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3 years ago

Simplify: -6(x + 4)

Mathematics

2 answers:

Norma-Jean [14]3 years ago

6 0

Answer:

A) -10x-24

Step-by-step explanation:

$-6(\frac{5}{3} x+4)=-6\times\frac{5}{3} x+4\times(-6)=-10x-24$

$a(b+c)=ab+ac$

Bess [88]3 years ago

4 0

Answer:

A) -10x - 24

Step-by-step explanation:

1. To simplify this expression, we apply the distributive property.

$(-6)(\frac{5}{3}x)+(-6)(4)$
$\frac{-30}{3}x-24$
$-10x - 24$

Therefore, the answer is A) -10x - 24.

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Studentka2010 [4]

Step-by-step explanation:

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3 years ago

It took a skydive 6 seconds to drop 720feet. What is the rate (in feet per/second) of the skydive's drop?

Lostsunrise [7]

Answer:

120ft/sec

Step-by-step explanation:

Assuming that there is no acceleration, divide the amount of feet (720) with the time (6 seconds):

720 ft/6 sec = 120 ft/1 sec

For every second, the skydiver drops 120 ft.

120ft/sec.

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3 years ago

A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2

Artemon [7]

Answer:

a) The height decreases at a rate of $\frac{7}{12}$ ft/sec.

b) The area increases at a rate of $\frac{527}{24}$ ft^2/sec

c) The angle is increasing at a rate of $\frac{1}{12}$ rad/sec

Step-by-step explanation:

Attached you will find a sketch of the situation. The ladder forms a triangle of base b and height h with the house. The key to any type of problem is to identify the formula we want to differentiate, by having in mind the rules of differentiation.

a) Using pythagorean theorem, we have that $25^2 = h^2+b^2$ . From here, we have that

$h^2 = 25^2-b^2$

if we differentiate with respecto to t (t is time), by implicit differentiation we get

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

Then,

$\frac{dh}{dt} = -\frac{b}{h}\frac{db}{dt}$ .

We are told that the base is increasing at a rate of 2 ft/s (that is the value of db/dt). Using the pythagorean theorem, when b = 7, then h = 24. So,

$\frac{dh}{dt} = -\frac{2\cdot 7}{24}= \frac{-7}{12}$

b) The area of the triangle is given by

$A = \frac{1}{2}bh$

By differentiating with respect to t, using the product formula we get

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

when b=7, we know that h=24 and dh/dt = -1/12. Then

$\frac{dA}{dt} = \frac{1}{2}(2\cdot 24- 7\frac{7}{12}) = \frac{527}{24}$

c) Based on the drawing, we have that

$\sin(\theta)= \frac{b}{25}$

If we differentiate with respect of t, and recalling that the derivative of sine is cosine, we get

$\cos(\theta)\frac{d\theta}{dt}=\frac{1}{25}\frac{db}{dt}$ or, by replacing the value of db/dt

$\frac{d\theta}{dt}=\frac{2}{25\cos(\theta)}$

when b = 7, we have that h = 24, then $\cos(\theta) = \frac{24}{25}$ , then

$\frac{d\theta}{dt} = \frac{2}{25\frac{24}{25}} = \frac{2}{24} = \frac{1}{12}$

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3 years ago

Https://prnt.sc/zozycx<br> va rog rapid !

stellarik [79]

Answer:

what are u asking?

Step-by-step explanation: im confused

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3 years ago

The computers of six faculty members in a certain department are to be replaced. Two of the faculty members have selected laptop

Nadusha1986 [10]

Answer:

The answer is 0.067.

Step-by-step explanation:

Let the entire sample size be = s

Now there are 2 laptops in sample size, hence these can be chosen in one way only.

The required probability that both selected setups are for laptop computers can be found as:

$p(two laptops)=\frac{s(two laptops)}{s}$

= $\frac{1}{15}$ or 0.067.

So, the probability is 0.067.

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3 years ago

Simplify: -6(x + 4) ​

Simplify: -6(x + 4)