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taurus [48]
3 years ago
8

T he area of a square postage stamp is 81/100 in 2. What is the side length of the stamp?

Mathematics
1 answer:
mixas84 [53]3 years ago
8 0

We have been given that area of a square postage stamp is \frac{81}{100} \text{ in}^2

We have to find the side length of the stamp. In order to find the same, we use the formula for area of a square.

The area of a square with side length 'a' is given by

A=a^2

Substituting the value of area in this formula, we get

\frac{81}{100} = a^2\\
\\
a=\frac{9}{10}

Therefore, the side length of the stamp is given by 9/10 inches.

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Find an equation of the plane orthogonal to the line
jolli1 [7]

The given line is orthogonal to the plane you want to find, so the tangent vector of this line can be used as the normal vector for the plane.

The tangent vector for the line is

d/d<em>t</em> (⟨0, 9, 6⟩ + ⟨7, -7, -6⟩<em>t </em>) = ⟨7, -7, -6⟩

Then the plane that passes through the origin with this as its normal vector has equation

⟨<em>x</em>, <em>y</em>, <em>z</em>⟩ • ⟨7, -7, -6⟩ = 0

We want the plane to pass through the point (9, 6, 0), so we just translate every vector pointing to the plane itself by adding ⟨9, 6, 0⟩,

(⟨<em>x</em>, <em>y</em>, <em>z</em>⟩ - ⟨9, 6, 0⟩) • ⟨7, -7, -6⟩ = 0

Simplifying this expression and writing it standard form gives

⟨<em>x</em> - 9, <em>y</em> - 6, <em>z</em>⟩ • ⟨7, -7, -6⟩ = 0

7 (<em>x</em> - 9) - 7 (<em>y</em> - 6) - 6<em>z</em> = 0

7<em>x</em> - 63 - 7<em>y</em> + 42 - 6<em>z</em> = 0

7<em>x</em> - 7<em>y</em> - 6<em>z</em> = 21

so that

<em>a</em> = 7, <em>b</em> = -7, <em>c</em> = -6, and <em>d</em> = 21

4 0
3 years ago
Brainliest to who answers correctly
LenKa [72]
The correct answer would be the 3rd one because the number simplified equals that
6 0
3 years ago
Read 2 more answers
Evaluate the expression if m = 3.<br><br> 3m^2<br><br><br> (SHOW YOUR WORK)
iragen [17]

The value of given expression when m = 3 is 27

<h3><u>Solution:</u></h3>

Given expression is 3m^2

We have to evaluate the given expression for m = 3

To find for m is equal to 3, substitute m = 3 in given expression

From given expression,

\rightarrow 3m^2

Plug in m = 3 in above expression

\rightarrow 3(3)^2 ------ eqn 1

We know that,

a^2 can be expanded as,

a^2=a \times a

Applying this in eqn 1, we get

\rightarrow 3(3)^2=3 \times (3 \times 3)

Simplify the above expression

\rightarrow 3(3)^2=3 \times (3 \times 3) = 3 \times 9 = 27

Therefore, for m = 3 we get,

\rightarrow 3(3)^2=27

Thus value of given expression when m = 3 is found

5 0
3 years ago
A recipe uses 6 cups of cheese to serve 30 people. How much cheese is needed for 50 people
yanalaym [24]
\bf \begin{array}{ccll}&#10;\stackrel{cheese}{cups}&people\\&#10;\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\&#10;6&30\\&#10;c&50&#10;\end{array}\implies \cfrac{6}{c}=\cfrac{30}{50}\implies \cfrac{6\cdot 50}{30}=c
7 0
3 years ago
Use the model to solve for x.<br> A) x = -5 <br> B) x = 5/4<br> C) x = 5/3<br> D) x = -5/4
STatiana [176]

i think this answer would be C that would be my choice :)

8 0
3 years ago
Read 2 more answers
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