Solve for x in simplest radical form. 2x2 + 2x + 4 = x2 + 6x + 5

A cars tire pressure decreased by 0.098 of its original pressure write 0.098 as a percent

balandron [24]

To write this as a percent, just move the decimal two places to the right. So instead of .098, this becomes 9.8%. hope this helps!

5 0

3 years ago

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Solve the initial value problem where y′′+4y′−21 y=0, y(1)=1, y′(1)=0 . Use t as the independent variable.

igor_vitrenko [27]

Answer:

$y = \frac{7}{10} e^{3(t - 1)} + \frac{3}{10}e^{-7(t - 1)}$

Step-by-step explanation:

y′′ + 4y′ − 21y = 0

The auxiliary equation is given by

m² + 4m - 21 = 0

We solve this using the quadratic formula. So

$m = \frac{-4 +/- \sqrt{4^{2} - 4 X 1 X (-21))} }{2 X 1}\\ = \frac{-4 +/- \sqrt{16 + 84} }{2}\\= \frac{-4 +/- \sqrt{100} }{2}\\= \frac{-4 +/- 10 }{2}\\= -2 +/- 5\\= -2 + 5 or -2 -5\\= 3 or -7$

So, the solution of the equation is

$y = Ae^{m_{1} t} + Be^{m_{2} t}$

where m₁ = 3 and m₂ = -7.

So,

$y = Ae^{3t} + Be^{-7t}$

Also,

$y' = 3Ae^{3t} - 7e^{-7t}$

Since y(1) = 1 and y'(1) = 0, we substitute them into the equations above. So,

$y(1) = Ae^{3X1} + Be^{-7X1}\\1 = Ae^{3} + Be^{-7}\\Ae^{3} + Be^{-7} = 1 (1)$

$y'(1) = 3Ae^{3X1} - 7Be^{-7X1}\\0 = 3Ae^{3} - 7Be^{-7}\\3Ae^{3} - 7Be^{-7} = 0 \\3Ae^{3} = 7Be^{-7}\\A = \frac{7}{3} Be^{-10}$

Substituting A into (1) above, we have

$\frac{7}{3}B e^{-10}e^{3} + Be^{-7} = 1 \\\frac{7}{3}B e^{-7} + Be^{-7} = 1\\\frac{10}{3}B e^{-7} = 1\\B = \frac{3}{10} e^{7}$

Substituting B into A, we have

$A = \frac{7}{3} \frac{3}{10} e^{7}e^{-10}\\A = \frac{7}{10} e^{-3}$

Substituting A and B into y, we have

$y = Ae^{3t} + Be^{-7t}\\y = \frac{7}{10} e^{-3}e^{3t} + \frac{3}{10} e^{7}e^{-7t}\\y = \frac{7}{10} e^{3(t - 1)} + \frac{3}{10}e^{-7(t - 1)}$

So the solution to the differential equation is

$y = \frac{7}{10} e^{3(t - 1)} + \frac{3}{10}e^{-7(t - 1)}$

6 0

3 years ago

Can someone help me please

saul85 [17]

Using the Law of Sines (sina/A=sinb/B=sincC for any triangle)

sinc/28=sin90/53 (sin90=1) multiply both sides by 28

sinc=28/53 take the inverse of sin (arcsin) of both sides

c=arcsin(28/53)°

c≈31.89° (to nearest hundredth of a degree)

So it is obvious that they rounded to nearest tenth of a degree

c≈31.9°

5 0

3 years ago

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Game Go charges $0.79 per game rental and a membership fee of $24. Action Games charges $1.19 per game rental. With how many gam

nexus9112 [7]

Answer:

x=60

Step-by-step explanation:

Simplifying

0.79x + 24 = 1.19x

Reorder the terms:

24 + 0.79x = 1.19x

Solving

24 + 0.79x = 1.19x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.19x' to each side of the equation.

24 + 0.79x + -1.19x = 1.19x + -1.19x

Combine like terms: 0.79x + -1.19x = -0.4x

24 + -0.4x = 1.19x + -1.19x

Combine like terms: 1.19x + -1.19x = 0.00

24 + -0.4x = 0.00

Add '-24' to each side of the equation.

24 + -24 + -0.4x = 0.00 + -24

Combine like terms: 24 + -24 = 0

0 + -0.4x = 0.00 + -24

-0.4x = 0.00 + -24

Combine like terms: 0.00 + -24 = -24

-0.4x = -24

Divide each side by '-0.4'.

x = 60

Simplifying

x = 60

8 0

3 years ago

Jessie says to round 763,400 to the nearest ten thousand, he will round to 770,000 is he right ? explain

weqwewe [10]

For this case we have the following definition:

ten thousand place: number of five digits whose absolute value is greater than zero.

Then, we have the following rounding rule:

1) If the previous number is greater than or equal to five, then the next number increases by one unit.

2) If the previous number is less than or equal to five, then the next number remains the same.

We then have the following number:

763,400

Rounding to the nearest ten thousand we have:

760,000

Answer:

Jessie is wrong. The correct answer is:

760,000

3 0

3 years ago

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