Rotate 90 counter clockwise around the origin and then reflect over the c-axis
Answers
In order to get the same outcomes as a form mirrored across the y-axis and turned counterclockwise, a shape can be reflected across the x-axis and then rotated 90 degrees in a clockwise manner around the origin. This suggests a similarity between these two transformative sequences.
What does mathematics mean by reflection?
A flip is the term used in geometry to describe a reflection. The mirror image of the form is a reflection. An image can reflect through a line known as the line of reflection. When all of the points in a figure are evenly spaced away from one another, the two figures are said to reflect each other.
(X, Y) > when a form is rotated 90 degrees counterclockwise (y, -x).
When the picture is reflected across the y-axis, (x, y) > (-x, y).
When those two transformations are used, it is the same as reflecting a shape across the line y = -x, where (x, y) > (-y, -x).
For instance: After being rotated 90 degrees clockwise and reflecting across the y-axis,
(2, 1) > (1, -2) > (-1, -2); and
(2, 1) > (-1, -2)
after being reflected across the y = -x line
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Related Questions
In 2001 there were 6680 electric-powered vehicles in use in the United States. In 1998 only 4760 electric vehicles were being used. (Source: U. S. Energy Information Administration)
a. Assume that the relationship between time, x, and number of electric-powered vehicles, y, is linear. Write an equation in slope-intercept form describing this relationship. Use ordered pairs of the form (years past 1998 comma number of vehicles).
Answers
An equation of slope-intercept form describing this relationship. Use ordered pairs of the form the equation, y = 640x + 4760
Since there were 4760 electric vehicles in 1998, when x=0 (indicating 0 years have passed since 1998), y=4760. There were 1,920 more electric vehicles on the road after three years. 1920 / 3 = 640 is the average rate of change every year. Between 1998 and 2001, there were 640 more automobiles every year.Our slope measures m=640. By dividing the change in y by 4760, or 1920, we can determine the slope.The y-intercept is just the starting point, or x=0. At this point, x=0. The y-intercept is shown here: (0, 4760). Equation of slope intercept: y = 640x + 4760 where b=4760.
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If f(x) = 10 - 200 and g(x) = 25x2 + 90, the value of f (4) - g (2) is:
Answers
As function f(x) is not completely right i assume it to be like f(x)= 10x-200.
Acc. to which the answer is -350.
What is a function?
A function from a set X to a set Y allocates exactly one element of Y to each element of X.
Main Body:
f(x)= 10x-200
f(4)= 10*4-200
= 40-200
=-160
g(x)= 25[tex]x^{2}[/tex]+90
g(2)= 25*(2)² +90
= 25*4+90
=190
So, f(4)-g(2) = -160-190
= -350
Therefore the answer is -350.
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In the football club, 36 footballer are Latvian, while there are 4 time le footballer of other nationalitie. How many total athlete doe the football club have?
Answers
The total number of athletes, the football club has is 180.
Given, In the football club, 36 footballers are Latvian, while there are 4 times the footballers of other nationalities.
as, footballers that are Latvian = 36
now, footballers of other nationalities = 4×36
footballers of other nationalities = 144
so the total number of footballers = 144 + 36 = 180
Therefore, the total number of athletes, the football club has is 180.
Hence, the total number of athletes, the football club has is 180.
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please help lol I need help
Answers
The expression can be expanded as 125/64
Evaluating an ExpressionTo evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations.
To solve this problem, we need to evaluate the expression given;
For this, we can find the cube of the numerator and cube of the denominator.
(5/4)³ = 125/64
The solution to the problem is 125/64
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Translate the sentence into an equation.
Seven more than the quotient of a number and 6 is equal to 2.
Use the variable x for the unknown number.
Answers
Answer:
Step-by-step explanation:
Let's break down the problem:
Quotient = result obtained by dividing one quantity by another
So its division of x (a number implying variable) by 6
Then it says equal to 2 so we can piece together an equation like this
x/6 = 2
Then we use algebra to solve it
6(x/6)= (2)6
x = 12
So 12 is the unknown number
when 1515 is appended to a list of integers, the mean is increased by 22. when 11 is appended to the enlarged list, the mean of the enlarged list is decreased by 11. how many integers were in the original list?
Answers
In the initial list, there were 4 integers.
We have the following system if the mean is m, x is the list's initial sum, and n is the number of integers in the list:
m = x/n , m + 2 = (x + 15) / (n + 1) and m + 1 = (x + 16) / (n + 2).
The initial equation is x = mn.
Therefore, changing x in the other two equations:
m + 2 = (mn + 15) / (n + 1) ..............(1)
m + 1 = (mn + 16) / (n + 2)...............(2)
Based on equation (1):
(m + 2)(n + 1) = mn + 15
mn + m + 2n + 2 = mn + 15
m + 2n + 2 = 15
m + 2n = 13
m = 13 - 2n.
Now change m in equation (2) to:
13 - 2n + 1 = ( n(13 - 2n) + 16) / (n + 2)
14 - 2n = (13n - 2n^2 + 16) / (n + 2) Through-multiplication by n + 2:
(14 - 2n)(n + 2) = 13n - 2n^2 + 16
14n + 28 - 2n^2 - 4n = 13n - 2n^2 + 16
10n + 28 = 13n + 16
12 = 3n
n = 4.
Hence, there were 4 integers in the original list.
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Carrie visited two different pet adoption centers. At the first adoption center, the ratio of dogs to birds was 4:24. The ratio of dogs to birds at the second adoption center was equivalent.
Which is the ratio of dogs to birds at the second adoption center?
Answers
The ratio of dogs to birds at the second adoption center that are equivalent is 2:12.
What is a ratio?Ratio demonstrates how many times one number can fit into another number. They contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
At the first adoption center, the ratio of dogs to birds was 4:24. The ratio will be:
= 4 / 24
= 1/6
= 1:6
Since the ratio of dogs to birds at the second adoption center is equivalent, this can be 2 to 12. This will be:
= 2/12.
= 1/6
= 1:6
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1 . 10. A life insurance company found that among its last 200 claims, there were six dozen smokers. What is the ratio of smokers to nonsmokers in this group of claimants? Write in lowest terms
2. A woman threw 60 darts and hit the target a dozen times. What is her ratio of hits to misses? Write in lowest terms
3. . While watching television for one week, a consumer group counted 1240 acts of violence and 40 acts of kindness. What is the violence to kindness ratio for television, according to this group. Write in lowest terms
Answers
Answer for No.2
Answer: 1/4
Step-by-step explanation:
Hits = 12
Misses = 60-12 = 48
Ratio of hits to misses = 12/48 = ¼
So the answer is 1/4.
(100 POINTS) HELP ASAP
Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents.
y to the three fourths power, all over y to the one half power
the eighth root of y to the third power
the square root of y to the three fourths power
the fourth root of y
the square root of y
Answers
Answer:
[tex]^4\sqrt{2}[/tex]
Answer: Option C
Step-by-step explanation: just took the test.
The school art club at a large high school is in charge of designing school T-shirts and getting them printed this year. A local business charges $35 to set up their T-shirt printing machine with the design and $4.25 in materials per T-shirt to print.
1). Create an equation to represent the average cost C(x), in dollars, per T-shirt if x T-shirts are printed by this business.
2). what is the average cost per shirt to print 25 shirts? 100 shirts?
3). what is the cheapest the average cost per T-shirt will get? Explain or show your reasoning.
Answers
Total cost includes initial charge for printer set up and material cost.
C(x) = 4.25x + 35 represents the total cost, where C(x) is the cost of x T- shirts.Part 1Average cost per T-shirt is
C(x)/ x = (4.25x + 35)/x = 4.25 + 35/xPart 2Average cost to print 25 T-shirts
4.25 + 35/25 = $5.65Average cost to print 100 T-shirts
4.25 + 35/100 = $4.60Part 3The average cost 4.25 + 35/x depends on the number of T-shirts printed.
The larger the x, the smaller is 35/x. It will be closer to but greater than $4.25.
An artist connects stained glass pieces with lead strips. In this rectangular window, the strips
are cut so that FH = 22 in. Find JG.
Answers
An artist connects stained glass pieces with lead strips and cut the strips so that FH = 22 in and JG = 11 in.
What is a rectangle?
A plane shape, as opposed to a square, with four straight sides and four right angles, particularly one with uneven neighboring sides.
Here, we have
FH ≅ GH
FH = EG = 22in
If diagonals bisect each other then, an artist connects stained glass pieces with lead strips
1/2(EG) = JG
1/2 (22) = JG
11 = JG
Hence, an artist connects stained glass pieces with lead strips and cut the strips so that FH = 22 in and JG = 11 in.
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5
The equation of a line is y=-x+9.
8
(a) What is the slope of a line parallel to it?
(b) What is the slope of a line perpendicular to it?
(a) The slope of a line parallel to it is. (Simplify your answer.)
(b) The slope of a line perpendicular to it is
(Simplify your answer.)
Answers
a. The slope of the line that is parallel to y = 5/8x + 9 is: 5/8.
b. The slope of the line that is perpendicular to y = 5/8x + 9 is: -8/5.
What is the Slope of Parallel and Perpendicular Lines?When two lines are parallel to each other, the lines will have the same slope value (m). However, if both lines are perpendicular to each other, they would have slope values that are negative reciprocals, meaning the product of their slope would be -1.
a. Given the equation, y = 5/8x + 9, the slope (m) of the line is 5/8.
Therefore, it implies that the line that is parallel to y = 5/8x + 9 will have a slope that is the same as 5/8.
Thus, the slope of the parallel line to the equation, y = 5/8x + 9, is: 5/8.
b. The negative reciprocal of 5/8 is -8/5.
Therefore, the slope of the line that is perpendicular to y = 5/8x + 9 would be: -8/5.
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Question
Graph x=−6.
Answers
A graph of the given mathematical expression (x = -6) is shown in the image attached below.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.
In this scenario, a number line would be used to graph the given mathematical expression because it only contains one (1) variable.
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this is geometry, finding the rules for sequences of congruence transformations
Answers
The rules for the rotation and translation for the rectangle RSTU is:
Rotation: (x,y) ↔ (-y,x)
Translation : (x,y) ↔ (x+k , y)
Given,
we have rectangle R'S'T'U' which is the image of the rectangle RSTU under a rotation 90° counterclockwise about the origin followed by a translation.
we are asked to determine the rule of rotation and translation.
Rotation :
Our point A(x,y) becomes A' when a point is rotated 90 degrees counterclockwise about the origin (-y,x).
so the rule is:
Rotation: (x,y) ↔ (-y,x)
Translation:
When the shape is moved towards the right by k units, then replace x with x + k.
let's check:
R(-6,3) ↔ 90° counterclockwise rotation ↔ (-3,-6) ↔ translation↔R'(-3+9,-6) → R'(6,-6)
S(-4,7) ↔ 90° counterclockwise rotation ↔ (-7,-4) ↔ translation↔S'(-7+9,-4) → R'(2,-4)
Hence we get the required rules for sequences of congruence transformations.
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the distribution of results from a cholesterol test has a mean of 180 and a standard deviation of 20. a sample size of 40 is drawn randomly. find the probability that the sum of the 40 values is greater than 7,450. (round your answer to four decimal places.)
Answers
The probability that the sum of the 40 values is greater than 7,450 is 0.0239
Define Normal Distribution.
A normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable.Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.Formula of Normal Distribution isZ = (x - μ ) / (σ / √n )
We have given following info,
mean μ = 180
Standard deviation σ = 20
n = 40
σ(mean of x) = σ / √ n
= 20 / √40
= 3.16
Sample average (mean of x) = 7450 / 40
= 186.25
P(x > 186.25) = 1 - P(x < 186.25)
= 1 - P( (x - μ ) / σ(mean of x) ) < ( [186.25 - 180] / 3.16) )
= 1 - P( Z < 1.98)
Using Normal distribution table,
= 1 - 0.9761
P(x > 186.25) = 0.0239
Therefore,the probability that the sum of the 40 values is greater than 7,450 is 0.0239
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a large animal preserve has noticed that an albino panther is born unpredictably once every 8 years; and that can happen at any time of the year. a) what are the expected value and standard deviation of the number of albino panthers which will be born in the next 40 years?
Answers
The expected value of the number of albino panthers is 5
The standard deviation of the number of albino panthers is 2.09
Given that albino panther is born once every 8 years, probability p, of one albino to be born in 8 years is 1/8
Expected value=n*p, where n is 40 years, and p=1/8
=40*1/8
=5 albino panthers
Hence, the expected value is 5 albino panthers
Standard deviation=(Expected value*(1-p))^1/2
=(5*(1-1/8))^1/2
=4.375^1/2
=2.09
Hence, standard deviation is 2.09
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Determine the quadratic function of the form f(x)= a(x - h)² + k whose graph is given on the
right.
Answers
The quadratic function will be f(x) = 2[tex]x^{2}[/tex] + 4x + 15
General equation of quadratic is
f(x) = a[tex]x^{2}[/tex] + bx + c
and Standard form is
f(x) =a [tex](x-h)^{2}[/tex] + k
where h , k are coordinates of vertex
and x , y represent some point on the graph.
By replacing f(x) with y in standard equation we get
y = a[tex](x-h)^{2}[/tex] + k
Put value of x , y , h , k from the graph.
h = -2
k = 7
x = 0
y = 9
9 = a (4) + 7
a = 2
Now put value of a in standard equation
f(x) = 2 [tex](x + 2)^{2}[/tex] + 7
f(x) = 2[tex]x^{2}[/tex] + 4x + 15
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Write the equation of the graph shown below in factored form.
a graph that starts at the top left and continues down through the x axis at negative one to a minimum around y equals negative twelve point two five and goes up to touch the x axis at two and the goes back down to a minimum around y equals negative one half and goes back up through the x axis at two.
f(x) = (x − 2)2(x + 1)(x − 3)
f(x) = (x + 2)2(x − 1)(x + 3)
f(x) = (x + 2)2(x + 1)(x + 3)
f(x) = (x − 2)2(x − 1)(x − 3)
Answers
The answer is
f(x) = (x - 1) 2(x +1)(x - 3 ).
Given equation
f(x) = (x − 2)2(x + 1)(x − 3)
f(x) = (x + 2)2(x − 1)(x + 3)
f(x) = (x + 2)2(x + 1)(x + 3)
f(x) = (x − 2)2(x − 1)(x − 3)
Factored form is a product of stayed and linear elements.
by checking of the red line cross the x-axis.it will give you the zero.
it passes at -1, touches at 1, and crosses again at 3.
This implies that the zeroes are -1, 1 and 3.
The factors 2(x+1), (x - 3), and (x - 1) must be evaluated.
Therefore the answer is
f(x) = (x - 1) 2(x +1)(x - 3 ).
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Decide whether each equation is true for all, one, or no values of x.
Answers
1. 3x + 9 = -4.5x + 20 ; This is true for one value of x.
2. 9(x + 3) = 9x + 12 ; This is true for no values of x.
3. 4(2x + 3) = 12 + 8x ; True for any values of x.
Given,
The equations;
1. 3x + 9 = -4.5x + 20
2. 9(x + 3) = 9x + 12
3. 4(2x + 3) = 12 + 8x
We have to find whether each equation is true for all, one or no values of x.
Here,
1. 3x + 9 = -4.5x + 20
Solve for x;
3x + 4.5x = 20 - 9
7.5x = 11
x = 11/7.5
x = 1.47
Then,
This is true for one value of x.
2. 9(x + 3) = 9x + 12
Solve using distributive property;
9x + 27 = 9x + 12
9x - 9x = 12 - 27
0 = -15
This is true for no values of x.
3. 4(2x + 3) = 12 + 8x
Use distributive property and solve;
8x + 12 = 12 + 8x
8x - 8x = 12 - 12
0 = 0
True for any values of x.
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Explain how the equations 2/3m=-4 and -4m=24 are equivalent?
Answers
Both 2/3m=-4 and -4m=24 have a solution of 1/6 and are equivalent
What are algebraic expressions?Algebraic expressions are described as expressions that contains terms, variables, coefficients, constants and factors.
They are also known to be made up of some arithmetic operations, such as;
AdditionSubtractionMultiplicationDivisionBracket ParenthesesWe have the equations;
2/3m=4 and -4m=24
Let's solve for m in the first equation
12m = 2
Divide both side by coefficient of m
m = 2/ 12 = 1/ 6
For the second equation
-4m = 24
Divide both sides by - 4
m = 24/-4
m = 6/ -1
Take inverse
m = 1/6
Hence, the equations are equivalent
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What is the area of the figure?
17.5 yd2
20.0 yd
19.1 yd
35.0 yd2
Answers
The area of the triangle is A. 17.5yd².
How to find the area?Using this formula to find the area
Area = 1/2 ( b × h)
Where:
b = base = 5
h = Height = 7
Hence,
Area = 1/2 (5 ×7)
Area = 1/2 (35)
Area = 1× 35/2
Area = 35/2
Area = 17.5yd²
Therefore the correct option is A.
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Find a polynomial function of least degree having only real
coefficients, a leading coefficient of 1, and zeros of 4 and
3 + i.
Answers
The polynomial function of least degree having only real coefficient is f(x) = [tex]x^3 -10x^2 +34x-40[/tex]
Given,
In the question:
A leading coefficient of 1, and zeros of 4 and 3 + i.
To find the polynomial function of least degree having only real coefficients.
Now, According to the question;
The function has 4 and 3 + i .
As, i's roots
So, 3 - i is also its root a leading coefficient of 1 .
So, The function of polynomial is :
f(x) = (x - 4) [tex][(x - 3)^2 + 1][/tex]
To solve the function;
f(x) = [tex]x^3 -10x^2 +34x-40[/tex]
Hence, The polynomial function of least degree having only real coefficient is f(x) = [tex]x^3 -10x^2 +34x-40[/tex]
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Quadrilateral TEAM is rotated-180° about the origin.
Draw the image of this rotation.
Answers
The area of the quadrilateral is determined as follows if the diagonal and the length of the perpendiculars from the vertices are known: The formula for calculating the area of a quadrilateral is (12) diagonal length the sum of the lengths of the perpendiculars drawn from the other two vertices.
Explain about the Quadrilateral?A polygon with four sides, four angles, and four vertices is called a quadrilateral. The Latin words Quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral. A quadrilateral is shown in the above image as an example. quadrilateral pieces.
Quadrilaterals with four congruent sides, four right angles, and two sets of parallel sides are called squares. Quadrilaterals having two sets of parallel sides are known as parallelograms. All squares are parallelograms because squares must have quadrilaterals with two sets of parallel sides.
Four sides and four angles make up a quadrilateral. Any convex polygon's exterior angles (i.e., no interior angle is less than 180 degrees) sum up to 360 degrees ( 4 right angles).
In the quadrilateral, each point's coordinates change as follows:
(x, y) → (-x, -y)
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What is the solution set for 5 - 5 = 15, given the replacement set {0, 1, 2, 3, 4}? O x = 4 O x = 3 O x = 2 O x = 1 x = 0
Answers
The solution set for the given equations is x = 4.
What is a set?
A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is a mathematical model for a collection of various things.
Here,
we put the value of x in the given equation and justify our answer
when we x=4, we get
5x−5=15
5(4) - 5 = 15
20 - 5 = 15
15 = 15
Hence, the solution set for the given equations is x = 4.
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Triangle ABC has vertices A(0, -1), B(6, 5), and C(-4, 3). Which statement about triangle ABC is true?
Answers
The coordinates of the vertices of triangle ΔABC, A(0, -1), B(6, 5), and C(-4, 3), indicates that the triangle ΔABCD is a right triangle with all sides of different length.
What is a right triangle?A right triangle is a triangle that has an interior angle of 90°, and therefore, it has two sides known as the legs that are perpendicular.
The lengths of the sides of the triangle ΔABC can be found using the Pythagorean formula for finding the distance, d, between two points, (x₁, y₁) and (x₂, y₂) on the coordinate plane as follows;
d² = (x₂ - x₁)² + (y₂ - y₁)²
The vertices of the triangle ΔABC are; A(0, -1), B(6, 5), and C(-4, 3), which gives;
[tex]\overline{AB}^2[/tex] = (6 - 0)²+ (5 - (-1))² = 72, AB = 6·√2
[tex]\overline{AC}^2[/tex] = (-4 - 0)² + (3 - (-1))² = 32, AC = 4·√2
[tex]\overline{BC}^2[/tex] = (-4 - 6)² + (3 - 5)² = 104, BC = 2·√(26)
72 + 32 = 104
Therefore; [tex]\overline{AB}^2[/tex] + [tex]\overline{AC}^2[/tex] = [tex]\overline{BC}^2[/tex]
ΔABC is a right triangle
The slopes of the equation of the lines of the sides of the triangle are;
Slope of side AB = (5 - (-1))/(6 - 0) = 1
Slope of side BC = (3 - 5)/(-4 - 6) = 0.2
Slope of side AC = (3 - (-1))/(-4 - 0) = -1
Therefore;
[tex]\overline{AB}[/tex] ⊥ [tex]\overline{AC}[/tex]
Which gives;
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The angles of elevation of the top of a tower with respect to points A and B are 30° and 75°respectively. Points A and B are 175 feet apart and at equal elevations, and the base of the tower lies on the line between them. Find the height of the tower. Round your final answer to the nearest ten thousandth.
Answers
The height of the tower is 87.4870 feet
What is Angle of elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.
The body of the calculation is contained in the attached file.
In conclusion, the height of the tower to the nearest ten thousandth is 87.4870 feet
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Hannah swims in a swimming pool of 25 metres long.
How many laps does she need to complete for a total distance of 0.5 kilometre?
Answers
She needs to complete 20 laps for a total distance of 0.5 kilometer.
1 kilometers = 1000 meters
0.5 kilometers = 500 meters
Length of swimming pool = 25 meters
That means, she covers 25 meters in 1 lap.
Laps to cover 500 meters = 500/25
= 20
Hence, she needs to do 20 laps.
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What would a, b, c be??
Answers
The values of a, b and c from the given polynomial are a = -1 , b = 2 and, c= -35.
We are given the expression:-
[tex]x^2+2x-35[/tex]
We know that, the general form of a quadratic expression is :-
[tex]ax^2+bx+c[/tex]
We can rewrite the given expression as:-
[tex]-1x^2+2x+(-35)[/tex]
Comparing it with the given equation, we get:-
a = -1 , b = 2 , c= -35
Polynomial
A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division (No division operation by a variable).
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will give u brainliest!
Answers
Answer:
3.46
Step-by-step explanation:
[tex]\sqrt{21-9}[/tex]
[tex]\sqrt{12}[/tex]
3.46
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if the least-squares line provides a reasonable model for the data, the pattern of points in the plot will seem random and unstructured about the horizontal line at . is this the case for the residual plot?
Answers
Yes. The residuals' distribution pattern resembles a haphazard dispersion around the horizontal line at 0.
The horizontal plot in this instance comprises points that are unstructured and randomly dispersed around the horizontal mean line.
These are also points below the mean above the mean. This shows that some points in the distribution of data points are above and some are below the least square line, which crosses through the distribution.
The least-square line model would not produce adequate results if, in a residual plot, the majority of the data points are located roughly in a straight line or on either side of the horizontal line.
A residual plot must have data points randomly distributed on both sides of the horizontal mean line in order to produce good results.
To know more about Residual plots, refer to this link:
https://brainly.com/question/16821224
#SPJ4
COMPLETE QUESTION:
if the least-squares line provides a reasonable model for the data, the pattern of points in the plot will seem random and unstructured about the horizontal line at 0. is this the case for the residual plot?