A line passes through the points (2, –3) and (–4, 3). What is its equation in slope-intercept form?

Answer:

B. y=x+4

Step-by-step explanation:

Answer:  see proof below

Step-by-step explanation:

Note: The given equation cannot be proven. Instead I will prove:

[tex]\cot(2\alpha)=\dfrac{\cot^2\alpha-1}{2\cot \alpha}[/tex]

Use the Reciprocal Identity:  cot A = (cos A)/(sin A)

Use the following Double Angle Identities:

cos (2A) = cos² A - sin² A

sin (2A) = 2 sin A · cos A

Proof LHS → RHS:

LHS:                        cot (2A)

[tex]\text{Reciprocal:}\qquad \qquad \dfrac{\cos (2\alpha)}{\sin (2\alpha)}[/tex]

[tex]\text{Double Angle:}\qquad \quad \dfrac{\cos^2 \alpha-\sin^2 \alpha}{2\sin \alpha \cdot \cos \alpha}[/tex]

[tex]\text{Manipulate:}\qquad \quad \dfrac{\cos^2 \alpha-\sin^2 \alpha}{2\sin \alpha \cdot \cos \alpha}\bigg(\dfrac{\frac{1}{\sin^2 \alpha}}{\frac{1}{\sin^2 \alpha}}\bigg)[/tex]

                         [tex]=\dfrac{\frac{\cos^2 \alpha}{\sin^2 \alpha}-\frac{\sin^2 \alpha}{\sin^2 \alpha}}{\frac{2\sin \alpa \cdot \cos \alpha}{\sin \alpha \cdot \sin \alpha}}[/tex]

                         [tex]=\dfrac{\cot^2 \alpha-1}{2\cot \alpha}[/tex]

LHS = RHS [tex]\checkmark[/tex]

Answer:

see proof below

Step-by-step explanation:

cot(2a) = (cot^2a - 1)/2cota

Remember that cotangent is the inverse of tan...

cot = 1/tan => cot(2a) = 1/tan2a

Here I used the formula for tan2a, or in other words tan2a = 2tana/1 - tan^2a

Therefore the inverse of tan2a, 1/tan2a, should be the inverse of 2tanA/1 - tan^2a, or 1 - tan^2a/2tana => 1/tan2a = 1 - tan^2a/2tana = cot(2a)

The reverse is true as well, tan is the inverse of cotangent...tanA = 1/cotA

cot(2a) = 1 - tan^2a/2tana = 1 - (1/cot^2a)/2(1/cota)

= cot^2a - 1/cot^2a * cota/2

= cot^2a - 1/2cota

L.H.S = R.H.S, hence proved

Answer:

oil and vinegar ( it's actually water )

Step-by-step explanation:

tha answer is milk and eggs

Answer: x = -5

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

Your answer is correct.

Step-by-step explanation:

82.3 - 46.5 = 35.8

Answer:

the answer is 12

Step-by-step explanation:

you substitute the y with 12

Answer:

(0, - 1). thats the answer

To solve this problem, we need to know 2 relationships:

The distance of AC is the sum of AB and BC.

[tex]AC = AB + BC[/tex]

We know this since the distance of going from A to C (AC) is the same as going from A to B (AB), then B to C (BC).

The distance of AB is the same as AC.

[tex]AB = BC[/tex]

We know this since B is in the middle of AC, so the distance from B to A (BA) is the same as the distance from B to C (BC).

You can see the attached image (at the bottom) for a visualization of this.

Since we know the values of AB and BC...

[tex]AB = x+9\\BC = 3x-7[/tex]

...we can put these values into our 2nd equation and solve for x:

[tex]AB = BC\\x + 9 = 3x -7[/tex]

Add 7 to both sides:

[tex]x + 16 = 3x[/tex]

Subtract x from both sides:

[tex]16 = 2x[/tex]

Divide both sides by 2:

[tex]8 = x\\x = 8[/tex]

Knowing x, we can find the distance of AC using our first equation.

[tex]AC = AB + BC[/tex]

Let's put in the values of AB and BC:

[tex]AC = (x+9) + (3x-7)[/tex]

Before we put in x = 8, we can simplify this:

[tex]AC = (x+9) + (3x-7)\\AC = x + 9 + 3x -7\\AC = x + 3x + 9 -7\\AC = 4x + 9 - 7\\AC = 4x+2[/tex]

We group x and 3x and add those together. Then we subtract 7 from 9.

With this equation, we can put in x = 8:

[tex]AC = 4x +2\\AC = 4*8 + 2[/tex]

Since 4 * 8 = 32:

[tex]AC = 4 * 8 + 2\\AC = 32 + 2\\AC = 34[/tex]

Finally, we have found both x and AC.

x = 8

AC = 34

Answer:

110

Step-by-step explanation:

Answer: A. $5 × 25

Step-by-step explanation:

Given the following :

Number of cartons of specialty paper ordered = 24 cartons

Regular price for a carton = $6.88

Discount given off each carton = $1.75

Hence,

Discounted price per carton = $(6.88 - 1.75) = $5.13

Actual amount to be paid for the order :

Discounted price * number of cartons to be ordered

$5.13 * 24

Hence, a reasonable estimate will be :

$5.13 = $5( nearest whole number)

24 can be rounded to 25 (this covers for the $0.13 on the discounted cost per carton)

Reasonable estimate :

$5 × 25

Answer:

The answer is  A. $5 × 25

Step-by-step explanation:

Given that the total number of cartons is 24

the price per carton originally is $6.88

the discount is $1.75

hence the company will have to pay 6.88-1.75= $5.13

hence the price per carton upon removal of the discount is  $5.13

for all 24 cartons, the company will have to pay 24*5.13  

A reasonable estimate from the given option is  

A. $5 × 25

Answer:

2<x<3

Step-by-step explanation:

we can divide all sides of this inequality by 2 to isolate x. 2<x<3. this means that x is in between the values of 2 and 3 for this inequality to make sense.

Step-by-step explanation:

i belive it would be 54 degrees. hope this helped

x = 25°

Hi !

We know  : the sum of the measures of any triangle is 180 degrees.

A + B + C = 180°

(3x - 13) + (2x + 4) + (180 - 116) = 180

5x - 13 + 4 + 64 = 180

5x = 180 - 64 - 4 + 13

5x = 125

x = 125 : 5

x = 25°

Good luck !

Answer:

36

Step-by-step explanation:

you just devide 18 by 6, which was three, then you multiply from there up to 9, which gives you 36 ( that probably made no sense, im bad at math )

Answer:

it should be B

mark me as the brainliest please

Answer:

a=10

b=37

Step-by-step explanation:

a+5 is equal to the opposite line, 15. 10+5=15 therefore, a must equate to 10

3b is the same angle as 111 therefore 3*b has to equate to 111. 111 divided by 3 equals 37. B has to then equate to 37 to make the proper angle.

Hope my explanation wasn't too confusing, and hope this helps! Good luck!!!

Answer:

7x+39>=53 and 16x+ 15>31 x>=2 (no solutions exist)

Step-by-step explanation:

AnB is correctswer:

Step-by-step explanation:

Answer:

B.) On a coordinate plane, a line goes through points (0, 4) and (8, 0).

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

Answer:

16

Step-by-step explanation:

-2 × 2 = -4 but any number squared is positive

so -4^2 is still (+)16

Answer:

c

Step-by-step explanation:

Answer:

2:1

Step-by-step explanation:

$2 for 1 pound of meat purchased

Answer:I think 2 Because if you have 7 and You add another its 14 so 2

Step-by-step explanation:Also can you make be braniest poss if not its ok :)

Answer:

The square root of a negative number does not exist among the set of Real Numbers.

Step-by-step explanation:

no way to multiply a number times itself and get a negative so you cannot get a square root of -93

The sum of the interior angles in each triangle is 180 degrees.

so :

12 + 40 + x = 180

52 + x = 180

x = 180 - 52

x = 128

so the third angle of the triangle is 128 degrees which means C is correct.

Answer:

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

From the question the equation is

[tex]y = - \frac{3}{2} x + 8[/tex]

Comparing with the general equation above

[tex]Slope = - \frac{3}{2} \\ [/tex]

Hope this helps you

Hello there!

The slope is -3/2

Remember y=mx+b (Slope-Intercept Form)

m is the slope, and b is the y-intercept

m is -3/2, and b is 8

Hope this helps

~Just a gloomy gal who misses her best friend

#CarryOnLearning

[tex]SilentNature[/tex]

Answer:

The answer is -8/5

Step-by-step explanation:

i took the the quiz.

Answer:

-8/5

Step-by-step explanation:

did the assinmant

Answer:

Step-by-step explanation:

19 and 7

Answer: x = 6

---------------------

Answer:

2

Step-by-step explanation:

The Y intercept is where x is = to zero.

If x is zero that is one section of the chart back.

so 1 would be subtracted from Y.

Answer:

y= 1/3x + 2

Step-by-step explanation:

I used desmos