The total cost (in dollars) of producing x food processors is C(x) = 2400 + 40x - 0.4^2
find the exact cost of producing the 31st food processor

The vertex of the given function is (0,4)  

What is a quadratic equation?

A quadratic equation is a second-order polynomial equation with a single variable such as x, where ax²+bx+c=0. with a ≠ 0 . Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution. Real or complicated solutions are both possible.

identify the coefficients a and b of the quadratic function

y =ax² +bx+c-------(1)

a=2, b=0

x-coordinate of the vertex is x= -b/2a = -(0)/(2(2)) = 0

Substitute  x=0 into given equation  to get y-coordinate of the vertex

y= 2(0)² + 4 = 0+4 = 4

Vertex= (x,y) = (0,4)

The vertex of the given function is (0,4)

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Answer:

x = 81

Step-by-step explanation:

If a is directly proportional to y²:

[tex]\boxed{a \propto y^2 \implies a=ky^2}[/tex]

If b is inversely proportional to y:

[tex]\boxed{b \propto \dfrac{1}{y} \implies b=\dfrac{m}{y}}[/tex]

Given equation:

[tex]x=a+b+4[/tex]

Substitute the derived expressions for a and b into the given equation:

[tex]\implies x=ky^2+\dfrac{m}{y}+4[/tex]

Substitute the given values of x and y into the equation to create two equations in terms of k and m.

Given that x = -3 when y = 1:

[tex]\implies -3=k+m+4[/tex]

Given that x = 18 when y = 2:

[tex]\implies 18=4k+\dfrac{m}{2}+4[/tex]

Rewrite the first equation to isolate k:

[tex]\implies k=-m-7[/tex]

Substitute the expression for k into the second equation and solve for m:

[tex]\implies 18=4(-m-7)+\dfrac{m}{2}+4[/tex]

[tex]\implies 18=-4m-28+\dfrac{m}{2}+4[/tex]

[tex]\implies -4m+\dfrac{m}{2}=42[/tex]

[tex]\implies -8m+m=84[/tex]

[tex]\implies -7m=84[/tex]

[tex]\implies m=-12[/tex]

Substitute the found value of m into the expression for k and solve for k:

[tex]\implies k=-(-12)-7[/tex]

[tex]\implies k=5[/tex]

Substitute the found values of k and m into the equation to create an equation for x in terms of y:

[tex]\boxed{x=5y^2-\dfrac{12}{y}+4}[/tex]

Finally, to find the value of x when y = 4, substitute y = 4 into the equation and solve for x:

[tex]\implies x=5(4)^2-\dfrac{12}{4}+4[/tex]

[tex]\implies x=5(16)-3+4[/tex]

[tex]\implies x=80-3+4[/tex]

[tex]\implies x=81[/tex]

The number of ways to arrange all the letters if the arrangement must end in a vowel is; 25,200.

The number of arrangement using only five letters is; 6720.

Since there are 5 options for the last letter, and there a 7 letters left to make an arrangement of 7.

Hence, The number of ways can you arrange all of the letters if the arrangement must end in a vowel is; 5 × 7!

= 5 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 25,200.

b). The number of arrangements if one can only use five letters is; ⁸P₅

= 6720.

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Answer:

See below for solution steps for parts (a) and (c)

Step-by-step explanation:

The trick here is to get all the roots to have the same radical. Each of the lowest radical is the square root pf a prime so cannot be reduced further

For example, in a, the lowest is [tex]\sqrt{3}[/tex]

So get all the others to this level a[tex]\sqrt{3}[/tex]  and then you can just add up the non-radicals and use the radical as the common expression

I will solve a couple and that will give you a general idea of solving the rest

Let's do a.
[tex]5\sqrt{3} , \sqrt{3}[/tex] are already at the lowest radical level of [tex]\sqrt{3}[/tex] so let's reduce 108 to have [tex]\sqrt{108}[/tex] to have [tex]\sqrt{3}[/tex] as one of its components

We can factor 108 as follows;

108/3 = 36

So 108 = 36 x 3

√108 = √36 × √3 = 6√3

Therefore the original expression becomes

[tex]5\sqrt{3} - 6\sqrt{3} + \sqrt{3} = (5 - 6 + 1)\sqrt{3} = 0 \sqrt{3} = 0[/tex]

[tex]-------------------------------[/tex]

c.
[tex]2\sqrt{20} - 7\sqrt{5} + \sqrt{45}[/tex]

Lowest radical is [tex]\sqrt{5}[/tex] whose coefficient is 7

Factor 20 = 4 x 5

[tex]2\sqrt{20} = 2\sqrt{4 \times 5} = 2\sqrt{4} \times \sqrt{5} = 2\times 2 \times \sqrt{5}\\= \bold{4\sqrt{5}}[/tex]

Factor 45:
45 = 9 x 5

[tex]\sqrt{45} = \sqrt{9} \times \sqrt{5} = \bold{3\sqrt{5}}[/tex]

Original expression becomes:
[tex]4\sqrt{5} - 7\sqrt{5} + 3\sqrt{5}\\\\=(4 - 7 + 3)\sqrt{5}\\\\= 0 \sqrt{5}\\\\= 0\\----------------------------[/tex]

I am sure you can do the rest. If not post them as another question. Maybe someone else will answer a few of the ones I did not.

All the best

The equation for the graphed quadratic function is:

y = -1*(x - 3)^2 + 2

Here we have the graph of a quadratic equation. Remember that if the leading coefficient is a and the vertex is (h, k) then we can write:

y = a*(x - h)^2 + k

Here the vertex is at (3, 2) then we can write:

y = a*(x - 3)^2 + 2

We can see that it also passes through the point (1, -2), replacing these values we will get:

-2 = a*(1 - 3)^2 + 2

-2 = a*4 + 2

-2 - 2 = a*4

-4/4 = a = -1

Then the quadratic equation is:

y = -1*(x - 3)^2 + 2

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Answer:

5(3-2)

Step-by-step explanation:

15-10

5×3-5×2

Answer:

slope

Step-by-step explanation:

Step-by-step explanation:

always find the quantity of 100%.

then

1% = 100%/100

then calculate the absolute quantity change.

then divide the quantity change by 1% to see how many % fit into it.

and that is your answer.

so, if the original quantity is q1, the new quantity is q2, then the % of quantity change is

|q1 - q2| / (q1/100)

or

100 × |q1 - q2| / q1

where || means the absolute value.

The lateral surface area of the mailer is 234 In²

It is important to note that the formula for the lateral area of a triangular prism is expressed as;

A = (a + b+ c) h

Given that the parameters are enumerated as;

Now, substitute the values into the equation, we have;

Lateral area, A = (4 + 4 + 5) 18

Add the values

Lateral area = (13)(18)

Multiply the values

Lateral area = 234 In²

Hence, the value is 234 In²

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The amount after 13 years with a compound interest of 6.9 % is given by the equation A = $ 5,149.69

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

Let the amount after compound interest be represented as A

Now , the equation will be

The principal amount P = $ 2,100

The rate of interest r = 6.9 %

The number of years b = 13 years

when compounded continuously ,

The compound interest amount A = Pe^rt

Substituting the values in the equation , we get

A = 2,100.00 ( 2.71828 ) ^ ( 0.069 ) ( 13 )

A = 2,100 ( 2.71828 )^( 0.897 )

On further simplification , we get

A = $ 5,149.69

Hence , the amount after 13 years is $ 5,149.69

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Answer: To find the percent error, we can use the formula:

percent error = (estimated value - actual value) / actual value * 100

Plugging in the values:

percent error = (76 - 59) / 59 * 100 = 29.49%

Rounding to the nearest tenth of a percent:

percent error = 29.5%

So the percent error is 29.5%.

Step-by-step explanation:

The point that lies in the solution to the system of inequalities is (5,-2). The correct answer would be an option (B).

An Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The system of inequalities is given in the question, as follows:

y ≤ x -5 and y ≥ -x-4

Since the required point is to satisfy the system of inequalities.

Then the graph attached below represents a solution to the system of inequalities.

Point A (-5,2) does not lie in the solution to the system of inequalities.

Point B (5,-2) lies in the solution to the system of inequalities.

Point C (-5,-2) does not lie in the solution to the system of inequalities.

Point D (5,2) does not lie in the solution to the system of inequalities.

Therefore, the point that lies in the solution to the system of inequalities is (5,-2).

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Answer:

Given that s = 1.5, the expressions that have a value of 13.5 are:

(1) 5s + 8 = 5 × 1.5 + 8 = 13.5

(2) 2s^2 + 9 = 2 × 1.5^2 + 9 = 13.5

Note: The value of any other expression will depend on the specific formula and the value of other variables used in the expression.

Answer:

Step-by-step explanation: Option A is correct.

The value of x that will make L||m is 9.

Geometry is a branch of mathematics that deals with shapes, angles, dimensions and sizes of different things we see in everyday life

The angle (4x²- 324)° is equal to 90°. That is:

(4x²- 324)° = 90°

4x²- 324 = 90

4x² = 90 + 324

4x² = 324

x² = 324/4

x² = 81

x = √81

x = 9

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The mixture should contain 12 pounds of cashews and 18 pounds of Brazil nuts.

A physical combination of two or more unrelated substances is referred to as a mixture. For instance, water and salt are two different substances that, when combined, form a combination.

Let's call the amount of cashews used in pounds "x". The amount of Brazil nuts used in pounds can be calculated as 30 - x.

We know that the total cost of the mixture is $6.08 per pound * 30 pounds = $182.40.

The cost of the cashews in the mixture is $7.70 per pound * x pounds =$7.70x.

The cost of the Brazil nuts in the mixture is $5.00 per pound * (30 - x) pounds = $150 - $5.00x.

The total cost of the cashews and Brazil nuts in the mixture must equal $182.40, so we can set up the equation:

$7.70x + ($150 - $5.00x) = $182.40

Expanding and simplifying the equation:

$2.70x = $32.40

Dividing both sides by 2.70:

$x = 12

So, the mixture should contain 12 pounds of cashews and 18 pounds of Brazil nuts.

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Answer:

C) 0.24 kg

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

Find the weight of two loaves of bread:

Find the difference of weights of 2 loaves of bread and 6 muffins:

The matching choice is C.

The difference of weights of 2 loaves of bread and 6 muffins:

= 0.24 kg

We have to given that,

One loaf of bread weighs 0.68 kilogram.

And, Six muffins weigh 1.12 kilograms.

Now, We can Find the weight of two loaves of bread:

Here, One loaf of bread weighs 0.68 kilogram.

Hence, the weight of two loaves of bread:

0.68 x 2 = 1.36 kg

Hence, the difference of weights of 2 loaves of bread and 6 muffins:

= 1.36 kg - 1.12 kg

= 0.24 kg

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The values of x and y would be   [tex]x=\frac{20 \sqrt{3}}{3}[/tex] and [tex]y=\frac{40\sqrt{3}}{3}[/tex].

What are trigonometric ratios?

Trigonometric ratios are mathematical functions that describe the relationship between the angles and sides of a right triangle. The three main trigonometric ratios are the sine, cosine, and tangent.

In the given figure, by using trigonometric ratios, we can find x

tan60° = 20/x

√3 = 20/x

x = 20/√3

=> [tex]x=\frac{20 \sqrt{3}}{3}[/tex]

Now by using the ratio sin60°

sin60° = 20/y

√3/2  = 20/y

y = 40/√3

[tex]y=\frac{40\sqrt{3}}{3}[/tex]

Hence, the values of x and y would be   [tex]x=\frac{20 \sqrt{3}}{3}[/tex] and [tex]y=\frac{40\sqrt{3}}{3}[/tex].

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Answer:32768/7

Step-by-step explanation:

double every term

Answer:

661,068.8j

Step-by-step explanation:

The car has 661068.8 J of potential energy at a height of 62 m having a mass of 1088 grams.

Potential energy is a form of stored energy that is dependent on the relationship between different system components. When a spring is compressed or stretched, its potential energy increases.

We know, The gravitational constant is 9.8 m/s².

From the given information, m = 1088 grams, h = 62 meters.

Therefore, The amount of potential energy the car has is,

PE = mgh.

PE = 1088×9.8×62 J.

PE = 661068.8 J.

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The equation of the inner boundary of the circular walkway around the monument is x² + y² = 900.

The equation of the outer boundary of the circular walkway around the monument is x² + y² = 1369.

A circle is a conic section whenever the plane cuts the cone parallel to its base. Every point of the circumference lies at the same distance from its center. The equation of a circle is (x-h)² + (y-k)² = r², where (h, k) is the center and r is the radius.

a.

According to the diagram, the radius of the inner boundary is 30 feet and the center is (0, 0).

Substitute h = 0, k = 0, and r = 30 into the equation of circle (x-h)² + (y-k)² = r².

(x-0)² + (y-0)² = 30²

x² + y² = 900

Therefore, the obtained answer is x² + y² = 900.

b.

According to the diagram, the radius of the outer boundary is 37 feet (30 feet + 7 feet) and the center is (0, 0).

Substitute h = 0, k = 0, and r = 37 into the equation of circle (x-h)² + (y-k)² = r².

(x-0)² + (y-0)² = 37²

x² + y² = 1369

Therefore, the obtained answer is x² + y² = 1369.

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The complete question is mentioned in the image below.

6x8 is 48. You can't simplify 48/5, so that's your answer. If you wanted to create a mixed number, you could write 9 3/5

To find the distance from a point P to a plane defined by three points Q, R, and S, we can use the following formula:

distance = |(A * x + B * y + C * z + D) / √(A^2 + B^2 + C^2)|

where (A, B, C) are the coefficients of the normal vector of the plane, (x, y, z) are the coordinates of the point P, and D is the constant in the equation of the plane.

To find the coefficients of the normal vector, we can use the cross product of two vectors lying in the plane, say, QR and RS.

Let's first find the vectors QR and RS:

QR = (5 - 0, 0 - (-1), 3 - 7) = (5, 1, -4)

RS = (7 - 0, 5 - (-1), 0 - 7) = (7, 6, -7)

Next, we find the cross product of QR and RS:

cross product of QR and RS = (B, C, A) = (7, -30, 15)

So, the normal vector of the plane is (15, -30, 7).

Now we substitute the values for the coefficients and the coordinates of the point P into the formula:

distance = |(15 * 3 + (-30) * 1 + 7 * 7 + D) / √(15^2 + (-30)^2 + 7^2)|

To find the value of D, we can use any of the three points on the plane and substitute their coordinates into the equation of the plane in the form Ax + By + Cz + D = 0.

Let's use the point Q:

15 * 5 + (-30) * 0 + 7 * 3 + D = 0

Expanding and solving for D, we get:

75 + 21 + D = 0

D = -96

Finally, substituting the values back into the formula for distance, we get:

distance = |(15 * 3 + (-30) * 1 + 7 * 7 + -96) / √(15^2 + (-30)^2 + 7^2)|

distance = |(-24 + -30 + 49 - 96) / √(15^2 + (-30)^2 + 7^2)|

distance = |(-101) / √(15^2 + (-30)^2 + 7^2)|

distance = |(-101) / √(15^2 + (-30)^2 + 7^2)|

distance = |(-101) / √(225 + 900 + 49)|

distance = |(-101) / √1274|

distance = |(-101) / 35.6|

distance = 2.85

So, the distance between the point P and the plane is approximately 2.85.

The formula to calculate the nth term of the sequence is an = -3n+18.

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence.

Given that the arithmetic series is 15,12,9,6.....

The nth term of the arithmetic sequence will be calculated as:-

an = a₁ + (n-1)d

The first term is 15 and the common difference for the series is 12-15 = -3.

The nth term will be calculated as:-

an = a₁ + (n-1)d

an = 15 + (n-1)-3

an = 15 -3n +3

an = -3n + 18

Therefore, an = -3n+18 is the formula to find the nth term in the sequence.

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The equivalent trigonometric expression to sin(2x)cos(x) is given as follows:

sin(2x)cos(x) = 2sin(x)cos²(x).

The expression for this problem is defined as follows:

sin(2x)cos(x).

The trigonometric identity used to simplify sin(2x) is given as follows:

sin(2x) = 2sin(x)cos(x).

Hence the expression can be written as follows:

sin(2x)cos(x) = 2sin(x)cos(x)cos(x)

sin(2x)cos(x) = 2sin(x)cos²(x).

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Answer:

12 and 5

Step-by-step explanation:

12+5=17

12x5=60

Answer:

Step-by-step explanation:

5 12 step by step