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SOVA2 [1]
3 years ago
10

The length of a rectangle is 3x +2 and the width of the rectangle is 6x-1. Express the

Mathematics
1 answer:
WINSTONCH [101]3 years ago
4 0

Answer:

2(3x+2+6x-1)

=2(9x+1)

=18x+2

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If there are four quarters in a dollar, which expression correctly shows how you might figure out how many quarters are in $9.25
xxMikexx [17]

Answer:

37

Step-by-step explanation:

4(9) + 1 = 37

7 0
3 years ago
Read 2 more answers
The chemistry class was making 300 gallons of 30% isopropyl alcohol. They mixed 12% with 42%. How much of each did they use?
alexgriva [62]

Answer:

<u>The chemistry class mixed 120 gallons of 12% isopropyl alcohol and 180 gallons of 42% isopropyl alcohol.</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Amount of isopropyl alcohol made by the chemistry class = 300 of 30%

Amount of 12% isopropyl alcohol mixed by the chemistry class = x

Amount of 42% isopropyl alcohol mixed by the chemistry class = 300 - x

2. How much of each did they use?

Let's write our equation to solve for x, this way:

30% = 0.3, 12% = 0.12, 42% = 0.42

0.12x + 0.42 (300 - x) = 0.3 * 300

0.12x + 126 - 0.42x = 90

-0.3x = 90 - 126

-0.3x = -36

x = -36/-0.3

<u>x = 120 ⇒ 300 - x = 180</u>

<u>Let's prove x = 120 is correct</u>

0.12x + 0.42 (300 - x) = 0.3 * 300

0.12 * 120 + 0.42 (300 - 120) = 0.3 * 300

14.4 + 75.6 = 90

90 = 90

<u>We proved x = 120 is correct</u>

5 0
3 years ago
Amy wants to carpet a room that is 12 feet by 8 feet.
Alex17521 [72]
1\ ft=0.333\ yards\\8\ ft=8\cdot0.333=2.664\ yards\\12\ ft=12\cdot0.333=3.996\ yards\\\\2.664\cdot3.996=10.645\ square\ yards\\\\She\ need\ 10.645\ square\ yards\ of\ carpet.
4 0
3 years ago
If √3 = 1.73 to 2 dp, find the value of 4/√3 to 2 dp​
Mashutka [201]

Answer:2.31

Step-by-step explanation: considering that the root of 3 has already been given. Will just divide 4 by the root of 3 which is 1.73. and the answer it gives is 2.31

3 0
3 years ago
37. Verify Green's theorem in the plane for f (3x2- 8y2) dx + (4y - 6xy) dy, where C is the boundary of the
Nastasia [14]

I'll only look at (37) here, since

• (38) was addressed in 24438105

• (39) was addressed in 24434477

• (40) and (41) were both addressed in 24434541

In both parts, we're considering the line integral

\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dy

and I assume <em>C</em> has a positive orientation in both cases

(a) It looks like the region has the curves <em>y</em> = <em>x</em> and <em>y</em> = <em>x</em> ² as its boundary***, so that the interior of <em>C</em> is the set <em>D</em> given by

D = \left\{(x,y) \mid 0\le x\le1 \text{ and }x^2\le y\le x\right\}

• Compute the line integral directly by splitting up <em>C</em> into two component curves,

<em>C₁ </em>: <em>x</em> = <em>t</em> and <em>y</em> = <em>t</em> ² with 0 ≤ <em>t</em> ≤ 1

<em>C₂</em> : <em>x</em> = 1 - <em>t</em> and <em>y</em> = 1 - <em>t</em> with 0 ≤ <em>t</em> ≤ 1

Then

\displaystyle \int_C = \int_{C_1} + \int_{C_2} \\\\ = \int_0^1 \left((3t^2-8t^4)+(4t^2-6t^3)(2t))\right)\,\mathrm dt \\+ \int_0^1 \left((-5(1-t)^2)(-1)+(4(1-t)-6(1-t)^2)(-1)\right)\,\mathrm dt \\\\ = \int_0^1 (7-18t+14t^2+8t^3-20t^4)\,\mathrm dt = \boxed{\frac23}

*** Obviously this interpretation is incorrect if the solution is supposed to be 3/2, so make the appropriate adjustment when you work this out for yourself.

• Compute the same integral using Green's theorem:

\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dy = \iint_D \frac{\partial(4y-6xy)}{\partial x} - \frac{\partial(3x^2-8y^2)}{\partial y}\,\mathrm dx\,\mathrm dy \\\\ = \int_0^1\int_{x^2}^x 10y\,\mathrm dy\,\mathrm dx = \boxed{\frac23}

(b) <em>C</em> is the boundary of the region

D = \left\{(x,y) \mid 0\le x\le 1\text{ and }0\le y\le1-x\right\}

• Compute the line integral directly, splitting up <em>C</em> into 3 components,

<em>C₁</em> : <em>x</em> = <em>t</em> and <em>y</em> = 0 with 0 ≤ <em>t</em> ≤ 1

<em>C₂</em> : <em>x</em> = 1 - <em>t</em> and <em>y</em> = <em>t</em> with 0 ≤ <em>t</em> ≤ 1

<em>C₃</em> : <em>x</em> = 0 and <em>y</em> = 1 - <em>t</em> with 0 ≤ <em>t</em> ≤ 1

Then

\displaystyle \int_C = \int_{C_1} + \int_{C_2} + \int_{C_3} \\\\ = \int_0^1 3t^2\,\mathrm dt + \int_0^1 (11t^2+4t-3)\,\mathrm dt + \int_0^1(4t-4)\,\mathrm dt \\\\ = \int_0^1 (14t^2+8t-7)\,\mathrm dt = \boxed{\frac53}

• Using Green's theorem:

\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dx = \int_0^1\int_0^{1-x}10y\,\mathrm dy\,\mathrm dx = \boxed{\frac53}

4 0
3 years ago
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