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hodyreva [135]
3 years ago
11

Solve this system of equations: y=(3/4)x; y=-x-7 *

Mathematics
1 answer:
ladessa [460]3 years ago
6 0

Answer: x

=

−

4

,

y

=

−

11

Step-by-step explanation:

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The slope of a line perpendicular to the line whose equation is y = 3x - 4 is
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Answer:

m = -1/3

Step-by-step explanation:

y = 3x-4

This is in slope intercept form

y = mx+b  m is the slope and b is the y intercept

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Perpendicular lines have slopes that multiply to -1

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Solve for w, where w is a real number.
Ber [7]

Answer:

w= 9

Step-by-step explanation:

\sqrt{ - 4w + 61}  = w - 4

Square both sides:

-4w +61= (w -4)²

\boxed{(a - b)^{2}  = a^2 -2ab + b^2 }

Expand:

-4w +61= w² -2(w)(4) +4²

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Simplify:

w² -8w +16 +4w -61= 0

w² -4w -45= 0

Factorize:

(w -9)(w +5)= 0

w -9= 0 or w +5= 0

w= 9 or w= -5 (reject)

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-5 is rejected since we are only taking the positive value of the square root here. If the negative square root is taken into consideration, then w= -5 would give us -9 on both sides of the equation.

<u>Why </u><u>do </u><u>we </u><u>use </u><u>negative </u><u>square </u><u>root?</u>

When solving an equation such as x²= 4,

we have to consider than squaring any number removes the negative sign i.e., the result of a squared number is always positive.

In the case of x²= 4, x can be 2 or -2. Thus, whenever we introduce a square root, a '±' must be used.

However, back to our question, we did not introduce the square root so we should not consider the negative square root value.

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