Answer:
6(2x - 1)
Step-by-step explanation:
Given
12x - 6 ← factor out common factor of 6 from both terms
= 6(2x - 1) ← in factored form
Answer:
The scale factor of the dilation that transforms the triangle is 1/3
Step-by-step explanation:
9x1/3 is 3. 6x1/3 is 2, etc.
Answer:
h = 4.5 inches
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 (b1+b2) h
We know A b1 and b2
20.25 = 1/2 (5+4)*h
20.25 = 9/2 h
Multiply each side by 2/9 to isolate h
2/9 * 20.25 = 2/9 *9/2 h
4.5 =h
9514 1404 393
Answer:
2x² +5x -12 = 0
Step-by-step explanation:
When p and q are roots of a quadratic, its factored form can be written as ...
(x -p)(x -q) = 0
Here, the roots are given as -4 and 3/2, so the factored form would be ...
(x -(-4))(x -(3/2) = 0
Multiplying by 2 gives us ...
(x +4)(2x -3) = 0
Expanding the product, we find the desired quadratic is ...
2x² +5x -12 = 0
The hotel is $250 plus $25 per person so the equation would be
y= 25x + 250
(Y is the total cost and x is the number of people)
the restaurant is $100 plus $40 per person so the equation would be
y = 40x + 100
What we want to know is which x value would make the y values equal to each other. So you can just replace the "y" in one equation with the other equation:
25x + 250 = 40x + 100
and then solve...
1. subtract 100 from both sides
25x + 150 = 40x
2. subtract 25x from both sides
150 = 15 x
3. divide both sides by 15
10 = x
you can check by plugging 10 into the original equations
25(10) + 250
250 + 250 = 500
and
40(10) + 100
400 + 100 = 500
they both cost $500 when you invite 10 people
