(Ans: 500)
4) The minimum charge of telephone calls up to 175 calls is Rs. 200 the charge for each
extra call of 2 minutes duration is Rs. 1. If a man paid Rs. 870.10 with 10% T.S.C and 13%
VAT for Rs telephone bill, find the number of extra calls made.
5) The distance between kalanki and Thamel is 5.4 Km. the minimum fare is Rs. 221 at the
first and the fare goes on at the rate of Rs. 11.10 per 200 meters. Find the taxi fare
between Kalanki and Thamel. (Ans Rs. 320.70)
6) Mr. Gopal hired a taxi and travelled a certain distance at 10:30pm he paid the total fare
of Rs. 345 including the additional waiting charge for 10 minutes. If the minimum fare is
RS. 21, the fare per 200m is a Rs 10.80 and the waiting charge is Rs. 10.80 per 2 minutes
find the distance travelled by him. (Ans: 5Km)
Algebraic Expression and simplification
Solved examples:
1. A) Factorize : a) 2 + 10 +
a
Sol" here,
+ 10 +
62
a?
21b2
21b2
a2
21b2
a2
7 ab
3 ab​

Answer:

50°

Step-by-step explanation:

50 + (3x + 14) + (7x - 4) = 180

50 + 3x + 14 + 7x - 4 = 180

60 + 10x = 180

10x = 180 - 60

10x = 120

x = 120/10

x = 12

So, Angle A is:

(3 * 12) + 14

36 + 14 = 50°

Answer:

a.) [tex]x=12[/tex]

b.) [tex]A=50[/tex]

Step-by-step explanation:

a.) Remember: the sum of all angles in a triangle will always be 180°.

Make an equation in which all given angles add up to 180:

∠1+∠2+∠3=180

[tex](3x+14)+(7x-4)+50=180[/tex]

Solve the equation for the value of x. Remove the parentheses:

[tex]3x+14+7x-4+50=180[/tex]

Combine like terms:

[tex](3x+7x)+(14-4+50)=180\\\\10x+60=180[/tex]

Subtract 60 from both sides:

[tex]10x+60-60=180-60\\\\10x=120[/tex]

Divide both sides by 10:

[tex]\frac{10x}{10}=\frac{120}{10} \\\\x=12[/tex]

The value of x is 12.

b.) Insert the value of x into the given value of ∠A:

[tex]A=3x+14\\\\A=3(12)+14[/tex]

Simplify multiplication:

[tex]A=36+14[/tex]

Add:

[tex]A=50[/tex]

∠A is 50°.

:Done

Check Your Work:

To make sure the given values are true, solve for ∠B:

[tex]B=7(12)-4\\\\B=84-4\\\\B=80[/tex]

Now add all angle values to determine if they add up to 180°:

[tex]50+50+80=180\\\\100+80=180\\\\180=180[/tex]

Since 180 is equal to 180, the values are true.

Answer:

the rate charged per hour by the first mechanic is 75 $/hr and the rate charged per hour by the second mechanic is 100 $/hr.

Step-by-step explanation:

A system of equations is a set of two or more equations in various unknowns in which you want to find a common solution.

So, first of all it is convenient to define the system variables:

If the sum of the two rates were $ 175 per hour, then the mathematical expression that represents this situation is: x + y= 175

You know that the first mechanic worked for 20 hours, and the second mechanic worked for 15 hours.  Then the amount of money won by the first and second mechanic respectively is expressed by 20*x and 15*y. Together they charged a total of $3000, then 20*x + 15*y=3000

So, the system of equations to solve is:

[tex]\left \{ {{x+y=175} \atop {20*x+15*y=3000}} \right.[/tex]

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.

There are several methods for solving a system of equations. One of them is the substitution method, which consists of solving or isolating one of the unknowns (for example, x) and substituting its expression in the other equation. In this way, you obtain an equation of the first degree with the other unknown. Once solved, you must calculate the value of x by substituting the already known value of y.

In this case, you isolate the variable x from the first expression:

x= 175 - y

Replacing this expression in the second equation:

20*(175 - y)+15*y=3000

and solving you get:

20*175 -20*y +15*y=3000

3500 -20*y +15*y=3000

3500 -5*y=3000

-5*y=3000 -3500

-5*y= -500

y= (-500)÷(-5)

y= 100

So:

x=175 -y

x=175 -100

x=75

Then the rate charged per hour by the first mechanic is 75 $/hr and the rate charged per hour by the second mechanic is 100 $/hr.

Answer:

The rate charged by the first mechanic is $75/h and by the second is $100/h.

Step-by-step explanation:

We have that the two mechanics charged a total of $3000:

[tex] A + B = \$3000 [/tex]    

[tex] A = \$3000 - B [/tex]  (1)

The sum of the rate of the two mechanics was $175 per hour:

[tex] R_{A} + R_{B} = \$175/h [/tex]   (2)          

The rate of the first (A) and second (B) mechanic is:      

[tex] R_{A} = \frac{A}{t_{A}} = \frac{A}{20 h} [/tex]   (3)

[tex] R_{B} = \frac{B}{t_{B}} = \frac{B}{15 h} [/tex]   (4)  

By entering equation (3) and (4) into (2):

[tex] \frac{A}{20 h} + \frac{B}{15 h} = \$175/h [/tex]   (5)            

Now, by entering equation (1) into (5) we have:

[tex] \frac{\$3000 - B}{20 h} + \frac{B}{15 h} = \$175/h [/tex]        

[tex] \frac{-3B + 4B}{60 h} = \$175/h - \$150/h [/tex]

[tex] B = \$25/h*60 h = \$1500 [/tex]        

Now, for the first mechanic we have:

[tex] A = \$3000 - B = \$3000 - \$1500 = \$1500 [/tex]

Finally, from equation (3) and (4) we can find the rate charged per hour by each mechanic:

[tex] R_{A} = \frac{A}{20 h} = \frac{\$1500}{20 h} = \$75/h [/tex]                

[tex] R_{B} = \frac{B}{15 h} = \frac{\$1500}{15 h} = \$100/h [/tex]

Therefore, the rate charged by the first mechanic is $75/h and by the second is $100/h.

I hope it helps you!    

Answer:

n/6 = 1/2

2n = 6

n = 3

Hope my answer is correct

Answer:

n = 3

Step-by-step explanation:

There's two ways, first cross multiplication:

n/6 = 1/2

Cross multiplication so 2 times n and 6 times 1

2n = 6

n = 3

Second way:

n/6 = 1/2

(n/6 = 1/2) times 6

n = 6/2

n = 3

Answer: 12 hours

Step-by-step explanation:

We can use direct proportion to solve this, we need to calculate the constant of proportionality first. This will be:

y = kx

where y = 174

x = 3

k = 174/3

k = 58 miles per hour

If the ski resort is 696 miles from his home, the number of hours used will be:

= 696/58

= 12 hours

Answer:

im not sure about the 1st one but sec one is 162 i think and im  i dont know the last eaither srry  

Step-by-step explanation:

Answer:

8/15

Step-by-step explanation:

Of The fiction books is a key word telling us to multiply 2/3 x 4/5  because OF when using fractions means that you multiply. So to multiply you just multiply the numerators and denominators to get 2 x 4 = 8 and 3 x 5 = 15, which is 8/15.

Hope this helps!

Have a great day! :)

Answer:

y=2x-7

Step-by-step explanation:

so here's my work

I just plugged stuff in so:

y+1=2(x-3)

y+1=2x-6

y=2x-7

Answer:

Ax + By = C

5x + 4y = -20

a is 5, b is 4

Step-by-step explanation:

Find slope:

  m = (y₂ - y₁) / (x₂ - x₁)

      = (0 - (-5)) / (-4 - 0)

     = 5 / -4

  m = -5/4

Use m above and anyone point to find y-intercept, let's use (-4, 0):

  y = mx + b

  0 = -5/4(-4) + b

  0 = 5 + b

  b = -5

Slope intercept form using m and b from above:

  y = mx + b

  y = -5/4x - 5

Standard form Ax + By = C:

  y = -5/4x - 5

  5/4x + y = -5

  5x + 4y = -20

Answer:

Please check the explanation!

Step-by-step explanation:

As the discrimination expression is

[tex]b^2-4ac[/tex]

if

[tex]b^2-4ac\:<0[/tex]

then the equation has no real solution.

Given the equation

[tex]mx^2+3x+1-m=0[/tex]

by comparing the quadratic equation

[tex]\:ax^2+bx+c=0[/tex]

[tex]mx^2+3x+1-m=0[/tex]

we can observe that

[tex]a=m[/tex]

[tex]b=3[/tex]

[tex]c=(1-m)[/tex]

substituting the values in discrimination to find the values of m

so

[tex]3^2-4m\left(1-m\right)=0[/tex]

[tex]9-4m+4m^2=0[/tex]

[tex]4m^2-4m+9=0[/tex]

[tex]\frac{-4m+4m^2}{4}=\frac{-9}{4}[/tex]

[tex]-m+m^2=-\frac{9}{4}[/tex]

[tex]\left(m-\frac{1}{2}\right)^2=-2[/tex]

as

[tex]\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}[/tex]

so solving

[tex]m-\frac{1}{2}=\sqrt{-2}[/tex]

[tex]m-\frac{1}{2}=\sqrt{-1}\sqrt{2}[/tex]    

[tex]m-\frac{1}{2}=\sqrt{2}i[/tex]              ∵  [tex]\sqrt{-1}=i[/tex]

[tex]m=\sqrt{2}i+\frac{1}{2}[/tex]

and also solving

[tex]m-\frac{1}{2}=-\sqrt{-2}[/tex]

[tex]m-\frac{1}{2}=-\sqrt{2}i[/tex]

[tex]m=-\sqrt{2}i+\frac{1}{2}[/tex]

As we know that

if

[tex]b^2-4ac\:<0[/tex]

then the equation has no real solution.

Therefore, for the values of [tex]m=\sqrt{2}i+\frac{1}{2},\:m=-\sqrt{2}i+\frac{1}{2}[/tex], for which the equation  [tex]mx^2+3x+1-m=0[/tex] will have no solution.

Answer:

igbr8gv9rt0ingr3tebegvijb3tu9hrn9vuorgnbrugngfboipbn tufgnvigfuobrengty98bnvfrgubndifvnjthbi rvjunmtybtbtbfgbN

Step-by-step explanation:

vdf fvfvrg

Answer:

k=1

Step-by-step explanation:

Since the coefficient of [tex]x^{3}[/tex] is 1, that is what you put for k

Answer:

21.5m^2

Step-by-step explanation:

Start by finding the area of the triangle including the rectangle.

The bottom side equals 7m and the other side equals 9m.

To find the area of the triangle, you multiply the base by the height, then divide by 2: (bh)÷2

(7*9)÷2=63/2m^2 or 31.5m^2

Now you can find the area of just the shaded region. To do this, you will want to find the area of the rectangle then subtract it from the area of the triangle.

To find the area of the rectangle, multiply the length by width.

2*5=10m^2

Now you can subtract the areas.

31.5-10=21.5m^2

yes so y did u need r help?????

Answer:

5/8

Explanation:

6 = 5x  - 2

8 = 5x

5/8 = x

The unknown number two less than five times a number is equal to 6 will be 5 / 8.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that two less than five times a number is equal to 6 is the number. The unknown number will be calculated as below:-

Let the number be x now form an expression.

6 = 5x  - 2

8 = 5x

5/8 = x

Therefore, the unknown number two less than five times a number is equal to 6 will be 5 / 8.

To know more about an expression follow

https://brainly.com/question/723406

#SPJ2

Answer:

32 drops of blue food coloring is needed

Step-by-step explanation:

If :

12 drops of yellow food coloring = 8 drops of blue food coloring.

48 drops of yellow food coloring = x

Cross Multiply

12 drops × x = 48 drops × 8 drops

x = 48 drops × 8 drops/12 drops

x = 32 drops of blue food coloring.

If you want to make the same shade of green frosting using 48 drops of yellow food coloring, you would be needing 32 drops of blue food coloring

Answer:

D=34

Step-by-step explanation:

2.1+31.8= 33.9

Answer:

D

Step-by-step explanation:

None of the other answer make sense.

If you are adding, why would your estimate be lower than the factors?

Answer:

8/17

Step-by-step explanation:

Answer:

For every x feet of rope purchased, the total cost(y) increases by $6.85.

Step-by-step explanation:

Answer:

You are correct, this is not a good explanation

Step-by-step explanation:

Answer:

it can be simplify by c²

Answer:

2c

Step-by-step explanation:

6, 10, 20. Domain is the x-coordinates of all values.

Answer:

X=9

Step-by-step explanation:

9+6=15

15-7=8

Absolute value equals a positive

Answer:

c. 84 time pi m squared

Step-by-step explanation:

Formula for volume of a cone: pi times radius squared times height divided by 3

for this you don't need to multiply by pi so it's

12 and radius is 6

6 squared  times 7/3

36 times 7/3

83.99999

rounded to 84 time pi m squared

Answer:

c

Step-by-step explanation:

a p e x

Answer:

30 feet away

Step-by-step explanation:

hope this helps

Answer:

11.040

Step-by-step explanation:

To get this answer you would add 7.740 please 3.500 and get 11.040

Answer:

Generally it's one that is just out of the way, the extreme outcast.

Answer:

X = -1

Step-by-step explanation:

3(x - 4) + 6 = 5(x - 1) + 1     -distribute

3x - 12 + 6 = 5x - 5 + 1     -combine like terms

3x - 6 = 5x - 4        -subtract 3x

-6 = 2x - 4        -add 4

-2 = 2x      -divide by 2

-1 = x

Hope this helps. Pls give brainliest.

Answer:

x= -1

Step-by-step explanation:

open brackets and calculate

3x - 12 + 6 = 5x -5 + 1

Calculate

3x - 6 = 5x - 4

transpose

3x - 5x = - 4 + 6

Calculate

- 2x = 2

x= 2/-2

x= -1