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Tasya [4]
3 years ago
10

if you add the digits in a two-digit number and multiply the sum by 7, you get the original number. If you reverse the digits in

the two-digit number, the new number is 18 more than the sum of its two digits. What is the original number?
Mathematics
1 answer:
ANTONII [103]3 years ago
4 0
Let m the tens digit and n the ones
the Original number is 10m+n
7(m+n) =10m+n
7m+7n=10m+n
6n=3m

Reversing the number 10n+m
10n+m=18+n+m
9n=18
n=2

6n=3m
6(2)=3m
3m=12
m=4
the number is 10m+n=10(4)+2=42
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A tank initially contains 50 gallons of brine, with 30 pounds of salt in solution. Water runs into the tank at 6 gallons per min
balandron [24]

Answer:

1.857 minutes

Step-by-step explanation:

From the given information:

Consider the amount of salt present in the tank as x(t) at a given time (t); &

The volume of the solution = V(t)

At t = 0 i.e. (at initial conditions)  x(0) = 30; and V(0) = 50

However, the overall increase taken place for 1 gallon per minute is:

V(t) = 50 + t

The amount of salt x(t) at any given point for time (t) is;

\dfrac{x(t)}{V(t)}= \dfrac{x(t)}{50+t}

After 5 gallons of solution exit per minute; the concentration of the salt solution changes at:

\dfrac{dx(t)}{dt}= -\dfrac{5x(t)}{50+t}

Taking the integral of what we have above, we get:

In x(t) = - 5 In(t + 50) + In (C)

In x(t) = In (t+ 50)⁻⁵ + In (C)

In x(t) = In C ( t + 50)⁻⁵

x(t) = C(t + 50)⁻⁵      (General solution)

To estimate the required solution; we apply the initial conditions x(0) = 30;

Thus;

x(0) = C(50)⁻⁵ = 30

⇒ C = 30 × 50⁵

Hence; x(t) =  30 × 50⁵ × (t + 50)⁻⁵

The above expression can be re-written as:

x(t) = 25 \implies 30 \times \bigg ( \dfrac{50}{t+50} \bigg ) ^5= 25

i.e.

\bigg ( \dfrac{50}{t+50} \bigg ) ^5= \dfrac{25}{30}

\dfrac{50}{t+50}= \bigg ( \dfrac{25}{30}\bigg) ^{\dfrac{1}{5}}

\dfrac{50}{t+50}= 0.964192504

{50}= 0.964192504(t+50)

50 = 0.964192504t + 48.2096252

50 - 48.2096252 = 0.964192504t

1.7903748 =  0.964192504t

t = 1.7903748 / 0.964192504

t ≅ 1.857 minutes

We can thereby conclude that the estimated time it will require until there are 25 pounds of salt in the tank is 1.857 minutes.

7 0
2 years ago
A credit card company charges an annual simple interest rate of 24%. in august, your purchases totaled $956. How much will you p
Oksana_A [137]

Answer:

83  

I know because I did this problem a few years ago

3 0
2 years ago
A)14 xy + 3 xy + 2[x[y - 17)<br> Simplify the expression.
tankabanditka [31]

Answer:

Let's simplify step-by-step.

14xy+3xy+2x(y−17)

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5 0
3 years ago
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lakkis [162]

Answer:

The given point A (6,13) lies on the equation.  True

The given point  B(21,33) lies on the equation.  True

The given point  C (99, 137) lies on the equation.  True

Step-by-step explanation:

Here, the given equation is : y =\frac{4}{3} x + 5

Now,check the given equation for the given points.

1)  A (6,13)

Substitute x = 6 in the given equationy =\frac{4}{3} x + 5

y =\frac{4}{3} (6) + 5  = 4(2) + 5  = 8 + 5 =  13

⇒ y= 13

Hence, the given point A (6,13) lies on the equation.

2)  B  (21,33)

Substitute x = 21 in the given equationy =\frac{4}{3} x + 5

y =\frac{4}{3} (21) + 5  = 4(7) + 5  = 28 + 5 =  33

⇒ y  = 33

Hence, the given point  B(21,33) lies on the equation.

3)  C (99, 137)

Substitute x = 99 in the given equationy =\frac{4}{3} x + 5

y =\frac{4}{3} (99) + 5  = 4(33) + 5  = 132 + 5 =  137

⇒ y  = 137

Hence, the given point  C (99, 137) lies on the equation.

7 0
3 years ago
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What is p ÷ 6 = 9 ? I'm not really understanding it
Shalnov [3]
Let's figure this out. Step by step:

P /  6 = 9

P = 6(9)

P = 54 is your answer.

I hope this helps :)
8 0
3 years ago
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