Evaluate k + np2
if k = 0.5, n = –3, and p = –2.

Answer:

I've pretty much already solved this, in my discussion above:

| 3 | = 3

| –3 | = 3

So then x must be equal to 3 or equal to –3.

But how am I supposed to solve this if I don't already know the answer? I will use the positive / negative property of the absolute value to split the equation into two cases, and I will use the fact that the "minus" sign in the negative case indicates "the opposite sign", not "a negative number".

For example, if I have x = –6, then "–x " indicates "the opposite of x" or, in this case, –(–6) = +6, a positive number. The "minus" sign in "–x" just indicates that I am changing the sign on x. It does not indicate a negative number. This distinction is crucial!

Whatever the value of x might be, taking the absolute value of x makes it positive. Since x might originally have been positive and might originally have been negative, I must acknowledge this fact when I remove the absolute-value bars. I do this by splitting the equation into two cases. For this exercise, these cases are as follows:

a. If the value of x was non-negative (that is, if it was positive or zero) to start with, then I can bring that value out of the absolute-value bars without changing its sign, giving me the equation x = 3.

b. If the value of x was negative to start with, then I can bring that value out of the absolute-value bars by changing the sign on x, giving me the equation –x = 3, which solves as x = –3.

Then my solution

Answer:

7 and [tex]\frac{16}{5}[/tex]

Step-by-step explanation:

(a)

Δ ABC and Δ ADE are similar thus the ratios of corresponding sides are equal

[tex]\frac{AB}{AD}[/tex] = [tex]\frac{AC}{AE}[/tex] , substitute values

[tex]\frac{2}{4}[/tex] = [tex]\frac{x}{x+7}[/tex] ( cross- multiply )

4x = 2(x + 7) ← distribute

4x = 2x + 14 ( subtract 2x from both sides )

2x = 14 ( divide both sides by 2 )

x = 7

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

(b)

Δ ABC and Δ CDF are similar thus ratios of corresponding sides are equal

[tex]\frac{AB}{CD}[/tex] = [tex]\frac{BC}{DF}[/tex] , substitute values

[tex]\frac{2}{5}[/tex] = [tex]\frac{x}{8}[/tex] ( cross- multiply )

5x = 16 ( divide both sides by 5 )

x = [tex]\frac{16}{5}[/tex]

Answer: 5/6

Step-by-step explanation:

p - 1/6 = 2/3

    +1/6   +1/6

p = 5/6

Answer:

p = 5/6

Step-by-step explanation:

For this problem, simply take the words of the problem and convert them into an equation as such:

The difference of p and one-sixth implies --> p - 1/6

is two-thirds implies --> 2/3

So, our equation:

p - 1/6 = 2/3

Now simply solve for p, and combine the fractions.

p - 1/6 = 2/3

p - 1/6 + 1/6 = 2/3 + 1/6

p = 2/3 + 1/6

p = 4/6 + 1/6

p = 5/6

Cheers.

basically you wrote the answer

Answer is B

Answer:

Well since u know the answer (LOL) its B

Step-by-step explanation:

U already solved it so u know how!

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{18}}}}}[/tex]

Step-by-step explanation:

Given, y = 3 , z = 3

[tex] \sf{z(y + y)}[/tex]

Plug the value of y and z

⇒[tex] \sf{3(3 + 3)}[/tex]

Add the numbers : 3 and 3

⇒[tex] \sf{3 \times 6}[/tex]

Multiply the numbers : 3 and 6

⇒[tex] \sf{18}[/tex]

Hope I helped!

Best regards! :D

Answer:

8 miles

Step-by-step explanation:

Downhill

speed = s+2

time = 2 h

then distance d = (s+2)2....i

Uphill

speed = s

time = 4 h

then distance d= 4s...ii

According to question i = ii

⇒(s+2)2 =4s

s = 2 miles/h

then distance d = 2×4 = 8 miles [from eq. ii]

Answer:

I think the scale factor is 2 because 12 divided by 6 is 2.

Answer:

1.368

Step-by-step explanation:

[tex]2ln(x-1)=-2\\\\\text{divide by 2}\\\\ln(x-1)=-1\\\text{take the exponential}\\\\x-1=e^{-1}\\\\\Large \boxed{\sf \bf x = 1+\dfrac{1}{e}}[/tex]

Thanks

Answer:

0-3+5=2

Step-by-step explanation:

It starts in 0

The first line moves three spaces to the left so that's -3

the second line moves 5 spaces to the right so that's +5

add all up

0-3+5=2

Answer:

2

Step-by-step explanation:

1st line 0 → -3 = -3

2nd line -3  → 2 = 5

sum = 0 + (-3) + 5 = 2

Answer:

5 + -155 = -150

Step-by-step explanation:

"A number sentence is a mathematical sentence, made up of numbers and signs." - splashlearn.com

To make one, pick a random number, add a math sign (+, -, ×, ÷), add another number, and put the corresponding answer to the numbers and symbol. For example: 6 - 2 = 4

For this specific question start with the answer (-150). Then add an equals sign: -150 =

Then pick a random number that isn't too dramatic, like 5. Add five to the number sentence: -150 = 5

Next pick a math symbol. Add it to the number sentence: -150 = 5 +

Lastly, pick another number that would make sense in this situation:

-150 = 5 + -155

Switch it around and you're done: 5 + -155 = -150

Answer:

Parallel

Step-by-step explanation:

2x+5 slope: 2

-6x+3y=30 slope: 2

Hence the answer is parallel

Answer:

1) V = 12 π  ㏑ 3

2) [tex]\mathbf{V = \dfrac{328 \pi}{9}}[/tex]

Step-by-step explanation:

Given that:

the graphs of the equations about each given line is:

[tex]y = \dfrac{6}{x^2}, y =0 , x=1 , x=3[/tex]

Using Shell method to determine the required volume,

where;

shell radius = x;   &

height of the shell = [tex]\dfrac{6}{x^2}[/tex]

∴

Volume V = [tex]\int ^b_{x-1} \ 2 \pi ( x) ( \dfrac{6}{x^2}) \ dx[/tex]

[tex]V = \int ^3_{x-1} \ 2 \pi ( x) ( \dfrac{6}{x^2}) \ dx[/tex]

[tex]V = 12 \pi \int ^3_{x-1} \dfrac{1}{x} \ dx[/tex]

[tex]V = 12 \pi ( In \ x ) ^3_{x-1}[/tex]

V = 12 π ( ㏑ 3 - ㏑ 1)

V = 12 π ( ㏑ 3 - 0)

V = 12 π  ㏑ 3

2) Find the line y=6

Using the disk method here;

where,

Inner radius [tex]r(x) = 6 - \dfrac{6}{x^2}[/tex]

outer radius R(x) = 6

Thus, the volume of the solid is as follows:

[tex]V = \int ^3_{x-1} \begin {bmatrix} \pi (6)^2 - \pi ( 6 - \dfrac{6}{x^2})^2 \end {bmatrix} \ dx[/tex]

[tex]V = \pi (6)^2 \int ^3_{x-1} \begin {bmatrix} 1 - \pi ( 1 - \dfrac{1}{x^2})^2 \end {bmatrix} \ dx[/tex]

[tex]V = 36 \pi \int ^3_{x-1} \begin {bmatrix} 1 - ( 1 + \dfrac{1}{x^4}- \dfrac{2}{x^2}) \end {bmatrix} \ dx[/tex]

[tex]V = 36 \pi \int ^3_{x-1} \begin {bmatrix} - \dfrac{1}{x^4}+ \dfrac{2}{x^2} \end {bmatrix} \ dx[/tex]

[tex]V = 36 \pi \int ^3_{x-1} \begin {bmatrix} {-x^{-4}}+ 2x^{-2} \end {bmatrix} \ dx[/tex]

Recall that:

[tex]\int x^n dx = \dfrac{x^n +1}{n+1}[/tex]

Then:

[tex]V = 36 \pi ( -\dfrac{x^{-3}}{-3}+ \dfrac{2x^{-1}}{-1})^3_{x-1}[/tex]

[tex]V = 36 \pi ( \dfrac{1}{3x^3}- \dfrac{2}{x})^3_{x-1}[/tex]

[tex]V = 36 \pi \begin {bmatrix} ( \dfrac{1}{3(3)^3}- \dfrac{2}{3}) - ( \dfrac{1}{3(1)^3}- \dfrac{2}{1}) \end {bmatrix}[/tex]

[tex]V = 36 \pi (\dfrac{82}{81})[/tex]

[tex]\mathbf{V = \dfrac{328 \pi}{9}}[/tex]

The graph of equation for 1 and 2 is also attached in the file below.

Answer:

B. $213.30

Step-by-step explanation:

Mean amount spent on Christmas gifts = Σx / n

Where,

Σ= sum of

x= cost of each Christmas gifts

n= number of Christmas gift

Mean amount spent on Christmas gifts = Σx / n

= ( $178.622 + $247.583 + $228.454 + $176.645 + $180.226 + $268.45 ) / 6

= $1,279.98 / 6

= $213.33

Round to the nearest cent

= $213.30

Option b is the correct answer

Answer: (a) y = 2.7394x - 118.1368

             (b) R² = 0.8215 or 82.15%

Step-by-step explanation: Regression line is the best line that relates the variables in the data.

To calculate the fitted regression equation:

1) Calculate average of x-values ([tex]x_{i}[/tex]) and average of y-values ([tex]y_{i}[/tex]);

2) Calculate the slope, b, by doing:

[tex]b=\frac{\Sigma (x-x_{i})(y-y_{i})}{\Sigma (x-x_{i})^{2}}[/tex]

3) Calculate y-intercept, a, by doing:

[tex]a=y_{i}-bx_{i}[/tex]

4) Then, it gives regression equation: y = bx + a

For the data on chemical reactions:

(a) [tex]b=\frac{ [(136.24-105.3955)+...+(86.18-105.3955)].[(234.5-170.58)+...+(106-170.58)]}{(136.24-105.3955)^{2}+...+(86.18-105.3955)^{2}}[/tex]

b = 2.7394

[tex]a=170.58-2.7394(105.3955)[/tex]

a = -118.1368

y = 2.7394x - 118.1368

The fittest regression equation is y = 2.7394x - 118.1368.

(b) R is correlation coefficient and measures the strength of the relationship between the variables. It is calculated as:

[tex]R=\frac{n\Sigma(xy)-(\Sigma x)(\Sigma y)}{\sqrt{[n\Sigma x^{2}-(\Sigma x^{2})][n\Sigma y^{2}-(\Sigmay^{2})]} }[/tex]

For this fit, R = 0.9064

The variable R² is the coefficient of determination, is the square of correlation coefficient and is usually stated as a percent.

What the variable represents is the percent of variation in the dependent variable (y) explained by the variation in the independent variable (x).

For this fit:

[tex]R^{2} = 0.9064^{2}[/tex]

[tex]R^{2} =[/tex] 0.8215

What it entails is that 82.15% of the variation of retention time is due to the molecular weight of each chemical compound.

Answer:

[tex]V=9\pi\sqrt{3}[/tex]

Step-by-step explanation:

In order to solve this problem we must start by graphing the given function and finding the differential area we will use to set our integral up. (See attached picture).

The formula we will use for this problem is the following:

[tex]V=\int\limits^b_a {\pi r^{2}} \, dy[/tex]

where:

[tex]r=6-(6-3 sec(y))[/tex]

[tex]r=3 sec(y)[/tex]

a=0

[tex]b=\frac{\pi}{3}[/tex]

so the volume becomes:

[tex]V=\int\limits^\frac{\pi}{3}_0 {\pi (3 sec(y))^{2}} \, dy[/tex]

This can be simplified to:

[tex]V=\int\limits^\frac{\pi}{3}_0 {9\pi sec^{2}(y)} \, dy[/tex]

and the integral can be rewritten like this:

[tex]V=9\pi\int\limits^\frac{\pi}{3}_0 {sec^{2}(y)} \, dy[/tex]

which is a standard integral so we solve it to:

[tex]V=9\pi[tan y]\limits^\frac{\pi}{3}_0[/tex]

so we get:

[tex]V=9\pi[tan \frac{\pi}{3} - tan 0][/tex]

which yields:

[tex]V=9\pi\sqrt{3}[/tex]]

Answer:

180

Step-by-step explanation:

-5= -a/36

-5*36= -a

-180= -a

180 = a

Answer:

1 : 7

Step-by-step explanation:

Answer:

1:7

Step-by-step explanation:

5/5=1 35/5=7

Answer:

44 inches

Step-by-step explanation:

Yes, it is 44, but it's just 44 in, not square inches.  Square inches is for area, and you're just measuring the length for perimeter.

Answer:

2 feet

Step-by-step explanation:

Given the question :

A 6 foot wide painting should be centered on a 10 foot wide wall. How many feet (x) should be on each side of the painting?

Width of painting = 6 foot

Width of wall = 10 foot

Since the painting is required to be centered on the wall, hence the space left on euth side of the wall after placing the painting should be equal.

Therefore,

Difference between painting width and wall width :

(10 - 6) foot = 4 foot

Hence, number of feet (x) on either side of the wall:

4 feet / 2 = 2 feet

Answer:

p = 2

Step-by-step explanation:

17 - 2p = 2p + 5 + 2p  

- 2p - 2p - 2p = 5 - 17

- 6p = - 12

p =  -12 / -6

p = 2

Answer:

B. Yes, they both mean the same thing. They can also both be represented by the expression y - 6.

Step-by-step explanation:

They are the same I think because 6 less than a number y means 6 less than y so y-6. 6 less a number y is the same.

Answer:

a) $675000

b) $289000 profit,3300 set, $190 per set

c) 3225 set, $272687.5 profit, $192.5 per set

Step-by-step explanation:

a) Revenue R(x) = xp(x) = x(300 - x/30) = 300x - x²/30

The maximum revenue is at R'(x) =0

R'(x) = 300 - 2x/30 = 300 - x/15

But we need to compute R'(x) = 0:

300 - x/15 = 0

x/15 = 300

x = 4500

Also the second derivative of R(x) is given as:

R"(x) = -1/15 < 0 This means that the maximum revenue is at x = 4500. Hence:

R(4500) = 300 (4500) - (4500)²/30 = $675000  

B) Profit P(x) = R(x) - C(x) = 300x - x²/30 - (74000 + 80x) = -x²/30 + 300x - 80x - 74000

P(x) = -x²/30 + 220x - 74000

The maximum revenue is at P'(x) =0

P'(x) = - 2x/30 + 220= -x/15 + 220

But we need to compute P'(x) = 0:

-x/15 + 220 = 0

x/15 = 220

x = 3300

Also the second derivative of P(x) is given as:

P"(x) = -1/15 < 0 This means that the maximum profit is at x = 3300. Hence:

P(3300) =  -(3300)²/30 + 220(3300) - 74000 = $289000  

The price for each set is:

p(3300) = 300 -3300/30 = $190 per set

c) The new cost is:

C(x) = 74000 + 80x + 5x = 74000 + 85x

Profit P(x) = R(x) - C(x) = 300x - x²/30 - (74000 + 85x) = -x²/30 + 300x - 85x - 74000

P(x) = -x²/30 + 215x - 74000

The maximum revenue is at P'(x) =0

P'(x) = - 2x/30 + 215= -x/15 + 215

But we need to compute P'(x) = 0:

-x/15 + 215 = 0

x/15 = 215

x = 3225

Also the second derivative of P(x) is given as:

P"(x) = -1/15 < 0 This means that the maximum profit is at x = 3225. Hence:

P(3225) =  -(3225)²/30 + 215(3225) - 74000 = $272687.5

The money to be charge for each set is:

p(x) = 300 - 3225/30 = $192.5 per set

When taxed $5, the maximum profit is $272687.5

Answer:

b) $289000 profit,3300 set, $190 per set

Answer:

15

Step-by-step explanation:

-3x = -5-10

-x=-15

therefore, x=15

Answer:

for 11 to be an integer, 11 has to be a whole number. Furthermore, for 11 to be an integer, you should be able to write 11 without a fractional or decimal component. 11 is a whole number that can be written without a fractional component, thus 11 is an integer

Step-by-step explanation:

Answer:

The magnitude is  [tex]\Delta f(0,8)  =  72[/tex]

The  direction  is  [tex]i[/tex] i.e toward the x-axis

Step-by-step explanation:

From the question we are told that

   The function is  [tex]f(x, y) = 9sin(xy) \ \ \[/tex]

    The point considered is  [tex](0,8 )[/tex]

Generally the maximum rate of change of f at the given point and the direction is mathematically represented as

            [tex]\Delta f(x,y) =  [\frac{\delta  f(x,y)}{\delta x } i + \frac{\delta  f(x,y)}{\delta y } j  ][/tex]

             [tex]\Delta f(x,y) =  [\frac{\delta  (9sin(xy))}{\delta x} i  + \frac{\delta  (9sin(xy))}{\delta y} i   ][/tex]

            [tex]\Delta f(x,y) = [9y cos (x,y) i +  9xcos (x,y) j][/tex]

At  [tex](0,8 )[/tex]

            [tex]\Delta  f (0,8) =  [9(8) cos(0* 8)i  + 9(8) sin(0* 8)j  ][/tex]

            [tex]\Delta  f (0,8) = 72 i [/tex]

Answer:

48

Step-by-step explanation:

not sure

The area of the figure is equal to 75 inches²

The formula for area is equal to the product of the length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides.

Given: The length and breadth of the larger rectangle as 15 , 6 respectively

And area of the interior rectangle that forms a part of the larger rectangle is given by : Area (smaller)=3×5

                                          = 15 inches²

While Area of the larger rectangle that contains the smaller rectangle is

= 15×6

=90 inches²

Thus the required area is = 90-15

                                           =75 inches²

Hence, The area of the required rectangle is given by 75  inches²

Learn more about the area here:

https://brainly.com/question/20693059

#SPJ2

Answer:

(4x)¯² (4x)³ (4x)⁹ = (4x)¹⁰

Step-by-step explanation:

(4x)¯² (4x)³ (4x)⁹

The above expression can be simplified as follow:

Recall:

When we have two or more index number with same base and a multiplication sign in between them, we easily simply by adding the index number together while keeping the base constant. This is illustrated below:

a^m x a^n = a^(m + n)

Therefore,

(4x)¯² (4x)³ (4x)⁹ = (4x)^(-2 + 3 +9)

(4x)¯² (4x)³ (4x)⁹ = (4x)¹⁰

Answer:  68 ft

Step-by-step explanation:

Use Pythagorean Theorem: x² + y² = d²

51² + h² = 85²

        h² = 85² - 51²

        h² = 4624

        [tex]h=\sqrt{4624}[/tex]

        h = 68

when we divides m(x) ÷n(x) quotient and remainder is

Answer:

(x - 3)(x + 7)

Step-by-step explanation:

x^2 + 4x - 21

=> x^2 + 7x - 3x - 21

=> x(x + 7) -3(x + 7)

=> (x + 7)(x - 3)

Answer:

[tex](x+7)(x-3)[/tex]

Step-by-step explanation:

So we want to factor the expression:

[tex]x^2+4x-21[/tex]

When factoring, we want to find two numbers that equals (a)(c) and add up to b. We can then substitute it for b.

So, we want two numbers that when multiplied equals (1)(-21)=-21 and adds up to 4.

We can use 7 and -3.

So:

[tex]x^2+4x-21\\=x^2-3x+7x-21[/tex]

Factor out an x from the first two terms, and a 7 from the third and fourth terms:

[tex]=x(x+3)+7(x-3)[/tex]

Grouping:

[tex]=(x+7)(x-3)[/tex]

And we are done :)