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3 years ago

Use the figure to find the product (x + 3)(x + 2). (Hint: Find the area of each small square or rectangle, then add.)

Mathematics

2 answers:

uysha [10]3 years ago

6 0

Answer:

The product is x² + 5x + 6 which is same with the product of (x + 3)(x + 2)

Step-by-step explanation:

Using the smaller square or rectangle to find the product of (x + 3)(x + 2) , we find the area of each rectangle or square. The area means multiplying the length of each square or rectangle to it width.

The first row can be multiplied with each column as follow

x² + x + x + x = x² + 3x

second row with each column

x + 1 + 1 + 1 = x +3

third row with each column

x + 1 + 1 + 1 = x + 3

adding the whole results

x² + 3x + x + 3 + x + 3 = x² + 5x + 6 which is the same as the product of (x + 3)(x + 2)

Keith_Richards [23]3 years ago

5 0

(x+3)(x+2)
x^2+2x+3x+6
x^2+5x+6<<<<<< answer

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3 years ago

Which statements accurately describe the function f(x) = 3(16)^3/4? Check all that apply.

uysha [10]

Answers:

These are the statements that apply:

The initial value is 3.

The range is y >0.

The simplified base is 8.

Explanation:

1) Given expression:

$f(x)=3(16)^{\frac{3}{4} x$

2) Check every statement:

a) The initial value is 3?

initial value ⇒ x = 0 ⇒

$f(0)=3(16)^{0}=3(1)=3$

∴ The statement is right.

b) The initial value is 48?

Not, as it was already proved that it is 3.

c) The domain is x > 0?

No, because the domain of the exponential functions is all the Real numbers.

d) The range is y > 0?

That is correct, the exponential function is continuous, and monotonon increasing.

The limit when x → - ∞ is zero, but y never reaches zero, and the limit when x → ∞ is + ∞, meaning that the range is y > 0.

e) The simplified base is 12?

This is how you simplify the base:

$3(16)^{\frac{3}{4} x}=3{{(16}^{(3/4)})}^x=3(16^{3/4}})^{x}=3((2^4)^{3/4})^x=3(2^3)^x=3(8)^x$

Which shows that the simplified base is 8 (not 12).

f) The simplified base is 8?

Yes; this was just proved.

6 0

3 years ago

Read 2 more answers