At Factory Y, a worker's wages for a 40-hour week is $200. She is paid 10% of her regular weekly wages for every hour that she works overtime. At the end of a certain week she received $380. Calculate the number of hours of overtime that she worked.

Answer:

Dimensions of rectangle are length = 7 cm and width = 2 cm

Step-by-step explanation:

Let l = length and w = width of the rectangle.

Given that, length is 5 cm less than 6 times width. Rewriting it in equation form,

L =  6 w - 5  cm

Also given that area of rectangle is 14 cm²

Now using formula for area of rectangle,

Area of rectangle = length × width

Area of rectangle = l × w

Substituting the values,

14 = (6 w - 5) × w

Simplifying by using distributive rule,

14 = 6 w² - 5 w

To find the value of b, use the quadratic formula. So rewriting the equation in quadratic form ax²+bx+c=0

Subtracting 14 on both sides,

0 = 6 w² - 5 w - 14

Rewriting,

6 w² - 5 w - 14  = 0

Now applying quadratic formula,

Rewriting the formula in terms of w,

From the 6 w² - 5 w - 14  = 0, value of a = 6 , b = - 5 and c = - 14.

Substituting the values,

Simplifying,

Since √361 = 19,

There will be two values of w,

and

Simplifying,

and

and

Reducing the fraction in lowest form, divide first expression by 12 and second expression by 2.

and

Since the length of width cannot be negative, so value of w = 2 cm

To find the value of length, Use equation L =  6 w - 5  cm

L =  6 (2) - 5  cm

L =  12 - 5  cm

L =  7  cm

Therefore l = 7 cm and w = 2 cm are the dimensions of the rectangle.

Answer:

x = 90 - 2α

Step-by-step explanation:

Solution:-

- Consider the right angled triangle " ABD ". The sum of angles of an triangle is always "180°".

                       < BAD > + < ADB > + < ABD > = 180°

                       < ABD > = 180 - 90° - α

                        < ABD > = 90° - α

- Then we look at the figure for the triangle "ABE". Where " E " is the midpoint and intersection point of two diagonals " AC and BD ".

- We name the foot of the perpendicular bisector as " F ":  " BF " would be the perpendicular bisector. The angle < BAE > is equal to < ABD >.

                    < ABD > = < BAE >  = 90° - α   ... ( Isosceles triangle " BEA " )

Where, sides ( BE = AE ).

- Use the law of sum of angles in a triangle and consider the triangle " BFA " as follows:

                     < ABF> + < BFA > + < BAF > = 180°

                     < ABF > = 180 - (90° - α) - 90°

                    < ABF > = α  

Where,       < BAF > = < BAE >

- The angle < ABD > = < ABE > is comprised of two angles namely, < ABF > and < FBE >  = x.

                        < ABD > = < ABE > = < ABF > + x

                         90° - α = α + x

                        x = 90 - 2α   ... Answer

Answer:

Step-by-step explanation:

The length of this triangle is 10 squares

and the width is 4 squares

The diagonals divide the rectangle into four triangles

These traingles are isoceles

Each two triangles facing each others are identical

<B = 90 degree

B = alpha + Beta

Let Beta be the angle next alpha

The segment that is crossing Beta is its bisector since it perpendicular to the diagonals wich means that:

Beta = 2x

Then B = alpha + 2x

90 = alpha +2x

90-alpha = 2x

x = (90-alpha)/2

Step-by-step explanation:

mid point=(1+(-4),(-3+(-0.5)

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

2 2

.mid point =-³/2,3.5/2

Answer:

number of nurses employed at the hospital is 9x = 9 * (7n/9) = 7n, and the number of doctors is 2x = 2 * (7n/9) = (14n/9).

Step-by-step explanation:

Given the ratio of nurses to doctors is 9:2, we can express this as:

Number of nurses (9x) : Number of doctors (2x)

Now, you've mentioned that the total number of nurses and doctors employed at the hospital is 77n. So, we can set up an equation:

9x + 2x = 77n

Combine like terms:

11x = 77n

Now, to find the number of nurses (9x) and the number of doctors (2x), we need to divide both sides by 11:

9x = (77n) / 11

9x = 7n

Now, we can solve for x:

x = (7n) / 9

So, the number of nurses employed at the hospital is 9x = 9 * (7n/9) = 7n, and the number of doctors is 2x = 2 * (7n/9) = (14n/9).

In summary:

- Number of nurses = 7n

- Number of doctors = (14n/9)

solved by MG