What are the rigid transformations that will map
△ABC to △DEF?
Translate vertex A to vertex D, and then reflect
△ABC across the line containing AC.
Translate vertex B to vertex D, and then rotate
△ABC around point B to align the sides and angles.
Translate vertex B to vertex D, and then reflect
△ABC across the line containing AC.
Translate vertex A to vertex D, and then rotate
△ABC around point A to align the sides and angles.
Answers
Answer:
The answer above is correct! The answer is option D.
Step-by-step explanation:
Hope this helped clarify :D
Translating vertex A to vertex D, and then rotate △ABC around
point A to align the sides and angles will bring about a rigid
transformation.
What is Rigid transformation?This is the transformation which preserves the Euclidean
distance between every pair of points. This could be as a result
of the following:
RotationReflectionTranslation etc.Option D when done will preserve the distance between the
points when vertex A is translated to vertex D as they contain
the same angle with other sides and angles being made to
align.
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Related Questions
C: -5/2 D: 5/2 help please
Answers
Choose the point on the terminal side of -45°. (-3, -3) (4, -4) (5, 5) (-2, 2)
Answers
-45° is in quadrant IV and the point (4, -4) is the only point out of the points given that is also in quadrant IV
The point (4,-4) is the only one that satisfies that condition
hope that helps
(15 POINTS) Identify an equation in standard form for an ellipse with its center at the origin, a vertex at (13, 0), and a focus at (12, 0).
Answers
An equation in standard form for an ellipse with its center at the origin, a vertex at (13, 0), and a focus at (12, 0) is [tex]\bold{\frac{x^2}{169} +\frac{y^2}{25} =1}[/tex]
The correct answer is option (A)
What is equation of ellipse?"The standard form of equation of ellipse with center (0, 0) is, [tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex]
What are vertices of the standard ellipse?"The vertices of the standard ellipse [tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex] are [tex](\pm a,0)[/tex] "
What is focus of the standard ellipse?"The foci of the standard ellipse [tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex] are [tex](\pm c,0)[/tex], where [tex]c^{2} =a^{2}- b^{2}[/tex] "
For given question,
The center of the ellipse is at the origin.
Using the standard form of equation of the ellipse,
[tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex]
A vertex at (13, 0)
⇒ (a, 0) = (13, 0)
⇒ a = 13
And a focus at (12, 0).
⇒ (c, 0) = (12, 0)
⇒ c = 12
We know, [tex]c^{2}= a^{2}- b^{2}[/tex]
Now, we find the value of b i.e., minor axis
[tex]\Rightarrow 12^{2} =13^{2}- b^{2}\\\\\Rightarrow b^2=169-144\\\\ \Rightarrow b^2=25\\\\\Rightarrow b=\pm 5[/tex]
Substituting these values in the standard form of equation of ellipse with center (0, 0),
[tex]\Rightarrow \frac{x^2}{a^2} +\frac{y^2}{b^2} =1\\\\\Rightarrow \bold{\frac{x^2}{169} +\frac{y^2}{25} =1}[/tex]
Therefore, an equation in standard form for an ellipse with its center at the origin, a vertex at (13, 0), and a focus at (12, 0) is [tex]\bold{\frac{x^2}{169} +\frac{y^2}{25} =1}[/tex]
The correct answer is option (A)
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what is the exact solutions of x2=5x+2
Answers
x²-5x-2 = 0
Solve with x₁,₂ = (-b±√Δ)/2a
Δ = b²-4ac
call a (1)x², b -5 and c -2
x1,2 = (-(-5)±√(-5)²-4*1*(-2))/2*1
x1,2 = (5±√25+8)/2
x1,2 = (5±√33)/2
x1 = (5+√33)/2
x2 = (5-√33)/2
Answer:
The answer has a positive 5 and 33.
Step-by-step explanation:
I used a calculator.
If you start with a number divide it by 4 then multiply it by two you end up with 8 squared
Answers
8 squared = 64
so
(x/4)*2 = 64
divide x/4 by 2 to get x/2=64
now multiply both sides by 2 to get x=128
x = 128
House is 50.0 ft long and 26 ft wide and has 8.0-ft- m high ceilings. what is the volume of the interior of the house in cubic meters and in cubic centimeters?
Answers
What is 320 1/4 rounded to the nearest whole number?
Answers
320.25=320
I would say the correct answer is 320
hope this helps:)
Let's first turn the number into a decimal.
320.25
Now round to the nearest whole number
The answer is 320
Hope this helps! :)
Please help me ASAP.
David had a coupon for the grocery store. He graphed on the x-axis what his total bill would be if he didn’t use the coupon and graphed on the y-axis what his total bill would be if he used the coupon.
Based on the information in the graph, if David’s bill came to $66 after the coupon was applied, how much would his bill have been if he hadn’t used the coupon?
a.$64
b. $65
c. $67
d. $68
Answers
Answer:
d. $68Step-by-step explanation:
First, let's find the equation of the line.
The slope is defined by
[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
Where we are gonna use points (2,0) and (9,7).
[tex]m=\frac{7-0}{9-2}=\frac{7}{7}=1[/tex]
Then, we use the point-slope formula to find the equation.
[tex]y-y_{1} =m(x-x_{1} )\\y-0=1(x-2)\\y=x-2[/tex]
So, if David's bill came to $66 after coupon, it means [tex]y=66[/tex].
Replacing this value in the equation, we have
[tex]y=x-2\\66=x-2\\x=66+2\\x=68[/tex]
Therefore, the price without coupon is $68.
A coach wants to know if football players who warm up before a game will score more points than those who don't warm up. He will break the team up into two groups and make sure each player gets equal time on the field. He will then count how many points each player makes during the game. What statistic should he study?
Answers
The statistic that the coach should study is mean or the average score of the two teams. If the coach wants to know if football players who warm up before a game will score more points than those who don't warm up. He will break the team up into two groups and make sure each player gets equal time on the field. He will then count how many points each player makes during the game. After counting them, add the scores of the group that he divided and then divided it by the number of player in that group to get an average score on teams that warm up or do not warm up before the game.
(15 POINTS) A student is chosen at random from a school. Why are the events "choosing a student of age group 5−10" and "choosing a student of age group 11−15" mutually exclusive?
a) They are independent.
b) They are dependent.
c) A student can belong to only one age group.
d) A student can belong to both the age groups.
Answers
Hence, the answer to this question is letter C.
If x varies directly with y and x = 3.5 when y = 14, find x when y = 18.
Answers
x = 3.5 when y = 14
so
14 = 3.5k
k = 14/3.5
k = 4
when y = 18.
y = kx
18 = 4x
x = 18/4
x = 4.5
answer
when y = 18, x = 4.5
Answer:
the value of x= 4.5
Step-by-step explanation:
If x varies directly with y and x = 3.5 when y = 14
x varies directly with y , so equation is x= ky
where k is the constant of proportionality
x = 3.5 when y = 14, use the given values and find out k
Plug in the given values in x=k y
3.5= k * 14
Divide by 14 on both sides
0.25= k
So the value of k = 0.25
Now find out x when y= 18
x= ky
x= 0.25 * 18= 4.5
Calculate each unit rate
$11.49 for 3 packages
Answers
simplify 7p³ + 2m³ - 6m³ + 4p - 9p + 6p³
a) -4m³ + 8p²
b) 8p² - 4
c) 4m³ - 13p³ + 5p
d) -4m³ + 13p³ - 5p
Answers
= 13p³ - 4m³ - 5p
= -4m³ + 13p³ - 5p
answer
d) -4m³ + 13p³ - 5p
Final answer:
The simplified expression of 7p³ + 2m³ - 6m³ + 4p - 9p + 6p³ is -4m³ + 13p³ - 5p, which is option d).
Explanation:
To simplify the expression 7p³ + 2m³ - 6m³ + 4p - 9p + 6p³, we need to combine like terms.
Like terms have the same variable raised to the same power.
In this case, terms with p raised to the third power can be combined, and terms with m raised to the third power can also be combined, as well as the terms with just p.
Combine terms with p³: 7p³ + 6p³ = 13p³.Combine terms with m³: 2m³ - 6m³ = -4m³.Combine terms with p: 4p - 9p = -5p.Now the expression is simplified to -4m³ + 13p³ - 5p, which corresponds to option d).
PLEASE HELP!!!
The first two steps in determining the solution set of the system of equations, y = –x2 + 4x + 12 and y = –3x + 24, algebraically are shown in the table. Which represents the solution(s) of this system of equations? (3, 15) (–4, 36) (3, 15) and (4, 12) (–3, 33) and (–4, 36)
Answers
y = –3x + 24
so
–x2 + 4x + 12 = –3x + 24
x^2 -7x + 12 = 0
(x - 4)(x - 3) = 0
x - 4 =0; x =4
x - 3 = 0; x= 3
y = –3x + 24 = -3(3) + 24 = -9+24 = 15 (when x = 3)
y = –3x + 24 = -3(4) + 24 = -12+24 = 12 (when x = 4)
answer
(3, 15) and (4, 12)
Answer:
C
Step-by-step explanation:
or (3, 15) and (4, 12)
Suppose the line of best fit is being found for some data points that have an r-value of 0.657. If the standard deviation of the x-coordinates is 2.445, and the standard deviation of the y-coordinates is 9.902, what is the slope of the line to three decimal places?
Answers
r-value = 0.657 (r)
standard deviation of x-coordinates = 2.445 (Sx)
standard deviation of y-coordinates = 9.902 (Sy)
We are asked to find the slope of the line up to 3 decimal places.
To find the slope of the line, based on the data that we have, we can use this formula:
slope, b = r * (Sy / Sx)
substitute the values to the formula:
b = 0.657 * ( 9.902 / 2.445 )
Solve for the b.
Therefore, the slope of the line is
b = 2.66078, round off to three decimal places:
b = 2.661 is the slope of the line.
Answer: 2.661
Step-by-step explanation:
A P E X
Which answer correctly describes the relationship between two of the lines in the figure?
Answers
Joyce is trying to solve the equation y = x2 − 8x + 7 using the quadratic formula. She has made an error in one of the steps below. Find the step where Joyce went wrong. (1 point)
Step 1: x equals negative 8 plus or minus the square root of the quantity eight squared minus four times one times seven, end quantity, all over two times one.
Step 2: x equals negative 8 plus or minus the square root of sixty-four minus twenty-eight all over two times one.
Step 3: x equals negative 8 plus or minus the square root of thirty-six all over two times one.
Step 4: x equals negative 8 plus or minus six all over two.
Step 1
Step 2
Step 3
Step 4
Answers
[tex]x= \frac{-b+/- \sqrt{ b^{2}-4ac } }{2a} [/tex]
The parameters a, b and c represent the coefficients of the standard form of the quadratic equation: y = ax^2 + bx + c. Thus, for the equation y = x2 − 8x + 7,
a = 1
b = -8
c = 7
The mistake Joyce made was in Step 1. Because Step 1 is wrong, the rest of the equation is wrong consequently. The mistake was made by Joyce when she assigned b = 8. She forgot to include the negative sign of -8x.
Her mistake is in the first step, she wrote the equation incorrectly.
Solving quadratic equations:
A general quadratic equation:
ax^2 + bx + c = 0
has the solutions:
x = (-b ± √(b^2 - 4ac))/(2a)
In this case, the equation is:
y = x^2 - 8x + 7
And what Joyce writes in each step is:
Step 1:
x = (-8 ± √(8^2 - 4*1*7))/(2*1)
Then we can already see the mistake.
Notice that in the given equation, we have:
b = -8
And the general solution has:
x = (-b ± √(b^2 - 4ac))/(2a)
-b would be equal to 8, then what Joyce must have written here is:
x = (8 ± √((-8)^2 - 4*1*7))/(2*1)
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What is the common difference of a 43-term arithmetic sequence where the first term is -13 and the sum is 9,374?
Answers
so.. .we know the first term is -13, and the 43rd term's value is 449...so...this is an arithmetic sequence, thus, in order for us to get from -13 to 449 in 43 hops, we had to add "d" the common difference, 42 times.
so -13, -13 + d, (-13+d)+d, (-13+d+d)+d, ..... and so on.
but in short d + d + d + ... 42 times is just 42d
so, we know that
[tex]\bf \begin{array}{llll} -13+42d=&449\\ \ \uparrow &\ \uparrow\\ a_1&a_{43} \end{array}\implies 42d=462\implies d=\cfrac{462}{42}\implies \boxed{d=11}[/tex]
Christine buys 7 hamburgers and 3 sodas for $27.95. Laura buys 5 hamburgers and 4 sodas for $23.40. How much does a hamburger cost?
A. 1 .85
B. $3.20
C. $6.80
D. $6.55
E. $3.50
Answers
3s=27.95-7h divide both sides by 3
s=(27.95-7h)/3
Then we are told:
5h+4s=23.4, using s found above makes this equation become:
5h+4(27.95-7h)/3=23.4 multiply both sides by 3
15h+4(27.95-7h=70.2 perform indicated multiplication on left side
15h+111.8-28h=70.2 combine like terms on left side
-13h+111.8=70.2 subtract 111.8 from both sides
-13h=-41.6 divide both sides by -13
h=$3.20
I won tickets to a trip for four to the Super Bowl. I have eight friends but I can only bring three of them. In how many ways can I form my Super Bowl party?
Answers
Answer:
56
Step-by-step explanation:
PLEASE HELP
Probability allows a person to effectively measure the risks in selecting one alternative over others.
True
False
Answers
-10-2v<6 and 6v+12<-6.
need some help with this problem i keep messing a step
Answers
-2v < 6 + 10 6v < -6 - 12
-2v < 16 6v < -18
v > -16/2 v < -18/6
v > -8 v < -3
solution is : -8 < v < -3
3. what is the simplified form of x+4/7 - x+3/x+5
Answers
------- * ----- - ----------- * --- = --------------------
7 (x+5) (x + 5) 7 7( x + 5)
The expression [(x + 4) / (7)] - [(x + 3) / (x + 5)] in simplified form will be (x² + 2x - 1) / 7(x + 5). Then the correct option is A.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ [(x + 4) / (7)] - [(x + 3) / (x + 5)]
Simplify the expression, then we have
⇒ [(x + 4) / (7)] - [(x + 3) / (x + 5)]
⇒ [(x + 4)(x + 5) - 7(x + 3)] / [7(x + 5)]
⇒ [x² + 9x + 20 - 7x - 21] / [7(x + 5)]
⇒ (x² + 2x - 1) / 7(x + 5)
The expression [(x + 4) / (7)] - [(x + 3) / (x + 5)] in simplified form will be (x² + 2x - 1) / 7(x + 5). Then the correct option is A.
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A randomly generated list of numbers from 0 to 4 is being used to simulate an event, with the number 4 representing a success. What is the estimated probability of a success?
A.75%
B.60
C.25%
D.40%
Answers
The solution would be like this for this specific problem:
Given:
{0, 1, 2, 3, 4}
Success = 2, 3, and 4
Solution:
Success = 3 numbers
Sample = 5
= 3 / 5
= .6
= .6 * 100%
= 60%
So, the estimated probability of a success based from the randomly generated list of numbers being used to simulate an event is 60%.
To add, the measure of the likelihood that an event will occur is called probability and it is quantified as a number between 0 and 1, where, loosely speaking, 0 indicates impossibility and 1 indicates certainty.
Corrugated Specialties produces boxes of all kinds, and they manufacture an average of 67,000 shirt-size boxes per month. In November, they were told to increase production by 35%. How many shirt-size boxes will they produce in November? Hint: This question requires two calculations. A. 91,125 B. 23,625 C. 23,450 D. 90,450
Answers
67,000×0.35=23,450
So they will produce in November
67,000+23,450=90,450....answer
A catering service offers 12 appetizers, 6 main courses, and 7 desserts. A banquet chairperson is to select 6 appetizers, 2 main courses, and 5 desserts for a banquet. In how many ways can this be done?
Answers
= 291060
15 * 4 2/3 please help
Answers
4 2/3 = 14/3
15 = 15/1
14/3 * 15/1 = 14*15=210, 3*1 = 3
210/3 = 70
answer is 70
Your Cell Phone plane cost 55 dollars a month, plus 35 cents per minute. Write an equation to represent the monthly bill of the cell phone plan
Answers
T= total
55+35m=t
Hope this helps!
Answer:
F( x) = 0.35 x + 55
Merlin industries bought a laptop for $2100. It is expected to depreciate at a rate of 14% per year. What will the value of the laptop be in 5 years? Round to the nearest dollar.
Answers
f=ir^t, f=final value, i=initial value, r=common ratio or "rate", and t=times rate is applied or "time".
In this case i=2100 and r=(100-14)/100=0.86 so the equation is:
f=2100(0.86^t) and in five years...
f(5)=2100(0.86^5)
f(5)≈$987.90 (to nearest whole cent)
Sam scored 43 48 and 42 points on 3 test how many points should he get on the fourth test to get in average score of 50
Answers
(133+x)/4=50
133+x=200
x=67