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3 years ago

I need help... the question is confusing

Mathematics

1 answer:

ziro4ka [17]3 years ago

8 0

$\bf \stackrel{line~J}{y+8=-(x-2)}\implies y+8=-x+2
\\\\\\
y=-x-6\implies y=\stackrel{slope}{-1}x-6$

now we know the slope of line J is -1.

a line perpendicular to J, will have a negative reciprocal slope, therefore,

$\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad -1\implies \cfrac{-1}{\underline{1}}\\\\
negative\implies +\cfrac{1}{{{ \underline{1}}}}\qquad reciprocal\implies + \cfrac{{{ \underline{1}}}}{1}\implies 1$

therefore, line K has a slope of 1, and passes through 3,4,

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1\\
% (a,b)
&&(~{{ 3}} &,&{{ 4}}~)
\end{array}
\\\\\\
% slope = m
slope = {{ m}}\implies 1
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-4=1(x-3)\implies y-4=x-3
\\\\\\
y=x+1$

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CAN SOMEONE PLS TELL ME DOMAIN AND RANGE

lorasvet [3.4K]

Answers:

Domain is (-4, 3]
Range is (-5, 5]

=====================================================

Explanation:

The domain is the set of allowed x input values, aka the set of all allowed x coordinates of the points. We see that $-4 < x \le 3$ . It might help to draw vertical lines through the endpoints until you reach the x axis. Note the open hole at x = -4 to indicate we do not include this as part of the domain (hence the lack of "or equal to" for the first inequality sign).

The interval $-4 < x \le 3$ then can be condensed into the shorthand form (-4, 3] which is the domain in interval notation.

It says: x is between -4 and 3. It can't equal -4 but it can equal 3.

So the use of parenthesis versus square brackets tells the reader which endpoint is included or not.

--------------------------------------------------

The range describes all possible y outputs. We see that y = 5 is the largest it gets and y = -5 is the lower bound. It might help to draw horizontal lines through the endpoints until you reach the y axis. The open hole means -5 is not part of the range.

The range as a compound inequality is $-5 < y \le 5$ . This condenses into the shorthand of (-5, 5] which is the range in interval notation.

Verbally, the range is the set of y values such that y is between -5 and 5. It can't equal -5 but it can equal 5.

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Heyy can you help me out on this question please

defon

We can use quadratic formula to determine the roots of the given quadratic equation.

The quadratic formula is:

$x= \frac{-b+- \sqrt{ b^{2}-4ac } }{2a}$

b = coefficient of x term = 5
a = coefficient of squared term = 1
c = constant term = 7

Using the values, we get:

$x= \frac{-5+- \sqrt{25-4(1)(7)} }{2(1)} \\ \\ 
x= \frac{-5+- \sqrt{-3} }{2}$

So, the correct answer to this question are option E and F

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