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Dima020 [189]
3 years ago
15

I need help on number 9

Mathematics
1 answer:
asambeis [7]3 years ago
5 0
They can spend $4.72 on food per student
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Classify the system as independent, dependent, or inconsistent.
Anastasy [175]
1. 4x + 8y = 12....divide by 4
     x + 2y = 3
     2y = -x + 3
     y = -1/2x + 3/2...slope is -1/2, y int is 3/2
 
     x + 2y = -3
     2y = -x - 3
     y = -1/2x - 3/2...slope is -1/2 and y int is -3/2

when the slopes are the same, and the y int are different, then the lines are parallel and never intersect...so they have no solution and are inconsistent
=================
2. y = 2x - 1...slope is 2 and y int is -1
    y = -2x + 5 ...slope is -2 and y int is 5
when the slopes are different and the y int are different, then there is 1 solution making it independent
=================
3. 4x - 12y = 8...divide by 4
     x - 3y = 2
same as other equation meaning the equations are the same line...meaning they have infinite solutions making them dependent
7 0
3 years ago
Can someone show me how to factor this please?
Alex_Xolod [135]

Answer:

\displaystyle \theta = \left\{\frac{7\pi}{6}, \, \frac{3\pi}{2}, \frac{11\pi}{6}\right\}

Step-by-step explanation:

We want to solve the equation:

2\sin ^2 \theta + 3\sin \theta + 1 = 0

In the interval [0, 2π).

Notice that this is in quadratic form. Namely, by letting u = sin(θ), we acquire:

\displaystyle 2u^2 + 3u + 1 = 0

Factor:

\displaystyle (2u+1)(u+1) = 0

By the Zero Product Property:

\displaystyle 2u + 1 = 0\text{ or } u + 1 = 0

Solve for each case:

\displaystyle u = -\frac{1}{2} \text{ or } u = -1

Back-substitute:

\displaystyle \sin \theta = -\frac{1}{2} \text{ or } \sin \theta =-1

Use the Unit Circle. Hence, our three solutions in the interval [0, 2π) are:

\displaystyle \theta = \left\{\frac{7\pi}{6}, \, \frac{3\pi}{2}, \frac{11\pi}{6}\right\}

8 0
3 years ago
Consider the universal relation r = {a, b, c, d, e, f, g, h, i, j} and the set of functional dependencies f = { {a, b } → {c}, {
nekit [7.7K]

Answer:

relation of FDs are {a, b, d, h}. From these all but {h}

seem plausibly part of keys. Calculating the closures of likely candidates gives:

{a, b} + = {a b, c, i}

{b, d} + = {b, d, e, f}

{a, d} + = {a, d, g, h, i, j}

{a, b, d} + = {a, b, c, d, e, f, g, h, i, j}  

decompose r into 2nf and then 3nf relations shown in attachment.                    

Step- by-Step Explanation

Explanation is given in the attachment.

8 0
3 years ago
Write a formula for y in terms of x
garik1379 [7]

Answer:

question is incomplete

information is missing

4 0
2 years ago
If you have 8/12 of pizza, how many thirds do you have?
Deffense [45]
8/12 is equivalent to 2/3.

5 0
3 years ago
Read 2 more answers
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