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evablogger [386]
2 years ago
13

Dylan uses the expressions (x^2 -2x+8) and (2x^2 + 5x - 7) to represent the length and width of his bedroom. Which expression re

presents the area (lw) of Dylan’s room ?
Mathematics
2 answers:
Oksanka [162]2 years ago
5 0

2x^4 + x^3 - x^2 +54x - 56 expression represents the area of Dylan’s room

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

Given that,

Length of room = x^2 -2x+8

Width of room = 2x^2 + 5x - 7

To find: Expression that the area (lw) of Dylan’s room

Since bedroom is generally of rectangular shape, we can use area of rectangle

<em><u>The area of rectangle is given as:</u></em>

\text {area of rectangle }=\text { length } \times \text { width }

Substituting the given expressions of length and width,

area = (x^2 -2x+8)(2x^2 + 5x - 7)

We multiply each term inside first parenthesis with each term inside the second parenthesis.

So it becomes,

2x^4 + 5x^3 - 7x^2 -4x^3 -10x^2 +14x +16x^2 +40x - 56

Now combine like terms,

2x^4 + x^3 - x^2 +54x - 56

Thus the above expression represents the area of Dylan’s room

Margaret [11]2 years ago
5 0

Answer:

c

Step-by-step explanation:

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What is the sum of 4.9 × 102 and 6.8 × 103?
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Answer:

The sum is

7.92\times 10^3

Step-by-step explanation:

We want to add

4.9\times 10^2 and 6.8\times 10^3

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4.9\times 10^2 +6.8\times 10^3

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4.9\times 100 +6.8\times 1000

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Read 2 more answers
Consider the following planes. x + y + z = 6, x + 7y + 7z = 6 (a) Find parametric equations for the line of intersection of the
Lelechka [254]

Answer:

a.x=6,y=-6t,z=6t

b.\theta=29.5^{\circ}

Step-by-step explanation:

We are given that

x+y+z=6

x+7y+7z=6

a.Substitute z=0

x+y=6...(1)

x+7y=6..(2)

Subtract equation (1) from equation (2)

6y=0

y=0

Substitute y=0 in equation(1)

x=6

The point (6,0,0) lie on a line.

r_0=(x_0,y_0,z_0)=(6,0,0)

Let A=

B=

A\times B=\begin{vmatrix}i&j&k\\1&1&1\\1&7&7\end{vmatrix}

A\times B=i(7-7)-j(7-1)+k(7-1)=-6j+6k

Therefore, the vector a'=(a,b,c)=

Line is parallel to vector a' and passing through the point (6,0,0).

The parametric equation is given by

x=x_0+at,y=y_0+bt,z=z_0+ct

Using the formula

The parametric equation is given by

x=6,y=-6t,z=6t

Angle between two plane

a_1x+b_1y+c_1z=d_1

and a_2x+b_2y+c_2z=d_2

cos\theta=\frac{(a_1,b_1,c_1)\cdot (a_2,b_2,c_2)}{\sqrt{a^2_1+b^2_1+c^2_1}\cdot \sqrt{a^2_2+b^2_2+c^2_2}}

Using the formula

cos\theta=\frac{(1,1,1)\cdot(1,7,7)}{\sqrt{1+1+1}\times \sqrt{1+7^2+7^2}}

cos\theta=\frac{1+7+7}{\sqrt 3\times 3\sqrt{11}}

cos\theta=\frac{15}{3\sqrt{33}}}=\frac{5}{\sqrt{33}}

\theta=cos^{-1}(0.87)=29.5^{\circ}

Where \theta in degree.

3 0
3 years ago
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