Ask question

Ask question

All categories

2 years ago

11

a system of two linear equations has infinitely many solutions. one of the equations in the system is y-3x=-3.write an equation

that can be used to complete the system so that it has infinitely many solutions.solve your system using any method to show that it has infinitely many solutions.

1 answer:

Troyanec [42]2 years ago

8 0

The other equation could be

2y - 6x = -6

Solving:-

y - 3x = -3..........(1)
2y - 6x = -6........(2)
multiplyng the first equation by 2 gives
2y - 6x = -6

so equations (1) and (2) are the same equation
If we graph them they will be the same line
Every point on that line will be a solution.

So there are infinitely many solutions

You might be interested in

The height h in feet of a ball thrown vertically upward from the top of a 288-foot tall building is given by h=288+48t-16t^2 whe

mr Goodwill [35]

6 sec can take penny to strike the ground.

Solution:

Given data:

$H_0=288$ feet

$V_0=48$ feet

$h(t)=288+48t-16t^2$

Re-arrange the terms from greatest degree to smallest degree.

$h(t)=-16t^2+48t+288$

We can solve it by applying quadratic formula,

$$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Here a = –16, b = 48, c = 288

$$t=\frac{-48\pm \sqrt{48^2-4(-16)(288)}}{2(-16)}$

$$t=\frac{-48\pm \sqrt{2304+18432}}{-32}$

$$t=\frac{-48\pm \sqrt{20736}}{-32}$

$$t=\frac{-48\pm144}{-32}$

Now, write find two t's using plus and minus operation.

$$t=\frac{-48+144}{-32},\ \ t=\frac{-48-144}{-32}$

$$t=\frac{96}{-32},\ \ t=\frac{-192}{-32}$

t = –3 (or) t = 6

We cannot write time is negative. so neglect t = –3.

Therefore t = 6.

Hence 6 sec can take penny to strike the ground.

8 0

2 years ago

The value of a certain car decreases by 16% each year. What is the 1⁄2-life of the car?

svet-max [94.6K]

Answer:

The half life of the car is 3.98 years.

Step-by-step explanation:

The value of the car after t years is given by the following equation:

$V(t) = V(0)(1-r)^{t}$

In which V(0) is the initial value and r is the constant decay rate, as a decimal.

The value of a certain car decreases by 16% each year.

This means that $r = 0.16$

So

$V(t) = V(0)(1-r)^{t}$

$V(t) = V(0)(1-0.16)^{t}$

$V(t) = V(0)(0.84)^{t}$

What is the 1⁄2-life of the car?

This is t for which V(t) = 0.5V(0). So

$V(t) = V(0)(0.84)^{t}$

$0.5V(0) = V(0)(0.84)^{t}$

$(0.84)^{t} = 0.5$

$\log{(0.84)^{t}} = \log{0.5}$

$t\log{0.84} = \log{0.5}$

$t = \frac{\log{0.5}}{\log{0.84}}$

$t = 3.98$

The half life of the car is 3.98 years.

7 0

3 years ago

A number increased by 100% and decreased by 20% is x. what is the number ? NEEDED TODAY

vodka [1.7K]

Answer:

Let's assume the number be 100.

According to the problem , 100 is increased by 100%.

So, new number will be 100+100=200

Now 200 will decreased by 20%.

So, 20% of 200= 0.20*200= 40.

So, again the number has been changed into 200+40=240.

So, x=240

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

After simplifying, which expressions are equivalent? Select three options. (3.42 – 1.75) + (235a – 3.95) (2.5a + 1.65) + (3.4a +

poizon [28]

9514 1404 393

Answer:

C, D, E

Step-by-step explanation:

Collect terms. The last three options are all equivalent to ...

5.9a - 5.6b

3 0

2 years ago

Find x and y. Please help this is on a test!!!

ozzi

To find the x-intercepts algebraically, we let y = 0 y=0 y=0 in the equation and then solve for values of x. In the same manner, to find for y-intercepts algebraically, we let x = 0 x=0 x=0 in the equation and then solve for y.

6 0

2 years ago

Read 2 more answers