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Colt1911 [192]
2 years ago
5

Explain how you know if an equation has one solution, infinitely many solutions, or no solution

Mathematics
1 answer:
lubasha [3.4K]2 years ago
8 0
No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true. :)
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Isabella purchased 3 books from the book store. She now owns 11 books that she wants to read before the end of the year. If x re
Vesna [10]
The answer is X = 11 - 3. This is because to calculate the original value of how many books Isabella had, you have to take away the amount purchased from the overall total amount. Therefore, the equation is x = 11-3
4 0
3 years ago
Given vectors u = (−1, 2, 3) and v = (3, 4, 2) in R 3 , consider the linear span: Span{u, v} := {αu + βv: α, β ∈ R}. Are the vec
julia-pushkina [17]

Answer:

(2,6,6) \not \in \text{Span}(u,v)

(-9,-2,5)\in \text{Span}(u,v)

Step-by-step explanation:

Let b=(b_1,b_2,b_3) \in \mathbb{R}^3. We have that b\in \text{Span}\{u,v\} if and only if we can find scalars \alpha,\beta \in \mathbb{R} such that \alpha u + \beta v = b. This can be translated to the following equations:

1. -\alpha + 3 \beta = b_1

2.2\alpha+4 \beta = b_2

3. 3 \alpha +2 \beta = b_3

Which is a system of 3 equations a 2 variables. We can take two of this equations, find the solutions for \alpha,\beta and check if the third equationd is fulfilled.

Case (2,6,6)

Using equations 1 and 2 we get

-\alpha + 3 \beta = 2

2\alpha+4 \beta = 6

whose unique solutions are \alpha =1 = \beta, but note that for this values, the third equation doesn't hold (3+2 = 5 \neq 6). So this vector is not in the generated space of u and v.

Case (-9,-2,5)

Using equations 1 and 2 we get

-\alpha + 3 \beta = -9

2\alpha+4 \beta = -2

whose unique solutions are \alpha=3, \beta=-2. Note that in this case, the third equation holds, since 3(3)+2(-2)=5. So this vector is in the generated space of u and v.

4 0
2 years ago
Where to place the lines
vazorg [7]
Use photo math it works well
7 0
3 years ago
A transformation translates the point S (-1,1) down 2 units and right 3 units. What rule describes this translation. A. (x,y)=(x
allochka39001 [22]
The answer is D (x+3,y-2)
4 0
3 years ago
Solve for c. Show all work. a = 11(4b + c)
inessss [21]
Step 1: Flip the equation.

44b+11c=a

Step 2: Add -44b to both sides.

44b+11c+−44b=a+−44b

11c=a−44b

Step 3: Divide both sides by 11.

11c11=a−44b11

c=111a−4b

Answer:

c=111a−4b

4 0
3 years ago
Read 2 more answers
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