4. What is the mass of a truck if it produces a force of 14,000N while accelerating at a rate of

24 students in a class took an algebra test.

Vlada [557]

Answer:

75 % passed

25 % did NOT pass

Step-by-step explanation:

8 0

2 years ago

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Find the obtuse angle between the following pair of straight lines.

ioda

Given:

$y=-2$

$y=\sqrt{3}x-1$

To find:

The obtuse angle between the given pair of straight lines.

Solution:

The slope intercept form of a line is

$y=mx+b$ ...(i)

where, m is slope and b is y-intercept.

The given equations are

$y=0x-2$

$y=\sqrt{3}x-1$

On comparing these equations with (i), we get

$m_1=0$

$m_2=\sqrt{3}$

Angle between two lines whose slopes are $m_1\text{ and }m_2$ is

$\tan \theta=\left|\dfrac{m_2-m_1}{1+m_1m_2}\right|$

Putting $m_1=0$ and $m_2=\sqrt{3}$ , we get

$\tan \theta=\left|\dfrac{\sqrt{3}-0}{1+(0)(\sqrt{3})}\right|$

$\tan \theta=\left|\dfrac{\sqrt{3}}{1+0}\right|$

$\tan \theta=\pm \sqrt{3}$

Now,

$\tan \theta= \sqrt{3}$ and $\tan \theta=-\sqrt{3}$

$\tan \theta= \tan 60^\circ$ and $\tan \theta=\tan (180^\circ-60^\circ)$

$\theta= 60^\circ$ and $\theta=120^\circ$

$120>90$ , so it is an obtuse angle and $60$ , so it is an acute angle.

Therefore, the obtuse angle between the given pair of straight lines is 120°.

6 0

3 years ago

Two cylindrical containers, C and D, with different capacities are shown below. What is the total volume of liquid held in these

Zielflug [23.3K]

Answer:

Option D. (x + 4)(x + 1)

Step-by-step explanation:

From the question given above, the following data were obtained:

C = (6x + 2) L

D = (3x² + 6x + 9) L

Also, we were told that half of container C is full and one third of container D is full. Thus the volume of liquid in each container can be obtained as follow:

Volume in C = ½C

Volume in C = ½(6x + 2)

Volume in C = (3x + 1) L

Volume in D = ⅓D

Volume in D = ⅓(3x² + 6x + 9)

Volume in D = (x² + 2x + 3) L

Finally, we shall determine the total volume of liquid in the two containers. This can be obtained as follow:

Volume in C = (3x + 1) L

Volume in D = (x² + 2x + 3) L

Total volume =?

Total volume = Volume in C + Volume in D

Total volume = (3x + 1) + (x² + 2x + 3)

= 3x + 1 + x² + 2x + 3

= x² + 5x + 4

Factorise

x² + 5x + 4

x² + x + 4x + 4

x(x + 1) + 4(x + 1)

(x + 4)(x + 1)

Thus, the total volume of liquid in the two containers is (x + 4)(x + 1) L.

6 0

3 years ago

help this is hard Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s

Nesterboy [21]

Answer:

x = $-\frac{3}{b}$

x = -1

Step-by-step explanation:

The given equation is,

-2(bx - 5) = 16

Dividing by (-2) on both sides of the equation,

$\frac{-2(bx-5)}{(-2)}=\frac{16}{(-2)}$

(bx - 5) = -8

By adding 5 on both the sides of the equation,

(bx - 5) + 5 = -8 + 5

bx = -3

Dividing by 'b' on both the sides of the equation,

$\frac{bx}{b}=\frac{-3}{b}$

x = $-\frac{3}{b}$

If b = 3,

x = $-\frac{3}{3}$

x = -1

6 0

3 years ago

Answer ASAP and both questions :D

dangina [55]

the student needed to place a ten outside the radical, as a perfect square of 100 composes 200. This way, a two should be left under the radical sign. Also, this would be about 14.1 because 14^2 is 196 and 15^2 is 225. The correct answer must be less than 225, more than 196, but closer to 196. Therefore, a .1 is added to the 14

4 0

3 years ago

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