Draw the image of ∆PQR after a rotation of 180° about the origin. Label the image ∆P'Q'R'.
Draw the image of ∆PQR after a reflection across the x-axis. Label the image ∆P"Q"R".
Answers
A - when doing a 180 degree rotation, the coordinates (x,y) would become (-x,-y), in other words, the inverse of the numbers in the x and y places, (-1,2)->(1,-2)
B - when reflecting over the x axis, only the y coordinate inverts, (x,y) becomes (x,-y), (1,-2)->(1,2)
To obtain the image of triangle ∆PQR after a 180° rotation about the origin, we applied the rotation formula to each vertex, resulting in the new coordinates P'(-1, 1), Q'(-3, 2), and R'(-3, 4). Connecting these points forms the rotated triangle ∆P'Q'R'.
To draw the image of triangle ∆PQR after a 180° rotation about the origin, we'll need to find the new coordinates of the vertices P', Q', and R'. The general formula for rotating a point (x, y) by 180° about the origin is to negate both the x and y coordinates, resulting in the point (-x, -y). Let's apply this formula to each vertex:
Vertex P(1, -1) is rotated to P'(-1, 1).
Vertex Q(3, -2) is rotated to Q'(-3, 2).
Vertex R(3, -4) is rotated to R'(-3, 4).
Now, we have the new coordinates for the vertices of the rotated triangle ∆P'Q'R'. Let's plot these points on a coordinate plane:
P'(-1, 1)
|
|
| Q'(-3, 2)
| /
|/
R'(-3, 4)
The triangle ∆P'Q'R' is formed by connecting these three points, and it is the image of ∆PQR after a 180° rotation about the origin.
For more such information on: triangle
https://brainly.com/question/30561079
#SPJ12
Related Questions
△VAT≅△BDT.
¯¯¯¯¯
What is length of BT ?
Answers
Answer:
[tex]BT=6.3[/tex]
Step-by-step explanation:
We have been given that triangle VAT is congruent to triangle BDT. We are asked to find the length of segment BT.
Since both triangles are congruent, therefore, their corresponding sides will be equal by the definition of congruence.
[tex]\Delta VAT\cong \Delta BDT[/tex]
By the definition of congruence:
[tex]VA=BD[/tex]
[tex]AT=DT[/tex]
[tex]VT=BT[/tex]
Since the length of side VT is 6.3 units, therefore the length of BT is 6.3 units as well.
The container that holds the water for the football team is 7/10 full. after pouring out 6 gallons of water, it is 1/2 full. how many gallons can the container hold?
Answers
7/10 = 7/10 & 1/2 = 5/10
7/10 - 6 gallons = 5/10
7/10 - 5/10 = 6 gallons
2/10 = 6 gallons
multiply each side by 5
10/10 = 30 gallons
container can hold 30 gallons
The total capacity of the container is 30 gallons in volume.
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying it with the value of a single unit.
Given is that the container that holds the water for the football team is 7/10 full. After pouring out 6 gallons of water, it is 1/2 full.
Assume that the container total capacity is [x] gallons. Then, according to the question -
7x/10 - 6 = x/2
7x/10 - x/2 = 6
x(0.7 - 0.5) = 6
0.2x = 6
x = 6/0.2
x = 6/(1/5)
x = 30 gallons
Therefore, the total capacity of the container is 30 gallons in volume.
To solve more questions on unitary method, visit the link below-
brainly.com/question/18174151
#SPJ5
What are 3 consecutive integers who's sum is 396?
Answers
x+x+1+x+2 = 396.
Combine like terms. All the x's will add together to become 3x, while the ones without will be 1+2 = 3.
3x+3 = 396.
We need to start getting the x by itself. We must subtract 3 from both sides. This is how it should end up:
3x = 393.
Then, we will finally get x by itself by dividing 3 by both sides.
x = 131. The answer is x = 131.
Two cars leave the origin; one goes north at 45 mph and the other goes south at 40 mph. after how many hours will they be 350 miles apart?
Answers
so, say car N goes north at 45mph, and car S goes south at 40mph.
after "some time" they'd be apart 350 miles, when that happens, N has been travelling for say "t" hours, and S has been travelling for the same "t" hours, their time has to be the same.
now, we know they'd be 350 miles apart, so if say N has gone "d" miles, then S has gone the slack, or "350 - d".
and we know their rates.
[tex]\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ \textit{Car N}&d&45&t\\ \textit{Car S}&350-d&40&t \end{array} \\\\\\ \begin{cases} \boxed{d}=45t\\ 350-d=40t\\ --------\\ 350-\boxed{45t}=40t \end{cases} \\\\\\ 350=85t\implies \cfrac{350}{85}=t\implies \cfrac{70}{17}=t\implies 4\frac{2}{17}=t[/tex]
which is about 4 hours and 7 minutes with 3.5 seconds.
To find the time when two cars traveling in opposite directions are 350 miles apart, we calculate their relative speed, which is 85 mph. We then divide the distance (350 miles) by this speed to get approximately 4 hours and 7 minutes.
Explanation:The question is asking to find out after how many hours two cars traveling in opposite directions will be 350 miles apart, with one car going north at 45 mph and the other south at 40 mph. To solve this, we need to apply the concept of relative speed.
The relative speed is the sum of the individual speeds when two objects are moving in opposite directions. In this case, it's 45 mph + 40 mph = 85 mph. This is the speed at which the distance between the two cars is increasing.
Next, to find the time 't' when they will be 350 miles apart, we use the formula:
Distance = Speed × Time
350 miles = 85 mph × t
To solve for 't', we divide both sides by 85 mph:
t = 350 miles / 85 mph = 4.1176 hours, or approximately 4 hours and 7 minutes.
Find the length of the hypotenuse if the legs of a triangle are 5cm and 12 cm.
Question 5 options:
7cm
13cm
17cm
169cm
Answers
13 cm is length of the hypotenuse
________________________________
c² = a² + b² ;
In which "c" is the hypotenuse;
a = 5 ;
b = 12 ;
c = ? ;
Solve for "c"
+√(c²) =√(a² + b²) ;
c = √(5² + 12²) ;
c = √(25 + 144) ;
c = √169 ;
c = 13 cm .
_______________________________________________________
The correct answer is: [B]: " 13 cm" .
_______________________________________________________
Owen jarred 10 liters of jam after 2 days. How many days did Owen spend making jam if he jarred 15 liters of jam?
Answers
So 10 +5=16
So, he spent three days making jam to get 15 liters.
Hope this helps and please mark brainiest.
in diagram below, fg=10 and HJ=10. Which additional facts would guarantee that fghj is a parallelogram? Check all that apply.
Answers
* Sides fj and sides gh should be equal
* The blue angles should not be equal to the red angles
* The blue angles should be equal
* The red angles should be equal
For a data set, the mean is 3.17 and the range is 1.4. The data set is transformed by adding 0.5 to each data value. What are the mean and range of the new data set?
a. mean: 3.67; range: 1.9
b. mean: 3.67; range: 1.4
c. mean: 3.17; range: 1.9
d. mean: 3.17; range: 1.4
Answers
Adding 0.5 to each value in the data set increases the mean to 3.67 while the range remains at 1.4. Hence, the correct answer is option b.
When a constant is added to each data value in a data set, the mean of the data set increases by that constant, while the range remains unchanged. In this case, adding 0.5 to each data value will increase the mean by 0.5 but the range will stay the same.
Given the original mean: 3.17 and original range: 1.4:
New mean = 3.17 + 0.5 = 3.67
New range = 1.4
Therefore, the correct answer is option b: mean: 3.67; range: 1.4.
The perimeter of this shape is 82 cm. what is the length of side d? cm
Answers
A bag contains equal numbers of green and blue marbles. You can divide all the green marbles into groups of 12 and all the blue marbles into groups of 16. What is the least number of each color of marble that can be in that bags?
Answers
To solve this problem, we need to find for the LCM of each number. That is:
12: 12, 24, 36, 48, 60
16: 16, 32, 48, 64, 80
So we can see that the LCM is 48.
Therefore the least number of each color of marble must be 48.
Answer:48
Step-by-step explanation:love ya thank me later
Expand and simplify 2(2x-3)+2(3x+4)
Answers
= 4x - 6 + 6x + 8
= 10x + 2
answer
10x + 2
twice the sum of a number and 5 equals 9 as a equation
Answers
I believe it looks like this..
2*x+5=9
Btw, x = 3 is your answer if you're wondering..
Hope this helps! ☺♥
x= r-h/y
solve for h and r
Answers
Let's first solve for h :)
Add h/y to both sides.
h/y + x = r
So, r = h/y + x
Now, let's solve for h.
x = r-h/y
Subtract r from both sides.
-r + x = -h/y
Multiply both sides by y.
y(-r + x) = y(-h/y)
Simplify.
-ry + xy = -h
Divide both sides by -1.
ry - xy = h
So, h = ry - xy
~Hope I helped!~
To solve for h, rearrange the equation to h = r - xy, and to solve for r, rearrange it to r = xy + h. This process involves basic algebraic manipulation to isolate each variable on one side of the equation.
Explanation:The original equation given is x = r - h/y. To solve for h, we need to get h by itself on one side of the equation. First, we can rearrange the equation to isolate h:
Multiply both sides by y to get rid of the fraction: xy = r - h.Move all terms containing h to one side and the rest to the opposite side: h = r - xy.To solve for r, we take the original equation and solve for r explicitly:
First, isolate the term containing r: r = xy + h.Now we have both variables solved in terms of x, y, and each other.
I shuffle a standard deck with 52 cards and randomly draw the ace of hearts, then put it to one side. what is the probability that the next card i draw is either an ace or a heart?
Answers
Hi! Please help me with this question! 12 points and brainliest to whoever answers it correctly first!
1. Given: -3x + y = 1. Write the equation in general form Ax + By + C =0.
3x - y + 1 = 0
-3x + y - 1 = 0 (not this one)
3x - y = -1
Answers
Which of the following is not a pair of similar polygons?
Answers
Answer: The answer is the last figure, figure (D). Attached the image.
Step-by-step explanation: We are given four pairs of polygons and we are to select the pair in which the two polygons are not similar.
In the first pair of polygons, the ratio of the corresponding sides will be same as follows:
[tex]\dfrac{2}{\frac{2}{3}}=\dfrac{4}{\frac{4}{3}}=3.[/tex]
So, the polygons are similar.
In the second pair of polygons, the ratio of the corresponding sides will be same as follows:
[tex]\dfrac{2.82}{1.41}=\dfrac{2.24}{1.12}=\dfrac{3}{1.5}=2.[/tex]
So, the polygons are similar.
In the third pair of polygons, the ratio of the corresponding sides will be same as follows:
[tex]\dfrac{1.41}{1.41}=\dfrac{1.12}{1.12}=\dfrac{1.5}{1.5}=1.[/tex]
So, the polygons are similar.
In the fourth pair of polygons, we have
[tex]\dfrac{12}{\frac{4}{3}}=12\times\dfrac{3}{4}=9,[/tex]
and
[tex]\dfrac{4}{\frac{2}{3}}=4\times\dfrac{3}{2}=6\neq 9.[/tex]
So, the polygons are not similar in this case.
Thus, the last figure, attached herewith, is the correct option.
All of the figures are pair of similar polygons
What are similar shapes?Similar shapes have the same shape but may differ in size.
Their corresponding angles are equal, and their corresponding sides are in proportion.
This property allows for resizing through a constant scale factor while maintaining identical angles.
We can test of the polygons are similar by checking the ratio of their corresponding sides are equal.
Fig 1 = 2/2/3 = 3
4/4/3 = 3
therefore the pair of polygons in fig1 are similar.
fig 2 = 3/1.5 = 2
2.82/1.41 = 2
therefore fig2 is a pair of similar polygons.
Therefore, all of the figures are pair of similar polygons
learn more about similar shapes from
https://brainly.com/question/14285697
#SPJ3
What is the reason for Statement 2 of the two-column proof?
a) Linear Pair Postulate
b) Definition of angle
c) Definition of bisect
d) Angle Addition Postulate
Answers
We have been given that PQ bisects [tex]\angle RPS[/tex]. In the second statement of the given two-column proof, the statement is [tex]\angle RPQ\cong\angle QPS[/tex].
This implies that the two angles formed by bisection of angle [tex]\angle RPS[/tex] by the line PQ are equal. We know that the reason for this is simple. It is the definition of bisection of an angle that the two smaller angles formed will be equal to each other.
Therefore, the reason for statement 2 of the given two column proof is c) Definition of bisect
The graph illustrates a reflection of . What is the line of reflection?
A.
x-axis
B.
y-axis
C.
y=x
D.
y=2x
Answers
Answer:
A. x-axis
Step-by-step explanation:
It is a mirror image. The doesn't change.
The figure J'K'M' is just reflected over the x-axis.
So it is reflection about the x-axis.
Therefore, answer is A. x-axis
Hope this will helpful.
Thank you.
Which phrase best describes a rock? A. a chemical arranged in a lattice B. a gabbro of minerals C. a mixture of crystals D. a fire-formed crystal
Answers
Your answer is B. a gabbro of minerals
Hope this helps :)
-Take Care Now-
~Ans~
A baseball player got 102 hits in the last 300 times at bat.
What percent of the times at-bat did the player get a hit?
The player got a hit ? % of the time.
Answers
answer is 34%
The answer to your awesome question is 34%. this is because you have to divide in order to find the answer. 102 divided by 300 = 0.34, therefore your answer would be 34%!
Have a great day!
PLZ Help I really need to know how to do this
SKIING The distance in meters that a person
travels on skis can be modeled by d(t) = 0.2t^2 + 3t,
where t is the time in seconds. Use the Remainder
Theorem to find the distance traveled after 45
seconds.
Answers
An investment is currently worth 2.125 × 10^4 dollars . Ten years ago, the investment was worth 1.25 × 10^3 dollars. How many times greater is the value of the investment today than the value of the investment ten years ago?
Answers
The investment today is 17 times greater than it was ten years ago.
To find out how many times greater the value of the investment is today compared to ten years ago, you can divide the current value by the value ten years ago.
So, let's do the calculation:
Current value = 2.125 × 10^4 dollars
Value ten years ago = 1.25 × 10^3 dollars
[tex]\( \text{Times Greater} = \frac{\text{Current Value}}{\text{Value Ten Years Ago}} \)[/tex]
Substitute the values:
[tex]\( \text{Times Greater} = \frac{2.125 \times 10^4}{1.25 \times 10^3} \)[/tex]
To divide these numbers, subtract the exponents:
[tex]\( 10^4 \div 10^3 = 10^{4-3} = 10^1 = 10 \)[/tex]
So,
[tex]\( \text{Times Greater} = \frac{2.125}{1.25} \times 10 = 1.7 \times 10 = 17 \)[/tex]
Therefore, the value of the investment today is 17 times greater than the value of the investment ten years ago.
what is the average rate of change from x = 0 to x=4
A. 0
B. 1
C. 4
D. 8
Answers
Mary invests £12000 in a savings account. The account pays 1.5% compound interest per year. Work out the value of her investment after 2 years
Answers
Jasmine bought computer which was discounted from 350 to 273. What is the discount rate
Answers
subtract the 2 numbers to find amount of discount
350 - 273 = 77
now divide 77 by 350 = 0.22
0.22 = 22% discount
Answer:
22%
Step-by-step explanation:
The discount rate given on the cost of an item is the ratio of the discount to the old price expressed as a percentage.
The discount is the difference between the old and new price while the new price is known as the discounted price.
the discount = $350 - $273
= $77
The discount rate
= $77/$350
= 0.22
= 22%
Ethan invested £500 in the bank for 2 years. he earned £40 simple interest in total. what was the simple interest rate per annum
Answers
I=prt
I interest earned 40
P principle 500
R interest rate?
T time 2 years
Solve the formula for r by dividing both sides by pt to get
R=I/pt
R=40÷(500×2)
R=0.04×100
R=4%
Hope it helps!
Answer:
4%.
Step-by-step explanation:
We have been given that Ethan invested £500 in the bank for 2 years. He earned £40 simple interest in total. We are asked to find the annual interest rate.
We will use simple interest formula to solve our given problem.
[tex]I=Prt[/tex], where,
I = Amount of interest,
P = Principal amount,
r = Annual interest rate in decimal form,
t = Time in years.
Upon substituting our given values in above formula, we will get:
[tex]40=500*r*2[/tex]
[tex]40=1000*r[/tex]
Now, we will divide both sides of our given equation by 100.
[tex]\frac{40}{1000}=\frac{1000*r}{1000}[/tex]
[tex]\frac{4}{100}=r[/tex]
[tex]\frac{1}{25}=r[/tex]
[tex]0.04=r[/tex]
Since our given interest rate is in decimal form, so we need to convert it in percentage.
[tex]0.04\times 100\%=4\%[/tex]
Therefore, the simple interest rate per annum is 4%.
c) Solve the equation you wrote in part b to find how many hours you would have to work to pay for the first year of video streaming service. Show your work and round your answer to the nearest tenth.
Answers
Every Month $68 $18 $18 $18 $18 $18 $18 $18 $18 $18 $18 $18
Total For Year$68 $86 $104 $122 $140 $158 $176 $194 $212 $230 $248 $266
Which ordered triple is a solution of this system?
2x + y - z = 7
-x - 2y + 4z = -15
x + 2y - 5z = 17
a) (3, 1, 0)
b) (1, 3, -2)
c) (2, 5, 2)
d) (-2, 6, -5)
Answers
Answer:
b) (1, 3, -2)
Step-by-step explanation:
A suitable calculator can give you the answer to this right away. Or, you can try the answer choices in the equations to see which works.
The answer choice that works is choice B.
2·1 +3 -(-2) = 7
-1 -2(3) +4(-2) = -15
1 +2(3) -5(-2) = 17
Explain in detail why the degree of the polynomial below is not 6. 3x^2+6xy-10x^5+y^6-10x^3y^5
Answers
p(x,y) = 3x² + 6xy - 10x⁵ + y⁶ - 10x³y⁵
To determine the degree of the polynomial, let us determine the degrees of the monomials.
3x² has degree 2,
6xy has degree 1+1 = 2,
10x⁵ has degree 5,
y⁶ has degree 6,
10x³y⁵ has degree 3+5 = 8
Answer:
The degree of the polynomial is not 6, but 8.
Explanation:
The degree of the polynomial is 8 because that is the highest degree of the terms in the polynomial.
Triangle lmn is similar to triangle nop. both are right triangles. which statements about the two triangles must be true? choose all answers that are correct.
a. sides ln and np have the same slope.
b. sides ln and np are congruent.
c. triangle lmn and nop are congruent.
d. sides lm and mn are proportional to sides no and op.
Answers
The slopes might be the same
All right triangles are congruent,
The corresponding parts or congruent triangles are congruent
"sides ln and np have the same slope." and "sides lm and mn are proportional to sides no and op." are correct for Triangle lmn is similar to triangle nop. both are right triangles.
What are Similar Triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
"Congruent" means the same
Two triangles are said to be congruent if they both have same length and same angles.
"Similar" means the area and sides will be proportional, it means when we divide or multiply with a number we get the measure of the other.
If triangle lmn is similar to triangle nop. both are right triangles.
Then we need to check which options will be correct and holds.
a. sides ln and np have the same slope it is correct because the triangle will have same slopes
b. It must not be true "sides ln and np are congruent" because as they are congruent the sides should be same.
c. triangle lmn and nop are congruent, is not true because there measures are different.
d. As the triangles are similar " sides lm and mn are proportional to sides no and op." must be true, because of proportionality.
Hence "sides ln and np have the same slope." and "sides lm and mn are proportional to sides no and op." are correct for Triangle lmn is similar to triangle nop. both are right triangles.
To learn more on similar triangles click:
https://brainly.com/question/25882965
#SPJ5