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jok3333
13 days ago
15

A rectangular prism with integer side lengths has a height of $3$. If the surface area of the prism is equal to $52$, then what

is the volume of the prism?
Mathematics
1 answer:
lawyer [9.2K]13 days ago
3 0
The given details include: Height of the rectangular prism, h = 3 units, Surface area of the prism, A = 52 sq units. We need to determine the volume of the prism. The volume of a rectangular prism can be calculated using the formula: l = length and b = breadth. Given that the surface area of the prism, A = lb, we have it equal to 52 sq units. Consequently, the volume is 156 cubic units.
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What is the approximate area of the shaded sector in the circle shown below
PIT_PIT [9117]
\bf \textit{area of a sector of a circle}\\\\
A=\cfrac{\theta \pi r^2}{360}~~
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
r=4.5\\
\theta =150
\end{cases}\implies A=\cfrac{(150)(\pi )(4.5)^2}{360}\\\\\\ A=\cfrac{3037.5\pi }{360}
8 0
6 days ago
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If m<DBC=(12x-3)°, m<DBE=(5x+12)°, and m<EBC=(3x+13)°, find m<EBC.
Leona [9271]

Answer:

m∠EBC=34°

Step-by-step explanation:

We establish that

m∠DBC=m∠DBE+m∠EBC

Refer to the accompanying diagram for clarity on the issue

Replace the known values in the equation and determine x

(12x-3)\°=(5x+12)\°+(3x+13)\°\\12x-3=8x+25\\12x-8x=25+3\\4x=28\\x=7

Calculate the size of angle EBC

m∠EBC=(3x+13)°

Insert the value for x

m∠EBC=(3(7)+13)°

m∠EBC=(21+13)°

m∠EBC=34°

8 0
1 month ago
The construction of copying ∠"QPR" is started below. The next step is to set the width of the compass to the length of ("AB" ).
zzz [9080]

Answer:

The length AB equals length TU.

Step-by-step explanation:

Procedure: Replicate angle <QPR so that;

<QPR matches <TSU

Set the compass so that each leg touches points A and B to replicate the distance AB.

Next, position the compass at T to draw an arc that marks point U. Draw a straight line from S to U.

Consequently,

<QPR is congruent to <TSU

This method guarantees that angles are congruent by maintaining the same radius, thus AB = TU.

4 0
1 month ago
How does the graph of g (x) = StartFraction 1 Over x + 4 EndFraction minus 6 compare to the graph of the parent function f (x) =
lawyer [9240]

The adjusted equation $g(x)=\frac{1}{x+4}-6$, indicating that the graph has been altered 4 units leftward and 6 units downward.

Clarification:

The parent equation is $f(x)=\frac{1}{x}$.

The transformed equation is $g(x)=\frac{1}{x+4}-6$.

Applying the function transformation rules, it's clear that the parent function $f(x)=\frac{1}{x}$ has been modified into the function $g(x)=\frac{1}{x+4}-6$.

According to the function transformation rules,

$f(x+b)$ indicates shifting the function b units to the left.

Thus, the transformed function reflects a shift 4 units to the left.

Additionally, from the function transformation rules, we understand that,

$f(x)-b$ indicates shifting the function b units downward.

Consequently, the transformed function mirrors a shift of 6 units downward.

In summary, the adjusted equation $g(x)=\frac{1}{x+4}-6$, shows the graph shifted 4 units to the left and 6 units downward.

6 0
1 month ago
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The yearly income for an individual with an associate’s degree in 2001 was $53,166 and in 2003 it was $56,970. What is the ratio
Zina [9171]

Response:

8861: 9495

Detailed explanation:

The income ratio for the years 2001 to 2003:

53,166: 56,970

To simplify, divide both sides by 6:

8,861: 9,495

This can't be simplified further, so that is the final result!

8861: 9495

I hope this helps! Have a great day:)

6 0
6 days ago
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