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3 years ago

Please solve z-6√z+8=0 (Only "z" is on the square root)

Mathematics

1 answer:

kifflom [539]3 years ago

4 0

Answer:

$\large\boxed{z=4\ or\ z=16}$

Step-by-step explanation:

$z-6\sqrt{z}+8=0\\\\\text{Domain}:\ z\geq0\\\\\text{substitute}\ \sqrt{z}=t\geq0,\ \text{then}\ z=t^2:\\\\t^2-6t+8=0\\\\t^2-4t-2t+8=0\\\\t(t-4)-2(t-4)=0\\\\(t-4)(t-2)=0\iff t-4=0\ \vee\ t-2=0\\\\t-4=0\to\sqrt{z}-4=0\qquad\text{add 4 to both sides}\\\\\sqrt{z}=4\iff\boxed{z=16}\\\\t-2=0\to\sqrt{z}-2=0\qquad\text{add 2 to both sides}\\\\\sqrt{z}=2\iff \boxed{z=4}$

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A line, y = mx + b, passes through the point (10, 3) and is parallel to the line 2x+5y=12.

slava [35]

We have been given that a line $y=mx+b$ passes through the point (10, 3) and is parallel to the line $2x+5y=12$ . We are asked to find the y-intercept of the line.

First of all we will rewrite our given equation in slope-intercept form as:

$2x-2x+5y=12-2x$

$5y=-2x+12$

$\frac{5y}{5}=-\frac{2}{5}x+\frac{12}{5}$

$y=-\frac{2}{5}x+\frac{12}{5}$

We know that slope of parallel lines is equal, so slope of parallel line to our given line would be $-\frac{2}{5}$ .

Now we will use slope-intercept form of equation to find y-intercept.

$y=mx+b$ , where,

m = Slope,

b = The y-intercept.

Let us substitute $m=-\frac{2}{5}$ and coordinates of point $(10,3)$ in above equation as:

$3=-\frac{2}{5}(10)+b$

$3=-2(2)+b$

$3=-4+b$

$3+4=-4+4+b$

$7=b$

Therefore, the y-intercept is 7 and our required equation would be $y=-\frac{2}{5}x+7$ .

5 0

3 years ago

this is part 2 and you just have to find the total area in sq ft and also answer how much material do you need to make 3 backpac

Lubov Fominskaja [6]

1. 1 1/8= 18/16

5/16*2= 10/16

4/16*2= 8/16

9/16= 9/16

1/2= 8/16

18/16 + 10/16 + 8/16 + 9/16 + 8/16= 53/16

Simplify:

4 & 5/16sq ft

2. All you do is multiply that by 3... so 4 & 5/16 = 53/16 53/16*3 = 159/16 = 9 & 15/16 sq ft

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3 years ago

Solve the following system of equations:

Vladimir79 [104]

Answer:

(-1,1)

Step-by-step explanation:

We can solve this by either graphing and finding ther point the lines intersect, or mathematically, I'll do both.

Graphing:

Mathematically:

−2x + 4y = 6

y = 2x + 3

See the attached graph. The lines intersect at (-1,1)

--------------------

I'll rearrange the first equation (to make it easier for me):

−2x + 4y = 6

4y = 2x + 6

y = (1/2)x + 1.5

Now lets substitute the second equation into the first so that we can eliminate y:

y = 2x + 3

[(1/2)x + 1.5] = 2x + 3

- (3/2)x = (3/2)

x = -1

If x = -1:

y = 2(-1) + 3

y = 1

The solution is x = -1 and y = 1, or (-1,1)

=================

Both approaches give us (-1,1), the solution to the system of equations. It is the only point that satisfies both equations.

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2 years ago

There are 12 students in a classroom, including the triplets joey, chloe, and zoe. If 3 of the 12 are randomly selcted to give s

forsale [732]

The probability of choosing Joey first is 1/12 .

If that happens, the probability of choosing Chloe next is 1/11 .

Then, the probability of choosing Zoe after that is 1/10 .

The probability of all these things happening is

(1/12) x (1/11) x (1/10)

= 1/1320 = 0.00076 = 0.076 percent

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4 years ago

Please help me I need it

Kobotan [32]

Answer:

Step-by-step explanation:

You use the quadratic equation and substitute these values from the equation given

a=1,b=5, c=2

Which gives you the value of option A

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