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4 years ago

How many possible numbers of solutions are there to the system of equations?

Mathematics

1 answer:

storchak [24]4 years ago

3 0

Explanation:

Assuming a system of linear equations:

If the equations have the same slope, there are no possible solutions. Lines with the same slope run parallel and never intersect. Without an intersection, there is no solution. The solution is the point of intersection of graphs.

If the equations are equivalent, there are an infinite number of solutions. Equations can be equivalent in many ways. If one equation is rearranged to isolate one of its variables, the new equations looks different but it is equivalent. (Most commonly, two equivalent equations are in different forms, like standard, slope-intercept or point-intercept). If an equation has all of its terms multiplied or divided by the same number, the new equation is equivalent.

In any other case, there is only one solution.

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Please help me I need help please

MakcuM [25]

Answer:

p = 4

Step-by-step explanation:

Given equation:

$x^2+(p-3)y^2-4x+6y-16=0$

Standard equation of a circle:

$(x-a)^2+(y-b)^2=r^2$

(where $(a,b)$ is the centre of the circle, and $r$ is the radius)

If you expand this equation, you will see that the coefficient of $y^2$ is always one.

Therefore, $p-3=1$

$\implies p=1+3=4$

Additional information

To rewrite the given equation in the standard form:

$\implies x^2+y^2-4x+6y-16=0$

$\implies x^2-4x+y^2+6y=16$

$\implies (x-2)^2-4+(y+3)^2-9=16$

$\implies (x-2)^2+(y+3)^2=16+4+9$

$\implies (x-2)^2+(y+3)^2=29$

So this is a circle with centre (2, -3) and radius √29

3 0

2 years ago

Plz help need help fast plz

vodka [1.7K]

The Surface area of the rectangular prism is 238
Formula A=2(wl+hl+hw)
insert the numbers 2(4*11+5*11+5*4)
11*4=44
5*11=55
5*4=20
add them all up
44+55+20=119
new equation 2(119) or 2*119
2*119=238
Hope this helps :D

8 0

3 years ago

A sample of 80 high school senlors, 45% of which are female, were surveyed as to whether or not they are employed

fgiga [73]

Answer:

33 boys

Step-by-step explanation:

Since 45% of the participants were female and there were a total of 80 students, 36 of the 80 students were female. That means that 44 of the students were male.

25% of 44 is 11. So there are 11 boys that are not employed. From there you can just subtract 44 - 11 and get 33.

33 boys are employed

3 0

3 years ago

Read 2 more answers

Write an equation in slope-intercept form of the line shown.

tankabanditka [31]

Answer:

y = 3/4x - 2

Step-by-step explanation:

slope intercept form: y = mx + b

y-intercept(when x= 0) is given by b

slope is given by m

lets find the slope using the two given points, (4,1) and (8,4)

m = y2-y1 / x2-x1

m = 4 - 1 / 8 - 4

m = 3/4

Now use any of the given points to begin writing your equation, which will help you find the y intercept - ill use (4,1).

1 = 3/4(4) - b

1 = 3 - b

b = -2

now you have m and b so you can finish writing your equation.

y = mx + b

y = 3/4x - 2

4 0

3 years ago

6.7.35

valentinak56 [21]

Answer:

Step-by-step explanation:

This is most easily solved with calculus, believe it or not. It is way more direct and to the point, with a whole lot less math!

The position function is given. The velocity function is the first derivative of the position, so if we find the velocity function and set it equal to 0, we can solve for the amount of time it takes for the rocket to reach its max height. Remember from physics that at the top of a parabolic path, the velocity is 0.

If:

$s(t)=-16t^2+112t+360$ , then the velocity function, the first derivative is:

v(t) = -32t + 112 and solve for t:

-112 = -32t so

t = 3.5 seconds. Now we know how long it takes to get to the max height, we just need to find out what the max height is.

Go back to the position function and sub in 3.5 for t to tell us that position of the rocket at 3.5 seconds, which translates to the max height:

$s(3.5)=-16(3.5)^2+112(3.5)+360$ and

s(3.5) = 206 feet. I imagine that your answer, if you had to choose one from the list, would be 200 feet, rounded a lot.

6 0

3 years ago