What is the area for the problem

Step-by-step explanation:

=(11+4)÷3×√64

=15÷3×8

=5×8

=40

hope it helps

Answer:

3,125

Step-by-step explanation:

25 out of 200 is 12.5%

and 12.5% of 25,000 is 3,125

(I'm not sure)

Answer:

Identity

Step-by-step explanation:

7+2=2+7

is an identity

Answer:

5 1/2 + 3/4

11/2 + 3/4

22+3/4

25/4

=6 1/4

In differentiation , qA = 13/5  , qB = 11/5 are  values of qA and qB maximize the revenue .

What does mathematics differentiation serve?

In mathematics, differentiation is used to compute rates of change. For instance, in mechanics, velocity is the amount at which a displacement changes over time.

                   The acceleration is the speed at which velocity is changing with respect to time.

R = 40qA + 50qB − 6qA2 − 9qB2 − 4qAqB

Let aA = x , qB = y

so,

 R= 40x + 50y - 6x² - 9y² - xy

Partially differentiate above equation with respect to x and y .

Rx = 40 - 12x - 4y

Ry = 50 - 18y - 4y

Set Rx = 0 and Ry = 0 solve x and y .

40 - 12x - 4y = 0

50 - 18y - 4x = 0

Solving above questions

 x = 13/5 , y = 11/5

therefore,

      qA = 13/5  , qB = 11/5

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Domain of a any cubic function \(f(x)=ax^3+bx^2+cx+d\) is defined to be always \(\mathbb{R}\).

The derivative with respect to x of your cubic function is,

\(\dfrac{d}{dx}f(x)=f'(x)\)

to find the derivative of a polynomial function, simply take a derivative of each factor and sum them up,

\(\dfrac{d}{dx}x^3=3x^2\) by the rule \(\dfrac{d}{dx}x^m=mx^{m-1}\) where \(m\in\mathbb{R}\)

\(\dfrac{d}{dx}-6x=-6\)

\(\dfrac{d}{dx}3=0\)

So the derivative is,

\(f'(x)=3x^2-6\)

both derivative and the original function have equal domain.

Hope this helps :)

Step-by-step explanation:

\(thank \: you\)

Answer:

The three options that result in a difference of squares are:

(x minus y)(x plus y)

(6 minus y)(6 plus y)

(64 y squared + x squared)(64 y squared - x squared)

The bench costs $375, and the garden table costs $295. Together, they amount to $670, with the table being $80 cheaper than the bench.

Let the cost of the bench be x. Then the cost of the garden table is x-80. The sum of the costs of both items is $670. So we have the equation: x + (x-80) = $670.

Simplifying this, we get 2x - 80 = $670  + 80 2x = $750  x = $375. So the cost of the bench is $375. The garden table costs $375 - $80 = $295. A garden table and a bench cost $670 combined.

The garden table costs $80 less than the bench. To find the cost of the bench, we can use algebraic equations. Let the cost of the bench be x. Then, the cost of the garden table is x - 80.

The sum of both costs is $670. Using this information, we can form an equation: x + (x - 80) = $670. Simplifying, we get 2x - 80 = $670 + 80. Solving for x, we get x = $375.

Therefore, the cost of the bench is $375, and the cost of the garden table is $295.

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The simplified mixed number upon evaluation is \(3\frac{11}{27}\).

Given:

a = −3/5 and b = −6.75

We have to determine the value of (2a−1/3) ÷ b/15.

Substituting the values of a and b in the expression, we get

(2(−3/5)−1/3) ÷ (−6.75)/15

⇒ (-6/5 - 1/3) ÷ (-0.45)

⇒ (-23/15) ÷ (-0.45)

⇒ 23/15 × 100/45

⇒ 92/27

⇒ \(3\frac{11}{27}\)

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The sum \(\sum_k^4 (-2)^{(k-1)\) is equal to 1 + (-2) + 4 + (-8) = -5.

The expression \(\sum_k^4 (-2)^{(k-1)\) represents the sum of the terms \((-2)^{(k-1)\)  for k ranging from 1 to 4. To evaluate this sum, we can substitute k=1, k=2, k=3, and k=4 into the expression \((-2)^{(k-1)\) and add up the resulting terms.

When k=1, we have \((-2)^{(k-1)\) \(= (-2)^{(1-1)} = (-2)^0 = 1\).

When k=2, we have \((-2)^{(k-1)\) \(= (-2)^{(2-1) }= (-2)^1 = -2\).

When k=3, we have  \((-2)^{(k-1)} = (-2)^{(3-1) }= (-2)^2 = 4\).

When k=4, we have \((-2)^{(k-1)}= (-2)^{(4-1)} = (-2)^3 = -8\).

Therefore, the sum \(\sum_k^4 (-2)^{(k-1)\) is equal to 1 + (-2) + 4 + (-8) = -5.

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Answer:

We use the rule,

\((a^b)^c = a^{bc}\)

a. (10^7)²

\((10^7)^2 = 10^{(7)(2)} = 10^{14}\)

10^14

b. (10^9)³

\((10^9)^3 = 10^{(9)(3)} = 10^{27}\)

10^27

c. (10^6)³

\(10^{(6)(3)}= 10^{18}\)

10^18

d. (10^2)³

\(10^{(2)(3)} = 10^{6}\)

10^6

e. (10³)²

\(10^{(3)(2)}=10^{6}\)

10^6

f. (10^5)^7

\(10^{(5)(7)} = 10^{35}\)

10^35

Step-by-step explanation:

Answer:

x = 5

y = 1

Step-by-step explanation:

2x - y = 9

3x + 4y = 19

We multiply the first equation by 4

8x - 4y = 36

3x + 4y = 19

11x = 55

x = 5

Now we put 5 in for x and solve for y

2(5) - y = 9

10 - y = 9

-y = -1

y = 1

Let's Check the answer

2(5) - 1 = 9

10 - 1 = 9

9 = 9

So, x = 5 and y = 1 is the correct answer.

Answer:

The roots are -2 and 4

Step-by-step explanation:

Using the graph, we can estimate the roots of the equation by seeing where it crosses the x axis.

It appears to cross the x axis at -2 and 4.

The roots are -2 and 4

Since the equation of the parabola is in standard form, then the x-coordinate of the vertex can be found like this:

In this case, you have

Now that you have the x coordinate of the vertex, you can replace this value into the original equation of the parabola to find the y coordinate of the vertex:

Therefore, the vertex of this parable is (-8,0).

The two types of figures are open and closed, geometric figures respectively. Figures that don't end where they begin are said to be open figures.

Closed geometric shapes are made up of points, line segments, circles, and curves. All around us, we can observe these types of shapes. Circle, rectangle, triangle, and other geometric shapes are a few examples. The triangle-shaped slices of a pizza are round.

Straight lines have been drawn on the floor, the door, the window, and the zebra crossing by the roadside in the classrooms. Even though angles are used in building construction, they also have connections to disciplines like physics and chemistry.

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Step-by-step explanation:

Slope 1/2    point    5,1  

  in point slope form would be

    (y-1) = 1/2 (x-5)

Hi there!

a.

Recall the equation for a Taylor expansion:

\(P_n(x) = f(c) + \frac{f^{'}(x)}{1!}(x - c)^1 + ... +\frac{f^{n}(x)}{n!}(x - c)^n\)

**Where the numerator of the coefficient is the derivative evaluated at the point, and c = where the polynomial is centered.

We can plug in the given values to solve.

\(P_5(0.2) = f(0) + \frac{f^{'}(0)}{1!}(0.2 - 0)^1 + \frac{f^{''}(0)}{2!}(0.2 - 0)^2 + \frac{f^{'''}(0)}{3!}(0.2 - 0)^3 + \frac{f^{4}(0)}{4!}(0.2 - 0)^4 \\\\P_5(0.2) = 4 + \frac{5}{1}(0.2) + \frac{-1}{2}(0.2)^2 + \frac{-15}{12}(0.2)^3 + \frac{23}{4!}(0.2)^4\\\\P_5(0.2) = 4 + 1 -0.02 -0.01 + 0.0015 = \boxed{4.9715}\)

b.

At x = 0, f(x³) = f(x) because 0³ = 0, so we can simply take the derivative of the polynomial to find g'(x).

Differentiate the following.
\(P_5(x) = f(0) + \frac{5}{1!}(x- 0)^1 + \frac{-1}{2!}(x - 0)^2 + \frac{-15}{2* 3!}(x- 0)^3 + \frac{23}{4!}(x - 0)^4\)
Simplify:
\(P_5(x) = 4 + 5x+ \frac{-1}{2}x^2 + \frac{-15}{12}x^3 + \frac{23}{24}x^4\\\\\boxed{\frac{d}{dx}P_5(x) = 5 -x - \frac{15}{4}x^2 + \frac{23}{6}x^3}\)

c.

The third degree will include n = 0, 1, and 2. Also, c = 1 in this instance, so using the format above:
\(P_n(x) = f(1) + \frac{f^{'}(1)}{1!}(x - 1)^1 + +\frac{f^{''}(1)}{2!}(x - 1)^2\\\\= 8 + \frac{3}{1!}(x - 1)^1 +\frac{-2}{2!}(x - 1)^2\\\\\boxed{= 8 + 3(x - 1) -(x - 1)^2}\)

d.

Using the equation for the Lagrange error bound:
\(| R_n| \leq \frac{f^{n + 1}(z) |(x - c)|^{n+ 1}}{(n + 1)!}\)

\(f^{n+1} (z)\) is the maximum value of the fourth derivative (since we are doing a third-degree polynomial), which is given to us in the problem.

We also know that:
n = 3

c = 1

x = 1.1

We can plug in the values:

\(|R_n| \leq \frac{(300) |(1.1 - 1)|^{3+ 1}}{(3 + 1)!} = \frac{300(0.1^4)}{4!} = \boxed{0.00125}\)

Answer:

12-(11)5=-43

Step-by-step explanation:

i hope this helps

Answer:

D. (X + 3 ) ( X +1 )

process:

x² + 4x + 3

= x² + (3 + 1)x +3

= x² + 3x + x + 3

= X (x+3) + 1 (X+3)

= (X + 3 ) ( X +1 )

Answer:

Item price now= 3.95

Step-by-step explanation:

To find out the price now, we will subtract 79 (original price) by 95% of 75. That will equal the discounted price. Finding the percentage of anything, we can use the formula, Total amount•percentage/100. The total amount is 79, and the percentage is 95. 79•95=7505, 7505/100=75.05. Now, 95% of 79 is 75.05, 79-75.05=3.95. $3.95 is the price now of the item. Though, I am unsure what a ALEKS calculator is. Have a nuce time, and joyful day

the population of the country in 2003 is, 368.3 million.

What is exponential?

The exponential is an example of a mathematical function that is useful in determining if something is increasing or decreasing exponentially is the exponential function. As implied by its name, an exponential function uses exponents. But take note that an exponential function does not have a variable as its exponent and a constant as its base (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

The population's description is provided by the exponential model a = 368.3e0.002t.

"a" denotes a nation's population in millions,

following 2003 by t years.

We must ascertain the country's population in 2003.

At 2003, t = 0.

In the exponential model above, enter t = 0.

a = 368.3e^0.002(0) (0)

a = 368.3e^0

a = 368.3

Hence, the population of the country in 2003 is, 368.3 million.

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Navern's manufacturing cycle efficiency (MCE) for its elevators is: 41.4%

The formula for obtaining the manufacturing cycle efficiency is value-added time divided by the production cycle time * 100. In the data given, the process and inspection times qualify as a value-added time

Process time = 23 days

Inspection time = 13 days

Value added time = 23 + 13 = 36days

The production cycle time = Move time + process time + queue time + inspection time + wait time

= 22 + 12 + 23 + 13 + 17 days

= 87 days

So, the manufacturing efficiency time = 36/87 * 100

= 41.4%

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The missing dimensions from the given expression should be completed with the following:

(81.) A) 2

(82.) AD) x

(83.) E) 12

The expression as a product should be written as: DE) 2(x + 12).

In Mathematics and Geometry, a factored form can be defined as a type of quadratic expression that is typically written as the product of two (2) linear factors and a constant.

In this scenario and exercise, we would complete the table above by showing the factored form and expanded form of each of the given expressions as follows;

        x           12

2      2x         24

Note: 2x/2 = x.

         24/2 = 12.

(2x + 24) = 2(x + 12).

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The surface area of the composite figure is 2005 in².

To find the surface area of the composite figure, we need to calculate the sum of the areas of its individual components.

Let's break down the figure into its different parts and calculate the surface area step by step:

Rectangular Prism: The rectangular prism has dimensions of 20 in, 11 in, and 5 in. The surface area of a rectangular prism can be found by adding the areas of its six faces. The total surface area of the rectangular prism is given by:

Surface Area of Rectangular Prism = 2lw + 2lh + 2wh

Plugging in the values, we have:

Surface Area of Rectangular Prism = 2(20)(11) + 2(20)(5) + 2(11)(5) = 440 + 200 + 110 = 750 in²

Rectangular Prism: Another rectangular prism has dimensions of 19 in, 12 in, and 12 in. Following the same process as above, we can calculate the surface area of this rectangular prism:

Surface Area of Rectangular Prism = 2lw + 2lh + 2wh

Plugging in the values, we have:

Surface Area of Rectangular Prism = 2(19)(12) + 2(19)(12) + 2(12)(12) = 456 + 456 + 288 = 1200 in²

Base: The base is a rectangle with dimensions 11 in and 5 in. The surface area of a rectangle is given by the formula:

Surface Area of Rectangle = lw

Plugging in the values, we have:

Surface Area of Rectangle = (11)(5) = 55 in²

Finally, to find the total surface area of the composite figure, we add the surface areas of the individual components:

Total Surface Area = Surface Area of Rectangular Prism + Surface Area of Rectangular Prism + Surface Area of Rectangle

Total Surface Area = 750 in² + 1200 in² + 55 in² = 2005 in²

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So, the equation of the axis of the segment AB is (A) y = 1/2 - x/2.

What is slope?

In mathematics, slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for every unit change in the independent variable.

The slope of the line passing through points A and B can be calculated as follows:

slope = (change in y) / (change in x) = (1-0) / (1-0) = 1/1 = 1

The equation of a line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

To find the y-intercept, we can use point A (0,0) and substitute the slope value.

y = mx + b

0 = 1(0) + b

b = 0

Therefore, the equation of the line passing through points A and B is:

y = 1x + 0

Simplifying, we get:

y = x

So, the answer is (A) y = 1/2 - x/2. However, this is not one of the given answer choices. We can also write the equation in point-slope form as y - y1 = m(x - x1) using point A, which gives:

y - 0 = 1(x - 0)

y = x

This confirms our earlier answer.

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The output value of (g/f)(x) is 9x/(7x + 28).

The domain of g/f is (-∞, -4) U (-4, ∞)..

In this exercise, we would determine the corresponding composite function of f(x) and g(x) under the given mathematical operations in simplified form as follows;

(g/f)(x) = (9/(x + 4)) ÷ 7/x

By rearranging the mathematical expression using the multiplication operation, we have the following:

(g/f)(x) = (9/(x + 4)) × x/7

(g/f)(x) = 9x/(7x + 28)

For the restrictions on the domain, we would have to equate the denominator of the rational function to zero and then evaluate as follows;

7x + 28 ≠ 0

7x ≠ -28

x ≠ -4

Domain = (-∞, -4) U (-4, ∞).

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Answer:

2

Step-by-step explanation:

-8-(-12)=4

1.8-12=-4

2.-8+12=4

3.-8-12=-20

4.-(8+12)=-4

The area that will be painted grey is approximately 38 ft².

The circumference of the free-throw circle is given as 30.77 feet, and we know that the free-throw circle is a perfect circle. We can use the formula for circumference to find the radius of the circle, which will be necessary to calculate its area.

Circumference of a circle = 2πr

30.77 = 2 x 3.14 x r

r = 30.77 / (2 x  3.14) = 4.9 feet

Half of the circle will be painted grey. Find the area of half the circle using the formula for the area of a circle.

Area of a circle = π x r²

Area of half the circle = 0.5 x  π x r²

Area of half the circle = 0.5 x 3.14 x 4.9²

Area of half the circle = 37.73 ft²

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The cost of each shirt is $6 and the cost of each pant for the given condition is $9.

The elimination approach involves taking one variable out of the system of linear equations by utilising addition or subtraction together with multiplication or division of the variable coefficients.

Let us suppose the cost of shirt = x.

Let us suppose the cost of pant = y.

Given that 3 shirts and 3 pants cost $45, this is represented as:

3x + 3y = 45 (equation 1)

1 shirt and 2 pants cost $24, this is represented as:

x + 2y = 24 (equation 2)

Using the elimination method to solve:

Multiply the second equation with 3 and change the signs of all the variables.

(x + 2y = 24) (3)

-3x - 6y = -72 (equation 3)

3x + 3y = 45

Comparing equation 1 and equation 3, the x term is cancelled, and the remaining equation after subtracting both equations is:

- 3y = -27

y = 9

Substitute the value of y in equation 2.

x + 2y = 24

x + 2(9) = 24

x + 18 = 24

x = 24 -18

x = 6

Hence, the cost of each shirt is $6 and the cost of each pant is $9.

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