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3 years ago

Solve this quadratic equation by completing the square.

Mathematics

1 answer:

erastova [34]3 years ago

5 0

Answer:

Step-by-step explanation:

x² + 6x = 18

To complete the square, take the coefficient of the x term, halve it, square the result, then add to both sides.

(6/2)² = 3² = 9

x² + 6x + 9 = 18 + 9

(x + 3)² = 27

x + 3 = ±√27

x = -3 ± √27

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Write the equation of the line perpendicular to -6x+3y=6 that passes through (2,0). Write you answer in slope-intercept form

Svetach [21]

Answer:

The answer is: y - 0 = -1/2(x - 2)

Step-by-step explanation:

Given - an equation in standard form:

-6x + 3y = 6

Solve for y:

Add 6x to both sides:

3y = 6 + 6x

y = 2 + 2x

y = 2x + 2, so the slope is 2.

The perpendicular slope is the negative inverse of 2, which is -1/2.

Point slope form is:

y - y1 = m(x - x1)

Substitute in the numbers from the point (2,0) and the slope -1/2:

y - 0 = -1/2(x - 2)

Taking it to y intercept form:

y = -1/2x + 1

4 0

3 years ago

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HI GUYS PLEASE HELPP, PLEASE!!!

BARSIC [14]

Answer:‘12.92

Step-by-step explanation:

4 0

3 years ago

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HELP PLS FOR BRAINLIEST!

igomit [66]

Answer:

Electric force = 8.20x10⁻⁸ N

Gravitational force = 3.61x10⁻⁴⁷ N

Step-by-step explanation:

1. The electric force can be found using the following equation:

$F_{e} = \frac{Kq_{e}q_{p}}{d^{2}}$

Where:

K: is the Coulomb's constant = 9x10⁹ N.m²/C²

$q_{p}$ : is the charge of the proton = 1.6x10⁻¹⁹ C

$q_{e}$ : is the charge of the electron = -1.6x10⁻¹⁹ C

d: is the distance = 5.3x10⁻¹¹ m

Hence, the magnitude of the electric force is:

$|F_{e}| = \frac{9\cdot 10^{9} N.m^{2}/C^{2}*(-1.6\cdot 10^{-19} C)*1.6 \cdot 10^{-19} C}{(5.3 \cdot 10^{-11} m)^{2}} = 8.20 \cdot 10^{-8} N$

2. The gravitational force can be calculated as follows:

$F_{g} = \frac{Gm_{e}m_{p}}{d^{2}}$

Where:

$m_{e}$ : is the electron's mass = 9.1x10⁻³¹ kg

$m_{p}$ : is the proton's mass = 1.67x10⁻²⁷ kg

G: is the gravitational constant = 6.67x10⁻¹¹ N.m²/kg²

Therefore, the gravitational force is:

$F_{g} = \frac{6.67 \cdot 10^{-11} N.m^{2}/kg^{2}*9.1 \cdot 10^{-31} kg*1.67 \cdot 10^{-27} kg}{(5.3 \cdot 10^{-11} m)^{2}} = 3.61 \cdot 10^{-47} N$

As we can see, the gravitational force is much less than the electric force.

I hope it helps you!

5 0

3 years ago

6/2-(5-4)+2(8-2/2)÷8

Firdavs [7]

Answer:

$3\frac{3}{4}=\frac{15}{4} =3.75$

Step-by-step explanation:

Hope this helps.

7 0

3 years ago

5 more than the quotient of a number and 8 is 42

Zepler [3.9K]

Answer:

<u>The number is 296.</u>

Step-by-step explanation:

Let's call "x" to the number we are looking for.

Now, the problem states that "5 more than the quotient of a number and 8 is 42". This means that this number is being divided by 8, it's also being additioned 5 and the final result is 42. Therefore, the expression of this operations on this number is the following:

$\frac{x}{8}+5=42$ . Let's solve the equation to find x.

1. Write the expression.

$\frac{x}{8}+5=42$

2. Substract 5 from both sides and simplify.

$\frac{x}{8}+5-5=42-5\\\\\frac{x}{8}=37\\\\$

3. Multiply 8 on both sides and simplify.

$8*\frac{x}{8}=37*8\\\\x=296$

<u>We have found our number, it's 296!</u>

3 0

2 years ago

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