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Natasha_Volkova [10]
3 years ago
14

Which statement completes the syllogism

Mathematics
1 answer:
Svet_ta [14]3 years ago
4 0

Answer:

The form of hypothetical syllogism is;

If P, then Q.

If Q, then R.

Therefore, if P, then R.

From the given statement we have:

M represents "If a, b, and c are real numbers such that a=b",

N represents "a+c=b+c"

O represents "c+a=c+b".

we have;

If M, then N

If N, then O

Therefore, by hypothetical syllogism.

therefore, if M, then O.

Therefore, the statement completes the syllogism is:

If a+c=b+c, then c+a=c+b.

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What is the equation of the line that passes through the point (4, 3) and is perpendicular to the line x + y = 4?
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y - x = - 1

EXPLANATION

The required equation passes through:

(4,3) and is perpendicular to x+y=4.

Rewrite the given equation in slope-intercept form:

y = - x + 4

The slope of this line is -1.

The slope of the required line is perpendicular to this line, so we find the negative reciprocal of this slope.

m= - \frac{1}{ - 1} = 1

The equation of the line can be found using:

y - y_1 = m(x - x_1)

We substitute the slope and point to obtain:

y - 3 = 1(x - 4)

We simplify to get:

y - 3 = x - 4

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The required equation is

y - x = - 1
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