20. The ratio of the areas of two

Mathematics

1 answer:

Ivanshal [37]3 years ago

6 0

Answer:

Step-by-step explanation:

Beacuse if you divide 25 by 100 and turn it into a fraction you would get B 1:5

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Anthony wants to find the value of k for which given points W(0,-2), I(2,0) and L(5,k) are collinear

Bogdan [553]

Given:

The three points are W(0,-2), I(2,0) and L(5,k).

To find:

The value of k for which the given points are collinear.

Solution:

We know that, three points are collinear if the area of the triangle formed by these three points is 0.

$\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|=0$

$x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)=0$

The three points are W(0,-2), I(2,0) and L(5,k). So,

$0(0-k)+2(k-(-2))+5(-2-0)=0$

$0+2(k+2)+5(-2)=0$

$2k+4-10=0$

$2k-6=0$

Adding 6 on both sides, we get

$2k=6$

$k=\dfrac{6}{2}$

$k=3$

Therefore, the correct option is E.

5 0

3 years ago

The two triangles are similar. Create and solve proportions (two of them) to find the missing side measures. Drag and drop your

lilavasa [31]

Answer:

Step-by-step explanation:

the smaller triangle is the larger triangle divided by 4 so 16÷4 is 4.

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3 years ago

Find the circumference of a circle whose area is 24 pi ft ^2

lianna [129]

$\bf \textit{area of a circle}\\\\
A=\pi r^2~~
\begin{cases}
r=radius\\
-----\\
A=24\pi 
\end{cases}\implies 24\pi =\pi r^2\implies \cfrac{24\pi }{\pi }=r^2
\\\\\\
24=r^2\implies \boxed{\sqrt{24}=r}\\\\
-------------------------------\\\\
\textit{circumference of a circle}\\\\
C=2\pi r\qquad \qquad \implies C=2\pi\left( \boxed{\sqrt{24}} \right)~~
\begin{cases}
24=2\cdot 2\cdot 2\cdot 3\\
\qquad 2^2\cdot 6
\end{cases}
\\\\\\
C=2\pi \sqrt{2^2\cdot 6}\implies C=2\pi (2\sqrt{6})\implies C=4\sqrt{6}~\pi$