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3 years ago

3. The functions f and g are defined by f: x → ax – b where a and b are constants and g: x → X+4.

Mathematics

1 answer:

valentinak56 [21]3 years ago

5 0

Answer:

fg(2) = 9 means that f(g(2)) = 9

We know that g(2) = 6

So f(6) = 9 which means that

6a - b = 9 (note 1)

And we know that g(f(1/2)) = 2

And we know that f(1/2) = 1/2(a) - b

So g(1/2(a) - b) = 2

Meaning that 1/2(a) - b + 4 = 2

So 1/2(a) - b = - 2 (note 2)

Using note 1 and 2 we can solve the equation

11/2(a) = 11 so a = 2 and b = 3

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Jon collects 2,578 ounces of honey from his beehive. he will put the honey in jars that hold 6 ounces each. which expression is

belka [17]

Answer:

With j = number of jars: 2,578 / 6 = j

Step-by-step explanation:

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3 years ago

On the graph shown, what is f(-1)? (5 points) The first segment joints the point negative three comma five exclusively and negat

tatiyna

ANSWER

$f( - 1) = 2$

EXPLANATION

The given function is a piecewise defined function.

$f( - 1)$
is the y-value that corresponds to
$x = - 1.$

To determine that y-value, we need to trace from
$x = - 1$
to where it meets the graph.

We then trace to the y-axis to determine the corresponding y-value as shown in the diagram.

From the graph, we can see that this x-value corresponds to a y-value of
$2$

This implies that, when
$x = - 1,y = 2$

Therefore
$f( - 1) = 2$
See graph.

8 0

3 years ago

Use factoring to write an expression that is equivalent to 28w - 40.

mote1985 [20]

Answer:

4(7w+10)

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Suppose that you toss a fair six-sided {1,2,3,4,5,6} die and let X represent the outcome obtained. Find the expected volume of a

timofeeve [1]

Answer:

The expected volume of the box is 364 cubic inches.

Step-by-step explanation:

Since the die is fair, then P(X=k) = 1/6 for any k in {1,2,3,4,5,6}. Let Y represent the volume of the box in cubic inches. For how the box is formed, Y = X²*24. Thus, the value of Y depends directly on the value of X, and we have

(When X = 1) Y = 1²*24 = 24, with probability 1/6 (the same than P(X=1)

(When X = 2) Y = 2²*24 = 96, with probability 1/6 (the same than P(X=2)

(When X = 3) Y = 3²*24 = 216, with probability 1/6 (the same than P(X=3)

(When X = 4) Y = 4²*24 = 384, with probability 1/6 (the same than P(X=4)

(When X = 5) Y = 5²*24 = 600, with probability 1/6 (the same than P(X=5)

(When X = 6) Y = 6²*24 = 864, with probability 1/6 (the same than P(X=6)

As a consequence, the expected volume of the box in cubic inches is

E(Y) = 1/6 * 24 + 1/6*96 + 1/6*216+ 1/6*384+ 1/6*600+1/6*864 = 364

3 0

3 years ago

What is the area of a wall that is 28' wide by 10' high at the sides and has a triangular gable that measures 7' high?

Karolina [17]

Answer:

378 ft²

Step-by-step explanation:

Given:

The Width of the wall = 28'

The Length of the wall = 10'

The Height of the gable = 7'

Now, the width of the gable will be equal to the width of the wall = 28'

therefore,

Area of the wall = Area of the rectangle section of wall + area of the gable

Total area of the wall = ( 28' × 10' ) + ( $\frac{1}{2}\times28'\times7'$ )

Total area of the wall = 280 + 98 = 378 ft²

7 0

3 years ago