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Gennadij [26K]
3 years ago
9

The length of a rectangle is 4 inches longer than its width. The area of the rectangle is 32 inches square. What is the width ?

The width is ___ inches
Mathematics
1 answer:
Deffense [45]3 years ago
5 0

Answer:

I hope this helps dear

Step-by-step explanation:

P = 2(L + W) = 32 in

L = W + 4

2[(W + 4) + W] = 32 in ⇒

W = 6 in

L = W + 4 = (6 + 4) in = 10 in

A = LW = (10)(6) in2 = 60 in2

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Given that u =< 2,12 >, and z =< -7,5 >
swat32

Using the dot product:

For any vector x, we have

||x|| = √(x • x)

This means that

||w|| = √(w • w)

… = √((u + z) • (u + z))

… = √((u • u) + (u • z) + (z • u) + (z • z))

… = √(||u||² + 2 (u • z) + ||z||²)

We have

u = ⟨2, 12⟩   ⇒   ||u|| = √(2² + 12²) = 2√37

z = ⟨-7, 5⟩   ⇒   ||z|| = √((-7)² + 5²) = √74

u • z = ⟨2, 12⟩ • ⟨-7, 5⟩ = -14 + 60 = 46

and so

||w|| = √((2√37)² + 2•46 + (√74)²)

… = √(4•37 + 2•46 + 74)

… = √314 ≈ 17.720

Alternatively, without mentioning the dot product,

w = u + z = ⟨2, 12⟩ + ⟨-7, 5⟩ = ⟨-5, 17⟩

and so

||w|| = √((-5)² + 17²) = √314 ≈ 17.720

7 0
2 years ago
Q # 1 Graph the function<br>Y = |X + 2| - 3
Svetllana [295]
First of all we know the Absolute Value Function that is:

\left | x \right |= \left \{ {{x \ \ \ \ x \geq 0} \atop {-x \ \ \ \ x\ \textless \ 0}} \right.

This is called the Parent Function <em>of the Absolute Value Function.</em>

From the equation:

y=\left | x+2 \right |-3

The term:

\left | x+2 \right |

means that the the Parent Function is <em>shifted</em> two units <em>to the left</em>.

On the other hand, the term:

-3

means that the function \left | x+2 \right | is <em>shifted</em> three units <em>downward. </em>So the result is the graph shown below

4 0
3 years ago
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Two numbers have a sum of 49. If one number is x,express the other number in terms of x
Ymorist [56]

Answer:

y = 49 - x

Step-by-step explanation:

Let the other number be y.

Given x + y = 49

x+y-x = 49 - x

y = 49 - x

5 0
3 years ago
The first two terms in an arithmetic progression are 57 and 46. The last term is -207. Find the sum of all the terms in this pro
statuscvo [17]

Answer:

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Step-by-step explanation:

An arithmetic sequence has a common difference as a sequence. Here the common differnece is -11.

So our sequence so far looks like,

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We need to find the nth term so

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which is

\frac{a  _{1} + a _{n}   }{2} n

\frac{57 + ( - 207)}{2} (25) =

\frac{ -  150}{2} (25)

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Vesnalui [34]

Answer:

10^24

Step-by-step explanation:

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4 years ago
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