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3 years ago

The graph above represents the following polynomial function.

Mathematics

1 answer:

Korvikt [17]3 years ago

6 0

Answer:

C. 0, -1, 3

Step-by-step explanation:

Note: There is no graph. I assume you mean "zeroes/roots" by "solutions".

x(x^2-2x-3)=0

/(x^2-2x-3)

x=0

x^2-2x-3 = x^2+x-3x-3 = x(x+1) + ( -3(x+1) = (x-3)(x+1)

/(x-3) --> x +1 =0, x=-1

/(x+1) --> x-3 = 0, x=3

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The graph of $y = ax^2 + bx + c$ is shown below. Find $a \cdot b \cdot c$. (The distance between the grid lines is one unit.)

Savatey [412]

Answer:

$a\cdot b\cdot c=\frac{15}{4}$

Step-by-step explanation:

Vertex is the minimum or maximum point of parabola

Vertex of parabola is (h,k)

Therefore, from given graph (-3,-2) is the lowest point.

Vertex of parabola is at (-3,-2).

Standard equation of parabola

$y-k=a(x-h)^2$

Substitute the values

$y-(-2)=a(x-(-3))^2=a(x+3)^2$

$y+2=a(x+3)^2$

(-1,0) lies on the parabola.

Therefore, it satisfied the equation of parabola.

$0+2=a(-1+3)^2=4a$

$a=2/4=1/2$

Now, using the value of a

$y+2=1/2(x+3)^2=1/2(x^2+6x+9)$

$y+2=\frac{1}{2}x^2+3x+\frac{9}{2}$

$y=\frac{1}{2}x^2+3x+\frac{9}{2}-2$

$y=\frac{1}{2}x^2+3x+\frac{9-4}{2}$

$y=\frac{1}{2}x^2+3x+\frac{5}{2}$

By comparing with

$y=ax^2+bx+c$

We get

$a=\frac{1}{2}, b=3, c=5/2$

$a\cdot b\cdot c=\frac{1}{2}\times 3\times \frac{5}{2}$

$a\cdot b\cdot c=\frac{15}{4}$

7 0

2 years ago

Find the highest common factor (HCF) of 72 and 98.

Y_Kistochka [10]

Answer:

2

Step-by-step explanation:

The factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

The factors of 98: 1, 2, 7, 14, 49, 98

Your greatest common factor is 2.

Hope this helps. Have a nice day.

3 0

3 years ago

The volume of a cone is 3rx? cubic units and its height is x units. Which expression represents the radius of the cone's base, i

Marianna [84]

Answer:

It is given that the volume of a cone = $3\pi x^3$ cubic units

Volume of cone with radius 'r' and height 'h' = $\frac{1}{3}\pi r^2h$

Equating the given volumes, we get

$3\pi x^3=\frac{1}{3}\pi r^2h$

$r^2h=3$ × $3x^3$

$r^2h=9 x^3$

It is given that the height is 'x' units.

Therefore, $r^2x=9x^3$

$r^2=9x^2$

Therefore, $r=3 x$

So, the expression ' $3 x$ ' represents the radius of the cone's base in units.

3 0

1 year ago

The sum of 8 times a number and 7 equals 9!

Vladimir [108]

Answer:

0.25*8+7=9

Step-by-step explanation:

8x+7=9

2/8=x

0.25=x

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3 years ago

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zubka84 [21]

The answer to your question is 300,000

6 0

3 years ago