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3 years ago

Which shows one way to determine the factors of x3 + 5x2 – 6x – 30 by grouping?

Mathematics

1 answer:

frutty [35]3 years ago

6 0

Answer:

Step-by-step explanation:

group them first :

( x3+5x2) and ( -6x-30)

then simply by gcf ( greatest common factor) :

x2(x+5) and -6(x+5)

and just add them together:

x2(x+5)-6(x+5)

bonus :

it can be written as (x2-6)(x+5)

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Consider the trial on which a 3 is first observed in successive rolls of a six-sided die. Let A be the event that 3 is observed

Gwar [14]

Answer:

1) 0.1667

2) 0.8333

3) 1

Step-by-step explanation:

Let A be the event that 3 is observed on the first trial.

Let B be the event that at least two trials are required to observe a 3

a) A six-sided die has 6 possible outcomes of 1,2,3,4,5,6

3 is one of the six possible outcomes

P(A) = no of favourable outcomes /no of possible outcomes

P(A) = 1/6 = 0.1667

b) The event of requiring at least two trials to observe a 3 is the event of not observing a 3 on the first trial.

P(B) = P(A')

P(A')= 1 - P(A)

P(B) = 1 - 1/6

= 5/6 = 0.8333

c) P(AnB) = P(A) + P(B)

= 1/6 + 5/6

= 6/6 = 1

7 0

2 years ago

he width and length of a rectangle (in feet)are consecutive odd integers. If the length is increased by 5 feet, the area of the

Ivanshal [37]

The original area of the rectangle is $35ft^{2}$

<u>Explanation:</u>

width = x

length = x + 2

area of the rectangle = x (x+2)

length = x + 2 + 5 = x+7

$60 = (x+7) (x)\\60=x^{2} + 7x\\x^{2} + 7x - 60 =0\\$

Solving this equation, we get

x =5ft

So, original width = 5ft

original length = 5+2ft = 7ft

Thus, original area of the rectangle = 5 X 7ft = $35ft^{2}$

Therefore, the original area of the rectangle is $35ft^{2}$

3 0

3 years ago

If Jane has 23 cats and I have 2 cats, and then Jane gives me 5 cats, how many more cats does Jane have than I? Rhonda has 12 ma

Dimas [21]

Answer:

11 cats

Step-by-step explanation:

Given :

Jane's initial = 23

My initial = 2

Jane gives out 5 cats to me ;

Jane's new = 23 - 5 = 18

My new = 2 + 5 = 7

Number of cats Jane has than me :

Jane's new - My new

18 - 7 = 11 cats

Second question is incomplete. We aren't told what to calculate.

6 0

3 years ago

Solve the inequality 8(x - 2) + 9 < 3(x - 1) + 5x

zvonat [6]

Answer:

no solution

Step-by-step explanation:

4 0

3 years ago

Which of the following integrals will find the volume of the solid that is formed when the region bounded by the graphs of y=e^x

dimulka [17.4K]

The fourth option is correct.

See the attached image. The red cylinder represents a washer formed by the described revolution. Its volume is

$\pi((\text{outer radius})^2-(\text{inner radius})^2)(\text{height})$

so when we integrate, we take

$\displaystyle\pi\int_0^1((e^x+2)^2-3^2)\,\mathrm dx$

7 0

2 years ago