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Gre4nikov [31]
3 years ago
11

one endpoint of AB has coordinates (-3,5) If the coordinates of the midpoint of AB are (2,-6),what is the length of AB?

Mathematics
1 answer:
avanturin [10]3 years ago
3 0
We know that (-3,5) is the location of one of the endpoints.... and we know the midpoint is at (2,-6)... .now.. what's the distance between those two guys?

\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
&({{ -3}}\quad ,&{{ 5}})\quad 
%  (c,d)
&({{ 2}}\quad ,&{{ -6}})
\end{array}\qquad 
%  distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
d=\sqrt{[2-(-3)]^2+[-6-5]^2}\implies d=\sqrt{(2+3)^2+(-6-5)^2}
\\\\\\
d=\sqrt{5^2+(-11)^2}\implies d=\sqrt{25+121}\implies d=\sqrt{146}

so, the distance "d" from the midpoint to that endpoint is that much.  And the distance from the midpoint to the other endpoint is the same "d" distance, because the midpoint is half-way in between both endpoints.

so, the length of AB is twice that distance, or   \bf 2\sqrt{146}
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kifflom [539]

Answer:

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by  

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8 0
3 years ago
PLEASE HELP PLEASE WILL GIVE BRAINILIEST 5 STARS AND THANK YOU TO WHOEVER CAN HELP!
Mnenie [13.5K]
Ok so the lines with two triangles are parralel to eachother. The lines with one are parallel to eachother.

The angle of 109° and angle of z° equal eachother. Z=109°

Since 109°, 33° and y° form a triangle, the sum of the angles will equal 180. Add 109 and 33 to get 142. Subtract 142 from 180 to get y°=38°.

Since z=109, this means that the triangle is congruent with the other. Since the congruent triangles are in a rhombus, then the angles are flipped. Thus, angle x =33°.

z=109°
y=38°
x=33°
3 0
3 years ago
Steve likes to entertain friends at parties with "wire tricks." Suppose he takes a piece of wire 60 inches long and cuts it into
Alex_Xolod [135]

Answer:

a) the length of the wire for the circle = (\frac{60\pi }{\pi+4}) in

b)the length of the wire for the square = (\frac{240}{\pi+4}) in

c) the smallest possible area = 126.02 in² into two decimal places

Step-by-step explanation:

If one piece of wire for the square is y; and another piece of wire for circle is (60-y).

Then; we can say; let the side of the square be b

so 4(b)=y

         b=\frac{y}{4}

Area of the square which is L² can now be said to be;

A_S=(\frac{y}{4})^2 = \frac{y^2}{16}

On the otherhand; let the radius (r) of the  circle be;

2πr = 60-y

r = \frac{60-y}{2\pi }

Area of the circle which is πr² can now be;

A_C= \pi (\frac{60-y}{2\pi } )^2

     =( \frac{60-y}{4\pi } )^2

Total Area (A);

A = A_S+A_C

   = \frac{y^2}{16} +(\frac{60-y}{4\pi } )^2

For the smallest possible area; \frac{dA}{dy}=0

∴ \frac{2y}{16}+\frac{2(60-y)(-1)}{4\pi}=0

If we divide through with (2) and each entity move to the opposite side; we have:

\frac{y}{18}=\frac{(60-y)}{2\pi}

By cross multiplying; we have:

2πy = 480 - 8y

collect like terms

(2π + 8) y = 480

which can be reduced to (π + 4)y = 240 by dividing through with 2

y= \frac{240}{\pi+4}

∴ since y= \frac{240}{\pi+4}, we can determine for the length of the circle ;

60-y can now be;

= 60-\frac{240}{\pi+4}

= \frac{(\pi+4)*60-240}{\pi+40}

= \frac{60\pi+240-240}{\pi+4}

= (\frac{60\pi}{\pi+4})in

also, the length of wire for the square  (y) ; y= (\frac{240}{\pi+4})in

The smallest possible area (A) = \frac{1}{16} (\frac{240}{\pi+4})^2+(\frac{60\pi}{\pi+y})^2(\frac{1}{4\pi})

= 126.0223095 in²

≅ 126.02 in² ( to two decimal places)

4 0
3 years ago
Please help with this problem
Natali [406]
I’m pretty sure it’s chad
6 0
3 years ago
The function f(x) = 16,800(0.9)x represents the population of a town x years after it was established. What was the original pop
Setler79 [48]

I am guessing that the correct form of equation is:

f(x) = 16,800(0.9)^x
where x is the exponent of (0.9)  

Since we are looking for the original population and x stand sfor the number of years, therefore x=0
substituting:
f(x) = 16,800(0.9)^0

Since (0.9)^0  would just be equal to 1. Therefore the original population is 16,800. 

 

Answer: B. 16,800

3 0
3 years ago
Read 2 more answers
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