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3 years ago

5y + 3 > −7y + 13 Multi-step linear inequalities

Mathematics

1 answer:

Artemon [7]3 years ago

3 0

Answer:

y > $\frac{5}{6}$

Step-by-step explanation:

Given

5y + 3 > - 7y + 13 ( add 7y to both sides )

12y + 3 > 13 ( subtract 3 from both sides )

12y > 10 ( divide both sides by 12 )

y > $\frac{10}{12}$ , that is

y > $\frac{5}{6}$

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How many times can 19 go into 225?

Tatiana [17]

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Ksivusya [100]

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3 years ago

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Solve 2x2 – 6x + 10 = 0 by completing the square.

astraxan [27]

Answer: x = 6.32 or -0.32

Step-by-step explanation:

2x² - 6x + 10 = 0

No we divide the expression by 2 to make the coefficient of x² equals 1

We now have

x² - 3x + 5 = 0

Now we remove 5 to the other side of the equation

x² - 3x = -5

we add to both side square of half the coefficient of x which is 3

x² - 3x + ( ⁻³/₂)² = -5 + (⁻³/₂)²

(x - ³/₂)² = -5 + ⁹/₄

Resolve into fraction

(x - ³/₂)² = ⁻¹¹/4

Take the roots of the equation

x - ³/₂ = √¹¹/₄

x - ³/₂ = √11/₂

x = ³/₂ ± 3.32/₂

= 3+ 3.32 or 3 - 3.32

= 6.32 or - 0.32

4 0

3 years ago

What is the missing number in the sequence shown? 5, 9, 14, 20, __, 35

Sonja [21]

$\sf{ 27}$

Step-by-step explanation:

5+4=9
9+5=14
14+6=20
20+7=27
27+8=35

So The sequence is 5,9,14,20,27,35

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3 years ago

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Element X decays radioactively with a half life of 15 minutes. If there are 960 grams of Element X, how long, to the nearest ten

labwork [276]

An equation is formed of two equal expressions. It will take for the radioactive element to decay from 960 grams to 295 grams in 25.54 minutes.

<h3>What is an equation?</h3>

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The radioactive decay of an element is given by the formula,

$N = N_0 \cdot e^{-\lambda t}$

Given the half-life of the element is 15 minutes, therefore, we can write,

$\dfrac12 = e^{-\lambda\times 15}\\\\\ln (0.5) = -\lambda\times 15\\\\\lambda = 0.0462$

Now, the time it will take for 960 grams to decay to 295 grams is,

$295 = 960 \cdot e^{-0.0462 \times t}\\\\\ln (\dfrac{295}{960}) = -0.0462 \times t\\\\t = 25.54\rm\ minutes$

Hence, it will take for the radioactive element to decay from 960 grams to 295 grams in 25.54 minutes.

Learn more about Equation:

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2 years ago