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3 years ago

Perform the indicated operation. 15b/4 * 8/9a^2b^2

Mathematics

1 answer:

Sergio [31]3 years ago

7 0

Answer:

The simplified expression is $\frac{10}{3 a^2 b}$

Step-by-step explanation:

The given expression is:

$\frac{15b}{4} * \frac{8}{9a^2 b^2}$

Multiply the items in the numerator together ( 15b * 8 = 120 b). Also multiply the items in the denominator together ( 4 * 9a²b² = 36a²b²). The expression thus becomes:

$= \frac{120b}{36 a^2 b^2} \\\\$

Divide both the numerator and the denominator by 12b:

$= \frac{120b /12b}{36 a^2 b^2/12b}$

The expression finally becomes:

$= \frac{10}{3 a^2 b}$

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3 years ago

PLEASE HELP! 20 POINTS 1) A ball is thrown starting at a time of 0 and a height of 2 meters. The height of the ball follows the

drek231 [11]

Answer:

1) The height of the ball from 0 to 5 seconds are;

At t = 0 second, height = 2

At t = 1 second, height h = 22.1

At t = 2 seconds, height h = 32.4

At t = 3 seconds, height h = 32.9

At t = 4 seconds, height h = 23.6

At t = 5 seconds, height h = 4.5

2) The correct option is;

D. -16·t² + 25·t + 1

Step-by-step explanation:

1) The equation of motion of the ball is given as follows;

H(t) = -4.9·t² + 25·t + 2

The height of the ball from 0 to 5 seconds are;

H(0) = -4.9×(0)² + 25×(0) + 2 = 2

H(1) = -4.9×(1)² + 25×(1) + 2 = 22.1

H(2) = -4.9×(2)² + 25×(2) + 2 = 32.4

H(3) = -4.9×(3)² + 25×(3) + 2 = 32.9

H(4) = -4.9×(4)² + 25×(4) + 2 = 23.6

H(5) = -4.9×(5)² + 25×(5) + 2 = 4.5

Therefore, we have;

The height of the ball are

At t = 0 second, height = 2

At t = 1 second, height h = 22.1

At t = 2 seconds, height h = 32.4

At t = 3 seconds, height h = 32.9

At t = 4 seconds, height h = 23.6

At t = 5 seconds, height h = 4.5

2) Given that the equation of the ball is that of a projectile motion, such as follows;

h = h₀ + v₀·sin(θ₀)·t - 1/2·g·t² which is equivalent to h = -1/2·g·t²+ h₀+v₀·sin(θ₀)·t

it is best represented by the quadratic equation of an upside down parabola which is option D. -16·t² + 25·t + 1

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3 years ago

Sierra left $4.50 as a tip for a waiter. This was 18% of the bill before the tip. How much was her total bill before the tip? En

IrinaVladis [17]

Answer: $20.5

Step-by-step explanation:

Let x denotes the amount for total bill.

We are given that , Sierra left $4.50 as a tip for a waiter.

This was 18% of the bill before the tip.

We can write 18% = 0.18. [To convert percent into decimal we divide it by 100.]

Then, the tip amount = 0.18 x Total bill

$\Rightarrow\ 4.5=0.18x\\\\\Rightarrow\ x=\dfrac{4.5}{0.18}=25$

So, the total bill amount = $25

Hence, her total bill before the tip= Total bill amount - Tip amount

= $25- $4.50=$20.5

Thus ,her total bill before the tip= $20.5

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3 years ago

What is the surface area of the triangular prism shown? A triangular prism. The triangle faces have base 14 meters and height 24

Alekssandra [29.7K]

Answer:

1064 m²

Step-by-step explanation:

The surface area of the prism can be gotten by saying

14 * 14 + 14 * 14 + 14 * 24 =

196 + 196 + 336 =

728 m²

Again, after dealing with the rectangle, we then face the triangle.

Area of triangle is

1/2 * 14 * 24

There are 2 triangles so this makes it

2 * 1/2 * 14 * 24 =

336

The surface area is finally

336 + 728 = 1064 m²

Surface area of the triangular prism has been calculated to be 1064 m²

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3 years ago