Enter the equation of the following using line in slope-intercept form.

2x + 3y = 51<br>- x+2y = 8) substitution method

Free_Kalibri [48]

Answer:

Step-by-step explanation:

2x + 3y = 51........(1)

- x+2y = 8...........(2)

Making x as subject in equation (2)

-x = -2y + 8

x = 2y - 8.........(3)

Substituting (3) in (1)

2(2y - 8) + 3y = 51

4y - 16 + 3y = 51

Collecting like terms

4y + 3y = 51 + 16

7y = 67

y = 67/7

y = 9 4/7

And x = 2y - 8

x = 2(67/7) - 8

x = 134/7 - 8

x = (134 - 56)/7

x = 78/7

x = 11 1/7

7 0

3 years ago

Suppose the position of an object moving horizontally after t seconds is given by the following functions s=f(t), s equals f , o

Scilla [17]

Answer:

(a) The graph of position function is shown below.

(b) The velocity function is $v(t)=-2t+4$ and the graph of position function is shown below. The object is stationary at t=2, moving to the right at t>2, and moving to the left at t<2.

(c) Velocity and acceleration of the object at t=1 are 2 and -2 respectively.

(d) The acceleration of the object is -2 when its velocity is zero.

(e) The speed is not increasing at any interval because the acceleration is constant.

Step-by-step explanation:

(a)

The given function is

$f(t)=-t^2+4t-3; 0\leq t\leq 5$

The position of an object moving horizontally after t seconds is given by

$s=f(t)=-t^2+4t-3$

The graph of position function is shown below.

(b)

Differentiate the position function with respect to time to find the velocity function.

$v=f'(t)=-2t+4$

Put v=0 to find the time when the object is stationary.

$0=-2t+4$

$2t=4$

$t=2$

The object is stationary at t=2 because the velocity of the object is 0 at t=2.

The velocity function is $v(t)=-2t+4$ and the graph of position function is shown below. The object is stationary at t=2, moving to the right at t>2, and moving to the left at t<2.

(c)

The velocity function is

$v=f'(t)=-2t+4$

Substitute t=1 in the above function.

$v=f'(1)=-2(1)+4=2$

Differentiate the velocity function with respect to time to find the acceleration function.

$a=f''(t)=-2$

Substitute t=1 in the above function.

$a=f''(1)=-2$

Therefore the velocity and acceleration of the object at t=1 are 2 and -2 respectively.

(d)

The velocity of the object is 0 at t=2.

Substitute t=2 in the acceleration function to find the acceleration of the object when its velocity is zero.

$a=f''(2)=-2$

The acceleration of the object is -2 when its velocity is zero.

(e)

The acceleration function of the object is

$a=f''(t)=-2$

It is a constant function.

Therefore the speed is not increasing at any interval because the acceleration is constant.

7 0

3 years ago

Given parallelogram JKLM, find x and y.

Aneli [31]

Answer:

Step-by-step explanation:

X=5

Y=20

8 0

3 years ago

If you transform x2+ y2 = 25 into 4x2+ 4y2 = 25, which option below describes the effect of this transformation on the

balu736 [363]

Answer:

It divides the radius by 2, which is the last option in your list of possible answers.

Step-by-step explanation:

Recall that the standard equation of a circle of radius R centered at the origin of coordinates is given by:

$x^2+y^2=R^2$

so when you have the first equation of the circle:

$x^2+y^2=R^2\\x^2+y^2=25\\x^2+y^2=5^2$

The radius of the circle was 5

Now, when you work with the second equation, we need to divide both sides by 4 in order to get the standard form of the circle and be able to understand what the radius is:

$4x^2+4y^2=25\\x^2+y^2=\frac{25}{4} \\x^2+y^2=(\frac{5}{2})^2$

So we see that the initial radius 5 is now divided by 2.

8 0

4 years ago

What is the nth term of 4 9 16 25 36?

Neporo4naja [7]

T(n)=(n+1)^2 where t(n) is the value of the nth term and n is the term number.

3 0

3 years ago