Find the composition of
transformations that
map ABCD to EHGF.
Reflect over the [? l-axis,
then translate
(x+[ 1. y+[ l).
Note:
Enter x or y for axis.
Enter
Answers
The composition of transformations that map ABCD to EHGF is: reflect over the x-axis, then translate (x + 3. y + 1).
What is a reflection?In Mathematics and Geometry, a reflection over the x-axis is modeled by this transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over the x-axis would maintain the same x-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.
Since triangle ABCD was reflected over the x-axis, the coordinate A of triangle ABCD can be calculated as follows;
(x, y) → (x, -y)
A (-5, 2) → (-5, -(2)) = (-5, -2)
For the translation, we have:
(x, y) → (x + a, y + b)
A (-5, -2) → E (-2, 1)
-5 + a = -2
a = -2 + 5
a = 3
-2 + b = -1
b = -1 + 2
b = 1
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Related Questions
Use the system of inequalities:
y ≥ 0, x ≥ 0, y ≤ -2x + 4
and find the minimum value of f(x,y) = 3x + y
for the feasible region.
a. 6
b. 4
c. 2
d. 0
Answers
Using the system of inequalities y ≥ 0, x ≥ 0, y ≤ -2x + 4 the minimum value of f(x,y) = 3x + y for the feasible region is d) 0.
We need to find the minimum value of the function
f(x,y) = 3x + y
we can use Lagrange multipliers method defining
F(x,y) = f(x,y) - λx g(x,y) , where g(x,y) = x²+36 x y² - 1, such that
Fx(x,y) = fx(x,y) - λx gx(x,y) = 0
Fy(x,y) = fy(x,y) - λx gy(x,y) = 0
g(x,y)=0
where the sub-indices x and y represent the partial derivatives with respect to x and y, then
fx(x,y) - λx gx(x,y) = 3 - λx(2x) = 0 → x =3/(2xλ)
fy(x,y) - λx gy(x,y) = 1 - λx(36x2xy) = 0 → y =1/(72xλ)
x²+36xy² - 1 = 0 → [3/(2xλ)]²+36*[1/(72xλ)]² - 1 = 0
therefore, Using the system of inequalities y ≥ 0, x ≥ 0, y ≤ -2x + 4 the minimum value of f(x,y) = 3x + y for the feasible region is d) 0.
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1000+1000^3 I NEED HELP PLEASE
Answers
To solve this expression, we can use the order of operations, also known as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (performed left to right), and Addition and Subtraction (performed left to right).
Following this order, we first need to evaluate the exponent, which gives:
1000^3 = 1,000,000,000
Then, we can substitute this value back into the expression:
1000 + 1000^3 = 1000 + 1,000,000,000 = 1,000,000,000 + 1000 = 1,000,001,000
Therefore, 1000 + 1000^3 equals 1,000,001,000.
Answer: 8000000000
Step-by-step explanation:
Which could be the function graphed below?
a. f(x)=√x-2
b. f(x)=√x-3+1
c. f(x)=√2x+4
d. f(x)=√x+1+8
Answers
Answer:A
Step-by-step explanation:
It would have the greatest chance to be the line on the graph
jamilla is building a square sandbox with sides 8 1/2 feet long. she wants to put sand 2 1/2 feet deep in the box. how much sand should jamilla order?
Answers
The amount of sand Jamilla have to order to fill the square sandbox with sides 8 1/2 feet long and 2 1/2 feet deep is 180.625 cubic feet of sand.
To calculate the amount of sand that Jamilla should order, you need to calculate the volume of the sandbox. Given that Jamilla is building a square sandbox with sides 8 1/2 feet long and wants to put sand 2 1/2 feet deep in the box. Thus, the volume of the sandbox is calculated as follows:
Volume of the sandbox = Length * Width * Depth
Volume of the sandbox = (8 1/2 feet) * (8 1/2 feet) * (2 1/2 feet)
Converting each mixed fraction to its corresponding improper fraction, we get:
8 1/2 feet = 17/2 feet
2 1/2 feet = 5/2 feet
On simplifying the above equation we get:
Volume of the sandbox = (17/2 feet)² * (5/2 feet)
Volume of the sandbox = (289/4) * (5/2) cubic feet
Volume of the sandbox = 1445/8 cubic feet
Volume of the sandbox = 180.625 cubic feet
Therefore, Jamilla should order 180.625 cubic feet of sand.
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