79 miles per hour.
How to calculate the time taken?From the information Illustrated, it should be noted that the t in seconds that it takes a car to accelerate to ask mph can be described by T = 0.001 × 0.732X² + 15.417X + 603.738.
In this case, it is important to note that x in the function simply represents the seconds.
Therefore, based on the information, the miles per hour is the car going after 8.55 seconds will be:
T = 0.001 × 0.732X² + 15.417X + 603.738.
T = 0.001 × 0.732(8.55)² + 15.417(8.55) + 603.738
T = 0.001 × 53.511 × 131.815 + 603.738
T = 610.79
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Let p be the statement "He is tall" and let q be the statement the following statements in symbolic form using p and q. He is handsome". Write each of /1/ He is tall and handsome. /2/ He is tall but not handsome. /3/ He is false that he is short or handsome. /4/ He is neither tall nor handsome. /5/ He is tall, or he is short and handsome /6/ It is not true that he is short or not handsome
Answers
On solving the provided question we can say that by logarithm the statement is true he is short.
what is logarithm?The logarithm is a power's reciprocal in mathematics. Accordingly, the exponent by which b must be raised to obtain a number x equals the logarithm of that number in base b. For instance, since 1000 = 103, its base-10 logarithm is 3, or log10 = 3. As an illustration, the base 10 logarithm of 10 is 2, while the square of 10 is 100. Log 100 = 2. To answer a question like, For example, how many times must a base of 10 be multiplied by itself to achieve 1,000, a logarithm (or log) is the mathematical term utilized. The solution is 3 (1,000 = 10 10 10).
He is tall, or he is short and handsome
It is not true that he is short or not handsome
by logarithm,
the statement is true he is short.
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In JKL, KL = 14, LJ = 3, and JK =12. Which statement about the angles of JKL must be true?
Answers
Answer:
D. [tex]L > J > K[/tex]
Step-by-step explanation:
Givenwe are given the vertecies (angles) of the trianglewe are given the side lengths of the triangleWhat to UtilizeThus, we have to utilize the angle relationships in a triangle.
Angle Relationships in a Triangle⭐The largest side is always opposite of the largest angle
⭐The smallest side is always opposite of the smallest angle
Application1. Identify the side lengths of triangle JKL
KL = 14LJ = 3JK = 122. Determine which vertecies are opposite of each side length (draw the figure)
Angle L is opposite of JK (14)Angle K is opposite of LJ (3)Angle J is opposite of KL (12)3. Determine which angles are the greatest, smallest, and in-between
Angle L is the LARGEST angle because it is opposite of the LARGEST side lengthAngle K is the SMALLEST angle because it is opposite of the SMALLEST side lengthWe know that angle J isn't the LARGEST or SMALLEST, but is in the middle4. Write what you found in #3 in terms of inequalities
∠L > ∠J > ∠K
angle L is greater than angle J, and angle J is greater than angle Kif this response helped you, please mark it the "brainliest"!
While analyzing a data set, a scientist notices one data value that is 2 IQRs below the first quartile. She decides to remove this value from further analysis.
What might happen to the mean, median, and mode of the data set after the value's removal?
(select all right answers)
The mode will increase.
The median may stay the same.
The mean will increase.
The mode will stay the same.
The median may decrease.
The mean will decrease.
Answers
The required correct options of data set after the value's removal.
1. The mean will increase. 3. The median may stay the same. 5. The mode will stay the same.
What is the value's removal?The Index Sponsor computes the Removal Value in the same way that Fund Interests in the linked Fund are valued.
Here,
While analyzing a data set, a scientist notices one data value that is 2 IQRs below the first quartile.
As for the properties of statistics, Change in the IQR does affect the median and mode, So options 3 and 5 are correct.
And also mean will increase.
Thus, the correct options are shown above.
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Discussion Topic
How did the United States' entry into World War I change the culture and
international political policies of the country?
Answers
The United States' entry into World War I led to a rise in nationalism and patriotism, as well as a shift towards a more interventionist foreign policy. This had a lasting impact on the culture and international political policies of the country.
Explanation:The United States' entry into World War I marked a significant shift in the culture of the country. Prior to the war, the United States had maintained a policy of isolationism, with a focus on avoiding involvement in foreign conflicts. However, the country's entry into the war marked a shift towards a more interventionist foreign policy, as the United States began to take a more active role in international affairs.
HOPE IT HELPS!Find the value of x .
Answers
Answer:
x = 45°
Step-by-step explanation:
x° + 45° + 90° = 180°
x° + 135° = 180°
x° = 180° – 135°
x° = 45°
i hope this helped
17.
Marita purchased an item for 25% off the original price, plus an additional 20% off the
sale price. She also had a $10-off coupon, which the salesclerk applied after these two discounts. Marita's
final purchase price for the item was $30. Assuming she paid no sales tax, what was the original price of the
item Marita purchased?
Answers
Answer:
Marita had a $10-off coupon, so she paid $50 - $10 = $40 for the item
Step-by-step explanation:
To find the original price of the item, we need to work backwards through the discounts and find the price of the item before any discounts were applied.
We'll call the original price of the item "x."
First, we know that Marita received a 25% discount on the item, which means she paid 100% - 25% = 75% of the original price.
Then, Marita received an additional 20% discount on the sale price, which means she paid 100% - 20% = 80% of the 75% discounted price.
So, Marita paid 80% of the original price, which was reduced by a 25% discount. That means she paid 0.8 * 0.75 = 0.6 * original price = $30.
Therefore, the original price of the item was $30 / 0.6 = $<<30/0.6=50>>50.
Finally, Marita had a $10-off coupon, so she paid $50 - $10 = $40 for the item.
I need help with this PLEASE!!!
Answers
Answer:
See the image for marked congruences.
1. JM ≅ LM | Given
2. △JML is isosceles | definition of isosceles
3. ∠MJL ≅ ∠MLJ | isosceles triangle theorem
4. m∠MJL = m∠MLJ | definition of ≅
5. JK ≅ LK | Given
6. △JKL is isosceles | definition of isosceles
7. m∠KJL = m∠KLJ | isosceles triangle theorem
8. m∠MJL + m∠KJM = m∠KJL | adjacent angle theorem
9. m∠MLJ + m∠KMJ = m∠KLJ | adjacent angle theorem
10. m∠MJL + m∠KJM = m∠MLJ + m∠KLM | transitive property of =
11. m∠MJL + m∠KJM = m∠MJL + m∠KLM | substitution
12. m∠KJM = m∠KMJ | subtraction
13. ∠KJM ≅ ∠KLM | definition of ≅
14. △KJM ≅ △KLM | SAS theorem
15. ∠JKM ≅ ∠LKM | CPCTC
16. KM bisects ∠JKL | definition of bisector
A flexible metamateria/ is developed for use in robotics and prosthetics. A block of metamaterial is in the shape of a cube with a surface area of 600 square centimeters. What is the edge length of the block of metamaterial?
Answers
The edge of a block of metamaterial is 10 centimeters.
What is surface area of a cube?The surface area of the cube all six faces of the cube are made up of squares of the same dimensions then the total surface area of the cube will be the surface area of one face added six times to itself. The formula to find the surface area of a cube is 6a², where a is edge.
Given that, a block of metamaterial is in the shape of a cube with a surface area of 600 square centimeters.
Here, 6a²=600
a²=100
a=10 centimeters
Therefore, the edge of a block of metamaterial is 10 centimeters.
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