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3 years ago

4. What is the domain of the graph shown below? Yo someone answer ASAP plzz

Mathematics

2 answers:

NikAS [45]3 years ago

6 0

Answer:

-6 < x ≤ 6

Step-by-step explanation:

Remember, the domain is the range of the x values.

Also recall that a non-shaded circle represents that that point is not included in the graph. That means it is greater than, not greater than or equal to.

A shaded circle means that that point is included in the graph, meaning that it is less on equal to, not only less than.

If you count the coordinates, you'll see that the non-shaded endpoint is at (-6, -6) and the shaded one is at (6, 6).

To determine the domain, we only need to know the x values.

The x values are -6 and 6, and x is is anywhere between these values: greater than -6, but less than or equal to 6.

Therefore, we produce the inequality -6 < x ≤ 6.

Hope this helps :)

Sati [7]3 years ago

4 0

Answer:

-6 < x ≤ 6

Step-by-step explanation:

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Suppose a principal amount of $7500 was invested at an interest rate of 6%. How long did it take to reach $10650?

Oliga [24]

Based on the information how long did it take to reach $10650 is 7years.

Given:

Principal=$7,500

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Amount=$10650

Time=?

Simple Interest(SI)=A-P

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Time=(100×SI)/(p×r)

T=(100×3150)/(7500×6)

T=315,000/45,000

T=7 years

Inconclusion how long did it take to reach $10650 is 7years.

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2 years ago

14a+16= what is the answer

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2 years ago

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Find f(g(x)). State the domain of the composite function.<br> f(x) = 3x-2/x+1<br> g(x) = x+5/2x-3

AnnyKZ [126]

Answer:

ℝ - {(-2/3),(3/2)}

Step-by-step explanation:

We want the domain of f(g(x)). So, firstly, we have to find the domain for g(x) and, then, for f(g(x)).

- Domain of g(x): Since the expression is a fracion, we must exclude the values of x that make null the denominator. Hence,

$g(x)=\dfrac{x+5}{2x-3}\Longrightarrow 2x-3\neq 0\iff \boxed{x\neq\dfrac{3}{2}}$

- Domain of f(g(x)): We'll find its expression:

$f(x) = \dfrac{3x-2}{x+1}\\\\f(g(x)) = \dfrac{3g(x)-2}{g(x)+1}\\\\f(g(x)) = \dfrac{3\cdot\dfrac{x+5}{2x-3}-2}{\dfrac{x+5}{2x-3}+1}=\dfrac{~~~\dfrac{3(x+5)-2(2x-3)}{2x-3}~~~}{\dfrac{(x+5)+(2x-3)}{2x-3}}\\\\f(g(x)) =\dfrac{3(x+5)-2(2x-3)}{(x+5)+(2x-3)}=\dfrac{3x+15-4x+6}{x+5+2x-3}\\\\\boxed{f(g(x)) =\dfrac{21-x}{3x+2}}$

Now, once again, we have to exclude the values of x that make the denominator equals to zero. Thus,

$f(g(x)) =\dfrac{21-x}{3x+2}\Longrightarrow 3x+2\neq0\iff \boxed{x\neq-\dfrac{2}{3}}$

Lastly, we may write the domanin of f(g(x)):

$D(f(g(x)) = \left]-\infty,-\dfrac{2}{3}\right[\cup\left]-\dfrac{2}{3},\dfrac{3}{2}\right[\cup\left]\dfrac{3}{2},\infty\right[$

or, just writing in a shorter way:

$\boxed{D(f(g(x)) = \mathbb{R}-\left\{-\dfrac{2}{3},\dfrac{3}{2}\right\}}$

7 0

2 years ago

Your fi nancial advisor recommends buying a 10-year bond with a face value of $1,000 and an annual coupon of $80. The current in

rusak2 [61]

Answer:

Bond Price= $1,070.24

Step-by-step explanation:

Giving the following information:

Cupon= $80

Number of periods= 10 years

Face value= $1,000

Interest rate= 7%

<u>To calculate the price of the bond, we need to use the following formula:</u>

Bond Price= cupon*{[1 - (1+i)^-n] / i} + [face value/(1+i)^n]

Bond Price= 80*{[1 - (1.07^-10)] / 0.07} + [1,000 / (1.07^10)]

Bond Price= 561.89 + 508.35

Bond Price= $1,070.24

8 0

2 years ago