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2 years ago

Solve: 5x + 4 < 3 – 3x

Mathematics

1 answer:

MrRissso [65]2 years ago

3 0

Answer:

x = -1/8

Step-by-step explanation:

The greater than sign can be replaced with an equal sign to solve.

5x + 4 < 3 – 3x =>

5x + 4 = 3 - 3x =>

+3x -4 +3x - 4

---------------------------

8x = -1

x = -1/8

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Solve the inequality and express your answer in interval notation. X^2-6x+7<0

kakasveta [241]

Answer:

Step-by-step explanation:

2×6=8

8+7 =15

2+7 =9

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3 years ago

A train leaves a point A at 5 pm and reach another point B at 11 pm. Another train leaves point B at 7 pm and reach point A at 1

Alexus [3.1K]

Answer: I think the two trains meet at 9pm

Explanation: A=train a B=train b

If A is traveling for 6 hours and B is traveling for 3 hours, then you minus 3 hours from A, so you are left with 3 hours. Convert that into time, and you are left with 9pm!

Hope this helps! :)

3 0

1 year ago

Read 2 more answers

Y''+y'+y=0, y(0)=1, y'(0)=0

mars1129 [50]

Answer:

$y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

Step-by-step explanation:

A second order linear , homogeneous ordinary differential equation has form $ay''+by'+cy=0$ .

Given: $y''+y'+y=0$

Let $y=e^{rt}$ be it's solution.

We get,

$\left ( r^2+r+1 \right )e^{rt}=0$

Since $e^{rt}\neq 0$ , $r^2+r+1=0$

{ we know that for equation $ax^2+bx+c=0$ , roots are of form $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ }

We get,

$y=\frac{-1\pm \sqrt{1^2-4}}{2}=\frac{-1\pm \sqrt{3}i}{2}$

For two complex roots $r_1=\alpha +i\beta \,,\,r_2=\alpha -i\beta$ , the general solution is of form $y=e^{\alpha t}\left ( c_1\cos \beta t+c_2\sin \beta t \right )$

i.e $y=e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

Applying conditions y(0)=1 on $e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$ , $c_1=1$

So, equation becomes $y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

On differentiating with respect to t, we get

$y'=\frac{-1}{2}e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )+e^{\frac{-t}{2}}\left ( \frac{-\sqrt{3}}{2} \sin \left ( \frac{\sqrt{3}t}{2} \right )+c_2\frac{\sqrt{3}}{2}\cos\left ( \frac{\sqrt{3}t}{2} \right )\right )$

Applying condition: y'(0)=0, we get $0=\frac{-1}{2}+\frac{\sqrt{3}}{2}c_2\Rightarrow c_2=\frac{1}{\sqrt{3}}$

Therefore,

$y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

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2 years ago

A bag contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the coins, 16% are pennies and 38% are dimes

nadya68 [22]

Answer:

$25.8

Step-by-step explanation:

4 0

2 years ago

What is the meaning of an absolute value

storchak [24]

Answer:

"Absolute value" is the non-negative value of a number, disregarding whether or not it has a sign.

Step-by-step explanation:

"Absolute value" is the non-negative value of a number, disregarding whether or not it has a sign. It can be thought of as how far it is away from the number of 0, whether it's to the left or right. Absolute value of a number is written as |x|, where x = any number. Let's say x was -1. |-1| would be 1 because it's 1 away from 0. If x was just 1, then the number would stay the same.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

6 0

2 years ago