Answer:
Vertex form: f(x) = -10(x − 2)^2 + 3
Standard form: y = -10x^2 + 40x - 37
Step-by-step explanation:
h and k are the vertex coordinates
Substitute them in the vertex form equation:
f(x) = a(x − 2)^2 + 3
Calculate "a" by replacing "f(x)" with -7 and "x" with 1:
-7 = a(1 − 2)^2 + 3
Simplify:
-7 = a(1 − 2)^2 + 3
-7 = a(-1)^2 + 3
-7 = a + 3
-10 = a
Replace a to get the final vertex form equation:
f(x) = -10(x − 2)^2 + 3
Convert to standard form:
y = -10(x − 2)^2 + 3
Expand using binomial theorem:
y = -10(x^2 − 4x + 4) + 3
Simplify:
y = -10x^2 + 40x - 40 + 3
y = -10x^2 + 40x - 37
Answer:
Equation: (2x+5)4=(2x+8)3
X: 2
Perimeter: 36
Step-by-step explanation:
You would multiply 2x+5 and 4 because there are four sides to a square, so the perimeter of the square would be 8x+20. This would go same for the triangle, making the perimeter 6x+24.
So 8x+20=6x+24 is your new equation. Then, you do the opposite of the order of operations, and add or subtract first. It would be easiest to subtract 20 and 6x from both sides.
That leaves you with 2x=4. Dividing 2 by both sides means x=2
You can plug this in to prove if it is correct.
16+20=36
12+24=36
Lmk if you get it!
Answer:
Sorry but the correct answer is (x+3)2+(y−1)2=81
Step-by-step explanation:
Because the radius squared is the answer of the equation
Answer:
The volume of the jewelry box will be given by,

Step-by-step explanation:
It is provided that, Jasmine found a wooden jewelry box shaped like a right rectangular prism.
Consider the diagram below for the shape of a right rectangular prism.
The volume of a right rectangular prism is given by the formula:

Here,
l = length of the rectangle
w = width of the rectangle
h = height of the rectangular prism
Thus, the volume of the jewelry box will be given by,

Answer:
The area of the outdoor carpet = 60 - 6 - 6 = 48 ft²
Step-by-step explanation:
The picture below is what you are referring to .
The whole area of the shape forms a rectangle. A triangle and a rectangle has been cut off from the whole carpet rectangle. The square ft or area of the carpet is the subtraction of the area of the rectangle and triangle cut off from the whole area of the rectangle .
Area of the rectangle = Lb
where
L = 12 ft
b = 5 ft
area = 12 × 5 = 60 ft²
The cut off triangle area
area = 1/2 × base × height
area = 1/2 × 4 × 3
area = 12/2 = 6 ft²
The cut off rectangle area
area = Lb
area = 3 × 2
area = 6 ft²
The area of the outdoor carpet = 60 - 6 - 6 = 48 ft²