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4 years ago

A ray that contains a point that is equidistant from both sides of the angle. *

Mathematics

1 answer:

seraphim [82]4 years ago

3 0

<span>Consider a angle â BAC and the point D on its defector Assume that DB is perpendicular to AB and DC is perpendicular to AC. Lets prove DB and DC are congruent (that is point D is equidistant from sides of an angle â BAC Proof Consider triangles Î”ADB and Î”ADC Both are right angle, â ABD= â ACD=90 degree They have congruent acute angle â BAD and â CAD( since AD is angle bisector) They share hypotenuse AD therefore these right angle are congruent by two angle and sides and, therefore, their sides DB and DC are congruent too, as luing across congruent angles</span>

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What is the equation of the perpendicular to y=2/3x+1 that passes through the point (12,-6)

postnew [5]

Well, first off let's check what is the slope of y = 2/3x+1.... .hmmmmm, notice $\bf y=\stackrel{slope}{\cfrac{2}{3}}x+1$ , since the equation is already in slope-intercept form, we can see it has a slope of 2/3.

well then, a line perpendicular to that one, will have a negative reciprocal to it.

$\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{2}{3}\\\\
slope=\cfrac{2}{{{ 3}}}\qquad negative\implies -\cfrac{2}{{{ 3}}}\qquad reciprocal\implies - \cfrac{{{ 3}}}{2}$

so, we're really looking for the equation of a line whose slope is -3/2 and goes through 12, -6.

$\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ 12}}\quad ,&{{ -6}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies -\cfrac{3}{2}
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-6)=-\cfrac{3}{2}(x-12)
\\\\\\
y+6=-\cfrac{3}{2}x+18\implies y=-\cfrac{3}{2}x+12$

7 0

3 years ago

1) A rectangle has the lengths shown <br> Find the perimeter of the rectangle.

maks197457 [2]

Hi there! :)

$\large\boxed{P = 32cm}$

Find the perimeter by solving for y.

We know that a rectangle contains two pairs of parallel and congruent sides, therefore:

5y - 1 = 2y + 8

We can solve for y using this expression. Begin by subtracting 2y from both sides:

5y - 2y - 1 = 2y - 2y + 8

3y - 1 = 8

Add 1 to both sides:

3y - 1 + 1 = 8 + 1

3y = 9

Divide both sides by 3:

y = 3

Recall that the perimeter of a rectangle is:

P = 2l + 2w

Plug in the given expressions for the side lengths to find one equation:

P = 2(5y - 1) + 2(y - 1)

Simplify by distribution:

P = 10y - 2 + 2y - 2

Combine like terms:

P = 12y - 4

Plug in the solved value of y into this equation:

P = 12(3) - 4

P = 36 - 4

P = 32 cm.

3 0

3 years ago

Find the missing value. If not whole number, leave in simplest radical form. PLEASE HELP!!

otez555 [7]

Answer:

I think the answer is:

-Y = 7

-Z = 10.63

-X = 9.22

Step-by-step explanation:

Hope this helps!

6 0

3 years ago

Can someone solve this for me please, i really need help

Aleksandr [31]

Answer:

I sorted them by colors: red goes with red, blue with blue, purple with purple and brown with brown :))

Step-by-step explanation:

5 0

3 years ago

How would you write 1 17/20 as a percent

Over [174]

1 17/20

the 1 is ur whole number....it stays ur whole number
17/20 = 0.85

so we have 1.85.....to turn it into a percent, move the decimal 2 spaces to the right = 185%

5 0

3 years ago