what set of transformations could be applied to rectangle ABCD to create A’B’C’D’?
A)Reflected over the x-axis and rotated 180 degrees
B)Reflected over the y-axis and rotated 180 degrees
C)Reflected over the x-axis and rotated 90 degrees counterclockwise
D)Reflected over the y-axis and rotated 90 degrees counterclockwise
Answers
Rectangle ABCD has vertices A(-4,2), B(-4,1), C(-1,1) and D(-1,2).
1. Apply the reflection over the x-axis that has a rule
(x,y)→(x,-y).
Then
A(-4,2)→A''(-4,-2);B(-4,1)→B''(-4,-1);C(-1,1)→C''(-1,-1);D(-1,2)→D''(-1,-2).2. The second transformation is rotation by 90° counterclockwise about the origin. This transformation has a rule
(x,y)→(-y,x).
Then
A''(-4,-2)→A'(2,-4);B''(-4,-1)→B'(1,-4);C''(-1,-1)→C'(1,-1);D''(-1,-2)→D'(2,-1).As you can see these points are exactly those frome the diagram.
Answer: 1st transformation is reflection over the x-axis and second transformation is rotation by 90° counterclockwise about the origin.
Related Questions
If the length of a rectangle is decreased by 4 cm and the width is increased by 5 cm, the result will be a square, the area of which will be 40 cm2 greater than the area of the rectangle. Find the area of the rectangle.
Answers
(x +4)*(x -5) +40 = x^2
x^2 -x -20 +40 = x^2
20 = x
The rectangle is 15 cm by 24 cm, and its area is 360 cm^2.
What is reconciling your bank statement?
Answers
Answer:
Compare your personal records to the bank's statement
HELP PLEASE HELP HELP
Answers
The answer is D
Amir's checking account charges a $9.75 monthly service fee and a $0.12 per-check fee. If Amir writes 15 checks per month, should he switch to a checking account that charges an $11.50 monthly service fee and no per-check fee
Answers
[tex]0.12(15) = 1.80 [/tex]
[tex]1.80 + 9.75 = 11.55[/tex]
Yes Amir should switch because it's a nickel less
Solve for x in the equation x2+20x+100=36
Answers
[tex] x = - 64 \div 22 = -2.909091[/tex]
But if x2 was supposed to be x^2 then the answer is:
[tex]x = - 4.-16[/tex]
Answer:
x = -4 and x = -16.
Step-by-step explanation:
We have the equation,
[tex]x^{2}+20x+100=36[/tex]
i.e. [tex]x^{2}+20x+64=0[/tex]
As the solution of a quadratic equation [tex]ax^{2}+bx+c=0[/tex] is given by [tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex].
On comparing, a = 1, b = 20, c = 64.
So, the solution is,
[tex]x=\frac{-20\pm \sqrt{(20)^{2}-4\times 1\times 64}}{2a\times 1}[/tex].
i.e. [tex]x=\frac{-20\pm \sqrt{400-256}}{2}[/tex].
i.e. [tex]x=\frac{-20\pm \sqrt{144}}{2}[/tex].
i.e. [tex]x=\frac{-20\pm 12}{2}[/tex].
i.e. [tex]x=\frac{-20+12}{2}[/tex] and [tex]x=\frac{-20-12}{2}[/tex].
i.e. [tex]x=\frac{-8}{2}[/tex] and [tex]x=\frac{-32}{2}[/tex].
i.e. x = -4 and x = -16
Thus, the solution of the given equation is x = -4 and x = -16.
What is 59.69 in expanded form
Answers
50 +9 + 0.6+ 0.09
Expanded Factors Form:
5 × 10 +9 × 1 +6 × 0.1+9 × 0.01
Expanded Exponential Form:
5 × 101+9 × 100+6 × 10-1+9 × 10-2
Word Form:
fifty-nine and sixty-nine hundredths
What is the value of x?
Enter your answer, as a decimal, in the box.
Answers
How many times would a coin have to show heads in 50 tosses to have an experimental probability of 20% more than the theoretical probability of getting heads? 10 25 35 45
Answers
Is the system of equations is consistent, consistent and coincident, or inconsistent?
y=−3x+12y=−6x+2
Select the correct answer from the drop-down menu.
Answers
Coincident is one line on the graph
Consistent is two parallel lines
Answer:
The given system of equations is inconsistent.
Step-by-step explanation:
We have been given a system of equations and we are asked to find whether our given system of equation is consistent, consistent and coincident, or inconsistent.
[tex]y=-3x+12...(1)[/tex]
[tex]y=-6x+2...(2)[/tex]
Since we know that a system of equations is inconsistent if it has no solution. Parallel lines are inconsistent because they do not intersect.
Consistent system of equations can have one or infinitely many solution. As if two lines are same then they will have infinitely many solution. If lines intersect at only one point, then they will have only one solution.
Now let us check slope of given lines.
Upon dividing equation (2) by 2 we will get,
[tex]y=-3x+1...(2)[/tex]
We can see that both lines have slope of negative 3. Since y-intercept of both equations are different, so they will not intersect at any point.
Since our given equations represent parallel lines, therefore, our given system of equations is inconsistent.
John Street Barber Shop pays $25 per month for water for the first 8,000 gallons and $3.50 per thousand gallons above 8,000. Calculate the total water cost when the barber shop uses 7,000 gallons, 10,000 gallons, and 13,000 gallons.
Answers
Using Excel (see attached image) we find that the equation of the line is:
y = 0.0035x - 3
We evaluate for:
For x = 7000:
y = 0.0035 * (7000) - 3
y = 21.5 $
For x = 10000
y = 0.0035 * (10000) - 3
y = 32 $
For x = 13000
y = 0.0035 * (13000) - 3
y = 42.5 $
Answer:
The total water cost when the barber shop uses 7,000 gallons, 10,000 gallons, and 13,000 gallons is:
21.5 $, 32 $, 42.5 $, respectively.
Final answer:
The John Street Barber Shop pays a flat rate of $25 for the first 8,000 gallons of water, with an additional charge of $3.50 per thousand gallons above this threshold. Accordingly, the total costs for using 7,000 gallons is $25, for 10,000 gallons is $32, and for 13,000 gallons is $42.50.
Explanation:
The John Street Barber Shop pays $25 per month for the first 8,000 gallons of water and $3.50 per thousand gallons above 8,000 gallons. To calculate the total water cost when the barber shop uses 7,000 gallons, 10,000 gallons, and 13,000 gallons, we follow this methodology:
For 7,000 gallons, since it's below 8,000 gallons, the cost is just the flat rate of $25.For 10,000 gallons, the cost is $25 for the first 8,000 gallons, plus $3.50 for each of the 2,000 gallons above 8,000. This gives $25 + ($3.50 * 2) = $32.For 13,000 gallons, the cost is $25 for the first 8,000 gallons, plus $3.50 for each of the 5,000 gallons above 8,000. This gives $25 + ($3.50 * 5) = $42.50.Thus, the total costs for using 7,000 gallons, 10,000 gallons, and 13,000 gallons are $25, $32, and $42.50 respectively.
factor the GCF: 15a+25b
Answers
The factored form of the expression 15a + 25b with respect to the Greatest Common Factor (GCF) is 5 (3a + 5b). The GCF of 15 and 25 is 5.
Explanation:To factor the Greatest Common Factor (GCF) from 15a + 25b, we first have to identify the GCF. The GCF of 15 and 25 is 5. Hence, we divide each term in the expression by this GCF.
We get: 5 (3a + 5b). So, the expression 15a + 25b factored by the GCF is 5 (3a + 5b).
Learn more about Factoring here:https://brainly.com/question/33624529
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What happens to the area when the perimeter of square efgh efgh is doubled? explain.answers?
Answers
The area of EFGH will be multiplied by 4 if its perimeter is doubled.
_____
Original perimeter = s + s + s + s = 4s. Original area = s^2.
New perimeter = 2s + 2s + 2s + 2s = 8s. New area = (2s)^2 = 4s^2, 4 times the original area.
Which expression is equivalent to 8+18a−2+6a? A.24a+6 B.24a + 10 C.8(1+2a)−(2+6a) D.30a
Answers
[tex]8 + 18a - 2 + 6a [/tex]
Combine Like terms: [tex]18a, 6a, \\ \\ 8,2 [/tex]
So, [tex](18a + 6a) = 24a \\ \\ 8+ (-2) = 6 [/tex]
[tex]Answer: 24a + 6 [/tex] would be [tex]equivalent [/tex] to: [tex]8 + 18a - 2 + 6a[/tex]
Good luck on your assignment and enjoy your day!
~[tex]LoveYourselfFirst:)[/tex]
what is the change of entropy for a heat engine using 500.0j at 20.0c
Answers
hope it helps :D!!
The formula to find change in entropy is given by :
[tex] Change in entropy = \frac{Q}{T} [/tex]
where Q is change in heat and T is temperature.
We are given Q = 500 joule and T = 20 degree C
Plugging these values in the formula,
[tex] Change in entropy = \frac{500}{20} [/tex]
We get change in entropy = 25 J/Celsius.
With $3500 each, Martin and Edward opened separate accounts. Each account offered 4.5% interest over 10 years. At the end of 10 years, Edward earned more than Martin. Why? A. Edward invested for a different amount of time than Martin. B. Edward had a different interest rate than Martin. C. Edward earned compound interest, and Martin earned simple interest. D. Edward e
Soomeone helpppp meeee
Answers
The interest earned from above cash under simple interest will be:
S.I=(PRT)/100
S.I=3500*4.5/100*10=$1575
the total amount after 10 years will therefore be:
1575+3500
=$5075
The same amount if it was compounded annually, the amount after 10 years will be:
FV=P(1+r/100)^n
FV=3500(1+3.5/100)^10
FV=4,937.10
we therefore conclude that the answer is:
Edward must have earned simple interest while Martin earned compound interest.
helppppppppppppppppppppppppppppp
Answers
We have then:
2 (16x ^ 3y) ^ (1/3) + 4 (54x ^ 6y ^ 5) ^ (1/3)
We then have to use properties of exponents:
4 ((2 ^ (1/3) xy ^ (1/3)) + 12 ((2 ^ (1/3)) x ^ 2y ^ (5/3))
4 ((2 ^ (1/3) xy ^ (1/3)) + 12 ((2 ^ (1/3)) x ^ 2 * y * y ^ (2/3))
We rewrite:
4x ((2y) ^ (1/3)) + 12 * x ^ 2 * y ((2y ^ 2) ^ (1/3))
Answer:
4x ((2y) ^ (1/3)) + 12 * x ^ 2 * y ((2y ^ 2) ^ (1/3))
option 1
Raul used the steps shown below to solve the equation. In which step did Raul make a mistake?
5x-3(2x+7)=2x+9
Step 1: 5x-6x-21=2x+9
Step 2: -11x-21=2x+9
Step 3: -12x=30
Step 4: x=-30/12
A. Step 1
B. Step 2
C. Step 3
D. Step 4
Answers
5x-3(2x+7)=2x+9
This is the equation and Raul had to solve it for x
So he started with simplifying the parenthesis first
To simplify the parenthesis -3 gets multiplied with 2x and 7 , to get rid of parenthesis
So it came out to be
5x-3(2x+7)=2x+9
STEP-1
5x-6x -21 = 2x+9 , So the STEP-1 is correct,
After this in Step -2 , he has combined the like terms on left side, the like terms are 5x and -6x , 5x-6x should combine to -x , because 5-6 = -1
So
STEP-2
-x -21 = 2x+9 , So STEP -2 is INCORRECT
So he made a mistake in STEP-2
After that subtract 2x from both sides
-3x -21 = 9
add 21 to both sides
-3x = 30
divide both sides by -3
x=-10
Hence Option B is correct , he made a mistake in STEP -2
Find the midpoint of the line segment whose endpoints are (7,5) and (7,11)
Answers
which statement about sqrt x-5 minus sqrt x=5 true?
-3 is a true solution
-3 is a extraneous solution
9 is a true solution
9 is a extraneous solution
Answers
Answer:
9 is an extraneous solution.
Step-by-step explanation:
Extraneous solution is a solution that when plugged into the equation do not hold true.
Here we are given an algebraic equation in terms of single variable x as:
[tex]\sqrt{x-5}-\sqrt{x}=5-----(1)[/tex]
Now, we will solve this equation to obtain the solution as:
on squaring both side of the equation we obtain:
[tex](\sqrt{x-5}-\sqrt{x})^2=5^2[/tex]
[tex]x-5+x-2\sqrt{x-5}\sqrt{x}=25\\\\2x-5-2\sqrt{x-5}\sqrt{x}=25\\\\2x-30=2\sqrt{x-5}\sqrt{x}\\\\on\ dividing\ both\ side\ by\ 2\ we\ obtain:\\\\x-15=\sqrt{x-5}\sqrt{x}[/tex]
Again on squaring both side of the equation we obtain:
[tex]x^2+225-30x=(x-5)x\\\\\x^2+225-30x=x^2-5x\\\\225=-5x+30x\\\\225=25x\\\\x=9[/tex]
Now when we plug x=9 back to the original equation i.e. equation (1) we get:
[tex]\sqrt{9-5}-\sqrt{9}=5\\\\\sqrt{4}-\sqrt{9}=5\\\\2-3=5\\\\-1=5[/tex]
Hence, the equation does not hold true.
Hence, 9 is a extraneous solution
Hellllllllłllllllllllllllllllllllllllllllllllpp
Answers
Organize the following expressions from greatest to least by number of terms: x + 2xyz 9x2yz 18x2 + 5ab − 6y 4x3 + 3x2 − x − 4
Answers
Answer:
The answer is the option C
IV, III,I,II
Step-by-step explanation:
NEED HELP ASAP PLEASE HELP
Find m
Select one:
a. 120°
b. 100°
c. 90°
d. 80°
Answers
<DAE = 80
<EAC = 100
m must be somewhere, but I can't see it
The rectangle is the image after a dilation with the center of dilation at the origin of rectangle ABCD. The pre-image of A' point A, has coordinates of (–4, 3.2). What is the scale factor of the dilation and what are the coordinates of point C?
Answers
Answer:
The scale factor is 2.5 and the coordinates of point C are (–2.4, –0.8).
Step-by-step explanation:
The circumference (C) of a swimming pool is 47 feet. Which formula can you use to find the radius (r) if you know that C = 2πr ?
Answers
2. you get r = c/2π
Answer:
r=C/2*pie
Step-by-step explanation:
I got it correct on TTM
PLEASE HELP I NEED THE ANSWER TO THIS ASAP. YOU JUST NEED TO MATCH EACH THING ON THE LEFT TO ITS CORRECT ANSWER ON THE RIGHT.
Match the following items.
Complete the proof for Theorem 3-13. (if you dont know what this theorem is i added a picture that explains it so you can help)
Answers
But I'll give it a try:
1) l // m ___ Given
2) <1 = <3 ___ if parallel lines, then corresponding angles (<s) are equal
3) <2 = <3 ___ Vertical <s are equal
4) <1 = <2 ___ Substitution
The complete proof of the theorem in chronological order is;
GivenIf lines are ∥, corresponding angles are equal.Vertical angles are equalSubstitutionHow to complete a proof?The proof that when a transversal cut two parallel lines, alternate angles are equal.
1.
Statement: l ∥ m
Reason: Given
2.
Statement: m ∠ 1 = m ∠ 3
Reason: If lines are ∥, corresponding angles are equal.
3.
Statement: m ∠ 2 = m ∠ 3
Reason: Vertical angles are equal
4.
Statement: m ∠ 1 = m ∠ 2
Reason: Substitution
Therefore, alternate exterior angles are equal when a transversal cut two parallel lines,
Read more on vertical angles:
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Triangle FGH is similar to JKM.
If f = 14.4 cm, g = 16.56 cm, h = 25.92 cm, and k = 9.2 cm, what is the measure of m?
A. 5.104 cm
B. 14.4 cm
C. 10.58 cm
D. 8 cm
Answers
so we can find the scale that FHG was dilated by.
[tex]16.56 \div 9.2 = 1.8[/tex]
so the sides of the triangle KMJ were multiplied by 1.8.
to find m :
[tex]25.92 \div 1.8 = 14.4[/tex]
m=14.4
hope this helps
Simplify (3x − 5) − (5x + 1).
−2x + 6
−2x − 6
2x − 6
2x + 6
can you please work this out for me?
thank you verymuch.
Answers
we have been asked to simplify
[tex] (3x-5)-(5x + 1) [/tex]
To Simplify this, we will first open the parenthesis, as below
[tex] (3x-5)-(5x + 1)=3x-5-5x-1\\
\\
\text{take the like terms together and simplify we get}\\
\\
(3x-5)-(5x + 1)=3x-5x-5-1\\
\\
(3x-5)-(5x + 1)=-2x-6\\
\\
[/tex]
Hence the simplified expression is -2x-6
Answer:
-2x-6
Step-by-step explanation:
Parts of Complex Numbers
z=4.1i+85
Re(z)=_____
Im(z)=_____
Answers
where a is the real number of z (Re z) while b is the imaginary part of z (im z)
Therefore in this case; z=4.1 i +85, therefore
Re(z) =85
Im(z) = 4.1
A 4040 inch wire is to be cut. one piece is to be bent into the shape of a square, whereas the other piece is to be bent into the shape of a rectangle whose length is twice the width. find the width of the rectangle that will minimize the total area. what is the width of the rectangle that will minimize the total area?
Answers
perimeters: 40 = 4s + 2(r + 2r) = 4s + 6r → s = (1/4)(40 - 6r) = 10 - 1.5r areas: A = s² + 2r² = (10 - 1.5r)² + 2r² = 100 - 30r + 4.25r²
Then dA/dr = 0 = 9.5r - 30 r = 30/9.5 = 3.16 in ← width of rectangle (length is twice the width) d²A/dr² = 9.5 > 0, so it is a minimum.
For the figures below, assume they are made of semicircles, quarter circles and squares. For each shape, find the area and perimeter. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answers
Figure 1)
a) The area is A = 36( π - 2) ст²
b) The perimeter is P = 6 (π + 2√2) [tex]cm^2[/tex]
Figure 2)
a) The area is A = 576 cm²
b) The perimeter is P = 24(π+2) [tex]cm^2[/tex]
Figure 1)
a) To find the area of the figure 1 we have to do the substraction
The area of figure 1 is equivalent to the area of a triangle less the area of a quarter circle.
The area of quarter circle is equal to
A = 2
we have
r = 12 cm
Put the value r as given
A = (12)2
A = 36 [tex]cm^2[/tex]
Area of a triangle formula is
A = (b)(h)
Given information,
b=12 cm
h = 12 cm
substitute
A = (12) (12)
A = 72 cm²
therefore
The area of the figure is
A = (36π - 72) [tex]cm^2[/tex]
Simplify
A = 36(π -2) [tex]cm^2[/tex]
b)
The perimeter of the figure 1 is equal to the circumference of a quarter circle plus the side AC of triangle
The perimeter of a quarter of circle is formula
C = 2πr
simplify
C = r
we have
r=12 cm
substitute
C = (12)
C = 67 cm
Find the length side AC
Applying the Pythagorean Theorem
[tex]AC^2 = 12^2 + 12^2[/tex]
[tex]AC^2 = 144+ 144\\AC^2 = 288\\AC = \sqrt{288}[/tex]
AC = 12√2 cm
P = (6π +12√2) cm
Taking 6 as a common multiplier we get
P = 6(π+2√2)
The perimeter of the figure 1 is
P = 6(π+2√2) cm
Part 2)
a) As we can see,
The area of a semicircle plus the area of a square less the area of a semicircle equals the area of figure 2.
The figure's area and the square's area are equal.
A = [tex]24^2[/tex]
A = 576 cm²
b) Find the perimeter of the figure 2
we know that
The perimeter of the figure 2 is equal to the length side AB plus the length side DC plus the circumference of two semicircles
The perimeter of the figure 2 is equal to two times the length side AB plus the circumference of one circle
P = 2(AB) + π D
P = 2(24) + π(24)
P = 48 + π(24)
Take out 24
P = 24 (2 + π ) cm