4x-10y=-16 and -7x+20y=23 elimination

Choose one of the factors of 6x^3 + 6

ivanzaharov [21]

Answer: First option is correct.

Step-by-step explanation:

Since we have given that

$6x^3+6$

Now, by factorising , we get

$6x^3+6\\=6(x^3+1)$

Now, we use the formula i.e.

$a^3+b^3=(a+b)(a^2-ab+b^2)$

By using this, we get ,

$6(x^3+1)\\=6(x+1)(x^2-x+1)$

So,

$(x+1) \text{ is the factor of }6x^3+6.$

6 0

3 years ago

Read 2 more answers

Laura takes very good care of her vehicles. She owns a blue van and a red truck. Although she bought them both new, she has owne

MrRissso [65]

The age of the van owned = 12 years

The age of the truck owned = 29 years

Step-by-step explanation:

Here, the given question is INCOMPLETE.

Laura takes very good care of her vehicles. She owns a blue van and a red truck. Although she bought them both new, she has owned the truck for 17 years longer than she has owned the van. If the sum of the ages of the vehicles is 41 years, how old is the van and how old is the truck?

Let us assume the number of years Laura has owned the van = S years

So, according to the question:

The number of years she has owned truck = S + 17 years

Now, Sum of the age of ( Truck + Van) = 41 years

⇒ (S + 17 years) + (S years) = 41 years

or, 2 S + 17 = 41

or, 2 S = 4 1 -1 7 = 24

or, S = 24/2 = 12 years

or, S = 12 years

Hence the age of the van owned = 12 years

The age of the truck owned = S + 17 = 12 + 17 = 29 years

6 0

3 years ago

Compare the numbers by entering <, >, or =.

Andrew [12]

Your answer would be:
596.64 = 596.640
Reasoning= If you just take away the zero from 596.640 you would have the same answer as 596.64. Now if you add a zero to 596.64 you still would have the same answer, therefore they are equal.
Hope this helps! (:

6 0

3 years ago

the height h(t) of a trianle is increasing at 2.5 cm/min, while it's area A(t) is also increasing at 4.7 cm2/min. at what rate i

nekit [7.7K]

Answer:

The base of the triangle decreases at a rate of 2.262 centimeters per minute.

Step-by-step explanation:

From Geometry we understand that area of triangle is determined by the following expression:

$A = \frac{1}{2}\cdot b\cdot h$ (Eq. 1)

Where:

$A$ - Area of the triangle, measured in square centimeters.

$b$ - Base of the triangle, measured in centimeters.

$h$ - Height of the triangle, measured in centimeters.

By Differential Calculus we deduce an expression for the rate of change of the area in time:

$\frac{dA}{dt} = \frac{1}{2}\cdot \frac{db}{dt}\cdot h + \frac{1}{2}\cdot b \cdot \frac{dh}{dt}$ (Eq. 2)

Where:

$\frac{dA}{dt}$ - Rate of change of area in time, measured in square centimeters per minute.

$\frac{db}{dt}$ - Rate of change of base in time, measured in centimeters per minute.

$\frac{dh}{dt}$ - Rate of change of height in time, measured in centimeters per minute.

Now we clear the rate of change of base in time within (Eq, 2):

$\frac{1}{2}\cdot\frac{db}{dt}\cdot h = \frac{dA}{dt}-\frac{1}{2}\cdot b\cdot \frac{dh}{dt}$

$\frac{db}{dt} = \frac{2}{h}\cdot \frac{dA}{dt} -\frac{b}{h}\cdot \frac{dh}{dt}$ (Eq. 3)

The base of the triangle can be found clearing respective variable within (Eq. 1):

$b = \frac{2\cdot A}{h}$

If we know that $A = 130\,cm^{2}$ , $h = 15\,cm$ , $\frac{dh}{dt} = 2.5\,\frac{cm}{min}$ and $\frac{dA}{dt} = 4.7\,\frac{cm^{2}}{min}$ , the rate of change of the base of the triangle in time is:

$b = \frac{2\cdot (130\,cm^{2})}{15\,cm}$

$b = 17.333\,cm$

$\frac{db}{dt} = \left(\frac{2}{15\,cm}\right)\cdot \left(4.7\,\frac{cm^{2}}{min} \right) -\left(\frac{17.333\,cm}{15\,cm} \right)\cdot \left(2.5\,\frac{cm}{min} \right)$