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3 years ago

How many solutions does the system have? y=3x+3 y=-2x+3

Mathematics

2 answers:

STatiana [176]3 years ago

8 0

Answer:

One solution (0, 3).

Step-by-step explanation:

As both expressions in x are equal to y:

3x + 3 = -2x + 3

3x + 2x = 3 - 3

5x = 0

x =0.

So y = 3(0) + 3 = 3.

padilas [110]3 years ago

3 0

Answer:

The system has a unique solution pair (x,y)

Step-by-step explanation:

Since both linear equations are given to you solved for "y", each equation is in "slope-intercept form" which is unique. These equations show that they possess different slopes (signaled in bold in the equations below):

y = 3 x +3

y = -2 x +3

(one has slope "3" and the other one slope "-2"), and therefore they are forced to intersect. One represents a line going up (positive slope) and the other one a line going down (negative slope). That means that the system will intersect in one well defined point on the plane, giving a UNIQUE solution to the system.

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Read 2 more answers

The volume of a cone varies jointly with the area of the base and the height. when the area of the base is

strojnjashka [21]

The volume of a cone varies jointly with the area of the base and the height of the cone.

$V = kAh$

where
V = volume
k = constant of proportionality
A = area of the base
h = height of the cone

The given info is for A = 27, and h = 6, then V = 54 (all using appropriate units for area, length, and volume, respectively.)

Now we can find k, the constant of proportionality.

V = kAh

54 = k * 27 * 6

k = 54/(27 * 6)

k = 1/3

The formula is

$V = \dfrac{1}{3}Ah$

Now we use the second set of info, the height and the volume, and we find the area of the base.

$V = \dfrac{1}{3}Ah$

$124 = \dfrac{1}{3} \times A \times 12$

$124 = 4A$

$A = 31$

Answer: the area of the base is 31 cm^2

3 0

3 years ago