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2 years ago

8x/10x-2 equals 5x+3/7x solve for x

Mathematics

1 answer:

Andrews [41]2 years ago

4 0

<u>Answer:</u>

x = $\frac{1}{3}$ & 3

<u>Step-by-step explanation:</u>

$\frac{8x}{10x-2}$ = $\frac{5x+3}{7x}$

Cross multiply:

$\frac{8x}{10x-2}$ = $\frac{5x+3}{7x}$ ⇒ (8x)(7x) = (5x+3)(10x-2)

Simplify both sides:

(8x)(7x) = (5x+3)(10x-2) ⇒ 56x² = 50x²+20x-6

Set equation equal to 0:

56x² = 50x²+20x-6 ⇒ 0 = -6x²+20x-6

Factor the trinomial:

0 = -6x²+20x-6 = (-6x+2)(x-3)

Solve for X:

-6x+2 = 0

-6x = -2

x = $\frac{1}{3}$ ;

x-3 = 0

x = 3;

x = $\frac{1}{3}$ , 3

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Baby Amelia's parents measure her height every month.

jonny [76]

The statement H(30) = H(25) + 5 means that, "when Amelia was 30 months old, she was 5 centimeters taller than when she was 25 months old"

<h3><u>Solution:</u></h3>

Given that,

Baby Amelia's parents measure her height every month

It is given that H(t) models Amelia's height (in centimeters) when she was "t" months old

Given statement is H(30) = H(25) + 5

So, we can say that H(30) = Amelia's height when she was 30 months old

H(25) = Amelia's height when she was 25 months old

So H(30) = H(25) + 5 means that,

Height of Amelia when she was 30 months old is 5 centimeter more than Amelia height when she was 25 years old

Or we can say that,

When Amelia was 30 months old, she was 5 centimeters taller than when she was 25 months old

7 0

2 years ago

2. A fair dice is rolled. What is the probability that a number divisible by 3 is rolled?

Anni [7]

Answer: 2

Step-by-step explanation:

A dice has 6 numbers on it, 1,2,3,4,5, and 6.

how many pairs of 3 can you make?

(1 2 3) (4 5 6)

There are 2 pairs, so your answer is 2

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3 years ago

Miles bought a car that cost $23,556.to the nearest ten thousand,how much did the car cost

laila [671]

$20,000
In word form. he has twenty three thousand five hundred and fifty six, so we look to the digit next to the thousands, 3, and since its below 5, we keep 2 the same.

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2 years ago

A gas is said to be compressed adiabatically if there is no gain or loss of heat. When such a gas is diatomic (has two atoms per

Tems11 [23]

Answer:

The pressure is changing at $\frac{dP}{dt}=3.68$

Step-by-step explanation:

Suppose we have two quantities, which are connected to each other and both changing with time. A related rate problem is a problem in which we know the rate of change of one of the quantities and want to find the rate of change of the other quantity.

We know that the volume is decreasing at the rate of $\frac{dV}{dt}=-4 \:{\frac{cm^3}{min}}$ and we want to find at what rate is the pressure changing.

The equation that model this situation is

$PV^{1.4}=k$

Differentiate both sides with respect to time t.

$\frac{d}{dt}(PV^{1.4})= \frac{d}{dt}k\\$

The Product rule tells us how to differentiate expressions that are the product of two other, more basic, expressions:

$\frac{d}{{dx}}\left( {f\left( x \right)g\left( x \right)} \right) = f\left( x \right)\frac{d}{{dx}}g\left( x \right) + \frac{d}{{dx}}f\left( x \right)g\left( x \right)$

Apply this rule to our expression we get

$V^{1.4}\cdot \frac{dP}{dt}+1.4\cdot P \cdot V^{0.4} \cdot \frac{dV}{dt}=0$

Solve for $\frac{dP}{dt}$

$V^{1.4}\cdot \frac{dP}{dt}=-1.4\cdot P \cdot V^{0.4} \cdot \frac{dV}{dt}\\\\\frac{dP}{dt}=\frac{-1.4\cdot P \cdot V^{0.4} \cdot \frac{dV}{dt}}{V^{1.4}} \\\\\frac{dP}{dt}=\frac{-1.4\cdot P \cdot \frac{dV}{dt}}{V}}$