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2 years ago

Use the commutative and associative properties of multiplication to write an expression equivalent to (4⋅5)⋅3.

1 answer:

4 0

Commutaive property says
ab=ba or expanded to say
abc=cba

associative peropty =
a(bc)=(ab)c

so using that
first mix them up knowing that we can move the parenthaseese
all possible equivelnt ones are
4*(5*3)
(3*5)*4
3*(5*4)
(3*4)*5
3*(4*5)

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Anna11 [10]

Answer:

140°

Step-by-step explanation:

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3 years ago

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3 years ago

< ADF measures 2x degrees and < FDC measures x + 12 degrees. What is the measure

gtnhenbr [62]

Answer:

<h2>Angle ADF is equal to 52° and angle FDC is equal to 38°.</h2>

Step-by-step explanation:

In the image attaches, you can observe that angles ADF and FDC are complementary angles, because they sum 90°.

$\angle ADF + \angle FDC = 90\°$

And we know that

$\angle ADF=2x\\\angle FDC = x+12$

Replacing these expressions, we have

$2x+x+12=90\°\\3x=90\° - 12\°\\x=\frac{78}{3}\\ x=26$

Then, we replace this value in each expression to find both angles measures.

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Therefore, angle ADF is equal to 52° and angle FDC is equal to 38°.

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2 years ago

The points A(1, 4), B(5,1) lie on a circle. The line segment AB is a chord. Find the equation of a diameter of the circle.

tangare [24]

Check the picture below.

well, we want only the equation of the diametrical line, now, the diameter can touch the chord at any several angles, as well at a right-angle.

bearing in mind that <u>perpendicular lines have negative reciprocal</u> slopes, hmm let's find firstly the slope of AB, and the negative reciprocal of that will be the slope of the diameter, that is passing through the midpoint of AB.

$\bf A(\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{1}}}\implies \cfrac{-3}{4} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{slope of AB}}{-\cfrac{3}{4}}\qquad \qquad \qquad \stackrel{\textit{\underline{negative reciprocal} and slope of the diameter}}{\cfrac{4}{3}}$

so, it passes through the midpoint of AB,

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{5+1}{2}~~,~~\cfrac{1+4}{2} \right)\implies \left(3~~,~~\cfrac{5}{2} \right)$

so, we're really looking for the equation of a line whose slope is 4/3 and runs through (3 , 5/2)

$\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{\frac{5}{2}}) \stackrel{slope}{m}\implies \cfrac{4}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{\cfrac{5}{2}}=\stackrel{m}{\cfrac{4}{3}}(x-\stackrel{x_1}{3})\implies y-\cfrac{5}{2}=\cfrac{4}{3}x-4 \\\\\\ y=\cfrac{4}{3}x-4+\cfrac{5}{2}\implies y=\cfrac{4}{3}x-\cfrac{3}{2}$

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2 years ago

What can u use to float a boat

Mamont248 [21]

Air? Unless you mean like a toy boat? IDK, I do know that huge ships like the Titanic are able to float because they have trapped oxygen. Think about if you're swimming; often when you hold your breath you float a bit better than if you were heavily breathing. Sorry i know its not alot to go off of, did i help you a little?

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2 years ago

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