Factor the polynomial completely.
(y - 8)^2 - 16

Answer:

Option A is the correct answer.

Step-by-step explanation:

Line is passing through the point[tex] (2, - 6) = (x_1, \: y_1) [/tex] and its slope is - 3.

Equation of line in slope point form is given as:

[tex] y-y_1 = m(x-x_1) \\

\therefore y-(-6) = - 3(x-2) \\

\huge \red {\boxed {\therefore y + 6 = - 3(x-2)}} \\[/tex]

Answer: A

Step-by-step explanation:

Point-slope form is the following: y - y1 = m(x - x1). So all that is needed is to substitute y1 for -6, x1 for 2, and -3 for m(the slope).

y - y1 = m(x - x1)

y - (-6) = -3(x - (2))

y + 6 = -3(x - 2)

Steps:

Step 1: Simplify both sides of the equation.

3(a−2/3)=3/4a+21/4

(3)(a)+(3)(−2/3)=3/4a+21/4(Distribute)

3a+−2=34a+2143a−2=3/4a+21/4

3a+−2=34a+2143a−2=3/4a+21/4

Step 2: Subtract 3/4a from both sides.

3a−2−3/4a=3/4a+21/4−3/4a

9/4a−2=21/4

Step 3: Add 2 to both sides.

9/4a−2+2=21/4+2

9/4a=29/4

Step 4: Multiply both sides by 4/9.

(4/9)*(9/4a)=(4/9)*(29/4)

Answer:

A=29/9

Please mark me brainliest

Hope this helps.

Answer:

213.69 units

Step-by-step explanation:

We have to first find the height of the cone.

We can use Pythagoras rule because the slant height, height and radius of a cone all form a right angled triangle:

[tex]h^2 = a^2 + b^2[/tex]

where h = hypotenuse

a and b = the other two sides of the triangle

The radius is 4 units and the slant height is 13 units:

[tex]13^2 = a^2 + 4^2\\\\169 = a^2 + 16\\\\a^2 = 169 - 16 = 153\\\\a = \sqrt{153}\\\\a = 12.37units[/tex]

The height of the cone is 12.37 units.

The surface area of a cone is given as:

SA = [tex]\pi r (r + \sqrt{h^2 + r^2} )[/tex]

[tex]SA = \pi * 4(4 + \sqrt{12.37^2 + 4^2} )\\\\SA = 12.57(4 + \sqrt{13^2} )\\SA = 12.57 (4 + 13)\\\\SA = 12.57(17)\\\\SA = 213.69 units[/tex]

The surface area of the cone is 213.69 units.

Answer:

x=8

Step-by-step explanation:

Area of a rectangle=length×width

Area=104

Width=x

Length=5+x

104=x*(5+x)

104=5x+x^2

104-5x-x^2=0

x^2+5x-104=0

Can also be written as

-x^2-5x+104=0

Solve the quadratic equation using formula

−x2−5x+104=0

using the Quadratic Formula where

a = -1, b = -5, and c = 104

x=−b±√b2−4ac/2a

x=−(−5)±√(−5)2−4(−1)(104)/2(−1)

x=5±√25−(−416)/−2

x=5±√441/−2

The discriminant b^2−4ac>0

so, there are two real roots.

Simplify the Radical:

x=5±21/−2

x=-26/2 or 16/2

x=-13 or 8

The value of x can't be negative

So, x=8 is the answer

Answer:

[tex]\fbox{\begin{minipage}{10em}Option A: Simulation \end{minipage}}[/tex]

Step-by-step explanation:

The data is not collected from the world outside, but a computer.

=> The data can be generated under assumption from simulation only.

=> Option A is correct.

Hope this helps!

:)

Answer:

  a.  Simulation

Step-by-step explanation:

A computer model is generally a simulation of the real world. Certainly, a model of Earth's climate is a simulation.

__

In some cases, the data of interest is the performance of the computer itself (as opposed to some system outside the computer). In those cases, the running of the computer under different scenarios might be considered an experiment.

Answer:

They would fall in the same year every 10 years

Step-by-step explanation:

Here in this question, we are interrelated in calculating the number of years it will take the alumni reunion and the alumni soccer game to fall in the same year.

Now looking at the number of years, we can see we have every 2 and every 10 years

To get the year in which they happen at the same time, we can simply find the lowest common multiple of 2 and 10 and that would be 10

This can be visualized in a way that;

The reunion has happened now, and will happen in the next 10 years.

Now since the soccer game has happened now, in the next 10 years, we shall be having 5 episodes. This means that it will take up to the 10th year before we have the soccer game and the alumni reunion occurring at the same time and the mathematical reason for this is that , 10 is the lowest common multiple of 10 and 2

Answer:

1 times

Step-by-step explanation:

Hello,

The alumni have reunions every 10 years

But also have football games every 2 years

We have to find how often do the football and reunion fall the same year.

Working with a space of 10 years

In 10 years, reunions happen only once

In 10 years, soccer games happen five times

Assuming we're in the year 2020,

The next reunion would likely occur in year 2030.

But soccer games will happen in year 2022, 2024, 2026, 2028 and finally 2030.

Checking both soccer and reunion coincidence, we can only find one which is in year 2030.

So, soccer games and reunions happen once in 10 years

Answer:

34

Step-by-step explanation

1- 4

2- 4(2) - 2 = 6

3- 6(2) - 2 = 10

4- 10(2) - 2 = 18

5- 18(2) -2 = 34

Answer:

17

Step-by-step explanation:

Use ratio method

98:2

850:x

so, x = (850 x 2) divided by 98 = 17.3469388

Round it to nearest whole number = 17

Answer :

Answer:

Initial Fee is $2.

Step-by-step explanation:

Answer:

-40

Step-by-step explanation:

-20-(-5)*(-2^2)

- and a - = positive

-2^2 = -4 but if it was (-2)^2 then it would be 4

-20+5*(-4)

order of operations

-20-20

-40

hope this helps

Answer:

h = -4

Step-by-step explanation:

7h-5(3h-8) = 72

Distribute

7h - 15h +40 = 72

Combine like terms

-8h +40 = 72

Subtract 40 from each side

-8h+40-40 = 72-40

-8h = 32

Divide each side by -8

-8h/-8 = -32/-8

h = -4

Steps:

Step 1: Simplify both sides of the equation.

7h−5(3h−8)=72

7h+(−5)(3h)+(−5)(−8)=72(Distribute)

7h+−15h+40=72

(7h+−15h)+(40)=72(Combine Like Terms)

−8h+40=72 −8h+40=72

Step 2: Subtract 40 from both sides.

−8h+40−40=72−40

−8h=32

Step 3: Divide both sides by -8

Answer:  h=−4

The answer for this question is h=-4

Please mark me brainliest

Hope this helps.

Answer:

$550+/-$20.79

= ( $529.21, $570.79)

Therefore, the 95% confidence interval (a,b) = ( $529.21, $570.79)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = $550

Standard deviation r = $75

Number of samples n = 50

Confidence interval = 95%

z(at 95% confidence) = 1.96

Substituting the values we have;

$550+/-1.96($75/√50)

$550+/-1.96($10.60660171779)

$550+/-$20.7889393668

$550+/-$20.79

= ( $529.21, $570.79)

Therefore, the 95% confidence interval (a,b) = ( $529.21, $570.79)

Answer:

1/8

Step-by-step explanation:

1/2= 4(1/2) = 4/8

4/8+3/8= 7/8

7/8 + 1/8 = 1

2/3 ÷ 1/2 = 1.33333333333 or 1.3 for short

-Peter

Answer:

2*2/3 = 4/3

Step-by-step explanation:

2*2/3 = 4/3

Answer:

(0,7)

Step-by-step explanation:

This is in the form

y = mx+b where m is the slope and b is the y intercept

y = -5x +7

The slope is -5 and the y intercept is 7

(0,7)

Answer:

(0,7)

Step-by-step explanation:

y=mx+b

y=-5x+7

so y intercept is (0,7)

Answer:

0.46 m

Step-by-step explanation:

area of desks: 8 m by 12 m = 8 m * 12 m = 96 m^2

20% of this area is 20% * 96 m^2 = 19.2 m^2

The area of the border is 19.2 m^2.

Let the path around the desks have width x.

The area of desks plus path is a rectangle 2x + 8 by 2x + 12.

area of desks plus path = (2x + 8)(2x + 12)

= 4x^2 + 24x + 16x + 96 = 4x^2 + 40x + 96

The area of the border is the area of the rectangle that includes the border minus the rectangle that has just the desks.

area of border = (4x^2 + 40x + 96) - (96) =

= 4x^2 + 40x

Above, we have the area of border = 19.2, so we get this equation:

4x^2 + 40x = 19.2

4x^2 + 40x - 19.2 = 0

x^2 + 10x - 4.8 = 0

We now use the quadratic formula to solve the equation for x.

[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]

[tex] x = \dfrac{-10 \pm \sqrt{10^2 - 4(1)(-4.8)}{2(1)} [/tex]

[tex] x = \dfrac{-10 \pm \sqrt{100 + 19.2 )}{2} [/tex]

[tex] x = \dfrac{-10 \pm \sqrt{119.2 )}{2} [/tex]

[tex] x = 0.46 [/tex]  or  [tex] x = -10.46 [/tex]

We discard the negative solution.

Answer: the border is 0.46 m wide.

Answer:

2 in by 3 in

Step-by-step explanation:

1 in = 4 ft Divide both sides with 4

0.25 in = 1 ft

0.25 * 8 = 2 in

0.25 * 12 = 3 in  

2 in by 3 in

Answer: 2 in by 3 in

Step-by-step explanation:

1 in = 4 ft Divide both sides with 4 0.25 in = 1 ft 0.25 * 8 = 2 in 0.25 * 12 = 3 in 2 in by 3 in

Answer:

0.350

Step-by-step explanation:

Probability is defined as the chances that an event will occur or not occur. The entire idea of probability has to do with 'chance' events. Thus, the probability that an event will surely occur is 1, while the probability that an event will never occur is zero. Probabilities range between 0-1.

Probability of an event is obtained from

Probability= expected outcome/total number of outcomes

In this case,

Expected outcome= 35

Total number of outcomes = 100

Probability= 35/100= 0.350

Answer:

C

Step-by-step explanation:

Both A and B are true identities.

See attachment.

Answer:

4:3

Step-by-step explanation:

240:180=

60(4):60(3)=

4:3

Hope this helps!

Answer:

4:3

Step-by-step explanation:

24:18

4:3

Answer:

Step-by-step explanation:

Given the function f(x) = 1/4x -12. To get the inverse of the function, first we will let y = f(x) to have y = 1/4x - 12.

Then we will make x the subject of the formula as shown:

y = 1/4x - 12

adding 12 to  both sides we have;

y + 12= 1/4x - 12 + 12

y + 12 = 1/4x

Multiplying both sides by 4 we have;

4(y+12) = x

x = 4y + 48

Substituting y for x

y = 4x+48

f^-1(x) = 4x+48

h(x) = 4x+48

Thee final expression will give the inverse of the function

Answer:

h(x) = 4x+48

Step-by-step explanation:

Given the function f(x) = 1/4x -12. To get the inverse of the function, first we will let y = f(x) to have y = 1/4x - 12.

Then we will make x the subject of the formula as shown:

y = 1/4x - 12

adding 12 to  both sides we have;

y + 12= 1/4x - 12 + 12

y + 12 = 1/4x

Multiplying both sides by 4 we have;

4(y+12) = x

x = 4y + 48

Substituting y for x

y = 4x+48

f^-1(x) = 4x+48

h(x) = 4x+48

Thee final expression will give the inverse of the function

Answer:

So first lets find g(-1)

so we plug in the answers:

-2 * -1 ^2 -4

-2*1-4 = -2-4 =

-6

Now lets solve for f(-2)

-2^2-3

4-3=1

-6+1 = 5

3*5 = 15

Im getting answer of 15 but it shows -15 or something, so I dont know if I got it wrong or if its like a dash then the answer.

Answer:

[tex]m\angle B=52^{\circ}[/tex]

Step-by-step explanation:

Two or more angles are said to be complementary if they sum up to 90 degrees.

Given that angles A and B are complementary, then:

[tex]\angle A+\angle B=90^\circ\\m\angle A=(2x+18)^{\circ}\\m\angle B=(6x-8)^{\circ}\\$Therefore:\\(2x+18)^{\circ}+(6x-8)^{\circ}=90^\circ\\2x+6x+18-8=90^\circ\\8x+10^\circ=90^\circ\\8x=90^\circ-10^\circ\\8x=80^\circ\\$Divide both sides by 8\\x=10^\circ\\$Therefore:\\m\angle B=(6x-8)^{\circ}\\m\angle B=(6(10)-8)^{\circ}\\=60-8\\m\angle B=52^{\circ}[/tex]

Answer:

56 :)

Step-by-step explanation:

Answer:

(4x-1)(4x-1)

(x-6)(x+5)

(3x-7)(3x+7)

(3x-1)(x+6)

Step-by-step explanation:

yes

Answer: a=4

Step-by-step explanation:

Es facil. La diagonales de un rectangulo se cortan en su punto medio por tanto la diagonal es 10 (el doble de 5).

Por pitagoras entonces:

[tex]a=\sqrt{10^2-8^2}=\sqrt{100-64}=\sqrt{36}=4[/tex]

Answer:

The answer is 1800!

Step-by-step explanation:

Answer:

B. 1800 degrees.

Step-by-step explanation:

Just took the quiz on Edg (2020-2021)!

Answer:

C.

Step-by-step explanation:

If you are distributing, you must distribute the outside to both terms in the inside.

Answer:

16x9= 144 cm2

Step-by-step explanation:

Option D( X=15)

Solution,

2x=15+x

or, 2x-x=15

X=15

hope it helps...

Good luck on your assignment...

Answer:

[tex]x = 15[/tex]

Step-by-step explanation:

[tex]2x = 15 + x \\ 2x - x = 15 \\ x = 15[/tex]

Answer D is correct