All categories

3 years ago

3[x + 3(4x – 5)] = 15x – 24

Mathematics

1 answer:

Alex17521 [72]3 years ago

5 0

Answer:

$\boxed{ \bold{ \huge{ \boxed{ \sf{x = 0.875}}}}}$

Step-by-step explanation:

$\sf{3[ x + 3(4x - 5)] = 15x - 24}$

Distribute 3 through the parentheses

⇒ $\sf{3[ x + 12x - 15 ] = 15x - 24}$

Collect like terms : 12x and x

⇒ $\sf{3[ 13x - 15 ] = 15x - 24}$

Distribute 3 through the parentheses

⇒ $\sf{39x - 45 = 15x - 24}$

Move 15x to left hand side and change it's sign

Similarly, move 45 to right hand side and change it's sign

⇒ $\sf{39x - 15x = - 24 + 45}$

Collect like terms

⇒ $\sf{24x = - 24 + 45}$

Calculate

⇒ $\sf{24x = 21}$

Divide both sides of the equation by 24

⇒ $\sf{ \frac{24x}{24} = \frac{21}{24}}$

Calculate

⇒ $\sf{x = 0.875}$

Hope I helped!

Best regards! :D

You might be interested in

The local grocery store has sorted apples by size. The distribution is approximately normal. The large apples have a mean diamet

NikAS [45]

Answer:

Step-by-step explanation:

Approximately 0.2% of the apples will be more than three standard deviations above the mean size. In a bin of 100 apples, 0.2% of 100=0.2% apples, this rounds down to zero apples that size or larger. (In a bin of 500 apples, there could be one apple of that size.)

3 0

3 years ago

if 20 men can finish a piece of work in 30 days how many additional numbers of mains will be employed to finish the work in 24 d

Cerrena [4.2K]

Answer:

Step-by-step explanation:

no of days no of men

30 20

24 20

30/24=x/20

24 x=30*20

24x=600

x=600/24

x=25

therefore 5 more men are needed to complete the work in 24 days

8 0

3 years ago

Find the six trig function values of the angle 240*Show all work, do not use calculator

-BARSIC- [3]

Solution:

Given:

$240^0$

To get sin 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, sin 240 will be negative.

$sin240^0=sin(180+60)$

Using the trigonometric identity;

$sin(x+y)=sinx\text{ }cosy+cosx\text{ }siny$

Hence,

$\begin{gathered} sin(180+60)=sin180cos60+cos180sin60 \\ sin180=0 \\ cos60=\frac{1}{2} \\ cos180=-1 \\ sin60=\frac{\sqrt{3}}{2} \\ \\ Thus, \\ sin180cos60+cos180sin60=0(\frac{1}{2})+(-1)(\frac{\sqrt{3}}{2}) \\ sin180cos60+cos180sin60=0-\frac{\sqrt{3}}{2} \\ sin180cos60+cos180sin60=-\frac{\sqrt{3}}{2} \\ \\ Hence, \\ sin240^0=-\frac{\sqrt{3}}{2} \end{gathered}$

To get cos 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, cos 240 will be negative.

$cos240^0=cos(180+60)$

Using the trigonometric identity;

$cos(x+y)=cosx\text{ }cosy-sinx\text{ }siny$

Hence,

$\begin{gathered} cos(180+60)=cos180cos60-sin180sin60 \\ sin180=0 \\ cos60=\frac{1}{2} \\ cos180=-1 \\ sin60=\frac{\sqrt{3}}{2} \\ \\ Thus, \\ cos180cos60-sin180sin60=-1(\frac{1}{2})-0(\frac{\sqrt{3}}{2}) \\ cos180cos60-sin180sin60=-\frac{1}{2}-0 \\ cos180cos60-sin180sin60=-\frac{1}{2} \\ \\ Hence, \\ cos240^0=-\frac{1}{2} \end{gathered}$

To get tan 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, tan 240 will be positive.

$tan240^0=tan(180+60)$

Using the trigonometric identity;

$tan(180+x)=tan\text{ }x$

Hence,

$\begin{gathered} tan(180+60)=tan60 \\ tan60=\sqrt{3} \\ \\ Hence, \\ tan240^0=\sqrt{3} \end{gathered}$

To get cosec 240 degrees:

$\begin{gathered} cosec\text{ }x=\frac{1}{sinx} \\ csc240=\frac{1}{sin240} \\ sin240=-\frac{\sqrt{3}}{2} \\ \\ Hence, \\ csc240=\frac{1}{\frac{-\sqrt{3}}{2}} \\ csc240=-\frac{2}{\sqrt{3}} \\ \\ Rationalizing\text{ the denominator;} \\ csc240=-\frac{2}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}} \\ \\ Thus, \\ csc240^0=-\frac{2\sqrt{3}}{3} \end{gathered}$

To get sec 240 degrees:

$\begin{gathered} sec\text{ }x=\frac{1}{cosx} \\ sec240=\frac{1}{cos240} \\ cos240=-\frac{1}{2} \\ \\ Hence, \\ sec240=\frac{1}{\frac{-1}{2}} \\ sec240=-2 \\ \\ Thus, \\ sec240^0=-2 \end{gathered}$

To get cot 240 degrees:

$\begin{gathered} cot\text{ }x=\frac{1}{tan\text{ }x} \\ cot240=\frac{1}{tan240} \\ tan240=\sqrt{3} \\ \\ Hence, \\ cot240=\frac{1}{\sqrt{3}} \\ \\ Rationalizing\text{ the denominator;} \\ cot240=\frac{1}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}} \\ \\ Thus, \\ cot240^0=\frac{\sqrt{3}}{3} \end{gathered}$

5 0

9 months ago

WILL GIVE BRAINLIEST ANSWER! A circular flower bed is 21 m in diameter and has a circular sidewalk around it that is 33m wide. F

Alina [70]

Answer:

The area of the sidewalk is 144.44 m².

The 2-m wide walk adds 4 m to the diameter, making it 21+4=25.

Since the radius is half the diameter, r = 25/2 = 12.5.

The area of the entire bed with walkway is 3.14(12.5)² = 490.625 m².

The diameter of the bed is 21, so the radius is 21/2 = 10.5.

The area of just the flower bed is 3.14(10.5)² = 346.185.

The difference between the two is 490.625-346.185 = 144.44 m². This is the area of the walkway.

<em>Have a Great Day!</em>

5 0

3 years ago

Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 10

WINSTONCH [101]

Answer:

The function for the outside temperature is represented by $T(t) = 85\º + 15\º \cdot \sin \left[\frac{t-6\,h}{24\,h} \right]$ , where t is measured in hours.

Step-by-step explanation:

Since outside temperature can be modelled as a sinusoidal function, the period is of 24 hours and amplitude of temperature and average temperature are, respectively:

Amplitude

$A = \frac{100\º-70\º}{2}$