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FinnZ [79.3K]
3 years ago
7

Use the given conditions to write an equation for the line in slope-intercept form.

Mathematics
1 answer:
krek1111 [17]3 years ago
6 0
Use the points and do y2-y1 divided by x2-x1
You will get -2 which is the m (slope)
Substitute one of the points into the y and x to get the b (y-intercept)
You will get -6
Put everything into the equation
y=-2x-6
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What property is illustrated by the statement 2/3 x 3/2 =1
Mariulka [41]

Answer:

Multiplicative inverse or reciprocal.

Step-by-step explanation:

Multiplicative inverse or reciprocal.

6 0
1 year ago
Read 2 more answers
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
5p + 6 = -4p - 8<br> Solve for p
Fofino [41]
9p=-14

p=-14/9 is the answer to the problem

5p+4p+6= -8
9p= -8-6
9p=-14
p= -14/9
7 0
2 years ago
<img src="https://tex.z-dn.net/?f=%20-%20%284x%20-%2015%29%20%5Cgeqslant%20-%209%283%20%2B%20x%29" id="TexFormula1" title=" - (4
Kay [80]

- (4x - 15) \geqslant  - 9(3 + x) \\  - 4x + 15 \geqslant  - 27 - 9x \\  - 4x + 9x \geqslant  - 27 - 15 \\ 5x \geqslant  - 42 \\ x \geqslant  - 8 \dfrac{2}{5}


21 + x > 2( - 2 - 5x) + 6x \\ 21 + x >  - 4 - 10x + 6x \\ x + 10x - 6x >  - 4 - 21 \\ 5x >  - 25 \\ x >  - 5

Hope this helps. - M
5 0
2 years ago
+(-6) + (-8)= -4<br> What’s the missing number???
Darya [45]

Answer:

10

Step by step explanation:

In general, if we have an equation that has just one variable, such as x, then "solving the equation" means finding the set of all values that can be substituted for the one variable to produce a valid equation.

Isolate "x" on one side of the algebraic equation by adding the negative number that appears on the same side of the equation as the "x." For example, in the equation "x - 5 = 12", rewrite the equation as "x = 12 + 5" and solve for "x."

x + (-6) + (-8) = -4

x + (-6 + -8) = -4

x + (-14) = -4

x + (-14 + 14) = -4 + 14

x = 10

5 0
2 years ago
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