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konstantin123 [22]
3 years ago
6

Senior classes high school A and high school B planned separate trips to New York City. The senior class at high school A rented

and filled 1 van and 6 buses with 324 students. High school B filled 9 vans and 3 buses with 264 students. Each van in each bus carry the same number of students. How many students can a van carry? How many students can a bus carry? show work please
Mathematics
1 answer:
ICE Princess25 [194]3 years ago
3 0
Let van =v and bus=b
V+6B=324
9V+3B=264×2 this will become
18V+6B=528 minus equ 1 from equ 2
-17V=-204 divide both side by -17
V=-204/-17=12
if V is 12 put it in equ 1
12+6B=324,6B=324-12=312 divide both side by 6
B=312/6=52
therefore the van and bus will take 12 and 52 persons respectively
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Answer:

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

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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

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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.

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Answer:

x = 11

Step-by-step explanation:

12x - 5 = 8x - x + 50 \\ 12x - 5 = 7x + 50 \\ 12x - 5 - 7x = 7x + 50 - 7x \\ 12x - 7x - 5 = 50  \\ 5x - 5 = 50 \\ 5x - 5 + 5 = 50 + 5 \\ 5x = 55 \\ x = 11

and check:

12(11) - 5 = 8(11) - (11) + 50 \\ 132 - 5 = 77 + 50 \\ 127 = 127

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3 years ago
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Answer:

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The area of her picture is 21/32 square inches.

Yes, I agree the area of the picture is 21/32 square inches.

The area must be in square inches. So she need to specify it.

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