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2 years ago

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Katherine wants to prove that the measures of the interior angles of a triangle have a sum of 180. She draws a triangle and exte

nds one of the sides through a vertex. She then draws a line through this vertex that is parallel to the opposite side

1 answer:

Oliga [24]2 years ago

8 0

Answer:

As we know, if we add up the interior and exterior angles of one corner of a triangle, we always get 180. the exterior angle in question is equal to the sum of the other two angles in the triangle

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The difference of twice a number and 10 is less than 22

valentinak56 [21]

2(n-10)≤ 28 or n ≤ 24

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3 years ago

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in the following equation A & B are both integers. What is the value of a? What is the value of b?

MariettaO [177]

3ax-8a=b-18x
3ax+18x=b+8a
3x(a+6)=b+8a

3x=(b+8a)/(a+6)
x=(b+8a)/3(a+6)
3a*(b+8a)/3(a+6)=b-18*(b+8a)/3(a+6)
a(b+8a)/(a+6)=b-6(b+8a)/(a+6)
a(b+8a)=b(a+6)-6(b+8a)
ab+8a^2=ab+6b-6b-48a
ab+8a^2=ab-48a
8a^2=-48a
8a^2+48a=0
8a(a+6)=0 so a=0,-6
0=b-18x or -18x+48=b-18x
-b=-18x or 48=b
let b=18 if a =-6

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2 years ago

Round 624 to the nearest hundred

Zolol [24]

Your answer is 600. i hope this helps!

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2 years ago

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What is the distance between the points (4,5) and (10,13) on a coordinate plane?

Readme [11.4K]

The distacne between the points (x1,y1) and (x2,y2) is
$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
so the distance between (4,5) and (10,13) is
well, first
x1=4
y1=5
x2=10
y2=13
so

$D=\sqrt{(10-4)^2+(13-5)^2}$
$D=\sqrt{(6)^2+(8)^2}$
$D=\sqrt{36+64}$
D=√100
D=10
the distance is 10 units

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2 years ago

What two numbers multiply to -126 and add up to -65

Airida [17]

Xy = -126
x + y = -65

$xy = -126$
$\frac{xy}{x} = \frac{-126}{x}$
$y = \frac{-126}{x}$

$x + y = -65$
$x + \frac{-126}{x} = -65$
$\frac{x^{2}}{x} + \frac{-126}{x} = -65$
$\frac{x^{2} - 126}{x} = -65$
$-65x = x^{2} - 126$
$0 = x^{2} + 65x - 126$
$x = \frac{-(65) \+ \sqrt{(65)^{2} - 4(1)(-126)}}{2(1)}$
$x = \frac{-65 \± \sqrt{4225 + 504}}{2}$
$x = \frac{-65 \± \sqrt{4729}}{2}$
$x = \frac{-65 \± 68.8}{2}$
$x = \frac{-65 + 68.8}{2}$ $or$ $x = \frac{-65 - 68.8}{2}$
$x = \frac{3.8}{2}$ $or$ $x = \frac{-133.8}{2}$
$x = 1.9$ $or$ $x = -66.9$

x + y = -65
  1.9 + y = -65
- 1.9   - 1.9
y = -66.9
  (x, y) = (1.9, -66.9)

or

  x + y = -65
  -66.9 + y = -65
+ 66.9 + 66.9
y = 1.9
  (x, y) = (-66.9, 1.9)

The two numbers that add up to -65 and can multiply to -126 are the numbers -66.9 and 1.9.

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3 years ago