the tens digit of a two digit number is 5 greater the units digit. If you subtract double the reversed number from it, the result is a fourth of the original number. Find the original number.

Answers

Answer 1

Given:

The tens digit of a two digit number is 5 greater the units digit.

If you subtract double the reversed number from it, the result is a fourth of the original number.

To find:

The original number.

Solution:

Let n be the two digit number and x be the unit digit. Then tens digit is (x+5) and the original number is:

[tex]n=(x+5)\times 10+x\times 1[/tex]

[tex]n=10x+50+x[/tex]

[tex]n=11x+50[/tex]

Reversed number is:

[tex]x\times 10+(x+5)\times 1=10x+x+5[/tex]

[tex]x\times 10+(x+5)\times 1=11x+5[/tex]

If you subtract double the reversed number from it, the result is a fourth of the original number.

[tex]11x+50-2(11x+5)=\dfrac{1}{4}(11x+50)[/tex]

[tex]11x+50-22x-10=\dfrac{1}{4}(11x+50)[/tex]

[tex]40-11x=\dfrac{1}{4}(11x+50)[/tex]

Multiply both sides by 4.

[tex]160-44x=11x+50[/tex]

[tex]160-50=11x+44x[/tex]

[tex]110=55x[/tex]

Divide both sides by 55.

[tex]\dfrac{110}{55}=x[/tex]

[tex]2=x[/tex]

The unit digit is 2. So, the tens digit is [tex]2+5=7[/tex].

Therefore, the original number is 72.


Related Questions

Caroline,Colin & Sarah share some money in the ratio 5:9:6.
In total, Caroline and Sarah receive £44. How much does Colin get?

Answers

Answer:

Caroline gets 4*5 = 20 pounds

Colin gets 9 * 4     = 36 pounds

Sarah gets 6*4      = 24 pounds.

Step-by-step explanation:

The ratios are 5x + 9x + 6x

5x + 6x = 11x

Caroline and Sarah get a total of 44 pounds. They don't get 44 pounds each.

11x = 44            Divide by 11

x = 44/11

x = 4

Colin gets 9x

x = 4

9*4 = 36

Colin gets 35 pounds.

Caroline gets 4*5 = 20 pounds

Colin gets 9 * 4     = 36 pounds

Sarah gets 6*4      = 24 pounds.

Caroline and Sarah get 20 + 24 = 44

1 pump can fill a pool in 8 hours the other pump can fill the pool in 10 hours if both of the pumps were turned on at the same time to fill the pool how long will it take

Answers

Answer:

4 4/9 hours

Step-by-step explanation:

In one hour pump1 can fill 1/8 of the tank and pump2 can fill 1/10 of the tank.

Two pumps can fill:

1/8 + 1/10 = 5/40 + 4/40 = 9/40 of the tank in one hour

Time required to fill the tank:

1/(9/40) = 40/9 = 4 4/9 hours

Tiana uses the equation c = 21h to figure out the total amount, c, she should
charge a customer for babysitting for h hours.
a. What is the constant of proportionality? What does it mean?
b. Tiana charges $94.50 for a job. How long did she babysit for?
Show your work.

Answers

Answer:

a. The constant of proportionality is, 21

b. Tiana charges $94.50 for a job, so, c=94.50

from the given equation,

c = 21h

or, 94.50 = 21h

or, h = 94.50/21

or, h = 4.5

She babysit for 4.5 hours.

Answered by GAUTHMATH

The constant of proportionality is 21 and it means the constant value that connects two variables together. If Tiana charges $94.50 for a job, she spent 4.5hours babysitting.

The equation used by Tiana c = 21h to figure out the total amount (c) she should charge a customer for babysitting for h hours.

The constant of proportionality, denoted by K, in a linear relationship shows how two variables relate to one another. In this case, the total amount (c) is directly proportional to time (h).

The constant of proportionality, which is 21, connects the variables 'c' and 'h'.

If Tiana charges $94.50 for a job, we can calculate the time spent on doing the job by using:

c = 21h

94.50 = 21h

h = 94.50 ÷ 21

h = 4.5hours.

Therefore, Tiana spent 4½ hours babysitting.

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How many gallons equal 26 liters

Answers

Answer:

6.8 gallions i believe. im not quite sure

Instructions: Find the measure of the indicated angle to the nearest degree.

Answers

Step-by-step explanation:

I don't have a calculator with me right now but I can give you the equation to work out your answer.

cos-1(35/38)

There should be a function of "cos-1" on you're calculator, not just "cos"

hope it helps :)

If m ≠ 1 and mn - 3 = 3 - n , then what is the value of n?
A) 6/ m+1
B) 6/ m-1
C) 6/ m+n
D) 6/ m-n

Answers

[tex]n = \frac{6}{m + 1} [/tex]

Hope it helps you...

The value of n is n= 6/( m+1).

What is expression?

An expression is a set of terms combined using the operations +, – , x or , /.

Given:

mn - 3 = 3 - n

mn + n = 6

n(m+ 1) =6

n= 6/( m+1)

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Rewrite using exponents

AxAxAxAxAxAxA



need answer quick!!! please

Answers

Answer:

A^7

Step-by-step explanation:

Help what is x
When x^5 is 225

Answers

Answer:

Solution given:

x^5=225

we have

x=[tex] \sqrt[5]{225} [/tex]

x=2.9541

Hello!

[tex] \bf {x}^{5} = 225[/tex]

Extract the radical on both sides of the equation.

[tex] \bf x = \sqrt[5]{225} [/tex]

[tex] \bf x ≈2.95418[/tex]

Answer: x 2,95418

Good luck! :)

Construct 5 equivalent equations for the equation - 3 + 2x = -4.

Answers

Answer:C

Step-by-step explanation:

3-2x = 4-2x = 12x = -1x = -1/2-x = 1/2

The midpoint of a segment is (6,−4) and one endpoint is (13,−2). Find the coordinates of the other endpoint.

A. (20, -6)
B. (-1, 0)
C. (-1, -6)
D. (20, 0)

Answers

Answer:

(-1,-6)

Step-by-step explanation:

(13 + x)/2 = 6

13+x= 12

x = -1

~~~~~~~~~~~~~~~

(-2 + y ) / 2 = -4

-2 + y = -8

y = -6

The coordinates of the other endpoint will be (-1,-6). The correct option is C.

What is the midpoint of the line?

Divide the measurement of the distance between the two end locations by 2. The middle of that line is located at this separation from either end.

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.

Given that the midpoint of a segment is (6,−4) and one endpoint is (13,−2).

The x- coordinate will be calculated as:-

(13 + x)/2 = 6

13+x= 12

x = -1

The y-coordinate will be calculated as:-

(-2 + y ) / 2 = -4

-2 + y = -8

y = -6

Therefore, the coordinates of the other endpoint will be (-1,-6). The correct option is C.

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HELPPPP MEEEEE OUTTTTT PLEASEEEE ASAPPPP!!!!

Answers

Answer:

sin X =35/37

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin X = opp side / hypotenuse

sin X =35/37

Estimate the product of 32 and 19 ?

Answers

Answer:

608

Step-by-step explanation:

32 x 19

= 32 x ( 10 + 9 )

= 320 + 288

= 608

help pls with explanation!!!

Answers

Answer:

18c - 30d + 36

Step-by-step explanation:

To apply the distributive property, we must "distribute" (multiply) the outer term by the terms in the parentheses. In this case, the outer term is 6, and the inner terms are 3c, 5d, and 6. Then, if there's any like terms, you must combine them.

6(3c - 5d + 6)

(6 · 3c) + (6 · -5d) + (6 · 6)

18c + -30d + 36

As you can see, there's no like terms in this expression, so the equivalent expression to 6(3c - 5d + 6) is 18c + -30d + 36.

A triangle and a parallelogram have the same base and the same area.
If the sides of the triangle are 26 cm, 28 cm and 30 cm and the
parallelogram stands on the base 28 cm. Find the height of the
parallelogram.

Answers

Answer:

12 centimeters

Step-by-step explanation:

The side lengths of the triangle are: 26, 28, and 30 centimeters

a = 26 cm, b = 28 cm, c = 30 cm

To find the area, we first must find the semi-perimeter with the following equation:

s = (a+b+c)/2

  = (28+26+30)/2

  = 42 centimeters

Now, to find the area, we can use Heron's formula:

A = [tex]\sqrt{s (s-a)(s-b)(s-c)}[/tex]

     [tex]\sqrt{42(42-28)(42-26)(42-30)[/tex]

     [tex]\sqrt{42(14)(16)(12)}[/tex]

     [tex]\sqrt{112896}[/tex]

     336 squared centimeters

Since the area of the parallelogram is equal to the area of our triangle:

Area of Parallelogram = Area of Triangle

base ⋅ height = 336 squared centimeters

28 ⋅ height = 336 squared centimeters

height = 336/28

height = 12 centimeters

Which segment is the hypotenuse?​

Answers

Answer:

SU

Step-by-step explanation:

The hypotenuse is opposite the right angle

The hypotenuse is US  or SU

We have to pick,

The segment which is hypotenuse,

Hypotenuse will be the opposite segment of the right angle.

Now it will be,

→ SU (or) US

Hence, SU is the hypotenuse.

can someone please help me with this?!?!!

Answers

Answer:

I can't help but I hope you succeed

Graph the solution to the following system of inequalities.
y-2x-9
y<2x+7

Answers

Answer:

Tb bight by icing I jb Yves j by by by navy by iffy i by by by

Use a double-angle or half-angle identity to find the exact value of each expression

Answers

If 180° < θ < 270°, then 90° < θ/2 < 135°, which places θ/2 in the second quadrant so that sin(θ/2) > 0 and cos(θ/2) < 0.

Recall that

cos²(θ/2) = (1 + cos(θ))/2

==>   cos(θ/2) = -√[(1 + (-15/17))/2] = -1/√17

and

sin²(θ/2) = (1 - cos(θ))/2

==>   sin(θ/2) = +√[(1 - (-15/17))/2] = 4/√17

Then

tan(θ/2) = sin(θ/2) / cos(θ/2)

… = (4/√17) / (-1/√17)

… = -4

Anyone knows the answer?

Answers

Answer:

D) (2,-1)

Step-by-step explanation:

These are two concentric circles of radius 3 and 4 at the origin. That means that any point within the inner is also within the outer. So focusing on the inner, the points plugged into its equation must be less than or equal to the radius squared or 9. That is only valid with point D.

The equation of line a is y=-x+ 3. If line b runs perpendicular to line a and
passes through (2, 6), what would be the equation of line b?

Answers

Answer:

y = 4x -2

Step-by-step explanation:

y = 4x + b

6 = 4(2) + b

6 = 8 + b

-2 = b

Can someone help me please ?

Answers

Answer:

I would say D is your answer

Step-by-step explanation:

Answer:

the fourth one

use mathaway its like my best friend for math!!!

Step-by-step explanation:

Can anyone help me please

Answers

Answer:

1

Step-by-step explanation:

Basically you just need to find the square root of all of them

36=6    -1=1      9=3 .     -1=1

6-1-3-1=1

HELP ITS DUE IN THE MORNING AND ITS 3:57​

Answers

Answer:

A " (1,-2)

B " (4,0)

C " (6,-3)

Step-by-step explanation:

Hope it helped.

° ° °

PLEASE PLEASE PLEASE HELP. I WILL BE SO SO SO HAPPY!! WILL GOVE BRANLIEST! AND FOREVER BE SO HAPPY! POINTS!

Answers

Answer:

a

Step-by-step explanation:

follows geometric sequence. starting value is 1/3 and is multiplied by 1/3 every time

Solve the following quadratic function
by utilizing the square root method.
y = 100 – x2

Answers

Answer:

x = ± 10

Step-by-step explanation:

To solve the equation let y = 0 , that is

0 = 100 - x²( add x² to both sides )

x² = 100 (I take the square root of both sides )

x = ± [tex]\sqrt{100}[/tex] = ± 10

Then solution is x = - 10, x = 10

Answer:

10

Step-by-step explanation:

the guy on top put -10 he's right but it's just 10

Help!!

I think I got these wrong, so please help!! Thank you!

Answers

Answer:

(x+3)(x+4)(x-4)

x+2 and x-3 are not factors but x-4 is

Step-by-step explanation:

let's factor it :)

x^3 + 3x^2 - 16x -48

first we will factor this:

x^3 + 3x^2

x^2(x + 3)

then factor the second part :

- 16x - 48

-16(x + 3)

so now,

x^2(x + 3) - 16(x + 3)

factor out x+3

(x+3)(x^2 - 16)

factor x^2 - 16

(x+3)(x+4)(x-4)

Graph: f(x) = 3/2 (2)x
Step 1: Calculate the initial value of the function.
f(0)=

Answers

Answer:

Step 1: 1.5

Step 2: Plot the points (0, 1.5)

Step 3: 3, then 0.75

Step 4: Plot the points (1, 3) and (-1, 0.75)

Step 5: y=0

Step-by-step explanation:

Ur welcome and have a nice day :>

The initial value of the function f(x) = 3/2 (2)^x is 3/2

How to calculate the initial value of the function?

The function expression is given s:

f(x) = 3/2 (2)^x

Substitute 0 for x

f(0) = 3/2 (2)^0

Evaluate the exponent

f(0) = 3/2 * 1

Evaluate the product

f(0) = 3/2

Hence, the initial value of the function is 3/2

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Alex can cut a cord into 7 pieces in 36 seconds. How long will it take him to cut the cord into 12 pieces? (the answer is NOT 61 or 62.)

Answers

Answer:

x=61.71428 or 61 5/7

Step-by-step explanation:

We can use a ratio to solve

7 pieces              12 pieces

-----------------   = ---------------

36 seconds          x seconds

Using cross products

7x = 36*12

7x = 432

Divide by 7

7x/7 = 432/7

61 5/7

x=61.71428

Answer:

66

Step-by-step explanation:

Guys Help me

Does (4, 7) make the equation y = 2x + 7 true?

Answers

Answer:

false

Step-by-step explanation:

x=4andy=7

2×4+7 isnot equal to 7

Answer:

Tue equation is

y=2x+7

So, the answer is

(2,7)

And (4,7) is wrong

what is the reason for statement 8
a. third angle theorem
b. triangle proportionality theorem
c. congruent complements theorem

Answers

i need points sorry about this
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