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2 years ago

The graph below belongs to which function family?

Mathematics

2 answers:

max2010maxim [7]2 years ago

8 0

Answer:

D) on edge (absolute value)

Step-by-step explanation:

atroni [7]2 years ago

6 0

Answer:

The graph is of an absolute value function.

Step-by-step explanation:

For x ≥ 0, the graph is given by $\frac{x}{6} +\frac{y}{3}=1$

⇒ x + 2y = 6

⇒ $y = 3-\frac{x}{2}$

⇒ $y-3=-\frac{x}{2}$ ........ (1)

Again, for x < 0, the graph is given by $\frac{x}{-6} +\frac{y}{3} =1$

⇒ - x + 2y = 6

⇒ $y = 3+\frac{x}{2}$

⇒ $y-3 = \frac{x}{2}$ ...... (2)

So, from equations (1) and (2) the function can be written as

$y-3 = - |\frac{x}{2} |$

Therefore, the graph is of an absolute value function. (Answer)

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Evaluate the logarithm.

eimsori [14]

Answer:

$x \approx 0.954$

Step-by-step explanation:

The logarithm is evaluated as follows:

$x = 2\cdot \log 3$

$x = \log 3^{2}$

$x = \log 9$

The value of the logarithm can be estimated by means numeric methods, which can be easily used on calculators (i.e. Macaulay Series)

$x \approx 0.954$

8 0

3 years ago

Part A: Create a third-degree polynomial in standard form. How do you know it is in standard form? (5 points)

Svetlanka [38]

Answer:

(See explanation for further details)

Step-by-step explanation:

a) Let consider the polynomial $p(x) = 5\cdot x^{3} +2\cdot x^{2} - 6 \cdot x +17$ . The polynomial is in standards when has the form $p(x) = \Sigma \limit_{i=0}^{n} \,a_{i}\cdot x^{i}$ , where $n$ is the order of the polynomial. The example has the following information:

$n = 3$ , $a_{0} = 17$ , $a_{1} = -6$ , $a_{2} = 2$ , $a_{3} = 5$ .

b) The closure property means that polynomials must be closed with respect to addition and multiplication, which is demonstrated hereafter:

Closure with respect to addition:

Let consider polynomials $p_{1}$ and $p_{2}$ such that:

$p_{1} = \Sigma \limits_{i=0}^{m} \,a_{i}\cdot x^{i}$ and $p_{2} = \Sigma \limits_{i=0}^{n}\,b_{i}\cdot x^{i}$ , where $m \geq n$

$p_{1}+p_{2} = \Sigma \limits_{i=0}^{n}\,(a_{i}+b_{i})\cdot x^{i} + \Sigma_{i=n+1}^{m}\,a_{i} \cdot x^{i}$

Hence, polynomials are closed with respect to addition.

Closure with respect to multiplication:

Let be $p_{1}$ a polynomial such that:

$p_{1} = \Sigma \limits_{i=0}^{m} \,a_{i}\cdot x^{i}$

And $\alpha$ an scalar. If the polynomial is multiplied by the scalar number, then:

$\alpha \cdot p_{1} = \alpha \cdot \Sigma \limits_{i = 0}^{m}\,a_{i}\cdot x^{i}$

Lastly, the following expression is constructed by distributive property:

$\alpha \cdot p_{1} = \Sigma \limits_{i=0}^{m}\,(\alpha\cdot a_{i})\cdot x^{i}$

Hence, polynomials are closed with respect to multiplication.

4 0

2 years ago

Find the domain of h(x)= 1/ 3x^2-15x

Schach [20]

Hello!

To find the domain of the function h(x), we need to find the values of x where it is undefined.

We can begin by factoring the denominator of the rational function, h(x).

h(x) = 1/(3x² - 15x) (factor 3x from the binomial)

h(x) = 1/3x(x - 5)

After factoring the denominator, apply the zero product property.

3x = 0 (divide both sides by 3)

x = 0

x - 5 = 0 (add 5 to both sides)

x = 5

The values of 0 and 5 cause h(x) to be undefined. The function h(x) comes from negative infinity to zero, where there is an asymptote. Also, from zero to five, there is also an asymptote. Finally, the function h(x) also goes to infinity from five.

So therefore, the domain of the function h(x) is: (-∞, 0) ∪ (0, 5) ∪ (5, ∞).

8 0

2 years ago

Read 2 more answers

What Should i write down basically i just need the answers and let me copy and paste

Anastaziya [24]

Answer:

✔️Ratio of weight to mass in simplest form: 49/5 or 49 : 5

✔️x = 110

Step-by-step explanation:

Since the ratio of weight to mass is constant, therefore we can use any pair of values from the table to find the ratio that represents the table. Let's pick the first row:

(20, 196)

Ratio of weight to mass = 196 : 20

= 196/20

= 49/5

Or 49 : 5

✔️Let's use this ratio/proportion to find x in the table

Ratio of weight to mass = 49:5

Thus:

1078/x = 49/5

Cross multiply

x*49 = 1078*5

49x = 5,390

x = 5,390/49

x = 110

5 0

2 years ago

Factor<br> 80x5-70x2 60x?

LuckyWell [14K]

Answer:

200(−91x+2)

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers