All categories

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:

You might be interested in

HELLLLLLLLLLLLLLLLPPPPPPP PLEASE! Is the number 4.78 a solution of x < 5? Is the number 6 a solution of x < 6? PLEASE EXPL

Karolina [17]

As you know, 4.78 is less than 5, so
.. yes, x=4.78 is a solution to x < 5

As you know, 6 = 6, but is not less than 6.
.. no, x=6 is not a solution to x < 6.

7 0

3 years ago

How much time has Passed from 6:25.Am Unitil 10:25 pm

stealth61 [152]

16 hours has passed

6 0

2 years ago

The board of a large company is made up of 7 women and 9 men. 6 of them will go as a delegation to a national conference.

Burka [1]

Answer:

a) 5765760

b) 60480

c) 5705280

Step-by-step explanation:

Assuming that order is not important:

Number of women = 7

Number of men = 9

Members of the delegation = 6

a) How many delegations are possible?

$n=\frac{16!}{(16-6)!}=16*15*14*13*12*11\\ n= 5765760$

b) How many of these delegations have all men?

$n_{men} = \frac{9!}{(9-6)!}=9*8*7*6*5*4 \\n_{men} = 60480$

c) How many of these delegations have at least one woman?

$n_{women >0}=n-n_{men}\\n_{women >0} =5765760-60480\\n_{women >0} =5705280$

4 0

3 years ago

A NASA spacecraft measures the rate R of at which atmospheric pressure on Mars decreases with altitude. The result at a certain

AysviL [449]

Answer:

$R = 0.0000498 \frac{KJ}{ m m^3}=0.0000498 \frac{KJ}{m^4}=4.98x10^{-5}\frac{KJ}{m^4}$

Step-by-step explanation:

For this case we have the following value:

$R = 0.0498 \frac{Kpa}{Km}$

We can convert this first to $\frac{Kpa}{m}$ like this:

$R=0.0498 \frac{Kpa}{Km} *\frac{1km}{1000m}=0.0000498 \frac{Kpa}{m}$

Now we use the fact the the pressure is defined as $P =\frac{F}{A}$ , whre P is the pressure, F the force and A the area, so then $Kpa= \frac{KN}{m^2}$ and then we can replace this:

$R=0.0000498 \frac{KN}{m^3}$

Now from definition of work we know that $W= Fd$ where W is the work, F the force and d the distance, so then is equivalent $KN =\frac{KJ}{m}$

And if we replace this into the equation we got:

$R = 0.0000498 \frac{KJ}{ m m^3}=0.0000498 \frac{KJ}{m^4}=4.98x10^{-5}\frac{KJ}{m^4}$

4 0

3 years ago

ABC is isosceles with AB=AC=8 units and BC=6 units. D and E are midpoints of AB and BC respectively. Calculate the length of DE?

Allushta [10]

The triangle is drawn and is shown in the image attached with.

We get two similar triangles. Triangle ABC and Triangle ADE. Since the triangles are similar the ratio of their corresponding sides will be the same.

D and E are the midpoints of AB and BC, therefore, AD and AE are both 4 units in length. Using the property of similar triangles, we can say:

AD : DE= AB : BC
AD = 4 units
AB = 8 units
BC = 6 units
DE = unknown = x units

So,

$4 :x = 8 : 6 \\ \\ 
 \frac{4}{x} = \frac{8}{6} \\ \\ 
x=4* \frac{6}{8}=3 
$

Therefore, the length of DE will be 3 units

6 0

3 years ago