In the square pyramid shown, points and are midpoints of the edges of one face. If the figure is sliced through points and and through the base, which best describes the shape of the resulting cross section? The picture shows a triangular prism. M and N are the points on the prism. A. rectangle B. trapezoid C. quadrilateral D. parallelogram

A statement that correctly compares the graph of function g with the graph of function f include the following: C. The graph of function g is a vertical compression of the graph of function f.

In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.

Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.

When the parent function [tex]f(x) = e^x -4[/tex] is vertically compressed by a scale factor of 1/2, the transformed function g(x) is given by the following equation;

g(x) = kf(x)

g(x) = 1/2f(x)

[tex]g(x) = \frac{1}{2} e^x -4[/tex]

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The quadratic equation from the given root is 4x² - 41x + 45 = 0

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

Roots = 5/x and 4

The equation of the function can be calculated as

(x - root) * (x - root) = 0

using the above as a guide, we have the following:

(x - 5/4) * (x - 9) = 0

When expanded, we have

(4x - 5)(x - 9)/4 = 0

This gives

4x² - 5x - 36x + 45 = 4 * 0

So, we have

4x² - 41x + 45 = 0

Hence, the quadratic equation from the given root is 4x² - 41x + 45 = 0

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Carey's graph will be a straight line with a slope of -1 and a y-intercept of 3.

Carey correctly graphs a linear function with a slope of -1 and a y-intercept of 3. A linear function is represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

In this case, the slope is -1, which means that for every unit increase in the x-coordinate, the y-coordinate decreases by 1 unit. The y-intercept is 3, indicating that the graph intersects the y-axis at the point (0, 3).

To plot the graph, Carey starts by marking the point (0, 3) on the graph. Then, for every unit increase in the x-coordinate, Carey moves one unit downward. Similarly, for every unit decrease in the x-coordinate, Carey moves one unit upward. These steps ensure the correct slope of -1.

After connecting the points, Carey will obtain a line that starts at the y-intercept (0, 3) and slants downward, with a slope of -1. The resulting graph will be a straight line extending to both sides of the coordinate plane.

In conclusion, it is represented by the equation y = -x + 3.

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a. The graph represents a proportional relationship.

b. The graph does not represent a proportional relationship.

c. The graph does not represent a proportional relationship.

d. The graph represents a proportional relationship.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable exists.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero presented as follows:

y = kx.

Hence graphs a and d represent proportional relationship, as they have intercepts at the origin.

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The magnitude of angle Z include the following:

cosZ = 0.471

sinZ = 0.88

tanZ = 1.875

In order to determine the magnitude of angle Z, we would apply the basic trigonometric ratio because the given side lengths represent the adjacent side, opposite side, and hypotenuse of a right-angled triangle.

cos(θ) = Adj/Hyp

Where:

For cosZ, we would apply the cosine trigonometric ratio as follows;

cosZ = 13.6/28.9

cosZ = 0.4706

Z = cos⁻¹(0.4706)

Z = 61.93°.

For sinZ, we would apply the sine trigonometric ratio as follows;

sinZ = 25.5/28.9

sinZ = 0.8824

Z = sin⁻¹(0.8824)

Z = 118.07.

For tanZ, we would apply the sine trigonometric ratio as follows;

tanZ = 25.5/13.6

tanZ = 1.875

Z = tan⁻¹(1.875)

Z = 61.93.

Printer A has the better rate of cost per page because the approximate rate of Printer A, $0.24 per page, is greater than the approximate rate of Printer B, $0.23 per page.

Rate demonstrates how many times one number can fit into another number. It contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

In this case, Printer A prints 100 pages for $23.99. The rate is:

[tex]\sf = \dfrac{\$23.99}{100}[/tex]

[tex]\sf = 0.2399\thickapprox\$0.24 \ per \ page[/tex]

Printer B prints 275 sheets for $63.99. The rate is:

[tex]\sf = \dfrac{\$63.99}{275}[/tex]

[tex]\sf = 0.2327\thickapprox\$0.23 \ per \ page[/tex]

Therefore, based on the above calculations, we can see that Printer A has the better rate of cost per page because the approximate rate of Printer A, $0.24 per page, is greater than the approximate rate of Printer B, $0.23 per page.

So option (A) is correct.

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first off, let's take a peek at the picture above

hmmm the hyperbola is opening sideways, that means it has a horizontal traverse axis, it also means that the positive fraction will be the one with the "x" variable in it.

now, the length of the horizontal traverse axis is 4 units, from vertex to vertex, that means the "a" component of the hyperbola is half that or 2 units, and 2² = 4, with a center at the origin.

[tex]\textit{hyperbolas, horizontal traverse axis } \\\\ \cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(x- 0)^2}{ 2^2}-\cfrac{(y- 0)^2}{ (\sqrt{3})^2}=1\implies {\Large \begin{array}{llll} \cfrac{x^2}{4}-\cfrac{y^2}{3}=1 \end{array}}[/tex]

The statements that are true about triangle PQR are QR = (sqrt(3))/2 * PQ and PR = (sqrt(3))/2 * PQ.The correct answer is option B and D.

Let's analyze the statements one by one:

A. PQ = 2PR:

This statement is not true. In a 30-60-90 triangle, the ratio of the lengths of the sides is as follows: opposite the 30-degree angle is x, opposite the 60-degree angle is x√3, and the hypotenuse (opposite the 90-degree angle) is 2x.

Therefore, PQ = x, and PR = x√3. Since √3 is not equal to 2, this statement is false.

B. QR = (sqrt(3))/2 * PQ:

This statement is true. In a 30-60-90 triangle, the ratio of the lengths of the sides is as follows: opposite the 30-degree angle is x, opposite the 60-degree angle is x√3, and the hypotenuse (opposite the 90-degree angle) is 2x.

Therefore, QR = x√3/2 = (sqrt(3))/2 * x = (sqrt(3))/2 * PQ. This statement holds true.

C. OR = 2PR:

We don't have any information regarding the length of OR, so we cannot determine if this statement is true or false based on the given information.

D. PR = (sqrt(3))/2 * PQ:

This statement is true. In a 30-60-90 triangle, the ratio of the lengths of the sides is as follows: opposite the 30-degree angle is x, opposite the 60-degree angle is x√3, and the hypotenuse (opposite the 90-degree angle) is 2x. Therefore, PR = x√3 = (sqrt(3))/2 * 2x = (sqrt(3))/2 * PQ. This statement is correct.

E. QR = sqrt(3) * PR:

This statement is not true. In a 30-60-90 triangle, the ratio of the lengths of the sides is as follows: opposite the 30-degree angle is x, opposite the 60-degree angle is x√3, and the hypotenuse (opposite the 90-degree angle) is 2x. Therefore, QR = x√3, and PR = x√3. So, QR = PR, but not QR = sqrt(3) * PR.

F. PQ = sqrt(3) * PR:

This statement is not true. In a 30-60-90 triangle, the ratio of the lengths of the sides is as follows: opposite the 30-degree angle is x, opposite the 60-degree angle is x√3, and the hypotenuse (opposite the 90-degree angle) is 2x. Therefore, PQ = x, and PR = x√3. So, PQ = PR/√3, but not PQ = sqrt(3) * PR.

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The probable question may be:

In triangle PQR , m angle P = 60 deg , m angle Q = 30 deg and m angle R = 90 deg Which of the following statements about triangle PQR are true?

Check all that apply

A. PQ = 2PR

B.QR = (sqrt(3))/2 * PQ

C. OR = 2PR

D.PR = (sqrt(3))/2 * PQ

E. QR = sqrt(3) * PR

F. PQ = sqrt(3) * PR

Answer:

The answer is 11

Step-by-step explanation:

brother only=12-8=4

sister only=13-8=5

brother and sister =8

neither of them=x

28=4+8+5+x

28=17+x

x=28-17

x=11

Answer:

  11

Step-by-step explanation:

You want to know the number of students with no brother or sister, given that 12 of 28 have at least one brother, 13 have at least one sister, and 8 have both.

The attachment shows the two-way table that can be formed from the given information. The four given numbers are shown in green at lower right. The other numbers in the table are filled in to make the totals accurate.

The number of students not having either a brother or sister is 11.

__

Additional comment

In terms of probability, which is the fraction that each event is of the total, you have ...

  P(B∪S) = P(B) +P(S) -P(B∩S) . . . . . . . useful relation to memorize

  P(B'∩S') = 1 -P(B∪S) = 1 -(12/28 +13/28 -8/28) = 11/28

This tells you 11 of the 28 students do not have a brother or sister.

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The graph should visually represent the shaded regions A and B, as well as their overlap in region AB. It's important to note that without a specific scale or values, the graph may not accurately depict the exact shape and position of the shaded regions.

To graph the system of inequalities 2x - y < 4 and x + y > -1, we can start by graphing each inequality separately and then determining the overlapping region.

For the inequality 2x - y < 4:

Start by graphing the line 2x - y = 4. Choose two points on the line, such as (0, -4) and (2, 0), and connect them to draw the line.

Since the inequality is "less than" (<), shade the region below the line. Label this shaded region as A.

For the inequality x + y > -1:

Graph the line x + y = -1 using points such as (-2, 1) and (0, -1). Connect the points to draw the line.

Since the inequality is "greater than" (>), shade the region above the line. Label this shaded region as B.

Finally, identify the overlapping region of the shaded regions A and B. This region represents the solution to the system of inequalities and is labeled as AB. This region indicates the values of x and y that satisfy both inequalities simultaneously.

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Answer:

Step-by-step explanation:

2x − y < 4

x + y > −1

In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB.

Answer: D

Step-by-step explanation:

The scale factor of the image after the dilation is k = 2

Given data ,

Polygon ABCD with vertices at A(1,-1) B(3,-1), C(3,-2) and D(1-2)

Now , the dilated polygon is represented as A'B'C'D'

where the coordinates are A’(2,-2), B(6,-2), C’(6,-4) and D’(2,-4).

Now , we can compare the corresponding side lengths of the two polygons to determine the scale factor:

Scale factor = (corresponding side length of dilated polygon) / (corresponding side length of original polygon)

So, A'/A = 2 / 1

A' = 2A

So, the scale factor is k = 2

Hence , the dilation is solved.

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The 36th derivative of f(x) = cos(2x) is [tex]2^{17}[/tex]* cos(2x).

To find the 36th derivative of the function f(x) = cos(2x), we can apply the chain rule repeatedly. The chain rule states that if we have a composite function y = f(g(x)), then its derivative is given by dy/dx = f'(g(x)) * g'(x).

Let's start by finding the first few derivatives of f(x) = cos(2x):

f'(x) = -2sin(2x)

f''(x) = -4cos(2x)

f'''(x) = 8sin(2x)

f''''(x) = 16cos(2x)

We observe a pattern where the derivatives of cos(2x) alternate between sin(2x) and cos(2x), with the signs changing accordingly.

Based on this pattern, we can see that the 36th derivative will be:

f^(36)(x) =[tex](-1)^{17} * 2^{17} *[/tex] cos(2x)

Simplifying this expression, we have:

f^(36)(x) = [tex]2^{17} * cos(2x)[/tex]

Therefore, the 36th derivative of f(x) = cos(2x) is[tex]2^{17[/tex] * cos(2x).

It's important to note that in this case, the number 36 is even, and since the derivatives of cos(2x) follow a repeating pattern every 4 derivatives, the sign (-1) raised to the power of 17 accounts for the change in sign in the 36th derivative.

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Answer:

X^2-8x+16

X^2-4x-4x+16

Factorise by gouping terms

X(x-4)-4(x-4)

=(x-4)(x-4)

There are a couple of formulas that we should know about quadratic functions, and this one utilizes this one:

(x - a)^2 = x^2 -2ax + a^2

Notice how x^2 - 8x + 16 fits into the formula:

x^2 - 8x + 16

x^2 - 2*x*4 + 4^2

(x - 4)^2

(x - 4)(x - 4)

Of course, not all expanded quadratic expressions fit into that formula, so there is a universal method to factor quadratic expressions:

x^2 + x(a + b) + ab —> (x + a)(x + b)

Basically, the middle term is the sum of an and b times x, and the last term is the product of an and b. So, if we are using the expression given in the problem, notice how -4 * -4 is 16, and the sum of -4 and -4 is -8. Thus, a and b are both -4 and the factored form is (x - 4)(x - 4)

The angle measure of an arc π meters is 45°.

Given that, the diameter of a circle is 8 meters.

Radius of a circle = 8/2 = 4 meters

The formula to find the arc length of a circle is θ/360° ×2πr.

Here, θ/360° ×2πr.

π=θ/360° ×2π×4

1=θ/360° ×8

360°=8θ

θ=360°/8

θ=45°

Therefore, the angle measure of an arc π meters is 45°.

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The maximum profit is achieved when the manufacturer spends $4,000 on development and $4,000 on promotion.

The profit is given by

(150 - 50) * (320y/(y+2) + 160x/(x+4)) - x - y

= 100 * (320y/(y+2) + 160x/(x+4)) - x - y

= 32000y/(y+2) + 16000x/(x+4) - x - y

We want to maximize this function subject to the constraint that x + y = 8.

We can do this by using Lagrange multipliers. The Lagrangian is given by

L = 32000y/(y+2) + 16000x/(x+4) - x - y + lambda(x + y - 8)

Setting the partial derivatives of L with respect to x, y, and lambda equal to zero, we get the following equations:

32000/(y+2) - 1 - lambda = 0

16000/(x+4) - 1 - lambda = 0

x + y - 8 = 0

Solving these equations, we get x = 4, y = 4, and lambda = 0.

Therefore, the maximum profit is achieved when the manufacturer spends $4,000 on development and $4,000 on promotion.

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The Equation of circle for Circle B is (x - 2) ² + (y + 4)²  = 38.4.

For circle A:

Radius of circle A = √36 = 6

Area of circle A = π(6)^2 = 36π

Let's assume the radius of circle B is r.

Circumference of circle A = 2π(6) = 12π

Circumference of circle B = 3.2 x Circumference of circle A

= 3.2 x 12π

= 38.4π

Since the ratio of the areas is equal to the ratio of the circumferences, we have:

Area of circle B / Area of circle A = (r^2π) / (36π) = 38.4π / 36π

Simplifying, we get:

r² / 36 = 38.4 / 36

Cross-multiplying, we have:

36 x r² = 38.4 x 36

Dividing both sides by 36:

r^2 = 38.4

Taking the square root of both sides:

r = √38.4

Now we have the radius of circle B. Let's substitute this value into the equation for circle B:

(x - 2) ² + (y + 4)² = (√38.4)²

Simplifying:

(x - 2) ² + (y + 4)²  = 38.4

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Step-by-step explanation:

The formula:

�

�

=

�

2

(

�

1

+

�

�

)

S

n

=

2

n

(a

1

+a

n

)

is used to solve for the sum of the arithmetic sequence given the first term a₁, the number of terms n, and the last term in an.

Example:

3, 6, 9, 12, 15,...,123

The first term, a₁ = 3

The last term an = 123

Common difference, d = 3 (because the sequence are multiples of 3)

Number of terms, n= ?

Find the number of terms, n:

an = a₁ + (n-1) (d)

123 = 3 + (n-1) (3)

123 = 3 - 3 + 3n

123/3 = 3n/3

n = 41

To find the sum of the given sequence without adding 3 + 6 + 9, ... + 123, we use the formula:

S₄₁ = (41/2) (3 + 123)

S₄₁ = (41/2) (126)

S₄₁ = (41)(63)

S₄₁ = 2,583 ⇒ the sum of the given sequence

The linear relationship is proportional

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

Using the above as a guide, we have the following:

Unit rate = Cost of banana/Number of banans

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

Unit rate = 9/1

Evaluate

Unit rate = 9 cent per banana

This means that the linear relationship is proportional

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We can determine the shortest distance from the surface xy+15x+z^2=209 to the origin.

Given the equation of the surface is xy + 15x + z^2 = 209.

Let's determine the shortest distance from the surface to the origin.

The shortest distance between the surface and the origin is given by the perpendicular distance, which can be calculated as follows:

Firstly, we need to determine the gradient of the surface, which is the vector normal to the surface.

For this purpose, we need to write the surface equation in the standard form, which is:xy + 15x + z^2 = 209 xy + 15x + (0)z^2 - 209 = 0 (the coefficients of x, y, and z are a, b, and c).

The gradient of the surface is given by the vector: ∇f = (a, b, c) = (y + 15, x, 2z) at the point P(x, y, z), which is a point on the surface.

Here, the normal vector is ∇f = (y + 15, x, 2z).

Now, let's consider a point A on the surface which is closest to the origin.

Let the coordinates of A be (a, b, c).

Therefore, the position vector of A is given by: OA = ai + bj + ck.

The direction of the position vector is in the direction of the normal vector, and therefore: OA is parallel to ∇f.

Thus, we can write: OA = λ∇f = λ(y + 15)i + λxj + 2λzkWhere λ is a scalar.

Since A lies on the surface, we have: a*b + 15a + c^2 = 209.

We also know that OA passes through the origin.

Therefore, the position vector of A is perpendicular to the direction vector OA.

This gives us: OA·OA = 0⟹ (ai + bj + ck)·(λ(y + 15)i + λxj + 2λzk) = 0

Simplifying this equation gives us:aλ(y + 15) + bλx + c(2λz) = 0

Also, we know that OA passes through the origin.

Therefore, the magnitude of OA is equal to the distance of A from the origin.

Hence, we can write: |OA| = √(a^2 + b^2 + c^2)

The value of λ can be obtained from the equation: aλ(y + 15) + bλx + c(2λz) = 0orλ = -2cz / (b + a(y + 15))

Substituting this value of λ in OA, we get: OA = λ(y + 15)i + λxj + 2λzk= -2cz/(b + a(y + 15)) (y + 15)i - 2cz/(b + a(y + 15)) xj - 4cz^2/(b + a(y + 15))k

Substituting this value of λ in |OA|, we get: |OA| = √[(2cz/(b + a(y + 15)))^2 + (2cz/(b + a(y + 15)))^2 + (4cz^2/(b + a(y + 15)))^2] = 2cz√[(y + 15)^2 + x^2 + 4z^2] / |b + a(y + 15)|

The distance of the point A from the origin is |OA|, which is minimized when the denominator is maximized. The denominator is given by |b + a(y + 15)|.

Thus, we have to maximize the denominator with respect to a and b. The condition for maximum value of the denominator is obtained by differentiating the denominator with respect to a and b separately and equating it to zero. The values of a and b obtained from these equations are substituted in the equation a*b + 15a + c^2 = 209 to obtain the coordinates of the point A, which is closest to the origin.

Hence, we can determine the shortest distance from the surface xy+15x+z^2=209 to the origin.

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Based on the calculations using unit pricing, Toilet paper B has a lower unit price and is the better deal between the two. Customers will save more money if they purchase toilet paper B rather than toilet paper A because the price per mega roll is lower. (option b)

Saving money while shopping is one of the best ways to reduce your expenses and have more disposable income for other things. Unit pricing is a pricing system that displays prices in standard units, allowing customers to compare prices across different brands and package sizes and save money. To determine which toilet paper deal is better, we can use the unit price method, which divides the price by the number of units in the package. The toilet paper with the lower unit price is the better deal.
The formula for unit pricing is as follows:
Unit price = total price ÷ number of units
Using the above formula, we can calculate the unit price of toilet paper A and toilet paper B as follows:
For Toilet paper A:
Unit price = $4.59 ÷ 6 mega rolls
Unit price = $0.765 per mega roll
For Toilet paper B:
Unit price = $9.02 ÷ 12 mega rolls
Unit price = $0.751 per mega roll
Therefore, based on the calculations, Toilet paper B has a lower unit price and is the better deal between the two. Customers will save more money if they purchase toilet paper B rather than toilet paper A because the price per mega roll is lower. (option b)
Unit pricing is a great way to compare prices, and consumers should always use it to determine the better deal between two products, as this will help them save money and stick to their budget.

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The pulley ratio is approximately 0.6667, calculated by dividing the Diameter of pulley A (5.74 cm) by the diameter of pulley B (8.61 cm).

The pulley ratio, we need to compare the diameters of the two pulleys. The pulley ratio is the ratio of the diameters of pulley A to pulley B.

Given that the diameter of pulley A is 5.74 cm and the diameter of pulley B is 8.61 cm, we can calculate the pulley ratio using the following steps:

Step 1: Write down the diameters of pulley A and pulley B.

  Diameter of pulley A = 5.74 cm

  Diameter of pulley B = 8.61 cm

Step 2: Calculate the pulley ratio.

  Pulley ratio = Diameter of pulley A / Diameter of pulley B

Substituting the given values, we have:

  Pulley ratio = 5.74 cm / 8.61 cm

Step 3: Simplify the ratio if possible.

  In this case, the ratio cannot be simplified further since the diameters do not have any common factors other than 1.

Step 4: Calculate the final result.

  Pulley ratio = 5.74 cm / 8.61 cm ≈ 0.6667 (rounded to four decimal places)

Therefore, the pulley ratio is approximately 0.6667.

When discussing technical concepts and calculations, it is important to maintain academic integrity and avoid plagiarism. Plagiarism involves using someone else's work or ideas without proper attribution. To ensure originality, it is essential to express the information in your own words and provide accurate calculations based on the given data.

In conclusion, the pulley ratio is approximately 0.6667, calculated by dividing the diameter of pulley A (5.74 cm) by the diameter of pulley B (8.61 cm).

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Answer:

centre = (- 5, - 2 ) , radius r = 18

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r the radius

(x + 5)² + (y + 2)² = 324 ← is in standard form , that is

(x - (- 5))² + (y - (- 2))² = 18²

with centre = (- 5, - 2 ) and r = 18

Answer:

Center = (-5, -2)

Radius = 18

Step-by-step explanation:

The equation of a circle in standard form is:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h, k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

If we compare the given equation of (x + 5)² + (y + 2)² = 324 to the standard form, we get:

Therefore, the center of the circle is (-5, -2).

To find the radius, square root 324:

[tex]r^2=324 \implies r=\sqrt{324}=18[/tex]

Therefore, the radius of the circle is 18.

Answer:
The factors correlate with the x-intercepts. For example, with the factor (x - 3), there is an x-intercept at (3, 0). Likewise, with the factor (x + 2), there is an x-intercept at (-2, 0). This suggests that the opposite sign of the factors are the x-intercepts in the graph.

Given: AE is a tangent to circle OO, m/FAE = 85, m AB = 40, m BC = 16, m CD = 10, m 212 = 55, m ZGAK = 75.What is required to be found out?We need to find mEGAP. So, mEGAP = 230/2 = 115.

Solution:According to the Theorem, "If a line is drawn tangent to a circle at the endpoint of a diameter, then the angle formed by the line and the diameter is a right angle."Therefore, the diameter would be OO.Now, we need to find the value of m EGA.From the angle of the segment, we know that a circle is 360 degrees and that an arc is equal to the angle subtended by it.

If 212° = 55°, then arc AKB = 360° - 212° = 148°.

Similarly, we can calculate arc GAC = 360° - 75° = 285°.So, arc AKC = arc AKB + arc GAC = 148° + 285° = 433°.As arcs AKC and KGD are opposite, they are equal.

Therefore, arc KGD = 433°.It is given that the length of arc KGD is 40+16+10 = 66. Therefore, the length of the entire circle is 433/360 x 66 = 80.02.

Most importantly, the value of m EGA is 360° - 75° - 55° = 230°.Therefore, m EGAP = 230/2 = 115.Answer: m EGAP = 115.

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Step-by-step explanation:

First    2x * 2x =   4x^2

Outer   2x * -3 =  -6x

Inner     3 * 2x = 6x

Last    3 * - 3 = -9

4x^2 -6x + 6x - 9   =  4x^2 - 9

Answer

4x²-9

Step-by-step explanation:

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There is no whole number by which you can multiply or divide 16087 to make it a perfect square.

To determine by which number you should multiply or divide 16087 to make it a perfect square, we can analyze its prime factorization. The prime factorization of 16087 is 13 × 1237.

In order to make 16087 a perfect square, we need each prime factor to have an even exponent. However, when we examine the prime factors of 16087, we find that both 13 and 1237 have an exponent of 1.

To make the exponents even, we need to multiply or divide 16087 by additional prime factors and their respective exponents. However, since 16087 is a product of two prime numbers (13 and 1237), we cannot introduce any additional prime factors to make the exponents even.

A perfect square is a number that can be expressed as the product of two equal factors. In the case of 16087, it cannot be transformed into a perfect square by multiplying or dividing by any whole number. The prime factors 13 and 1237 remain with an exponent of 1 each, indicating that there is no integer that can be applied to make them equal and convert 16087 into a perfect square.

Therefore, there is no whole number by which you can multiply or divide 16087 to make it a perfect square.

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The general rule for the given Sequence is a_n = 1 – 2n, where n = 1, 2, 3, ... This equation allows us to calculate any term in the sequence by substituting the corresponding value of n.

The given sequence –1, –3, –5, –7, –9,... follows a specific pattern or rule. To determine the general rule for n = 1, 2, 3,..., we can observe the sequence and identify the relationship between the terms.

Looking at the sequence, we notice that each term is decreasing by 2. Starting with –1, we subtract 2 to get the next term –3. Then, we subtract 2 again to get –5, and so on. Therefore, the rule for generating the terms in this sequence is to start with –1 and subtract 2 from each subsequent term.

We can express this rule algebraically as follows:

a_n = a_1 + (n – 1) * d

Where:

a_n represents the nth term of the sequence,

a_1 represents the first term of the sequence,

n represents the position of the term in the sequence,

d represents the common difference between the terms.

In this case, a_1 = –1 and d = –2 (since each term is decreasing by 2). Plugging these values into the equation, we get:

a_n = –1 + (n – 1) * (–2)

Simplifying further, we have:

a_n = –1 – 2n + 2

a_n = 1 – 2n

Therefore, the general rule for the given sequence is a_n = 1 – 2n, where n = 1, 2, 3, ... This equation allows us to calculate any term in the sequence by substituting the corresponding value of n.

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Note the full question may be :

From the following sequence: – 1, – 3, – 5, – 7, – 9,…, What is the general rule for n=1, 2, 3,…?

The point in the solution set from the graph is (0, 0)

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

y < -5/2x - 2

y ≥ -1/2x + 2

Next, we plot the graph of the system of the inequalities

The graph is given

From the graph, we have solution to the system to be the shaded region

The point in the solution set from the graph is (0, 0)

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