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3 years ago

If a(x)=3x+1 and b(x)=square root x-4, what is the domain of (b o a)(x)?

Mathematics

2 answers:

Dennis_Churaev [7]3 years ago

4 0

Answer:

C. (1,infinity)

Step-by-step explanation:

Bond [772]3 years ago

3 0

ANSWER

$[1, \infty ]$

EXPLANATION

The given functions are:

$a(x) = 3x + 1$

$b(x) = \sqrt{x - 4}$

We want to find the domain of the composite function;

$(b \circ \: a)(x) = b(a(x))$

$(b \circ \: a)(x) = b(3x + 1)$

$(b \circ \: a)(x) = \sqrt{3x + 1 - 4}$

This simplifies to,

$(b \circ \: a)(x) = \sqrt{3x - 3}$

This function is defined for

$3x - 3 \geqslant 0$

$3x \geqslant 3$

$x \geqslant 1$

This can be rewritten as,

$[1, \infty ]$

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Mrs.Vega brought a new aquarium for her turtles. How much space will the turtles have in the aquarium if the length is 5.2 ft, t

MrRissso [65]

Answer:

18.72 cubic feet

Step-by-step explanation:

Volume of the aquarium = lwh

l = 5.2 ft,
w = 1.8 ft
h = 2 ft

V = 5.2*1.8*2 = 18.72 cubic feet

3 0

3 years ago

At Prairieview Middle School, 100 students participate in at least one of three after-school clubs: soccer club, art club, and g

Tresset [83]

Answer:

Step-by-step explanation:

Number of students in soccer club, n(S) = 50

Number of students in Art club, n(A) = 53

Number of students in Gaming club, n(G)

n( $S \cup A\cup G$ ) = 100

n( $S \cap A\cap G$ ) = 9

n( $S \cap A$ ) = 20

n( $A \cap G$ ) = 35

n( $G \cap S$ ) = 29

Formula:

n ( A ∪ B ∪ C ) = n(A) + n(B) + n(C) – n ( A ∩ B ) – n(B ∩ C) – n (A ∩ C) + n( A ∩ B ∩ C )

Putting the values:

100 = 50 + 53 + n(G) - 20 - 35 - 29 + 9

100 = 112 + n(G) - 84

n(G) = 72

Number of students in gaming club only = n(G) - n( $G \cap S$ ) - n( $A \cap G$ ) + n( $S \cap A\cap G$ )

= 72 - 35 - 29 + 9

= <em>17</em>

6 0

3 years ago

Two dice are rolled simultaneously and the difference of the numbers are

zavuch27 [327]

Answer:

Step-by-step explanation:

you can draw a table that has 7 rows and 7 columns, put the 6 numbers and their difference( 1-1=0, 1-2= -1, 1-3= -2,...)

- 1 2 3 4 5 6

1 0 1 2 3 4 5

2 -1 0 1 2 3 4

3 -2 -1 0 1 2 3

4 -3 -2 -1 0 1 2

5 -4 -3 -2 -1 0 1

6 -5 -4 -3 -2 -1 0

8 0

3 years ago

Enter the correct answer in the box. solve the equation x2 − 16x 54 = 0 by completing the square. fill in the values of a and b

poizon [28]

The roots of the given polynomials exist $x=8+\sqrt{10}$ , and $x=8-\sqrt{10}$ .

<h3>What is the formula of the quadratic equation?</h3>

For a quadratic equation of the form $a x^{2}+b x+c=0$ the solutions are

$x_{1,2}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Therefore by using the formula we have

$x^{2}-16 x+54=0$$

Let, a = 1, b = -16 and c = 54

Substitute the values in the above equation, and we get

$x_{1,2}=\frac{-(-16) \pm \sqrt{(-16)^{2}-4 \cdot 1 \cdot 54}}{2 \cdot 1}$$

simplifying the equation, we get

$$&x_{1,2}=\frac{-(-16) \pm 2 \sqrt{10}}{2 \cdot 1} \\$

$$&x_{1}=\frac{-(-16)+2 \sqrt{10}}{2 \cdot 1}, x_{2}=\frac{-(-16)-2 \sqrt{10}}{2 \cdot 1} \\$

$$&x=8+\sqrt{10}, x=8-\sqrt{10}$

Therefore, the roots of the given polynomials are $x=8+\sqrt{10}$ , and

$x=8-\sqrt{10}$ .

To learn more about quadratic equations refer to:

brainly.com/question/1214333

#SPJ4

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1 year ago

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What is Q3 for this data set?

Kisachek [45]

The same as last time

Step-by-step explanation:

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1 year ago

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