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Art [367]
2 years ago
7

Solve x2 + 8x + 22 = 0 by completing the square.

Mathematics
1 answer:
Liula [17]2 years ago
6 0

Answer:

A)

Step-by-step explanation:

the solution of a squared equation is

x = (-b ± sqrt(b² - 4ac)) / (2a)

in our case

a = 1

b = 8

c = 22

x = (-8 ± sqrt(64 - 88))/2 = (-8 ± sqrt(-24))/2 =

= (-8 ± sqrt(4×-6))/2 = (-8 ± 2×sqrt(-6))/2 =

= -4 ± sqrt(-6) = -4 ± i×sqrt(6)

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The equation A= 1750(1.04)^t represents an account balance t years after the account was created. Which statement is correct?
Eddi Din [679]

Answer:

<u>The correct statement is D. The account balance will increase 4% each year.</u>

Correct statement and question:

The equation A = 1750(1.04)^t represents an account balance t years after the  account was created.

Which statement is correct?

A. The account balance will decrease 0.04% each year.

B. The account balance will increase 0.04% each year.

C. The account balance will decrease 4% each year.

D. The account balance will increase 4% each year.

Source:

Tennessee Comprehensive  Assessment Program  - Algebra I Practice Test

Step-by-step explanation:

Let's recall that 1.04 is the result of adding:

1 + 0.04 and, we can also write 0.04 as 4/100 or 4%,

in consequence,

1.04 = 1 + 4%, where we're increasing an additional 4%.

<u>The correct statement is D. The account balance will increase 4% each year.</u>

7 0
3 years ago
What is the measure of AVM
Zolol [24]
The answer is C because all you have to do is divide 70 in half.
5 0
3 years ago
Read 2 more answers
I REALLY NEED HELP PLEASE
Nezavi [6.7K]

Answer:

10

Step-by-step explanation:

given

\frac{s + ( - 7)}{ - 1}

we first need to simplify the expression before we find it's value when s=-3

positive times negative=negative

so the equation becomes

\frac{s - 7}{ - 1}

substituting s=-3 into the equation.

\frac{ - 3 - 7}{ - 1}

=

\frac{ - 10}{ - 1}

=the negatives cancel out leaving

= 10

7 0
3 years ago
A square lawn has area 128128 ft squared .ft2. a sprinkler placed at the center of the lawn sprays water in a circular pattern t
fenix001 [56]
For this case what you must do is find the diagonal of the square to find the diameter of the circle and then be able to obtain the radius.
 We have then:
 A = L ^ 2 = 128
 L = root (128)
 L = 11.3137085
 Then, the diagonal of the square knowing its sides is:
 d = root ((L) ^ 2 + (L) ^ 2)
 d = root ((11.3137085) ^ 2 + (11.3137085) ^ 2)
 d = 16 feet
 Finally the radius of the circle is:
 r = d / 2
 r = (16) / 2
 r = 8feet
 answer:
 the radius of the circle is
 r = 8feet
6 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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