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4 years ago

Can someone please do number 30.

Mathematics

1 answer:

Mamont248 [21]4 years ago

6 0

$To\ find\ b\ you\ have\ to\ put\ (2,6)\ into\ second\ eqution:\\\\y=2.5x+b\\\\6=2.5\cdot2+b\\6=5+b\\6-5=b\\b=1\\\\b\ have\ to\ be\ equal\ 1.$

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26. Define a relation ∼ ∼ on R 2 R2 by stating that ( a , b ) ∼ ( c , d ) (a,b)∼(c,d) if and only if a 2 + b 2 ≤ c 2 + d 2 . a2+

Tresset [83]

Answer:

~ is reflexive.

~ is asymmetric.

~ is transitive.

Step-by-step explanation:

~ is reflexive:

i.e., to prove $\forall (a, b) \in \mathbb{R}^2$ , $(a, b) R(a, b)$ .

That is, every element in the domain is related to itself.

The given relation is $\sim: (a,b) \sim (c, d) \iff a^2 + b^2 \leq c^2 + d^2$

Reflexive:

$(a, b) \sim (a, b)$ since $a^2 + b^2 = a^2 + b^2$

This is true for any pair of numbers in $\mathbb{R}^2$ . So, $\sim$ is reflexive.

Symmetry:

$\sim$ is symmetry iff whenever $(a, b) \sim (c, d)$ then $(c, d) \sim (a, b)$ .

Consider the following counter - example.

Let (a, b) = (2, 3) and (c, d) = (6, 3)

$a^2 + b^2 = 2^2 + 3^2 = 4 + 9 = 13$

$c^2 + d^2 = 6^2 + 3^2 = 36 + 9 = 42$

Hence, $(a, b) \sim (c, d)$ since $a^2 + b^2 \leq c^2 + d^2$

Note that $c^2 + d^2 \nleq a^2 + b^2$

Hence, the given relation is not symmetric.

Transitive:

$\sim$ is transitive iff whenever $(a, b) \sim (c, d) \hspace{2mm} \& \hspace{2mm} (c, d) \sim (e, f)$ then $(a, b) \sim (e, f)$

To prove transitivity let us assume $(a, b) \sim (c, d)$ and $(c, d) \sim (e, f)$ .

We have to show $(a, b) \sim (e, f)$

Since $(a, b) \sim (c, d)$ we have: $a^2 + b^2 \leq c^2 + d^2$

Since $(c, d) \sim (e, f)$ we have: $c^2 + d^2 \leq e^2 + f^2$

Combining both the inequalities we get:

$a^2 + b^2 \leq c^2 + d^2 \leq e^2 + f^2$

Therefore, we get: $a^2 + b^2 \leq e^2 + f^2$

Therefore, $\sim$ is transitive.

Hence, proved.

3 0

3 years ago

Determine the total annual FICA tax for an annual salary of $110,330. Use $106,800 for maximum taxable earningsa.$822.14b.$844.0

Agata [3.3K]

<span>The Federal Insurance Contributions Act (FICA) requires employers to withhold a certain percentage of an employee's income as tax. The categories are: 6.2% as social security tax 1.45% as Medicare tax 0.9% as Medicare surtax for employees earning more than $200,000 In this case, the percentage of tax applied will be 6.2 + 1.45 = 7.65% The FICA tax will be 110,330 * 0.0765 FICA tax = $8,440.24</span>

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3 years ago

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100 point giveaway and brainliest to first answer

Dmitry_Shevchenko [17]

Answer:

Thx!!!!!

Step-by-step explanation:

thx soooo much

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3 years ago

Marcus hikes at a rate of 3 miles per hour. If he hikes for 7 and a half hours, how many miles will he hike?

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The answer is 22.5 you multiply the 7 and the 3

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4 years ago

Which of the equations below represents the relationship shown in the table?

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Step-by-step explanation:

just check at least two

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3 years ago