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4 years ago

Use the distributive property to simplify the following expression: 5(x + 2)

Mathematics

1 answer:

OLga [1]4 years ago

5 0

Answer:

5x + 10

Step-by-step explanation:

Each term in the parenthesis is multiplied by the 5 outside, that is

(5 × x) + (5 × 2) = 5x + 10

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The radius of the base of a cylinder is increasing at a rate of 11 meter per hour and the height of the cylinder is decreasing a

musickatia [10]

Answer:

The volume of the cylinder is decreasing at a rate of 83629.2 m³/h.

Step-by-step explanation:

The volume of a is given by:

$V = \pi r^{2}h$

Where:

r: is the radius = 55 m

h: is the height = 88 m

We can express the rate of change of the volume of the cylinder as follows:

$\frac{dV}{dt} = \pi[h\frac{2rdr}{dt} + r^{2}\frac{dh}{dt}]$

If dr/dt = 11 m/h and dh/dt = -44m/h, we have:

$\frac{dV}{dt} = \pi[88 m*2*55 m*11 m/h + (55 m)^{2}*(-44 m/h)] = -83629.2 m^{3}/h$

Therefore, the volume of the cylinder is decreasing at a rate of 83629.2 m³/h.

I hope it helps you!

5 0

3 years ago

In a field there are cows, birds, and spiders. Spiders have 4 eyes and 8 legs each. In the field there are 20 eyes and 30 legs.

Kitty [74]

Answer:

1 spider, 3 cows, 5 birds.

Step-by-step explanation:

Cows (C): 4 legs, 2 eyes.

Birds (B): 2 legs, 2 eyes.

Spiders (S): 8 legs, 4 eyes.

The number of legs and eyes are given, respectively by:

$30 = 4C+2B+8S\\20 = 2C+2B+4S$

Multiplying the second equation by -2 and adding it to the first one gives us the number of birds:

$30 -40= 4C-4C+2B-4B+8S-8S\\-10 = -2B\\B=5$

Rewriting the original equations with B =5:

$30 = 4C+2*5+8S\\20 = 2C+2*5+4S\\20 = 4C+8S\\10 = 2C+4S\\C=5-2S$

Since the number of cows cannot be negative, and both C and S must be odd numbers, the only possible value of S is 1:

$C=5-2S\\S=1\\C=3$

7 0

3 years ago

What force would be required to accelerate a 1,100 kg car to 0.5m/s?

ira [324]

Answer:

550 N

Step-by-step explanation:

We can solve the problem by using Newton's second law:

$F=ma$

F is the force required to accelerate the car

m is the mass of the car

a is the acceleration of the car

In this problem, the mass is m=1100 kg, while the acceleration is a=0.5 m/s^2, therefore the force required to accelerate the car is

$F=ma=(1100kg)(0.5m/s^{2} )=550N$

Hope this helps!

3 0

3 years ago

An order of luxury watch parts is shipped from spain to an assembly plant in the uniited states. The package is weighed before s

Paladinen [302]

Answer:

A. 89.07

Step-by-step explanation:

A kilogram = 2.20462

40.4 kilograms = 40.4 X 2.20462

89.066648

Nearest hundreth = 89.07

7 0

3 years ago

Select the two values of x that are roots of this equation. 2x+11x+15= 0

Amiraneli [1.4K]

Answer:

The roots of the equation are x=-3 and x=-2.5

Step-by-step explanation:

The correct quadratic equation is

2x^2+11x+15=0

we know that

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$2x^{2} +11x+15=0$

$a=2\\b=11\\c=15$

substitute in the formula

$x=\frac{-11(+/-)\sqrt{11^{2}-4(2)(15)}} {2(2)}$

$x=\frac{-11(+/-)\sqrt{121-120}} {4}$

$x=\frac{-11(+/-)\sqrt{1}} {4}$

$x=\frac{-11(+/-)1} {4}$

$x_1=\frac{-11(+)1}{4}=-2.5$

$x_2=\frac{-11(-)1}{4}=-3$

therefore

The roots of the equation are x=-3 and x=-2.5

5 0

3 years ago