Simplify the expression to a polynomial in standard form:
(x + 1)(3x2 – 10x + 8)
WHAT IS THIS???

The number of ceiling boards in the room is 5000

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

Measurement = 5 cm by 10 cm

Room = square of 5 m dimension

The area of the room is calculated as

Area = (5 m)²

When evaluated, we have

Area = 25 m²

The area of the board is

Area = 5 cm * 10 cm

So, we have

Area = 50 cm²

So, we have

Boards = (25 m²)/(50 cm²)

Evaluate the quotient

Boards = 5000

Hence, the number of boards is 5000

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The value of x is 65. Please note that this solution is based on the assumption that the angles QRP and PSQ are supplementary. If this assumption doesn't hold, feel free to let me know.

We need to find the value of x in the equation ZQRP = (2x + 20)° given that ZPSQ = 30°. Since the question doesn't provide enough information about the relationship between angles QRP and PSQ, I'll assume that they are supplementary angles (angles that add up to 180°). This assumption is based on the possibility that the angles form a straight line or a linear pair.

If angles QRP and PSQ are supplementary, their sum is 180°:

(2x + 20)° + 30° = 180°

Now, we can solve for x:

2x + 50 = 180

Subtract 50 from both sides:

2x = 130

Divide by 2:

x = 65

Answer:

z = z

Step-by-step explanation:

first you should combine like terms on the left side of the equation

9z + 7z = 16z

now rewrite

16z-6 = 16z-6

add 6 to both sides

16z = 16z

divide both sides by 16

z = z

Answer:

Both sides are equal. z has no solution. The input is an identity. It is true for all values.

Step-by-step explanation:

9z - 6 + 7z = 16z - 6

16z - 6 = 16z - 6

Both sides are equal. z has no solution. The input is an identity. It is true for all values.

The system of equations models this situation Perla and Tracene made is:

p + t = 18

p = 3t + 2

correct option: (A)

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.

Given that,

Perla made p number of home runs and Tracene made t number of home runs.

Now, Perla and Tracene have hit 18 home runs combined during the baseball season, so the equation becomes:

p + t = 18 ....... (i)

Perla has hit three more than twice the number of home runs that Tracene has:

p = 3t + 2 ....... (ii)

Thus, the system of equations models this situation Perla and Tracene made is:

p + t = 18

p = 3t + 2

so, correct option: (A)

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Answer:

Slant height = 10.2 cm

Step-by-step explanation:

Thus, we can find the slant height using the Pythagorean theorem, which is given by:

a^2 + b^2 = c^2, where

Thus, we can plug in 2 and 10 for a and b to solve for c, the slant height rounded to the nearest tenth:

Step 1:  Plug in 2 and 10 for a and b and simplify:

2^2 + 10^2 = c^2

4 + 100 = c^2

104 = c^2

Step 2:  Take the square root of both sides and round to the nearest tenth to find c, the length of the slant height:

√(104) = √(c^2)

10.19803903 = c

10.2 = c

Thus, the slant height is about 10.2 cm.

Answer:

y = 8x + 3

Step-by-step explanation:

here, m is the slope and b is the y-intercept.

      m = 8 and b = 3

          y = 8x + 3

Answer:

f = 144 degrees

Step-by-step explanation:

Since there are 6 angles (a,b,c,d,e,f), this means that it is a 6-sided polygon. The formula to find the total sum of interior angles is (n-2)*180, n being the amount of sides.
Let's plug it into the formula: (6-2)*180 = 720
This means that a+b+c+d+e+f = 720, but we can substitute (a+b+c+d+e) for 576.
576+f=720
f = 144 degrees

Answer:

10a+5b-30

Step-by-step explanation:

Apply the distributive law = ma + mb +  mc

5 (2a+b-6) = 5 2a + 5b + 5 (-6)

Then Simplify: 5 2a + 5b + 5 (-6)

= 10a+5b-30

Hope this helps :D

The equivalent of the given expression -8.2-5 is -13.2.

It is a sentence with a minimum of two numbers or variables and at least one math operation.

The given expression is -8.2-5.

Its simplified value is -13.2.

Hence, the equivalent expression is negative 13.2.

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Answer:

a=53

Step-by-step explanation:

\( \sin(45) = \frac{a}{53 \sqrt{2} } \\ \frac{ \sqrt{2} }{2} = \frac{a}{53 \sqrt{2} } \\ a = 53\)

I hope I helped you^_^

Answer:

a = 53

Step-by-step explanation:

This is a 45- 45- 90 triangle with sides in the ratio x : x : x\(\sqrt{2}\)

x are the legs and x\(\sqrt{2}\) the hypotenuse

Here x\(\sqrt{2}\) = 53\(\sqrt{2}\) , then x = 53

That is the leg a = 53

The equation of the perpendicular bisector of the segment with endpoints G (-2,0) and H(8,-6) would be, y = -(3/4)x + (9/2)

What is Perpendicular bisector of the segment?

A perpendicular bisector is a line that cuts another line segment through the junction point at a straight angle. As a result, a perpendicular bisector always cuts a line segment through its midway. The term bisect means to divide equally or uniformly.

The midpoint of the segment GH is the point (3,-3).

The slope of the line perpendicular to GH is the negative reciprocal of the slope of GH, which is -6/8 = -3/4

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

The point-slope form of the equation of the line is y - y1 = m(x - x1)

So we have

y - (-3) = (-3/4)(x - 3)

y + 3 = (-3/4)x + (9/2)

We can find the equation of the perpendicular bisector of the segment G(x1, y1) and H(x2, y2) by using the midpoint of the segment, (x1 + x2)/2, and (y1 + y2)/2, and the slope of the segment, (y2 - y1)/(x2 - x1)

so our final equation is y = -(3/4)x + (9/2)

Therefore, equation of the perpendicular bisector of the segment with endpoints G (-2,0) and H(8,-6) would be, y = -(3/4)x + (9/2)

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Answer:

C) 12.56ft

Step-by-step explanation:

if diameter = 4 ft. then radius = 2 ft ( 1/2 diameter)

2 \(\pi\) r = 2 x \(\pi\) x 2 = 2 x 3.14 x 2 = 12.56 ft

Answer:

19%

Step-by-step explanation:

What is the probability that those who ordered a large drink was a cold one?

27 drinks in total

5 cold

5/27*100%

Hope this helps!

Answer:

n=63/5 or 12.6

Step-by-step explanation:

Explanation is in the screen shot!

Answer:

n=63

Step-by-step explanation:

The solution for x in the compound inequality is 18 < x ≤ 3

The compound inequality is given as

6x − 10 ≤ 8 or 1/3x + 6 > 12

Add or subtract the constant to both sides of the compound inequality

So, we have

6x ≤ 18 or 1/3x > 6

Divide both sides of the compound inequality by the coefficient of x

So, we have

x ≤ 3 or x > 18

Rewrite as

x > 18 or x ≤ 3

Combine both inequalities

18 < x ≤ 3

Hence, the solution for x in the compound inequality is 18 < x ≤ 3

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Answer: line c

Step-by-step explanation: we know that

If two figures are similar, then the ratio of its corresponding sides is equal and is called the scale factor

Let

z-----> the scale factor

m----> the distance from P to the dilated line

we have

The dilated line at  units of P is the line c

Answer:

Line c don’t rate

Step-by-step explanation:

In order to determine the integer that makes true the given expression:

______ x 7 = -14

consider that such integer must be equal to the quotient between -14 and 7:

-14/7 = -2

In fact, you have:

-2 x 7 = -14

Hence, the integer is -2

Answer:

y = 2x + 1

Step-by-step explanation:

1. Find the slope;  (change in y values)/(change in x values)

Slope = (-5 - 3)/ (-3 - 1) = -8/-4 = 2

2. Find the y-intercept (b) using  the slope intercept formula: y = mx + b

    m = 2 and using point (1, 3) , solve for "b"

       y = mx + b

       3 = 2(1) + b

       3 = 2 + b

      1 = b

3.  Write the linear equation: y = 2x + 1

We must conclude that there are infinitely many primes of the form 3k + 2, where k is a non-negative integer.

To adapt the proof:

We can use a similar contradiction argument.

Suppose that there are only finitely many primes of the form 3k + 2, say p1, p2, ..., pn.

Let N = 3p1p2...pn + 2. Note that N is of the form 3k + 2 for some non-negative integer k.

Now, let's consider the prime factorization of N. Either N is prime and of the form 3k + 2, in which case we have found a new prime of the desired form, contradicting our assumption that there are only finitely many such primes. Or, N is composite and has a prime factorization consisting only of primes of the form 3k + 1 (since any prime of the form 3k + 2 would divide N). But this implies that N itself is of the form 3k + 1.

Now, let's consider the number M = 3N + 2. M is also of the form 3k + 2, and so must have a prime factorization consisting only of primes of the form 3k + 1. But since N is of the form 3k + 1, we have

M = 3(3p1p2...pn + 1) + 2 = 9p1p2...pn + 5. This means that M has a prime factorization consisting of primes of the form 3k + 2, which contradicts our assumption that there are only finitely many such primes.

Therefore, we must conclude that there are infinitely many primes of the form 3k + 2, where k is a non-negative integer.

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Answer:

c/sin(60°) = 14/sin(25°)

c = 14sin(60°)/sin(25°) = 28.7

Answer + Explanation:

Since you just flip the fraction if you have a negative power, you get

1.) 6 to the power of -1 = 1/6

2.) 6 to the power of -2 = 1/36

3.) 6 to the power of -3 = 1/216

4.) 6 to the power of -4 = 1/1296

The text discusses a production function and addresses various aspects of a firm's decision-making. It covers profit maximization, factor demand functions, supply function, profit function, Hotelling's lemma, cost minimization, conditional factor demand functions, and the cost function. These concepts are derived using mathematical calculations and formulas. Hotelling's lemma is verified, and the cost function is determined.

(a) The firm's profit maximization problem can be stated as follows: Maximize profits (π) by choosing the optimal levels of inputs (z and zo) that maximize the output (y) given the prices of output (p) and inputs (w, w₂).

(b) To derive the firm's factor demand functions, we need to find the conditions that maximize profits.

The first-order condition for input z is given by:

∂π/∂z = p * (∂f/∂z) - w = 0

Substituting the production function f(z) = z^(1/4) / z^(1/2) into the above equation, we have:

p * (1/4 * z^(-3/4) / z^(1/2)) - w = 0

Simplifying, we get:

p * (1/4 * z^(-7/4)) - w = 0

Solving for z, we find:

z = (4w/p)^(4/7)

Similarly, for input zo, the first-order condition is:

∂π/∂zo = p * (∂f/∂zo) - w₂ = 0

Substituting the production function f(zo) = z^(1/4) / z^(1/2) into the above equation, we have:

p * (1/2 * z^(1/4) * zo^(-3/2)) - w₂ = 0

Simplifying, we get:

p * (1/2 * z^(1/4) * zo^(-3/2)) - w₂ = 0

Solving for zo, we find:

zo = (2w₂ / (pz^(1/4)))^(2/3)

(c) To derive the firm's supply function, we need to find the level of output (y) that maximizes profits.

Using the production function f(z), we can express y as a function of z:

y = z^(1/4) / z^(1/2)

Given the factor demand functions for z and zo, we can substitute them into the production function to obtain the supply function for y:

y = (4w/p)^(4/7)^(1/4) / (4w/p)^(4/7)^(1/2)

Simplifying, we get:

y = (4w/p)^(1/7)

(d) The firm's profit function is given by:

π = p * y - w * z - w₂ * zo

Substituting the expressions for y, z, and zo derived earlier, we have:

π = p * ((4w/p)^(1/7)) - w * ((4w/p)^(4/7)) - w₂ * ((2w₂ / (pz^(1/4)))^(2/3))

(e) To verify Hotelling's lemma, we need to calculate the partial derivatives of the profit function with respect to the prices of output (p), input z (z₁), and input zo (z₂).

Hotelling's lemma states that the partial derivatives of the profit function with respect to the prices are equal to the respective factor demands:

∂π/∂p = y - z * (∂y/∂z) - zo * (∂y/∂zo) = 0

∂π/∂z₁ = -w + p * (∂y/∂z₁) = 0

∂π/∂z₂ = -w₂ + p * (∂y/∂z₂) = 0

By calculating these partial derivatives and equating them to zero, we can verify Hotelling's lemma.

(f) The firm's cost minimization problem can be stated as follows: Minimize the cost of production (C) given the level of output (y), prices of inputs (w, w₂), and factor demand functions for inputs (z, zo).

(g) To derive the firm's conditional factor demand functions, we need to find the conditions that minimize costs. We can express the cost function as follows:

C = w * z + w₂ * zo

Taking the derivative of the cost function with respect to z and setting it to zero, we get:

∂C/∂z = w - p * (∂y/∂z) = 0

Simplifying, we have:

w = p * (1/4 * z^(-3/4) / z^(1/2))

Solving for z, we find the conditional factor demand for z.

Similarly, taking the derivative of the cost function with respect to zo and setting it to zero, we get:

∂C/∂zo = w₂ - p * (∂y/∂zo) = 0

Simplifying, we have:

w₂ = p * (1/2 * z^(1/4) * zo^(-3/2))

Solving for zo, we find the conditional factor demand for zo.

(h) The firm's cost function is given by:

C = w * z + w₂ * zo

Substituting the expressions for z and zo derived earlier, we have:

C = w * ((4w/p)^(4/7)) + w₂ * ((2w₂ / (pz^(1/4)))^(2/3))

This represents the firm's cost function.

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the general solution to the system of equations Bx = b is: x = [2 - t, 4, t, 2, 4 - t] where t is a real parameter

To find the basis of the row space, range, and null space of matrix B, and to determine the rank and verify the rank-nullity theorem, we can perform row reduction on matrix B.

Matrix B:

1 2 1

3 0 0

1 1 1

3 2 0

1 1 1

Performing row reduction on B:

R2 = R2 - 3R1

R3 = R3 - R1

R4 = R4 - 3R1

1 2 1

0 -6 -3

0 -1 0

0 -4 -1

0 -1 0

R3 = -R3

R4 = R4 - 4R3

1 2 1

0 -6 -3

0 1 0

0 0 -1

0 -1 0

R4 = -R4

R2 = R2 + 6R4

1 2 1

0 0 -3

0 1 0

0 0 1

0 0 0

R1 = R1 - 2R3

R2 = -R2

R3 = R3 - R4

1 0 1

0 0 3

0 1 0

0 0 1

0 0 0

Now, we have the row-echelon form of matrix B. The pivot columns are the first, third, and fifth columns. We can observe that the rank of B is 3 since there are 3 pivot columns.

Next, let's determine the basis of the row space. We can take the rows corresponding to the pivot columns:

Row 1: [1 0 1]

Row 3: [0 1 0]

Row 4: [0 0 1]

Therefore, a basis of the row space of B is {[1 0 1], [0 1 0], [0 0 1]}.

To find the basis of the range, we can take the columns corresponding to the pivot columns:

Column 1: [1 3 1 3 1]

Column 3: [1 0 1 0 0]

Column 5: [1 1 1 1 0]

Therefore, a basis of the range of B is {[1 3 1 3 1], [1 0 1 0 0], [1 1 1 1 0]}.

Next, let's find the null space of B. We need to solve the homogeneous system Bx = 0. From the row-echelon form, we can see that the last column (column 6) is a free variable. We can assign it a parameter, say t. Then we can solve for the remaining variables:

x₁ + x₃ + t = 0

3x₁ - 3x₃ + 0 = 0

x₂ + t = 0

Simplifying the system, we have:

x₁ + x₃ = -t

x₂ = -t

Therefore, the null space of B can be represented as the vector:

[-t, -t, t]

Now, let's verify the rank-nullity theorem. The rank of B is 3, and the nullity can be determined by counting the number of free variables, which is 1 (the parameter t). The nullity is 1. According to the rank-nullity theorem, the sum of the rank and nullity should be equal to the number of columns in B, which is

5. Indeed, 3 + 1 = 4, satisfying the rank-nullity theorem.

Finally, let's find the general solution to the system of equations Bx = b, where b = C₁ + C₅. The given b is the sum of the first and last column of B:

b = [1 3 1 3 1] + [1 1 1 1 0] = [2 4 2 4 1]

We can substitute the values of the pivot variables in the row-echelon form with the corresponding values from b:

x₁ = 2 - x₃

x₂ = 4

x₄ = 2

x₅ = 4 - x₃

The free variable t can be used to represent x₃. Therefore, the general solution is:

x₁ = 2 - t

x₂ = 4

x₃ = t

x₄ = 2

x₅ = 4 - t

Thus, the general solution to the system of equations Bx = b is:

x = [2 - t, 4, t, 2, 4 - t] where t is a real parameter.

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Part A: The stated values is; x = 31π/6

A circle has 360 degrees. We must decrease the present angle to an angle between 0° and 360° in order to determine the reference angle.

As, 360° = 2π radians, subtract 2π = 12π/6 radians for each iteration.

Iteration 1 =>  31π/6 - 12π/6 = 19π/6

Iteration 2 =>  19π/6 - 12π/6 = 7π/6

0 ≤ 7π/6 ≤ 12π/6

Thus, reference angle is found as 7π/6 radians

Part B) The value for the sin x, tan x, and sec x.

sin (7π/6) = -1/2

tan (7π/6) = 1/√3

sec (7π/6) =  1/cos(7π/6) = -1/(√3)/2

sec (7π/6) = -2/√3

Thus, the simplest values of sin x, tan x, and sec x are found.

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The indicated z score is -1.5, which is a measure of the number of standard deviations away from the mean of zero that a given data point is located on the standard normal distribution. A z score of -1.5 would indicate that the data point is 1.5 standard deviations below the mean.

z = -1.5

Mean = 0

Standard Deviation = 1

z = (x - Mean)/Standard Deviation

-1.5 = (x - 0)/1

x = -1.5 The indicated z score is -1.5.

To find the indicated z score, first determine the mean of the distribution and the standard deviation (which is 1). Then, calculate the distance from the mean to the data point, in terms of standard deviations. This can be done by subtracting the mean from the data point and dividing by the standard deviation. For the given example, the z score is -1.5, indicating the data point is 1.5 standard deviations below the mean.

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the value of the iterated integral is (π/8) (2 - e^(-16)).

We have the iterated integral:

∫[0,4] ∫[0,√(16-x^2)] e^(-x^2-y^2) dy dx

To convert this to polar coordinates, we need to express x and y in terms of r and θ.

We have:

x = r cos(θ)

y = r sin(θ)

We also need to express the differential element dA in terms of polar coordinates. We have:

dA = r dr dθ

Substituting these expressions into the given integral, we get:

∫[0,π/2] ∫[0,4] e^(-r^2) r dr dθ

The limits of integration for θ are 0 to π/2 because the region lies in the first and second quadrants.

We can evaluate this integral using the fact that the integral of e^(-r^2) is √π/2:

∫[0,π/2] ∫[0,4] e^(-r^2) r dr dθ

= ∫[0,π/2] [-1/2 e^(-r^2)] [0,4] dθ

= ∫[0,π/2] (1/2 - 1/2 e^(-16)) dθ

= π/4 - π/8 (1 - e^(-16))

= (π/8) (2 - e^(-16))

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Answer:

3/7 (simplified)

Step-by-step explanation:

The original answer would be 6/14 because 6 out of 14 people said tennis. However, you divide both by 2 to get 3/7. The percent would be 42% if that is needed.

The area of the polygon is 128units²

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles e.t.c

The polygon is a regular polygon, this means that the sides and angles are equal. It is an octagon, i.e 8 sided. it is sub divided into triangles.

Area of triangle = 1/2 bh

where B is the base and h is the height

A = 1/2 × 8 × 17

A = 4 × 17

A = 68

Since the area of one triangle is 68 units², then the area of the polygon with 16 triangles is

= 68 × 8

= 128 units²

therefore the area of the polygon is 128 units²

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The value of x if number of men is equal to number of women, is,

⇒ x = 8

We have to given that;

Number of men voters = √(9+2x) - √2x

And, Number of women voters = 5/√9+2x

Now, We have number of men is equal to number of women. ​

Hence, We get;

⇒ √(9+2x) - √2x = 5/√9+2x

⇒ √(9+2x) - 5/√9+2x = √2x

⇒ [(9 + 2x) - 5] /√9+2x = √2x

⇒ (4 + 2x) / √9+2x = √2x

⇒ (4 + 2x) =  √9+2x × √2x

⇒ (4 + 2x)² = 2x (9 + 2x)

⇒ 4x² + 16 + 16x = 18x + 4x²

⇒ 16 = 2x

⇒ x = 16 / 2

⇒ x = 8

Thus, The value of x is,

⇒ x = 8

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Answer:

(-0.8, 2.2)

Step-by-step explanation:

Where the two lines intersect is the solution to the System of Equations.

Answer:

the answer would be (-0.8, 2.2) since it hasn't hit -3 yet and if it were to be -1 it would be in the bottom left