Please look at the image below. By the way this is my homework.Use the definition of congruence to decide whether the two figures are congruent. Explain your answer. Give coordinate notation for the transformations you use.
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Congruent Shapes
Two congruent shapes have the same size and shape, which means all of their side lengths are equal and all of their internal angles are congruent (have the same measure),
All of the rigid transformations map the original figure to a congruent figure. One of the transformations is the reflection.
The image shows two shapes SRQP and EDCB. They seem to have the same shape and size, but it must be proven by finding the appropriate transformation used.
Comparing the corresponding vertices we can find that out. For example, the coordinates of S are (-6,4) and the coordinates of E are (4,4). The x-coordinate of the midpoint between them is
xm = (-6+4)/2 = -1
Now analyze the points P(-8,2) and B(6,2). The x-coordinate of the midpoint is:
xm = (-8+6)/2 = -1
For the points R(-4,-6) and D(2,-6):
xm = (-4+2)/2 = -1
For the points Q(-9,-4) and D(8,-4):
xm = (-9+8)/2 = -0.5
Since this last pair of corresponding points don't have the same axis of symmetry as the others, the shapes don't have the same size and angles, thus they are not congruent
For both shapes to be congruent, the coordinates of Q should have been (-10,-4)
Related Questions
Solve the system you any method. State the final answer as an ordered pair. DO NOT include spaces or dollar signs in your answer.
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To solve the problem, we notice that both of the equations are written with the y solved then we can equate the expressions of x and solve the resulting equation of x:
[tex]\begin{gathered} x-12=-3x+12 \\ x+3x=12+12 \\ 4x=24 \\ x=\frac{24}{4} \\ x=6 \end{gathered}[/tex]Once we have the value of x we plug it on the first equation to find y:
[tex]\begin{gathered} y=6-12 \\ y=-6 \end{gathered}[/tex]Therefore, the solution of the system of equations is (6,-6)
What is 44 over 13 rounded to the nearest 10 tenths
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we have that
44/13=3.38
rounded to the nearest tenths
3.38=3.4
the answer is 3.4linear equation in deletion method2x + y − 3z = 13x − y − 4z = 75x + 2y − 6z = 5
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The given system is:
[tex]\begin{gathered} 2x+y-3z=1\ldots(i) \\ 3x-y-4z=7\ldots(ii) \\ 5x+2y-6z=5\ldots(iii) \end{gathered}[/tex]Add (i) and (ii) to get:
[tex]\begin{gathered} 2x+y-3z=1 \\ + \\ 3x-y-4z=7 \\ 5x-7z=8\ldots(iv) \end{gathered}[/tex]Multiply (ii) by 2 to get:
[tex]6x-2y-8z=14\ldots(v)[/tex]Add (iii) and (v) to get:
[tex]\begin{gathered} 6x-2y-8z=14 \\ + \\ 5x+2y-6z=5 \\ 11x-14z=19\ldots(vi) \end{gathered}[/tex]Multiply (iv) by 2 to get:
[tex]10x-14z=16\ldots(vii)[/tex]Subtract (vii) from (vi) to get:
[tex]\begin{gathered} 11x-14z=19 \\ - \\ 10x-14z=16 \\ x=3 \end{gathered}[/tex]Put x=3 in (iv) to get:
[tex]\begin{gathered} 5\times3-7z=8 \\ -7z=8-15 \\ -7z=-7 \\ z=1 \end{gathered}[/tex]Put x=3 and z=1 in (i) to get:
[tex]\begin{gathered} 2(3)+y-3(1)=1 \\ 6+y-3=1 \\ y+3=1 \\ y=-2 \end{gathered}[/tex]So the values are x=3,y=-2 and z=1.
How many rays are in the next two terms in the sequence?
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The sequnce is
2, 3, 5, 9, ....
this sequence follows the next formula:
[tex]a_n=2^{n-1}+1[/tex]where an is the nth term.
[tex]\begin{gathered} a_1=2^{1-1}+1=1 \\ a_2=2^{2-1}+1=3 \\ a_3=2^{3-1}+1=5 \\ a_4=2^{4-1}+1=9 \\ a_5=2^{5-1}+1=17 \\ a_6=2^{6-1}+1=33 \end{gathered}[/tex]The next two terms are 17 and 33
which property justifies the equation 0.5 (8.4 -1.6) equals 0.5 (8.4) -0.5 (1.6)?
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Given the following expression:
[tex]\text{0}.5(8.4-1.6)=0.5(8.4)-0.5(1.6)[/tex]Remember that we have the following general rule:
[tex]a(b+c)=a\cdot b+a\cdot c[/tex]this rule is called the distributive property, which is used on our given expression.
May I please get help with this math problem. I am so lost and confused
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We are given three angles and we are asked to determine if the angles are the angles of a triangle. To do that we need to have into account that the measure of the angles of a triangle always adds up to 180, therefore, if we add up the angles and the result is 180, then these angles can be angles measures of a triangle. If the result is different from 180 the angles can't be the angle measures of a triangle. Taking the first set of three angles we get:
[tex]58+34+42=134[/tex]Since the result is different from 180 then these angles can't be the angle measure of a triangle.
The same procedure is used to determine the other sets of angles.
PLEASE HELP
OFFERING 10 POINTS
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Answer: AAS
Step-by-step explanation:
Two sides are congruent, two angles are congruent, and vertical angles are congruent
The graph of which function has a minimum located at (4,-3)
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We need to obtain the first derivate
[tex]\begin{gathered} f\mleft(x\mright)=-\frac{1}{2}x^2+4x-11 \\ f^{\prime}(x)=-x+4 \end{gathered}[/tex][tex]\begin{gathered} f\mleft(x\mright)=-2x^2+16x-35 \\ f^{\prime}(x)=-4x+16 \end{gathered}[/tex][tex]\begin{gathered} \: f\mleft(x\mright)=\frac{1}{2}x^2-4x+5 \\ f^{\prime}(x)=x^{}-4 \end{gathered}[/tex][tex]\begin{gathered} f(x)=2x^2-16x+5 \\ f^{\prime}(x)=4x-16 \end{gathered}[/tex]Answer: B on edge23
Step-by-step explanation:
f(x) = 1/2^x2–4x + 5
Escriba la razón del primer número al segundo: 32 a 44 simplifique si es posible.
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Write the ratio of the first number to the second.
[tex]\begin{gathered} 32\colon44 \\ \text{Ratio}=\frac{32}{44} \\ \text{Ratio}=\frac{8}{11} \\ \text{The ratio therefore is 8}\colon11 \end{gathered}[/tex]Suppose that $16,065 is invested at an interest rate of 6.6% per year, compounded continuously. a) Find the exponential function that describes the amount in the account after time t, in years. b) What is the balance after 1 year? 2 years?5 years? 10 years? c) What is the doubling time?
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Okay, here we have this:
Considering the provided information we obtain the following:
a)
Replacing in the Compound Interest formula we obtain the following:
[tex]\begin{gathered} A(t)=Pe^{rt} \\ A(t)=16065e^{0.066t} \end{gathered}[/tex]b)
After 1 year (t=1):
[tex]\begin{gathered} A(1)=16065e^{0.066(1)} \\ A(1)\approx17,161.06 \end{gathered}[/tex]We obtain that after one year the balance is aproximately $17,161.06.
After 2 years (t=2):
[tex]\begin{gathered} A(2)=16065e^{0.066(2)} \\ A(2)=18331.90 \end{gathered}[/tex]We obtain that after two years the balance is aproximately $18,331.90
After 5 years (t=5):
[tex]\begin{gathered} A(5)=16065e^{0.066(5)} \\ A(5)=$22,345.90$ \end{gathered}[/tex]We obtain that after five years the balance is aproximately $22,345.90.
After 10 years (t=10):
[tex]\begin{gathered} A(10)=16065e^{0.066(10)} \\ A(10)=$31,082.44$ \end{gathered}[/tex]We obtain that after ten years the balance is aproximately $31,082.44.
c)
In this case the doubling time will be when she has double what she initially had, that is: $16,065*2=$32130, replacing in the formula:
[tex]32130=16065e^{0.066t}[/tex]Let's solve for t:
[tex]\begin{gathered} 32130=16065e^{0.066t} \\ 16065e^{\mleft\{0.066t\mright\}}=32130 \\ \frac{16065e^{0.066t}}{16065}=\frac{32130}{16065} \\ e^{\mleft\{0.066t\mright\}}=2 \\ 0.066t=\ln \mleft(2\mright) \\ t=\frac{\ln\left(2\right)}{0.066} \\ t\approx10.502years \end{gathered}[/tex]Finally we obtain that the doubling time is approximately 10.502 years or about 10 years 6 months.
Select all the situations in which a proportional relationship is described.
Jackson saves $10 in the first month and $30 in the next 3 months.
Mia saves $8 in the first 2 months and $4 in the next month.
Piyoli spends $2 in the first 2 days of the week and $5 in the next 5 days.
Robert spends $2 in the first 3 days of the week and $5 in the next 4 days.
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Answer:
Jackson saves $10 in the first month and $30 in the next 3 months.
Mia saves $8 in the first 2 months and $4 in the next month.
Piyoli spends $2 in the first 2 days of the week and $5 in the next 5 days.
Step-by-step explanation:
A proportional relationship is one that has a constant of proportionality.
In this case, the correct options are Mia, Piyoli, and Robert.
Julie is 6 feet tall if she stands 15 feet from the flagpole and holds a cardboard square the edges of the square light up with the top and bottom of the flagpole approximate the height of the flagpole
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Using tangent function:
[tex]\begin{gathered} \tan (\theta)=\frac{opposite}{adjacent} \\ \frac{6}{15}=\frac{15}{x-6} \\ solve_{\text{ }}for_{\text{ }}x\colon \\ 6(x-6)=15^2 \\ 6x-36=225 \\ 6x=225+36 \\ 6x=261 \\ x=\frac{261}{6} \\ x=43.5ft \end{gathered}[/tex]How many offices are between 41 and 50 meters ?
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Solution
For this case we want to find the number of offices between 41 and 50 m and the answer is:
2 meters
Construct a scatterplot and identify the mathematical model that best fits the data. Assume that the model is to be used only for the scope of the given data and consider only linear, quadratic, logarithmic, exponential, and power models. Use a calculator or computer to obtain the regression equation of the model that best fits the data. You may need to fit several models and compare the values of R2.Average sunset times are taken for six months across the summer. Giving the months April through September values 1 through 6, find the regression equation of the best model.y = –0.357x2 + 2.17x + 17.87y = 21.24 e0.983xy = 21.20 – 0.343xy = 20.62x–0.029
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We will have the following:
From the options given we graph each possible solution with the data, that is:
In order:
From this, we can see that the function that best fits the data is:
[tex]y=-0.357x^2+2.17x+17.87[/tex]x+3y=6 2x+6y=-18 solve
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The system of equation x + 3y = 6 and 2x + 6y = -18 has no solution.
What is the solution to the given system of equation?Given the system of equation in the question;
x + 3y = 6
2x + 6y = -18
To find the solution to the system of equation, first solve for x in the first equation.
x + 3y = 6
Subtract 3y from both sides
x + 3y - 3y = 6 - 3y
x = 6 - 3y
Now, replace all occurrence of x in the second equation with 6 - 3y and solve for y
2x + 6y = -18
2( 6 - 3y ) + 6y = -18
Apply distributive property to remove the parenthesis
12 - 6y + 6y = -18
-6y and +6y cancels out
12 = -18
Since 12 equal -18 is not true, there is no solution to the system of equation.
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A factory makes car batteries. The probability that a battery is defective is1/6 If 400 batteries are tested, about how many are expected to be defective?A. 40 B. 25C. 16D. 375
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Since there are 400 batteries are tested
Since the probability of the defective batteries is 1/6
The number of defective batteries =
[tex]\frac{1}{16}\times400=25[/tex]The answer is B
Given the equations and the table below, what is the first x-value when the y-value of equation 2 is greater than the y-value of equation 1 after the functions first intersect?Equation 1: f(x)=5x^3Equation 2: f(x)=2x+3
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the first x value, when the y-value of the equation is greater than the y value of equation one, is x=15
Because the y-value of equation 2 with x=15 is 32771, while the y-value of equation 1 is 16875
Complete a triangulation calculation to measure the distance between actual objects in or near your home. include a well-labeled diagram.
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Triangulation means the measuring of distances in surveys with triangles. If the distance of two objects and the angle between is knwon, the distance between these objects can be calculated.
Given the diagram we have:
So, the distance between both objects will be calculated by:
[tex]c=\sqrt{a^2+b^2-2ab\cdot\cos\theta}[/tex]Where:
Distance to the first object a = 6
Distance to the first object b = 6
Angle between both objects θ = 60°
Substitute the values, we have:
[tex]c=\sqrt{6^2+6^2-2(6)(6)\cdot\cos60}[/tex]Simplify:
[tex]c=\sqrt{36+36-72(0.5)}=\sqrt{72-36}=\sqrt{36}=6[/tex]So, the distance between both objects c = 6 inches
determine whether the equation is linear to x. 5-3x=0
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By definition a linear equation is an equation in which the highest power of any variable in the equation is always 1. In this case we have the equation:
[tex]5-3x=0[/tex]We notice that this equation only has one variable, x, and that its power is 1. Therefore, the equation is linear.
10.1.3The hour hand of a clock moves from 5 to 9 o'clock. Through how many degrees does it move?
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Step 1: Lets calculate angle on each hour hand
since the wall clock takes the shape of a cirle
Therefore,
The total angles in a walk clock is 360°
Angle on each hour hand is
There are 12 hour hands on the clock ,
Therefore,
[tex]\begin{gathered} \text{Angle on each hour hand is =}\frac{360^0}{hands\text{ on the clock}}^{} \\ \text{Angle on each hour hand =}\frac{360^0}{12}=30^0 \end{gathered}[/tex]Since the hour hand moved from 5 o'clock to 9 o'clock
It has moved a distance of (9 - 5)= 4 hands on the clock
If each hand on the clock=30°
Therefore,
The angle in degrees moved through 4 hour hands on the clock will be calculated as,
[tex]\begin{gathered} \text{Angle moved = angle on each hand}\times no\text{ of hands moved} \\ \text{Angle moved=30}^0\times4=120^0 \end{gathered}[/tex]The hour hand of the clock moved from 5 o'clock to 9 o'clock through an angle of 120°
A package of 5 pairs of insulated socks costs 27.95$. What is the unit price of the pairs of ?
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Answer:
$5.59
Step-by-step explanation:
You want the unit price of a pair of socks, given that 5 pairs cost $27.95.
Unit priceThe unit price is found by dividing the price by the number of units.
$27.95/5 = $5.59
The unit price of a pair of socks is $5.59.
Three commercials are played in a row between songs on the radio. The three commercials fill exactly 3 minutes of time. If the first commercial uses 1 – minutes, and the second uses 3 minute, how long is the third commercial? The third commercial is minutes long.
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3 commercials
3 minutes
3 = 1st commercial + 2nd commercial + 3rd commercial
3 = 1 1/5 + 3/4 + 3rd commercial
3rd commercial = 3 - 6/5 - 3/4
= 60/20 - 24/20 - 15/20
= 21/20
The third commercial last = 21/20 or 1 1/20.
Solve for x: 4 open parentheses 2 x minus 1 close parentheses plus 8 minus 14 x equals negative 8 x plus 4 plus 2 x The solution is X = _________
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Answer:
x = 1
Step-by-step explanation:
4(2x-1)+8-14= -8x+ 4+ 2x
Triangle ABC lies on the coordinate plane with vertices located at A(7,6), B(-3,5), and C(-4,9). The triangle is transformed using the rule (x,y) -> (2x,y-3) to create triangle A'B'C'. Select all possible answers for the vertices of triangle A'B'C'. Question 1 options: (14,3) (9,3) (-6,10) (-8,6) (-6,2)
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All of the possible answers for the vertices of triangle A'B'C' after using this translation rule (x, y) → (2x, y - 3) include the following:
A. (14, 3)
D. (-8, 6)
What is a translation?In Geometry, a translation can be defined as a type of transformation which moves every point of a geometric figure or object in the same direction, as well as for the same distance.
Next, we would transform triangle ABC by using this translation rule (x, y) → (2x, y - 3) to create the vertices of triangle A'B'C' as follows:
(x, y) → (2x, y - 3)
Coordinate A = (7, 6) → Coordinate A' (2(7), 6 - 3) = (14, 3)
Coordinate B = (-3, 5) → Coordinate B' = (2(-2), 5 - 3) = (-4, 2)
Coordinate C = (-4, 9) → Coordinate C' = (2(-4), 9 - 3) = (-8, 6)
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under normal conditions, 1.5 feet of snow will melt into 2 inches of water. after a recent snowstorm, there were 4 feet if snow. how many inches of water will there be when the snow MELTS? express your answer as a fraction reduced to lowest terms or decimal rounded correctly to two decimals places. Do not include units with this answer.
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If 1.5 feet of snow melts into 2 inches of water, this implies that:
[tex]undefined[/tex]Consider the following expression:-27 x (-18)By the laws of signs, this is equivalent to27 x 18 this is equivalent to:27 x 18= 486we can conclude thatthe correct answer is:486I feel like that’s wrong, it’s not algebra can anyone help
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The answer is actually CORRECT.
The correct procedure is when two negatives multiply each other, the answer is always a positive.
Therefore;
[tex]\begin{gathered} -27\times(-18)=27\times18 \\ 27\times18=486 \end{gathered}[/tex]We can conclude that the correct answer is 486
The revenue for a small company is given by the quadratic function r(t) = 5tsquared + 5t + 630 where t is the number of years since 1988 and r(t) is in thousands of dollars. If this trend continues, find the year after 1998 in which the company’s revenue will be $730 thousand. Round to the nearest whole year.
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for:
[tex]\begin{gathered} r(t)=730 \\ 5t^2+5t+630=730 \\ so\colon \\ 5t^2+5t-100=0 \end{gathered}[/tex]Divide both sides by 5:
[tex]t^2+t-20=0[/tex]Factor:
The factors of -20 which sum to 1, are -4 and 5 so:
[tex](t-4)(t+5)=0[/tex]So:
[tex]\begin{gathered} t=4 \\ or \\ t=-5 \end{gathered}[/tex]Since a negative year wouldn't make any sense:
[tex]t=4[/tex]Therefore, the company revenue will be $730 for the year:
[tex]1998+t=1998+4=2002[/tex]Answer:
2002
express the fuction graphed on the axes below as a piecewise function
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Concept
Find the equation of line for the second line.
x1 = -2 y1 = 1
x2 = -4 y2 = 2
Next, apply equation of a line formula
[tex]\begin{gathered} \frac{y-y_1}{x-x_1\text{ }}\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \frac{y\text{ - 1}}{x\text{ + 2}}\text{ = }\frac{2\text{ - 1}}{-4\text{ + 2}} \\ \frac{y\text{ - 1}}{x\text{ + 2}}\text{ = }\frac{1}{-2} \\ -2(y\text{ - 1) = 1(x + 2)} \\ -2y\text{ + 2 = x + 2} \\ -2y\text{ = x} \\ y\text{ = }\frac{-1}{2}x \end{gathered}[/tex]Final answer
The graphed as a piecewise function is given below
A salad recipe requires 3 cups of spinach and 1/2 cup of pecans. At this rate, what amount of pecans should be used with 2 cups of spinach?
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We need 3 cups of spinach for each 1/2 cup of pecans.
Then we have:
[tex]\begin{gathered} \frac{2\text{ cups of spinach}}{3\text{ cups of spinach}}=\frac{x\text{ cups of pecans}}{\frac{1}{2}\text{ cups of pecans}} \\ \frac{x}{\frac{1}{2}}=\frac{2}{3} \\ x=\frac{1}{2}\cdot\frac{2}{3} \\ x=\frac{1}{3} \end{gathered}[/tex]Answer: It will be needed 1/3 cup of pecans
Compare A and B in three ways, where A = 51527 is the number of deaths due to a deadly disease in the United States in 2005 and B = 17241 is the number of deaths due to the same disease in the United States in 2009. a. Find the ratio of A to B. b. Find the ratio of B to A. c. Complete the sentence: A is ____ percent of B.
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ANSWER
Ratio of A to B = 2.99 (to 2 decimal places)
Ratio of B to A = 0.33 (to 2 decimal places)
A is 299% of B (to nearest integer)
STEP BY STEP EXPLANATION
for ratio of A to B:
[tex]\begin{gathered} \frac{A}{B}\text{ = }\frac{51527}{17241}\text{ = }2.98863 \\ \text{ = 2.99 (to 2 decimal places)} \end{gathered}[/tex]for ratio of B to A:
[tex]\begin{gathered} \frac{B}{A}\text{ = }\frac{17241}{51527}\text{ = 0.33460 } \\ \text{ = 0.33 (to 2 decimal places)} \end{gathered}[/tex]A is x % of B:
[tex]\begin{gathered} A\text{ = }\frac{x}{100}\times B \\ x\text{ = }\frac{100\text{ }\times A}{B} \\ x\text{ = }\frac{100\text{ }\times\text{ 51527}}{17241}\text{ = 298.86} \\ x\text{ = 299\% (to nearest integer)} \end{gathered}[/tex]Hence, the ratio of A to B = 2.99 (to 2 decimal places), B to A = 0.33 (to 2 decimal places) and A is 299% of B (to nearest integer).