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alexandr1967 [171]
4 years ago
15

Is the sum of 4.2 and the square root of 2 rational or irrational?

Mathematics
1 answer:
andrew-mc [135]4 years ago
4 0
A rational number can be expressed as a fraction with an integer numerator and denominator. The square root of 2 is irrational, and adding 4.2 doesn't change this, since there are no integers that, when divided, form this sum.
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Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
Svetllana [295]

The equation x^{2} -4=0~~and~~4x^2=16 are true for  x = -2 and x = 2.

The given equations are given as:

x^2-4=0\\\\x^2=-4\\\\3x^2+12=0\\\\4x^2=16\\\\2(x-2)^2=0

We need to select two equations that are true for x = -2 and x = 2.

<h3>What are the solutions to an equation ?</h3>

The solutions of an equation are the values that satisfy the given equation or make the equation true when substituted for unknowns in the equations.

Example:

x - 2 = 2

Here the solution for x - 2 = 2 is 4 because x = 4 will make the equation true.

4 - 2 = 2

2 = 2

Let's find the solutions for each equation.

1.

x^2 - 4=0

x^{2} = 4

x = \sqrt{4} = ± 2

x = = 2 and x = -2

2.

x^2 =-4

x = \sqrt{-4}

x = \sqrt{-1 \times 4} = \sqrt{-1}\times\sqrt{4}

x = ± 2 \sqrt{-1}

x = 2i and x = -2i         where i = \sqrt{-1}

3.

3x^{2} + 12  = 0

x^{2} = -12 / 3 = -4

x = \sqrt{-1} \sqrt{4}

x = ± 2\sqrt{-1}

x = 2i and x = -2i

4.

4x^{2} = 16

x^{2} = 16 / 4

x^{2} = 4

x = \sqrt{4}

x = ±2

x = 2 and x = -2

5.

2(x-2)^2 = 0

(x-2)^2 = 0

x - 2 = 0

x = 2.

Thus the equation x^{2} -4=0~~and~~4x^2=16 have solutions x = -2 and x = 2.

Learn more about solutions of equations here:

brainly.com/question/14506845

#SPJ1

4 0
2 years ago
2 3/7÷2/3×3/4<br><br> Please help I need the homework done by tomorrow
Alex73 [517]
I dont know if the "2" at the beginning is involved and is getting multiplied (ex. 2x3/7)
but if it is,i would sat 27/28 is the answer
4 0
3 years ago
The newest invention of the 6.431x staff is a three-sided die. On any roll of this die, the result is 1 with probability 1/2, 2
Gwar [14]

Answer:

<h2>The answer is 0.23(approx).</h2>

Step-by-step explanation:

The given die is a three sided die, hence, there are only three possibilities of getting the outcomes.

We need to find the probability of getting exactly 3s as the result.

From the sequence of 6 independent rolls, 2 rolls can be chosen in ^6C_2 = \frac{6!}{2!\times4!} = \frac{30}{2} = 15 ways.

The probability of getting two 3 as outcome is \frac{1}{4} \times\frac{1}{4} = \frac{1}{16}.

In the rest of the 4 sequences, will not be any 3 as outcome.

Probability of not getting a outcome rather than 3 is 1 - \frac{1}{4} = \frac{3}{4}.

Hence, the required probability is 15\times\frac{1}{16}(\frac{3}{4})^4 = \frac{1215}{4096}≅0.2966 or, 0.23.

4 0
3 years ago
an item is regularly priced at $90. John bought it on sale for 20% off regular price. How much did John pay
Svetlanka [38]

Answer:

John paid $72

Step-by-step explanation:

To find the discount, we take the regular price and multiply it by the discount percentage

Discount = 90 * .2

               = $18

The new price is the regular price minus the discount

New price = 90 -18

                 = $72

5 0
3 years ago
Read 2 more answers
!!! Help ASAP please!!!!In DEF, sin D = 24/26 What is cos E?
Georgia [21]

Answer:

A

Step-by-step explanation:

Cosine is the ratio of "adjacent" to "hypotenuse"

With respect to the Angle E, the adjacent side is FE and the hypotenuse (always opposite side to 90 degree angle) is DE.

We are given DE = 26, but we need FE. We will solve for FE using Pythagorean Theorem, which tells us:

leg^2 + another leg^2 = hypotenuse^2

So, we will have:

10^2 + FE^2 = 26^2

Now, we solve for FE:

10^2 + FE^2 = 26^2\\100+FE^2=676\\FE^2=576\\FE=24

So,

Cos(E) = adj/hyp = 24/26

Correct answer is A

7 0
3 years ago
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