Solve the real-world situation by using the substitution method. The number of DVDs sold at a store in a month was 935 and the number of DVDs sold decreased by 12 per month. The number of Blu-ray discs sold in the same store in the same month was 517 and the number of Blu-ray discs sold increased by 26 per month. Let d represent the number of discs sold and t represent the time in months. The system of equations lbrace d = 935 − 12t d = 517 + 26t can be used to represent this situation. If this trend continues, how many months will the number of DVDs sold equal the number of Blu-ray discs sold? How many of each is sold in that month? There will be ______ DVDs and Blu-Ray discs sold per month in ______ months.

Answer:

2 - sqrt(3)

Step-by-step explanation:

Split pi/12 into two angles where the values of the six trigonometric functions are known.

tan (pi/4 - pi/6)

Apply the difference of angles identity

[tex]\frac{tan(pi/4) - tan(pi/6)}{1 + tan(pi/4)tan(pi/6)}[/tex]

tan(pi/4) = 1 , tan(pi/6) = (sqroot3)/3

Plug in and Simplify

[tex]\frac{1-\frac{\sqrt{3} }{3} }{1+1\frac{\sqrt{3} }{3} }[/tex]

[tex]\frac{\frac{3-\sqrt{3} }{3} }{\frac{3+\sqrt{3} }{3} }[/tex]

[tex]\frac{3-\sqrt{3} }{3} *\frac{3}{3+\sqrt{3} }[/tex]

[tex]\frac{3-\sqrt{3} }{3+\sqrt{3}}[/tex] Need to multiply this by [tex]\frac{3+\sqrt{3} }{3+\sqrt{3} }[/tex]

Expand and simplify numerator: [tex]\frac{6}{(3+\sqrt{3} )^{2} }[/tex]

Expand and simplify denominator: [tex]\frac{6}{12+6\sqrt{3}}[/tex]

Cancel the common factor: [tex]\frac{1}{2+\sqrt{3}}[/tex]

Answer:

D: 1/2 - √3.

Step-by-step explanation:

The Unit Circle is a circle with radius 1 that is used to determine the value of sine and cosine of any angle.

But that table do not directly give the exact value so to solve for its exact value, express π/12 as a sum or difference of two angles where the values of the six trigonometric functions are known.

tan π/12 = tangent (π/4 - π/6)

Using the the difference of angles identity we get,

tan (π/4 - π/6) = (1 - √3 / 3) / (1 + 1 x √3 / 3)

Multiply by 3,

tan (π/4 - π/6) = (3 - √3) / (3 + √3)

Multiply by 3 - √3

tangent (π/4 - π/6) = (3 - √3)(3 - √3) / (3 - √3)(3 + √3)

FOIL and simplify.

tangent (π/4 - π/6) = 9 - 6√3 + 3 / 9 -3

tangent (π/4 - π/6) = 1/2 - √3

Answer:

Graph A

Step-by-step explanation:

The line is going to pass through -3 as the y intercept then you go over 4 blocks and up 3 of x

Answer:

Graph A

Step-by-step explanation:

If you take a pair of x,y coordinates from each graph and input it into the equation (y=3/4x-3), only Graph A makes the equation true.

Answer:

15.9%

Step-by-step explanation:

Percent decrease formula =

(Initial value - New value/Initial value) × 100

Initial value = 9200kg

New value = 7739.4kg

Percent decrease = (9200 - 7739.4/9200) × 100

Percent decrease = (1460.6/9200) × 100

Percent decrease = 15.8760869565%

Approximately = 15.9%

The percent of decrease in the amount of strawberries used annually is 15.9%

Answer:

69.75 miles

Step-by-step explanation:

15.5 miles = 1 hour

x miles = 4.5 hours

Cross product

15.5 * 4.5 = 1 * x

69.75 = x

x = 69.75 miles

Rico will bicycle 69.75 miles in 4.5 hours

Answer:

Could you retake the photo plz so i can see the full question and answer choices

Step-by-step explanation:

Answer:

42 and 21 are composite numbers

Answer:

option c

Step-by-step explanation:

Answer:

its A

Step-by-step explanation:

because in the end QP go together so it either A or B and it A because thats how the triabgle goes

for brainliest

Answer:

h=(3v)/(pi r^2)

Step-by-step explanation:

you simply have to move everything to one side.

Answer:

h = [tex]\frac{3V}{\pi r^2}[/tex]

Step-by-step explanation:

Given

V = [tex]\frac{1}{3}[/tex]πr²h ( multiply both sides by 3 to clear the fraction )

3V = πr²h ( isolate h by dividing both sides by πr² )

[tex]\frac{3V}{\pi r^2}[/tex] = h

Answer:

y = 6(x + 8)² + 4

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Using the method of completing the square.

y = 6x² + 96x + 388

The coefficient of the x² term must be 1, so

factor out 6 from 6x² + 96x

y = 6(x² + 16x ) + 388

To complete the square

add/subtract (half the coefficient of the x- term)² to x² + 16x

y = 6(x² + 2(8)x + 64 - 64) + 388

  = 6(x + 8)² - 384 + 388

y = 6(x + 8)² + 4 ← in vertex form

Answer:

Step-by-step explanation:

(5f-3)(-2)

-10f + 6 = 0

f= 6 + 10

f = 16

Answer:

well 25x4=100 so multiply 23 by 4 and that would be 92 so you would have an A or 92%

Answer:

271000

Step-by-step explanation:

Answer: 300,000

Step-by-step explanation:

Answer:

the answer is A =3 ... this is the correct answer

Answer:

B I think

Step-by-step explanation:

Answer-

√(-1 - -7) 2 + (-5 - 7) 2

Step-by-step explanation:

This would be the equation if i am not mistaken. Hope it helps, have a great day!

Answer:

y-y1=m (x- x1)…………..(1)

Here m=1/2 and (x1,y1)= (4,-2)

(1) => y-4=1/2(x+2)

=> 2y-8=x+2

=> x-2y-10=0

So, equation of line is x-2y-10=0.

Answer:

The 12-pound bag of dog food.

Step-by-step explanation:

To find out which is the better buy you start by divinging 10.80 by 12 and then you divide 10.20 by 8 and you get .90 cents for the 12 pound while you get 1.275 dollars. Which means the 12 pound bag is the better by because it is less money per pound than the 8 pound bag.

Answer:

x = 13.5

Step-by-step explanation:

To find x, we use the sine rule

For the sine rule,

the ratio of the sides to the sine of the angle facing the side is equal for all the sides of the triangle

Thus,

x/sin 34 = 11/ sin 27

x = 11 sin 34/sin 27

x = 13.5

Answer:

A. 15.8

Step-by-step explanation:

First the perimeter of a rectangle = 2 (L +W)

So; 46.4 = 2(L + 7.4)

46.4 = 2L + 14.8

2L = 46.4 - 14.8

2L = 31.6

L =15.8

Answer:

-1/24 < x < 0

Step-by-step explanation:

Answer:

$56.09

Step-by-step explanation:

76% of $233.70 is $177.61

$233.70 - $177.61 = $56.09

Answer:

The answer for the given expression is 23 after putting the values of a,b and c.

Step-by-step explanation:

Given expression is:

[tex](\frac{2c}{a})^2-10*\frac{(b+a)}{c}[/tex]

We have to find the value of expression, when

a = -2, b = 3 and c = 5

We will put these values in the given expression and then simplify the given expression,

[tex](\frac{2*5}{-2})^2-10*\frac{3+(-2)}{5}\\\\(\frac{10}{-2})^2-10*\frac{3-2}{5}\\\\(-5)^2-10*\frac{1}{5}\\25-2\\23[/tex]

Hence,

The answer for the given expression is 23 after putting the values of a,b and c.

Answer:

Total cost to conduct survey = $2075

Step-by-step explanation:

Given that:

Number of questions on survey = 15

Number of people = 500

Base fee = $1000

Per question charge = $5

Per person surveyed = $2

Let,

q be the number of questions

p be the number of people

Total cost = Base fee + 5q + 2p

Total cost = 1000 + 5(15) + 2(500)

Total cost = 1000 + 75 + 1000

Total cost = $2075

Hence,

Total cost to conduct survey = $2075

Answer:

3.5 inches

Step-by-step explanation:

Answer:

a = 11

b = 11

c = 11√2

It is an equilateral triangle, because to angles are equal (45°).

[tex] |a| = |b| = 11 \\ |c^{2} | = \sqrt{ {a}^{2} + {b}^{2} } \\ c = \sqrt{ {11}^{2} + {11}^{2} } \\ c = 11 \sqrt{2} [/tex]

Answer:

c

ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

Answer:

0.82

Step-by-step explanation:

I literally took the test

Subtract (2x - 2y) from the sum of (10x - 2y) and (-3y) is 8x -3y.

Subtraction is a mathematic operation. Which is used to remove terms or objects in an expression.

The sum of  (10x - 2y) and (-3y).

(10x - 2y) + (-3y),

= 10x -2y -3y

= 10x -5y

Subtract (2x - 2y) from the sum of (10x - 2y) and (-3y),

= 10x -5y - (2x - 2y)

= 8x -3y

Therefore, the expression is 8x -3y.

To learn more about the subtraction;

https://brainly.com/question/2346316

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