Find the graph of the inequality y>-(1/6)x+1.

Answer:

x = 8 ± 2i[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Given

x² - 16x + 60 = - 12 ( subtract 60 from both sides )

x² - 16x = - 72

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 8)x + 64 = - 72 + 64, thus

(x - 8)² = - 8 ( take the square root of both sides )

x - 8 = ± [tex]\sqrt{-8}[/tex] = ± 2i[tex]\sqrt{2}[/tex] ( add 8 to both sides )

x = 8 ± 2i[tex]\sqrt{2}[/tex]

The solution of the given expression is ±2√2i+8

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that

x² - 16x + 60 = - 12

Then subtract 60 from both sides;

x² - 16x = - 72

To complete the square then add ( half the coefficient of the x- term )² to both sides

x² + 2(- 8)x + 64 = - 72 + 64,

(x - 8)² = - 8 ( take the square root of both sides )

x =  ±2√2i+8

Learn more about equations here;

https://brainly.com/question/25180086

#SPJ2

Answer:

867.44 ft²

Step-by-step explanation:

The area of the shaded region is A = 196π + 252.

We have the dimensions of the unshaded region are 14ft x 18ft.

We have to find the area of shaded region.

The area of a rectangle is -

A(R) = Length x Breadth = L x B

and the area of Circle is -

A(C) = [tex]\pi r^{2}[/tex]

According to the question -

Dimensions of the unshaded region -

L = 18ft

B = 14ft

Area of the shaded region (A) = Total Area - Area of Rectangle

Total Area = Area of 2 semicircles of radius (7 + 7) 14ft + Area of rectangle of length 18ft and breadth 28ft.

Total Area = ( [tex]2\times \frac{1}{2}\times \pi \times14 \times 14[/tex] ) + ( 18 x 28)

Total Area = 196π + 504

Area of the shaded region (A) = 196π + 504 - 252 = 196π + 252

Hence, the area of the shaded region is A = 196π + 252.

To solve more questions on Area of Figures, visit the link below -

https://brainly.com/question/9720037

#SPJ2

Answer:se

Step-by-step explanation:

Answer:

f(x) = 60(2)ˣ

Step-by-step explanation:

f(x) = a(b)ˣ

After one month:

120 = a(b)¹

After four months:

960 = a(b)⁴

Divide the second equation by the first:

8 = b³

b = 2

Plug into either equation and find a.

120 = a(2)¹

a = 60

Therefore, f(x) = 60(2)ˣ.

Answer:

[tex]A. H_o: \mu = 74 ^{\circ} F[/tex]

Step-by-step explanation:

A null hypothesis refers to the hypothesis in which there is no important difference taken place and it is used in statistics and it also does not have any relation between the two measured events or variables  or group association

It can be denoted by

[tex]A. H_o: \mu = 74 ^{\circ} F[/tex]

Therefore the above null hypothesis is the correct answer

Answer:

Step-by-step explanation:

The processing cost of split-off Orapine units is ...

  GH¢20,000/(5000 units) = GH¢4/unit

The increase in revenue from the further processing is ...

  GH¢25 -GH¢20 = GH¢5

The increased processing cost is less than the increased revenue, so there is additional profit from further processing 5000 units.

__

The processing cost of split-off Banango units is ...

  GH¢20,000/(10000 units) = GH¢2/unit

The increase in revenue from the further processing is ...

  GH¢16 -GH¢15 = GH¢1

The increased processing cost is more than the increased revenue, so the company takes a loss from further processing 10000 units. No additional processing of Banango units should be undertaken.

Answer:

Please check if the answer is a = 4 or not

Answer:

Step-by-step explanation:

A short web search will turn up the authors of the given titles:

  The Old Man and the Sea - Hemingway

  Huckleberry Finn - Twain

  Moby D.ick - Melville

  1984 - Orwell

  Crime and Punishment - Dostoevsky

Answer:

D. The statement is false. Double blinding is used to decrease the placebo effect.

Step-by-step explanation:

In a double blind study, neither researchers nor the participants know which group is receiving the placebo. If the researchers do not know which group took the medication, they cannot influence the behavior of this group, knowingly or nor, by suggesting how they should behave.

Therefore, a​ double-blind experiment is used to decrease the placebo effect.

Answer:

the smaller is 9 while the digger is 18

Answer:

Option 1: -7x (x - 7)

Step-by-step explanation:

Factor -7x out of -7x^2.

= -7x (x) + 49x

Factor -7x out of 49x.

= -7x (x) -7x (-7)

Factor -7x out of -7x (x) - 7x (-7).

= -7x (x - 7)

(Also I took the test and got this answer right)

You did not give any options but i will try to answer.

y < -lxl basically means that the value of y is less than the absolute value of x time - 1.

So if x = 2, then y is any number less than -2.

And if x is -3. then y is any number less than -3.

Happy to help!

Answer:

Step-by-step explanation:

I do not understand your question very well but I think that the state of the glass of the water would be liquid and solid at the same time since the water would not freeze 100% and would be with small pieces of solid and some parts liquid, in terms of temperature, I think that at 5 minutes it would be 5 ° C and at 10 it would be 3-4 ° C the longer it is in the freezer the less its temperature will be

(All of that is my point of view)

Average temperature 30 °

So :

30 ÷ 15 = 2 °

30 ÷ 10 = 3 °

30 ÷ 5 = 6 °

Answer:

1/6

Step-by-step explanation:

As we already know that selected bulb is defective the required probability doesn't depend on functional bulbs at all.

The probability, that selected defective bulb is from Box2 is number of defective bulbs in Box 2  divided by total number of defective bulbs.

P(defective in box 2)= N(defective in box 2)/N(defective total)

As we know there is only 1 defective lamp in box 2.

So N(defective in box 2)=1

Total number of defective bulbs is Box1- 2 defective  bulbs,  box2- 1 defective bulbs, box3 - 3 defective bulbs. Total are 6 defective bulbs.

So N(defective total)=6

So P(defective in box 2)=1/6

Answer:  width = 2.4 in, length = 5

Step-by-step explanation:

The max area of a right triangle is half the area of the original triangle.

Area of the triangle = (6 x 8)/2  = 24

--> area of rectangle = 24 ÷ 2 = 12

Next, let's find the dimensions.

The length is adjacent to the hypotenuse. Since we know the area is half, we should also know that the length will be half of the hypotenuse.

length = 10 ÷ 2 = 5

Use the area formula to find the width:

A = length x width

12 = 5 w

12/5 = w

2.4 = w

The dimensions of the rectangle with greatest area is length is 3 inch and the width is 4 inch.

Let the length and width of the rectangle be x and y.

Then Area of the rectangle = xy

Now, from the triangle we can conclude that

[tex]\frac{6-x}{y} =\frac{6}{8} \\y=8(\frac{6-x}{6} ).[/tex]

Put the value of y in Area we get

[tex]A(x)=x\frac{8}{6} (6-x)\\A(x)=\frac{8}{6}(6x-x^{2} )\\[/tex]

Differentiating it w.r.t x we get

[tex]A'(x)=\frac{8}{6}(6-2x )\\A''(x)=\frac{8}{6}(0-2 )\\A''(x)=\frac{-8}{3}[/tex]

Put A'(x)=0 for maximum /minimum value

[tex]A'(x)=0\\\frac{8}{6}(6-2x)=0\\x=3[/tex]

Now, [tex]A''(3)=-\frac{8}{3} &lt;0[/tex]

Therefore the area of the rectangle is maximum for x=3 inch

Now,

[tex]y=\frac{8}{6} (6-3)\\y=4[/tex]

Thus the dimensions of the rectangle with greatest area is 3 inch by 4 inch.

Learn more:httpshttps://brainly.com/question/10678642

Answer:

See below

Step-by-step explanation:

Proof:

Statements                                    |  Reasons

AD ≅ BC                                         | Given

AD ║ BC                                         | Given

AC ≅ AC                                         |  Reflexive Property

∠DAC ≅ ∠ACB                               | If 2 || lines are cut by a trans., the                                                                       |  alternate interior ∠s are congruent.

ΔADC ≅ ΔBCA                               | S.A.S  Postulate

BA ≅ DC                                         | Corresponding sides of congruent Δs

So, quad. ABCD is a ║gm             | If a quad. has its opposite sides

                                                       | congruent, the quad. is a parallelogram.

It is prove that given quadrilateral is a parallelogram.

            AD ≅ BC      and AD ║ BC              

            AC ≅ AC            

       So that,   ∠DAC ≅ ∠ACB                              

            ΔADC ≅ ΔBCA    

        So that, BA ≅ DC                                        

Hence, opposite sides of given quadrilateral are equal. Therefore, given quadrilateral are parallelogram.

Learn more:

https://brainly.com/question/16702162

Answer:

Hey there!

An equilateral triangle has all sides equal to each other, so the perimeter would be 3x, where x is the length of one side.

Thus, the perimeter for this equilateral triangle would be 3(12)=36

Hope this helps :)

Answer:

[tex]\boxed{Perimeter = 36 \ units}[/tex]

Step-by-step explanation:

Perimeter = sum of all sides

Perimeter = 12 +12 + 12

Perimeter = 36 units

Answer: :o I FINALLY MADE IT

(5, 2)

x = 5

y = 2

Step-by-step explanation:

First, I graphed both equations.  They meet at the points (5,2) and (2,5).  Because y < 5, the solution is (5, 2)

Hope it helps <3

Answer:

[tex]x=5\\y=2[/tex]

Step-by-step explanation:

[tex]x^2 +y^2 =29[/tex]

[tex]x+y=7[/tex]

Solve for x in the second equation.

[tex]x+y=7[/tex]

[tex]x+y-y=7-y[/tex]

[tex]x=7-y[/tex]

Plug in the value for x in the first equation and solve for y.

[tex](7-y)^2 +y^2 =29[/tex]

[tex]y^2-14y+49+y^2 =29[/tex]

[tex]2y^2-14y+20=0[/tex]

[tex]2(y-2)(y-5)=0[/tex]

[tex]2(y-2)=0\\y-2=0\\y=2[/tex]

[tex]y-5=0\\y=5[/tex]

[tex]y<4[/tex]

[tex]y=2[/tex]

[tex]y\neq 5[/tex]

Plug y as 2 in the second equation and solve for x.

[tex]x+y=7[/tex]

[tex]x=7-y[/tex]

[tex]x=7-2[/tex]

[tex]x=5[/tex]

ANSWER :

6i - (1-i)

Step - by - step explanation:

( 4 + 2i ) - ( 1 - i )

( 4 + 2 × i) - ( 1 - i )

( 6× i ) - ( 1 - i )

= 6i- (1-i)

Hope this helps and pls mark as brainliest :)

Answer:

after 6 half lives: 210(1/2)^6= 3.28125

Step-by-step explanation:

isotope to be reduced to half its initial mass at first:

210(1/2)=105 half it is original weight

after second life: 210(1/2)^2=105(1/2)=52.5

after third : 210(1/2)^3=52.5/2=26.25

after fourth : 26.25/2=12.125

after fifth : 13.125/2

after 6 half lives: 210(1/2)^6= 3.28125

Answer:

The  class width is  [tex]C_w \approx 13[/tex]

Step-by-step explanation:

From the question we are told that

 The  upper class limits is [tex]max = 121[/tex]

  The  lower class limits is  [tex]min = 14[/tex]

   The number of classes is  [tex]n = 8 \ classes[/tex]

The class width is mathematically represented as  

       [tex]C_w = \frac{max - min}{n }[/tex]

substituting values

       [tex]C_w = \frac{121 - 14}{8 }[/tex]

       [tex]C_w = 13.38[/tex]

      [tex]C_w \approx 13[/tex]

Since

Answer: x(x-4) = 140 This equation can be solve to find the length.

Step-by-step explanation:

If the width of the rectangle will be 4 less than the length and the length is represented by x then we could have the equation   w=x - 4 for the width and the length is just x. And to find the area of a rectangle we multiply the length by the with so multiply x-4 by x  for it to equal 140 because 140 is the area.

x(x-4) = 140   solve for x

[tex]x^{2}[/tex] - 4x = 140   subtract 140 from both sides  

x^2 - 4x - 140 = 0  find a number that the product is 140 and the sum is -4

                                  -14 and 10 works out.

[tex]x^{2}[/tex] - 14x + 10x - 140 = 0  factor by grouping

x(x -14)  10(x-14) = 0     factor out x-14

(x-14) ( x+10) = 0         set them both equal zero.

x-14= 0      or   x+10 = 0

x = 14      or x= -10  

Since -10 can't represent a distance, the answer is 14.

Check.  

In this case the length is 14  and if the width is 4 less than the length then we will subtract 4 from 14.

14- 4 = 10  so the width is 10.

14 * 10 = 140

Answer:

3.

Step-by-step explanation:

Solve in the order of pemdas.

Answer:

[tex]\boxed{\sf 3}[/tex]

Step-by-step explanation:

Solve brackets first.

[tex]2[16-5 \cdot 2]\div4[/tex]

Multiply the terms in the brackets.

[tex]2[16-10]\div4[/tex]

Subtract the terms in the brackets.

[tex]2[6]\div4[/tex]

Divide the numbers.

[tex]2(\frac{6}{4} )[/tex]

Multiply.

[tex]\frac{12}{4} =3[/tex]

Answer:

Option D.

Step-by-step explanation:

The vertex form of an absolute function is

[tex]y=a|x-h|+k[/tex]

where, a is a constant, (h,k) is vertex.

It is given that, vertex of an absolute function is (2,3). So, h=2 and k=3.

[tex]y=a|x-2|+3[/tex]   ...(1)

It crosses the x-axis at (5,0). So put x=5 and y=0 to find the value of a.

[tex]0=a|5-2|+3[/tex]

[tex]-3=3a[/tex]

[tex]-1=a[/tex]

Put a=-1 in (1).

[tex]y=(-1)|x-2|+3[/tex]

[tex]y=-|x-2|+3[/tex]

Now, put y=0, to find the equation for this absolute value function when y=0.

[tex]0=-|x-2|+3[/tex]

Therefore, the correct option is D.

Answer:

I got this question on my test and I answered D cause if you look up the graph it matches the question

Step-by-step explanation:

D 0=−|x−2|+3

Answer:

x = 5

Step-by-step explanation:

x = 8 - 3

Thus, x = 5

Answer:   (-5, 5)

Step-by-step explanation:

J = (-3, 1)    K = (-8, 11)          ratio 2 : 3    --> 2 + 3  = 5 segments

x-distance from J to K: -8 - (-3) = -5 units

y-distance from J to K: 11 - 1 = 10 units

Divide those distance into 5 segments:

x = -5/5  = -1 unit per segment

y = 10/5 = 2 units per segment

The partition is 2 segments from J:

x = -3 +2(-1)  = -5

y = 1 + 2(2)   = 5

The partition is located at (-5, 5)

Answer:

5

Step-by-step explanation:

Answer:

Step-by-step explanation:

2.8 kilometers farther. Subtract 12.1km for Winchester and 9.3 for Stamford to get 2.8 kilometers.

Answer:

$9.95.

Step-by-step explanation:

Let's say that you are buying a avatars and b bats.

3a + 3b = 29.85

Divide all terms by 3.

a + b = 9.95

You will pay $9.95 if you buy one of each.

Hope this helps!

Answer:

$57

Since $71.25 was paid for working 7.5 hours.

That means he was being paid $9.5 per hour.

Which is 71.25÷7.5.

And on tuesday that's 9.5×6 which is $57