How would you write the equation with a slope of 2/3 and a y-intercept of (0,-3)?

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

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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:

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

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

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:

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:

E

Step-by-step explanation:

\sqrt 6 is an irrational number, as it cannot be written as the ratio of 2 numbers.

It is also a real number, as it does not include the square root of a negative number.

Therefore, E is the correct option.

Answer:

n> −1 and n < 1/3

Step-by-step explanation:

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:

Step-by-step explanation:

the line QP is a part of the line PR and PN

Answer:

48 mL 5% vinegar, 192 mL 15% vinegar

Step-by-step explanation:

If x is volume of 5% vinegar, and y is volume of 15% vinegar, then:

x + y = 240

0.05 x + 0.15 y = 0.13 (240)

Solve with substitution:

0.05 x + 0.15 (240 − x) = 0.13 (240)

0.05 x + 36 − 0.15 x = 31.2

0.10 x = 4.8

x = 48

y = 192

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: See below; x=1/6

Step-by-step explanation:

This problem may seem intimidating, but all you need to know are your exponent rules. Let's first work inside the parenthesis. Since the bases are the same, we can directly subtract the exponents.

[tex]\frac{3}{4} -\frac{3}{8}[/tex]                             [common denominator]

[tex]\frac{6}{8} -\frac{3}{8}[/tex]                             [subtract]

[tex]\frac{3}{8}[/tex]

Now, our new answer is [tex](3^\frac{3}{8} )^\frac{4}{9}[/tex].

Unfortunately, the answer is asking for an exponent with a single base. One of the properties is when the exponents are separated by parenthesis, you multiply them together.

[tex]\frac{3}{8} *\frac{4}{9}[/tex]                              [cross cancel to simplify]

[tex]\frac{1}{2} *\frac{1}{3}[/tex]                              [multiply]        

[tex]\frac{1}{6}[/tex]

Our final answer is [tex]3^\frac{1}{6}[/tex].

The value is x is [tex]\frac{1}{6}[/tex] since [tex]3^\frac{1}{6}[/tex] is equal to [tex]3^x[/tex], we know that [tex]x=\frac{1}{6}[/tex].

Answer:

21,31

Step-by-step explanation:

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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:

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

The maximum rate of change of function [tex]f(x,y)=ln(x^2+y^2)[/tex] is  [tex]\frac{\sqrt(2)}{2}[/tex] and the direction is [tex](\frac{-1}{2}, \frac{1}{2})[/tex]

Given data:

To find the maximum rate of change of the function [tex]f(x,y)=ln(x^2+y^2)[/tex] at the point (-2, 2), calculate the gradient vector (∇f) and evaluate it at that point.

The gradient vector is a vector that points in the direction of the steepest ascent of the function and its magnitude represents the rate of change of the function at that point.

To find the gradient vector (∇f), calculate the partial derivatives of f(x, y) with respect to x and y:

[tex]\frac{df}{dx} = \frac{(2x)}{ (x^2 + y^2)}[/tex]

[tex]\frac{df}{dy} = \frac{(2y)}{ (x^2 + y^2)}[/tex]

Evaluating these partial derivatives at the point (-2, 2):

[tex]\frac{df}{dx}_{-2,2}=-1/2[/tex]

[tex]\frac{df}{dy}_{-2,2}=--1/2[/tex]

So, the gradient vector (∇f) at the point (-2, 2) is (∇f) = (-1/2, 1/2).

The maximum rate of change of the function occurs in the direction of the gradient vector (∇f). Therefore, the direction in which the maximum rate of change occurs is in the direction of the vector (-1/2, 1/2).

Note that the magnitude of the gradient vector (∇f) represents the maximum rate of change. In this case, the magnitude of (∇f) is:

|∇f| = [tex](\frac{-1}{2}^2 + \frac{1}{2}^2)[/tex]

= √(1/4 + 1/4)

= √(1/2)

= 1/√(2)

[tex]=\frac{\sqrt(2)}{2}[/tex]

Hence, the maximum rate of change of f(x, y) at the point (-2, 2) is [tex]\frac{\sqrt(2)}{2}[/tex], and it occurs in the direction of the vector [tex](\frac{-1}{2}, \frac{1}{2})[/tex].

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Answer:

180

Step-by-step explanation:

-5= -a/36

-5*36= -a

-180= -a

180 = a

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:

5

Step-by-step explanation:

Remember:

Two negatives make a positive

A negative flips a sign

2 - (-4) + 3 + (-6) - (-2)

=

2+4+3-6+2

9-6+2

=5

Answer:

x = [tex]\frac{36}{7}[/tex]

Step-by-step explanation:

Given

12x - 17 = 5x + 19 ( subtract 5x from both sides )

7x - 17 = 19 ( add 17 to both sides )

7x = 36 ( divide both sides by 7 )

x = [tex]\frac{36}{7}[/tex]

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:

x+5x=84

6x=84

6x/6=84/6

x=14

so therefore

14+5(14)

14+70

The numbers are 14 and 70

The two parts are x = 70 and y = 14

We have a 2 - digit number -  84.

We have to split it into two parts such that one part is five times the other part.

Assume the two numbers to be x and y.

x + y = 24

A/Q -

y  = 3x

x + 3x =24

4x = 24

x = 6

and y = 3 x 6 = 18.

According to question, we have -

Number = 84

Assume the first part be x.

Then, the other part = [tex]\frac{x}{5}[/tex]

Therefore -

x + [tex]\frac{x}{5}[/tex] = 84

5x + x = 84 x 5

6x = 420

x = 70

and

y = [tex]\frac{x}{5} =\frac{70}{5}[/tex] = 14

Hence, the two parts are x = 70 and y = 14

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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:

The first blank is 81[tex]x^{2}[/tex]+9=x-1

The second blank is 9x+3=x^2-1

Step-by-step explanation:

For the first part, you must set up the equation (9x+3)^2       then you must multiply the exponent to the inside exponents [tex]9^{2} x^{2}[/tex]+[tex]3^{2}[/tex] next, simplify.

81[tex]x^{2}[/tex]+9=x-1

For part two, set up equation. [tex]x^{2} -1^{2}[/tex] Then simplify 9x+3= [tex]x^{2} -1[/tex]

9x + 3 = x - 1

Squaring the left side and simplifying results in​ 81x² + 53x + 10 = 0.

Squaring the right side and simplifying results in x² - 11x - 2 = 0.

Given,

9x + 3 = x -1

We need to square on the left side and right side separately and find the results.

(A + B)² = A² + 2AB + B²

(A - B)² = A² - 2AB + B²

We have,

9x + 3 = x - 1

Squaring the left side.

( 9x + 3)² = x - 1

(9x)² + 2 x (9x) x 3 + 3² = x - 1

81x² + 54x + 9 = x - 1

81x² + 54x - x + 9 + 1 = 0

81x² + 53x + 10 = 0

Now,

9x + 3 = x - 1

Squaring right side

9x + 3 = ( x - 1 ) ²

9x + 3 = x² - 2 x (x) x 1 + 1²

9x + 3 = x² -2x + 1

x² - 2x - 9x + 1 - 3 = 0

x² - 11x - 2 = 0

Thus the results after simplifying 9x + 3 = x - 1 are

Squaring on the left sides:

81x² + 53x + 10 = 0

Squaring on the right sides:

x² - 11x - 2 = 0

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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

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: (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:

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:

-1

Step-by-step explanation:

-3x(-5)-16

15-16

-1