f(x)=4x-3
g(x)-3x+3
find f(9)/g(9)

Answer:

Y = 7.60X + 1246.67

Step-by-step explanation:

Given the data:

Production Volume (units) Total Cost ($)

400 4000

450 5000

550 5400

600 5900

700 6400

750 7000

Using technology, the linear regression calculator, the regression model obtained by fitting the data is :

Y = 7.60X + 1246.67 ; which is the model giving the relationship between Production volume, x and total cost, y.

Slope = 7.60

Intercept = 1246.67

Answer:

the answer is b- 1440

Step-by-step explanation:

hope this helps

Answer:

b

Step-by-step explanation:

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.

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

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

Answer:

Both

Step-by-step explanation:

Khan

Both of their strategies completing the square and factoring the left-hand side would work.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given a quadratic equation x² + 8x = 2x - 8.

They both agreed that first subtract 2x and add 8 to both sides and rewrite the equation as

x² + 6x + 8 = 0.

Both of their strategies would work.

As x² + 6x + 9 = 1

(x + 3)² = 1.

x + 3 = ± 1

x = ± 1 - 3.

x = - 2 or - 4.

x² + 6x + 8 = 0.

x² + 4x + 2x + 8 = 0.

x(x + 4) + 2(x + 4) = 0.

(x + 4)(x + 2) = 0.

x = - 4 or x = - 2.

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There is a global minimum value of f(x, y) = 3x² + 4y² - 2xy subject to the constraint x + y = 27 located at (x, y) = (6.75, 20.25).

To find the extremum of f(x, y) = 3x² + 4y² - 2xy subject to the constraint x + y = 27, we can use the method of Lagrange multipliers.

Let L(x, y, λ) = f(x, y) - λ(x + y - 27) be the Lagrangian function, where λ is the Lagrange multiplier. Then we need to solve the system of equations:

∂L/∂x = 6x - 2y - λ = 0

∂L/∂y = 8y - 2x - λ = 0

∂L/∂λ = x + y - 27 = 0

Solving the first two equations for x and y in terms of λ, we get:

x = (1/2)λ

y = (3/2)λ

Substituting these expressions into the third equation, we get:

x + y = (1/2)λ + (3/2)λ = 2λ = 27

So λ = 13.5. Substituting this value of λ into the expressions for x and y, we get:

x = (1/2)(13.5) = 6.75

y = (3/2)(13.5) = 20.25

So the extremum of f(x, y) subject to the constraint x + y = 27 is located at (x, y) = (6.75, 20.25). To determine whether this is a maximum or minimum, we need to use the second partial derivative test.

Calculating the second partial derivatives of f(x, y), we get:

∂²f/∂x² = 6

∂²f/∂y² = 8

∂²f/∂x∂y = -2

Evaluating these second partial derivatives at (x, y) = (6.75, 20.25), we get:

∂²f/∂x² = 6 > 0

∂²f/∂y² = 8 > 0

∂²f/∂x∂y = -2 < 0

Since the second partial derivative test indicates that ∂²f/∂x² > 0 and ∂²f/∂y² > 0, we can conclude that (6.75, 20.25) is a local minimum of f(x, y) subject to the constraint x + y = 27. However, we still need to check whether this is the global minimum.

To check whether (6.75, 20.25) is the global minimum, we need to compare the value of f(x, y) at this point to the values of f(x, y) on the boundary of the constraint set x + y = 27. Since the boundary is a line, we can parameterize it as x = 27 - t and y = t for some value of t. Then we can express f(x, y) as a function of t:

f(t) = 3(27 - t)² + 4t² - 2(27 - t)t

= 2t² - 54t + 729

Taking the derivative of f(t) with respect to t, we get:

f'(t) = 4t - 54

Setting f'(t) = 0, we get t = 13.5, which is a critical point of f(t).

Evaluating f(t) at t = 13.5, we get:

f(13.5) = 2(13.5)² - 54(13.5) + 729

= 364.5

Therefore, the minimum value of f(x, y) subject to the constraint x + y = 27 is f(6.75, 20.25) = 364.5, and this is a global minimum since f(x, y) is a continuous function on a closed and bounded set.

In summary, there is a global minimum value of f(x, y) = 3x² + 4y² - 2xy subject to the constraint x + y = 27 located at (x, y) = (6.75, 20.25).

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Answer:

Step-by-step explanation:

a) 1012⁵ can be written as:

1012⁵ = 15¹² + 05¹¹ + 1*5¹º

= 5¹² + 5¹º

= 3125 + 625

= 3750

(b) 101⁵ can be written as:

101⁵ = 15⁴ + 05³ + 1*5²

= 5⁴ + 5²

= 625 + 25

= 650

(c) 1.1⁵ can be written as:

1.1⁵ = 15¹ + 15º

= 5¹ + 5º

= 25 + 5

= 30

(d) 10.21⁵ can be written as:

10.21⁵ = 15² + 05¹ + 25º + 15⁻¹

= 5² + 2*5º + 5⁻¹

= 25 + 10 + 0.2

= 35.2

(e) 210⁵ can be written as:

210⁵ = 25⁴ + 15²

= 2*625 + 25

= 1250 + 25

= 1275

The markup amount of the purchase is $1114

From the question, we have the following parameters that can be used in our computation:

Discount = 30%

Selling price = $780

The markup amount is calculated using the following equation

Selling price = Markup amount * (1 - discount)

Make the markup the subject

Markup = Selling price/(1 - discount)

Substitute the known values in the above equation, so, we have the following representation

Markup = 780/(1 - 30%)

Evaluate

Markup = 1114

Hence, the markup is $1114

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Answer:

small dogs= 5

large dogs= 3

Step-by-step explanation:

Step one:

given data

let the  number of small dogs be x

and the number of large dogs be y

Ryan earns $5 for each small dog he walks and $8 for each large dog he walks.

He walked 8 dogs and made a total of $49

so

5x+8y=49----------1

x+y=8---------------2

x=8-y

5(8-y)+8y=49

40-5y+8y=49

collect like terms

3y= 49-40

3y=9

divide both sides by 3

y=9/3

y=3

put y= 3 in eqn 2

x+3=8

x=8-3

x=5

Check the picture below.

\(\textit{Law of Sines} \\\\ \cfrac{a}{\sin(\measuredangle A)}=\cfrac{b}{\sin(\measuredangle B)}=\cfrac{c}{\sin(\measuredangle C)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{h}{\sin(157^o)}=\cfrac{240}{\sin(6^o)}\implies h\sin(6^o)=240\sin(157^o) \\\\\\ h=\cfrac{240\sin(157^o)}{\sin(6^o)}\implies h\approx 897.1~cm\)

Make sure your calculator is in Degree mode.

Answer:

320

Step-by-step explanation:

Distance to go

2km - 1.2 km = 0.8km = 800m

Revolutions needed

800/2.5 = 320

The required order from least to greatest is √3 − 1, 2√10 ÷ 5, √14, 3√2, √19 + 1 and 6

An arrangement of numbers in which the numbers are arranged from smallest to greatest numbers is called ascending order.

Given that, some numbers, 3√2, √3 − 1, √19 + 1, 6, 2√10 ÷ 5 and √14.

We need to order them from least to greatest,

3√2 = 4.24

√3 − 1 = 0.73

√19 + 1 = 5.35

6

2√10 ÷ 5 = 1.26

√14 = 3.74

The order from least to greatest is :-

0.73, 1.26, 3.74, 4.24, 5.35 and 6

i.e.

√3 − 1, 2√10 ÷ 5, √14, 3√2, √19 + 1 and 6

Hence, the required order from least to greatest is √3 − 1, 2√10 ÷ 5, √14, 3√2, √19 + 1 and 6

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Answer:

6.3

Step-by-step explanation:

Answer:

6.3

Step-by-step explanation:

Hope this helps

Answer:

58.9

Step-by-step explanation:

y²=x²+z²-2×z cos(y)

20²=22²+18²-2(22)(18) cos (y)

400=484+324-792 cos(y)

-408=-772 cos (y)

408/792=cos y

y=cos⁻¹(408/792)=58.9

hope it helps...

have a great day!!

The coordinate of point D and point E will be (x, y) and (-x, y), respectively.

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line in the m:n ratio, finding the mid-point of the line, etc.

Let the coordinate of the point D be (x, y).

Point E has a similar y-coordinate as point D. Then the ordinate of the points will be the same.

And the x-direction of point E is something contrary to the x-direction of point D. Then the coordinate of point E will be (-x, y).

The coordinate of point D and point E will be (x, y) and (-x, y), respectively.

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Answer:

Step-by-step explanation:

The total surface area is 28 square units.

Each of the 6 faces in the original cube has an area of 2* 2 = 4 square units. Thus, the original figure's surface area as a whole was 24 square units.

The new figure has the same surface area as the old one, plus six new faces that each have an area of one dollar per square unit, for a total surface area increase of six dollars. However, the 1 square unit of the bigger cube's top and the 1 square unit of the smaller cube's bottom are not surfaces and do not contribute to the surface area.

This results in a total surface area of 24 + 6 - 1 - 1 = 28 square units.

Therefore, The total surface area is 28 square units.

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Answer:

960 cm²

Step-by-step explanation:

Volume = height x length x width

Volume = 16 x 12 x 10

Volume = 1920 cm²

Since this prism is half

Volume = 1/2 ( 1920)

Volume = 960 cm²

The line that is an irregular line of a blank verse is A . “ He only says , ‘Good fences make good neighbours. ”

The irregularity of the line is that it has 11 syllables while other lines have 10 syllables .

Unrhymed but metric poetry with usually always iambic pentameter is referred to as "blank verse" in literature.

Going by the definition, the three bottom lines are regular lines in a blank verse as they have 10 syllables. However, the first line, has 11 syllables, thereby making it irregular.

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Among the given options, \(5\sqrt{2}.\sqrt{2}\) and \(\sqrt{9}.\sqrt{16}\) gives us a rational number.

The given options are -

1.  \(\sqrt{3}. \sqrt{2}\)

2. \(5\sqrt{2}.\sqrt{2}\)

3. \(\sqrt{9}.\sqrt{16}\)

4. \(\sqrt{11} .\sqrt{5}\)

Now, Considering the 1st option, that is,  \(\sqrt{3}. \sqrt{2}\)

3 and 2, both are nonperfect squares,

\(\sqrt{3}. \sqrt{2} =\sqrt{6}\) which is an irrational number.

Now, Considering the 2nd option, that is, \(5\sqrt{2}.\sqrt{2}\)

\(5\sqrt{2}.\sqrt{2} = 5*2 = 10\) which is a rational number.

Now, Considering the 3rd option, that is, \(\sqrt{9}.\sqrt{16}\)

9 and 16, both are perfect squares,

So, \(\sqrt{9}.\sqrt{16} = 3*4 = 12\) which is a rational number.

Considering the 4th option, that is,  

3 and 2, both are nonperfect squares, \(\sqrt{11} .\sqrt{5}\)

\(\sqrt{11} .\sqrt{5} = \sqrt{55}\) which is an irrational number.

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Answer:

\(10\:\mathrm{units^2}\)

Step-by-step explanation:

The area of a triangle can be given as \(\frac{1}{2}\cdot b \cdot h\). Notice that a base of the triangle is given as 4 units, and the height is marked as 5 units. We know that the segment marked as 5 units is the height of the triangle because it forms a \(90^{\circ}\) with the segment marked as 4 units and meets a vertex of the triangle.

Therefore, the area of the triangle is:

\(\frac{1}{2}\cdot 4 \cdot 5 = \fbox{$10$}\).

Answer:

Step-by-step explanation:

5*x+11=36

5*x=36-11

x=25/5

x=5

5 is the answer

Hey there!

Guide to follow

• Product = multiply/multiplication
• Sum = add/addition
• Quotient = divide/division
• Difference = subtract/subtraction

• Is = equal to/equivalent to

Question reads….
“The product of a 5 and a number plus 11 is 36”

We are not sure what the unknown number is, so we will label it as “w”

Your equation:

5 * w + 11 = 36

SOLVING for the answer to the equation:

5 * w + 11 = 36
5w + 11 = 36

SUBTRACT to both sides

5w + 11 - 11 = 36 - 11

SIMPLIFY it

5w = 25

DIVIDE 5 to BOTH SIDES

5w/5 = 25/5

SIMPLIFY it

w = 25/5

w = 5

Therefore, your unknown number should be: 5

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

i DON'T REALLY KNOW

Step-by-step explanation:

Sοlutiοn οf the equatiοn after factοring x=-5/6 and x=3/2

The methοd οf writing a number οr οther mathematical οbject as the tοtal οf several factοrs, typically smaller οr easier οbjects οf the same kind, is knοwn as factοrizatiοn οr factοring. An mathematical answer is said tο be factοrised when it is written as the sum οf its factοrs. It's pοssible that these elements, factοrs, οr algebraic expressiοns exist.

There are variοus methοds fοr calculating figures as well. While breaking dοwn a number intο its cοmpοnent cοmpοnents is simple, tackling mathematical prοblems takes mοre finesse. Sο let's learn hοw tο recοgnise the cοmpοnents οf a cubic equatiοn.

Given,

\(-12x^2+8x+15=0\)

\(Or, -12x^2+18x-10x+15=0\)

\(Or, -12x^2-10x+18x+15=0\)

\(Or, -2x(6x+5)+3(6x+5)=0\)

\(Or, (6x+5)(3-2x)=0\)

Sο,

(6x+5)=0

Or, x=-5/6

And

(3-2x)=0

Or, x=3/2

Sοlutiοn οf the equatiοn after factοring x=-5/6 and x=3/2

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Answer:

I think it’s step 2 where she distributed the exponents incorrectly but she got it right so since no explanation is really needed then I guess it’s step 2.

step 1 where she divided 5 on both sides. Step 3 is also correct since the answer is 0. so step 2 had the mistake.

Answer:

Step one.

Step-by-step explanation:

She needed to move all terms to the left side of the equation and simplify, she should have subtracted 245 from both sides and ended up with an equation that looked like this:

5(x+7)^2-245=0

Note: ^2 is a superscript.

Answer:

3×+9=5x-5

-2×=-14

×=7...thenCD=3(7)+9=30

Answer:

4x² + 24x + 36

Step-by-step explanation:

(2x + 6)² = (2x + 6)(2x + 6) = 4x² + 12x + 12x + 36 = 4x² + 24x + 36

Answer:

Step-by-step explanation:

At least 9 means more than 9 and includes 9

x ≥ 9     and    [9,  +∞)

At most 9 means numbers less than 9

x≤9       and  (-∞, 9]

more than 9 means bigger than 9 but not including 9

x > 9     and    (9,  +∞)

fewer than 9 means less than 9 but not including 9

x<9       and  (-∞, 9)

strictly between 7 and 9   means between 7 and 9 but not including

7<x<9      and    (7,9)       (This is the only one I'm unsure of.  Strictly, not sure if it includes or doesn't include, usually it just says include or doesn't include)

between 7 and 7 inclusive.   means it's just =7  There's no boundaries

x=7

no more than 7 means less than 7 and includes 7

x ≤ 7   and   (-∞, 7]