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3 years ago

(x+6)(x^2-7x+12) Algebra addition problem to find the area.

Mathematics

2 answers:

lisov135 [29]3 years ago

7 0

Answer:

$=x^3-x^2-30x+72$

Step-by-step explanation:

Distribute parentheses:

$=xx^2+x\left(-7x\right)+x\cdot \:12+6x^2+6\left(-7x\right)+6\cdot \:12$

Apply minus - plus rule:

$=x^2x-7xx+12x+6x^2-6\cdot \:7x+6\cdot \:12$

Simplified:

$=x^3-x^2-30x+72$

Its complicated but..

ikadub [295]3 years ago

7 0

Step-by-step explanation:

( x + 6 ) ( x^2 - 7x + 12 )

x ( x^2 - 7x + 12) + 6 ( x^2 - 7x + 12 )

x^3 - 7x^2 + 12x + 6x^2 - 42x + 72

x^3 + 6x^2 + 12x - 42x - 7x^2 + 72

19x - 49x + 72

30x + 72

x = 72/30

x = 2.4

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The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price

likoan [24]

Answer:

A) 3%

B) Product A

Step-by-step explanation:

Exponential Function

General form of an exponential function: $y=ab^x$

where:

a is the initial value (y-intercept)
b is the base (growth/decay factor) in decimal form
x is the independent variable
y is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Part A

Product A

Assuming the function for Product A is exponential:

$f(x) = 0.69(1.03)^x$

The base (b) is 1.03. As b > 1 then it is an increasing function.

To calculate the percentage increase/decrease, subtract 1 from the base:

⇒ 1.03 - 1 = 0.03 = 3%

Therefore, product A is increasing by 3% each year.

Part B

$\sf percentage\:change=\dfrac{final\:value-initial\:value}{initial\:value} \times 100$

To calculate the percentage change in Product B, use the percentage change formula with two consecutive values of f(t) from the given table:

$\implies \sf percentage\:change=\dfrac{10201-10100}{10100}\times 100=1\%$

Check using different two consecutive values of f(t):

$\implies \sf percentage\:change=\dfrac{10303.01-10201}{10201}\times 100=1\%$

Therefore, as 3% > 1%, Product A recorded a greater percentage change in price over the previous year.

Although the question has not asked, we can use the given information to easily create an exponential function for Product B.

Given:

a = 10,100
b = 1.01
n = t - 1 (as the initial value is for t = 1 not t = 0)

$\implies f(t) = 10100(1.01)^{t-1}$

To check this, substitute the values of t for 1 through 4 into the found function:

$\implies f(1) = 10100(1.01)^{1-1}=10100$

$\implies f(2) = 10100(1.01)^{2-1}=10201$

$\implies f(3) = 10100(1.01)^{3-1}=10303.01$

$\implies f(4) = 10100(1.01)^{4-1}=10406.04$

As these values match the values in the given table, this confirms that the found function for Product B is correct and that Product B increases by 1% per year.

4 0

2 years ago

Please someone help me to prove this.

morpeh [17]

Answer: see proof below

Step-by-step explanation:

Use the Double Angle Identity: sin 2Ф = 2sinФ · cosФ

Use the Sum/Difference Identities:

sin(α + β) = sinα · cosβ + cosα · sinβ

cos(α - β) = cosα · cosβ + sinα · sinβ

Use the Unit circle to evaluate: sin45 = cos45 = √2/2

Use the Double Angle Identities: sin2Ф = 2sinФ · cosФ

Use the Pythagorean Identity: cos²Ф + sin²Ф = 1

Proof LHS → RHS

LHS: 2sin(45 + 2A) · cos(45 - 2A)

Sum/Difference: 2 (sin45·cos2A + cos45·sin2A) (cos45·cos2A + sin45·sin2A)

Unit Circle: 2[(√2/2)cos2A + (√2/2)sin2A][(√2/2)cos2A +(√2/2)·sin2A)]

Expand: 2[(1/2)cos²2A + cos2A·sin2A + (1/2)sin²2A]

Distribute: cos²2A + 2cos2A·sin2A + sin²2A

Pythagorean Identity: 1 + 2cos2A·sin2A

Double Angle: 1 + sin4A

LHS = RHS: 1 + sin4A = 1 + sin4A $\checkmark$

6 0

2 years ago

I need a formula for this problem. Three workers each take home two packs Post-It Notes, at a cost of $.67 per pack

ludmilkaskok [199]

3[2(.67x)] I think and I hope I'm right

4 0

3 years ago

Read 2 more answers

A national survey indicated that 30% of adults conduct their banking online. It also found that 40% are under the age of 50. and

Svet_ta [14]

Answer:

Step-by-step explanation:

Hello!

I'll express all the given percentages as probabilities:

Given the events:

Banking online (Bo)

Under the age of 50 (<50)

P(Bo)= 0.30

P(<50)= 0.40

P(Bo ∩ <50)= 0.25

1) What percentage of adults do not conduct their banking online?

The event "adults that do not conduct their baking online" is the complement of the event "adults that conduct their baking online" Symbolically $Bo^c$

P( $Bo^c$ )= 1 - P(Bo)= 1 - 0.30 = 0.70

2) What type of probability is 25%?

The probability P(Bo ∩ <50)= 0.25 is a joint probability, it indicates the intersection between both events.

3) Construct a contingency table showing all joint and marginal probabilities.

Check attachment.

4) What is the probability that an individual conducts banking online given that the individual is under the age of 50?

Symbolically:

P(Bo/<50)= P(Bo ∩ <50) = 0.25 = 0.625

P(<50) 0.40

I hope it helps!

4 0

3 years ago

Perimeter=42 meters what is the length

Dominik [7]

4a= 42
a = 42/4 = 21/2cm

7 0

3 years ago