solve the equation for x 5x squared - 4x = 6

Answer:

[tex]\displaystyle 3 + 21x[/tex]

Step-by-step explanation:

[tex]\displaystyle 3[7x + 1] \hookrightarrow \boxed{21x + 3}[/tex]

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Answer:

3.6 miles

Step-by-step explanation:

Pythagorean Theorem:

[tex]2^{2}+3^{2} =\\4 + 9 = \sqrt{13}[/tex]

√13 = 3.60555127546

Nearest tenth = 3.6

The decimal computed shows that Tracy doesn't have enough for the construction.

From the information given, Tracy has three pieces of wood that are each 8 meters long and one piece that is 7 meters long. Therefore, the addition of the lengths will be:

= (3 × 8) + 7

= 24 + 7.

= 31m

Since Tracy needs 31.5 meters of wood for a porch railing, it shows that she doesn't have enough.

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Answer:

26.22 cubed inches

Step-by-step explanation:

V=πr2h

r = radius = diameter/2

h = height

π = pi = 3.14

v = 3.14([tex]1.2^{2}[/tex])5.8

v = 3.14(1.44)5.8

v = 4.52 x 5.8

v = 26.22

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PLEASE RATE!!

The volume of the cylindrical can is equal to 26.0 [tex]in^3[/tex].

Given the following data:

Radius = [tex]\frac{diameter}{2} =\frac{2.4}{2} =1.2\;in[/tex]

Mathematically, the volume of a cylinder is given by this formula:

[tex]V = \pi r^2h[/tex]

Where:

Substituting the given parameters into the formula, we have;

[tex]V = 3.14 \times 1.2^2 \times 5.8\\\\V = 4.5216 \times 5.8[/tex]

V = 26.22 ≈ 26.0 [tex]in^3[/tex].

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Answer:

Temperature is the measure of hotness or coldness expressed in terms of any of several scales. An example  would be "The cup of beans are boiling hot and has a temperature of 100 °C, whereas the water in the tub is just comfortably warm, with a temperature of about 38 °C. Although the water in the tub has a much lower temperature, it has greater thermal energy".

Step-by-step explanation:

Answer:

1.  $4200

2. $8000

3. Profit $3800

4. 90.48% (2 d.p.)

Step-by-step explanation:

40 x 105 = 4200

40 x 200 = 8000

8000 - 4200 = 3800

Rate of Return = (Final Value - Initial Value) divided by Initial Value

(8000-4200) divided by 4200 = 19/21 or 0.9047619048

= 90.48%

Answer:

1. $4,200

2. $8,000

3. $3,800 profit

4. 90.48%

Step-by-step explanation:

QUESTION 1:

The cost of one share two years ago was $105. Since you bought 40 shares, you would have to multiply that price by 40:

[tex]$105*40=4,200[/tex]

That means the total cost of purchasing 40 shares two years ago was $4,200.

QUESTION 2:

One share currently costs $200. Just like with problem 1, since they're asking about all 40 shares, you need to multiply that price by 40.

[tex]200*40=8,000[/tex]

That means that 40 shares is currently valued at $8,000.

QUESTION 3:

Profit or loss is calculated by subtracting the final value by the initial value. In this case, subtracting the current price by the price you originally bought the shares for.

[tex]8,000-4,200=3,800[/tex]

Because it's a positive number, you know that you've made a profit of $3,800 off of 40 shares.

QUESTION 4:

Rate of return is calculated by dividing the profit (or loss) by the original cost:

[tex]3,800/4,200=0.9048[/tex]

Of course, since rate of return is expressed in a percentage, you would need to multiply 0.9048 by 100 and tack a percent sign onto the end, giving you 90.48%. (I rounded the number to the nearest hundredth.)

I use complex analysis to compute the integrals in question.

First, notice that the first integrand is even:

[tex]\dfrac{\cos(-x)}{(-x)^2+1}=\dfrac{\cos(x)}{x^2+1}[/tex]

[tex]\implies\displaystyle\int_0^\infty\frac{\cos(x)}{x^2+1}\,dx=\frac12\int_{-\infty}^\infty\frac{\cos(x)}{x^2+1}\,dx[/tex]

Consider a contour C that's the union of

• Γ, a semicircle of radius R in the upper half-plane, and

• the line segment connecting the points (-R, 0) and (R, 0)

On Γ, we have [tex]z=Re^{it}[/tex] with 0 ≤ t ≤ π.

Consider the complex function

[tex]f(z)=\dfrac{e^{iz}}{z^2+1}[/tex]

and notice that our original integrand is the real part of f(z). Then the integral of f(z) over C is

[tex]\displaystyle\int_Cf(z)\,dz=\lim_{R\to\infty}\left(\int_{-R}^Rf(z)\,dz+\int_\Gamma f(z)\,dz\right)[/tex]

As R → ∞, the first integral on the right is exactly twice the one we want. Estimate the second one to be bounded by

[tex]\displaystyle\left|\int_\Gamma f(z)\,dz\right|\le\pi R|f(z)|\le\frac{\pi R}{R^2-1}[/tex]

since

[tex]|z^2+1|\ge\bigg||z^2|-|-1|\bigg|=|R^2-1|[/tex]

and so the integral along Γ vanishes.

f(z) has only one pole in the interior of C at z = i. By the residue theorem,

[tex]\displaystyle\int_Cf(z)\,dz=2\pi i\,\mathrm{Res}\left(f(z),z=i\right)=2\pi i\lim_{z\to i}(z-i)f(z)=\frac\pi e[/tex]

[tex]\implies\displaystyle\int_0^\infty\frac{\cos(x)}{x^2+1}\,dx=\frac12\mathrm{Re}\left(\int_Cf(z)\,dz\right)=\frac\pi{2e}[/tex]

For the second integral, we recall that for complex z,

[tex]\sqrt z=\exp\left(\dfrac12\left(\ln|z|+i\arg(z)\right)\right)[/tex]

Consider a keyhole contour C, the union of

• [tex]\Gamma_R[/tex], the larger circle with radius R and [tex]z=Re^{it}[/tex], with 0 < t < 2π ;

• [tex]\Gamma_\varepsilon[/tex], the smaller circle with radius ε and [tex]z=\varepsilon e^{-it}[/tex], with 0 < t < 2π ;

• [tex]\ell_1[/tex], the line segment above the positive real axis joining [tex]\Gamma_\varepsilon[/tex] to [tex]\Gamma_R[/tex] ; and

• [tex]\ell_2[/tex], the other line segment below the positive real axis joining [tex]\Gamma_R[/tex] to [tex]\Gamma_\varepsilon[/tex]

Then

[tex]\displaystyle\int_Cf(z)\,dz=\int_{\Gamma_R}f(z)\,dz+\int_{\ell_1}f(z)\,dz+\int_{\Gamma_\varepsilon}f(z)\,dz+\int_{\ell_2}f(z)\,dz[/tex]

and in the limit, the integral over [tex]\ell_1[/tex] converges to the one we want.

Estimate the integrals over the circular arcs:

• [tex]\Gamma_R[/tex] :

[tex]\displaystyle\left|\int_{\Gamma_R}f(z)\,dz\right|\le2\pi R|f(Re^{it})|\le\dfrac{2\pi R^{3/2}}{|R-\sqrt5|^2}\to0[/tex]

as R → ∞.

• [tex]\Gamma_\varepsilon[/tex] :

[tex]\displaystyle\left|\int_{\Gamma_\varepsilon}f(z)\,dz\right|\le2\pi \varepsilon|f(\varepsilon e^{-it})|\le\dfrac{2\pi\varepsilon^{3/2}}{|\varepsilon-\sqrt5|^2}\to0[/tex]

as ε → 0.

Consider the integral over [tex]\ell_2[/tex] :

[tex]\displaystyle\int_{\ell_2}f(z)\,dz=\int_R^\varepsilon\frac{\sqrt z}{z^2+2z+5}\,dz\\\\=\int_R^\varepsilon\frac{\exp\left(\dfrac12\left(\ln|z|+2\pi i\right)\right)}{z^2+2z+5}\,dz\\\\=-\int_R^\varepsilon\frac{\exp\left(\dfrac12\ln|z|\right)}{z^2+2z+5}\,dz\\\\=\int_\varepsilon^R\frac{\sqrt z}{z^2+2z+5}\,dz\\\\=\int_{\ell_1}f(z)\,dz[/tex]

so in fact,

[tex]\displaystyle\int_Cf(z)\,dz=2\int_0^\infty\frac{\sqrt x}{x^2+2x+5}\,dx[/tex]

By the residue theorem,

[tex]\displaystyle\int_Cf(z)\,dz=2\pi i\sum_{\rm poles}\mathrm{Res}\,f(z)[/tex]

We have poles at z = -1 + 2i and z = -1 - 2i. On our chosen branch,

[tex]\sqrt{-1+2i}=i\sqrt[4]{5}\exp\left(-\dfrac i2\tan^{-1}(2)\right)[/tex]

[tex]\sqrt{-1-2i}=i\sqrt[4]{5}\exp\left(\dfrac i2\tan^{-1}(2)\right)[/tex]

The residues are

[tex]\mathrm{Res}(f(z),z=-1-2i)=\dfrac{i\sqrt[4]{5}\exp\left(\frac i2\tan^{-1}(2)\right)}{-4i}[/tex]

[tex]\mathrm{Res}(f(z),z=-1+2i)=\dfrac{i\sqrt[4]{5}\exp\left(-\frac i2\tan^{-1}(2)\right)}{4i}[/tex]

Their sum is

[tex]\displaystyle\sum_{\rm poles}\mathrm{Res}\,f(z)=-\frac{\sqrt[4]{5}}2\sin\left(\dfrac12\tan^{-1}(2)\right)=-\frac{\sqrt[4]{5}}2\sqrt{\frac{5-\sqrt5}{10}}=-\frac i2\sqrt{\frac1\phi}[/tex]

where ɸ = (√5 + 1)/2 is the golden ratio, and so the overall integral is

[tex]\displaystyle\int_0^\infty\frac{\sqrt x}{x^2+2x+5}\,dx=\frac\pi2\sqrt{\frac1\phi}[/tex]

Lastly, recall

[tex]\displaystyle\sum_{k=0}^\infty\frac1{k!}=e[/tex]

Then our expression reduces to

[tex]\left(\dfrac{e\times\frac\pi{2e}}{\frac\pi2\sqrt{\frac1\phi}}\right)^2=\boxed{\phi}[/tex]

Answer:

10 - 10 rupees note

Step-by-step explanation:

have a good day .please mark as brainiest

Answer:

Equiangular triangle

Step-by-step explanation:

"equiangular triangle" means a triangle that has equal sides

knowing that the sum of the angles of a triangle is 180° each angle must be 60° because [tex]\frac{180}{3}=60[/tex]

Answer:

Step-by-step explanation:

Its The last one just took a test

Answer:

(5*85)/4-(7-4)

425/4-(7-4)

425/4-3

106.25-3

103.25

It is not 47.

Answer:

4n - 11 = (15 - 2)n

Step-by-step explanation:

Using the keywords;

'Difference of'

'Equal to'

'Less than'

'Times', we can find the equation.

Let's piece it together:

Difference of; 4n(four times n) and 11

Equal to( = )

(15 - 2)n, which is 15 less than 2, multiplied by n

Answer:

Large number: 20

Small number: 12

Step-by-step explanation:

Hello!

This problem is a word problem, and if we assign variables to find each of the numbers, it could help.
A variable is usually an unknown number that stands for that unknown.
Since in this problem we know there is a small and large number, let's assign the large number as the variable x and small number as variable y.

For the first part, it says two numbers whose difference is 8, which means the large number minus the smaller number equals 8.

x-y=8

For the second part is tricky. It's saying that the small number times three is 16 more than the large number itself. When constructing a equation, this is what we get:

x+16=3y   x plus 16 equals 3 times y

To solve this equation together so we can make it super easy, let's do the method of substitution, which is where we make an equation equal to a variable and input that equation into the second equation.
We can use x-y=8 to input, we can rearrange y and plug it to the right side to get x=8+y

Since x equals 8+y, let's input this into the second equation.

(8+y)+16=3y    input the rearranged equation into the second

24+y=3y         combine like terms

    -y   -y

24=2y              divide by two to get y by itself

12=y

We aren't done yet! We have to find x still; let's use the previous first equation to find x. We know y=12, so let's plug it in.

x-y=8    original formula

x-12=8      plug it in

+12  +12

x=20

Therefore, the large number is 20, and smaller number is 12.

Answer:

12 and 20

Step-by-step explanation:

                         small=x

                         big= (x+8)

(x+8) = 3x -16

24 = 2x

x=12 (small)

12+8 = 20(big)

Answer:

424

Step-by-step explanation:

Answer:

ok so scale means that for every 1/2 each is one foot so each inch 2 feet

so lets just multiply each one by 2 and say their feet

5*2=10 feet

11*2=22 feet

22 feet tall

10 feet wide

Hope This Helps!!!

Answer:

First choice.

Step-by-step explanation:

Th first  option.

(x + 1)^2 - 25

The minimum value is -25 because the minimum value of the squared term is 0.   A squared term cannot be negative,

Answer:

Renewable resources are abundant.

Step-by-step explanation

I have answered this question before

Answer:

A. Renewable resources are abundant.

Step-by-step explanation:

hope this helps

Answer/Step-by-step explanation:

Explanation for False ( Counterexample)

[2] False. Look at the picture below

[4] False Look at picture below

Answer:

ion know

beyond ma capacity

Answer:

Step-by-step explanation:

John spent and gave to his two friends a total of

1.25 + 1.20 + 1.20 = $3.65

Money left

8.50 - 3.65 = $4.85

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Answer:

$4.85

Step-by-step explanation:

Given;

Little John had $8.50

Spent $1.25 on sweets

Gave 2 friends $1.20

Step 1; [Solve Spend on Sweets]

$8.50 - $1.25=7.25

Step 2; Find amount given to his 2 friend]

[Gave $1.20 to each of his 2 friends]

$1.20 x 2 = 2.40

7.25 - 2.40=4.85  

Hence, Little John have $4.85 is left

[RevyBreeze]

Answer:

y=-3x+9

Step-by-step explanation:

Find the change, then plug in the point.

Solution:

Step-1: Find the area of the rectangle.

L = 5/8 foot; B = 4/9 foot

Step-2: Verify all the options.

Looking at all the options, we can see that Option C (1/4 ft²) is the best estimate of the area we obtained as 10/36 and 9/36 are really close fractions.

Thus, Option C is correct.

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Answer:

1. HP and MN

2. HM and PN

Step-by-step explanation:

The parallel sides are the ones that do not touch.

HP and MN don't touch.

HM and PN also don't touch.

Answer:

116

Step-by-step explanation:

$232=$2

if each brick is $2 and you spent $232 divide it

232/2 would be 116 so to check your answer

  116*$2(each brick) it would be 232

Answer:

116 bricks

Step-by-step explanation:

you divide 232 by 2

which will give you 116

and to make sure u got 232 you multiple 116 × 2=232

Answer:

x|x< -2

Step-by-step explanation:

3x < -6

divide each side by 3

x <-2

Answer:

it is D or C

Step-by-step explanation:

Answer:

D. complementary

Step-by-step explanation:

The two angles a and b add up to 90 degrees, so they are complementary.

Hopefully this helps - let me know if you have any questions!