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nlexa [21]
3 years ago
12

Which values are in the solution set of the compound inequality? Select two options. 4(x + 3) ≤ 0 or x+1>3 answer choices: –6

–3 0 3 8
Mathematics
1 answer:
balandron [24]3 years ago
6 0

Answer:

-6, -3

3, 8

Step-by-step explanation:

In order to find the number that are solutions to the compound inequalities, you first solve fr x on each inequality.

First inequality:

4(x+3)\leq 0\\\\4x+12\leq0\\\\4x\leq-12\\\\x\leq-3  interval = (-∞ , -3]

Second inequality:

x+1>3\\\\x>2   interval = (2 , ∞)

The interval solution is (-∞ , -3] U (2 , ∞)

The number that are included in the previous interval are:

-6, -3

or

3, 8

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First-order linear differential equations
kkurt [141]

Answer:

(1)\ logy\ =\ -sint\ +\ c

(2)\ log(y+\dfrac{1}{2})\ =\ t^2\ +\ c

Step-by-step explanation:

1. Given differential equation is

  \dfrac{dy}{dt}+ycost = 0

=>\ \dfrac{dy}{dt}\ =\ -ycost

=>\ \dfrac{dy}{y}\ =\ -cost dt

On integrating both sides, we will have

  \int{\dfrac{dy}{y}}\ =\ \int{-cost\ dt}

=>\ logy\ =\ -sint\ +\ c

Hence, the solution of given differential equation can be given by

logy\ =\ -sint\ +\ c.

2. Given differential equation,

    \dfrac{dy}{dt}\ -\ 2ty\ =\ t

=>\ \dfrac{dy}{dt}\ =\ t\ +\ 2ty

=>\ \dfrac{dy}{dt}\ =\ 2t(y+\dfrac{1}{2})

=>\ \dfrac{dy}{(y+\dfrac{1}{2})}\ =\ 2t dt

On integrating both sides, we will have

   \int{\dfrac{dy}{(y+\dfrac{1}{2})}}\ =\ \int{2t dt}

=>\ log(y+\dfrac{1}{2})\ =\ 2.\dfrac{t^2}{2}\ + c

=>\ log(y+\dfrac{1}{2})\ =\ t^2\ +\ c

Hence, the solution of given differential equation is

log(y+\dfrac{1}{2})\ =\ t^2\ +\ c

8 0
3 years ago
Select the best deal for tutoring help for your Algebra I class. A) $45 for 1 hour B) all the same rate C) $30 for 50 minutes D)
Lilit [14]
I think the answer would be c but I'm not positive
I hope I help :)
3 0
3 years ago
Read 2 more answers
What is the value of b in the equation (y Superscript b Baseline) Superscript 4 Baseline = StartFraction 1 Over y Superscript 24
shusha [124]

The value of b is -6.

Explanation:

The expression is \left(y^{b}\right)^{4}=\frac{1}{y^{24}}

To determine the value of b, we shall solve the expression.

Applying exponent rule, \left(a^{b}\right)^{c}=a^{b c}, we get,

y^{4b}=\frac{1}{y^{24}}

Applying exponent rule, \frac{1}{a^{b}}=a^{-b}, we have,

y^{4b}=y^{-24}

The expression is of the form, a^{f(x)}=a^{g(x)} then f(x)=g(x)

Applying this rule, we get,

4b=-24

Dividing both sides by 4, we have,

b=-6

Hence, the value of b is -6.

4 0
3 years ago
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Factor by using the perfect-square trinomial<br> 64x2 - 144x + 81
Tom [10]

Answer:

the answer is -34

4 0
2 years ago
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guajiro [1.7K]

Answer:

x > 3

Step-by-step explanation:

8 0
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