Imagine that you must cross the hallway staying an equal distance from each laser. Il you get closer to one laser than the other, it will blast you. Use a compass and straightedge to draw a safe path through the hallway.

Answer:

[tex] \frac{1 - 2 \sqrt{x} + x }{1 - x} [/tex]

Step-by-step explanation:

[tex] \frac{1 - \sqrt{x} }{1 + \sqrt{x} } [/tex]

Rationalize the denominator by multiplying by it conjugate.

[tex] \frac{1 - \sqrt{x} }{1 + \sqrt{x} } \times \frac{1 - \sqrt{x} }{1 - \sqrt{x} } = \frac{1 - 2 \sqrt{x} + x}{1 - x} [/tex]

Answer:

The 70% mixture makes up 0.7 liters of the solution whereas the 60% mixture makes up 2.8 liters of the solution.

Step-by-step explanation:

Let us have x liters of the .7 mixture and y liters of the .6 mixture.

We want total liters to be 3.5 which means we need x+y=3.5 . I don't like the decimal in the equation so I'm going to multiply both sides by 10: 10x+10y=35

We also need the .7x+.6y=.62(3.5) . I hate the decimal business going on in this question so I'm going to multiply by 1000 which gives 700x+600y=62(35) .

So we have the system

700x+600y=62(35)

10x+10y=35

I'm going to setup this up for linear combination/elimination.

Multiply bottom equation by 60.

700x+600y=62(35)

600x+600y=60(35)

Subtract equations (bottom from top):

(700-600)x+(600-600)y=35(62-60)

Simplify:

100x+0y=35(2)

100x=70

Divide both sides by 100:

x=70/100

x=7/10

Going back to x+y=3.5 along with x=7/10 or .7 liters to find y.

y=3.5-x with x=.7

y=3.5-0.7

y=2.8

The 70% mixture makes up 0.7 liters of the solution whereas the 60% mixture makes up 2.8 liters of the solution.

Pic added.

Another way to do problem:

.7x+.6(3.5-x)=.62(3.5)

Multiply and distribute:

.7x+2.1-.6x=2.17

Combine like terms on left:

.1x+2.1=2.17

Subtract 2.1 on both sides:

.1x=.07

Multiply both sides by 10:

x=0.7 liters

Now the other acid solution is 3.5-0.7 which is 2.8 litera.

B. -4/6

Step-by-step explanation:

5x+x=-4

6x=-4

x=-4/6

Answer:

Step-by-step explanation:

If you are solving for x then you should get something like this

A 5x-2+x=x- 4 B. 5x+x=x-4

6x-2=-4. 6x=x-4

6x-2-x=-4. 6x-x=-4

5x-2+2=-4+2. 5x=-4

5x/5=-2/5. 5x/5=-4/5

x=-2/5. x=-4/5

I hope this helped you out!

Answer:

12

Step-by-step explanation:

(2x-y)=4

Multiply the first equation by 3

3*(2x-y)=3*4

6x -3y = 12

Answer:

143.5

Step-by-step explanation:

4lnx=20

lnx=5

lnx= logeX

logeX=5

x=e^5

that is approximately equal to 2.7^5= 143.5

Answer:

x=148.4

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

5,9,15,21,26,34,43,47,50,55,63,72

Answer: it's 72

ok!! hope it helps

Answer:

672

Step-by-step explanation:

Given: 8 pizza hut's sold a total of 5,376 pizzas

Each pizza hut sold the same amount of pizzas

So number of pizzas sold from 1 pizza hut = 5376/8 = 672

Answer:

7.3

Step-by-step explanation:

The length of AB is found using the distance formula

We need to know the coordinates of A and B

A = (-5,-4) and B = (-3,3)

The distance is

d = sqrt ( (y2-y1)^2 + (x2-x1)^2)

   = sqrt( (3 - -4)^2 +(-3 - -5)^2)

   = sqrt( (3+4)^2 +(-3+5)^2)

   = sqrt(7^2+2^2)

   = sqrt(49+4)

  = sqrt(53)

  =7.280109889

To the nearest hundredth

 =7.3

Answer:

Step-by-step explanation:

Answer:

huh

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

By convention, it is C.

B is irrational but still real

D is irrational but still real

A is an integer which is real.

Answer: 4 + 9i

On edge2020.

Answer:

Step-by-step explanation:

A = [tex]\frac{x+y}{2}[/tex]

2A = x + y

y = 2A - x

Answer:

[tex]{ \bf{ \bar {MN}} \: means \: length \: between \: M \: and \: N}[/tex]

MN means line joining point M to point N.

Answer:

fraction of blue beads = 7/(4+7)

= 7/11

Answer:

3:5

Step-by-step explanation:

find a common numeral

Answer:

(10, -9)

Step-by-step explanation:

Xs = 5 -(0-5) = 5+5 = 10

Ys = -2 -(5-(-2)) = -2 - 7 = -9

so, the coordinates of point S => (10, -9)

Answer:

Step-by-step explanation:

Use midpoint formula and assume S(x, y):

Answer:

UW = 67

Step-by-step explanation:

In order to find UW, we need to add UV and VW because them together makes the entire line, also known in this problem as UW. This is our equation:

UV + UV = UW

This is the equation if you plug the numbers:

19 + 4x - 20 = 6x - 35

Combine like terms to make it easier to do the math:

4x - 1 = 6x - 35

Then do the math:

(4x - 4x) -1 = (6x - 4x) - 35

-1 = 2x - 35

(-1 + 35) = 2x (- 35 + 35)

34 = 2x

34/2 = 2x/2

x = 17

Then you plug in x for the UW expression:

6x - 35

6(17) - 35

102 - 35

67

UW = 67

Answer:

1) D: -8 < x ≤ 2, R: -4 ≤ y ≤ 11.

2) D: -8 ≤ x ≤ -3 U 2 ≤ x < ♾️,

R: -6 ≤ y ≤ -5 U -3 ≤ y < ♾️.

Answer:

52

Step-by-step explanation:

AB is the hypotenuse of the right triangle

sin34 = opp/hyp = 29/hyp

hyp = 29/sin34 = 51.860457849...

Answer:

[tex]let \: |ab| \: be \: x \\ \\ \frac{ \sin(90) }{x} = \frac{ \sin(34) }{29} \\ x \sin(34) = 29 \sin(90) \\ x = \frac{29 \sin(90) }{ \sin(34) } \\ x = 51.86(2.d.p) \\ |ab| = 51.86[/tex]

Answer:

Try h=(1-6πs)/6π

Step-by-step explanation:

That's the same answer in another format

Answer:

answer is in photo.

Green one is main answer and blue one is formula

Answer: to the nearest tenth i believe, 6.8

Step-by-step explanation:

The round off should be ones place.

Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.

Given:

20÷3

The resulting value is 6.666666667.

So, divide the money it should be round off to ones place to get a whole number which can make it easy to divide.

Hence, the round off should be ones place = 7

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Answer: [tex]2\sqrt{3}[/tex]

Step-by-step explanation:

First, start by expanding the expression to this

[tex]\frac{6}{\sqrt{3}} * \frac{\sqrt{3} }{\sqrt{3} }[/tex]

Then multiply the fractions by numerators and denominators (separately)

[tex]\frac{6*\sqrt{3} }{\sqrt{3}*\sqrt{3} }[/tex]

It results in this, the radical 3 * radical 3 get rid of the square root and result in 3

[tex]\frac{6\sqrt{3} }{3}[/tex]

Reduce the fraction by dividing the 6 by 3 so your solution is

[tex]2\sqrt{3}[/tex]

Answers:

The logarithmic function f(x) = ln(x) is the natural logarithmic function and has base  e  

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

Explanation:

The ln(x) or Ln(x) is the natural log function. The order of L and n is backwards compared to "natural log", but you can think of it "log that is natural" or something along those lines.

The Ln(x) function is of the form [tex]\log_b(x)[/tex] where the base b is the special constant e = 2.718... (this constant is similar to pi = 3.14...)

Answer:

Step-by-step explanation:

Answer:

[tex]x^{14}[/tex]

Step-by-step explanation:

[tex]x^{5}[/tex] × [tex]x^{3}[/tex] × [tex]x^{6}[/tex]

[tex]x^{5+3+6}[/tex]

[tex]x^{14}[/tex]

Answer:

x = -5  ±4sqrt(3)

Step-by-step explanation:

(x + 5)^2 = 48

Take the square root of each side

sqrt((x + 5)^2) = ±sqrt(48)

x+5 = ±sqrt(16*3)

x+5 = ±4sqrt(3)

Subtract 5 from each side

x = -5  ±4sqrt(3)

Answer: C. 1.44

Step-by-step explanation:

Each number gets multiplied by 2, so it's an exponential series in a way.

You must multiply .72 by 2 to get 1.44.

Answer:

common ratio=0.5, a1= 0.08

Step-by-step explanation:

r=a3/a2

r=a4/a3

compare both we get:

a3/a2=a4/a3

subtitute a2=0.04 and a4=1

a3/0.04=1/a3

(a3)^2=0.04*1

(a3)^2=0.04

taking square root in both sides

a3=0.02

For r, r=a3/a2

subtitute a3 and a2 above

r=0.02/0.04

r=0.5 common ratio

For a1

r=a2/a1

0.5=0.04/a1

a1=0.04/0.5

a1=0.08

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

The first term of the geometric sequence is 0.08.

The common ratio of the geometric sequence is 1/0.02.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

We have,

Geometric sequence:

The second term = 0.04

The fourth term = 1

In a geometric sequence the nth term is given as:

[tex]a_{n}[/tex] = [tex]a_1 r^{n-1}[/tex]

Second term = 0.04

[tex]a_2[/tex] = 0.04

[tex]a_1 r^1 = 0.04[/tex]

[tex]a_1r[/tex] = 0.04 _____(1)

Fourth term = 1

[tex]a_4 = 1[/tex]

[tex]a_1 r^3[/tex] = 1 _____(2)

From (1) and (2) we get,

0.04/r = 1/r³

r³ = r / 0.04

r² = 1/0.04

r = 1/0.02 ____(3)

Putting (3) in (1) we get

[tex]a_1[/tex] = 0.04 x 0.02 = 0.08

Thus,

The first term of the geometric sequence is 0.08.

The common ratio of the geometric sequence is 1/0.02.

Learn more about geometric sequence here:

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