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3 years ago

Given: F = {(0, 1), (2, 4), (4, 6), (6, 8)} and G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}

Mathematics

1 answer:

Snezhnost [94]3 years ago

6 0

9514 1404 393

Answer:

Step-by-step explanation:

The ordered pair (2, 4) in the relation for function F tells you F(2) = 4.

The ordered pair (2, 5) in the relation for function G tells you G(2) = 5.

Then the sum is ...

(F+G)(2) = F(2) +G(2) = 4 +5

(F+G)(2) = 9

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Simplify (5x−2+3x^2)+(4x+3)

Art [367]

Answer:

3x^2 + 9x + 1

3x ( x + 3 ) + 1

Step-by-step explanation:

(5x - 2 +3x^2 ) + (4x + 3 )

To make this a little bit more easier to read, you can remove the parentheses:

5x - 2 + 3x^2 + 4x + 3

Now, write in a way so that the like terms are next to each other:

3x^2 + 5x + 4x - 2 + 3

Now simplify the 'x' terms to get:

3x^2 + 9x - 2 + 3

Now, simplify the integers (the ones with now variables with them) to get:

3x^2 + 9x + 1

If you want, you can factor out the 3x for two of the terms to get :

3x ( x + 3 ) + 1

Therefore, your simplest form can either be 3x^2 + 9x + 1 OR 3x (x + 3 ) + 1

5 0

3 years ago

A heavy rope, 50 ft long, weighs 0.6 lb/ft and hangs over the edge of a building 120 ft high. Approximate the required work by a

Anastasy [175]

Answer:

Exercise (a)

The work done in pulling the rope to the top of the building is 750 lb·ft

Exercise (b)

The work done in pulling half the rope to the top of the building is 562.5 lb·ft

Step-by-step explanation:

Exercise (a)

The given parameters of the rope are;

The length of the rope = 50 ft.

The weight of the rope = 0.6 lb/ft.

The height of the building = 120 ft.

We have;

The work done in pulling a piece of the upper portion, ΔW₁ is given as follows;

ΔW₁ = 0.6Δx·x

The work done for the second half, ΔW₂, is given as follows;

ΔW₂ = 0.6Δx·x + 25×0.6 × 25 = 0.6Δx·x + 375

The total work done, W = W₁ + W₂ = 0.6Δx·x + 0.6Δx·x + 375

∴ We have;

W = $2 \times \int\limits^{25}_0 {0.6 \cdot x} \, dx + 375= 2 \times \left[0.6 \cdot \dfrac{x^2}{2} \right]^{25}_0 + 375 = 750$

The work done in pulling the rope to the top of the building, W = 750 lb·ft

Exercise (b)

The work done in pulling half the rope is given by W₂ as follows;

$W_2 = \int\limits^{25}_0 {0.6 \cdot x} \, dx + 375= \left[0.6 \cdot \dfrac{x^2}{2} \right]^{25}_0 + 375 = 562.5$

The work done in pulling half the rope, W₂ = 562.5 lb·ft

6 0

3 years ago

XYZ Company declares dividends of $50,000. Samuel Smith owns 50 shares of stock. The company has sold 25,000 total shares of sto

sweet [91]

50000/25000=2 per share
50*2=100

7 0

4 years ago

Read 2 more answers

Convert. 4600 g = _____ kg

faltersainse [42]

Answer:

4.6 Kilograms.

Step-by-step explanation:

6 0

3 years ago

Jessica has an account with a credit union. Her account earns 2.4% simple interest yearly. Exactly a year and a half ago, she op

Dafna1 [17]

The basic equation for interest is the investment amount(x) times the time in years(y) times the percent of interest(z).

That makes the equation:

x·y·z= amount with interest.

Lets plug in the numbers:

$900 x 1.5 x 2.4%

Now turn the percent into a decimal:

2.4% ----> .024

Now the equation is:

$900 x 1.5 x .024

Now do the math:

$900 x 1.5 = 1350
1350 x .024 = 32.4
1350 + 32.4 = 1382.4

The final answer is $1382.40

Hope this helps!

6 0

3 years ago