How many solutions does the quadratic system shown below have ?

If s(x) = x - 7 & t(x) = 4x^2 - x + 3, which expression is equivalent to (t × s) (x)

barxatty [35]

Answer:

4

x

3

−

29

x

2

+

10

x

−

21

Step-by-step explanation:

3 0

3 years ago

A ball is thrown into the air. The path it takes is modeled by the equation: -3t+24t = h, where t is the time in seconds and h i

astra-53 [7]

Given:

The given equation is:

$-3t^2+24t=h$

Where, t is the time in seconds and h is the height of the ball above the ground, measured in feet.

To find:

The inequality to model when the height of the ball is at least 36 feet above the ground. Then find time taken by ball to reach at or above 36 feet.

Solution:

We have,

$-3t^2+24t=h$

The height of the ball is at least 36 feet above the ground. It means $h\geq 36$ .

$-3t^2+24t\geq 36$

$-3t^2+24t-36\geq 0$

$-3(t^2-8t+12)\geq 0$

Splitting the middle term, we get

$-3(t^2-6t-2t+12)\geq 0$

$-3(t(t-6)-2(t-6))\geq 0$

$-3(t-2)(t-6)\geq 0$

The critical points are:

$-3(t-2)(t-6)=0$

$t=2,6$

These two points divide the number line in 3 intervals $(-\infty,2),(2,6),(6,\infty)$ .

Intervals Check point $-3(t-2)(t-6)\geq 0$ Result

$(-\infty,2)$ 0 $(-)(-)(-)=(-)$ False

$(2,6)$ 4 $(-)(+)(-)=+>0$ True

$(6,\infty)$ 8 $(-)(+)(+)=(-)$ False

The inequality is true for (2,6) and the sign of inequality is $\geq$ . So, the ball is above 36 feet between 2 to 6 seconds.

$6-2=4$

Therefore, the required inequality is $-3t^2+24t\geq 36$ and the ball is 36 feet above for 4 seconds.

3 0

2 years ago

2 times 2 and three forths

Mrrafil [7]

2 * 2 and 3/4.

2 and 3/4 = (4*2 + 3) / 4 = (8 + 3) / 4 = 11 / 4

2 * 11/4 = 22 / 4 = 5 and 2/4

= 5 and 2/4 or 5 and 1/2 or 5.5

Hope this helps.

6 0

3 years ago

Use the distributive property to expand: x^-3 y^0(x^2-3x^5 y^4)

Soloha48 [4]

${x}^{ - 3} {y}^{0} ( {x}^{2} - 3 {x}^{5} {y}^{4} ) \\ = {x}^{ - 3} (1) ( {x}^{2} - 3 {x}^{5} {y}^{4} ) \\ = {x}^{ - 1} - 3 {x}^{2} {y}^{4}$

4 0

3 years ago

A cubical box without a top is 4 cm on each edge.it contains 64 identical 1cm cubes that exactly fill the box. How many of these

Len [333]

Answer:

52

Step-by-step explanation:

A cubical box without a top is 4 cm on each edge containing 64 identical 1 cm cubes.

We have to find the number of small cubes that actually touch the box.

Now, there are 4 layers of 16 cubes from bottom to top.

In the bottom-most layer, all the 16 small cubes will touch the bottom of the large cube.

Again, from the top three layers, only the outer small cubes will touch the sides of the large cube.

So, there are 12 small cubes in each top three layers that will touch the large cube.

Hence, in total there will be (16 + 12 ×3) = 52 small cubes that actually touch the large cube box. (Answer)

8 0

2 years ago