The clownfish Kay wanted to buy for $12 last week has been marked up 8%. What is the new price of the fish?

The graph of the function f(x) = (x +2)(x + 6) is shown

dalvyx [7]

The true about the domain and the range of the function is:

The domain is all real numbers, and the range is all real numbers

greater than or equal to -4 ⇒ 1st answer

Step-by-step explanation:

f(x) = (x + 2)(x + 6) is a quadratic function with 2 factors (x + 2) and (x + 6)

By multiplying its two factors we will find the form of the quadratic function

∵ (x)(x) = x²

∵ (x)(6) = 6x

∵ (2)(x) = 2x

∵ (2)(6) = 12

∴ f(x) = x² + 6x + 2x + 12

- By adding like terms

∴ f(x) = x² + 8x + 12

The quadratic function represented graphically by a parabola

Look to the attached figure

The x-coordinate of the vertex point of the parabola h = $\frac{-b}{a}$

where b is the coefficient of x and a is the coefficient of x²

∵ f(x) = x² + 8x + 12

∴ a = 1 and b = 8

∴ h = $\frac{-8}{2*1}=-4$

The y-coordinate of the vertex point is k = f(h)

∵ h = -4

∴ k = f(-4)

∴ k = (-4)² + 8(-4) = 12 = 16 - 32 + 12

∴ k = -4

∴ The vertex point of the parabola is (-4 , -4)

∵ The parabola is opened upward

∴ Its vertex is minimum point

∴ The minimum value of f(x) is y = -4

∵ The domain of the function is the values of x

∵ The range of the function is the values of y corresponding to the

values of x

∵ x can be any real numbers

∴ x ∈ R, where R is the set of real numbers

∴ The domain of f(x) is all real numbers

∵ The minimum value of f(x) is y = -4

∴ y can be any real number greater than or equal to -4

∴ y ≥ -4

∴ The range is all real number greater than or equal to -4

The true about the domain and the range of the function is:

The domain is all real numbers, and the range is all real numbers

greater than or equal to -4

Learn more:

You can learn more about quadratic function in brainly.com/question/1332667

#LearnwithBrainly

7 0

3 years ago

A 100-gallon fish tank fills at a rate of x gallons per minute. The tank has already been filling for 5 minutes. The

vagabundo [1.1K]

Answer:

was shifted 5 unit right side then stretched vertically by the factor 100, Shifted 5 unit right side then stretched vertically by the factor 100

Step-by-step explanation:

Here, parent function,

Transformed function,

Since, if a function f(x) gives cf(x), where c is any number,

Then the function was vertically stretched by factor c,

While, the function gives f(x-c),

Then the function was shifted c unit right.

Hence, the graph of was shifted 5 unit right side then stretched vertically by the factor 100 to create the graph of

6 0

3 years ago

A student wants to construct the inscribed circle of a triangle. What is the first step he/she should take?

pantera1 [17]

The <em>correct answer</em> is:

d) Construct the angle bisector of each angle in the triangle

Explanation:

The incenter, or center of an inscribed circle, is the point where the angle bisectors of a triangle intersect. This means the first thing we will need to construct is the bisector of each angle of the triangle.

8 0

3 years ago

Read 2 more answers

At a 20th high school reunion, all the classmates were asked the number of children they had. The probability of having a partic

finlep [7]

Answer:

a) We need to check two conditions:

1) $\sum_{i=1}^n P_i = 1$

$0.05+0.14+0.34+0.24+0.11+0.07+0.02+0.02+0.01= 1$

2) $P_i \geq 0 , \forall i=1,2,...,n$

So we satisfy the two conditions so then we have a probability distribution

b) $P(C \geq 1)$

And we can use the complement rule and we got:

$P(C \geq 1)= 1-P(C$

c) $P(C=0) = 0.05$

d) For this case we see that the result from part b use the probability calculated from part c using the complement rule.

Step-by-step explanation:

For this case we have the following probability distribution given:

C 0 1 2 3 4 5 6 7 8

P 0.05 0.14 0.34 0.24 0.11 0.07 0.02 0.02 0.01

And we assume the following questions:

a) Verify that this is a probability distribution

We need to check two conditions:

1) $\sum_{i=1}^n P_i = 1$

$0.05+0.14+0.34+0.24+0.11+0.07+0.02+0.02+0.01= 1$

2) $P_i \geq 0 , \forall i=1,2,...,n$

So we satisfy the two conditions so then we have a probability distribution

b) What is the probability one randonmly chosen classmate has at least one child

For this case we want this probability:

$P(C \geq 1)$

And we can use the complement rule and we got:

$P(C \geq 1)= 1-P(C$

c) What is the probability one randonmly chosen classmate has no children

For this case we want this probability:

$P(C=0) = 0.05$

d) Look at the answers for parts b and c and explain their relationship

For this case we see that the result from part b use the probability calculated from part c using the complement rule.

5 0

3 years ago

This problem has to do with Fahrenheit and Celsius

Vinvika [58]

F = 1.8C + 32

С = -10 ⇒ F = 1.8·(-10) + 32 = 14 ⇒   (-10, 14)
С = 0 ⇒   F = 1.8·(0) + 32 = 32    ⇒ (0, 32)
С = 10 ⇒ F = 1.8·(10) + 32 = 50 ⇒ (10, 50)
С = 20   ⇒ F = 1.8·(20) + 32 = 68   ⇒ (20, 68)

8 0

3 years ago