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2 years ago

The graph of a proportional relationship contains the point (8, 4).

1 answer:

6 0

$\bf \qquad \qquad \textit{direct proportional variation}\\\\
\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------\\\\
(\stackrel{x}{8}~~,~~\stackrel{y}{4})\implies 
\begin{cases}
x=8\\
y=4
\end{cases}\implies 4=k8\implies \cfrac{4}{8}=k\implies \cfrac{1}{2}=k
\\\\\\
\boxed{y=\cfrac{1}{2}x}$

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antoniya [11.8K]

Answer:

\large \boxed{\textbf{Bowl = 300 g; cup = 200 g}}

Step-by-step explanation:

Let b = the mass of a bowl

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$\begin{array}{lrcl}(1) &2b + c & = & 800\\(2) & b + 2c & = & 700\\\end{array}$

Calculations:

$\begin{array}{lrcll}(3) & 4b + 2c &= & 1600&\text{ Multiplied (1) by 2}\\& 3b & = & 900&\text{Subtracted (2) from (3)}\\(4) & b & = & \mathbf{300}&\text{Divided each side by 3}\\ & 600 + c & = & 800&\text{Substituted (4) into (2}\\ & c & = & \mathbf{200}\\\end{array}\\\text{The mass of a bowl is $\large \boxed{\textbf{300 g}}$ and that of a cup is $\large \boxed{\textbf{200 g}}$}$

Check:

$\begin{array}{rlcrl}2(300) + 200& =800 & & 300 + 2(200) & = 700\\600 + 200 & = 800& & 300 + 400 & = 700\\800 & = 800& & 700 & = 700\\\end{array}$

OK.

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2 years ago

Translations, rotations, and reflections are rigid transformations. What can you conclude about the measures of sides and angles

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After a translation, the measures of the sides and angles on any triangle would be the same since translation only involves changing the coordinates of the vertices of the triangle.

After a rotation, the measures of the sides and angles of a triangle would also be the same. Similar to translation, the proportion of the triangle is unchanged after a rotation.

After a reflection, the triangle's sides and angles would still be the same since reflection is a rigid transformation and the proportion of the sides and angles are not changed.

Step-by-step explanation:

Rigid transformations, i.e. translations, rotations, and reflections, preserve the side lengths and angles of any figure. Therefore, after undergoing a series of rigid transformations, the side lengths and angle measures of any triangle will be the same as the original triangle, generally speaking, in another position.

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