The price of a colour TV is $ 13440, inclusive of sales tax. If the printed price of the colour TV be $ 12000 then find the rate of sales tax.

Answer:

[tex]\frac{\sqrt{10} }{2}[/tex]

Step-by-step explanation:

on a 45 - 45 - 90 triangle if the sides are x then the hypotenuse is x[tex]\sqrt{2}[/tex]

so,

[tex]\sqrt{5}[/tex] = x[tex]\sqrt{2}[/tex]                  (Divide by [tex]\sqrt{2}[/tex] )

[tex]\frac{\sqrt{5} }{\sqrt{2} }[/tex] = x                        (rationalize the denominator)

[tex]\frac{\sqrt{5} }{\sqrt{2} }[/tex] · [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex] = [tex]\frac{\sqrt{10} }{\sqrt{4} }[/tex] = [tex]\frac{\sqrt{10} }{2}[/tex]

The length of side is √10/2

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The given triangle is a 45-90-45 so if the sides are x then the hypotenuse will be x√2

From the figure the hypotenuse of triangle is √5

SO equation it to x√2

We get √5=x√2

Divide both sides by √2

√5/√2=x

As the denominator should be a whole number we have to rationalize the denominator.

Multiply numerator and denominator with √2

√5/√2×√√2/√2

√10/2

Hence, the length of side is √10/2

To learn more on trigonometry click:

https://brainly.com/question/25122835

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Answer:

C

Step-by-step explanation:

Given

sinR = [tex]\frac{5}{13}[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]

This is a 5- 12- 13 triangle with legs PQ = 5, QR = 12, hypotenuse PR = 13

cosR = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{QR}{PR}[/tex] = [tex]\frac{12}{13}[/tex]

Answer:

Inequality: [tex] 38.75p + 16.25 \le 365 [/tex]

Solution: [tex] p \le 9 [/tex]

Step-by-step explanation:

Let p = number of people.

Ticket for 1 person: $38.75

Tickets for n people: 38.75p

Parking: $16.25

[tex] 38.75p + 16.25 \le 365 [/tex]

[tex] 38.75p \le 348.75 [/tex]

[tex] p \le 9 [/tex]

Answer

380≥20.75p+15.5

Step-by-step explanation:

good luck

Answer:

number line is shown from negative 5 to 0 to positive 5. There are increments of 1 on either side of the number line. All the numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 4 is shown. Above this, another arrow pointing from negative 4 to negative 3 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow

Answer:

In this exercise we need to solve the equation

3(x-2) = 2x + 6 - 2

We operate the parentheses and the right side

3(x-2) = 2x + 4

3x - 6 = 2x + 4

We add 6 to both sides

3x -6 + 6 = 2x + 4 + 6

3x = 2x + 10

We substract 2x

3x - 2x = 2x + 10 - 2x

x = 10

x = 10

Step-by-step explanation:

Answer:

The perimeter is 109.8

Step-by-step explanation:

As we can see here, the angles of the triangles are congruent so we can say that both triangles are congruent

When two triangles are congruent, the ratio of their corresponding sides are equal

So we can get the scale factor here by looking at the sides facing each specific angle in both triangles

In the bigger triangle,

The side facing 34 degrees has a length of 30

In the smaller triangle,

The side facing 34 degree has a length of 27

So the scale factor to get the smaller from the bigger is 27/30 = 9/10 or 0.9

Likewise the side facing 51 degrees in the bigger is 40 while for the smaller, it is 36

So the ratio still stands at 36/40 = 9/10 or 0.9

In essence, the smaller triangle will have a perimeter that is 0.9 times that of the bigger

The perimeter of the bigger is simply the sum of the side lengths

We have this as;

(52 + 30 + 40) = 122

so that of the smaller would be;

122 * 0.9 = 109.8

Answer:

[see below]

Step-by-step explanation:

V = s^3

V = (x+4)^3

V = x^3 + 3x^2 * 4 + 3x * 4^2 + 4^3

V = x^3 + 12x^2 + 48x + 64

Hope this helps.

Answer:

18 pencils in 3 packs.

Step-by-step explanation:

Assuming that each pack will have the same amount of pencils. It is given that there are 36 pencils in all when one has 6 packs. Find the amount in each pack by dividing (total amount of pencils)/(amount of packs) = Amount of pencils per pack:

36/6 = 6

There are 6 pencils in each pack.

Now, Elsa wants to know how much pencils are in 3 packs. Multiply the amount of packs with the amount of pencils in each pack:

Total amount of pencils = amount of packs (3) x amount of pencils per pack (6)

                                       = 3 x 6

                                       = 18

There are 18 pencils in 3 packs.

~

Answer:

-2, -1

Step-by-step explanation:

B is the answer for you. Have a good day!

Answer:

Step-by-step explanation:

C * D = {(x,y): x is an element of C and y is an element of D.}

C * D = { (1,4), (1,5), (1,6), (2,4), (2,5), (2,6) }

Answer:

Step-by-step explanation:

Commission for  amount  Rs. 5,00,00 = [tex]\frac{2}{100}*500000[/tex]

                                                               = 2* 5000

                                                               = Rs. 10,000

total commission = Rs. 32,000

Remaining commission = 32500 - 10000

                                      = Rs. 22500

Let remaining amount of the restaurant = Rs. x

Commission on Rs. x = 22500

3% of x = 22500

[tex]\frac{3}{100}*x=22500\\\\x=22500*\frac{100}{3}\\\\x = 7500*100[/tex]

x = Rs. 750000

Price of the restaurant = 750000 + 500000

                                     =Rs . 1250000

Answer:

Reciprocal

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Yes! The diagonal of a rectangle is longer than any of its sides.

Consider PQRS as a rectangle. It is known to us that each interior angle of a rectangle measures 90°. Now, after making the diagonal of the rectangle PQRS, the rectangle has been split into 2 right-angled triangles i.e, ∆PRS and ∆RPQ. In the right angled triangle, hypotenuse is always the longest side. Here, in ∆PRS and ∆RPQ, the bases are RS and QP ; perpendiculars are PS and QR and both triangles' hypotenuse is PR. As, hypotenuse is always the longest side, so PR will be longer than RS,QP,PS and QR. Clearly, the diagonal of a rectangle is longer than any of its sides.

Answer:

10

Step-by-step explanation:

[tex]2250[/tex] = 2x5x5x5x3x3

therefore,2and 5 don't have a pair so , 2x5=10 .

So, the smallest number by which 2250 is 10

Answer: 60 miles

Step-by-step explanation:

Given

It takes ferry 2 hours to travel to town A and only [tex]1.5\ hr[/tex] to travel back to town B.

Speed of current is [tex]u=5\ mph[/tex]

Suppose the speed of the ferry is [tex]v[/tex] mph

Distance traveled in both the cases is same, but it took more time traveling to city A that is, ferry is moving upstream and downstream for returning time.

[tex]\Rightarrow 2(v-5)=1.5(v+5)\\\Rightarrow 2v-10=1.5v+7.5\\\Rightarrow 0.5v=17.5\\\Rightarrow v=35\ mph[/tex]

Distance between the towns is [tex]2\times (35-5)=60\ \text{miles}[/tex]

Answer:

The distance between the two towns is 60 miles.

Step-by-step explanation:

Let the distance between A and B is d.

A to B , t = 2 hour

B to A , t' = 1.5 hour

Speed of current, u = 5 mph

Let the speed of ferry is v.

distance = speed x time

d = (v - 5) x 2 = (v + 5) x 1.5

2 v - 10 = 1.5 v + 7.5

0.5 v = 17.5

v = 35 mph

So, the distance is

d = (35 - 5) x 2 = 60 miles.

Answer:

[tex]mDE=90[/tex]°

Step-by-step explanation:

In this problem, one is asked to find the measure of the arc in degrees. This problem provides one with a diagram since the center is unnamed, call the center point (O). One is given the information that angle (<DOE) has a measure of (90) degrees. One is asked to find the degree measure of the surrounding arc (DE).

The central angles theorem states that if an angle has its vertex on the center of a circle, the degree measure of the angle is equal to the degree measure of the surrounding arc. One can apply this here by stating the following:

[tex]m<DOE = mDE\\[/tex]

Substitute,

[tex]90=mDE[/tex]

Answer:

y = 3/2x -3

Step-by-step explanation:

The general equation of a straight line is;

y = mx + b

where m is slope and b is the y-intercept

Here, we can see that the graph intercepts the y-axis at the point y = -3

So b = -3

To get m, we can substitute any other point values on the plot

We can select (2,0)

So we have;

y = mx -3

0 = 2m -3

2m = 3

m = 3/2

so;

y = 3/2x -3

Answer:

$1,471.5625

Step-by-step explanation:

Monthly salary = $1850

Weekly salary = $1850/4 weeks

= $462.5

Hourly rate = $462.5/40 hours

= $11.5625

Overwork time = 62 hours - 40 hours

= 22 hours

Time and a half = 1.5 times the normal salary

Overwork time payment per hour = 1.5 × $11.5625

= $17.34375

Overwork time payment for 22 hours = 22 × $17.34375

= $381.5625

Last week salary = weekly salary + overtime payment

= $462.5 + $381.5625

= $84.0625

Gross salary for the month = 3 weeks regular salary + last week salary

= (3 × $462.5) + $84.0625

= $1387.5 + $84.0625

= $1,471.5625

Answer:

Step-by-step explanation:

Let's call the number x. The statement "...2 times a number" if the number is x looks like this:

2x

"8 less than" that looks like this:

... - 8

Putting the whole thing together:

2x - 8

Answer:

a. 18 percent

b. $90 billion

Step-by-step explanation:

a. Calculation to use Okun's law to determine the size of the GDP gap in percentage-point terms.

First step is to find the difference between ACTUAL RATE of unemployment and NATURAL RATE of unemployment

Difference=13%-4%

Difference= 9%

Based on the information above calculation we can see that the ACTUAL RATE of unemployment EXCEEDS the NATURAL RATE of unemployment by 9%, which indicates a CYCLICAL UNEMPLOYMENT.

Thus, According to Okun's law, this translates into an 18 % GDP gap in percentage-point terms (= 2 × 9%).

Therefore the the size of the GDP gap in percentage-point terms is 18 percent

b. Calculation to determine how much output is forgone because of cyclical unemployment

Forgone Output :

By applying Okun’s law we known that the GDP gap is 18%, which means that we are 18% below the GDP amount which is given as $500 billion,

Hence,

Output forgone = (18/100) ×$500 billion

Output forgone=0.18×$500 billion

Output forgone=$90 billion

Therefore the Forgone Output is $90 billion

Answer:

9 possible values of length and breadth.

Step-by-step explanation:

Given that the area of the rectangle is 18cm² . And the lengths of the sides are whole numbers. We need to tell the possible dimensions of the rectangle .

Let :-

[tex]\rm\implies Length = x [/tex]

[tex]\rm\implies Breadth = y [/tex]

We know that :-

[tex]\rm\implies Area = length \times breadth [/tex]

[tex]\rm\implies Area = x y \\\\\rm\implies xy = 18cm^2 [/tex]

Now look out for the possible factors of 18 . That is , ( 1 × 18 ) , ( 2 × 9) , ( 3 × 6 ) , ( 6 × 3 ) , ( 9 × 2 ) , (18 × 1 ) . That is total 9 possible values .

Answer:

Can u explain more pls?

Step-by-step explanation:

Answer:

Square

Step-by-step explanation:

Answer:

x = -0.70,-2.212.

Step-by-step explanation:

(a) The quadratic equation is :

[tex]6x^2 + 17x + 9 = 0[/tex]

Here,

a = 6, b = 17, c = 9

Put all the values in the quadratic formula.

[tex]x=\dfrac{-17+\sqrt{17^2-4\times 6\times 9}}{2(6)},\dfrac{-17-\sqrt{17^2-4\times 6\times 9}}{2(6)}\\\\x=-0.70,-2.12[/tex]

So, the solution of the given equation are -0.70,-2.212.

(b) Equation is : [tex]4x^2 -4x + 1 = 0[/tex].

Here, a = 4, b = -4 and c = 1

So,

[tex]x=\dfrac{-(-4)+\sqrt{(-4)^2-4\times 4\times 1}}{2(4)},\dfrac{-(-4)-\sqrt{(-4)^2-4\times 4\times 1}}{2(4)}\\\\x=0.5,0.5[/tex]

Hence, this is the required solution.

Answer:

[tex]2(6 + 4) - 3(5) \\ 12 + 8 - 15 \\ = 5[/tex]

Answer:

1

Step-by-step explanation:

2*6+4-3*5

12+4-15

16-15

1

Answer:

1.

Step-by-step explanation:

.

Answer: 72%

Step-by-step explanation:

Set Jamal's original ring price = x

[tex]x - x(0.2) = 2640\\x(1-0.2)=2640\\x(0.8)=2640\\x=\frac{2640}{0.8}=3300[/tex]

Jamal's original ring price = $3300

Set Naomi's discount = y

[tex]3300-3300(y)=924\\=3300(1-y)=924\\1-y=\frac{924}{3300} \\-y=\frac{924}{3300} -1\\y=1-\frac{924}{3300}=1-0.28=0.72[/tex]

Naomi's discount is 0.72 = 72%