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3 years ago

Which ratio is greater? 4:3 or 7:9. (Show necessary steps and calculations for your answer)

Mathematics

2 answers:

scoundrel [369]3 years ago

8 0

Answer:

4 : 3 > 7 : 9

Step-by-step explanation:

In order to compare two ratios or fractions, we make their denominators equal and then equate their numerators.

$4 : 3 = \frac{4}{3} = \frac{4 \times 3}{3 \times 3} = \frac{12}{9} \\ \\ 7 : 9 = \frac{7}{9} \\ \\ \because \: 12 > 7 \\ \\ \therefore \: \frac{4}{3} > \frac{7}{9} \\ \\ \implies \: 4 : 3 > 7 : 9$

stiks02 [169]3 years ago

7 0

4:3

= 4/3

= 1.333333...

7:9

= 7/9

= 0.777777...

4:3 is greater than 7:9

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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

$-\alpha + 3 \beta = -9$

$2\alpha+4 \beta = -2$

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.

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Read 2 more answers

Emilio writes the inequality 17(f+2)+45.99<200 The situation using the variable as to represent the number of friends solve a

larisa [96]

Answer:

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Step-by-step explanation:

Given the inequality expression

17(g+2)+45.99<200

We are to find the value of g that satisfies the inequality

Expand

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Subtract 79.99 from both sides

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