“The total cost of producing Q units of a given product is given by TC = 500+ 4Q2-12Q Compute Marginal cost and average cost “

The x-intercepts of the quadratic equation are given by x = -2 and x = 30.

A quadratic equation is modeled by:

y = ax² + bx + c.

The x-intercepts are the values of x when y = 0, given by:

[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]

[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]

In which:

[tex]\Delta = b^2 - 4ac[/tex]

In this problem, the equation is:

y = 60 + 28x - x².

Hence the coefficients are a = -1, b = 28, c = 60.

Then:

[tex]\Delta = 28^2 - 4(-1)(60) = 1024[/tex]

[tex]x_1 = \frac{-28 + \sqrt{1028}}{-2} = -2[/tex]

[tex]x_2 = \frac{-28 - \sqrt{1028}}{-2} = 30[/tex]

The x-intercepts of the quadratic equation are given by x = -2 and x = 30.

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Answer:

cUse the following equation

Step-by-step explanation:

Because of the way these angles are positioned, they must be equal to 180 together

(2x + 5) + (0.5x + 150) = 180

2.5x + 155 = 180

- 155 - 155

2.5x = 25

2.5x/2.5 = 25/2.5

x = 10

Put x into the original equations and solve

Answer:

Step-by-step explanation:

As ABCD is a rectangle, ∠A = 90°.

Diagonal BD will be the hypotenuse.

[tex]Sin \ 53^{ \circ} = \sf \dfrac{opposite \ of \ angle \ 53}{hypotenuse}\\\\\\0.7986=\dfrac{AB}{42.3}\\\\\\0.7986*42.3=AB\\\\\bold{AB = 33.8}[/tex]

Length = AB = 33.8 cm

[tex]\sf Cos \ 53^{ \circ} =\dfrac{adjacent \ side \ to \ angle \ 53}{hypotenuse}\\\\\\0.6018 = \dfrac{AD}{42.3}\\\\\\0.6018*42.3 =AD\\\\\bold{AD = 25.5 }[/tex]

Width = 25.5 cm

[tex]\huge \mathbb \orange{ANSWER} [/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \mathsf \purple{4 \frac{7}{9} - 2 \frac{1}{2} }[/tex]

[tex] \blue\implies \mathsf \pink{ 2(\frac{43}{9}) - (\frac{5}{2} )9 }[/tex]

[tex] \blue \implies \mathsf \purple{ \frac{86}{18} - \frac{45}{18} }[/tex]

[tex] \blue \implies \mathsf \pink{ \frac{41}{18} = 2 \frac{5}{18} }[/tex]

Answer:

No Solution

Step-by-step explanation:

-y = -2x + 8

y = 2x - 8

2x + 8 = 2x - 8

2x - 2x = -8 - 8

0 = -16

No Solution

You can also graph y = 2x + 8 and y = 2x - 8. The slope are the same and so they are parallel

Answer:

The process of photosynthesis is commonly written as: 6CO2 + 6H2O → C6H12O6 + 6O2.

Step-by-step explanation:

Answer:

1/27 units cubed or 0.037037... units cubed

Step-by-step explanation:

Volume of a cube = s*s*s : Where s is a side length.

The volume of the first cube is 1 cubed, which means that each side length is 1. (s=1)

The volume of the second cube in relation to the first cube can be found by multiplying each side length by 1/3.

Volume of second cube= (1/3s)(1/3s)(1/3)s

Volume of second cube= (1/3)(1/3)(1/3)

Volume of second cube= 1/27

Answer: 8.

Step-by-step explanation: There are 4 sizes, so let's say that the sizes are small, medium, large, and extra large.  There are 2 flavors, so let's say that the flavors are chocolate and vanilla.  The possible combinations are below:

As you can see, there are 8 possible combinations that she can choose from as far as 4 sizes and 2 flavors go.

Have a great day! :)

Answer:

750 decimeters

Step-by-step explanation:

1 meter is equal to 10 decimeters.

so 75 times 10 equals your answer: 750 decimeters

Hope that helps!

Answer:

what the heck question is this

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &2350\\ r=rate\to 35\%\to \frac{35}{100}\dotfill &0.35\\ t=years\dotfill &4\\ \end{cases} \\\\\\ A=2350(1 - 0.035)^{4}\implies A=2350(0.965)^4\implies A\approx 2037.87[/tex]

Answer:

78 is the number

Step-by-step explanation:

(65*6)÷5 = 78.

5/6 of a number is 65.

And the number is 78.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

A phrase: 5/6 of a number is 65.

To find the number:

Let the number be n.

Applying multiplication operation,

5/6 of n is 65.

(5/6)n = 65.

Applying cross multiplication,

n = 65 x 6/5

n = 390/5

n = 78.

Therefore, the number is 78.

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Answer:

Area = Base ×Height

Step-by-step explanation:

Area = Base × Height

Area = 3cm × 5cm

Area = 15cm

Area of the parrallelogram is 15cm

Considering a discrete distribution, it is found that the expected number of new employees to be hired by the​ airline is of 446.16.

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

In this problem, considering the situation described in the text, the distribution is given by:

Hence, the expected value is given by:

E(X) = 0.37(867) + 0.63(199) = 446.16.

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Answer:1.03125

Step-by-step explanation:

[tex]\qquad\qquad\huge\underline{{\sf Answer}}☂[/tex]

Standard equation of circle ~

[tex]\qquad \sf  \dashrightarrow \:(x - h) {}^{2} + (y - k) {}^{2} = r {}^{2} [/tex]

where,

Now, let's plug in the values ~

[tex]\qquad \sf  \dashrightarrow \:(x - (5)) {}^{2} + (y - ( - 8)) {}^{2} = {2}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:(x + 5) {}^{2} + (y + 8) {}^{2} = {4}^{} [/tex]

Therefore, the correct choice is B

➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖

The equation of the circle with a center of (4,5) and a radius of 2 units is (x + 5)² +(y + 8)² = 4

The center of the circle is given as:

Center (a,b) = (-5, -8)

The radius is given as:

Radius, r = 2

The equation of the circle is calculated using:

(x - a)² + (y - b)² = r²

Substitute values for r and (a,b)

(x + 5)² +(y + 8)² = 2²

Evaluate the square of 2

(x + 5)² +(y + 8)² = 4

Hence, the equation of the circle is (x + 5)² +(y + 8)² = 4

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Answer:

3,2,1,6,5,4

Step-by-step explanation:

Hope this helps!!!

All the correct steps to find the equation of the parabola with focus (-1, -8) and directrix y = - 12 are,

1. 2p + (- 8) = - 12                       Find p

2. Since the focus is at - 1,        Find the x - coordinates for the vertex.

then, vertex is at - 1

3. y = - 8 - 2                              Find the x - coordinates for the vertex.

4. (- 1, - 10)                                Vertex coordinates

5. (x + 1)² = 4(-2) (y+10)              Write the formula for the parabola.

6. (x + 1)² = -8 (y+10)                  Simplify the formula.

Given that,

In a parabola,

Focus = (-1 , - 8)

And, Directrix =; y = - 12

The standard equation of a parabola is,

[tex]y = - p (x - h)^2 + k[/tex]

Where, (h, k) is the vertex of the parabola.

Now, the Statement with reason to find the equation of a parabola is,

 Statement                                       Reason

1. 2p + (- 8) = - 12                       Find p

p = - 2

2. Since the focus is at - 1,        Find the x - coordinates for the vertex.

then, vertex is at - 1

3. y = - 8 - 2                              Find the x - coordinates for the vertex.

y = - 10

4. (- 1, - 10)                                Vertex coordinates

5. (x + 1)² = 4(-2) (y+10)              Write the formula for the parabola.

6. (x + 1)² = -8 (y+10)                  Simplify the formula.

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Answer:

y = x - 1

Step-by-step explanation:

First find the slope. Subtract the y's and put that on top of a fraction. Then subtract x's and put that on the bottom. Simplify if possible.

7-1 is 6 goes on top.

8-2 is 6 goes below.

6/6 is 1 when simplified.

Slope is 1.

Slope-intercept form is y = mx + b.

m is slope, so fill that in.

y = (1)x + b

Now we need to find b.

Use either one of the given points; they will give you the same answer no matter which one you choose. Let's use (2,1) because smaller numbers.

y is 1 and x is 2.

y= (1)x + b

1 = (1)2 + b

1 = 2 + b

-1 = b

Now fill in both m and b. Leave x and y as letters (variables)

y = (1)x + -1

Final answer:

y = x - 1

Answer:

Answer: LCM of 20,35 and 50 is 1400

Step-by-step explanation:

Answer:

[tex]\sqrt[3]{x^2}[/tex]

Step-by-step explanation:

The rule of exponents says that we must use subtraction for [tex]\frac{5}{6}[/tex] and [tex]\frac{1}{6}[/tex] since we are dividing.  

Thus, we have [tex]\frac{x^\frac{5}{6} }{x^\frac{1}{6} }\\\\\frac{5}{6}-\frac{1}{6}=x^\frac{4}{6}=x^\frac{2}{3}[/tex]

When dealing with fractions and radicals, we can find the simplest radical form by using the saying [tex]\frac{exponent}{index}[/tex]

Thus we have [tex]\sqrt[3]{x^2}[/tex]

Step-by-step explanation:

log 3 (10022)

= 8.38561

log n (155)= 8.38561

n^8.38561=155

log 10 (n)= log 10 (155)

lpg 10 (155)= 2.190331698

8.38561 log10 (n)=2.190331698

log10 n = 2.190331698÷8.38561

lo^-1 (0.2612012)

=1.825

n=1.825

Answer:

The list od prime number is a quadratic sequence, each time going up by n + 2. for example, 1, 4, 9, 16, 25. they are going up by 3, then + 2 and add 2 every step. The sequence is always going up by an odd number. a negative number take away a negative number always gives you a positive number, likewise, adding does too. Therefore, you can not get both of them to fit into the sequence of increasing odd numbers.

Step-by-step explanation:

let, the tulips be 'x'

According to the question,

heather=4x

& sarah=x

but heather planted 64 so,

4x=64

or, x=64/4

x=16

hence, sarah planted 16 tulips

Heather planted 4x Sarah's tulips. On the off chance that Heather has 64 tulips, Sarah has 16 tulips (64/4 = 16).

Let's utilize algebra to illuminate this issue. Let s speak to the number of tulips Sarah planted.

Concurring to the data given, Heather planted 4 times as numerous tulips as Sarah, so we will compose this as:

Heather's tulips = 4 * Sarah's tulips

64 = 4s

Presently, ready to fathom for s:

s = 64 / 4

s = 16

Sarah planted 16 tulips.

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Answer:

Rs 2464

Step-by-step explanation:

Given:

To find:

Solution : A/C to given data;

[tex]Length = 2 * Breadth\\L = 2 * B[/tex]---> (1) and [tex]Breadth = 2 * Height\\B = 2 * H[/tex]----> (2)

A/C to given data let, structure of room is cuboidal.

Now, we have to find out the height of the room, so we use formula of volume of the cuboid.

[tex]Volume of the room = L * B * H[from given data, and eq. {1} and eq. {2}][/tex]

[tex]512 = 2B * 2H * H[/tex]

[tex]512 = 2 * 2H * 2H * H[/tex]

[tex]512 = 4H * 2H^{2}[/tex]

[tex]512 = 8H^{3}[/tex]

[tex]H^{3} = \frac{512}{8}[/tex]

[tex]H^{3} = 64[/tex]

[tex]H = \sqrt[3]{64}[/tex]

[tex]H = 4 m[/tex]

[tex]Now, put\\ value\\ of \\H \\in \\eq. {2}[/tex]

[tex]B = 2 * H[/tex]

[tex]B = 2 * 4[/tex]

[tex]B = 8 m[/tex]

[tex]\\[/tex]Now, put value of B in eq. {1}

[tex]L = 2 * B[/tex]

[tex]L = 2 * 8[/tex]

[tex]L = 16 m[/tex]

Now, we have to find out area of the room, so we use formula of total surface area of cuboid.

[tex]Area of the room = 2*L*B + 2*L*H + 2*H*B[/tex]

[tex]Area of the room = 2 * 16 * 8 + 2 * 16 * 4 + 2 * 4 * 8[/tex]

[tex]Area of the room = 32 * 8 + 32 * 4 + 8 * 8[/tex]

[tex]Area of the room = 256 + 128 + 64[/tex]

[tex]Area of the room = 384 + 64[/tex]

[tex]Area of the room = 448 m^{2}[/tex]

Now, to find out room wall plastering cost

[tex]Room wall plastering cost = Area of the room * cost of plastering per ^{2}[/tex]

[tex]Room wall plastering cost = 448 * 5.50[/tex]

[tex]Room wall plastering cost = Rs 2464[/tex]

[tex]ence, the room wall plastering cost is Rs 2464.[/tex]

Topic : Midpoint between points

formula:

[tex]\sf \bold{(x_m, y_m) = (\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})}[/tex]

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

[tex]\hookrightarrow \sf \dfrac{x+(-5)}{2} ,\dfrac{y+2}{2} = (8, -8)[/tex]

separate taking coefficients:

[tex]\rightarrow \sf \dfrac{x-5}{2} =8, \ \dfrac{y+2}{2} = -8[/tex]

[tex]\rightarrow \sf x-5 =16, \ y+2 = -16[/tex]

[tex]\rightarrow \sf x =16+5, \ y= -16-2[/tex]

[tex]\rightarrow \sf x =21, \ y= -18[/tex]

coordinates of door: (21, -18)

Let that be (x,y)

So

[tex]\\ \rm\rightarrowtail (8,-8)=(\dfrac{x-5}{2},\dfrac{y+2}{2})[/tex]

[tex]\\ \rm\rightarrowtail \cfrac{x-5}{2}=8\implies x-5=16\implies x=21[/tex]

[tex]\\ \rm\rightarrowtail \cfrac{y+2}{2}=-8\implies y+2=-16\implies y=-18[/tex]

Answer:

Answer:

53

Step-by-step explanation:

[tex] \frac{sin(56)}{78.6} = \frac{sin(90)}{ab} \\ \\ absin(56) = sin(90) \times 78.6 \\ \\ ab = \frac{sin(90) \times 78.6}{sin(56)} \\ ab = 94.8 \\ \\ {x}^{2} + {78.6}^{2} = {94.8}^{2} \\ {x}^{2} = {94.8}^{2} - {78.6}^{2} \\ {x}^{2} = 8987.04 - 6177.96 \\ {x}^{2} = 2809.08 \\ x = \sqrt{2809.08} \\ x = 53[/tex]

Answer:

A. 20 / 7 = 3 (or 2.85)

B. 55 / 7 = 8 (or 7.85)

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Answer:

A.3

B.8

Step-by-step explanation:

this is the answer