Answers
If a figure has a vertex, (x, y) and it is rotated 180 degrees counterclockwise, the corresponding vertex of the new image would have a coordinate of (- x, - y)
Looking at the given figure, we would compare the corresponding coordinates of a given vertex. Looking at vertex A,
For the original figure, the coordinate is (1, 3)
For the ratated figure, the coordinate of A' is (- 1, - 3)
This corresponds to what was we stated earlier
Thus, it was rotated 180 degrees in the counterclockwise direction
Related Questions
Remmy establishes a loan for an $8000 vacation package to Transylvania. The vacation company charges 5.5% simple interest rate. Remy plans to pay back the loan over 1.5 years.How much interest will Remmy pay?
Answers
Remmy will pay $660 interest.
Step - by - Step Explanation
What to find? The amount of interest to be paid.
Given Parameters:
• Principal (P) = $8000
,• Rate of interest(R) = 5.5
,• Time(t in years) = 1.5
The formula for calculating simple interest is given below:
[tex]S.I=\frac{P\times R\times T}{100}[/tex]Where P is the principal.
R represents the rate.
T is the time given in years.
S.I is the simple interest.
Substitute the values into the formula and simplify.
[tex]S.I=\frac{8000\times5.5\times1.5}{100}[/tex][tex]S.I=\frac{80\cancel{00}\times5.5\times1.5}{1\cancel{00}}[/tex][tex]=80\times5.5\times1.5[/tex]= 660
Hen
Which operation results in a binomial?+(3y6 + 4)(9y12 - 12y6 + 16)ResetNextntum. All rights reserved.
Answers
Answer:
Explanations:
According to the question, we need to determine which of the signs will fit in that will make the expression a binomial.
In simple terms, a binomial is a two-term algebraic expression that contains variable, coefficient, exponents, and constant.
We need to determine the required sign by using the trial and error method.
Using the positive sign (+) first, we will have:
[tex]\begin{gathered} =\mleft(3y^6+4\mright)+(9y^{12}-12y^6+16) \\ =3y^6+4+9y^{12}-12y^6+16 \\ =3y^6-12y^6+4+9y^{12}+16 \\ =-9y^6+9y^{12}+20 \end{gathered}[/tex]Using the product sign, this will be expressed as:
[tex]\begin{gathered} (3y^6+4)\cdot(9y^{12}-12y^6+16) \\ (3y^6+4)\cdot\lbrack(3y^6)^2-(3y^6)(4)^{}+4^2)\rbrack \end{gathered}[/tex]According to the sum of two cubes;
[tex]a^3+b^3=\mleft(a+b\mright)•(a^2-ab+b^2)[/tex]Comparing this with the expression above, we will see that a = 3y^6 and
b = 4. This means that the resulting expression above can be written as a sum of two cubes to have;
[tex]\begin{gathered} (3y^6+4)\cdot\lbrack(3y^6)^2-(3y^6)(4)^{}+4^2)\rbrack^{} \\ =(3y^6)^3-4(3y^6)^2+4(3y^6)^2+16(3y^6)+4(3y^6)^2-16(3y^6)+4^3 \\ \end{gathered}[/tex]Collect the like terms:
[tex]undefined[/tex]Determine if the situation below are biased or unbiased and explain why. Two people from each 8th period class are askedwhat they think the theme of the next dance shouldbe.
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Answer
The situation is not biased because it takes a random sample from each group.
What are the lengths of segments PQ and QR? input the lengths. then click done.
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The length of a room is twice as its breadth and breadth is 6 cm. If it's height is 4 cm, find the total surface area.
Answers
The breadth of the room = 6 cm
Since the length of the room is twice its breadth
Then
Length of the room = 2 times 6cm = 12cm
The height of the room = 4cm
Since the shape of the room is a cuboid
The surface area of a cuboid is given as
[tex]SA=2(lh+lw+hw)[/tex]Substitute l = 12, w = 6 and h = 4 into the formula
This gives
[tex]SA=2(12\times4+12\times6+4\times6)_{}[/tex]Simplify the expression
[tex]\begin{gathered} SA=2(48+72+24) \\ SA=2(144) \\ SA=288 \end{gathered}[/tex]Therefore, the total surface area of the room is
[tex]288cm^2[/tex]state income tax? Jim Koslo earns $156,200 annually as a plant manager. He is married and supports 3 children. The state tax rate in his state is 3.55% of taxable income. What amount is withheld yearly for state income tax?
Answers
Answer:
44,000
Let me know if its wrong
Karen has 5 more quarters than dimes. She has $3.70. How many quarters and dimes she have?
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A dime is 10% of a dollar = 10/100 x 100 cent = 10 cents
A quater is 25% of a dollar = 25/100 x 100 cent = 25 cents
Since Karen has 5 more quaters than dimes
let quaters = q
let dimes = d
Then Karen has 5q : d = $ 3.70
$ 3.70 = 3.70 x 100 cents = 370 cents
Express the repeating decimal 0.2 as a fraction
Answers
Answer:
The fraction form of the repeating decimal is;
[tex]\frac{2}{9}[/tex]Explanation:
We want to express the repeating decimal 0.2 (2 repeating) as a fraction.
let x represent the fraction;
[tex]\begin{gathered} x=0.2222\ldots \\ 10x=2.222\ldots \end{gathered}[/tex]Then subtract x from 10x;
[tex]\begin{gathered} 10x-x=2.222\ldots-0.222\ldots \\ 9x=2.0 \end{gathered}[/tex]Then we can divide both sides by the coefficient of x;
[tex]\begin{gathered} \frac{9x}{9}=\frac{2}{9} \\ x=\frac{2}{9} \end{gathered}[/tex]Therefore, the fraction form of the repeating decimal is;
[tex]\frac{2}{9}[/tex]Bobby says the dilation can be represented by (1\3X, 1,\3Y)Betty says the dilation can be represented by (3X, 3Y)who is correct and why?
Answers
Bobby is right because the measurements were made smaller so the dilation factor must be a number less than 1, and 1/3 is less than 1
Instructions: Find the value of the trigonometric ratio. Makesure to simplify the fraction if needed.
Answers
sin C = 3/5
Explanation:Given:
CB = 32
AC = 40
AB = 24
To find:
sin C
To determine sinC, we will apply the sine ratio:
[tex]\begin{gathered} sin\text{ C = }\frac{opposite}{hypotenuse} \\ \\ oppoite\text{ =side opposite the angle = AB = 24} \\ hyp\text{ = 40} \end{gathered}[/tex][tex]\begin{gathered} sin\text{ C}=\text{ }\frac{24}{40} \\ \\ sin\text{ C}=\text{ }\frac{3}{5} \end{gathered}[/tex]1.- (picture) 2.-Assuming that the global population is seven billion and that no person receives the letter more than once, the maximum number of mailings is fourteen. Suppose that you are one of the recipients of mailing number 8 and there are ten names on the list (so your five outgoing letters will be in mailing number 9 and there will be nine names above yours on the list). If everyone who receives the letter participates, how much money will you receive?$
Answers
Kindly check below
Question 1) We can see that in the column "number of recipients" there is a Geometric Sequence whose common ratio is 5.
2) Therefore, we can fill in those gaps with the following:
[tex]\begin{gathered} Number\:of\:mailings|\:Number\:of\:recipients \\ 1\:|\:5 \\ 2\:|\:25 \\ 3\:|\:125 \\ 4\:|\:625 \\ 5\:|\:3125 \\ 6\:|\:15625 \\ 7\:|\:78125 \\ 8\:|\:390625 \\ 9\:|\:1953125 \\ 10\:|\:9765625 \\ 11\:|\:48828125 \\ 12\:|\:244140625 \\ 13\:|\:1220703125 \\ 14\:|\:6103515625 \\ \\ % \end{gathered}[/tex]3) Thus is the table.
Mary Bought her car for $20,000. After 5 years she decided to sell her car for a 25% increase invalue. What is the price that Mary decided to sell her car for?
Answers
Original Car price = $20,000
Price increase after 5 years = 25%
To calculate the price after 5 years, first multiply the original price (20,000) by the percentage increase in decimal form ( divided by 100) to obtain the increase amount:
20,000 x (25/100) = 20,000 x 0.25 = $5000
Finally, add the increase amount to the original price:
20,000+5,000 = $25,000
2) Corresponding angles are congruent L1 II L2 (2x + 20) (3x - 10)
Answers
Given angles are corresponding angles, they are congruent (have the same measure):
[tex](2x+20)=(3x-10)[/tex]Use the equation above to solve x;
[tex]\begin{gathered} 2x+20=3x-10 \\ \\ \text{Subtract 3x in both sides of the equation:} \\ 2x-3x+20=3x-3x-10 \\ -x+20=-10 \\ \\ \text{Subtract 20 in both sides of the equation:} \\ -x+20-20=-10-20 \\ -x=-30 \\ \\ \text{Multiply both sides of the equation by (-1):} \\ (-1)(-x)=(-1)(-30) \\ \\ x=30 \end{gathered}[/tex]You use the value of x=30 to find the measure of corresponding angles:
[tex]\begin{gathered} 2x+20 \\ 2(30)+20=80 \end{gathered}[/tex]Then, the meaure of the corresponding angles is 80°To prepare for disinfection of hard nonporous surfaces against canine parvovirus, mix a solution of bleach in 2.5 gallons of water at the rate of ¾ cup of bleach per 1 gallon of water. What is the volume of bleach added to the 2.5 gallons of water? a. 30 fl. oz b.15 fl. oz c.1 ¾ cups d.1 ½ cups and 2 tbsp
Answers
Answer:
b. 15 fl. oz
Explanation:
From the question, we are told that 3/4 cup of bleach is needed per 1 gallon of water.
Thus:
[tex]\begin{gathered} 1\text{ gallon of water requires }\frac{3}{4}\text{ cup of bleach} \\ \implies2.5\text{ gallons will require }\frac{3}{4}\times2.5\text{ cups of bleach} \\ \frac{3}{4}\times2.5=1\frac{7}{8}\text{ cups} \end{gathered}[/tex]Next, we represent the result in the form of the given options:
Using the standard rate of conversion: 1 cup = 8 fl. oz
[tex]\begin{gathered} 1\text{ cup}=8\text{ fl.oz} \\ \implies1\frac{7}{8}\text{ cups}=8\times1\frac{7}{8}floz=8\times\frac{15}{8}=15fl.oz \end{gathered}[/tex]The volume of bleach added to 2.5 gallons of water is 15 fl. oz.
xin uses 20 yards of fencing to build the walls of a square Chicken Coop which equation and solution represents x, the length, in yards, of each wall of the square coop?A: [tex]x + 4 = 20 \\ x = 16[/tex]b:[tex]x + 4 = 20 \\ x = 24[/tex]c:[tex]4x = 20 \\ x = 80[/tex]d:[tex]4x = 20 \\ x = 5[/tex]
Answers
Since the coop is in square shape The fencing is in the shape of a square
So equation is 4x=20, x=5
Find the degree measure of the central angle for sector C. (image attached)
Answers
We will determine the angle as follows:
We know that the whole circle contains 360°, so we determine the angle of 0.35 as follows:
[tex]C=\frac{0.35\ast360}{1}\Rightarrow C=126[/tex]So, the measure of the central angle for sector C is 126°.
Penelope graphed the function below using the domain { 0,1,2,3,4 } .X + y = 4 Which graph did Penelope make ?
Answers
Given data:
The given equation x+y=4.
Substitute 0 for x in the given equation.
0+y=4
y=4.
Substitute 0 for y in the given equation.
x+0=4
x=4
So, the graph of the equation must pass from (0,4) and (4,0).
Thus, the option (a) is correct.
Help!
find all zeros of p(x). include any multiplicities greater than one.
Answers
The most appropriate choice for polynomial will be given by
1) Zeroes of P(x) = 2, [tex]\frac{2 + \sqrt{2}i}{3}[/tex], [tex]\frac{2 - \sqrt{2}i}{3}[/tex]
where [tex]i = \sqrt{-1}[/tex]
2) Zeroes of P(x) = 3, 2i, -2i
3) Roots are 2i, -2i, [tex]\frac{3}{2}[/tex]
4) Roots are 0, 1, [tex]2 + \sqrt{5}[/tex], [tex]2 - \sqrt{5}[/tex]
What is a polynomial?
An algebraic expression of the form [tex]a_0 + a_1x +a_2x^2 + a_nx^n[/tex] is called a polynomial of degree n.
[tex]1) P(x ) = 3x^3 -10x^2 + 10x -4\\P(2) = 3(2)^3 - 10(2)^2 +10(2) - 4\\[/tex]
[tex]= 24 -40 + 20 -16\\= 0[/tex]
(x - 2) is a factor of P(x)
[tex]P(x) = 3x^2(x - 2) -4x(x - 2) +2(x-2)\\[/tex]
= [tex](x - 2)(3x^2 - 4x + 2)[/tex]
[tex]=(x-2)(x -a)(x - b)[/tex]
where,
[tex]a = \frac{-(-4)+\sqrt{(-4)^2 - 4\times 3\times 2}}{2\times 3}\\a =\frac{ 4 + \sqrt{-8}}{6}\\a = \frac{4 + 2\sqrt{2} i}{6}\\a = \frac{2(2 + \sqrt{2}i)}{6}\\a = \frac{2 + \sqrt{2}i}{3}[/tex]
[tex]b = \frac{-(-4)-\sqrt{(-4)^2 - 4\times 3\times 2}}{2\times 3}\\b =\frac{ 4 -\sqrt{-8}}{6}\\b = \frac{4 - 2\sqrt{2} i}{6}\\b = \frac{2(2 - \sqrt{2}i)}{6}\\b = \frac{2 - \sqrt{2}i}{3}[/tex]
Zeroes of P(x) = 2, [tex]\frac{2 + \sqrt{2}i}{3}[/tex], [tex]\frac{2 - \sqrt{2}i}{3}[/tex]
where [tex]i = \sqrt{-1}[/tex]
[tex]2) P(x) = x^3 - 3x^2+4x-12\\P(3) = (3)^3 - 3(3)^2 +4(3) -12\\ P(3) = 0[/tex]
(x - 3) is a factor of P(x)
[tex]x^2(x - 3) + 4(x - 3)\\(x - 3)(x^2 + 4)\\(x - 3)(x -a)(x-b)\\[/tex]
where,
[tex]a = \sqrt{-4}\\a = 2i[/tex]
[tex]b = -\sqrt{-4}\\a = -2i[/tex]
Zeroes of P(x) = 3, 2i, -2i
[tex]3) 2x^3 - 3x^2 +8x-12= 0\\[/tex]
x = 2 satisfies the equation
[tex]2x^2(x -\frac{3}{2}) + 8(x-\frac{3}{2})=0\\(2x^2+8)(x - \frac{3}{2}) = 0\\[/tex]
[tex]2x^2 + 8 = 0[/tex] or [tex]x - \frac{3}{2} = 0[/tex]
[tex]x^2 = -\frac{8}{2}[/tex] or [tex]x = \frac{3}{2}[/tex]
[tex]x^2 = -4[/tex] or [tex]x = \frac{3}{2}[/tex]
[tex]x = \sqrt{-4}[/tex] or [tex]x = \frac{3}{2}[/tex]
[tex]x = 2i[/tex] or [tex]x = -2i[/tex] or [tex]x = \frac{3}{2}[/tex]
Roots are 2i, -2i, [tex]\frac{3}{2}[/tex]
4)
[tex]x^4 - 5x^3 +3x^2 +x = 0\\x(x^3 -5x^2 + 3x +1) = 0\\[/tex]
[tex]x = 0[/tex] or [tex]x^3 -5x^2+3x +1 = 0[/tex]
For [tex]x^3 -5x^2+3x +1 = 0[/tex]
x = 1 satisfies the equation
[tex]x^2(x -1) -4x(x-1)-1(x-1) = 0\\(x - 1)(x^2 - 4x -1) = 0\\[/tex]
[tex]x -1 = 0[/tex] or [tex]x^2 - 4x -1 = 0[/tex]
Roots are x = 1 or x = a or x = b
where,
[tex]a = \frac{-(-4) + \sqrt{(-4)^2 - 4\times 1 \times(-1)}}{2\times 1}\\a = \frac{4+\sqrt{20}}{2}\\a = \frac{4 + 2\sqrt{5}}{2}\\a = \frac{2(2 + \sqrt{5})}{2}\\a = 2 + \sqrt{5}[/tex]
[tex]b = \frac{-(-4) - \sqrt{(-4)^2 - 4\times 1 \times(-1)}}{2\times 1}\\b = \frac{4-\sqrt{20}}{2}\\b = \frac{4 - 2\sqrt{5}}{2}\\b = \frac{2(2 - \sqrt{5})}{2}\\b = 2 - \sqrt{5}[/tex]
Roots are 0, 1, [tex]2 + \sqrt{5}[/tex], [tex]2 - \sqrt{5}[/tex]
To learn more about polynomial, refer to the link-
https://brainly.com/question/2833285
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f(x) = x ^ 3 + 3x ^ 2 + 4x + 5 and g(x) = 5 , then g(f(x)) =
Answers
we have the functions
[tex]\begin{gathered} f\mleft(x\mright)=x^3+3x^2+4x+5 \\ g(x)=5 \end{gathered}[/tex]so
g(f(x))=5What did the student do incorrectly in this problem? Thanks for the help!
Answers
Solution
We have the function
[tex]f(x)=\frac{(5x-2)(x-1)}{(x-1)(x+2)}[/tex]The graph of the function is
14 POINTS!!!!! BRAINLY!!!!A lamp produced a shadow of a man standing in the middle of a stage.How long is the shadow.A 9.60B 11.38C 20.98D 22.51
Answers
Given the graph:
The length of the shadow = y - x.
• To find x:
[tex]\begin{gathered} tan21\text{\degree}=\frac{opposite}{adjacent} \\ \\ tan21\text{\degree}=\frac{x}{25} \\ \\ x=25\times tan21\text{\degree = 9.6m} \end{gathered}[/tex]• To find y:
[tex]\begin{gathered} tan40\text{\degree}=\frac{y}{25} \\ \\ y=25\times tan40\text{\degree}=21m \end{gathered}[/tex]Length of the shadow:
[tex]\begin{gathered} length=21-9.6 \\ \text{ }=\text{ 11.4 m} \end{gathered}[/tex]ANSWER
Length of the shadow = 11.4 m
1(c). What is a better deal? Explain. Deal 1: 2 mediums 14'' (round) pizza for $14 total Deal 2: 1 large 20'' (round) pizza for $13 total
Answers
To get the better deal of the two, we need to find the cost per area of pizza for each deal and compare.
Deal 1: 2 medium 14'' (round) pizza for $14 total
The area of a circle is calculated as
[tex]A=\pi r^2[/tex]where r is the radius.
The area of the pizza is calculated to be:
[tex]\begin{gathered} r=14 \\ \therefore \\ A_1=\pi\times14^2=196\pi \end{gathered}[/tex]Hence, the total area for the two pizzas will be:
[tex]\Rightarrow196\pi\times2=392\pi[/tex]The cost per square inch of pizza is, therefore, calculated to be:
[tex]\Rightarrow\frac{14}{392\pi}=0.011[/tex]The pizza costs $0.011 per square inch.
Deal 2: 1 large 20'' (round) pizza for $13 total
The area of the pizza is calculated to be:
[tex]\begin{gathered} r=20 \\ \therefore \\ A_2=\pi\times20^2=400\pi \end{gathered}[/tex]Hence, the cost per square inch of pizza is calculated to be:
[tex]\Rightarrow\frac{13}{400\pi}=0.010[/tex]The pizza costs $0.010 per square inch.
CONCLUSION:
The better deal will be the deal with the lesser cost per square inch. As can be seen from the calculation, both deals are about the same price per square inch if approximated. However, without approximation, Deal 2 has a slightly lesser cost per square inch.
Therefore, DEAL 2 IS THE BETTER DEAL.
The population of a school of fish decreases at a rate of 18% per month. There are currently500 fish in the school. How many fish will there be in 3 months?
Answers
Population decreasing rate is
18% monthly
Actual population = 500
Then
In 1 month decreases (500/100)• 18 = 90
Population = 500-90= 410
No find (410/100)•18 = 73.8
410-73.8= 336.2
In 3 months
(336.2/100) •18 = 60.5
336.2 - 60.5 = 276 fishes
ANSWER IS 276 fishes remain
Use compatible numbers to determine if 455+ 229 is more than 650
Answers
Step 1
compatible numbers are the numbers that are easy to add, subtract, multiply, or divide mentally.
Step 2
Math problem
455 + 229
Compatible numbers
455 + 225 = 680
680 is close to 455+229 = 684
Step 3:
Hence
By compatible numbers, 455 + 229 is more than 650.
True or False. The graph is linear, but not proportional.
Answers
Answer:
True.
The graph is linear, but not proportional.
Explanation:
Given the graph in the attached image;
The graph is linear because it is a straight line graph.
A linear graph is always straight.
A proportional relationship in which the two components have a constant ratio.
The proportional graph is a straight line graph that passes through the origin (0,0).
Since the given graph does not pass through the origin, it is not a proportional graph.
Therefore, The graph is linear, but not proportional.
find the value of the 30th percentile of the following set of data
Answers
The given data is:
[tex]18,9,7,5,11,7,17,20,19,2,17,12,5,1,13,12,11,15,16,20[/tex]Rearrange the data in ascending order:
[tex]1,2,5,5,7,7,9,11,11,12,12,13,15,16,17,17,18,19,20,20[/tex]Find a polynomial function of lowest degree with rational coefficients that has the
given numbers as some of its zeros.
√3,51
The polynomial function in expanded form is f(x) =
Answers
Answer: [tex]f(x)=x^3 -51x^2 -3x+153[/tex]
Step-by-step explanation:
By the conjugate root theorem, the roots are [tex]\sqrt{3}, -\sqrt{3}, 51[/tex].
Letting the leading coefficient be 1,
[tex]f(x)=(x-\sqrt{3})(x+\sqrt{3})(x-51)\\\\=(x^2 -3)(x-51)\\\\=x^3 -51x^2 -3x+153[/tex]
In class, we determined that 11 peoplewould fit comfortably in a 5 ft by 5 ftsquare. How many square feet wouldeach person require?
Answers
We have to first determine the area of the square. The area of a square can be represented as follows
[tex]\begin{gathered} \text{Area of square = L}^2 \\ L\text{ = 5 ft} \\ \text{Area of square = 5}^2 \\ \text{Area of a square = 25 ft}^2 \end{gathered}[/tex]The number of each square feet each person will requre can be calculated as follows
[tex]\begin{gathered} numbers\text{ of each square ft each person require = 25/11} \\ numbers\text{ of each square ft each person require = }2.27272727273ft^2 \\ numbers\text{ of each square ft each person require }\approx\text{ }2.27ft^2 \end{gathered}[/tex]Solving linear systems graphicallySolving 3 x 3 linear systemsModeling with linear systemsLinear programmingMixed degree systems
Answers
ANSWER:
The system can only be consistent and independent
STEP-BY-STEP EXPLANATION:
We have to:
• If a system has at least one solution, it is said to be consistent.
,• If a consistent system has exactly one solution, it is independent.
,• If a consistent system has an infinite number of solutions, it is dependent
,• If a system has no solution, it is said to be inconsistent
We know that the system has 2 solutions, and we know that the system is only inconsistent when it has no solution, therefore the correct answer is:
The system can only be consistent and independent
Antonio has a balance of $4273.56 on a credit card with an annual percentage rate of 21.1%. He decides to not make any additional purchases with his card until he has paid off the balance. a) Many credit cards require a minimum monthly payment of 2% of the balance. What is Antonio's minimum payment on the balance of $4273.56? b) Find the amount of interest charged this month
Answers
a) To calculate the minimum payment of the balance, you calculate the 2% of $4273.56. You proceed as follow:
(2/100)(4273.56) = 85.47
Hence, the mimum payment of the balance is $85.47
b) You calculate the amount of interest charged this month as follow:
convert the annual percentage rate to decimal form:
21.1/100 = 0.211
divide the previous result by 12 to get the monthly interest rate:
0.2111/12 = 0.0175
multiply the previoues result by the balance:
0.0175 x 4273.56 = 75.143 ≈ 75.14
convert the monthly rate to a percentage:
0.0175 x 100 = 1.75%
Hence, the amount of interest was $75.14, which corresponds to a 1.75%