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3 years ago

Which fraction is equivalent to -(6/-7) A) -(6/7) B) (-6/7) C) (6/-7) D) (-6/-7)

2 answers:

5 0

- $\frac{6}{-7}$
Through the process of multiplication, we get the answer below:
↓
$\frac{-6}{-7}$

Your answer will be D

Len [333]3 years ago

4 0

Given fraction:
-(6/-7)
Apply plus/minus rule:
-(-a)=a and -(a)=-a
So -(6/-7) = -6/-7= 6/7
Option D is correct.

Answer: (-6/-7)

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F(x) = x2 + 10 What is the average rate of chan hange of f over the interval [-2, -1]?

Readme [11.4K]

The average rate of change is given by [f(b) - f(a)]/(b - a), where a and b represent the interval [a, b].

Let a = -2

Let b = -1

[(-1)^2 + 10 - ((-2)^2 + 10)]/(-1 -(-2))

[1 + 10 - (4 + 10)]/(-1 + 2)

[1 + 10 -4 -10]/(1)

[1 - 4]/(1)

-3/1

Answer: -3

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2 years ago

Find the GCF. 18c3 and 24c3

12345 [234]

Answer:

6c³

Step-by-step explanation:

18c³ = 2 × 3 × 3 × c × c × c

24c³ = 2 × 2 × 2 × 3 × c × c × c

Now we show the common factors in bold:

18c³ = 2 × 3 × 3 × c × c × c

24c³ = 2 × 2 × 2 × 3 × c × c × c

The common factor are:

2, 3, c, c, c

GCF = 2 × 3 × c × c × c = 6c³

6 0

2 years ago

In 2013, the population of China was estimated to be 1,360,760,100. Round off the number of people

Aleksandr [31]

Answer:

a) 1,360,760,000

b) 1,361,000,000

c) 1,400,000,000

d) 1,360,800,000

Step-by-step explanation:

We have to round off the given population number to certain digits.

The following are the rules to round of a number:

First identify the digit to be rounded.
If this digit is followed by 5,6,7,8,9 then we round up the number that is increase the digit by 1 and all the numbers to right becomes zero.
If this digit is followed by 0,1,2,3,4 then we round down the number that is decrease the digit by 1 and all the numbers to right becomes zero.

a) to the nearest thousand.

Thousands place: 0

Right Digit: 1

We round down the number

Rounded to the nearest 1,000 or t he thousands Place = 1,360,760,000

b) to the nearest million

Millions place: 0

Right Digit: 7

We round up the number

Rounded to the nearest million places = 1,361,000,000

c) to nearest hundred million

Hundred million place: 3

Right Digit: 6

We round up the number

Rounded to the nearest million places = 1,400,000,000

d) to the nearest hundred thousand.

hundred thousand place: 7

Right Digit: 6

We round up the number

Rounded to the nearest million places = 1,360,800,000

7 0

2 years ago

Read 2 more answers

Use the distributive property to simplify each expression (2b - 10) 3.2

Darya [45]

Answer: 6.4b - 32

Step-by-step explanation:

4 0

3 years ago

Consider a particle moving along the x-axis where x(t) is the position of the particle at time t, x' (t) is its velocity, and x'

vodka [1.7K]

Answer:

a) $v(t) =x'(t) = \frac{dx}{dt} = 3t^2 -12t +9$

$a(t) = x''(t) = v'(t) =6t-12$

b) $0$

c) $a(t) = x''(t) = v'(t) =6t-12$

When the acceleration is 0 we have:

$6t-12=0, t =2$

And if we replace t=2 in the velocity function we got:

$v(t) = 3(2)^2 -12(2) +9=-3$

Step-by-step explanation:

For this case we have defined the following function for the position of the particle:

$x(t) = t^3 -6t^2 +9t -5 , 0\leq t\leq 10$

Part a

From definition we know that the velocity is the first derivate of the position respect to time and the accelerations is the second derivate of the position respect the time so we have this:

$v(t) =x'(t) = \frac{dx}{dt} = 3t^2 -12t +9$

$a(t) = x''(t) = v'(t) =6t-12$

Part b

For this case we need to analyze the velocity function and where is increasing. The velocity function is given by:

$v(t) = 3t^2 -12t +9$

We can factorize this function as $v(t)= 3 (t^2- 4t +3)=3(t-3)(t-1)$

So from this we can see that we have two values where the function is equal to 0, t=3 and t=1, since our original interval is $0\leq t\leq 10$ we need to analyze the following intervals:

$0< t$

For this case if we select two values let's say 0.25 and 0.5 we see that

$v(0.25) =6.1875, v(0.5)=3.75$

And we see that for $a=0.5 >0.25=b$ we have that f(b)>f(a) so then the function is decreasing on this case.

$1$

We have a minimum at t=2 since at this value w ehave the vertex of the parabola :

$v_x =-\frac{b}{2a}= -\frac{-12}{2*3}= -2$

And at t=-2 v(2) = -3 that represent the minimum for this function, we see that if we select two values let's say 1.5 and 1.75

v(1.75) =-2.8125< -2.25= v(1.5) so then the function sis decreasing on the interval 1<t<2

$2$

We see that the function would be increasing.

$3$

For this interval we will see that for any two points a,b with $a>b$ we have $f(a)>f(b)$ for example let's say a=3 and b =4

$f(a=3) =0 , f(b=4) =9 , f(b)>f(a)$

The particle is moving to the right then the velocity is positive so then the answer for this case is: $0$

Part c

$a(t) = x''(t) = v'(t) =6t-12$

When the acceleration is 0 we have:

$6t-12=0, t =2$

And if we replace t=2 in the velocity function we got:

$v(t) = 3(2)^2 -12(2) +9=-3$

5 0

3 years ago