2. The ratio of
the profit, cost of
materials and labour
in the production of
an article is 5:7:13
respectively. If the
cost of materials is Le
840 more than that of
labour, find the total
cost of producing the
article​

Answer:

Below

Step-by-step explanation:

sin(2x) = 2 ×cos(x)× sin(x)

● sin(x) = 2 × cos(x) × sin(x)

● 2 × cos(x) = 1

● cos (x) = 1/2

So we can deduce that:

● x = Pi/3 + 2*k*Pi

● or x = -Pi/3 + 2*k*Pi

K is an integer

The Solution of x:

x = π/3 + 2πn, where n is an integer.

x = 2π/3 + 2πn, where n is an integer.

In degrees:

x = 60° + 360°n, where n is an integer.

x = 120° + 360°n, where n is an integer.

To solve the equation sin(2x) = sin(x), we can use the properties of trigonometric functions.

First, let's simplify the equation using the double angle identity for sine:

sin(2x) = 2sin(x)cos(x).

Now we can rewrite the equation as:

2sin(x)cos(x) = sin(x).

2cos(x) = 1.

Dividing both sides of the equation by cos(x), we get:

2 = 1/cos(x).

Now, we can find the value of cos(x) by taking the reciprocal of both sides:

cos(x) = 1/2.

From the unit circle or trigonometric values,

we know that cos(x) = 1/2 corresponds to angles of π/3 or 2π/3 (in radians) or 60° or 120° .

So, the solutions for x are:

x = π/3 + 2πn, where n is an integer.

or

x = 2π/3 + 2πn, where n is an integer.

In degrees:

x = 60° + 360°n, where n is an integer.

or

x = 120° + 360°n, where n is an integer.

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the graph will shift 3 units to the right

Answer:

C. $128

Step-by-step explanation:

320 x 0.5 = 160

320 - 160 = 160

160 x 0.20 = 32

160 - 32 = 128

Answer:

95 minutes

Step-by-step explanation:

Add together how long it has been cooking plus how long it needs to cook

48+47 = 95

95 minutes

Answer:

155

Step-by-step explanation:

Add 60 and 48 to get 108 then add 108 and 47 to get 155

Answer:

298.3 square centimeters

Step-by-step explanation:

We are given

Slant height (l)= 14cm

Radius (r)= 5cm

Since we are given the slant height ,

the formula for surface area of a cone =

πrl + πr²

πr(l + r)

π = 3.14

Hence,

3.14 × 5(14 + 5)

3.14 × 5(19)

= 298.3 square centimeters

Answer:

[tex]\boxed{\frac{1}{25} \text { OR } 0.04}}[/tex]

Step-by-step explanation:

[tex]5^{-2}\\\\\text {Apply Negative Exponent Rule: } a^{-b}=\frac{1}{a^b}\\\\5^{-2}=\frac{1}{5^2}=\boxed{{\frac{1}{25}} \text { OR } 0.04}[/tex]

Answer:

Add 7x to each side

Step-by-step explanation:

-8 - 7x = -5x - 10

Add 10 to each side

-8 - 7x+10 = -5x - 10+10

2 -7x = -5x

Add 7x to each side

2-7x+7x = -5x+7x

2 = 2x

Answer: See below

Step-by-step explanation:

[tex]-8 - 7x = -5x - 10[/tex]

I believe it is adding 8 on both sides

The next step after adding 8 on both sides is adding 5x on both sides

[tex]-7x=-5x-2[/tex]

[tex]-7x+5x=-5x-2+5x[/tex]

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

x=1

Answer:

54 inches

Step-by-step explanation:

First, let's convert the measurements into a common measurement.

Since inch is the smallest measurement here, let's use that.

Ella's pet snake is 42 inches long.

Roya's pet snake is 8 feet long. There are 12 inches in one foot. Therefore, 8 feet would mean 12 times 8 or 96 inches.

Therefore, Roya's snake is 96 inches long.

To find out how many inches longer is Roya's snake, subtract:

96 - 42 = 54.

Therefore, Roya's snake is 54 inches longer than Ella's.

Answer:

809mi

Step-by-step explanation:

There are two ways to travel form Tamaulipas to Sorona. The first if the direct route from Sorona to Tamaulipas which is 809mi. The another route is to travel to Colima from Sorona and then travel to Tamaulipas from Colima. This is the long distance routes in which there are two destination points. The direct route is shorter in length therefore preferable.

Answer:

x-√x -12

Step-by-step explanation:

(√x +3)(√x -4)=

x-√x -12

Answer:

the answer is C

Step-by-step explanation:

I used PEMDAS and school knowledge that I learned 2 years ago that I can't explain much, cause I i am bad at math, most of the time

Step-by-step explanation:

csc(4x) − 2 = 0

csc(4x) = 2

sin(4x) = 1/2

In radians:

4x = π/6 + 2kπ, 5π/6 + 2kπ

x = π/24 + kπ/2, 5π/24 + kπ/2

In degrees:

4x = 30° + 360°k, 150° + 360°k

x = 7.5° + 90°k, 37.5° + 90°k

Answer:

-6

Step-by-step explanation:

To solve this problem, you should move all of the variables onto one side, and all of the constants onto the other side as such:

3x-4=2x-10

   +10    +10

3x+6=2x

-3x     -3x

6=-x

/-1   /-1

x=-6

Hope this helps!

P.S. Please give me brainliest. Thanks :)

Answer:

[tex]x = -6[/tex]

Step-by-step explanation:

Looking at the expression [tex]3x - 4 = 2x - 10[/tex], our goal is to get rid of the x term on one side.

To do this, we can subtract 2x from both sides which gets us

[tex]x - 4 = -10[/tex]

Add 4 to both sides:

[tex]x = -6[/tex]

Hope this helped!

Answer:

Step-by-step explanation:

125 = 5 *5 * 5 = 5³

8 = 2 * 2 *2 = 2³

125x⁶ - 8 = 5³(x²)³ - 2³

               = (5x²)³ - 2³     { a³ - b³ = (a -b)(a² + ab + b²)

               = (5x² - 2) ([5x²]² + 5x²*2 + 2²)

                 = (5x² - 2)(25x⁴ + 10x² + 4)

Hint: (5x²)² = 5² * (x²)² = 25* x²ˣ² = 25x⁴

Answer:

(D) [tex]y=\frac{18}{6}x[/tex]

Step-by-step explanation:

We will be able to know if an equation has a constant of proportionality of 3 if the constant which is being multiplied by x is equal to 3.

[tex]\frac{8}{5} =1.6[/tex] so no for A.

[tex]\frac{1}{3} = 0.\overline{33}[/tex] so no for B too.

[tex]\frac{1}{4} = 0.25[/tex] so no for C as well.

[tex]\frac{18}{6} = 3[/tex], so D works.

Hope this helped!

Answer:

1

Step-by-step explanation:

Plug in t = 12 in the expression

[tex]5-\frac{t}{3}=5-\frac{12}{3}[/tex]    

         = 5 - 4/1

          = 5 - 4

           = 1

Answer:

[tex]\Huge \boxed{1}[/tex]

Step-by-step explanation:

[tex]\displaystyle 5-\frac{t}{3}[/tex]

The value of [tex]t[/tex] in the expression is 12.

Replace the [tex]t[/tex] variable with 12.

[tex]\displaystyle 5-\frac{12}{3}[/tex]

Evaluate the expression.

[tex]5-4[/tex]

[tex]1[/tex]

Answer:

She can go 120 km before she runs out of fuel

It will take 2 hours.

Step-by-step explanation:

150 km is the distance

60 km/ h is the speed

The gas tank is 20 liters

We can go 6 km per liter

Fuel costs .60 dollars per liter

We need to determine how far she can go on a tank of gas

20 liters * 6 km / liter = 120 km

She can go 120 km before she runs out of fuel

120 km  = 60 km/ h  *  x hours

Divide each side by 60

120/60 = x

2 hours

Answer:

Hopes this helps!

Step-by-step explanation:

Answer:

B. 1/2

Step-by-step explanation:

y = ax^2 + bx + c

14 = a(0)^2 + b(0) + c

c = 14

10.5 = a(1)^2 + b(1) + 14

10.5 = a + b + 14 ____(i)

8 = a(2)^2 + b(2) + 14

8 = 4a + 2b + 14

4 = 2a + b + 7 ___ (ii)

i - ii

10.5 - 4 = -a + 7

6.5 = -a + 7

a = 7- 6.5

a = 0.5

Value of a in the quadratic function is 0.5

In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function with one or more variables in which the highest-degree term is of the second degree

Given,

Quadratic function

y = [tex]ax^{2}+bx+c[/tex]

Consider values in the table x= 0 and  y =14

[tex]14=a(0)^{2}+b(0)+c\\ c=14[/tex]

Consider x=1 and y = 10.5

[tex]10.5=a(1^{2})+b(1)+c\\ a+b=10.5-14\\a+b=-3.5[/tex]

Consider x=2 and y =8

[tex]8=a(2^{2})+b(2)+c\\ a\\8=4a+2b+14\\4a+2b=-6\\2a+b=-3[/tex]

Subtract a + b= -3.5 from 2a + b= -3

a=-3--3.5=0.5

Hence, the Value of a in the quadratic function is 0.5

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Hi there! :)

Answer:

[tex]\huge\boxed{\frac{1}{25}}[/tex]

When evaluating an expression with a negative exponent, the reciprocal will need to be taken. Therefore:

[tex]5^{-2} = \frac{1}{5^{2} } = \frac{1}{25}[/tex]

Answer:

A = 8%, B = 5%

Step-by-step explanation:

Let

a=concentration of solution A (in percent)

b=concentration of solution B (in percent)

Given

2a+4b = 0.06*(2+4)  ...........(1)

4a+2b = 0.07*(4+2)  ...........(2)

2(1) - (2)

4a-4a +8b-2b = 6 (2*0.06-0.07)

6b = 6(0.05)

b = 0.05  .............(3)

Substitute (3) into (1) and solve for a

2a+4(0.05) = 0.36

2a = 0.16

a = 0.08

Answer:

5x=2x+2

3x=2

X=2/3

Hope this helps ФωФ

Answer:

Aw what animal

Step-by-step explanation:

Srry I need pointse

Answer:

I hope this helps!

Answer D

Step-by-step explanation:

Step-by-step explanation:

salary per day =$140

bonus on sales =14%

sales on Saturday =$600

bonus on Saturday sales=14/100*$600

=$84

sales on Sunday =$1200

bonus on Sunday sales=14/100*$1200

=$168

total amount she earned over the two days=$140+$84+$168

=$532

Answer:

both angles are the same, so you can use it interchangeably in proving.

But i suggest you to mantain only one, because it's easier to understand and it looks better.

Answer:

[tex]\boxed{478.02}[/tex]

Step-by-step explanation:

→ First understand what Pythagoras theorem is

Pythagoras is a theorem used to find the hypotenuse (the side opposite to the right-angle) of a triangle. We would need the base lengths as well the height in order to use Pythagoras.

→ State the formula and identify the letters

a² + b² = c² ⇒ where 'a' is 380cm, 'b' is 290cm and 'c' is what we are trying to work out

→ Substitute in the values into the formula

380² + 290² = c²

⇒ Simplify

144400 + 84100 = c²

⇒ Collect the numbers together

228500 = c²

⇒ Square root both sides to find 'c'

478.0167361 = c

→ The length of the diagonal is 478.02

Answer:

y = 4

Step-by-step explanation:

Move all terms not containing  y  to the right side of the equation.

-y = -4

Multiply each term in  − y  =  − 4  by  − 1

y = 4

Hope this can help you

Answer:

C. 10cm

Step-by-step explanation:

Bryce is making a model building.

He raises the walls of the building

by 2 centimeters five times. By how

many centimeters does Bryce raise

the walls all together?

(A) 2 cm

(C) 10 cm

(B) 5 cm

(D) 20 cm

Bryce raises the walls of the building 2centimeters five times

This means, he raises the walls 2centimeters five different times

By how many centimeters does Bryce raise the walls all together?

We can solve this by finding the product of 2centimeters five times

The total centimeters Bryce raises the walls altogether= 2 centimeters × 5 times

=2cm × 5

=10cm

Answer:

2

Step-by-step explanation:

|-6+8|

Add/subtract the numbers: -6 + 8 = 2

= |2|

Apply the absolute value rule: |a| = a, a ≥ 0

= 2

Answer:

1) The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle

2) The joint equations of diagonals are;

5·y = 56 - 6·x and 5·y = 6·x + 14.

Step-by-step explanation:

The equations are;

x² - 7·x + 6 = 0......................(1)

y² - 14·y + 40 = 0.................(2)

Factorizing equation (1) and equation (2) , we get

x² - 7·x + 6 = (x - 6)·(x - 1) = 0

Which are vertical lines at points x = 6 and x = 1

For equation (2) , we get

y² - 14·y + 40 = (y - 10)·(y - 4) = 0

Which are horizontal lines at point y = 4 and y = 10

The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle

2) The points of intersection of the equations are;

(1, 4), (1, 10), (6, 4), and (6, 10)

The end point of the diagonals are;

(1, 10), (6, 4) and  (1, 4), (6, 10)

The slope of the diagonals are;

(10 - 4)/(1 - 6) = -6/5 and (4 - 10)/(1 - 6) = 6/5

The equation of one of the diagonals are then, y - 10 = -6/5×(x - 1)

y = -6/5·x + 6/5 + 10 = -6/5·x + 56/5

5·y = 56 - 6·x

The other diagonal is therefore;

y - 4 = 6/5×(x - 1)

y = 6/5·x - 6/5 + 4 = 6/5·x + 14/5

5·y = 6·x + 14.

The joint equations of diagonals are therefore;

5·y = 56 - 6·x and 5·y = 6·x + 14.

Answer:

third option

Step-by-step explanation:

Given

f(x) = [tex]\frac{5x+5}{x^2+x-2}[/tex]

The denominator cannot be zero as this would make f(x) undefined.

Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non zero for these values then they are vertical asymptotes.

solve x² + x - 2 = 0 ← in standard form

(x + 2)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 1 = 0 ⇒ x = 1

The vertical asymptotes are x = 1 and x = - 2