how to write the rule for #14. if there is no rule, describe the transformation in words.
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Given the Pre-Image (the original figure) JKL, and the Image (the figure after the transformation) J'K'L', you can identify that the vertices of JKL are:
[tex]\begin{gathered} J(-2,-4) \\ K(-2,-2) \\ L(1,-2) \end{gathered}[/tex]And the vertices of the Image are:
[tex]\begin{gathered} J^{\prime}(4,2) \\ K^{\prime}(2,2) \\ L^{\prime}(-1,2) \end{gathered}[/tex]You can notice that the signs of the coordinates of the Image are obtained by multiplying the original coordinates by -1.
By definition, the rule for a Rotation of 180 degrees centered at the Origin is:
[tex](x,y)\rightarrow(-x,-y)[/tex]Hence, the answer is:
[tex](x,y)\rightarrow(-x,-y)[/tex]Related Questions
Which is the image of vertex P after the triangle is rotated 180 degreesabout the origin?
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For this case we know that the vertex P has the following coordinates:
[tex]P=(-3,2)[/tex]And we want to find the coordinates after rotate 180 degrees about the origin we assume that the translation is anticlockwise so then we just need to do the following :
[tex]P^{\prime}=(-x,-y)=(3,-2)[/tex]And then the solution ofr this case would be (3,-2)
How many solutions does the equation (2 sin x + 1)(sin x – 1) = 0 have over the interval 0 ≤ x < 2π?
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The initial equation is
[tex](2\sin x+1)(\sin x-1)=0[/tex]We can expand this expression as shown below
finding radius of cones base when only given the area of the base
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Given
A cone's height is equal to the radius of its base.
And, the base area is 1386 square units.
To find:
The radius and volume of the cone.
Explanation:
It is given that,
A cone's height is equal to the radius of its base.
And, the base area is 1386 square units.
Then,
[tex][/tex]can you pls help me i am unsure of how to solve this
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Since the profit in the first week is $70
Since it increases by $15 each week, then
We can solve it as an arithmetic progression
P = a + (n -1)d, where
a is the profit in the 1st week
d is the value of increasing each week
n is the number of the week
a = 70, d = 15, and n = 12 (12th week)
Substitute these values in the rule above
P = 70 + (12 - 1)(15)
P = 70 + 11(15)
P = 70 + 165
P = 235
The profit during the 12th week is $235
Garrett needs a baseball coach. Coach A is offering her services for an initial $4,800 in addition to $550per hour. Coach B is offering her services for an initial $4,500 in addition to $700 per hour. When will thetwo coaches charge the same amount of money?The two coaches will charge the same amount of money afterhours.
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Let's define
x: time is hours
Coach A services costs 4800 + 550x dollars
Coach B services costs 4500 + 700x dollars
If both coaches charge the same:
4800 + 550x = 4500 + 700x
4500 is adding on the right, then it will subtract on the left
550x is adding on the left, then it will subtract on the right
4800 - 4500 = 700x - 550x
300 = 150x
150 is multiplying on the left, then it will divide on the left
300/150 = x
2 = x
The two coaches will charge the same amount of money after 2 hours.
I’m doing math homework for summer school and I don’t get this . I provided a picture so you can see the problem. Thanks so much -Chris
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Solution:
Given the table;
Thus;
[tex]f(-2)=1[/tex]which of the following properties are used when rewriting the expression
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We note first that outside the parenthesis there is a negative power, besides, the x is in the denominator of a quotien and it is elevated to a power, then we will use the third opcion
negative power and quotient to a power.
what is the measure of
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For the propertie of similar angles we know that the angle J is equal to angle H so:
[tex]\angle H=67[/tex]then we can use the propertie of the sum of the internal angles of a triangle to dind x so:
[tex]x+67+46=180[/tex]and we solve for x
[tex]\begin{gathered} x=180-67-46 \\ x=67 \end{gathered}[/tex]Determine the number of solutions for the following system of linear equations. If there is only onesolution, find the solution.- 5x + 2y + 6z = -2x + 3y + 4z = - 36x + y – 2z = -1AnswerKeypadKeyboard ShortcutsSelecting an option will enable input for any required text boxes. If the selected option does not have anyassociated text boxes, then no further input is required.O No SolutionO Only One Solution=こ%3DO Infinitely Many Solutions
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We are given the following system of linear equations
[tex]\begin{gathered} -5x+2y+6z=-2 \\ x+3y+4z=-3 \\ 6x+y-2z=-1 \end{gathered}[/tex]Let us solve the given system of equations.
First, let us find the determinant.
The determinant is given by
[tex]\begin{gathered} D=\begin{bmatrix}{-5} & 2 & {6} \\ {1} & {3} & {4} \\ {6} & {1} & {-2}\end{bmatrix}=-5\begin{bmatrix}{3} & {4} \\ 1 & {-2}\end{bmatrix}-2\begin{bmatrix}{1} & {4} \\ {6} & {-2}\end{bmatrix}+6\begin{bmatrix}{1} & {3} \\ {6} & {1}\end{bmatrix} \\ D=\begin{bmatrix}{-5} & 2 & {6} \\ {1} & {3} & {4} \\ {6} & {1} & {-2}\end{bmatrix}=-5(3\cdot-2-4\cdot1)-2(1\cdot-2-4\cdot6)+6(1\cdot1-3\cdot6) \\ D=\begin{bmatrix}{-5} & 2 & {6} \\ {1} & {3} & {4} \\ {6} & {1} & {-2}\end{bmatrix}=-5(-6-4)-2(-2-24)+6(1-18) \\ D=\begin{bmatrix}{-5} & 2 & {6} \\ {1} & {3} & {4} \\ {6} & {1} & {-2}\end{bmatrix}=-5(-10)-2(-26)+6(-17) \\ D=\begin{bmatrix}{-5} & 2 & {6} \\ {1} & {3} & {4} \\ {6} & {1} & {-2}\end{bmatrix}=50+52-102 \\ D=\begin{bmatrix}{-5} & 2 & {6} \\ {1} & {3} & {4} \\ {6} & {1} & {-2}\end{bmatrix}=102-102 \\ D=\begin{bmatrix}{-5} & 2 & {6} \\ {1} & {3} & {4} \\ {6} & {1} & {-2}\end{bmatrix}=0 \end{gathered}[/tex]As you can see, the determinant of the matrix is 0
This means that the given system of equations has no solution.
You have a cup with 17 coins inside. The total inside the cup is $5.50. Determine how many half dollars and quarters are inside the cup.
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Let x be the number of half dollar and y, the number of quarter dollar
Thus,
[tex]x+y=17\text{ -----eq i)}[/tex]Half dollar is 50cent, quarter dollar is 25cents,
Thus,
[tex]0.5x+0.25y=5.50\text{ -----eq i}i)[/tex]Solving the two(2) equations simultaneously; we have:
From eq i)
[tex]\begin{gathered} x+y=17 \\ x=17-y\text{ -----eq }iii) \end{gathered}[/tex]Put eq iii) into ii), we have:
[tex]\begin{gathered} 0.5x+0.25y=5.50 \\ 0.5(17-y)+0.25y=5.50 \\ 8.5-0.5y+0.25y=5.50 \\ 8.5-0.25y=5.50 \\ 8.5-5.50=0.25y \\ 0.25y=3 \\ y=\frac{3}{0.25} \\ y=12 \end{gathered}[/tex]From eq iii)
[tex]\begin{gathered} x=17-y \\ x=17-12 \\ x=5 \end{gathered}[/tex]Hence, there are 5 half dollars and 12 quarter dollars inside the cup
If the angles of a triangle are 45°, 45°, and 90°,show that the length of the hypotenuse is 3 times as long as eachleg.V 1. Substitute the side lengths of the triangle into the Pythagoreantheoremq² + ² = 22. Combine like terms.
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Acording to pythagoras theorem,
[tex]\text{hypotenuse}^2=base^2+height^2[/tex]Here,
[tex]\begin{gathered} \text{hypotenuse}=c \\ \text{height}=a \\ \text{base}=a \end{gathered}[/tex]Therefore we have,
[tex]\begin{gathered} c^2=a^2+a^2 \\ c^2=2a^2 \\ c=\sqrt[]{2}a \end{gathered}[/tex]Hence the proof.
I need help with this problem.I will need to send you the picture of the problem because it couldn’t fit into the screenshot
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EXPLANATION :
From the problem, we have the radical expression :
[tex]\sqrt{36}+\sqrt{49}-\sqrt{16}[/tex]Note that the given radicals are perfect squares :
36 = 6^2
49 = 7^2
16 = 4^2
Then :
[tex]\begin{gathered} \sqrt{6^2}+\sqrt{7^2}-\sqrt{4^2} \\ =6+7-4 \\ =9 \end{gathered}[/tex]ANSWER :
The answer is 1 only
the measure of an interior angle of a regular polygon is given find the number of sides in the polygon show all work
Answers
Answer:
The polygon has 5 sides;
[tex]n=5[/tex]Explanation:
The measure of an interior angles of a regular polygon can be given by the formula;
[tex]x=\frac{(n-2)180}{n}[/tex]Where;
n = number of sides of the polygon
x = measure of each interior angle of the polygon
Given;
4.
[tex]x=108[/tex]substituting into the formula and solving for n, we have;
[tex]\begin{gathered} x=\frac{(n-2)180}{n} \\ 108=\frac{(n-2)180}{n} \\ \text{cross multiply and expand;} \\ 108n=180n-360 \\ 180n-108n=360 \\ 72n=360 \\ n=\frac{360}{72} \\ n=5 \end{gathered}[/tex]Therefore, the polygon has 5 sides;
[tex]n=5[/tex]Need help solving step by step and graphing Problem number 2
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f(x) = |x|
Since the variable x is given with absolute value signs, the function f(x) will always take on positive values for all values (negative or positive) of x.
To solution of a function is the value of the function such that f(x) = 0. The function f(x) = 0 when x = 0 because at every value of x on the graph, y = the same value.
e.g. when x =1, y=1. When x =2, y=2 etc...
This is the graph of f(x) = x (without the absolute value sign):
This is the graph of f(x) = |x| :
Find the magnitude and direction angle of the following vector. Write your angle in degrees rounded to four decimal places.
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Recall that the magnitude and direction of a vector:
[tex]\vec{v}=ai+bj[/tex]are given by the following formulas:
[tex]\begin{gathered} \vec{|v}|=\sqrt{a^2+b^2}, \\ \theta=tan^{-1}(\frac{b}{a}). \end{gathered}[/tex]Substituting
[tex]\begin{gathered} a=2, \\ b=8, \end{gathered}[/tex]in the above formulas, we get:
[tex]\begin{gathered} \vec{|v}|=\sqrt{2^2+8^2}=\sqrt{4+64}=\sqrt{68}. \\ \theta=\tan^{-1}(\frac{8}{2})=\tan^{-1}(4). \end{gathered}[/tex]Finally, we get:
[tex]\begin{gathered} \vec{|v}|=2\sqrt{17}, \\ \theta=75.9638^{\circ}. \end{gathered}[/tex]Answer: (|v|=2√17, θ=75.9638°)
[tex]\begin{gathered} \vec{\lvert\rvert v}\lvert\rvert=2\sqrt{17}, \\ \theta=75.9638^{\operatorname{\circ}}. \end{gathered}[/tex]help me with this question
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what we wrer asked to find is BUC
which means B union C
that also means numbers that are found both in set B and set C
so for
set B {4, 7, 11, 12,14}
set C {2, 4, 8, 10, 11, 12, 13}
therefore,
BUC {2, 4, 7, 8, 10, 11, 12, 13, 14}
so the correct option is B
EsparThe shorter leg of a right triangle is 7 m shorter than the longer leg. The hypotenuse is 7 m longer than the longer leg. Findthe side lengths of the triangle.entsLength of the shorter leg:Length of the longer leg:ImLength of the hypotenuse:Х$?
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
length of the shorter leg = ?
length of the longer leg = ?
length of the hypotenuse = ?
Step 02:
We must analyze the problem to find the solution.
x = length of the shorter leg
y = length of the longer leg
z = length of the hypotenuse
System of equations:
x = y - 7 (eq.1)
z = y + 7 (eq.2)
z² = x² + y² (eq.3)
eq.2 in eq.3
[tex]\begin{gathered} (y+7)^2=x^2+y^2\text{ } \\ y^2+14y+49=x^2+y^2 \\ 14y+49=x^2 \\ \\ \\ \end{gathered}[/tex]14y + 49 = x²
y - 7 = x * (-14) (eq.1)
14y + 49 = x²
-14y + 98 = -14x (eq.1)
__________________
147 = x² - 14x
x² - 14x - 147 = 0
Step 03:
Quadratic equation:
x² - 14x - 147 = 0
[tex]x=\frac{-(-14)\pm\sqrt[]{(-14)^2-4\cdot1\cdot(-147)}}{2.1}[/tex][tex]\begin{gathered} x1\text{ = }\frac{-(-14)+28_{}}{2}\text{ = 21} \\ x2=\frac{-(-14)-28}{2}\text{ }=\text{ -7} \end{gathered}[/tex]x = 21 (positive solution)
x = y - 7
21 + 7 = y
28 = y
z = y + 7 = 28 + 7 = 35
The answer is:
length of the shorter leg = 21
length of the longer leg = 28
length of the hypotenuse = 35
There are 53 members on the board of directors for a certain non-profit institution. If they must elect a chairperson, first vice chairperson, second vice chairperson, and secretary, how many different slates of candidates are possible? There are _ different slates of candidates possible.please answer the question above.
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For this problem the order of selection matter (the first person is the chairperson, the second the first vice chairperson and so on); since this is the case we need to use permutations. The permutation is given by:
[tex]_nP_k=\frac{n!}{(n-k)!}[/tex]we have a total of 53 members and the slates contain 4 people, then we have:
[tex]_{53}P_4=\frac{53!}{(53-4)!}=7027800[/tex]Therefore, there are 7,027,800 different slates of candidates.
Given the following information, determine which lines, if any, are parallel. State the postulate or theorem that justifies your answer.A. right angle 3 is congruent to right angle 7B. m right angle 7 + m right angle 12 = 180
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Situation A.
Angle 3 is congruent with angle 7.
That means that line a and b are parallel, because: Angle 3 and Angle 5 are vertical angles, and if Angle 3 is congruent with Angle 7, then Angle 5 is also congruent with Angle 7, therefore, the lines a an b are parallel.
Situation B.
Angle 7 is supplementary of Angle 12.
Angle 12 is supplementary to Angle 13.
Then Angle 13 and Angle 7 are congruent.
Then a and b are parallel and l and m are parallel.
A spinner with the colors purple, red, green, and yellow is spun. What is the theoretical probability of landing on purple? O P(purple) = 20% • O O P(purple) = 50% O P(purple) = 100% O P(purple) = 33.3% - O P(purple) = 25%
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Answer:
25%
Explanation:
Probability is the likelihood or chance that an event will occur. Mathematically;
Probability = Expected outcome/Total outcome
Since there are 4 colours to spun (purple, red, green, and yellow)
Total outcome = 4
If purple landed, then the expected outcome = 1
Substitute into the formula;
P(Purple) = 1/4
P(Purple) = 0.25
P(Purple) = 25%
Hence the theoretical probability of landing on purple is 25%
Wire the explicit expression that can be used to find the nth term in this sequence 3,7,11,15,19An = What would be the 20th term A20 =
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From the sequence given 3,7,11,15,19
first term (a) = 3
common difference(d) = 4
Hence to find the nth term, the expression is given as shown below
[tex]\begin{gathered} T_n\text{ = a + (n -1)d} \\ T_n\text{ = 3 + (n - 1)4} \\ \text{ = 3 + 4n -4} \\ \text{ = 4n - 4+ 3} \\ \text{ = 4n - 1} \end{gathered}[/tex]To find the 20th term, we have
[tex]\begin{gathered} T_n\text{ = a + (n -1)d} \\ a\text{ = 3, d = 4},\text{ n = 20} \\ T_n\text{ = a + (n -1)d} \\ T_n\text{ = 3 + (20 - 1)4} \\ T_{20}\text{ = 3 + (19)4 } \\ T_{20}\text{ = 3 +76} \\ T_{20}\text{ = 79} \end{gathered}[/tex]
Which function of x would have zeros of 1/3 and -5?
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The functions of x with zeros of 1/3 and -5
[tex]\begin{gathered} x\text{ = }\frac{1}{3}\text{ and x = -5} \\ (x\text{ - }\frac{1}{3})\text{ and (x + 5)} \\ \end{gathered}[/tex][tex]\begin{gathered} (x\text{ -}\frac{1}{3})(x\text{ + 5)} \\ x^2\text{ + 5x - }\frac{x}{3}\text{ - }\frac{5}{3} \\ \text{ multiply through by 3} \\ 3x^2\text{ + 15x - x - 5} \\ 3x^2\text{ + 14x - 5} \\ F(x)\text{ = }3x^2\text{ + 14x - 5} \end{gathered}[/tex]Hence the functions of x with zeros of 1/3 and -5 = 3x² + 14x - 5
Find y This is geometry (please start off with solution )
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Answer:
Explanation:
Given:
To find:
The value of y
We'll go ahead and use the cosine rule to find the value of y as seen below;
[tex]y^2=e^2+s^2-2es\cos E[/tex][tex]\begin{gathered} y^2=42^2+32^2-2*42*32*\cos78 \\ y^2=1764+1024-558.8666 \\ y^2=2788-558.8666 \\ y=\sqrt{2229.1334} \\ y=47.2\text{ cm} \end{gathered}[/tex]Therefore, the value of y is 47.2 cm
Hudson bought 4 pounds of cantaloupe for $11.25.What is the price, in dollars, of 2 lbs of cantaloupe?
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If 4 pounds of cantaloupe cost $11.25
then, 1 pound of cantaloupe will cost
[tex]\frac{11.25}{4}=\text{ \$2}.8125[/tex]if 1 pound of cantaloupe costs $2.8125
then, 2 pounds of cantaloupe will cost $2.8125 x 2
[tex]=\text{ \$5.625}[/tex]The answer is $5.625
StorageBoxCrate Size DimensionsWidth8 feet4 inchesHow many boxesfit along thelength of thiscrate?Height 8 feetLength 40 feet6 inches8 inchesA. 16 boxesB. 2 boxesC. 60 boxesD. 5 boxes
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5 boxes fit along the length of the crate (option D)
Explanation:Given:
Length of box = 8 in, width = 4 in, height = 6 in
Length of crate 40 ft, width = 8 ft, height = 8 ft
To find:
The number of boxes that can ft into the length of the crate
To determine the number of boxes that will fit into the length of the crate, we will divide the length of the crate by the length of the box
[tex]\begin{gathered} Number\text{ of boxes on the crate length = }\frac{40\text{ ft}}{8\text{ in}} \\ Number\text{ of boxes on the crate length = 5} \end{gathered}[/tex]5 boxes fit along the length of the crate (option D)
Triangle KAB is similar to triangle KML. Find the length of AB.L36B5430K50A
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Given the figure in the attached image;
The triangles KAB and KML are similar
[tex]\Delta KAB\text{ \textasciitilde}\Delta KML[/tex]So, the sides of the triangles are proportional.
[tex]\frac{KB}{KL}=\frac{AB}{ML}[/tex]Given in the figure;
[tex]\begin{gathered} KB=30 \\ KL=36 \\ ML=54 \end{gathered}[/tex]substituting the given values;
[tex]\begin{gathered} \frac{KB}{KL}=\frac{AB}{ML} \\ \frac{30}{36}=\frac{AB}{54} \\ AB=\frac{30\times54}{36} \\ AB=45 \end{gathered}[/tex]Therefore, the length of side AB is;
[tex]45\text{ units}[/tex]Is the triangles similar? If the triangles are similar then this is the statements that we have to use
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When two triangles are similar, their corresponding angles are equal.
So, the first step to solve the exercise is to find the measure of the missing angle in each triangle.
We know that the sum of the interior angles of a triangle is 180. Then, we have:
• Measure of angle R
[tex]\begin{gathered} 54\degree+68\degree+R=180\degree \\ 122\degree+R=180\degree \\ \text{ Subtract 122\degree from both sides} \\ 122\degree+R-122\degree=180\degree-122\degree \\ R=58\degree \end{gathered}[/tex]• Measure of angle U
[tex]\begin{gathered} 54\degree+67\degree+U=180\degree \\ 121\degree+U=180\degree \\ \text{ Subtract 121\degree from both sides} \\ 121\degree+U-121\degree=180\degree-121\degree \\ U=59\degree \end{gathered}[/tex]As we can see, the corresponding angles of the triangles RST and UVW are not equal.
Therefore, the triangles are not similar.
if Teresa used five and a third gallons of gas on Sunday and two and a quarter gallons of gas on Monday how many more gallons of gas did she use on Sunday
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Hence the difference is
[tex]5\frac{1}{3}-2\frac{1}{4}=3\frac{4-3}{12}=3\frac{1}{12}[/tex]Hence she used 3 1/12 more gallons of gas on Sunday
The current student population of Tucson is 2500. If the population increase at a rate of 15% each year. What will the student population be in 10 years?Write an exponential growth model for the future population (y) in terms of time x: y=What will the population be in 10 years? (Round to nearest student)
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Let's assume that we have a certain quantity y that increases at a rate of p% every x years. If the initial quantity (i.e. the quntity at x=0) is "a" then the value of y after x years is given by:
[tex]y=a\cdot(1+\frac{p}{100})^x[/tex]We are told that the current student population of Tucson is 2500 and that it will increase at a rate of 15% per year. Then the student population after x years is given by:
[tex]\begin{gathered} y=2500\cdot(1+\frac{15}{100})^x \\ y=2500\cdot1.15^x \end{gathered}[/tex]Then the student population after 10 years is given by:
[tex]y=2,500\cdot1.15^{10}=10113.89[/tex]AnswerThen the answers are:
[tex]y=2500\cdot1.15^x[/tex]The population will be 10114.
Can I have help with this pleasehow would I make a graph
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The Solution:
We are required to make a graph of the situation.
The above graph is the required graph.