To determine the amount of juice you will need you will multiply the number of students by how much juice each student will get. This is the idea of grouping. We will need 30 groups of 12 ounces.

30 x 12 = 360 ounces.

You will need 360 ounces of juice.

4 0

3 years ago

Select the graph that represents the inequality 2x + 3y <= 6

Tanzania [10]

I think the answer is B, the one with a complete line and shaded to the bottom

8 0

3 years ago

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when constructing the incenter of a triangle, The inersection of all three of which type of line needs to be found

lesantik [10]

Answer: Angle bisector

The angle bisector is the line that cuts an angle in half. The three angle bisectors all intersect at the same point which is the incenter. The incenter is the center of the circle in which is largest possible, yet it's fully inside the triangle. No part of this circle is outside the triangle.

3 0

3 years ago

let a = (a1, a2) and b = (b1, b2) and c = (c1,c2) be three non zero vectors. if a1b2 - a2b1 is not equal to 0. then show three a

Ksenya-84 [330]

Consider the contrapositive of the statement you want to prove.

The contrapositive of the logical statement

p ⇒ q

¬q ⇒ ¬p

In this case, the contrapositive claims that

"If there are no scalars α and β such that c = αa + βb, then a₁b₂ - a₂b₁ = 0."

The first equation is captured by a system of linear equations,

$\begin{cases}c_1 = \alpha a_1 + \beta b_1\\ c_2 = \alpha a_2 + \beta b_2\end{cases}$

or in matrix form,

$\begin{pmatrix}c_1\\c_2\end{pmatrix} = \begin{pmatrix}a_1&b_1\\a_2&b_2\end{pmatrix}\begin{pmatrix}\alpha\\\beta\end{pmatrix}$

If this system has no solution, then the coefficient matrix on the right side must be singular and its determinant would be

$\begin{vmatrix}a_1&b_1\\a_2&b_2\end{vmatrix} = a_1b_2-a_2b_1 = 0$

and this is what we wanted to prove. QED

3 0

3 years ago