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Answer:

[tex]\sf\longmapsto \: ( \sqrt{3} - 2)x + (2 \sqrt{3 } + 1)y = - 1 + 8 \sqrt{3} [/tex]

Step-by-step explanation:

It is given that –

Slope of the first line is–

[tex]\sf\longmapsto \: m_{1} = 2[/tex]

Let,

the slope of the Another line be –

[tex]\sf\longmapsto \: m _{2}[/tex]

Now,

The angle between the two lines is 60°.

Let's start solving!

[tex]\sf\longmapsto \: \tan(60°) | \frac{ m_{1} - m_ {2} }{1 + m_{1} m_ {2}} | [/tex]

[tex]\sf\longmapsto \: \sqrt{3} = | \frac{2 -m_{2} }{1 + 2m_{2}} | [/tex]

[tex]\sf\longmapsto \: \sqrt{3} = ± \: \: ( \frac{2 -m_{2} }{1 + 2m_{2}} )[/tex]

[tex]\sf\longmapsto \: \sqrt{3} = \frac{2 -m_{2} }{1 + 2m_{2}} [/tex]

[tex]\sf\longmapsto \: \sqrt{3} (1 + 2m_{2}) = 2 - m_{2}[/tex]

[tex]\sf\longmapsto \: \sqrt{3} + 2 \sqrt{3} m_{2} + m_{2} = 2[/tex]

[tex]\sf\longmapsto \: m_{2} = \frac{2 - \sqrt{3} }{(2 \sqrt{3} + 1) } [/tex]

The equation of line passing through point (2,3) and having a slope of –

[tex]\sf\longmapsto \: m_{2} = \frac{(2 - \sqrt{3} )}{2 \sqrt{3} + 1 } [/tex]

is–

[tex]\sf\longmapsto \: (y - 3) = \frac{2 - \sqrt{3} }{2 \sqrt{3} + 1 } (x - 2)[/tex]

[tex]\sf\longmapsto \: ( 2\sqrt{3} + 1)y - 3(2 \sqrt{3} + 1) = (2 - \sqrt{3} )x - 2(2 - \sqrt{3} [/tex]

[tex]\sf\longmapsto \: ( \sqrt{3} - 2)x + (2 \sqrt{3 } + 1)y = - 1 + 8 \sqrt{3} [/tex]

Hence the equation of the other line is -

[tex]\sf\longmapsto \: ( \sqrt{3} - 2)x + (2 \sqrt{3 } + 1)y = - 1 + 8 \sqrt{3} [/tex]

It will take twelve (12) plumbers 9 weeks to install the same number of lines

From the question,

We have that, 18 plumbers can install 540 water lines in 6 weeks,

To determine how long it will take 12 plumbers to install the same number of lines,

First, we will determine how long it will take 1 plumber.

If 18 plumbers can install 540 water lines in 6 weeks

Then,

1 plumber will install 540 water lines in 18 × 6 weeks

18 × 6 weeks = 108 weeks

∴ It will take 1 plumber 108 weeks to install 540 water lines

Now, for the number of weeks it will take 12 plumbers

If 1 plumber can install 540 water lines in 108 weeks

Then,

12 plumbers will install 540 water lines in [tex]\frac{108}{12}[/tex] weeks

[tex]\frac{108}{12} = 9 \ weeks[/tex]

Hence, it will take twelve (12) plumbers 9 weeks to install the same number of lines

Learn more here: https://brainly.com/question/18880656

Answer:

F=86°

G=75°

H=19°.........

Answer:

[tex]7.15*10^{-4}[/tex]

Step-by-step explanation:

[tex](8.1*10^{-4})-(9.5*10^{-5})=0.00081-0.000095\\\\=0.000715 = 7.15*10^{-4}[/tex]

Answer:

0.68 repeating as a fraction

0.68 repeating as a fraction

Answer:

a. ratio is 180:240

B. ratio is 240:180

C. ratio is 420:180

d. ratio is 240:420

Hope this helps!!

Answer:

the answer is a because it has no decimal

it is in square root

Answer:

Step-by-step explanation:

To solve, we first need to know how to find the average of a group of numbers. To find the average of a group of numbers, you add all the numbers together and divide that answer by the number of numbers you have. For instance, to find the average of 1, 2, 3, 4 and 5, we would add all the numbers together, which would equal 15. We would then divide that number by 5, because there are 5 numbers total: 15/5 = 3. So the average is 3.

Now, to find the average in your problem, we need to look at what we know:

He received an 85 and 60 on two of the test scores

He needs an overall average of 70

Let's set this up in equation form:

%2885+%2B+60+%2B+x%29%2F3+%3E=+70

Now, let's get rid of our fraction on the left. We can do this by multiplying the entire equation by 3, giving us:

85 + 60 + x >= 210

Next, combine the numbers on the left, which will give us:

145 + x >= 210

Finally, subtract 145 from both sides, which will give us our answer:

145 + x - 145 >= 210 - 145 =

x >= 65

So, in order to average at least 70, he must score a 65 or higher on his third test.

Answer:

(0, 7) is an ordered pair solution to 3x + y = 7

Step-by-step explanation:

Given the equation 3x + y = 7, find a solution (ordered pair).

There are an infinite number of possible solutions.  Let's focus on just one:

Let x = 0.  Then y = 7, and (0, 7) is an ordered pair solution to 3x + y = 7

Answer: 8 miles a day

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

We can use the points on the line to find the slope

(0,-1) and (1,5)

Using the slope formula

m = ( y2-y1)/(x2-x1)

   = (5 - -1)/(1-0)

   = (5+1)/(1-0)

    = 6/1

   = 6

Answer:

m = 6 units

Step-by-step explanation:

To get from point (0, -1) to point (1, 5) that are on the line we have to go up 6 units and 1 unit to the right

slope = rise /run = 6/ 1 = 6

Answer:

-12

Step-by-step explanation:

Answer:

12.2

Step-by-step explanation:

BC = √ABsq + √CAsq

BC = √11.9sq + √2.7sq

BC = √141.6 + √7.3

BC = √148.9

BC =  12.2

Answer:

heres my photo + answer

Step-by-step explanation:

0.15

+ 0.36

____

Answer:

Well, 1 gallon is 4 quarts so if Finn lives in a ½ Gallon tank divide 10 by 0.5 and you get 20, so his new tank is 20 times bigger than his old bowl.

Step-by-step explanation:

Math rocks! Have fun!

Answer:

264

Step-by-step explanation:

to find one hour

110÷5=22 per hour

12×22=264

Answer: Lamar would make $264 in 12 hours of work.

First we would try to find how much he would make in an hour, so technically the unit rate.

TO find the unit rate we have to do 110/5 which is equal to $22

Then we know that Lamar is working for 12 hours and that he makes $22 per hour. SO,  12 times 22 is 264.

Step-by-step explanation:

I hope this helps, if you are having a tough time with math you can use:

khan academy

math nation

and many more free sites!

Answer:

d. 4x+12

Step-by-step explanation:

distribute the 4

4*x =4x

4*3=12

therefore its

4x+12

Answer:

D

Step-by-step explanation:

4(x+3)

(4 times x) + (4 times 3)

4x + 12 = D

Let's solve your equation step-by-step.

(3x−2)(x+6)−(x−1)(2x)=103

Step 1: Simplify both sides of the equation.

x2+18x−12=103

Step 2: Subtract 103 from both sides.

x2+18x−12−103=103−103

x2+18x−115=0

Step 3: Factor left side of equation.

(x−5)(x+23)=0

Step 4: Set factors equal to 0.

x−5=0 or x+23=0

x=5 or x=−23

Answer:

x=5 or x=−23

Answer:

x=80, y=55

Step-by-step explanation:

x is on a line so 180-100=80

x= 80

angles of a triangle are 180 so 180-45-80=55

y=55

Answer:

it's D, 27

Anything in the middle would be both so just add only the yellow and red numbers, not orange

this is the full answer for you're Q

please give me good

The time taken by the object to hit the ground will be 9 seconds.

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given that an object is launched at 9.8 meters per second (m/s) from a 308.7-meter tall platform. The function that represents the object's height s at time t seconds after launch is

s(t) = −4.9t²+ 9.8t + 308.7

To find the time taken put the function equal to zero.

−4.9t²+ 9.8t + 308.7 = 0

t² - 2t - 63 = 0

t² - 9t + 7t - 63 = 0

t ( t - 9 ) +7 ( t - 9 ) = 0

( t - 9 ) ( t + 7 ) = 0

t = 9 and -7(ignore)

t = 9 seconds

Therefore, the time taken by the object to hit the ground will be 9 seconds.

To know more about a quadratic equation follow

https://brainly.com/question/2264627

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Answer:

The answer is 1, Hope that Helps! :)

Step-by-step explanation:

I answered first but didn't get braintlyist...ok.....

Answer:

the answer is 1

Step-by-step explanation:

one is the answer

Answer:

[tex]x=\pm i[/tex]

Step-by-step explanation:

[tex]3x^2+5=2[/tex]

[tex]3x^2=-3[/tex]

[tex]x^2=-1[/tex]

[tex]x=\pm i[/tex]

Answer:

-8

Step-by-step explanation:

I’ll substitute x for the blank space:

-2 = x + 6

-2 - 6 = x

x = -8

-8 + 6 = -2 ✅

Answer:

c. 2/3

Step-by-step explanation:

Since the line is going up to the right it is a positive slope. Therefore it can't be a or d.

The slope is 2/3 because to connect the dots you have to go up 2 and to the right 3.

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Answer:

4

Step-by-step explanation:

2 + 2 = 4

Answer:

x = 35°

Step-by-step explanation:

Co-interior angles add up to 180°, so:

2x + 43 + 2x - 3 = 180° (now, simplify)

4x + 40 = 180° (subtract 40 from both sides)

4x = 140° (divide both sides by 4)

x = 35°

Hope this helps!

Answer:

x=35

Step-by-step explanation:

given: two lines cut by a transversal to find x

solution: the given two angles are supplementary since they are consecutive interior angles.

(2x+43)+(2x-3)=180°

⇒ 4x+40=180°⇒4x=140°

⇒x=[tex]\frac{140}{4}[/tex]=35

hope this helps :)