prove that:
tan80°=2tan 70°+ tan10°​

Answer:

when x = 39.25, y = 2.75

when x = 2.75, x = 39.25

Step-by-step explanation:

use substitution method

x+y = 42 ------ (1)

xy = 108 ------ (2)

from (1) ,

x+y = 42

y = 42-x ------ (3)

substitute (3) into (2)

xy = 108

x( 42-x ) = 108

42x - x² = 108

-x² + 42x - 108 = 0

x² - 42x + 108 = 0

use the following formula to solve the value of x:

[tex]i) \: x = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \: \\ ii) \: x = \frac{ - b - \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

a = 1

b = -42

c = 108

[tex]i) \: x = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

[tex]x = \frac{ - ( - 42) + \sqrt{( - 42) {}^{2} - 4(1)(108)} }{2(1)} [/tex]

[tex]x = \frac{42 + \sqrt{1764 - 432} }{2} [/tex]

[tex]x = \frac{42 + \sqrt{1332} }{2} [/tex]

[tex]x = \frac{42 + 6 \sqrt{37} }{2} [/tex]

[tex]x = 21 + 3 \sqrt{37} [/tex]

[tex]x = 39.25[/tex]

[tex]ii) \: x \: \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

[tex]x = \frac{ - ( - 42) - \sqrt{( - 42) {}^{2} - 4(1)(108} }{2(1)} [/tex]

[tex]x = \frac{42 - \sqrt{1764 - 432} }{2} [/tex]

[tex]x = \frac{42 - \sqrt{1332} }{2} [/tex]

[tex]x = \frac{42 - 6 \sqrt{37} }{2} [/tex]

[tex]x = 21 - 3 \sqrt{37} [/tex]

[tex]x = 2.75[/tex]

the 2 values of x are x = 39.25 and x = 2.75

substitute x = 39.25 into (3)

y = 42-x

y = 42-39.25

y = 2.75

substitute x = 2.75 into (3)

y = 42-x

y = 42-2.75

y = 39.25

when x = 39.25, y = 2.75

when x = 2.75, x = 39.25

Answer: 3

Step-by-step explanation:

1. 2²=4

2. 4*5=20

3. 180/20=9

4. √9=3

Hope this helped :)

Answer:

x = 3

Choice 2

Step-by-step explanation:

180 = 2^2 * x^2 * 5

180 = 20x^2

9 = x^2

x = 3

Checking:

180 = 2^2 * 8^2 * 5

180 = 4 * 9 * 5

180 = 36 * 5

180 = 180

Answer:12

Step-by-step explanation:

3x+3x+x+x=16

8x=16 so x =2

2*3=6 6*2=12

Answer:

12 sq ft

Step-by-step explanation:

let w = width

let 3w = length

w + w + 3w + 3w = 16

8w = 16

x = 2

Area = 3(2) x 2

A = 6 x 2

Answer:

D) g(x) = 2x-8

Step-by-step explanation:

Answer:

y = 3x + 3

Step-by-step explanation:

...............................

Answer:

12

Step-by-step explanation:

Answer: 12

Step-by-step explanation: Subtract 6 - 4 = 2. 2 * 2 = 4. 4 + 5 = 9. 9 - 3  = 6. 6 +6 = 12

Answer:

I think it is b

Step-by-step explanation:

it is 3a times all of the numbers in parenthases

hope you pass your test

HAPPY NEW YEAR

Answer:

the answer is 15a+12ac+6ab

Step-by-step explanation:

3a(5+4c+2b)

(3a)(5+4c+2b)

(3a)(5)+(3a)(4c)+(3a)(2b)

15a+12ac+6ab

6ab+12ac+15a

hope this helps!

Answer:

The unit cost is $3.15

Step-by-step explanation:

Here, we want to get the price per gallon

mathematically, that will be total amount spent divided by the number of gallons

That will be;

44.10/14 = $3.15

Answer:

la repuedta es la tila idnjxnfozmsuzndybdjsnshsbsb

Answer:

y=2x−3

Step-by-step explanation:

Answer:

16.27778 m/s

97666.6667 cm/min

Step-by-step explanation:

a. To convert km/hr into m/sec, multiply the number by 5 and then divide it by 18.

m/s = (58.6 * 5) /18 = 16.27778 m/s

b. 1 Kilometer/Hour = 1666.66666666667 Centimeter/Minute

so 58.6 * 1666.666 =97666.6667 cm/min

Answer:

7p

Step-by-step explanation:

Since it is 7 dollars per person, and p stands for person, the admission fee would be 7p.

Thank you, I hope you learned from this answer! If it did help, please mark this as brainliest! Thank you!

Answer:

1

Step-by-step explanation:

multiply 25 by .04

Answer:

Slope: (y2-y1)/(x2-x1)

(4+2)/(-16-5) = 6/-21 = -2/7

Y = -2/7x + b

5 = -2/7(-2) + b, b = 31/7

Equation: y = -2/7x + 31/7

Step-by-step explanation:

Answer:

$40.86

Step-by-step explanation:

just multiply 49.99 times 0.15 then multiply 49.99 times 0.10 then add those together to get 12.49 then multiply 49.99 times 0.0675 to get 3.37 then subtract 12.49 from 49.99 then add 3.37 to that so like

(49.99 - 12.49) + 3.37 = 40.86

Answer:

if i right it (0,2)

Step-by-step explanation:

i hope u get it right

Answer:

No Solutions

The two equations do not have any intersecting points, so the answer would be zero solutions.

Step-by-step explanation:

Answer:

the answer is (7,5) (5,5)

Answer:

x=14

Step-by-step explanation:

11x+18=172, subtract 17 from both sides, 11x=154, divide 11 from both sides, x=14

-9 is the answer

your welcome

Answer: its most likely p to the power of 6 :)

Step-by-step explanation:

Answer:

The answer for (p^3)^2 is p^6

Step-by-step explanation:

Hope this helps!

Plz, mark brainiest! ^.^

Answer:

The number of people living in both countries is 1.704 x 10⁹

Step-by-step explanation:

Given;

Population of people in China, = 1.381 x 10⁹

Population of people in united states, = 3.23 x 10⁸

The total number of people living in both countries is given as;

Total population = 1.381 x 10⁹ + 3.23 x 10⁸

Total population = 1.381 x 10⁹ +  0.323 x 10⁹

Total population = (1.381 + 0.323) x 10⁹

Total population = 1.704 x 10⁹

Therefore, the number of people living in both countries is 1.704 x 10⁹

Answer:

Christmas is in 10 days!

Other:

Brainliest? Thanks!

Answer:

1/4

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Answer:

x = 1/9

Step-by-step explanation:

we want to solve the proportion;

we simply cross multiply the values

Mathematically, that will be calculated as follows;

6x * 21 = 2 * 7

6x * 21 = 14

6x = 14/21

2(3x) = 2(7/21)

3x = 7/21

3x = 1/3

x = 1/3/3

x = 1/9

Answer:

You keep the inequality sign.

Step-by-step explanation:

Please mark brainliest.

Answer: you would keep the sign

Answer:

x = -4

y= -10

Step-by-step explanation:

Solving for x

-4x-y = 26

-4x-(2x-2) = 26

-6x+2 = 26

-6x = 24

x = -4

Solving for y

y = 2x-2

y = 2(-4) -2

y= -8-2

y = -10

9514 1404 393

Answer:

Step-by-step explanation:

The x-terms are the same in each equation, so subtracting one equation from the other will eliminate the x-variable.

The y-terms are opposites in the two equations, so adding the two equations will eliminate the y-variable.

Both strategies (subtracting, adding) are applicable to this system of equations.

Answer:

-1/3

Step-by-step explanation: