Without drawing the graph of the equation, determine how many points the parabola has in common with the x-axis and whether its vertex lies above, on, or below the x-axis. y = 3x2 – 12x + 12

Answers

Answer 1

Answer: We are given with th equation y = 3x2 – 12x + 12. In this respect, we expect that this is a parabola and that the vertex does not lie on (0,0). Since the power or degree is 2, it is expected that per value of y, there are two equivalent x's in the plot. You can verify it in the graph.

Answer 2

Answer:

Answer:

The answer is, 1 point in common; vertex on x-axis

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If (−3.5, y) is a solution to the equation 2x − 5y = 10, what is the value of y?a) -3.4
b) 13.75
c) -0.6
d) -3.75

Answers

2x - 5y = 10
2(-3.5) - 5y = 10
-7 - 5y = 10
+7 +7
     -5y = 17
      -5    -5
      y = -3.4
The value of y is equal to A. -3.4.

one angle of a triangle is three times as large as another. the measure of the third angle is 40 degrees more than that of the smallest angle. find the measure of each angle

Answers

Hello,

Let x the second angle
the first is 3x
the third 40°

3x+x+40=180
==>4x=140
==>x=35°
3x=3*35=105°

A cube with side length 5h^2 is stacked on another cube with side length 3k What is the total volume of the cubes in factored form?

Answers

Answer:

$(5h^2+3k)(25h^4-15h^2k+9k^2)$

Step-by-step explanation:

We have been given that a cube with side length 5h^2 is stacked on another cube with side length 3k.

Since we know that the volume of cube is $a^3$ , where a represents the length of each side of cube.

Since one cubes is stacked on another cube, so the total volumes of both cubes will be equal to the sum of volumes of both cubes.

$\text{Total volume of both cubes}=(5h^2)^3+(3k)^3$

Since the volume of both cubes is sum of cubes, so we will use formula:

$a^3+b^3=(a+b)(a^2-ab+b^2)$

So factoring the volumes of cubes using sum of cubes we will get,

$\text{Total volume of both cubes}=(5h^2+3k)((5h^2)^2-5h^2* 3k+(3k)^2)$

$\text{Total volume of both cubes}=(5h^2+3k)(25h^4-15h^2k+9k^2)$

Therefore, the total volume of both cubes in factored form will be: $(5h^2+3k)(25h^4-15h^2k+9k^2)$

In order to compute the combined volume of the cubes, we may simply add the individual volumes of the cube. The volume of a cube is equivalent to the cube of one of its sides. The volume of the first cube is (5h^2)^3 = 125h^6. The volume of the second cube is (3k)^3 = 27k^3. The total volume is: 125h^6 + 27k^3Hope this helps. Let me know if you need additional help!

3x - 17 = 46 . solve for x