You have been asked by the police department to find three locations the Acute Perps gang is likely to hit in the coming weeks. Because the gang sticks to a triangular pattern, the locations could be a translation, reflection, or rotation of the original triangle. For this step, identify and label three points on the coordinate plane that are a translation of the original triangle. Next, use the coordinates of your translation along with the distance formula to show that the two triangles are congruent by the SSS postulate. You must show all work with the distance formula.
Answers
Note:
Images with coordinates or original and translated triangles are attached.
Answer:
The coordinates for the given triangle are A(6,3), B(6,-3) and C(-2,-3), respectively.
Let us translate this triangle by -6 units along the x-axis and +3 units along the y-axis. This means that 6 will be subtracted from each of the abcissas (x-points) and 3 will be added to each ordinates (y-points). Hence, our translated triangle will have the following coordinates: A'(0,6), B'(0,0) and C'(-8,0), respectively.
Now to prove that both triangles are congruent, we use the SSS postulate, which states that:
"If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent."
Distance between two point P1 and P2 will be:
[tex]|P_1P_2|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Now using distance formula to find sides of triangle ABC and triangle A'B'C'.
For Triangle ABC:
|AB| = [tex]\sqrt{(6-6)^2+(-3-3)^2} =\;6\;units[/tex]
|AC| = [tex]\sqrt{(-2-6)^2+(-3-3)^2} =\;10\;units[/tex]
|BC| = [tex]\sqrt{(-2-6)^2+[-3-(-3)]^2} =\;8\;units[/tex]
For Triangle A'B'C':
|A'B'| = [tex]\sqrt{(0-0)^2+(0-6)^2} =\;6\;units[/tex]
|A'C'| = [tex]\sqrt{(-8-0)^2+(0-6)^2} =\;10\;units[/tex]
|B'C'| = [tex]\sqrt{(-8-0)^2+(0-0)^2} =\;8\;units[/tex]
Hence, as the distances are equal, the two triangles are congruent by SSS postulate.
Related Questions
What segment is an altitude of triangle ABC?
segment AC
segment BC
segment BD
segment CD
...?
Answers
Line segment BD is the altitude of triangle ABC.
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Find the roots of the polynomial equation.
2x3 + 2x2 – 19x + 20 = 0
Answers
Answer:
1. a, -3,-1,1,3
2. a, 3+i/2, 3-i/2, -4
3. d, 6- sqrt 6
4. a, x3-8x2-11x+148=0
5. d, there are either 2 or 0 positive roots and one negative
Step-by-step explanation:
I did the quick check.
Final answer:
The roots of the polynomial equation 2x³ + 2x² – 19x + 20 = 0 are complex.
Explanation:
To find the roots of the polynomial equation 2x³ + 2x² – 19x + 20 = 0, we can use the factoring method or the quadratic formula. Let's use the quadratic formula. The formula is x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation. In this case, a = 2, b = 2, and c = 20. Plugging the values into the quadratic formula, we get:
x = (-2 ± √(2² - 4(2)(20))) / (2(2))
x = (-2 ± √(4 - 160)) / 4
x = (-2 ± √(-156)) / 4
Since we cannot take the square root of a negative number in the real number system, the roots of the given equation are complex, which means there are no real solutions.
Find the common ratio of the following geometric sequence.
If necessary, use the slash bar ( / ) to enter a fraction. Reduce fractions to their lowest terms.
(5/12),(1/3),(4/15),(16/75),(64/375)
Answers
= - 2 / 5
As you know, to find the common ratio we use this - r = T3/T2
Hope it's clear! Do hope you will find useful!
Marietta drives her tow truck 312 miles in 8 hours. What is her average speed in miles per hour? Be sure to include the equation for speed in your answer.
Answers
We have, distance = 312 miles &
Time = 8 hours,
Substitute their values into the expression,
Savg = 312 / 8 = 39 miles/hour
So, the final average speed is 39 miles / hour
Hope this helps!
The average speed in miles per hour is 39mi/hr
How to calculate Speed of a bodySpeed is the ratio of distance with respect to time. The formula for calculating speed is expressed as:
Speed = Distance/Time
Given the following
Distance = 312 miles
Time = 8 hours
Substitute
Speed = 312/8
Speed = 39mi/hr
Hence the average speed in miles per hour is 39mi/hr
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The Smiths plan to recarpet their family room, which measures 15 ft. by 20 ft. How many square yards of carpet are needed?
Answers
Area = width x length
w= 15 x 1/3 = 5
l = 20 x 1/3 = 6 2/3
Area = 5 x 6 2/3
33 1/3 square yards
Answer: [tex]33\frac{1}{3}[/tex] square yards of carpet is needed.
Step-by-step explanation:
Given: The dimensions for the carpet is 15 ft. by 20 ft.
We know that area ( in square units ) of a rectangle is given by :-
[tex]Area=length\times width[/tex]
Therefore, area of the required carpet is given by :-
[tex]Area=20\times15=300\text{ square feet}[/tex]
We know that 1 feet =1/3 yard
Now,
[tex]300\text{ square feet}=300\times\frac{1}{3}\times\frac{1}{3}\\=\frac{100}{3} \text{square yards}=33\frac{1}{3}\text{ square yards}[/tex]
Hence, [tex]33\frac{1}{3}[/tex] square yards of carpet is needed.
Find the exact area of a circle having the given circumference.
4(sqrt3 PI ) ...?
Answers
since C = 2*pi*r = 4sqrt(3)*pi:
r = C/2*pi = 4sqrt(3)*pi / 2* pi = 2sqrt(3)
Therefore, to solve for Area:
Area = pi*r^2 = pi*(2sqrt(3))^2 = 12pi
The area is 12pi.
Answer:
12(pi)
Step-by-step explanation:
find the inverse of f informally. verify that f(f^-1(x))=x and f^-1(f(x))=x
f(x)= (x-1)/5
Answers
To find the inverse of a function, switch x and y and solve for y. The inverse of f(x) = (x-1)/5 is f^-1(x) = 5x + 1. Verify that f(f^-1(x)) = x and f^-1(f(x)) = x.
Explanation:To find the inverse of a function, we need to switch the roles of x and y and solve for y. In other words, we need to solve the equation y = (x-1)/5 for x. Let's do that:
Step 1: Replace y with x and x with y: x = (y-1)/5.
Step 2: Solve for y: Multiply both sides by 5: 5x = y - 1. Add 1 to both sides: 5x + 1 = y.
So, the inverse of f(x) = (x-1)/5 is f-1(x) = 5x + 1.
To verify that f(f-1(x)) = x, substitute f-1(x) into f(x) and simplify:
f(f-1(x)) = f(5x + 1) = ((5x + 1) - 1)/5 = 5x/5 = x.
Similarly, to verify that f-1(f(x)) = x, substitute f(x) into f-1(x) and simplify:
f-1(f(x)) = f-1((x-1)/5) = 5((x-1)/5) + 1 = x-1+1 = x.
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Solve the system using elimination.
5x + 4y = 12
3x – 3y = 18
Answers
Final answer:
To solve the system of equations using elimination, multiply one equation by a constant so that the coefficients of one variable will be the same in both equations. Then add or subtract the equations to eliminate that variable. Finally, solve for the remaining variable and substitute back to find the complete solution.
Explanation:
To solve the system of equations using elimination, we need to eliminate one variable by adding or subtracting the two equations. In this case, we can eliminate the variable y by multiplying the first equation by 3 and the second equation by 4. This will give us:
15x + 12y = 36
12x - 12y = 72
Next, we can add the two equations together to eliminate y:
27x = 108
Dividing both sides by 27, we find that x = 4.
Substituting this value of x back into one of the original equations, we can solve for y:
5x + 4y = 12
5(4) + 4y = 12
20 + 4y = 12
Subtracting 20 from both sides, we get 4y = -8.
Dividing both sides by 4, we find that y = -2.
Therefore, the solution to the system of equations is x = 4 and y = -2.
The school that Scott goes to is selling tickets to a fall musical. On the first day of ticket sales the school sold 1 senior citizens tickets and 12 students tickets for a total of $130. The school took in $80 on the second day by selling 5 senior citizens tickets and 3 student tickets. Find the price of a senior citizens ticket and the price of a student tickets
Answers
Carol buys a reference book that originally cost $87.50 for 15% off. She pays a sales tax of 4.5%. What is the total cost of the book?
Answers
(87.5*.85)(1.045)
$77.72 (to nearest cent)
Answer:
$77.72
Step-by-step explanation:
This is the total cost of the book with tax.
What is the value of x? If necessary, round your answer to two decimal places.
Answers
write 158/4 as a mixed number in simplest terms. Thank you.
Answers
So, your final answer is 39 1/2
Hope this helps!
Final answer:
The mixed number of 158/4 simplified is 39 1/2. A proportion comparing the ratios 1/48 and w/16 is solved by cross-multiplication resulting in w = 1/3 as the solution.
Explanation:
To write 158/4 as a mixed number in simplest terms, we first divide 158 by 4. When we do this division, 4 goes into 158, 39 times completely, since 4 * 39 = 156, and we get a remainder of 2. Therefore, the mixed number form of 158/4 is 39 2/4. To simplify this fraction further, we divide the numerator and the denominator by their greatest common divisor, which in this case is 2. Simplifying 2/4 by dividing both the numerator and denominator by 2, we get 1/2. Hence, the mixed number in its simplest terms is 39 1/2.
To set up a proportion using the given ratios, we start with the ratio 1/48 and set it equal to w/16, which can be represented as:
1/48 = w/16
When solving for w, we cross-multiply to get:
1 * 16 = 48 * w
Which simplifies to:
16 = 48w
Finally, to find the value of w, we divide both sides of the equation by 48, which gives us w = 16/48. Simplifying by dividing both numerator and denominator by the greatest common divisor, 16, we get:
w = 1/3
Rich bought 5 cupcakes and one pie. He knows his total bill and knows the pie was $6.89, but he wants to find the price of the cupcakes. How can he determine the price of each cupcake?
Answers
To determine the price of each cupcake, subtract the price of the pie from the total bill and then divide the result by the number of cupcakes. Each cupcake costs $1.62.
Explanation:To determine the price of each cupcake, Rich can subtract the price of the pie from the total bill and then divide the result by the number of cupcakes:
Let's say the total bill is $15.00.Subtract the price of the pie ($6.89) from the total bill: $15.00 - $6.89 = $8.11.Divide the remaining amount by the number of cupcakes (5): $8.11 ÷ 5 = $1.62.Therefore, each cupcake costs $1.62.
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Consider the equation y = 8 - 3x. for every increase of 1 in the x- variable, what is the change in the y- variable?.
a. increase of 3.
b. increase of 8.
c. decrease of 3.
d. decrease of 8
Answers
Mrs. Gomes found that 40% of students at her high school take chemistry. She randomly surveys 12 students. What is the probability that exactly 4 students have taken chemistry? Round the answer to the nearest thousandth. A)0.005 B)0.008 C)0.213 D)0.227
Answers
[tex]P ( k = 4 ) = nCk * p ^{k}(1-p) ^{n}= \\ =495 * 0.4 ^{4}* ( 0.6 ) ^{8}= [/tex]
= 495 * 0.0256 * 0.0167961 =
= 0.21284 ≈ 0.213
Answer: C ) 0.213
Answer:
The correct option is C. 0.213
Step-by-step explanation:
Percentage of students at high school who takes chemistry = 40%
So, probability of students who take chemistry = 0.4
So, probability of students who do not take chemistry = 1 - 0.4
= 0.6
Total number of students taken for survey = 12
Now, we need to find the probability that exactly 4 students have taken chemistry among the 12 surveyed students.
By using binomial distribution :
n = 12 , p = 0.4 , q = 0.6 , k = 4
[tex]\text{Required Probability = }_{k}^{n}\textrm{C}\cdot(p)^k\cdot(q)^{n-k}\\\\\implies\text{Required Probability = }_{4}^{12}\textrm{C} \cdot(0.4)^4 \cdot(0.6)^8 \\\\\implies \text{Required Probability = }0.2128\approx 0.213[/tex]
Therefore, The correct option is C. 0.213
A moves points a specified distance along a line parallel to a specified line.
a. translation
b.reflection
c. rotation
d. dilation
Answers
Answer:
It's A. translation
Step-by-step explanation:
Jolie uses 2 tomatoes every day to prepare her salad. If n equals the number of tomatoes Jolie had before she made her salad and c equals the number of tomatoes left after the salad is made, which equation represents the number of tomatoes Jolie has after she made her salad?
n = 2 − c
c = n − 2
c = 2 − n
n = c − 2
please just give me the answer.
Answers
n - the number of tomatoes before the salad is made
c - the number of tomatoes after the salad is made
Jolie uses 2 tomatoes (n - 2) every day to prepare her salad and then c tomatoes remained: n - 2 = c
Or:
c = n - 2
Answer:
d the answer is d
Samuel drove 28 miles in 32 minutes. Beverly drove 42 miles in 48 minutes.
Are the ratios of miles to minutes for Samuel and Beverly proportional?
Answers
Apply to Beverly. 48 divided by 48 to give 1 minute. 42 divided by 48 is 0.875 miles in a minute.
The answer is yes, they are proportional.
Answer:
Yes. Ratios of miles to minutes for Samuel and Beverly are proportional
Step-by-step explanation:
Samuel's speed can be calculated as following:
[tex]28/32=0,875[/tex]
0,875 miles per minute.
On the other hand Beverly's speed can be calculated as following:
[tex]42/48=0,875[/tex]
0,875 miles per minute
If we convert the speed to mile per hour:
[tex]0,875*60=52,5[/tex]
It can be easily seen that both Samuel and Beverly drove at the same speed at 52,5 miles per hour.
The rectangles garden is 25ft by 15ft what is the area of the garden ?
Answers
Area=25x15
Area=375
what is the answer to this 10-4b
Answers
|10 - 4(8)|
|10 - 32|
|-22| = 22
The answer is 22.
10-32
-22
Hope this helps.
What are the roots of the equation 2x2 + 9x + 6 = 0?
Answers
On Saturday, a local hamburger shop sold a combined total of 464 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Saturday?
Answers
The number of hamburgers will be 348.
What is an expression?
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that On Saturday, a local hamburger shop sold a combined total of 464 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold.
The number of hamburgers will be calculated as below:-
Cheeseburgers= x
Hamburgers= 3x
3x+x=464
4x=464
x=116
Substitute the value of x in expression.
Hamburgers= 3x
Hamburgers= 3 x 116 = 348
Therefore, the number of hamburgers will be 348.
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The local hamburger shop sold 116 hamburgers on Saturday. We determined this by setting up an equation where the number of hamburgers (H) plus three times the hamburgers (3H) equaled the total sales of 464 burgers, and then solving for H.
Explanation:The question asks us to solve a basic algebra problem involving hamburgers and cheeseburgers. Let's define the number of hamburgers sold as H. Since the number of cheeseburgers sold was three times the number of hamburgers sold, we can represent the number of cheeseburgers as 3H. The total number of burgers sold was 464. Now, we can write down the equation:
H + 3H = 464
This simplifies to:
4H = 464
Now, we divide both sides by 4 to find the value of H:
H = 464 / 4
H = 116
So, the local hamburger shop sold 116 hamburgers on Saturday.
.002 times 900000 scientific notation
Answers
0,002×9.10^5
0,018.10^5
0,000018.10^-1
integrate 1 / sqrt(25 - 16x^2) dx
Answers
To integrate 1 / sqrt(25 - 16x^2) dx, we use trigonometric substitution with x = (5/4)sinθ. After substitution, integration, and back-substitution, the result is arcsin(4x/5) + C, where C is the constant of integration.
Explanation:The integral to solve is ∑ (1 / sqrt(25 - 16x^2)) dx, which resembles the inverse trigonometric function, specifically the arcsine function. To solve this integral, we can use a trigonometric substitution. Since the integral involves a square root of a difference of squares, we can substitute x with (5/4)sinθ, which simplifies the integral considerably.
After substitution, we can then use the derivative of sinθ, which is cosθ, in order to find the full differential dx to replace in our integral. The resulting integral in terms of θ can be integrated using standard techniques, yielding an arcsine function as the antiderivative. After integrating, we must then convert back from θ to x to express the solution to the original integral in the original variable.
The answer to the integral ∑ (1 / sqrt(25 - 16x^2)) dx is arcsin(4x/5) + C, where C is the constant of integration. The substitution step is crucial in solving this type of problem and is a commonly used method in calculus.
The letters from the word “integer” are placed on cards and put in a hat. If someone picks 1 card out of the hat, how many different outcomes are possible?
A.
1 outcome
B.
5 outcomes
C.
6 outcomes
D.
7 outcomes
Answers
you can only count "e" once because even though it is in the bag twice, drawing it a second time would be the same outcame.
hope this help
The gross weight of a package and its contents is 11 pounds 5 ounces . If the packaging weighs 1 pound 15 ounces , what's the net weight of the contents
Answers
The increase in a person’s body temperature T(t), above 98.6ºF, can be modeled by the function T(t)=(4t)/(t^2 +1), where t represents time elapsed. What is the meaning of the horizontal asymptote for this function? The horizontal asymptote of y = 0 means that the person’s temperature will approach 98.6ºF as time elapses. The horizontal asymptote of y = 0 means that the person’s temperature will approach 0ºF as time elapses. The horizontal asymptote of y = 4 means that the person’s temperature will approach 102.6ºF as time elapses. The horizontal asymptote of y = 4 means that the person’s temperature will approach 4ºF as time elapses.
Answers
The person's body temperature will approach 98.6ºF as time lapses. Option A is correct.
How to calculate the horizontal asymptotes of a function?A horizontal asymptote for a function is an imaginary line that is not part of the graph and lies along the x-axis of the graph either to the left or right.
The horizontal asymptote of the given function can be described as the nature of the function T(f) as t approaches infinity.
This is the point where the line y=0 which means that the person's body temperature will approach 0ºF above 98.6ºF as t goes to infinity.
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Management for a chain of restaurants recorded the number of appetizers, X, ordered by tables dining. They observed that X had the following probability distribution.
Value of X
0
1
2
3 or more
Probability
0.60
0.35
0.04
0.01
Reference: Ref 9-7
The probability that a randomly chosen table orders at least one appetizer is
A. 0.35.
B. 0.39.
C. 0.40.
D. none of the above.
Answers
Find the domain and range of the relation and determine whether it is a function.
Domain: positive integers; range: positive integers; no, it is not a function.
Domain: x > 3; range: y > 0; yes, it is a function.
Domain: all real numbers; range: all real numbers; yes, it is a function.
Domain: x ³ 0; range: y > 3; no, it is not a function.
Answers
Answer:
y>0
Step-by-step explanation:
How many 1/6 are in 1/2?
Answers
1/2=3/6
Which is 3 1/6
Answer:
3 1/6
Step-by-step explanation: it is because you would have to divide the 1 and the 6 well not really divide more of the multiplying then after that you switch 1 and 2 and the 2 is and the top and 1 at the bottom and you to butterfly some of you should know then you get 3 1/6