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3 years ago

(x+5)(x-4)(x+2) is identical to x^3+ax^2

Mathematics

1 answer:

nikdorinn [45]3 years ago

4 0

Answer:

a = 3

Step-by-step explanation:

Factorize (x+5)(x-4)(x+2)

(x+5)(x-4)(x+2)

= (x²-4x+5x-20)(x+2)

= (x²+x-20)(x+2)

= (x³+2x²+x²+2x-20x-40)

= x³+3x²-18x -40

Compare with x^3+ax^2

3x² = ax²

3 = a

Rearrange

a = 3

Hence the value of a that makes the expressions identical is 3

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Amir stands on a balcony and throws a ball to his dog, who is at ground level.

ludmilkaskok [199]

Answer:

6 seconds

Step-by-step explanation:

h(x)=-(x-2)^2+16

We want h(x) to be 0 ( that is when the ball hits the ground)

0 = -(x-2)^2+16

Subtract 16 from each side

-16 = -(x-2)^2+16-16

-16 = -(x-2)^2

Divide by -1

16 = (x-2)^2

Take the square root of each side

sqrt(16) = sqrt((x-2)^2)

±4 = x-2

Add 2 to each side

2±4 = x-2+2

2±4 =x

2+4 = x 2-4 = x

6 =x -2 =x

Time cannot be negative so x=6

3 0

3 years ago

If 10 pens cost 60 rupees, then the cost of 13 such pens will be rs.

NeX [460]

Answer: 78 rupees

Explanation: since 10 pens cost 60 rupees you can divide 60 by 10 to get the cost of a single pen. The cost of a single pen is 6 rupees so you can multiply that by 13 to find the cost of the 13 pens.

10p=60
60/10=6
p=6
so
13x6=78

Hope this helped! :)

4 0

3 years ago

A long-jumper lifts off 3 m after starting his run, and lands 6 m later. When he is 8 m from the start line, he is 5 cm above th

Alexeev081 [22]

Answer:

The equation of the parabola that models the path of the long jumper through the air is $y = -x^{2} +12$ × $x-27$

Step-by-step explanation:

Mathematically, we know that parabolas are second-order polynomials and every second-order polynomials, also known as quadratic functions, can be constructed by knowing three different points of the curve. The standard form of the parabola is:

$y = a$ × $x^{2} +b$ × $+ C$

Where:

x - Horizontal distance from the start line, measured in meters.

y - Height of the long jumper, measured in meters.

a,b,c - Polynomial constants, measured in $\frac{1}{m}$ , dimensionless and meters, respectively.

If we know that $(x_{1},y_{1}) = (3\,m, 0\,m), (x_{2},y_{2}) = (8\,m, 0.05\,m)$ and $(x_{3}, y_{3}) = (9\,m, 0\,m),$ this system of linear equations is presented below:

$9\cdot a + 3\cdot b + c = 0 (Eq. 1)81\cdot a + 9\cdot b + c = 0 (Eq. 2)64\cdot a + 8\cdot b + c = 0.05 (Eq. 3)$

The coefficients of the polynomial are, respectively:

$a = -\frac{1}{100}, b = \frac{3}{25}, c = -\frac{27}{100}$

The equation of the parabola that models the path of the long jumper through the air is $y' = -\frac{1}{100}\cdot x^{2}+\frac{3}{25}\cdot x -\frac{27}{100}.$