In order to determine the vertex of this, you can complete the square. To do that, first set the equation equal to 0, then move the -35 over to the other side by adding. That gives us
. Now we can complete the square. Do this by taking half of the linear term, squaring it, and adding it in to both sides. Our linear term is 2x. Half of 2 is 1, and 1 squared is 1. So we add 1 to both sides, creating something that looks like this:
. We will do the math on the right and get 36, and the left will be expressed as the perfect square binomial we created by doing this whole process.
. Now move the 36 over by subtraction and set it back to equal y and your vertex is apparent. It is (1, -36). You find the x-intercepts when y = 0. That means you need to set your original equation equal to zero and factor it. The easiest, surest way to do this is to use the quadratic formula. Doing that gives us x values of 7 and -5. And you're done!
Answer:
5√3 = b
5 = d
10√3 = a
15 = c
Step-by-step explanation:
Sin60° = opp/hyp
sin60° = b/10
10sin60° = b
5√3 = b
Cos60° = adj/hyp
Cos60° = d/10
10Cos60° = d
5 = d
Sin30° = opp/hyp
Sin30° = 5√3/a
a = 5√3/Sin30°
a = 10√3
Tan30° = opp/adj
Tan30° = 5√3/c
c = 5√3/tan30°
c = 15
Answer:
1.5 inch/hr
Step-by-step explanation:
Amount of snow falling = 18 inch
Time = 12
Rate = 18/12 = 1.5 inch/hr
I hope Im right!!!
Answer:
Step-by-step explanation:
Given expression is,
(2x - 1)² + 2(2x - 1) = (2x - 1)(2x + 1)
To prove this identity we will take the left hand side of the equation and will prove equal to the right side.
(2x - 1)² + 2(2x - 1) = (2x - 1)(2x + 1)
4x² - 4x + 1 + 4x - 2 = (2x - 1)(2x + 1)
4x² - 1 = (2x - 1)(2x + 1)
(2x - 1)(2x + 1) = (2x - 1)(2x + 1) [Since a² - b² = (a - b)(a + b)]
Answer:
The price of the cake is $24 and the price of the Pie is $15
Step-by-step explanation:
Given
<em>Represent price of Cake with C and Price of Pie with P</em>
Cakes sold = 8
Pies sold = 14
Required
Determine C and P
To represent the cakes and pies sold, we have the following expression
Substitute 9 + P for C
Open the bracket
Collect Like Terms
Divide both sides by 22
Recall that
<em>Hence, the price of the cake is $24 and the price of the Pie is $15</em>