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1 year ago

What will the new demensions of the rectangle below be after a dilation within scale factor of 9\4

Mathematics

1 answer:

timurjin [86]1 year ago

3 0

Answer

The new dimensions of the rectangle after dilation by scale factor of (9/4) include

New length = 72 feet

New width = 18 feet

Explanation

The relationship between new length, original length and scale factor of dilation is given as

New length = (Original length) × (Scale factor)

For this question,

Scale factor = (9/4)

Original length = 32 feet

New length = (Original length) × (Scale factor)

New length = 32 × (9/4) = 72 feet

New width = (Original width) × (Scale factor)

Original width = 8 feet

Scale factor = (9/4)

New width = (Original width) × (Scale factor)

New width = 8 × (9/4) = 18 feet

Hope this Helps!!!

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The vertices of ∆ABC are A(2, 8), B(16, 2), and C(6, 2). what is the perimeter and area in square units

ad-work [718]

Check the picture below.

the triangle has that base and that height, recall that A = 1/2 bh.

now as for the perimeter, you can pretty much count the units off the grid for the segment CB, so let's just find the lengths of AC and AB,

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&A&(~ 2 &,& 8~) 
% (c,d)
&C&(~ 6 &,& 2~)
\end{array}~~~ 
% distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
AC=\sqrt{(6-2)^2+(2-8)^2}\implies AC=\sqrt{4^2+(-6)^2}
\\\\\\
AC=\sqrt{16+36}\implies AC=\sqrt{52}\implies AC=\sqrt{4\cdot 13}
\\\\\\
AC=\sqrt{2^2\cdot 13}\implies AC=2\sqrt{13}$

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&A&(~ 2 &,& 8~) 
% (c,d)
&B&(~ 16 &,& 2~)
\end{array}\\\\\\
AB=\sqrt{(16-2)^2+(2-8)^2}\implies AB=\sqrt{14^2+(-6)^2}
\\\\\\
AB=\sqrt{196+36}\implies AB=\sqrt{232}\implies AB=\sqrt{4\cdot 58}
\\\\\\
AB=\sqrt{2^2\cdot 58}\implies AB=2\sqrt{58}$

so, add AC + AB + CB, and that's the perimeter of the triangle.

8 0

3 years ago

Olivia family drove to Disney land For spring break. Her mom and dad shared the driving duties for a total of 14 hours. her mom

Kay [80]

Mom drove for 11 hours.

Dad drove for 3 hours.

Step-by-step explanation:

Total hours = 14 hours

Total distance = 895 miles

Mom drove a speed of 65 mph

Dad drove a speed of 60 mph

Let 'x' be the number of hours drove by mom.

Let 'y' be the number of hours drove by dad.

x + y = 14 ---------------(1)

65x + 60y = 895 ---------(2)

Multiply eq(1) by 60 and subtract eq(2) from (1),

60x + 60y = 840

-(65x + 60y = 895)

-5x = -55

x = 55/5

x = 11

∴ Mom drove for 11 hours.

Substitute x=11 in eq(1)

11+y = 14

y = 3

∴ Dad drove for 3 hours.

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Answer:

Step-by-step explanation:

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