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3 years ago

Write the solution to the given inequality in interval notation.

Mathematics

2 answers:

wlad13 [49]3 years ago

7 0

<h2>Answer:</h2>

The solution to the given inequality in interval notation is:

[-3,∞)

<h2>Step-by-step explanation:</h2>

The solution of the given inequality is the set of all the possible x values.

By looking at the graph which is a number line such that the shaded region is to the right of -3 and the arrow of solution goes to infinity and also there is a closed circle at -3.

This means that -3 is included in the solution set.

This means that the solution is all the real values which are greater than or equal to -3.

i.e. The solution is: x ≥ -3

i.e. [-3,∞)

brilliants [131]3 years ago

6 0

[-3, infinity)
It is greater than or equal to -3 and goes on to infinity

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How to divide (x^2+5x-36)÷(x-4)

mr_godi [17]

Answer:

x + 9

Step-by-step explanation:

Since the divisor is in the form of <em>x - c</em>, use what is called <em>Synthetic Division</em>. Remember, in this formula, -c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:

4| 1 5 -36

↓ 4 36

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

1 9 0 → x + 9

You start by placing the c in the top left corner, then list all the coefficients of your dividend [x² + 5x - 36]. You bring down the original term closest to <em>c</em><em>,</em> then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have NO REMAINDER. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an x, and the 9 follows right behind it, giving you the other factor of x + 9.

If you are ever in need of assistance, do not hesitate to let me know by subscribing to my channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

4 0

3 years ago

Х- а<br>x-b<br>If f(x) = b.x-a÷b-a + a.x-b÷a - b<br>Prove that: f (a) + f(b) = f (a + b)

GenaCL600 [577]

Given:

Consider the given function:

$f(x)=\dfrac{b\cdot(x-a)}{b-a}+\dfrac{a\cdot(x-b)}{a-b}$

To prove:

$f(a)+f(b)=f(a+b)$

Solution:

We have,

$f(x)=\dfrac{b\cdot(x-a)}{b-a}+\dfrac{a\cdot (x-b)}{a-b}$

Substituting $x=a$ , we get

$f(a)=\dfrac{b\cdot(a-a)}{b-a}+\dfrac{a\cdot (a-b)}{a-b}$

$f(a)=\dfrac{b\cdot 0}{b-a}+\dfrac{a}{1}$

$f(a)=0+a$

$f(a)=a$

Substituting $x=b$ , we get

$f(b)=\dfrac{b\cdot(b-a)}{b-a}+\dfrac{a\cdot (b-b)}{a-b}$

$f(b)=\dfrac{b}{1}+\dfrac{a\cdot 0}{a-b}$

$f(b)=b+0$

$f(b)=b$

Substituting $x=a+b$ , we get

$f(a+b)=\dfrac{b\cdot(a+b-a)}{b-a}+\dfrac{a\cdot (a+b-b)}{a-b}$

$f(a+b)=\dfrac{b\cdot (b)}{b-a}+\dfrac{a\cdot (a)}{-(b-a)}$

$f(a+b)=\dfrac{b^2}{b-a}-\dfrac{a^2}{b-a}$

$f(a+b)=\dfrac{b^2-a^2}{b-a}$

Using the algebraic formula, we get

$f(a+b)=\dfrac{(b-a)(b+a)}{b-a}$ $[\because b^2-a^2=(b-a)(b+a)]$

$f(a+b)=b+a$

$f(a+b)=a+b$ [Commutative property of addition]

Now,

$LHS=f(a)+f(b)$

$LHS=a+b$

$LHS=f(a+b)$

$LHS=RHS$

Hence proved.

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3 years ago

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Yuri [45]

Answer:

Hello

The answer you're looking for is 12.56 or 12.5663

Step-by-step explanation:

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2 years ago

Compute a value for x that satisfies the equation below.

otez555 [7]

<h2>Linear equations</h2>

<em>The </em><em>graphical representation</em><em> of a linear equation is a straight line. To solve</em><em> linear equations</em><em>, i</em><em>t is important to keep in mind the following key concepts:</em>

<em>Maintain the balance of the equation by applying the </em><em>same operations</em><em> to both sides of the equation.</em>
<em>Clear the variable using like terms.</em>
<em>Use </em><em>inverse operations</em><em> to rearrange the equation.</em>

We will subtract 5 from both sides.

<em>We divide both sides by -1.</em>

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2 years ago

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katen-ka-za [31]

Answer:

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Step-by-step explanation:

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4 years ago