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3 years ago

HELP MEE! 100 POINTS AND BRAINLY! GIVE ME THE STEPS, AND A GOOD ANSWER OR I WILL DELETE YOUR ANSWER AND GET MY POINTS BACK!

Mathematics

2 answers:

salantis [7]3 years ago

8 0

Hi there! Hopefully this helps!

Answer: 11.47(to 2 decimal places).

Isolate one of the square roots: √(2x−5) = 1 + √(x−1)

Square both sides: 2x−5 = (1 + √(x−1))^2

We have removed one square root.

Expand right hand side: 2x−5 = 1 + 2√(x−1) + (x−1)

Simplify: 2x−5 = 2√(x−1) + x

Subtract x from both sides: x−5 = 2√(x−1)

Now do the "square root" thing again:

Isolate the square root: √(x−1) = (x−5)/2

Square both sides: x−1 = ((x−5)/2)^2

We have now successfully removed both square roots.

Let's continue with the solution.

Expand right hand side: x−1 = (x^2 − 10x + 25)/4

Since it is a Quadratic Equation! let's put it in standard form.

Multiply by 4 to remove division: 4x−4 = x^2 − 10x + 25

Bring all to left: 4x − 4 − x^2 + 10x − 25 = 0

Combine like terms: −x^2 + 14x − 29 = 0

Swap all signs: x^2 − 14x + 29 = 0

Using the Quadratic Formula (a=1, b=−14, c=29) gives the solutions:

2.53 and 11.47 (to 2 decimal places)

2.53: √(2×2.53−5) − √(2.53−1) ≈ −1 Oops! Should be plus 1. So it is not the solution.

11.47: √(2×11.47−5) − √(11.47−1) ≈ 1 Yes that one works.

Alexeev081 [22]3 years ago

3 0

Answer:

Solve the equation for

x by finding a , b , and c of the quadratic then applying the quadratic formula.

Exact Form:

x= 7 + 2 √ 5

Decimal Form:

x = 11.47213595 …

Step-by-step explanation:

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A sample of bacteria is decaying according to a half-life model. If the sample begins with 700 bacteria, and after 10 minutes th

Papessa [141]

Answer:

18 minutes

Step-by-step explanation:

A = A₀ (½)^(t / T)

where A is the final amount,

A₀ is the initial amount,

t is the time,

and T is the half life.

A = 140 when t = 10. Solve for the half life:

140 = 700 (½)^(10 / T)

0.2 = ½^(10 / T)

log 0.2 = (10 / T) log 0.5

10 / T = 2.32

T = 4.31

When A = 40, t is:

40 = 700 (½)^(t / 4.31)

0.057 = ½^(t / 4.31)

log 0.057 = (t / 4.31) log 0.5

t / 4.31 = 4.13

t = 17.8

Rounded to the nearest whole number, it takes 18 minutes.

4 0

3 years ago

Help will give 25 brainlest points

Alekssandra [29.7K]

Step-by-step explanation:

The ratio of the two shorter legs of the top triangle is

$\dfrac{5}{4} = 1.25$

The bottom triangle has the following ratio:

$\dfrac{7.5}{6} = 1.25$

Since their ratios are the same, this means that the two triangles are similar.

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I think it’s-10. Hope it’s right.

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Andy's weight is 5 kilograms less than twice his brother's. Together they weigh 100 kilograms. What are their weights?

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Answer:

Step-by-step explanation:

Let x be the brother's weight.

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4 0

3 years ago

The quotient of a number and 3 decreased by 121 is -164. Select the solution to the sentence shown.

docker41 [41]

Its algebra. The original equation is $\frac{x}{3} -121 = -164$

To solve for a variable, we reverse the order of operations, beginning with addition/subtraction, and then multiplication/division. To remove a number from one side, we must do the opposite to the other side. In this case, to get rid of the -121 we must add 121 to the -164. This gives us -43. Then, to get the x by itself, we must multiply the other side by 3. -43*3=129

When we are doing the opposite of an operation to the other side, we are really reversing the operation and, to keep both sides equal, we must do whatever we have done to one side to the other side. So when we have -121, we add 121 as it equals 0, therefore it is gone. Since a equation must be balanced, we have to do what we did to the other side (adding 121).

6 0

3 years ago