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4 years ago

Solve x2 + 4x + 1 = 0.

Mathematics

1 answer:

docker41 [41]4 years ago

5 0

Answer: Option C ( $x=-2$ ± $\sqrt{3}$ )

Step-by-step explanation:

1. To solve this problem you must use the Quadratic formula, which is used to solve quadratic equation. This formula is shown below:

$x=\frac{-b+/-\sqrt{b^{2}-4ac}}{2a}$

2. Substitute values. Then, you have:

$a=1\\b=4\\c=1$

$x=\frac{-4+/-\sqrt{4^{2}-4(1)(1)}}{2(1)}$

3. Then,you obtain the following result:

$x=-2$ ± $\sqrt{3}$

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At a certain clothing store, all shirts are on sale for the same price. Mr.Chan bought 6 shirts and paid a total of $62.99, incl

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You would subtract the tax first which 62.99-2.99=60$. Then you would divide the $60 left by 6 and 60 divided by 6 equals 10 so each shirt costs $10.

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3 years ago

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Jerry cycles a 36-mile loop every day for two weeks. What is the total

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The answer is: 18 miles.

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3 years ago

In list T, consists of 30 positive decimals. None of which are integers. The sum of the 30 decimals is S. The estimated sum of t

Masteriza [31]

Answer: E - S = (-16 and 6)

Step-by-step explanation:1/3 of the 30 decimals in T have an even tenths digit, it follows that 1/3*(30)=10 decimals in T have an even tenths digit.

Hence: Te =list of 10 decimals

Se = sum of all 10 decimals in Te

Ee =estimated sum of all 10 decimals in Te after rounding up.

Remaining 20 decimals in T all have an odd tenths digits.

To =list of this 20 decimals

So = sum of all 20 decimals in To

Eo = estimated sum of 20 decimals in To

Hence,

E = Ee + Eo and S =Se +So, hence:

E-S, =(Ee+Eo) - (Se+So) =(Ee-Se) +(Eo-So)

Ee-Se >10 (0.1)=1

S=10(1.8)+20(1.9) =18+38=56

E=10(2)+20(1)=40

E-S =40-56=-16.

AlsoS=10(1.2)+20(1.1)=34

E=10(2)+20(1)=40

E-S=40-34=6

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3 years ago

A circular rug has a diameter of 6 feet. What is the area of the rug?

podryga [215]

Answer:

The answer to your question is: letter B

Step-by-step explanation:

Data

diameter = 6 ft

area = ?

Formula

A = πr²

radius = diameter / 2

= 6 / 2

= 3 ft

Substitution

A = π(3)²

= 28.27 ft²

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4 years ago

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Determine the singular points of the given differential equation. Classify each singular point as regular or irregular. (Enter y

ludmilkaskok [199]

Answer:

Step-by-step explanation:

Given that:

The differential equation; $(x^2-4)^2y'' + (x + 2)y' + 7y = 0$

The above equation can be better expressed as:

$y'' + \dfrac{(x+2)}{(x^2-4)^2} \ y'+ \dfrac{7}{(x^2- 4)^2} \ y=0$

The pattern of the normalized differential equation can be represented as:

y'' + p(x)y' + q(x) y = 0

This implies that:

$p(x) = \dfrac{(x+2)}{(x^2-4)^2} \$

$p(x) = \dfrac{(x+2)}{(x+2)^2 (x-2)^2} \$

$p(x) = \dfrac{1}{(x+2)(x-2)^2}$

Also;

$q(x) = \dfrac{7}{(x^2-4)^2}$

$q(x) = \dfrac{7}{(x+2)^2(x-2)^2}$

From p(x) and q(x); we will realize that the zeroes of (x+2)(x-2)² = ±2

When x = - 2

$\lim \limits_{x \to-2} (x+ 2) p(x) = \lim \limits_{x \to2} (x+ 2) \dfrac{1}{(x+2)(x-2)^2}$

$\implies \lim \limits_{x \to2} \dfrac{1}{(x-2)^2}$

$\implies \dfrac{1}{16}$

$\lim \limits_{x \to-2} (x+ 2)^2 q(x) = \lim \limits_{x \to2} (x+ 2)^2 \dfrac{7}{(x+2)^2(x-2)^2}$

$\implies \lim \limits_{x \to2} \dfrac{7}{(x-2)^2}$

$\implies \dfrac{7}{16}$

Hence, one (1) of them is non-analytical at x = 2.

Thus, x = 2 is an irregular singular point.

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3 years ago