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3 years ago

43.77 as a mixed number in simplest form

Mathematics

1 answer:

valina [46]3 years ago

5 0

First you have to take the whole number (43) and then take the decimal and put it over 100 (77/100).

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What is the area of trapezoid ABCD ? (Enter your answer as a decimal or whole number)

MrRa [10]

Check the picture below.

bear in mind that, the "bases" are the two parallel sides, and the height is the distance between them.

$\bf \textit{area of this trapezoid}\\\\
A=\cfrac{AB(BC+AD)}{2}\\\\
-------------------------------\\\\
\textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
A&({{ -1}}\quad ,&{{ 5}})\quad 
% (c,d
B&({{ 3}}\quad ,&{{ 2}})
\end{array}\qquad 
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
AB=\sqrt{[3-(-1)]^2+[2-5]^2}\implies AB=\sqrt{(3+1)^2+(2-5)^2}
\\\\\\
AB=\sqrt{16+9}\implies AB=\sqrt{25}\implies \boxed{AB=5}$

$\bf -------------------------------\\\\
\textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
B&({{ 3}}\quad ,&{{ 2}})\quad 
% (c,d
C&({{ 0}}\quad ,&{{ -2}})
\end{array}
\\\\\\
BC=\sqrt{(0-3)^2+(-2-2)^2}\implies BC=\sqrt{9+16}
\\\\\\
BC=\sqrt{25}\implies \boxed{BC=5}$

$\bf -------------------------------\\\\
\textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
A&({{ -1}}\quad ,&{{ 5}})\quad 
% (c,d
D&({{ -13}}\quad ,&{{ -11}})
\end{array}
\\\\\\
AD=\sqrt{[-13-(-1)]^2+[-11-5]^2}
\\\\\\
AD=\sqrt{(-13+1)^2+(-16)^2}\implies AD=\sqrt{144+256}
\\\\\\
AD=\sqrt{400}\implies \boxed{AD=\sqrt{20}}$

so, the area for this trapezoid is then

$\bf A=\cfrac{5(5+20)}{2}\implies A=\cfrac{125}{2}\implies A=62\frac{1}{2}$

8 0

4 years ago

HOW MANY TEASPOONS ARE IN 15 MILLIMETERS? <br> 1 TSP = 5ML <br> 15ML = ?? TSP

valina [46]

Answer:

In cubic millimeter 15 in us teaspoon 0.00304326

Step-by-step explanation:

Hope I helped?

4 0

3 years ago

Please answer this question now

LUCKY_DIMON [66]

The answer is 72°
the m112°-40°= 72°

6 0

4 years ago

A rectangular flower garden in Samantha's backyard has 220 feet around its edge. The width of the garden is 50 feet. What is the

Ede4ka [16]

Answer: 60 ft

Step-by-step explanation:

Given

The perimeter of the garden is $220\ ft$

The width of the garden is $50\ ft$

Suppose the length of the garden is $x$

Perimeter is the sum of the lengths of the sides

$\Rightarrow 220=2(x+50)\\\Rightarrow 110=x+50\\\Rightarrow x=60\ ft$

So, the length of the garden is $60\ ft$

4 0

3 years ago

The length and width of a rectangle are measured as 30cm and 24cm, respectively, with an error in measured of

larisa [96]

Answer:

The maximum error in the calculated area of rectangle is 5.4 cm².

Step-by-step explanation:

Given : The length and width of a rectangle are measured as 30 cm and 24 cm, respectively, with an error in measured of at most 0.1 cm in each.

To find : Use differentials to estimate the maximum error in the calculated area of rectangle ?

Solution :

The area of the rectangle is $A=l\times w$

The derivative of the area is equal to the partial derivative of area w.r.t. length times the change in length plus the partial derivative of area w.r.t. width times the change in width.

i.e. $dA=\frac{\partial A}{\partial L}\Delta L+\frac{\partial A}{\partial W}\Delta W$

Here, $\frac{\partial A}{\partial L}=30,\ \frac{\partial A}{\partial W}=24 ,\ \Delta L=0.1,\ \Delta W=0.1$

Substitute the values,

$dA=(30)(0.1)+(24)(0.1)$

$dA=3+2.4$

$dA=5.4$

Therefore, the maximum error in the calculated area of rectangle is 5.4 cm².

7 0

3 years ago