All categories

3 years ago

Show that x = -2 is a solution of 3x² + 13x + 14 = 0

Mathematics

1 answer:

Oliga [24]3 years ago

3 0

Answer:

x= -2 is correct answer

Step-by-step explanation:

3(-2×-2)+13(-2)+14=0

3(4)+13(-2)+14=0

12+(-26)+14=0

12-26+14=0

12+14-26=0

26-26=0

0=0

You might be interested in

If it costs $3.50 per square foot, what is the approximate total cost of making this

Leni [432]

Answer:

the right answer would be C

7 0

2 years ago

Read 2 more answers

The altitude of Death Valley California is 282 ft below sea level of hot air balloon is launched From The Bottom Of Death Valley

asambeis [7]

Answer:

177 ft below sea level.

Step-by-step explanation:

Initial altitude of the hot air balloon = 282 below sea level

Rate of rise of balloon = 10 ft / second

Time = 12 seconds

Total rise in 12 seconds = Rate of rise of balloon $\times$ Time

$\Rightarrow 10 \times 12$ = 120 ft

Now, we will have to subtract to find the new altitude.

New altitude = 282 - 120 = 162 ft

Now, it is given that balloon Captain lowers the balloon 15 ft.

To find the final altitude, we will have to add it to the previous altitude.

Therefore, the final altitude = 162 + 15 = <em>177 ft below sea level </em>

6 0

3 years ago

Find the volume of the solid.

dmitriy555 [2]

In Cartesian coordinates, the region (call it $R$ ) is the set

$R = \left\{(x,y,z) ~:~ x\ge0 \text{ and } y\ge0 \text{ and } 2 \le z \le 4-x^2-y^2\right\}$

In the plane $z=2$ , we have

$2 = 4 - x^2 - y^2 \implies x^2 + y^2 = 2 = \left(\sqrt2\right)^2$

which is a circle with radius $\sqrt2$ . Then we can better describe the solid by

$R = \left\{(x,y,z) ~:~ 0 \le x \le \sqrt2 \text{ and } 0 \le y \le \sqrt{2 - x^2} \text{ and } 2 \le z \le 4 - x^2 - y^2 \right\}$

so that the volume is

$\displaystyle \iiint_R dV = \int_0^{\sqrt2} \int_0^{\sqrt{2-x^2}} \int_2^{4-x^2-y^2} dz \, dy \, dx$

While doable, it's easier to compute the volume in cylindrical coordinates.

$\begin{cases} x = r \cos(\theta) \\ y = r\sin(\theta) \\ z = \zeta \end{cases} \implies \begin{cases}x^2 + y^2 = r^2 \\ dV = r\,dr\,d\theta\,d\zeta\end{cases}$

Then we can describe $R$ in cylindrical coordinates by

$R = \left\{(r,\theta,\zeta) ~:~ 0 \le r \le \sqrt2 \text{ and } 0 \le \theta \le\dfrac\pi2 \text{ and } 2 \le \zeta \le 4 - r^2\right\}$

so that the volume is

$\displaystyle \iiint_R dV = \int_0^{\pi/2} \int_0^{\sqrt2} \int_2^{4-r^2} r \, d\zeta \, dr \, d\theta \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} \int_2^{4-r^2} r \, d\zeta\,dr \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} r((4 - r^2) - 2) \, dr \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} (2r-r^3) \, dr \\\\ ~~~~~~~~ = \frac\pi2 \left(\left(\sqrt2\right)^2 - \frac{\left(\sqrt2\right)^4}4\right) = \boxed{\frac\pi2}$

3 0

1 year ago

A contractor is installing tiles on a floor that measures 132 x 216 inches. If each tile measures 4 x 4 inches, how many tiles w

Kay [80]

Answer:

1782 tiles

Step-by-step explanation:

Given that:

Dimension fo floor = 132 x 216 inches

Area of floor = 132 * 216 = 28512 in²

Dimension of tiles = 4 * 4 inches

Area of tiles = 4 * 4 = 16 in²

Number of tiles needed to cover floor :

Area of floor / Area of tiles

28512 in² / 16 in²

= 1782 tiles

5 0

2 years ago

Base of triangle exceeds the height by 4. If the area is 178.5 square inches, find the length of the base and the height of the

xxMikexx [17]

Area of a triangle:
A= (1/2)(bh)

In this problem we are given:
A= 178.5 $in^{2}$
b= h+4 in
h= UNKNOWN ("h")

Plug in our values into the area equation and solve for "h":
$A= \frac{1}{2} bh$
$178.5 = \frac{1}{2} ((h+4)h)$ (multiply each side by 2 to get rid of the 1/2)
$357 = ((h+4)h)$
$357 = h^{2} +4h$
$0= h^{2} +4h -357$
(357/21=17)
$0= (h+21)(h-17)$ (solve both inequalities separately)

$0= (h+21)$
$-21= h$ ( a negative height is not possible so, this answer is incorrect.)

$0=(h-17)$
$h=17 in$

Answer: base = (h+4)= (17+ 4) b= 21 in h= 17in

Please comment with any further questions! :)

5 0

3 years ago

Show that x = -2 is a solution of 3x² + 13x + 14 = 0​

Show that x = -2 is a solution of 3x² + 13x + 14 = 0