Find the domain and range of these functions.
a. the function that assigns to each nonnegative integer its last digit.
b. the function that assigns the next largest integer to a positive integer
c. the function that assigns to a bit string the number of one bits in the string
d. the function that assigns to a bit string the number of bits in the string
Answers
a) Domain: All non-negative integers.
Range: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
b) Domain: Positive integers.
Range: All positive integers except for the greatest integer.
c) Domain: Any bit string.
Range: The set of non-negative integers from 0 to the length of the string inclusive.
d) Domain: Any bit string.
Range: Non-negative integers.
The requested terms, domain and range, refer to the values in the function. They are, however, quite different in nature. In this case, we'll need to define both terms before moving on to the actual problem.
The domain refers to the input values that a function can accept. It's the set of values that can be plugged into the function's equation to get a meaningful result. We'll say that a function has a restricted domain if it doesn't accept all input values.
The range is the set of output values that a function generates for each input value. It's the complete set of possible outcomes for a given function. It's vital to determine the range to ensure that the function is well-defined.
Let's apply this to the problem at hand:
a. the function that assigns to each non-negative integer its last digit.
Domain: All non-negative integers.
Range: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
b. the function that assigns the next largest integer to a positive integer.
Domain: Positive integers.
Range: All positive integers except for the greatest integer.
c. the function that assigns to a bit string the number of one bits in the string.
Domain: Any bit string.
Range: The set of non-negative integers from 0 to the length of the string inclusive.
d. the function that assigns to a bit string the number of bits in the string.
Domain: Any bit string.
Range: Non-negative integers.
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Related Questions
please someone please help me with this problem I’ll thank you forever
Answers
Answer:
The answer is about 9.85
Step-by-step explanation:
4 ^ 2 = 16
9 ^ 2 = 81
16 + 81 = 97
97 radical thing is ABOUT 9.85
What is the classification for this polynomial?
5a²b4-4ab-8
Click on the correct answer.
monomial
binomial
trinomial
Answers
Answer:
trinomial
Step-by-step explanation:
a monomial has 1 term
a binomial has 2 terms
a trinomial has 3 terms
5a²\(b^{4}\) - 4ab - 8 ← has 3 terms and is a trinomial
5a²\(b^{4}\) , - 4ab and - 8 being the 3 terms
The point P = (-5/3 squared, y) lies on the unit circle shown below. What is the value of
y in simplest form?
Answers
The required value of y for the unit circle is: 2/3
How to find the point on the unit circle ?The circle is defined as the locus of a point whose distance from a fixed point is constant i.e center (h, k).
The equation of the circle is given by:
(x - h)² + (y - k)² = r²
where:
h, k is the coordinate of the center of the circle on coordinate plane.
r is the radius of the circle.
Here,
Equation of the unit circle is given as,
x² + y² = 1
Now substitute the given value in the equation,
5/9 + y² = 1
y² = 1 - 5/9
y² = 4/ 9
y = √(4/9)
y = 2/3
Thus, the required value of y for the unit circle is 2/3
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which value of x is a solution to x³ = 216
A. 6
b.18
c.72
d.108
e.648
Answers
6•6•6
A medical researcher wants to determine how a new medication affects blood pressure.The equation of the regression line is Ý = 140 +(-0.0667)XAn amount of medication of 160 mg is found to result in a blood pressure of 127.74 mm Hg. What is the predicted blood pressure?
Answers
On solving the equation Ý = 140 + (-0.0667)X, the value for blood pressure is obtained as 129.328 mm Hg.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The equation is given as Ý = 140 + (-0.0667)X.
An amount of medication of 160 mg is found to result in a blood pressure of 127.74 mm Hg.
Here the value of X is X = 160.
The predicted blood pressure will be -
Ý = 140 + (-0.0667)160
Ý = 140 - 10.672
Ý = 129.328
The predicted blood pressure value is 129.328 mm Hg.
Here the predicted blood pressure value 129.328 mm Hg is greater than the actual blood pressure value 127.74 mm Hg.
Therefore, the observed value will be below the regression line.
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An Xbox has a retail price of $350. Best Buy is offering a 15% discount on the system. How much will the Xbox cost after the discount?
Answers
Answer:
About 297.50$
becuase since i actually have an xbox with that same discount i know the answer
Answer:
you will pay 297.50$
you are saving 52.50$
What part of the protractor do you line up with the vertex? zero line top of the protractor center mark degree line
Answers
Answer:
Place the "center point" (at the bottom of this protractor) on the vertex of the angle. 2. Line up one ray (side) of the angle with the zero degree mark of the protractor.
Step-by-step explanation:
M109) solve
cos²x + 2 cosx + 1 = 0
Answers
Answer:
Step-by-step explanation:
\( \: \: \: \: \: \: \: \: \: \huge \color{green}{ \fbox \colorbox{black}{ \fbox{ \green {Answer} \: }}}\)
\( \longrightarrow \sf \color{teal}{ \cos {}^{2} (x) + 2 \cos(x) + 1} = 0\)
\( \longrightarrow \sf \color{teal}{ \cos {}^{2} (x) + \cos(x) + \cos(x) + 1} = 0\)
\( \longrightarrow \sf \color{teal}{ \cos {}^{} (x) ( \cos(x) + 1)+ 1(\cos(x) + 1} )= 0\)
\( \longrightarrow \sf \color{teal}{ ( \cos(x) + 1)(\cos(x) + 1} )= 0\)
\( \longrightarrow \sf \color{teal}{ ( (\cos(x) + 1} {}^{} ) {}^{2} = 0\)
\( \longrightarrow \sf \color{teal}{ ( (\cos(x) + 1} {}^{} ) {}^{} = 0\)
\( \longrightarrow \sf \color{teal}{ \cos(x) {}^{} }= - 1\)
\(\longrightarrow \sf \color{teal}{ x{}^{} }= \cos {}^{ - 1}( - 1)\)
\(\longrightarrow \sf \color{teal}{ x = (2n + 1) \pi \: \: \: \: rad}\)
where, \({ n \in \{whole \:\; number\}} \)
Principle value -
\( \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = \cos {}^{ - 1} ( - 1) \)
\( \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = (2n + 1) \pi \: \: \: \: rad \: \)
put n = 0
\( \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = (2(0) + 1) \pi \: \: \: \: rad \: \)
\( \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = (0 + 1) \pi \: \: \: \: rad \: \)
\( \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = \pi \: \: \: \: rad \: = 180 \degree\)
approximately what percent of the world's plastic waste ends up being recycled? group of answer choices 20% 1% 9% 57%
Answers
Approximately 9% of the world's plastic waste ends up being recycled.
Here, we have,
given that,
approximately what percent of the world's plastic waste ends up being recycled.
we know that,
Of the 8.3 billion metric tons that has been produced,
6.3 billion metric tons has become plastic waste.
Of that, only nine percent has been recycled.
we have,
Only 9% of plastic waste is recycled
(15% is collected for recycling but 40% of that is disposed of as residues).
Hence, Approximately 9% of the world's plastic waste ends up being recycled.
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how many years after the 1972 ban did it take for ddt levels to move from a rapid to slower rate of decline
Answers
According to all Reports of U.S media and other,
approx. 97 years after in 1972 ban did it take for ddt levels to move from a rapid to slower rate of decline.
DDT (dichloro-diphenyl-trichloroethane) has been one of the most commonly used pesticide chemicals in the United States for many years and was first synthesized in 1874. However, its efficacy as an insecticide was not discovered until 1939. Shortly thereafter, especially during World War I, the United States began producing large amounts of DDT abroad to combat vector-borne diseases such as typhoid fever and malaria. It declined sharply, falling from a peak of about $80m that year to just under $12m in the early 1970s. Over 80% of the amount of pesticides used between 1970 and 1972 was on cotton, with the rest mainly on peanuts and soybeans. The decline in DDT use is due to
(1) increased resistance to insects
(2) development of more effective alternative pesticides
(3) Growing public concern about adverse environmental impacts.
(4) Strengthening government restrictions on the use of DDT.
Residues of the pesticide DDT in the food supply, human tissues, and the environment have declined in recent years, especially since the EPA banned the chemical from major uses in 1972.
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6x+3 what is the value of x?
Answers
Answer:
3
Step-by-step explanation:
6x+3
6+6+6=18
or 6 divided by 2 which is 3
What are all the values that a correlation r can possibly take?
A. 0 ≤ r ≤ 1
B. r ≥0
C. -1 ≤ r ≤ 1
D. None of the above.
Answers
The possible values that a correlation coefficient, r, can take are bounded between -1 and +1, where the correlation coefficient (r) is a statistical measure that quantifies the degree and direction of the linear relationship between two variables.
It ranges from -1 to +1, where a value of -1 represents a perfect negative correlation, a value of 0 represents no linear correlation, and a value of +1 represents a perfect positive correlation.
The magnitude of the correlation coefficient indicates the strength of the relationship between the two variables. It is a numerical value that ranges from -1 to +1. The value of r indicates the degree of association between two variables.
A positive value of r indicates a positive correlation, meaning that as one variable increases, the other variable tends to increase as well. A negative value of r indicates a negative correlation, meaning that as one variable increases, the other variable tends to decrease.
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find the perimeter of triangle whose sides are 5.2cm, 7.8 cm and 4cm.
Answers
Answer:
17 cm
SE SUMAN TODOS LOS LADOS
10 ft-lb of work is required to stretch a spring from its natural length of 12 inches to 36 inches. How much work is required to stretch the spring from 24 to 48 inches? 20 ft-lb 14 ft-lb 16 ft-lb 18 ft-lb 22 ft-lb
Answers
The work is required to stretch the spring from 24 to 48 inches is
14 ft-lb.
The work required to stretch a spring is given by the formula:
Work = (1/2)k(x^2 - x0^2)
Where:
- Work is the amount of work done on the spring (in ft-lb)
- k is the spring constant (in lb/in)
- x is the final length of the spring (in inches)
- x0 is the initial length of the spring (in inches)
In this case, we know that 10 ft-lb of work is required to stretch the spring from its natural length (x0 = 12 inches) to 36 inches (x = 36 inches). We can use this information to find the value of k.
10 = (1/2)k((36)^2 - (12)^2)
Simplifying the equation:
20 = k(36^2 - 12^2)
20 = k(1296 - 144)
20 = k(1152)
k = 20/1152
k ≈ 0.01736 lb/in
Now, we can use the value of k to find the work required to stretch the spring from 24 to 48 inches.
Work = (1/2)k((48)^2 - (24)^2)
Work = (1/2)(0.01736)(2304 - 576)
Work = (1/2)(0.01736)(1728)
Work ≈ 14 ft-lb
Therefore, the work required to stretch the spring from 24 to 48 inches is approximately 14 ft-lb.
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On average, Americans consume 13.9 pounds of ice cream per person over an entire year. Ben loves ice cream, but limits himself to one 6 ounce (oz) serving each week. Find the difference between the amount of ice cream that Ben consumes compared to the national average.
Answers
Answer:
5.6 pounds
Step-by-step explanation:
13.9 pounds of ice cream are consumed per year by individual.
Ben consumes 6 ounce serving per week.
The amount of ice cream consumed by Ben in a year can be determined by;
since there is an average of 52 weeks in a year, then;
6 ounces x 52 = 312 ounces
But,
1 ounce = 0.0625 pounds
So that,
312 ounces = x pounds
x = 312 x 0.0625
= 19.5
x = 19.5 pounds
Thus, Ben consumes 19.5 pounds of ice cream per year. He consumes more than the average value per person in a year.
The difference = Amount Ben consumes - National average
= 19.5 - 13.9
= 5.6 pounds
Explain what is meant when we say, "The product of any number and its reciprocal is 1." Give an example. When any number, such as is multiplied by its reciprocal, ___ the result is ___
Answers
When we say "The product of any number and its reciprocal is 1," it means that when a number is multiplied by its multiplicative inverse (reciprocal), the result is always equal to 1.
The reciprocal of a number is obtained by taking the multiplicative inverse of that number. The multiplicative inverse of a non-zero number "a" is denoted as 1/a. The product of a number "a" and its reciprocal 1/a is always equal to 1.
For example, let's consider the number 5. Its reciprocal is 1/5. If we multiply 5 by its reciprocal, we get:
5 * (1/5) = 1
Similarly, for any non-zero number "a", when we multiply "a" by its reciprocal 1/a, the result is always equal to 1:
a * (1/a) = 1
This property holds true for all non-zero numbers and is a fundamental concept in mathematics.
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What value of t makes the statement true? (4x3 5)(2x3 3) = 8x6 tx3 15.
Answers
The mathematical statement is true when the value of t is 22
The equation is given as:
\((4x^3- 5)(2x^3 -3) = 8x^6 -tx^3 +15\)
Expand the expression on the left-hand side
\(4x^3(2x^3 -3)- 5(2x^3 -3) = 8x^6 -tx^3 +15\)
Distribute the expression
\(8x^6 -12x^3- 10x^3 +15 = 8x^6 -tx^3 +15\)
Evaluate like terms
\(8x^6 -22x^3 +15 = 8x^6 -tx^3 +15\)
By comparing the expressions on both sides of the equation, we have:
\(-22x^3= -tx^3\)
Divide both sides of the equation by -x^3
\(22= t\)
Rewrite as:
\(t =22\)
Hence, the mathematical statement is true when the value of t is 22
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Answer:
22
Step-by-step explanation:
1. Lennox is in NYC and has $10 to get to his destination. The taxi charges $0.75 per mile with
a flat fee of $2.35. How many miles can he travel
Answers
Answer:
(10-2.35)/.75 =10.2 miles.
Step-by-step explanation:
Three friends were playing a game of marbles.
At the end of the game, Marcy had 25% of the
marbles, Roger had
2
1
of the marbles, and Ann
had the rest of the marbles. If there were 100
marbles altogether, how many marbles did Ann
have at the end of the game?
Answers
The number of marbles Ann had at the end is 54.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Total marbles = 100
The number of marbles:
Marcy:
= 25% of 100
= 1/4 x 100
= 25
Roger:
= 21
Now,
The number of marbles:
Ann = 100 - (25 + 21) = 100 - 46 = 54
Thus,
Ann has 54 marbles at the end.
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What is wrong with the following piece of mRNA? TACCAGGATCACTTTGCCA Multiple Choice It contains A. O It does not include an equal number of As and Ts. It does not include an equal number of Gs and Cs. It contains T and not U.
Answers
The wrong with following piece of mRNA, TACCAGGATCACTTTGCCA is that it contains T and not U. So, option(D) is right choice here.
Messenger RNA (mRNA) is present in DNA. DNA uses four bases in its code, adenine (A), guanine (G), cytosine (C) and thymine (T). RNA also uses four bases. However, instead of using "T" as DNA, it uses uracil (U). So, if your DNA sequence is 3' T C G T T C A G T 5', the mRNA sequence would be 5' A G C A A G U C A 3'. A strand of DNA is a template strand that has a nucleotide sequence on it that is read by RNA polymerases. Rna polymerase reads the template strand and encodes the m-RNA using the base-pairing rule. According to the rule, adenine pairs with thymine and guanosine with cytosine. So if the template DNA reads TAC GTT ACG, RNA polymerase will read it as AUG CAA UGC. Since no thymine is present in RNA, it will code for U instead of T.
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A function is represented by the values in the table.
Choose from the drop-down menu to complete the statement.
The function represented in the table Choose____linear.
Is or is not
PLEASE HELP ILL MARK BRAINLIEST!!!!!! Quick!!!!
Answers
Answer:
Is linear ;)
Step-by-step explanation:
The Answer Is {Linear}
If you divide all the numbers on the y-intercept it will equal to the numbers on the x-intercept.
Not only that, I Took The Test.
6.08 Quiz: Identify Linear Models
Tell whether the ordered pair is a solution of the given system:
(0,0) ; {y<-x+3
{y
Answers
Answer:
yes the ordered pair is a solution
Step-by-step explanation:
(x, y) = (0,0)
y < -x + 3
0 < - (0) + 3
0 < 3
true, ordered pair is a solution
x2 + 5x - 36 which binomial is a factor of the polynomial?
Answers
Thus, the two binomials that are factor of the polynomial are $(x + 9)$ and $(x - 4)$.
the number of bacteria in a culture is increasing according to the law of exponential growth. after 3 hours, there are 400 bacteria, and after 6 hours, there are 3,200 bacteria. write an equation that can be used to determine the number of bacteria y in the culture after t hours.
Answers
The number of bacteria y in the culture after x hours will be y = 50(2)ˣ.
What is exponential growth ?An exponential function faster and faster after every next value of the independent variable.
According to the given question the number of bacteria in a culture is increasing according to the law of exponential growth. after 3 hours, there are 400 bacteria, and after 6 hours, there are 3,200 bacteria.
We use the exponential growth equation y = arˣ where a is the initial value and r is common ratio and x represents time.
so 400=ar^3...(i) and 3200= ar^6...(i)
Dividing equation (ii) by equation (i) and solve for r we get r³ so r =2
substitute r into first equation 400=a(2)³
8a = 400.
a = 50.
∴ The no. of bacteria at any given time x will be. ( t is replaced by x)
y = 50(2)ˣ.
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à = 22 +33 B = -1 +23 Ā· B = 4 The angle between A and B is (in degrees):
Answers
The angle between vectors A and B is approximately 89.78 degrees.
To find the angle between vectors A and B, we can use the dot product formula:
A · B = |A| |B| cos(θ)
Given that Ā· B = 4 and knowing the magnitudes of vectors A and B:
|A| = √(22² + 33²)
= √(484 + 1089)
= √(1573)
≈ 39.69
|B| = √((-1)² + 23² )
= √(1 + 529)
= √(530)
≈ 23.02
Substituting the values into the dot product formula:
4 = (39.69)(23.02) cos(θ)
Now, solve for cos(θ):
cos(θ) = 4 / (39.69)(23.02)
cos(θ) ≈ 0.0183
To find the angle θ, we take the inverse cosine (arccos) of 0.0183:
θ = arccos(0.0183)
θ ≈ 89.78 degrees
Therefore, the angle between vectors A and B is approximately 89.78 degrees.
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Calculate the range, variance, and standard deviation for the following samples a. 43, 41, 48, 47, 49 b. 100, 1, 3, 95, 70, 4, 6, 10, 5 c. 100, 1, 3, 30, 70, 30, 43, 5 a. The range is 8 Type an integer or a decimal. Do not round.) The variance is 11.80 (Round to two decimal places as needed.) The standard deviation is 3.4 (Round to one decimal place as needed.) b. The range is 99 (Type an integer or a decimal. Do not round.) The variance is 1813.50 (Round to two decimal places as needed.) The standard deviation is 42.6 (Round to one decimal place as needed.) c. The range is 99 (Type an integer or a decimal. Do not round.) The variance is 1234.79 (Round to two decimal places as needed.) he standard deviation is (Round to one decimal place as needed.)
Answers
The range, variance, and standard deviation are 8, 21.10, 445.21.
The range, variance, and standard deviation are 99, 40.14,1612
What is data?
Data is a collection of measurements or observations used as a source of information. There are numerous types of data and numerous ways to represent data.
Given data is
43, 41, 48, 47, 49
Arrange them in ascending order:
41, 43, 47, 48,49
The range is (49 - 41) =8
The mean is (41+43+47+48+49)/5 =45.6
Data deviation from mean square deviation
41 4.6 21.16
43 2.6 6.76
47 -1.4 1.96
48 -2.4 5.76
49 -3.4 11.56
Total 47.2
The standard deviation is s = √[(x-μ)²/N] = 21.10
The variance is s² = 445.21
Given data is
100, 1, 3, 95, 70, 4, 6, 10, 5
Arrange them in ascending order:
1, 3, 4, 5, 6, 10, 70, 95, 100
The range is (100 - 1) = 99
The mean is (1+3+4+6+5+10+70+95+100)/9 =32.67
Data deviation from mean square deviation
1 31.67 1002.99
3 29.67 880.31
4 28.67 821.97
5 27.67 756.63
6 26.67 711.29
10 22.67 513.93
70 -37.33 1393.52
95 -62.33 3885.03
100 -3.33 4533.33
Total 14508.0001
The standard deviation is s = √[(x-μ)²/N] = 40.14
The variance is s² = 1612
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a. What is the nth fraction in the following sequence? 2
1
, 4
1
, 8
1
, 16
1
, 32
1
,… b. What is the sum of the first n of those fractions? To what number is the sum getting closer and closer? Two forces, A=80 N and B=44 N, act in opposite directions on a box, as shown in the diagram. What is the mass of the box (in kg ) if its acceleration is 4 m/s 2
?
Answers
A)an = 2*2^(n-1)`. B) `The sum of the first n fractions is `2*(2^n - 1)`.
a. The sequence is a geometric sequence with the first term `a1 = 2` and common ratio `r = 2`.Therefore, the nth term `an` is given by:`an = a1*r^(n-1)`
Substituting `a1 = 2` and `r = 2`, we have:`an = 2*2^(n-1)`
b. To find the sum of the first n terms, we use the formula for the sum of a geometric series:`S_n = a1*(1 - r^n)/(1 - r)
`Substituting `a1 = 2` and `r = 2`, we have:`S_n = 2*(1 - 2^n)/(1 - 2)
`Simplifying:`S_n = 2*(2^n - 1)
`The sum of the first n fractions is `2*(2^n - 1)`.As `n` gets larger and larger, the sum approaches `infinity`.
Thus, the sum is getting closer and closer to infinity.
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Rugged cabin co. provides pre-made materials to build cabins. to ensure materials are in supply and ready for quick delivery, the company offers cabins in only three sizes. each cabin has rectangular floor plan where the length is equal to 5 feet more than twice the width. which expression represents the area, in square feet, for each cabin size?
A. 2w^2 + 5w, where w is the width
B. 2w^2 + 5, where w is the width
C. 2w^2, where w is the width
D. 10w^2 + 5 w, where w is the width
Answers
The expression 5w + 2w² represents the area, in square feet, for each cabin size
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.
Area of a rectangle = length * width = l*w
length is equal to 5 feet more than twice the width.
=> l= 5+2w
So, area = ( 5+2w ) *w
= 5w + 2w²
Thus, the expression 5w + 2w² represents the area, in square feet, for each cabin size
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g(x)=2x+4 solve for c when g(x)-8
Answers
Answer: ( g+G) (x) =12+2x
Step-by-step explanation:
i used an math ap it is an app you can get on your phone
Triangle ABC, with A = (-2,3) B = (-4,1) and C = (-3,5), is rotated 180° counterclockwise (or 180° clockwise) about the origin to make Triangle A'B'C'. What is the coordinate point of C'?
choices
A. (-5,-3)
B. (5,-3)
C.(3,-5)
D.(3,5)
Answers
Solving for the coordinate point of C in the given problem, the answer is (3,-5). Therefore, option C is the appropriate option.
How to get Coordinate Points?To rotate a point about the origin by 180°, we can simply negate both the x-coordinate and the y-coordinate. So, to find the coordinates of A', B', and C', we simply negate the x-coordinate and the y-coordinate of A, B, and C, respectively.
The coordinates of A' would be (2,-3), the coordinates of B' would be (4,-1), and the coordinates of C' would be (3,-5).
Therefore, the answer is (C) (3,-5).
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