Answer:
Step-by-step explanation:
Given: In parallelogram DEFG,
DH = x + 1
HF = 3y
GH = 3x - 4
and HE = 5y + 1
Solution: Since, DH,HF, GH and HE represents the diagonals of the parallelogram and we know that the diagonals of the parallelogram bisect each other, therefore
x+1=3y (1)
3x-4=5y+1 (2)
Multiply equation (1) with 3 and then subtract equation (2) from it, we get
3x+3-3x+4=9y-5y-1
7=4y-1
y=2
Substituting the value of y=2 in equation (1), we get
x+1=3(2)
x=5
Therefore, the value of x and y are 5 and 2 respectively.
Answer:
f(g(x)) = 15x + 2
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Distributive Property
<u>Algebra I</u>
- Functions
- Function Notation
- Composite Functions
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
f(x) = 5x + 7
g(x) = 3x - 1
<u>Step 2: Find</u>
- Substitute in functions: f(g(x)) = 5(3x - 1) + 7
- [Distributive Property] Distribute 5: f(g(x)) = 15x - 5 + 7
- [Addition] Combine like terms: f(g(x)) = 15x + 2
Answer:
9% sales tax
Step-by-step explanation:
44.10/490 =
.09
.09 as a percentage is also 9%
Answer:
The area of Blanket A is 18yd^2
Answer:
5/3
Step-by-step explanation:
Tangent is defined as the length of the opposite side of the triangle divided by the length of the adjacent side of the triangle. Since you know that two of the legs are 3 and 4, using the pythagorean theorem you know that the last side is 5. Sin is defined as the length of the opposite side divided by the length of the hypotenuse, which in this case is 3/5. Cosecant is just the reciprocal of that, or 5/3. Hope this helps!
