Simplify the ratio:

42 : 28 : 21

Please explain step by step to get marked as brainliest!

[tex]r = \left(\dfrac{33}{13}\right)[/tex]

[tex]s = \left(\dfrac{10}{13}\right)[/tex]

Step-by-step explanation:

Let's multiply and divide the given fraction by the conjugate of the denominator:

[tex]\dfrac{6+\sqrt{27}}{4-\sqrt{3}}×\dfrac{4+\sqrt{3}}{4+\sqrt{3}}[/tex]

[tex]\;\;\;\;= \dfrac{24 + 6\sqrt{3} + 4\sqrt{3} + \sqrt{27}\sqrt{3}}{13}[/tex]

[tex]\;\;\;\;=\frac{1}{13}(24 + 10\sqrt{3} + \sqrt{81})[/tex]

[tex]\;\;\;\;=\frac{1}{13}(33 + 10\sqrt{3})[/tex]

[tex]\;\;\;\;=\left(\dfrac{33}{13}\right) + \left(\dfrac{10}{13}\right)\dfrac{\sqrt{3}}{13}[/tex]

We can see here that

[tex]r = \left(\dfrac{33}{13}\right)[/tex]

[tex]s = \left(\dfrac{10}{13}\right)[/tex]

The value of the variable 'r' and 's' will be 33 and 18, respectively.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The two equations are given below.

(6 + √27) / (4 - √3) and  (r + s√3) / 13

Simplify the expression (6 + √27) / (4 - √3), then we have

[tex]\rightarrow \dfrac{6 + \sqrt{27}} { 4 - \sqrt3} \times \dfrac{4 + \sqrt3} { 4 + \sqrt3} \\\\[/tex]

⇒ [(6 + 3√3)(4 + √3)] / (4² - 3)

⇒ [(24 + 6√3 + 12√3 + 9)] / (16 - 3)

⇒ (33 + 18√3) / 13

Compare the expression (33 + 18√3) / 13 with (r + s√3) / 13, then the value of r and s will be given as,

r = 33

s = 18

The value of the variable 'r' and 's' will be 33 and 18, respectively.

More about the Algebra link is given below.

https://brainly.com/question/953809

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Answer:

  (a)  500 kg·m/s west

Step-by-step explanation:

Momentum is the product of mass and velocity.

  p = mv

  p = (50 kg)(10 m/2 west)

  p = 500 kg·m/s west

Answer:

31/99

Step-by-step explanation:

Becuase the numerator is lesser than the denominator

Answer:

C. 31/99

Step-by-step explanation:

It's C because a proper fraction is a fraction with a numerator that is less that it's denominator in its lowest terms

Answer:

1230

Step-by-step explanation:

[tex]\frac{\pi }{3}[/tex] x 49 x 24 = 1230 cm^3

Step-by-step explanation:

I am sorry but please give detailed question

Answer:

the answer is : 180° - (61° +61°) = 58°

Answer: D

Step-by-step explanation:

this is in y=Mx+ b form. M stands for the slope and b stands for the y intercept, or where the line intersects with the y-axis.

Going left to right, the line slopes downwards, therefore it is a negative Slope. This narrows down your answer to either a or d. the slope is -1 because you can only ever write x by itself if it means 1x. In this case it is negative so it would look like this: -x

for the y-intercept, simply look at where the line passes through the y-axis. In this case, it is positive 2.

your finished equation would be: y=-x+2

i hope this is helpful

Answer:

10

Step-by-step explanation:

substitute -8 into x.

f(-8)=-8+18=10

Answer:

10

Step-by-step explanation:

Answer:

1. 0.25

2. 105-40

3. 0.375

4. 0.5

5. 0.4 same as the number 6

Step-by-step explanation:

i hope it helpful i guess?

Answer:

nose que dice no hablo inglesh :v

Answer:

x > 5

Step-by-step explanation:

multiply the fractions, break up the fraction, group like terms, convert integer into a fraction, combine the fraction, combine the numerator, etc. hope this helps.

Power is the rate of doing work, and the power of the generating plant or

turbine and the duration of generation, gives the energy generated.

The correct responses are;

Reasons:

Number of homes in the town = 3,000 homes

The given capacity of the power plant = 12 MW = 12,000 kW

Power consumed by a household = 8,000 kWh per year

The price for electrical energy = $0.10 per kWh

Number of wind turbines = 10

WFWP = The West Fremont Wind Project

Capacity of each wind turbine = 1.2 MW

Cost of each wind turbine for 25 years = $3 million

(a) Number of hours of operation of the power plant = 8,000 hrs/yr

Required:

The amount of kWh of electricity produced in a year by the plant.

Solution:

The energy produced = Power × Time

∴ The energy produced = 12,000 kW × 8000 hr = 96,000,000 kWh

Therefore;

The energy produced by the plant in a year, E = 96 × 10⁶ kWh

(b) Energy consumed = Energy consumed per home × Number of homes

Therefore;

Energy consumed = 8,000 kWh/home × 3,000 homes = 24,000,000 kWh

The energy the community consumes in one year = 24 × 10⁶ kWh

(c) The cost per kWh = $0.10

The cost, C, of the energy per year is therefore

C = 24,000,000 kWh × $0.10/kWh = $2,400,000

The cost for 25 years = 25 × C = 25 × $2,400,000 = $60,000,000

The number of wind turbines = 10

Cost per wind turbine = $3 million

Total cost to operate the 10 wind turbine = $3 million × 10 = $30 million

Energy consumed = 24,000,000 kWh

Therefore;

24,000,000 kWh × 25 = $30 million

[tex]\displaystyle 1 \ kWh = \frac{\$ 30 \ million}{25 \times 24,000,000 \ kWh} = \mathbf{\$0.05/kWh}[/tex]

The cost to the community of the electricity supplied by WFWP over 25 years is $0.05/kWh.

Learn more about energy and power here:

https://brainly.com/question/24592300

Answer:

6.9+1

Step-by-step explanation:

hope it helps

[tex]\huge\mathfrak\blue{ ☃ }[/tex]

Answer:

the product of six and nine is fifty five

so tan = me sun bathing for 2.5 second

Answer:

y = -2x - 1

See image

Step-by-step explanation:

The "slope-intercept" form of the equation is the

y = mx + b form

So you need to find the slope (m) and the y-intercept (b), which you are able to find on the image in the question.

Slope (m) tells how steep a line is and whether it goes up or down from left to right. It also works just like directions, from any point on the line to any other point on the line.

The y-intercept (b) is the point on the line where the line crosses the y-axis.

The slope is -2 and the y-intercept is -1

So the equation is

y = -2x - 1

See image

Answer:

1-2

Step-by-step explanation:

honestly idek what this stuff is I just need points

Answer:

Other factor is 70

Step-by-step explanation:

Let,

Other factor = x

Then,

x × 60 = 4200

x = 4200/60

x = 420/6

x = 70

∴Another factor is 70.

Answer:

Solution given

let two factor be a and b.

if one factor a=60, then b=?

we have

product of factor=4200

a*b=4200

60*b=4200

b=[tex]\frac{4200}{60}=70[/tex]

Step-by-step explanation:

it will be equal to the photo

median 5

Step-by-step explanation:

a lot of typos in the problem description.

if I understand correctly, the line contains the point (5, 10) and has a slope of 1.

and we need to give the line equation in slope-intercept form.

that means it has to look like

y = ax + b

a is the slope and b is the y-intercept (hence the name of the form).

we know a = 1.

we can use use the point-slope form to start and then transform it into the slope-intercept form.

point-slope means

y - y1 = a(x - x1)

a is again the slope, and (x1, y1) is a point on the line.

so,

y - 10 = 1(x - 5) = x - 5

now we transform it (adding 10 on both sides)

y = x + 5

and that's it.

Answer:

Width = 10 inches

Step-by-step explanation:

Given the perimeter of a rectangle of 68 inches, and a length that is 14 inches longer than its width.

We can establish the following values to help us solve for the width of a rectangle:

Perimeter (P) = 68 inches

Length (L) = 14 + W inches

Width (W) = unknown

P =  2(L + W)  ⇒ This is the same as P = 2L + 2W, except that 2 is factored out from the right-hand side.

Divide both sides by 2:

[tex]\displaystyle\mathsf{\frac{P}{2}\:=\:\frac{2(L\:+\:W)}{2}}[/tex]

[tex]\displaystyle\mathsf{\frac{P}{2}\:=L\:+\:W}[/tex]

Substitute the value of the Perimeter and the length (L) into the formula:

[tex]\displaystyle\mathsf{\frac{68}{2}\:=14\:+W\:+\:W}[/tex]

Combine like terms on the right-hand side, and simplify the left-hand side of the equation:

[tex]\displaystyle\mathsf{34\:=14\:+2W}[/tex]

Subtract 14 from both sides:

34 - 14 = 14 - 14 + 2W

20 = 2W

Divide both sides by 2 to solve for the width (W):

[tex]\displaystyle\mathsf{\frac{20}{2}\:=\:\frac{2W}{2}}[/tex]

W = 10 inches

Therefore, the width of the rectangle is 10 inches.

Verify whether the derived value for the width is correct:

P = 2L + 2W

68 = 2(14 + 10) + 2(10)

68 = 2(34) + 20

68 = 48 + 20

68 = 68 (True statement).  

Thus, the length of the rectangle is 34 inches, and the width is 10 inches.

Answer:

I think it's 28,700,000 feet

Step-by-step explanation:

Answer:

34,971.99

Step-by-step explanation:

Answer:

Hepatitis C.

Step-by-step explanation:

Answer:

p=14 ft

Step-by-step explanation:

The figure that meets these conditions is the square

The perimeter:

4(3.5) = 14 ft.

Hope this helps

150−28w

i think i dont know

Answer:

10.7°

Step-by-step explanation:

SOH CAH TOA

Tan(BCA) = x/y

= 4/21

BCA= Tan`¹(4/21)

= 10.7856

to 3SF = 10.7°

You have to add.

Step-by-step explanation:

I'm trash at math.