Find the equation of the line that
is perpendicular to y = -2x + 1
and contains the point (8, 2).
[?]
y =
x+ [

Answer:

The slope is 3

Step-by-step explanation:

12x−4y=3

Solve for y

Subtract 12x from each side

-12x +12x−4y=-12x+3

-4y = 12x+3

Divide each side by -4

-4y/-4 = -12x / -4 +3/-4

y = 3x -3/4

This is in slope intercept form

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

The slope is 3

Answer:

The slope is 3

Step-by-step explanation:

12x−4y=3

Solve for y

Subtract 12x from each side

-12x +12x−4y=-12x+3

-4y = 12x+3

Divide each side by -4

-4y/-4 = -12x / -4 +3/-4

y = 3x -3/4

This is in slope intercept form

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

The slope is 3

tan( 20 ) + 4 Sin( 20 ) =

( Sin( 20 ) / Cos( 20 ) ) + 4 Sin( 20 ) =

Sin( 20 ) + 4 Sin( 20 ).Cos( 20 ) / Cos( 20 ) =

Sin( 20 ) + 2 × 2 Sin(20).Cos(20)/ Cos(20) =

Sin( 20 ) + 2 × Sin( 40 ) / Cos( 20 ) =

Sin( 20 ) + 2Sin( 40 ) / Cos( 20 ) =

Sin( 20 ) + 2Cos( 50 ) / Cos ( 20 ) =

Sin( 20 ) + 2Cos( 20 + 30 ) / Cos( 20 ) =

________________________________

2 × Cos( 30 + 20 ) =

2 × [ Cos(30).Cos(20) - Sin(30).Sin(20) ] =

2 × [ √3/2 × Cos(20) - 1/2 × Sin(20) ] =

√3 Cos(20) - Sin(20)

_________________________________

Sin( 20 ) + 2Cos ( 20 + 30 ) / Cos( 20 ) =

Sin( 20 ) + √3 Cos(20) - Sin(20) / Cos(20) =

Sin(20) - Sin(20) + √3 Cos(20) / Cos(20) =

0 + √3 Cos(20) / Cos(20) =

√3 Cos(20) / Cos(20) =

Cos(20) simplifies from the numerator and denominator of fraction

√3 × 1 / 1 =

√3

And we're done ....

Answer:

Option D.

Step-by-step explanation:

Domain and range of inverse function:

The domain of the inverse function(x values) is the range(y values) of the original function.

The range of the interse function(y values) is the domain of the original function(x values).

Original function:

Domain: [tex]x \geq 0[/tex]

Range: [tex]y \leq -1[/tex]

Inverse function:

x values in the domain of the inverse function are the y values in the range of the original function. So

Domain: [tex]x \leq 1[/tex]

Same for range(exchange of y and x).

Range: [tex]y \geq 0[/tex]

The answer is given by option D.

Answer:

Volume: The space which fills up a certain object on the inside.

Answer:

Average strength of bond = 8.08 (Approx.)

Step-by-step explanation:

Given data;

11.5  12.1  9.9  9.3  7.8  6.2  6.6  7.0  13.4  17.1  9.3  5.6  5.7  5.4  5.2  5.1  4.9  10.7   15.2  8.5  4.2  4.0  3.9  3.8  3.6  3.4  20.6  25.5  13.8  12.6  13.1  8.9  8.2  10.7  14.2  7.6  5.2  5.5  5.1  5.0  5.2  4.8  4.1  3.8  3.7  3.6  3.6  3.6

Find:

Average strength of bond

Computation:

Average mean = Sum of all observation / Number of observation

Average strength of bond = [11.5 + 12.1 + 9.9 + 9.3 + 7.8 + 6.2 + 6.6 + 7.0 + 13.4 + 17.1 + 9.3 + 5.6 + 5.7 + 5.4 + 5.2 + 5.1 + 4.9 + 10.7 +  15.2 + 8.5 + 4.2 + 4.0 + 3.9 + 3.8 + 3.6 + 3.4 + 20.6 + 25.5 + 13.8 + 12.6 + 13.1 + 8.9 + 8.2 + 10.7 + 14.2 + 7.6 + 5.2 + 5.5 + 5.1 + 5.0 + 5.2 + 4.8 + 4.1 + 3.8 + 3.7 + 3.6 + 3.6 + 3.6] / 48

Average strength of bond = [387.8] / 48

Average strength of bond = 8.0791

Average strength of bond = 8.08 (Approx.)

Answer:

you add an image

Step-by-step explanation:

Answer:

... if it had the same slope in the y=mx+b equation where m is the slope and x is just x and b is the y-intercept

Step-by-step explanation:

say Car A had the equation y=2x+3- Car B would also have to have be y=2x but the y intercept could be any value

Answer:

$15,264 cost amount on new advertising.

Shown as new equation that includes (original + new customer base)

n3=15264a

Step-by-step explanation:

First we have to find original amount of customers as 3 represents a multiple of n

n3=13824a

n3 means n x 3 then customer base is one third

= 1/3 x 13,824  = 4608 original customers per year

= 4608 original customers +480 new customers

4608 + 480 = 5088 total orig+initial  customers

5088 x 3 = 15264 cost

= ($)15,264 cost

new equation

n3=15264a

Answer:

Step-by-step explanation:

Area of the circle = 1400π

ie. πr^2 = 1400π . ie r^2 =1400. So r=10√14

Area A = πr^2.Differentiate w.r.t.t

dA/dt = 2πr. dr/dt

900 = 2×π×10√14 .dr/dt

So. dr/dt = 900/2×π×10√14 = 45/π√14 m/sec.

Hope this answer helps you :)

Have a great day

Mark brainliest

Step-by-step explanation:

Given that,

A box is created from a sheet of cardboard 40in. on a side by cutting a square from each corner and folding up the sides.

Let x represent the length of the sides of squares removed from each corner.

(a) The volume of a cuboid is given by :

V = lbh

Put values,

V = x(40-2x)(40-2x)

(b) (40-2x) = -2(x-20)

So,

V = x(40-2x)(40-2x)

= [tex]4x\left(x-20\right)^2[/tex]

(c) [tex]4x\left(x-20\right)^2=4x^3-160x^2+1600x[/tex]

It is a cubic polynomial. Its degree is 3.

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

Explanation:

I'll be using the formula

[tex]_n C _r = \frac{n!}{r!*(n-r)!}[/tex]

which is the nCr combination formula. We use nCr instead of nPr because the order of coasters doesn't matter. The whole time, the value of n stays fixed at n = 17 which is the total number of coasters to pick from.

While n is constant, the value of r will vary. It ranges from r = 15 to r = 17 inclusive of both endpoints. In other words, r will take on values from the set {15,16,17}. So we have three cases to consider. The r value is how many coasters we select. This is due to the "at least 15" which means "15 or more".

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

If you ride r = 15 coasters, then we have the following number of combinations

[tex]_n C _r = \frac{n!}{r!*(n-r)!}\\\\_{17} C _{15} = \frac{17!}{15!*(17-15)!}\\\\_{17} C _{15} = \frac{17!}{15!*2!}\\\\_{17} C _{15} = \frac{17*16*15!}{15!*2!}\\\\_{17} C _{15} = \frac{17*16}{2!}\\\\_{17} C _{15} = \frac{17*16}{2*1}\\\\_{17} C _{15} = \frac{272}{2}\\\\_{17} C _{15} = 136\\\\[/tex]

There are 136 ways to ride exactly 15 coasters (when selecting from a pool of 17 total). The order doesn't matter.

We'll use this result later, so let x = 136.

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

If r = 16, then we follow the same steps as above. You should get 17C16 = 17

There are 17 ways to ride 16 coasters where order doesn't matter. Effectively this is the same as saying "there are 17 ways of picking a coaster that you won't ride"

Let y = 17 so we can use it later

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

Lastly, if r = 17, then nCr = 17C17 = 1 represents one way to ride all 17 coasters where order doesn't matter.

Let z = 1

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

Add up the values of x, y, and z to get the final answer

x+y+z = 136+17+1 = 154

Answer:

The right answer is "[tex]0.2<\mu d<7.2[/tex]".

Step-by-step explanation:

The given values are:

[tex]\bar{x_0} = 3.7[/tex]

[tex]s_o=4.95[/tex]

[tex]t_{\frac{0.05}{2} }=2.2621[/tex]

As we know,

95% confidence for [tex]\mu_0[/tex] will be:

= [tex]\bar{x_0} \pm t_{\frac{0.05}{2} },n-1\times \frac{s_o}{\sqrt{n} }[/tex]

The lower bound will be:

= [tex]3.7-2.2621\times \frac{4.95}{\sqrt{10} }[/tex]

= [tex]0.16\simeq 0.2[/tex]

The upper bound will be:

= [tex]3.7+2.2621\times \frac{4.95}{\sqrt{10} }[/tex]

= [tex]7.23\simeq7.2[/tex]

Thus the right answer is "[tex]0.2<\mu d<7.2[/tex]"

Answer:

B) the interquartile range of the data set is 2

Step-by-step explanation:

To find the interquartile range you have to subtract Q3-Q1. Which would be 3-1 and the answer is 2.

Hope this helped :)

Answer:

Option A, 1/8 pound would be the correct answer

Step-by-step explanation:

Since mode of the data is the number in the data that occurs the most, if noticed 1/8 occurs 4 times in the data set given and hence is the mode of the data set

Hope this helps!

With the given compound interest of 6% per year to reach the investment at $1500, it will take 18.3. years thus option (A) is correct.

Compound interest is applicable when there will be a change in principal amount after the given time period.

For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550.

As per the given,

Principle amount P = $500

Rate of interest r = 6% annually

Total investment = P(1 + r)^T

1500 = 500(1 + 0.06)^T

300 = 1.06^T

Take natural logs on both sides

ln300 = T ln1.06

T = 18.3 years

Hence "With the given compound interest of 6% per year to reach the investment at $1500, it will take 18.3. years".

For more information about compound interest,

brainly.com/question/26457073

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Answer:

800 Books were signed out

Step-by-step explanation:

20% of 4000 is 800

Hi there!  

»»————-　★　————-««

I believe your answer is:

800 books.

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{20 Percent of 4,000:}}\\\\\rightarrow 4,000* (20/100)\\\\\rightarrow \boxed{800}[/tex]

⸻⸻⸻⸻

There should be 800 books that were teen romance.

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

No, There is no any sentences are incorrect.

Hence, All sentences are correct.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

Consider the following statements about the effect of different values of a on the function,

⇒ y = a bˣ

Now, We know that;

For the value of a such that |a| > 1

The graph of y = bˣ is vertically stretch.

And, For the values of a such that 0 < |a| < 1;

The graph of y = bˣ is vertically compress.

And, When we take negative value of a.

Then, Function reflect y = bˣ across the y-axis.

Thus, There is no any sentences are incorrect.

Hence, All sentences are correct.

Learn more about the function visit:

https://brainly.com/question/11624077

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Answer:

y = 1/3x + 70/3

Step-by-step explanation:

2 points on the graph:

(20, 30) and (50, 40)

Slope:

m=(y2-y1)/(x2-x1)

m=(40 - 30)/(50 - 20)

m= 10/30

m= 1/3

Slope-intercept:

y - y1 = m(x - x1)

y - 30 = 1/3(x - 20)

y - 30 = 1/3x - 20/3

y = 1/3x + 70/3

9514 1404 393

Answer:

  3

Step-by-step explanation:

For x > 0, the function f(x) is ...

  f(x) = 3x -4 . . . . . . . . for x > 0

Translating this down 1 unit makes it ...

  g(x) = f(x) -1 = 3x -5

The rate of change for any interval such that x > 0 in the whole interval is the coefficient of x: 3.

The rate of change on the interval is 3.

__

If you like, you can find the rate of change from ...

  m = (g(5) -g(2))/(5 -2) = (10 -1)/3 = 9/3 = 3

The rate of change is 3.

Answer:

(-10, -4)

Step-by-step explanation:

That is the ordered pair

Answer:

2500

Step-by-step explanation:

Answer:86 Step-by-step explanation:

Answer:

the are would be 18

Step-by-step explanation:

bc 2x3=6 and then 4x3=12 so 12+6=18

Answer:

take 28 degree as reference angle

using sine angle

sin28=p/h

0.46=10/h

0.46h=10

h=10/0.46

h=21.73

therefore hypotenuse =21.73

again using sine rule

take 25 degree as reference angle

sin 25=p/h

0.42=SR/21.73

0.42*21.73=SR

9.12=SR

9.1=SR

Step-by-step explanation:

Answer:

Step-by-step explanation:

a.12÷36/7=7/3

12*7/36

84/36

7/3

b.let the number be x

x*1/2=x/2

x*1/2

x/2

A- True

12÷36/7 = 2.333...

7/3 = 2.333....

Hence it's true

B- True

Consider Any random number eg 10

multiplying it by 1/2 gives 5

and dividing by 2 also gives 5

hence it's true.

C- False

3/2 = 1.5

multiplying it to any number will produce half of the number more.

Answer:

1/9

Step-by-step explanation:

3 ^ -2

The negative in the exponent means to bring it to the denominator

1/ 3^2

1/9

Answer:

C. 1/9

Step-by-step explanation: