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3 years ago

Do two distinct lines always intersect at a point.

1 answer:

6 0

The answer to the question above is "not always". Only two lines with solution intersect. There are other two types of systems of linear equation. One of which are those which do not intersect because of they are parallel. Lastly, there are also systems of lines that intersect indefinitely because basically the equations represent the same line.

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Find the volume of the solid obtained by rotating the region bounded by the given curves about the speciﬁed axis. y = 64x−8x^2,

Mandarinka [93]

We need to get the limits first. When y = 0
0 = 64x - 8x^2
x = 0 and x = 8
The volume is
V = ∫ y dx from 0 to 8
V = ∫ (64x - 8x^2) dx from 0 to 8
V = 32x^2 - 8x^3/3 from 0 to 8
V = 682.67

4 0

2 years ago

A square postage stamp has area 1240 mm^2 about how long is each side?

Shtirlitz [24]

Sq.root of 1240 is approx 35 mm

6 0

3 years ago

Identify each function that has a remainder of -3 when divided x+6

Sergeu [11.5K]

Answer:

Step-by-step explanation:

According to remainder theorem, you can know the remainder of these polynomials if you plug in x = -6 into them.

So we will plug in -6 into x of all the polynomials ( A through D) and see which one equals -3.

For A:

$x^5 + 2x^2 - 30x + 30\\=(-6)^5 + 2(-6)^2 - 30(-6) + 30\\=-7494$

For B:

$x^4 + 4x^3 - 21x^2 - 53x + 12\\=(-6)^4 + 4(-6)^3 - 21(-6)^2 - 53(-6) + 12\\=6$

For C:

$x^3 - 10x^2 - 7\\=(-6)^3 - 10(-6)^2 - 7\\=-583$

For D:

$x^4 + 6x^3 - 10x - 63\\=(-6)^4 + 6(-6)^3 - 10(-6) - 63\\=-3$

The only function that has a remainder of -3 when divided by x + 6 is the fourth one, answer choice D.

5 0

2 years ago

A triangle has side lengths measuring 3x cm, 7x cm, and h cm. Which expression describes the possible values of h, in cm?

gladu [14]

Answer:

AnSum of two sides of triangle always greater than third side, so the possible values of h is:

7x-3x < h < 7x+3x

4x < h < 10x answer:

Step-by-step explanation:

5 0

2 years ago

A) Rate (R) 24/5 Time = 1 month Interest = Rs. 39.96

yKpoI14uk [10]

Answer: P = $ 1,998.01

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 24%/100 = 0.24 per year,

putting time into years for simplicity,

1 months ÷ 12 months/year = 0.083333 years,

then, solving our equation

P = 39.96 / ( 0.24 × 0.083333 ) = 1998.007992032

P = $ 1,998.01

The principal required to

accumulate interest of $ 39.96

on a rate of 24% per year for 0.083333 years (1 months) is $ 1,998.01.

5 0

3 years ago