Select the correct graph for the function ƒ(x) = –x – 7.

Using the washer method, the volume is given by the integral

[tex]\displaystyle\pi\int_{-\pi/3}^{\pi/3}\bigg((3-1)^2-((1+\sec x)-1)^2\bigg)\,\mathrm dx=2\pi\int_0^{\pi/3}(4-\sec^2x)\,\mathrm dx[/tex]

where 3 - 1 = 2 is the distance from y = 3 to the axis of revolution, and similarly (1 + sec(x)) - 1 = sec(x) is the distance from y = 1 + sec(x) to the axis. The integrand is symmetric about x = 0, so the integral "folds" in on itself, and the integral from -π/3 to π/3 is twice the integral from 0 to π/3.

So the volume is

[tex]\displaystyle2\pi\int_0^{\pi/3}(4-\sec^2x)\,\mathrm dx=2\pi(4x-\tan x)\bigg|_0^{\pi/3}=\boxed{\dfrac{8\pi^2}3-2\pi\sqrt3}[/tex]

Answer:

[tex]\frac{1}{64}[/tex]

Step-by-step explanation:

[tex]\left(2^3\right)^{-2}\\\\\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc},\:\quad \:a\ge 0\\\left(2^3\right)^{-2}=2^{3\left(-2\right)}\\\\3\left(-2\right)=-6\\=2^{-6}\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}\\2^{-6}=\frac{1}{2^6}\\\\2^6=64\\\\=\frac{1}{64}[/tex]

Answer:

1/64

Step-by-step explanation:

[tex]\left(2^3\right)^{-2}\\\\\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc},\\\left(2^3\right)^{-2}=2^{3\left(-2\right)}\\\\3\left(-2\right)=-6\\\\=2^{-6}\\\\=\frac{1}{2^6}\\\\2^6=64\\\\=\frac{1}{64}[/tex]

Answer:

x=1

Step-by-step explanation:

Let's solve your equation step-by-step.

10−5x+1=7x+11−12

Step 1: Simplify both sides of the equation.

10−5x+1=7x+11−12

10+−5x+1=7x+11+−12

(−5x)+(10+1)=(7x)+(11+−12)(Combine Like Terms)

−5x+11=7x+−1

−5x+11=7x−1

Step 2: Subtract 7x from both sides.

−5x+11−7x=7x−1−7x

−12x+11=−1

Step 3: Subtract 11 from both sides.

−12x+11−11=−1−11

−12x=−12

Step 4: Divide both sides by -12.

−12x

−12

=

−12

−12

x=1

Answer:

Step-by-step explanation:

9 3/4 acres in 3 3/8 days = 9 6/8 acres in 3 3/8 days

(72 + 6)/8 = 78/8

(24 + 3)/8 = 27/8

78/8 divided by 27/8 = 78/27 = 26/9 or 2 8/9 acres/day

Answer:

There are 11550 possible selections

Step-by-step explanation:

Given

[tex]Men = 7[/tex]

[tex]Women = 11[/tex]

Required

How many ways can 4 men and 4 women be selected

The keyword in the question is SELECTION and it means COMBINATION;

So, number of selection is:

[tex]Number = Men * Women[/tex]

[tex]Number = ^7C_4 * ^{11}C_4[/tex]

This gives

[tex]Number = \frac{7!}{(7-4)!4!} * \frac{11!}{(11-4)!4!}[/tex]

[tex]Number = \frac{7!}{3!4!} * \frac{11!}{7!4!}[/tex]

[tex]Number = \frac{7 * 6 * 5 * 4!}{3!4!} * \frac{11 * 10 * 9 * 8 * 7!}{7!4!}[/tex]

[tex]Number = \frac{7 * 6 * 5}{3!} * \frac{11 * 10 * 9 * 8}{4!}[/tex]

[tex]Number = \frac{7 * 6 * 5}{3 * 2 * 1} * \frac{11 * 10 * 9 * 8}{4 * 3 * 2 * 1}[/tex]

[tex]Number = \frac{7 * 6 * 5}{6} * \frac{11 * 10 * 9 * 8}{4 * 3 * 2 * 1}[/tex]

[tex]Number = 7 * 5 * \frac{11 * 10 * 9 * 8}{4 * 3 * 2 * 1}[/tex]

[tex]Number = 7 * 5 * \frac{7920}{24}[/tex]

[tex]Number = 7 * 5 * 330[/tex]

[tex]Number = 11550[/tex]

Hence;

There are 11550 possible selections

Answer:

Option A is the correct option.

Step-by-step explanation:

Let the sets be A and B

A = { 7 , 8 , 9 , 10 }

B = { 9 , 10 , 11 , 12 }

The intersection of sets A and B is the set of all ements which belongs to both A and B.

The intersection of sets A and N is denoted by ( A ∩ B ) and read as A intersection B.

A ∩ B = { 7 , 8 , 9 , 10 } { 9 , 10 , 11 , 11 , 12 }

Now, list the elements which are present in both sets. A ∩ B = { 9 , 10 }

Hope I helped!

Best regards!

Answer:

its a

Step-by-step explanation:

Answer:

A and B

Step-by-step explanation:

Quadratic Equations: f(x) = a(bx - h)² + k

Quadratic equations always have a degree of 2. That means that we will always have an x² term. Of the 4 choices, only A and B offer a term of x², making them a quadratic.

Answer:

Y = 5x - 3/2 + x^2

Y = x^2 + 5x - 2

Step-by-step explanation:

The function must contain x^2.

That is have a degree of 2.

Answer:

$430

Step-by-step explanation:

Step 1:

300 - 50

Step 2:

350 + 20

Step 2:

370 + 60

Answer:

$430

Hope This Helps :)

Answer:

y = -5x + 32

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Step 1: Write in known variables

slope m = -5

y = -5x + b

Step 2: Find b

7 = -5(5) + b

7 = -25 + b

b = 32

Step 3: Write linear equation

y = -5x + 32

Answer:

y - 7 = -5(x - 5)

Step-by-step explanation:

We are given that a line has a slope of -5 and contains the point (5,7).

We want to write the equation of this line.

The equation of this line can be written in three ways:

Either one of these ways works, but let's use point-slope form, as that form is the easiest.

We can immediately substitute the values into the formula to get the equation.

We can start with the slope; replace m with -5 in the formula.

[tex]y-y_1=m(x-x_1)[/tex] => [tex]y-y_1=-5(x-x_1)[/tex]

Now, we can replace [tex]x_1[/tex] and [tex]y_1[/tex] with 5 and 7 respectively to get:

y - 7 = -5(x - 5)

Answer:

x could be anything. you have to have a equation to solve for x.

Step-by-step explanation:

Answer:

37÷3,145

=85+5

=90-37

=53

Answer:

Area=84.5833333333

Step-by-step explanation:

Answer:

Step-by-step explanation:

To make this easy, convert them both into improper fractions.

Multiply 7x4= 28 + 1 = 29/4

Multiply 11 x 2 = 22 +3= 25/2

29/4 x 25/2 = 725/8

simplified it is 90 5/8

Hope this helps :)

Answer:

Total earnings per week

=18114.8¢

Step-by-step explanation:

He receives 14.20¢ per paper, 6 days a week.

He receives 50¢ for the Sunday paper.

He delivers

124 daily papers each day

He earns= 124*14.20*6

He earns=10564.8¢

151 Sunday papers each week.

He earns= 151*50

He earns= 7550¢

Total earnings per week

=10564.8+7550

=18114.8¢

Answer:

For each one it is shown below

Step-by-step explanation:

The computation of the prime time viewing percentage for the following data is shown below:l;

but before that we need do the total which is

= 6.2% + 8.1% + 7.4% + 6.4% + 3.1% + 2.8%

= 34%

Now for each one the viewing percentage is

For ABC

[tex]= \frac{6.2}{34}[/tex]

= 18.24%

For CBS

[tex]= \frac{8.1}{34}[/tex]

= 23.82%

For NBC

[tex]= \frac{6.4}{34}[/tex]

= 18.82%

For Warner brothers

[tex]= \frac{3.1}{34}[/tex]

= 9.12%

For fox

[tex]= \frac{7.4}{34}[/tex]

= 21.76%

For UPN

[tex]= \frac{2.8}{34}[/tex]

= 8.24%

Answer:

Step-by-step explanation:

9/2    /      8/3

9/2 x 3/8

27/16 = 1  13/16

Answer:

9/2    /    8/3

IS THE POSSIBLE ANSWER TO THIS EQUATION.

Answer:

A) 48 feet

B) 4 seconds

C) 0.54 seconds and 3.46 seconds

Step-by-step explanation:

So we have the function:

[tex]h(t)=64t-16t^2[/tex]

Which represents the height h(t) of the ball after t seconds.

A)

To find the height of the ball 1 second after it has been thrown, substitute 1 for t. Thus:

[tex]h(1)=64(1)-16(1)^2[/tex]

Simplify:

[tex]h(1)=64-16[/tex]

Subtract:

[tex]h(1)=48[/tex]

So, after 1 second, the height of the ball is 48 feet above the ground.

B)

To find out how many seconds after being thrown does the ball hit the ground, we'll set h(t) to 0. 0 means that it will be 0 feet above ground level: in other words, on the ground. So:

[tex]0=64t-16t^2[/tex]

Solve for t. Factor out a 16t:

[tex]0=16t(4-t)[/tex]

Zero Product Property:

[tex]16t=0\text{ or } 4-t=0[/tex]

Solve for t:

[tex]t=0\text{ or } t=4[/tex]

We'll ignore the first zero. So, the ball lands after 4 seconds of being thrown into the air.

C)

To find out at what time(s) the ball is 30 feet above the ground, set h(t) to 30 and solve for t:

[tex]30=64t-16t^2[/tex]

First, divide everything by 2 to simplify things:

[tex]15=32t-8t^2[/tex]

Subtract 15 from both sides:

[tex]-8t^2+32t-15=0[/tex]

Now, to find the zeros, we can use the quadratic formula. a is -8, b is 32, and c is -15. Thus:

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

Substitute:

[tex]x=\frac{-32\pm\sqrt{32^2-4(-8)(-15)}}{2(-8)}[/tex]

Simplify:

[tex]x=\frac{32\pm\sqrt{544}}{16}[/tex]

Use a calculator. Approximate:

[tex]x\approx0.5422\text{ or } x\approx 3.4577[/tex]

So, the ball is 30 feet above the ground after 0.54 seconds and 3.46 seconds.

And we're done :)

Answer:

We know that:

Energy released by fusion of hydrogen in 1 liter of solution A = 7.6x10^10 J

Energy used daily in a certain family home = 3x10^4 J

(you did not write the units, so i suppose that are the same in both cases)

Then, if x is the number of liters of solution A used, the energy produced will be:

E(x) = x*7.6x10^10 J

And we want this equal to 3x10^4

then:

E(x) = x*7.6x10^10 J = 3x10^4 j

now we solve this for x.

x = (3x10^4 j)/(7.6x10^10 j) = 3.9x10^-7

Then you need to use 3.9x10^-7 L of solution a.

Answer:

Distance= 73.333 feet

Step-by-step explanation:

Speed of the bicycle= 20 miles per hour

1 mile =

5280 feet

I hour= 3600 seconds

Speed in feet/seconds=( 20*5280)/(3600)

Speed in feet/second= 29.333 feet/s

Distance= speed*Time

Distance= 29.333*25

Distance= 73.333 feet

Answer:

Hey there!

-8=x+11/2

-16/2=x+11/2

-27/2=x

Let me know if this helps :)

Answer:  -27/2     or        -27

Step-by-step explanation:

You didn't use parentheses so the equation isn't clear.  

I answered for both possibilities.

                  [tex]-8=x+\dfrac{11}{2}\\\\\\-8-\dfrac{11}{2}=x\\\\\\-\dfrac{16}{2}-\dfrac{11}{2}=x\\\\\\\large\boxed{-\dfrac{27}{2}=x}[/tex]

                                                    [tex]-8=\dfrac{x+11}{2}\\\\\\-8(2)=\dfrac{x+11}{2}(2)\\\\\\-16=x+11\\\\\\-16-11=x\\\\\\\large\boxed{-27=x}[/tex]

Answer:

Step-by-step explanation:

x   - the length of the first piece

2x    - twice the length of the first piece (the length of the second piece)

6x   - six times the  length of the first piece

two inches more:

6x+2    - the length of the third piece

first + second + third = 47 in  {total length of the pieces of steel}

x + 2x + 6x + 2 = 47

9x + 2 = 47

9x = 45

x = 45:9

x = 5 in

first piece:   5 in

second piece: 2×5 = 10 in

third piece:   6×5 + 2 = 30 + 2 = 32 in

Answer:

Answer is 54 . IT is the correct answer

Step-by-step explanation:

Hope it is helpful for you

Answer:

4/4, 1 1/4, 1 1/2, 1 3/4

Step-by-step explanation:

It moves by fourths so it goes 1/4, 2/4, 3/4, and so on.

Hope This Helps :)

4/4, 5/4, and 6/4 will come in the given sequence of the pattern.

A pattern is a specific arrangement of numbers or any term which will follow a specific code or hint.

The hint which is present in a given pattern hides in the pattern only.

For example 2,4,6,8 in this, the difference between any two-term is only 2 and this will be its specific pattern.

Another example is 2,4,16,256 in this pattern each term is the square of the previous term and this will become its specific pattern.

Given the pattern,

1/4, 1/2, 3/4

Now if we look then we will get to know that if we add 1/4 consecutively then the next term will come.

For example

1/4 + 1/4 = 1/2

1/4 + 1/4 + 1/4 = 3/4

So,

The next three terms will be

4/4,5/4 and 6/4.

Hence "4/4, 5/4, and 6/4 will come in the given sequence of the pattern".

For more information about the pattern,

brainly.com/question/14013716

#SPJ2

Answer:

13 m

Step-by-step explanation:

The distance x is:

x = √12² + (13 -8)² = √144 + 25 = √169 = 13 m

Answer:

Low estimate

Step-by-step explanation:

2 5/6 rounded is 3 so the total would be 11 hours if everything is rounded.

Answer:

The answer is low

Answer:

x=1/10

Step-by-step explanation:

x^2=1/100

x=root(1/100)

x=1/10

Answer:

[tex]x = \frac{1}{10}[/tex]

Step-by-step explanation:

If x squared gets us [tex]\frac{1}{100}[/tex], then we can create the equation [tex]x^2 = \frac{1}{100}[/tex].

To solve for x, we find the square root of both sides.

[tex]\sqrt{x^2} = \sqrt{\frac{1}{100}}[/tex]

The square root of [tex]\frac{1}{100}[/tex] is [tex]\frac{1}{10}[/tex], since [tex]10\cdot10=100[/tex].

This means [tex]x = \frac{1}{10}[/tex].

Hope this helped!

Answer:

$5,608

Step-by-step explanation:

Since there are 12 months in one year, divide her annual salary by 12.

$67,300/12 = $5,608.33 ≈ $5,608

Josie makes $5,608 per month.

Answer:

5608

Step-by-step explanation:

annual salary=$67.3k

it is annual

so

monthly salary=$67.3÷12

=$5608.33333333

rounded off top the nearest dollar= $5608

please mark as brainliest

Answer:

3663 bacteria

Step-by-step explanation:

Answer:

(a) w = [tex](\frac{-7}{4} , \frac{9}{4}, \frac{1}{2})[/tex]

(b) -2u + 3v - 5w = ([tex]\frac{39}{4}[/tex], [tex]\frac{-54}{4}[/tex], [tex]\frac{3}{2}[/tex])

Step-by-step explanation:

Given:

u = (−2, 3, 1)

=> u = -2i + 3j + k                           --------------------------(i)

v = (−1, −1, 2)

=> v = -i - j + 2k                                --------------------(ii)

3u − 2v − 4w = (3, 2, −3)

=> 3u − 2v − 4w = 3i + 2j - 3k             ------------------(iii)

(A) TO FIND THE VECTOR w

Let:

w = (a, b, c) = ai + bj + ck

(a) Substitute u, v and w into equation (iii)

3u − 2v − 4w = 3i + 2j - 3k

3(-2i + 3j + k) - 2(-i - j + 2k) - 4(ai + bj + ck) = 3i + 2j - 3k

(b) Solve the equation in step (a) by opening the brackets and collecting like terms

(-6i + 9j + 3k) - (-2i - 2j + 4k) - (4ai + 4bj + 4ck) = 3i + 2j - 3k

open brackets

-6i + 9j + 3k + 2i + 2j - 4k - 4ai - 4bj - 4ck = 3i + 2j - 3k

collect like terms

-6i + 2i - 4ai + 9j + 2j - 4bj + 3k - 4k - 4ck = 3i + 2j - 3k

i(-4 - 4a) + j(11 - 4b) + k(-1 - 4c) = 3i + 2j - 3k

(c) Solve for a, b and c in step (b)

Comparing both sides of the equation, we have;

-4 - 4a = 3              ----------(*)

11 - 4b = 2              -----------(**)

-1 - 4c = -3             ------------(***)

From (*)

4a = -4 - 3

4a = -7

a = [tex]\frac{-7}{4}[/tex]

From (**)

4b = 11 - 2

4b = 9

b = [tex]\frac{9}{4}[/tex]

From (***)

-1 - 4c = -3

4c = -1 + 3

4c = 2

c = [tex]\frac{2}{4}[/tex]

c = [tex]\frac{1}{2}[/tex]

Remember that

w = (a, b, c)

w = ai + bj + ck

Therefore,

w = [tex](\frac{-7}{4} , \frac{9}{4}, \frac{1}{2})[/tex]

(B) TO FIND -2u + 3v - 5w

Remember that;

u = (−2, 3, 1)

v = (−1, −1, 2),

w = [tex](\frac{-7}{4} , \frac{9}{4}, \frac{1}{2})[/tex]

Substitute u, v, w into the expression as follows;

-2(−2, 3, 1) + 3(−1, −1, 2) - 5[tex](\frac{-7}{4} , \frac{9}{4}, \frac{1}{2})[/tex]

Expand

(4, -6, -2) + (−3, −3, 6) - [tex](\frac{-35}{4} , \frac{45}{4}, \frac{5}{2})[/tex]

Collect like terms

(4-3+[tex]\frac{35}{4}[/tex], -6-3-[tex]\frac{45}{4}[/tex], -2+6-[tex]\frac{5}{2}[/tex])

Solve

([tex]\frac{39}{4}[/tex], [tex]\frac{-54}{4}[/tex], [tex]\frac{3}{2}[/tex])

Therefore, -2u + 3v - 5w = ([tex]\frac{39}{4}[/tex], [tex]\frac{-54}{4}[/tex], [tex]\frac{3}{2}[/tex])

solution

Answer:

here we go 6×4+3

now 24+3

hence the answer is

27 ans

Answer:

x = -2

Step-by-step explanation:

f(x) = 6 x + 3×4

f(x) = 6 x + 12

6 (x + 2) = f(x)

x = -2

Hope I helped! Please label me as Brainliest!

Answer:

x =1

Step-by-step explanation: Correct solution

[tex]4=-2(x-3) \\\\\mathrm{Switch\:sides}\\-2\left(x-3\right)=4\\\\\mathrm{Divide\:both\:sides\:by\:}-2\\\frac{-2\left(x-3\right)}{-2}=\frac{4}{-2}\\\\Simplify\\x-3=-2\\x-3+3=-2+3\\\\Simplify\\x = 1[/tex]