On the accompanying grid, draw and label quadrilateral ABCD with points A(1,2), B(6,1), C(7,6), and D(3,7). On the same set of axes, plot and label quadrilateral A′B′C ′D′, the reflection of quadrilateral ABCD in the y-axis. Determine the area, in square units, of quadrilateral A′B′C′D′.
Answers
Answer: Refer to figure 1 for the diagram needed.
A ' = (-1, 2)
B ' = (-6, 1)
C ' = (-7, 6)
D ' = (-3, 7)
Area = 24 square units
============================================================
Explanation:
Start by drawing an xy axis. Plot the given points A,B,C,D on this grid.
To reflect any given point over the y axis, we apply this rule
[tex](x,y) \to (-x,y)[/tex]
which means we change the sign of the x coordinate, but keep the y coordinate the same. For example, a point like A(1,2) moves to A ' (-1,2). The other points are handled in a similar fashion.
After all of the points have been reflected, you'll get what is shown in figure 1.
------------------
To find the area of quadrilateral ABCD, we can form a bounding box as small as possible around the quadrilateral. Refer to figure 2.
The area of rectangle FEHG is 6*6 = 36 square units
Then we subtract off the areas of these four outer triangles
Triangle AED = 5*2/2 = 5Triangle AFB = 1*5/2 = 2.5Triangle BCG = 1*5/2 = 2.5Triangle CDH = 1*4/2 = 2Meaning we'll end up with 36-5-2.5-2.5-2 = 24 as the area of quadrilateral ABCD. Because a reflection is a mirror copy, quadrilateral A'B'C'D' will have the same area as ABCD.
Related Questions
A contestant on a game show spins a wheel that is located on a plane perpendicular to the floor. He grabs the only red peg on the circumference of the wheel, which is 1.5 m above the floor (the peg is) and pushes it downward. The peg reaches a min height of 0.25 m and a max height of 2.75 m above the floor. Sketch two cycles of the graph representing the height above the ground as a function of the total distance moved. Then determine the equation of the sine function
Answers
The spin of the wheel by the contestant is an illustration of a sine function whose equation is [tex]\mathbf{y =-1.25 sin(0.8x) + 0.25}[/tex]
The wheel is 1.5 m above the floor, and the peg reaches a maximum height of 2.75 m.
So, the amplitude is:
[tex]\mathbf{A = 1.5 - 2.75}[/tex]
[tex]\mathbf{A = -1.25}[/tex]
The vertical shift is the minimum height of the peg.
So, we have:
[tex]\mathbf{D = 0.25}[/tex]
The period (T) equals one circumference.
So, we have:
[tex]\mathbf{T = (max-min)\pi}[/tex]
This gives
[tex]\mathbf{T = (2.75-0.25)\pi}[/tex]
[tex]\mathbf{T = 2.5\pi}[/tex]
The frequency (B) is then calculated as:
[tex]\mathbf{B = \frac{2\pi}{T}}[/tex]
This gives
[tex]\mathbf{B = \frac{2\pi}{2.5\pi}}[/tex]
Divide
[tex]\mathbf{B = 0.8}[/tex]
A sine function is represented as:
[tex]\mathbf{y =A sin(B(x + C)) + D}[/tex]
Substitute the calculated values
[tex]\mathbf{y =-1.25 sin(0.8(x + C)) + 0.25}[/tex]
The horizontal shift (C) is 0.
So, the function becomes
[tex]\mathbf{y =-1.25 sin(0.8x) + 0.25}[/tex]
See attachment for the graph of the equation
Read more sine function at:
https://brainly.com/question/11904902
identify the like terms of 3x, chose all the apply
3y
5x
3xy
-2x
3
7y
x
Answers
Answer:
5x, -2x, and x
Step-by-step explanation:
Like terms share the same variable and powers. This means that the options with 'x' as an variable would be the like terms of 3x.
5x , -2x , and x are like terms because they share the same variable, 'x'.
Hope this helps.
I need help on Tales mathemathics below on image
Answers
Answer:
x=5
Step-by-step explanation:
i'm assuming the upper left expression is x-1 and that the 3 horizontal lines are parallel
the three horizontal lines seem to be parallel, so we have (x-1)/6 = 6/(x+4). cross multiply to get (x-1)(x+4) = 36, or x^2 +3x - 4 = 36. subtract 36 from both sides to get x^2 + 3x -40 = 0, factor or use the quadratic formula to get (x+8)(x-5)=0, so x=-8 or x=5, since we are looking for a length x can't equal -8, so x=5,
1. Describe the three-dimensional shape that is generated by
rotating the two-dimensional shape around the axis shown.
A rectangular prism
C cylinder
B cube
D triangular prism
Answers
Answer:
Cylinder and cube are three dimensional shape
Answer:
triangular prism
rectangular prism
Step-by-step explanation:
The lines represented by the equations 2y - 3x = 14 and y - 3/2x= 7 are
Answers
Answer:
00000
Step-by-step explanation:
[tex]\sqrt{5}+\sqrt{5}=?[/tex]
Answers
[tex]\sqrt 5 + \sqrt 5 \\\\=\sqrt 5(1+1) \\\\= 2 \sqrt 5[/tex]
Jessica's curtain company is making curtains for a local hotel. She wants each curtain to be 24 inches long. At the fabric store, fabric is sold by the foot. If Jessica's curtain company wants to make 79 curtains, how many feet of fabric will she need? 1 inch = 1 twelfth foot
Answers
Answer:
158 feet
Step-by-step explanation:
24 inches = 2 feet
79 x 2 = 158
Find the least common multiple of: 2v^2y^7 and 11v^4y^8x^3
Answers
Answer:
2v6y719x3
Step-by-step explanation:
(1): "x3" was replaced by "x^3". 2 more similar replacement(s).
STEP 1
Equation at the end of step 1
(((2v2 • y711) • v4) • y8) • x3
STEP 2
Final result :
2v6y719x3
What is (f•g)(x)?
f(x) = 4x + 6
g(x) = -5x
Answers
(f.g)(x) = (4x + 6)(-5x) = -20x^2 -30x
ok done. Thank to me :>
how many 3/5s are in 9/10
Answers
Answer:they are only 2
Step-by-step explanation:
3/5 + 3/5 = 6/10 so you need a 6/5 + 3/5 and it will equal 9/10
Answer:
1
Step-by-step explanation:
3/5's = 6/10 and 6/10 plus 6/10 would be 12/10 so only 1 3/5's can fit.
3/12 + 7/12 =
A) 5/6
B) 10/24
C) 5/24
D) 1/6
Answers
10/12
simplified (divide by 2) it’s
5/6
the answer is A
Answer:
A. 5/6
Step-by-step explanation:
Since our denominators match, we can add the numerators.
3 + 7 = 10
So 10/12 the answer but simplified would give 5/6
How many solutions does 3(x + 5) - 3 = 2(3x + 1) - 3x have? Show your work.
2noop
no
ordon
dos
SOLUTION I don’t want the answer I just wanna know how to solve it cause I’m bad at math
Answers
Answer:
No solution
Step-by-step explanation:
1.Simplify
3(x+5)-3 = 2(3x+1) -3x
3x+15-3=6x+2-3x
2.Simplify
3x+12=3x+2
3. Combine like terms
3x-3x+12-2=3x-3x+-2
10 does not equal 0
No solution
Answer:
[tex]\boxed{\boxed{\sf No\:Solution}}[/tex]
Step-by-step explanation:
[tex]\sf 3\left(x+5\right)-3=2\left(3x+1\right)-3x[/tex]
Expand: Apply distributive property:
[tex]\sf 3(x+5)-3[/tex]
[tex]\sf 3x+15-3[/tex] [tex]\sf 3x+12[/tex][tex]\sf 2(3x+1)[/tex]
[tex]\sf 3x+2[/tex][tex]\sf 3x+12=3x+2[/tex]
Subtract 12 from both sides:
[tex]\sf 3x+12-12=3x+2-12[/tex]
[tex]\sf 3x=3x-10[/tex]
Subtract 3x from both sides:
[tex]\sf 3x-3x=3x-10-3x[/tex]
[tex]\sf 0=-10[/tex]
Sides are not equal, so therefore there is no Solution.
___________________________________________
A flower pot in the shape of a truncated cone with a height of 8 in. was formed by slicing off the tip of a cone along a plane parallel to the base.The original cone had a height of 12 in. and a volume of 810 in3. What is the volume of the tip that was sliced off?
A)30 in3B)60 in3C)90 in3EliminateD)180 in3
Answers
the correct answer is B
hope I helped
A backpacking club can average 2 1/2 miles per hour. At that
rate, how long will it take for a hike of 8 3/4 miles?
Answers
Answer:
3.5 hours
Step-by-step explanation:
8.75/2.5=3.5
Answer:
3.5 miles
Step-by-step explanation:
0(-7) helppppppppppppppppppppp
Answers
Answer:
0
Step-by-step explanation:
anything multuplied by 0 is 0
How do you find the quotient in the equation 8÷304
Answers
Answer:
304 divided by 8 in decimal = 38
304 divided by 8 in fraction = 304/8
304 divided by 8 in percentage = 3800%
Step-by-step explanation: You just simply divide.
00
A student ran a distance of 33 miles each day for 5 days. Then the student ran a distance of 4 miles each day
for the next 5 days.
What was the total distance in miles the student ran during these 10 days?
Answers
10days = ... miles
= 5days × 2
= 33 × 2
= 66miles
Which number sentence is true?
A. -4.25 > -2 4/5
B. 6/11 > 6.11
C. 7/8 > -0.78
D. 14/8 > 8.1
Answers
Answer: C. Is true 7/8>-0.78
what is equivalent to |14-20|
Answers
Answer:
7/10
Step-by-step explanation:
Please help and please no links..thanks ¯\_(ツ)_/¯
Answers
Answer:
[tex]\frac{c}{4} +5 = 7[/tex]
Step-by-step explanation:
The wording, "the quotient of a number and 4," can be displayed as c/4. C would be our variable for the number because the question asks specifically for it. 5 more would demonstrate that we're adding 5 more to our equation. Which would result in c/4 + 5. However, since it equals 7, just add that portion to create the following equation:
[tex]\frac{c}{4} +5 = 7[/tex]
Answer:
c / 4 + 5 = 7
Hope this helps!
Step-by-step explanation:
5 + ( more ) than the quotient ( division ) of a number and ( + ) 4 is ( = ) 7
5 + c / 4 = 7
c / 4 + 5 = 7
The midpoint of DF is E(-5, 4). If the coordinates of Fare (-4, 2), What are the coordinates of D?
Answers
Answer:
(-6,6)
Step-by-step explanation:
Rachel has 16 chocolate bars . Tracy takes 4 and asks for the remaining quarter. what would she end up with?
Answers
Answer:
Rachel ends up with 9 chocolate bars.
Step-by-step explanation:
16 - 4 = 12
quater is 1/4, so
12 / 4 = 3
12 - 3 = 9
Answer:
9 chocolate bars
Step-by-step explanation:
Rachel had 16 chocolate bars and Tracy takes (minus) 4.Now she has 12.
Tracy asks for the remaining (12) quarter. A quarter is 1/4, and a quarter of 12 is 3.
That leaves Rachel with 9, because 12 - 3 is 9.
Write an equation in slope-intercept form of the line that passes through (0, 6) and (3, -3)
Answers
Answer:
y=-3x+6
Step-by-step explanation:
Using slope formula
[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex](0, 6) x1, y1(3, -3) x2, y2[tex]\frac{-3-6 }{3-0}=\frac{-9}{3}=-3[/tex]Amir invests £2000 into an savings account.
Amir gets 4.75% per year compound interest.
Work out how much Amir will have in the account after 9 years.
Answers
Answer:
£30000
Step-by-step explanation:
I used a couculator
which expression is equivalent to 3(x+5)-6
A) 3x-3
B)3x-1
C )3x+9
D) 15x-6
Answers
Answer:
answer C. 3x + 9
Step-by-step explanation:
3(x + 5) - 6 =
3x + 15 - 6 =
3x + (15 - 6 ) =
3x + 9
3(x+5)-6
Multiply 3 by the inside parenthesis:
3x+15-6
Subtract
3x+9
This means our answer is C) 3x+9
I hope this helps! :)
14. Choose the best description of the polynomial:
5y2 + 4y + 24.
A. 5th degree Trinomial
B. 3rd degree Binomial
C. 2nd degree Trinomial
D
4th degree Binomial
Answers
Find the exact length of the third side.
10
8
Answers
Answer: 6
Step-by-step explanation:
The typical way to solve this problem is with the Pythagorean Theorem, which states that a^2 + b^2 = c^2, where a and b are the legs of the right triangle, and c is the hypotenuse. Unfortunately, due to a lack of a diagram, I am forced to infer.
Because the most famous Pythagorean triplet is 3, 4, 5, and 8 and 10 are multiples of the latter two terms, I can infer that the final side length is 6.
Hope it helps :) and if it is wrong, please let me know, and repost another question with the provided diagram.
Find the equation of this line. i’m really confused and i really need help.
Answers
Ravi Makes lemonade by mixing lemon juice and water for every 1 cup of lemon juice he uses 4 cups of water.
Answers
Answer:1/4
Step-by-step explanation:
what is the pattern you notice when dividing 10,100,1000
Answers
Answer:
Step-by-step explanation:
Image result for what is the pattern you notice when dividing 10,100,1000
When dividing by ten, move the decimal point one place to the left. Place value is the value of a digit based on its location in the number. When dividing by 100, move the decimal place two places to the left. And, remember, if there's no decimal point, assume that the decimal falls at the end of the number.
Answer:
when you divide those numbers the place value shifts by 1.
Step-by-step explanation:
1000.0 to 100.00 to 10.000 to 1.0000 to .10000