Write the ratio 1.6 : 4 as a fraction in simplest form, with whole numbers in the numerator and denominator.

1 answer:

7 0

1.6 : 4

1.6 is also equal to 8/5

therefore,

8/5 : 4

(8/5)/4

**get the reciprocal of the denominator (4) which is equal to 1/4**

(8/5)*(1/4)

(8/4)*(1/5)

2*(1/5)

2/5

two fifth is the answer

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Which solution to the equation 1/x-1=x-2/2x^2-2 is extraneous?

olga2289 [7]

<span>An extraneous solution is a solution, such as that to an equation, that emerges from the process of solving the problem but is not a valid solution to the original problem.

Given the equation:
$\frac{1}{x-1} = \frac{x-2}{2x^2-2} \\ \\ 2x^2-2=(x-1)(x-2)=x^2-3x+2 \\ \\ x^2+3x-4=0 \\ \\ (x-1)(x+4)=0 \\ \\ x-1=0 \ or \ x+4=0 \\ \\ x=1 \ or \ x=-4$

From the equation, it is obtained that x = 1 and x = -4 are the solutions of the equation.

Now, we substitute x = 1 into the equation as follows:
</span><span> $\frac{1}{1-1} = \frac{1-2}{2(1)^2-2} \\ \\ \frac{1}{0} = \frac{-1}{2-2} \\ \\ \frac{1}{0} = \frac{-1}{0}$

As can be see, for x = 1, the equation is undefined.

Now, we substitute x = -4 into the equation as follows:
$\frac{1}{-4-1} = \frac{-4-2}{2(-4)^2-2} \\ \\ \frac{1}{-5} = \frac{-6}{2(16)-2} = \frac{-6}{32-2} = \frac{-6}{30} \\ \\ - \frac{1}{5} =- \frac{1}{5}$

It can be seen that x = -4 is a valid solution of the orignal equation.

Therefore, x = 1 is an extraneous solution to the equation
$\frac{1}{x-1} = \frac{x-2}{2x^2-2}$ </span>

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ou decide to bake some cakes. You need 150 g of flour for 12 cakes. How much flour do you need for 30 cakes? g

Brilliant_brown [7]

Short answer: 375 grams

Remark
You only need to set up a direct proportion

Givens
flour for 12 cakes = 150 grams
Number of cakes initially = 12
Amount of flouer for 30 cakes = x
Number of cakes = 30

Proportion
amount flour for 12 cakes / 12 cakes = x / 30

Sub and solve
150 grams / 12 cakes = x / 30 cakes Cross multiply
150 * 30 = 12 *x Multiply the left side.
4500 = 12 x Divide both sides by 12
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375 grams for 30 cakes. <<<<< Answer

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wolverine [178]

1. Answer: 15.7143

log (7x-10)=2

Use the identity: loga(x)=b = x=(a)(b)

7x-10=10^2

Evaluate the Power

7x-10=100

Addition Property of Equality

7x=110

Division Property of Equality

x=110/7 or 15.7143

2. Answer: 0.3107

log(3)+log(x^-3)=2
log(3x^-3)=2
log(3 x 1/x^3)=2
log(3/x^3)=2
3/x^3=10^2
3/x^3=100
3=100x^3
3/100=x^3
Answer Cube root 30 / 10 or 0.3107

3. Answer: 0.002

log(5) + log(x) = -2
log(5x)= -2
5x= 10^-2
5x=1/10^2
5x=1/100
x=1/500

Answer: 0.002

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