2. Rectangle WXYZ with vertices W(-3,-4), X(0,-5), Y(-2,-11),
and Z(-5, -10); 180° rotation about N(2,-3)
Answers
The rectangle WXYZ after a 180° rotation about the point N(2,-3) is W(3,-2), X(0,-1), Y(2,5), and Z(5,4).
To perform a 180° rotation about the point N(2,-3), we can follow these steps:
1. Translate the rectangle and the point N to the origin by subtracting their respective coordinates from each vertex and point.
2. Perform the rotation by multiplying the coordinates of each vertex and point by the 2x2 rotation matrix:
[cos(180°) -sin(180°)]
[sin(180°) cos(180°)]
which simplifies to:
[-1 0]
[ 0 -1]
3. Translate the rectangle and the point N back to their original positions by adding their respective coordinates to each vertex and point.
Let's apply these steps to rectangle WXYZ and point N:
1. Translate the rectangle and point N to the origin:
W' = (-3 - 2, -4 + 3) = (-5, -1)
X' = (0 - 2, -5 + 3) = (-2, -2)
Y' = (-2 - 2, -11 + 3) = (-4, -8)
Z' = (-5 - 2, -10 + 3) = (-7, -7)
N' = (2 - 2, -3 + 3) = (0, 0)
2. Perform the rotation using the matrix:
[-1 0]
[ 0 -1]
W'' = [-1 0] * [-5, -1] = [5, 1]
[0 -1]
X'' = [-1 0] * [-2, -2] = [2, 2]
[0 -1]
Y'' = [-1 0] * [-4, -8] = [4, 8]
[0 -1]
Z'' = [-1 0] * [-7, -7] = [7, 7]
[0 -1]
N'' = [-1 0] * [0, 0] = [0, 0]
[0 -1]
3. Translate the rectangle and point N back to their original positions:
W = [5 - 2, 1 - 3] = (3, -2)
X = [2 - 2, 2 - 3] = (0, -1)
Y = [4 - 2, 8 - 3] = (2, 5)
Z = [7 - 2, 7 - 3] = (5, 4)
N = [0 + 2, 0 + 3] = (2, 3)
Therefore, the rectangle WXYZ after a 180° rotation about the point N(2,-3) is W(3,-2), X(0,-1), Y(2,5), and Z(5,4).
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Related Questions
An online music site charges 15 POINTS N BRAINLIEST 14.a one-time
membership fee of $20, plus $0.80 for every
song that is downloaded.
a) Write an equation for the total cost,
Cdollars, for downloading n songs.
b) Jacques downloaded 109 songs. What was
the total cost?
c) Michelle paid a total cost of $120. How many
songs did she download?
Answers
Answer:a) 20+0.8c B) 0.8x109 C)120/0.8
Step-by-step explanation:
Plz brainliest I am almost an expert
Do they each have membership or is that to throw you off?
Well it doesn’t say so imma assume they don’t.
The equation would be
$20+.80
(B)
$87.09 for 109 song
(C)
150 songs
Ps hope this helps:)
hello pleASE I need helppppppp
Answers
I can help you with that problem i just did that on my own.
Section exercise 11-8 sales of people magazine are compared over a 5-week period at four borders outlets in chicago. weekly sales store 1 store 2 store 3 store 4 102 97 89 100 106 77 91 116 105 82 75 87 115 80 106 102 112 101 94 100 click here for the excel data file fill in the missing data. (round your p-value to 4 decimal places, mean values to 1 decimal place, and other answers to 2 decimal places.) treatment mean n std. dev store 1 store 2 store 3 store 4 total one-factor anova source ss df ms f p-value treatment error total (a) based on the given hypotheses choose the correct option. h0: μ1 = μ2 = μ3 = μ4 h1: not all the means are equal α = 0.05 reject the null hypothesis if f
Answers
If y’all in 6 grade help each other out with the answer
Answers
Answer:
You got it, I have been busy and I am glad to see someone feeling the same way as me!
Answer:
what the question
Step-by-step explanation:
One packet of biscuits requires 2 15/16 and 1 7/8 cups of sugar. Estimated total quantity of both ingredients used in 10 such packets of biscuits will be?
Answers
Answer:
Hey Mate! Here's your answer.
Step-by-step explanation:
One packet of biscuits requires 2½ cups of flour = \frac{5}{2}25
One packet of biscuits requires 1 \times \frac{2}{3}1×32
One packet of biscuits requires 1 \times \frac{2}{3}1×32cups of sugar. = \frac{5}{3}35
Total ingradiants for one packet of biscuits =
Total ingradiants for one packet of biscuits =( \frac{5}{2} + \frac{5}{3} ) = \frac{15 + 10}{6} = \frac{25}{6}(25+35)=615+10=625
Then, total quantity of both ingredients used in 10 such packets of biscuits =
Then, total quantity of both ingredients used in 10 such packets of biscuits =10 \times ( \frac{25}{6} ) = 5 \times ( \frac{25}{3} ) = \frac{125}{3} = 41 \times \frac{2}{3}10×(625)=5×(325)=3125=41×32
Hope it helped you!
the diameter is half of the radius
Answers
Answer:
true
Step-by-step explanation:
7) A normal population has a mean = 33 and standard deviationo= 10. What proportion of the population is less than 39? 8)A normal population has a mean u randomly chosen value will be greater than 36? 29 and standard deviation a 6. What is the probability that a
Answers
The proportion of the population that is less than 39 is 72.57%. The probability that a randomly chosen value will be greater than 36 is approximately 12.10%.
7) First, we have to find the proportion of the population with a value less than 39 in a normal distribution with a mean of 33 and a standard deviation of 10.
Calculate the z-score for the value 39.
z = (X - mean) / standard deviation
z = (39 - 33) / 10
z = 6 / 10
z = 0.6
Look up the z-score (0.6) in a standard normal distribution table or use a calculator to find the proportion.
The proportion for a z-score of 0.6 is approximately 0.7257.
So, approximately 72.57% of the population is less than 39.
8) Now, we have to find the probability that a randomly chosen value will be greater than 36 in a normal distribution with a mean of 29 and a standard deviation of 6.
Calculate the z-score for the value 36.
z = (X - mean) / standard deviation
z = (36 - 29) / 6
z = 7 / 6
z ≈ 1.17
Look up the z-score (1.17) in a standard normal distribution table or use a calculator to find the proportion.
The proportion for a z-score of 1.17 is approximately 0.8790.
Since we want the probability that a randomly chosen value will be greater than 36, we need to find the proportion of values above the z-score of 1.17.
Probability = 1 - proportion
Probability = 1 - 0.8790
Probability ≈ 0.1210
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Some campers are starting a 7-mile hike. If they stop to take pictures every ⅕-mile, how many stops will they make?
Answers
Answer:
35
Step-by-step explanation:
I did 1/5 into a decimal which is 0.2 and then i did 7/0.2 because 7 miles and 0.2 miles they stop and then you divide them and get 35
Write all the ways you can express 24
as the product of 2 whole numbers.
Answers
These pairs are all distinct, meaning that there are no other pairs of whole numbers that multiply to equal 24.
There are several ways to express 24 as the product of 2 whole numbers. Here are all the possible ways:
- 1 x 24
- 2 x 12
- 3 x 8
- 4 x 6
Each of these pairs of numbers multiplies to equal 24. It is important to note that the order of the factors does not matter, so 2 x 12 is the same as 12 x 2.
Additionally, these pairs are all distinct, meaning that there are no other pairs of whole numbers that multiply to equal 24.
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62+41+(2)+(4) what is the answer to this
Answers
Answer:
109.
Step-by-step explanation:
62+41+(2)+(4) we can remove the brackets:
= 62 + 41 + 2 + 4
= 109.
Is 4 (2x + 3) = (2x - 2) + 2 (3x + 7) a no solution equation or one solution equation?
Answers
Answer:
No solution equation
Step-by-step explanation:
bshs
Answer:
Step-by-step explanation:
4 (2x + 3) = (2x - 2) + 2 (3x + 7)
=> 8x + 12 = (2x - 2) + (6x + 14)
=> 8x + 12 = 8x + 12
Since, both the equations are same, it is more than 1 solution or infinite solutions.
Given that PQ/ST = QR/TU= RS/US, select the postulate or theorem that you can use to conclude that the triangles are similar.
Answers
Answer: SSS Similarity Theorem (Choice A)
This is because we have three pairs of corresponding sides that form the same ratio, as shown by the given equation PQ/ST = QR/TU = RS/US.
That equation is basically the shorthand version of PQ/ST = QR/TU and QR/TU = RS/US combined together as one.
BDсStatementsReasons1. AB || CDAC || BD1. GivenIf two parallel lines are cut by a transversal, then:2. ZABC ZBCDLACB LDBC2.1-13.3. Reflexive propertyI14. AACB SADBC4.IIL-:: alternate interior angles are congruent:: corresponding angles are congruent:: BD - AC:: BC – BC:: AB ~CD:: Angle-Side-Angle:: Angle-Angle-Side:: Side-Angle-Side
Answers
The diagram shows statements to prove that both triangles are congruent.
Hence;
\(\begin{gathered} (2) \\ \angle ABC\cong\angle BCD \\ \angle ACB\cong\angle DBC \\ Alternate\text{ interior angles are congruent } \end{gathered}\)\(\begin{gathered} (3) \\ BC\cong BC \\ \operatorname{Re}flexive\text{ property} \end{gathered}\)\(\begin{gathered} (4) \\ \Delta ACB\cong\Delta DBC \\ \text{Side}-\text{Angle}-\text{Side} \end{gathered}\)Step 1 showed two sides that are congruent for both triangles
Step 2 showed two angles that are congruent
Step 3 showed two sides that are congruent
Therefore, the triangles are congruent by the side-angle-side theorem
help please!!
Question: Determine if the graph above is proportional and select the response with the correct reasoning.
A:yes, because it increases
B:yes, because it starts at the origin (0,0)
C:no, because it is not a constant speed
D:no, because it does not start at the origin (0, 0)
Answers
What is 6/-1 expressed as an integer?
Answers
Answer:
-6
Step-by-step explanation:
Help aspp please thank you
Answers
The equation of the line would be y = (-3/4)x + 5.
What is the slope-point form of the line?
For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be
y - y1 = m(x - x1)
The given equation is \(y=-\frac{3}{4}x-17\)
The required line is parallel to the given line.
and we know that the slopes of the parallel lines are equal so the slope of the required line would be m = -3/4
And the required line passes through (8, -1)
so by using slope - point form of the line,
y - (-1) = (-3/4)(x - 8)
y + 1 = (-3/4)x - (-3/4)8
y + 1 = (-3/4)x + 24/4
y = (-3/4)x + (12/2 - 1)
y = (-3/4)x + 5
Hence, the equation of the line would be y = (-3/4)x + 5.
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Solve the equation. What is the result?
extrapolation:
d=54mm
d=54x10^-6 m
y=2x10^10(54x10^-6)^2+2+10^6(54x10^6-6)+12.529
v=2x10^10(54x10^-6)^2+2+10^6(54x10^6-6)+12.529
v=2x10^10(54x10^-6)^2+2+10^6(54x10^6-6)+12.529
=
Answers
the answer of the given equation d=54mm
d=54x10^-6 m
y=2x10^10(54x10^-6)^2+2+10^6(54x10^6-6)+12.529
v=2x10^10(54x10^-6)^2+2+10^6(54x10^6-6)+12.529
v=2x10^10(54x10^-6)^2+2+10^6(54x10^6-6)+12.529 is v=2.9.
The answer of the given equation is v = 2.9
Given,
y=2x10^10(54x10^-6)^2+2+10^6(54x10^6-6)+12.529
Now we have to find v
We have
y=2x10^10(54x10^-6)^2+2+10^6(54x10^6-6)+12.529v=2x10^10(54x10^-6)^2+2+10^6(54x10^6-6)+12.529
Put the given values
y=2x10^10(54x10^-6)^2+2+10^6(54x10^6-6)+12.529y=2.9v=2x10^10(54x10^-6)^2+2+10^6(54x10^6-6)+12.529v=2.9
Therefore, the answer of the given equation is v=2.9.
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can someone help me on this one ... this is pythagorean theorem and converse geometry
Answers
Answer:
The correct answer is D.
Step-by-step explanation:
According to the Pythagorean Theorem, the legs of a right triangle squared and added together is equivalent to the hypotenuse squared. To solve for x, you can use any of the two right triangles. Each of the bottom legs of the right triangles is 9 units since the two right triangles are congruent, so now we apply the Pythagorean Theorem to solve for x. \(x^2+9^2=19^2\) ⇒ \(x^2+81 = 361\) ⇒ \(x^2 = 280\) ⇒ \(x = \sqrt{280}\) ⇒ \(x = \sqrt{4 * 70}\) ⇒ \(x = \sqrt{4} * \sqrt{70}\) ⇒ \(x = 2\sqrt{70}\).
Emma's dad is a police officer. One
afternoon, he stopped 19 people for
speeding, which was 12 more than the
previous day and 7 more than the day
before that. How many people did
Emma's dad stop for speeding during
that three-day period?
Answers
19 - 12 is 7
19 - 7 is 12
And he stopped 19 today
He stopped 38 people’s in a 3 days periods
Answer:
Let's say he stopped 19 people on Wednesday.
Wed - 19 people stopped
Tues - 19-12 is 7, so he saved 7 people that day
Mon - 19-7 is 12. so 12 people stopped on monday
so in all (including Wednesday) he stopped 38 people
Step-by-step explanation:
I'm sorry if it's wrong
Need help with this!!
Answers
Answer:
last one
Step-by-step explanation:
the domain includes all real numbers and the range is y>0
Due tomorrow!!!!
Select all values of that are solutions to the equation (x−5)(7x−21)=0 .
Group of answer choices
A: -7
B: -5
C: -3
D: 0
E: 3
F: 5
G: 7
Answers
Answer:
answer is F. 5
Step-by-step explanation:
5 is the answer
Show that ∑
i=1
6
(dx
i
+e)=d(∑
i=1
6
x
i
)+6e 2. Show the equation below in a Sigma operator notation: (5x
3
+4)+(5x
3
+5)+(5x
3
+6)+(5x
3
+7)+(5x
3
+8)+(5x
3
+9)
Answers
Since both sides are equal, we have shown that ∑(i=1 to 6) (dx_i + e) = d(∑\((i=1 to 6) x_i\)) + 6e. This represents the summation of the terms \((5x_3 + i)\) for i = 1 to 6.
To show that ∑(i=1 to 6) \((dx_i + e)\)= d(∑(i=1 \(x_i\)) + 6e, we can expand both sides and compare.
Left-hand side:
∑\((i=1 to 6) (dx_i + e) = (dx_1 + e) + (dx_2 + e) + (dx_3 + e) + (dx_4 + e) +\)(dx_5 + \(e) + (dx_6 + e)\)
= \(dx_1 + dx_2 + dx_3 + dx_4 + dx_5 + dx_6 + e + e + e + e\)+ e + e
= \((dx_1 + dx_2 + dx_3 + dx_4 + dx_5 + dx_6) + 6e\)
Right-hand side:
d(∑\((i=1 to 6) x_i)\)+ 6e = d\((x_1 + x_2 + x_3 + x_4 + x_5 + x_6)\)+ 6e
Now, let's compare the two sides:
Left-hand side: \((dx_1 + dx_2 + dx_3 + dx_4 + dx_5 + dx_6)\) + 6e
Right-hand side: d\((x_1 + x_2 + x_3 + x_4 + x_5 + x_6)\) + 6e
Since both sides are equal, we have shown that ∑\((i=1 to 6) (dx_i + e)\) = d(∑(i=1 to 6)\(x_i)\) + 6e.
To represent the equation\((5x_3 + 4) + (5x_3 + 5) + (5x_3 + 6) + (5x_3 +\)7) + \((5x_3 + 8) + (5x_3 + 9)\) using a Sigma operator notation, we can write it as:
∑\((i=1 to 6) (5x_3 + i)\)
This represents the summation of the terms \((5x_3 + i)\)for i = 1 to 6.
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h(x)
=
x² + 3x
4x + 27
Find h(-8)
Answers
Explanation:
Equation:
h(-8) = (-8^2) + 3(-8) / 4(-8) + 27
1) Remove parenthesis:
h • -8 = -8^2 + 3 • -8 / 4 • -8 +27
2) Simplify 8^2 to 64:
h • -8 = -64 + 3 • -8 / 4 • -8 + 27
3) Simplify 3 • -8 to -24:
h • -8 = -64 -24 / 4 • -8 + 27
4) Simplify -64 - 24 to -88:
h • -8 = -88 / 4 • -8 + 27
5) Simplify 4 • -8 to -32:
h • -8 = -88 / -32 + 27
6) Simplify -32 + 27 to -5:
h • -8 = -88 / -5
7) Regroup terms:
-8h = -88/-5
8) The two negatives make it positive and divide both sides by -8:
-8h = 88/5
h = -88/5 / 8
9) Simplify 88/5 /8 to 88 / 5 • 8:
h = -88 / 5 • 8
10) Simplify 5 • 8 to 40:
h = -88/40
11) Simplify - 88/40 to - 11/5:
h = - 11 / 5
*This fraction is in simplest form
Answer: h = - 11/5
Step-by-step explanation:
it is -8 because negative times negative is positive
(-8)
Find the dimensions of a rectangle whose perimeter is 46 and area is 126
Answers
The dimension of a rectangle, whose perimeter is 46 and area is 126, is 14 × 9.
To find the dimensions of a rectangle whose perimeter is 46 and area is 126, we need to use the formulas for the perimeter and area of a rectangle.
The perimeter of a rectangle is given by the formula:
P = 2L + 2W
The area of a rectangle is given by the formula:
A = LW
We are given that P = 46 and A = 126. Substituting these values into the formulas, we get:
46 = 2L + 2W
126 = LW
Rearranging the first equation, we get:
2L = 46 - 2W
L = 23 - W
Substituting this value of L into the second equation, we get:
126 = (23 - W)W
126 = 23W - W²
Rearranging this equation, we get:
W² - 23W + 126 = 0
(W - 14) (W - 9) = 0
Hence, the solutions are:
W = 14 and W = 9
If W = 14, then L = 23 - 14 = 9.
If W = 9, then L = 23 - 9 = 14.
So the dimensions of the rectangle are 14 and 9.
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Find the area of this circle. Use 3 for .
A = r2
12 cm
[?] cm2
Answers
Answer:
452.16 cm²
Step-by-step explanation:
Given :-
Radius = 12cm .To find :-
Area of circle .Solution :-
As we know that ,
A = πr² A = 3.14 * (12 cm)² A = 3.14 * 144cm² A = 452.16 cm²Step-by-step explanation:
\(area = \pi {r}^{2} \\ = \pi \times {12}^{2} \\ = \pi \times 144 \\ = 3.14 \times 144 \\ = 452.16 {cm}^{2} \\ thank \: you\)
The membership fee for joining a local indoor trampoline park is $24 per year. The
trampoline park charges members of the park $3 for admission to the park.
Nonmembers of the trampoline park are charged $6. After how many visits to the
trampoline park is the total cost for members, including the membership fee, the same
as the total cost for nonmembers?
Answers
Answer:
calculator g
Step-by-step explanation:
Answer:
calculator g <3
Step-by-step explanation:
i know because i figured it out
Find a formula for the general term a_n of the sequence assuming the pattern of the first few terms continues. {6,3,0,-3,-6, ....} Assume the first term is a_1.
Answers
The formula for the general term, a_n, of the given sequence {6, 3, 0, -3, -6, ...} is a_n = 9 - 3n, where n represents the position of the term in the sequence.
In the given sequence, each term is decreasing by 3 compared to the previous term. This indicates a common difference of -3. To find the general term, we need to determine the relationship between the position of a term (n) and the value of the term (a_n).
We observe that the first term, a_1, is 6, and the second term, a_2, is 3. This suggests that as the position of a term increases by 1, the value of the term decreases by 3. We can express this relationship as a_n = a_1 - 3(n - 1). Simplifying further, we get a_n = 6 - 3(n - 1).
To eliminate the constant term 6, we rewrite the formula as a_n = 9 - 3n, which represents the general term of the sequence. This formula allows us to find the value of any term in the sequence by substituting its position, n, into the formula.
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A hemispherical tank is filled with water and has a diameter of 12 feet. If water weighs 62.4 pounds per cubic foot, what is the total weight of the water in a full tank, to the nearest pound?
Answers
Answer:
The total weight = 1286 × 62.4 = 80246 pounds.
Step-by-step explanation:
The formula of the volume of the sphere is
V = 4/3×π×r³
Given
d = 17 feet
d = 2r
r = d/2 = 17/2 = 8.5 feet
V = 4/3×π×r³
Since we need half of the volume as it is a hemispherical tank.
= 1286 ft³
Given that the weighs 62.4 pounds per cubic foot
Thus, the total weight = 1286 × 62.4 = 80246 pounds.
2x-6y=-6
-2x+12y=-12
Pls help
Answers
Answer:
y = -3
x = -12
Step-by-step explanation:
We can add both equations together to cancel out x
\(6y = - 18\)
Reduce
y = -3
We then plug y in the first equation to solve for x
\(2x - 6( - 3) = - 6\)
Reduce
2x = -24
x = -12
2(x+3)=2x+6 how many solutions dose it have
Answers
Answer:
The right side of the equation is only a different way of writing the left side, so any value of x will solve this equation.
The equation − 2 ( x + 3 ) = − 2 x − 6 does not have any specific solutions for the simple reason that the left and rigth sides are two representations of the same equation.
We have − 2 ( x + 3 ) means that each term inside the parenthesis should be multiplied with − 2 , i.e.
− 2 ( x + 3 ) = − 2 ⋅ x − 2 ⋅ ( + 3 ) = − 2 x − 6
Which is exactly what the right side says.
Any value of x will, therefore, fulfill this equation.