Answers
Answer:
The correct option is C.
Step-by-step explanation:
From the given figure it is clear that the vertices of the parallelogram are (0,0), (0,-6), (4,-8) and (4,-2).
If a figure rotated 180° about (a,b), then
[tex](x,y)\rightarrow (2a-x,2b-y)[/tex]
If the figure rotated 180° about (2,-4), then
[tex](x,y)\rightarrow (2(2)-x,2(-4)-y)[/tex]
[tex](x,y)\rightarrow (4-x,-8-y)[/tex]
So, the vertices of image after rotated 180° about (2,-4) are
[tex](0,0)\rightarrow (4,-8)[/tex]
[tex](0,-6)\rightarrow (4,-2)[/tex]
[tex](4,-8)\rightarrow (0,0)[/tex]
[tex](4,-2)\rightarrow (0,-6)[/tex]
The vertices of image are same as vertices of preimage. So, 180° rotation about (2,-4) maps the figure onto itself.
Therefore the correct option is C.
Related Questions
The quotient of -18 and the sum of -2 and d
Answers
The quotient of -18 and the sum of -2 and d: - 18 / (d - 2)
answer
- 18
---------
d - 2
The quotient of -18 and the sum of -2 and d can be represented mathematically as -18 ÷ (d - 2), where we subtract 2 from d and then divide -18 by that result.
Explanation:The quotient of -18 and the sum of -2 and d refers to dividing -18 by the result of adding -2 to d (which we can represent as d - 2 because adding a negative number is equivalent to subtracting). Mathematically, we can express this as -18 ÷ (d - 2).
To perform this operation, we first need to know the value of d. Once we have that, we subtract 2 from it, and then divide -18 by that result.
For example, if d was 4, we would perform the operation as follows: 4 - 2 gives us 2, then -18 ÷ 2 gives us -9. So, the quotient of -18 and the sum of -2 and 4 (d being 4) is -9.
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8 = 16 + 8n what is x
Answers
8 = 16 + 8x
Subtract 16 from both sides
-8 = 8x
Divide by 8 to both sides
-1 = x
x = -1
Find dy/dx by implicit differentiation. y cos x = 5x2 + 3y2
Answers
To find dy/dx by implicit differentiation, differentiate both sides of the equation with respect to x. Apply the product rule and isolate dy/dx by moving terms.
Explanation:To find dy/dx by implicit differentiation, we'll differentiate both sides of the equation with respect to x. Let's start by differentiating y cos x = 5x2 + 3y2:
Using the product rule, we have: dy/dx * cos x + y * (-sin x) = 10x + 6y * dy/dx
Next, isolate dy/dx by moving terms:
dy/dx * cos x - 6y * dy/dx = 10x - y * (-sin x)
dy/dx * (cos x - 6y) = 10x + y * sin x
dy/dx = (10x + y * sin x) / (cos x - 6y)
If y = 6x – 4, which of the following sets represents possible inputs and outputs of the function, represented as ordered pairs?
{(0, –4), (1, 2), (3, 14)}
{(5, 20), (2, 10), (–1, –3)}
{(–3, –15), (6, 25), (3, 5)}
{(4, 18), (0, 10), (0, –2)}
Answers
y = 6x - 4
ur answer is : {(0,-4), (1,2) , 3,14)} <==
What is 7% of 20.00
Answers
Answer:
Different cities have different levels of sales tax for items purchased. Find each amount of sales tax?
What is 10% of $19.90?
$1.99
What is 7% of $20.00?
$1.40
Right on edge
Step-by-step explanation:
7 percent of the number 20.00 is 1.4.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
Given that, 7% of 20.00
A percentage is a number or ratio that can be expressed as a fraction of 100.
Let x be the 7% of 20.00.
Here, 7% of 20.00 =x
7/100 ×20.00 =x (word "of" means multiplication)
0.07×20.00 =x
x=1.4
Therefore, 7 percent of the number 20.00 is 1.4.
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Can you help me with this, please?
Write an equation for each sentence.
The sum of 4x and -3 is 8
An athlete trains for 115 min each day for as many days as possible. Write an equation that relates to the number of days (d) that the athlete spends training when the athlete trains for 690min.
Answers
(Hopefully)
As for the second one, I ASSUMED it would be this but I'm kinda busy and my ADHD brain just needed a break from what I was doing so just equate it for me, will you? And tell me if I was right or wrong because I have NO IDEA what I'm doing.
Let the number of days he trains for be x
So, 115x = 690
Please show me the steps, I need to learn this:
Simplify: (5/3+i)
Answers
You lose one quarter, two dimes, and two nickels. Write the amount as a decimal.
Answers
2 dimes = 2(0.10) = 0.20
2 nickels = 2(0.05) = 0.10
for a total of : 0.25 + 0.20 + 0.10 = 0.55.....so u have lost 0.55
find values of x and y show your work
Answers
4y+8=24 y =4 4(4)=8= 16+8=24
24 = 4y + 8
24 - 8 = 4y
16 = 4y
y= 16÷4
y = 4
The side that has length 31 equals to 7x - 4
7x - 4 = 31
7x = 31 + 4
7x = 35
x = 35 ÷ 7
x = 5
Y=x3, vertically stretch by a factor of 4. How would the final equation look like?
Answers
a vertical stretch means that if (a, b) is in the original function, the second function will contain the point:
(a, 4b)
For example: (2, 8) is in the graph of the original function.
If the graph of the function is stretched vertically by a factor of 4, this means that (2, 8) becomes (2, 8*4)=(2, 32)
So to describe this stretch, the equation must be [tex]y=4x^3[/tex]
Answer: [tex]y=4x^3[/tex]
Vertically stretching the equation[tex]Y=x^3[/tex] by a factor of 4 results in the equation [tex]Y=4x^3[/tex]. This means that the value of the function increases four times for every x. Visually, the stretched function appears steeper along the y-axis.
Explanation:The equation represents[tex]Y=x^3[/tex] a cubic function. When you vertically stretch a function by a factor of 4, this means you multiply the output (Y-values) of the function by 4. Therefore, to vertically stretch Y=x3 by a factor of 4, you will multiply the entire function by 4. The final equation would look like [tex]Y=4x^3[/tex]
To clarify, the 'stretch' implies that for each x, the value of the function increases four times. This change can is noticeable graphically as the function will look 'steeper' or 'more stretched out' along the y-axis.
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Find the missing term.
The sum of______ and 7x2 is 10x2.
A: -3x^2
B: 3x^2
Answers
SELECT ALL THAT APPLY.
Which of the following is true of an outlier?
An outlier is a false data point.
An outlier does not affect measures of central tendency.
An outlier is not near the main cluster of data.
An outlier is always the highest or lowest value in a data set.
Answers
An outlier is a data point that is significantly different from the other data points in a set. It may or may not affect measures of central tendency. Outliers are not always the highest or lowest values in a data set.
Explanation:An outlier is a data point that is significantly different from the other data points in a set. It can be either higher or lower than the other values.
Outliers may be errors or abnormal data, or they may provide valuable insights into the population under study.
An outlier does not necessarily mean that it is a false data point. It needs to be examined closely to determine if it should be included in the analysis or not.
An outlier may or may not affect measures of central tendency, such as the mean, median, and mode.
It depends on the specific data set and the impact of the outlier on these measures. It is not always the highest or lowest value in a data set, as it can be any data point that deviates significantly from the rest.
PLEASE HELP on these problems! I really need the help and these are due in a few hours. Very urgent. I would really appreciate the help, so please help!!!
1. If f(x) = a(r)^x is an example of exponential decay, what must be the value of a and r?
2. The population of Greenfield was 52,500 at the beginning of 1980. Its population steadily decreased by 2.5% per year from 1980 through 1990. What is the population of Greenfield at the end of 1990?
3. If g(x) is the inverse of f(x) - 2x + 1, find a point on g(x) for which both coordinates are positive integers less than 10.
Answers
For 2, we apply that formula, getting 52500*(1-2.5%)^10 (because it's for 10 years and compounded annually). Since 100% is 1, 2.5% is 0.025, and
1-0.025=0.975. Plugging that in, we get 52500*(0.975)^10=around 40757 people.
For inverse functions, what we do is have y=2x+1, so we switch x and y and solve for y, so in x=2y+1 we subtract one from both sides to get x-1=2y. Next, dividing both sides by 2, we get (x-1)/2=y as our inverse. Since we want positive integers less than 10, (x-1) has to be even and therefore x has to be odd. Using a bit of guess and check, we get that x can be 9 while y can be 4 for (9, 4)
A spherical tank has a capacity of 400 gallons. using the fact that 1 gallon is about 0.1337 ft3, find the radius of the tank (to the nearest hundredth of a foot).
Answers
Final answer:
To find the radius of a spherical tank with a capacity of 400 gallons, calculate the volume and use the formula for the volume of a sphere.
Explanation:
A spherical tank has a capacity of 400 gallons, which is approximately 533.47 ft³ (400 gallons x 0.1337 ft³/gallon).
To find the radius, use the formula for the volume of a sphere: V = (4/3)πr³. Set this equal to the volume and solve for the radius.
Substitute the volume (533.47 ft³) into the formula, solve for r, and you will find that the radius is approximately 4.88 feet.
How many terms are in the algebraic expression 11;; +3 ?
Answers
What is the probability of winning three games in a row, if the probability of winning each game individually is 1/2?
Answers
P(winning 1 AND 2 GAMES) (1/2)(1/2) = 1/4 = 0.25
P(winning 1 AND 2 GAMES AND 3 GAMES)= (1/2)(1/2)(1/2) = 1/8 = 0.125
Find the equation of the circle in standard form for the given center (h,k) and radius r: (h,k)=(0,0), r=9
Answers
Answer: [tex]x^2+y^2=81[/tex]
Step-by-step explanation:
The equation of circle ( in general form ) is given by :_
[tex](x-h)^2+(y-k)^2=r^2[/tex]
, where r= radius of the circle .
(h,k) = center of the circle .
Given : Center = (h,k)= (0,0)
Radius = r = 9 units
Then the equation of the circle will be :-
[tex](x-0)^2+(y-0)^2=(9)^2[/tex]
[tex]\Rightarrow x^2+y^2=81[/tex]
Hence, the required equation of the circle = [tex]x^2+y^2=81[/tex]
Describe all solutions to ax = 0 in parametric vector form, where a is row equivalent to the given matrix.
Answers
Final answer:
The solutions to ax = 0 are all vectors in the null space of the matrix a. These solutions can be expressed as a parametric vector form, which may involve free variables if the matrix a has any. The general solution is a linear combination of the basis vectors for this null space.
Explanation:
The question is asking to describe all solutions to the equation ax = 0 in parametric vector form, given that a is row equivalent to a certain matrix. This matrix is understood to allow a decomposition of a vector into its perpendicular components. Such a matrix transformation typically reduces to finding the null space of the matrix.
To find the solution to ax = 0, we understand that any vector x that satisfies this equation is in the null space of a. The null vector is the most trivial solution, where all components of the vector are zero. But if there are free variables involved, the solutions may form a subspace spanned by these free variables. The general solution can then be expressed as a linear combination of these basis vectors that span the null space of a.
For instance, if our matrix a has one free variable, the parametric vector form of the solution might be t[1,0,0] if the first column of a is the pivot column and the rest are free columns. Here, t would be any scalar, representing a line through the origin in the direction of the vector [1,0,0] in three-dimensional space.
How to prove that two angles are complementary when two lines are perpendicular to each other?
Answers
In an election with exactly 2 candidates, 373 votes were cast. If the winner's margin of victory was 87 votes, how many did she receive?
Answers
number of votes the winner received = x + 87
total number of votes = 2x + 87
2x + 87 = 373
2x = 286
x = 143
number of votes the winner received = 143 + 87
= 230
She received 230 votes.
Which Algebraic expression has a term with a coefficient of 3?
A:5y-7
B:-2y+5+3
C:3(y-6)
D:3y+1
Answers
Answer:
D:3y+1
Step-by-step explanation:
find the Algebraic expression has a term with a coefficient of 3
The number before the variable is the coefficient
A:5y-7
y has a coefficient of 5
B:-2y+5+3
y has a coefficient of -2
C:3(y-6)
y or 1y are same
Here , y has a coefficient of 1
D:3y+1
y has a coefficient of 3
What is the measure of ∠B?
Answers
m<B = 360 - 285
m<B = 75
A 12 foot ladder is placed 4 feet away from a house as shown. What is the value of x, rounded to the nearest degree ?
Answers
cos(x) = adjacent/hypotenuse = 4/12 ≈ 0.3333 ⇒ x ≈ 71°
#2
71° is between 70° and 75°, so the answer is yes, the ladder being used safely.
x = 71 degrees. Yes, the ladder meets safety standards.
What is Hypotenuse?A hypotenuse is defined as the longest side of a right triangle, the side opposite the right angle where the length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of is the square of the lengths of the other two sides.
The equation is expressed as:
[tex]a^2 + b^2 = c^2[/tex]
a = side of right triangle
b = side of right triangle
c = hypotenuse
For above given information, the problem describes a right triangle with hypotenuse 12, the side against the ground is 4, and the angle between those two sides is "x".
For this triangle,
cosx = (side adjacent to angle) / hypotenuse
= 4 /12= 1/3
x is approximately 70.52° which is 71° rounded to the nearest degree.
Thus, x = 71 degrees. Yes, the ladder meets safety standards.
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Find an equation of the vertical line that passes through (x, y) = (14, 15).
Answers
Final answer:
The equation of the vertical line passing through the point (14, 15) is x = 14.
Explanation:
To find an equation of a vertical line that passes through the point (14, 15), we need to understand that a vertical line has an undefined slope and therefore cannot be represented by the slope-intercept form of a line, y = mx + b. Instead, vertical lines are represented by equations where x is equal to a constant value since every point on the vertical line will share the same x-coordinate. Thus, the equation of the vertical line passing through (x, y) = (14, 15) is simply x = 14.
The equation below shows the relationship between the temperature in degrees Celsius, C, and degrees Fahrenheit, F.
F = 9 over 5C + 32
Which of the following formulas correctly solves for C?
C = 5F - 32 over 9
C = 5 F over 9 - 32
C = 9 over 5(F – 32)
C = 5 over 9(F – 32)
Answers
F - 32 = 9/5C...multiply both sides by 5/9, eliminating the 9/5 on right
5/9(F - 32) = C <==
Answer:
C = 5 over 9(F – 32)
Step-by-step explanation:
The formula is [tex]F=(\frac{9}{5}C)+32[/tex]
We can do some algebra to solve for C (note the steps below):
[tex]F=(\frac{9}{5}C)+32\\F=(\frac{9C}{5})+32\\F-32=\frac{9}{5}C\\C=\frac{F-32}{\frac{9}{5}}\\C=\frac{5}{9}(F-32)[/tex]
Last answer choice is right.
For sisters bought a present for their father. They recieved a 10% discount on the original price of the gift . after the discount wss taken , each sister paid $9.00. What was the original price of the gift
Answers
x-0.1*x=0.9*x due to that we subtract the 10% discount (and it's 10% of the original price). In addition, the sisters paid 0.9*x, which is 36. Dividing both sides by 0.9, we get x=40
Paula has 24 coins in her drawer. seven of the coins are nickels and the rest are pennies. what is the total value in cents of the coins in her drawer?
Answers
24-7=17
17
pennies
7 nickles
total value is
5(7)+1(17)=35+17=52
cents
A restaurant worker server earns a base salary of $6 per hour plus tips. If he averages $12 per hour in tips, how many hours must he work to earn a total of $333?
Answers
To solve this problem, you first need to figure out the average amount of money per hour the worker earns.
That would be the base salary plus the average tips per hour. So
$6 + $12 = $18
Then to figure out how many hours the worker needs to work, divide the goal by the hourly earnings. So
$333 / $18 = 18.5 hours.
Therefore on average, it will take 18.5 hours to earn $333, assuming a base salary of $6/hour and an average of $12 in tips per hour.
What is the difference between independent and conditional probability? Which one requires the use of the Addition Rule?Explain.
Answers
Conditional probability means that an event happening only happened because another even had already occurred.
The addition rule i believe is a Conditional probability
hope this helps
Answer:
In probability, independent events are those that if one event occurs, it does not change the probability of the other event.
Whereas conditional probability is defined as the probability of one event occurring with some relationship to one or more other events.
The addition rule is used for both the independent and conditional probabilities.
For independent event the probability is shown as :
[tex]P(YorZ)=P(Y)+P(Z)[/tex]
For conditional: [tex]P(YorZ)=P(Y)+P(Z)-P(YandZ)[/tex]
Does every number have two qualities