4x. (2x^3 — x^2–18x+15) Standard Form

The length in feet of the metal frame that surrounds the trampoline is 44 ft.

The circumference of a circle is the distance round the circle.

The circumference of a circle = πD

3.14 x 14 = 44 ft

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The coordinates of point Q are (-10, 10, 4).

To find the coordinates of point Q, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points P(x1, y1, z1) and Q(x2, y2, z2) are given by the average of the coordinates:

R = ((x1 + x2) / 2, (y1 + y2) / 2, (z1 + z2) / 2)

In this case, we are given that the midpoint R has coordinates (-3, 2, -1) and one of the points P has coordinates (4, -6, -6). Plugging in these values into the midpoint formula, we can solve for the coordinates of point Q:

Q = (2 * R - P)

Q = (2 * (-3, 2, -1) - (4, -6, -6))

Q = (-6, 4, -2) - (4, -6, -6)

Q = (-10, 10, 4)

Final answer:

The surface area of a right rectangular prism with dimensions of 6cm by 14cm by 5cm is calculated by summing up the areas of all faces, resulting in a total surface area of 368cm².

Explanation:

To calculate the surface area of a right rectangular prism, we need to find the area of all the faces and add them together. For a prism with dimensions of 6cm by 14cm by 5cm, it has three pairs of identical faces: two faces that are 6cm by 14cm, two faces that are 6cm by 5cm, and two faces that are 14cm by 5cm.

Using the area formula for rectangles (Area = length × width), we find the areas of these faces:

For the 6cm by 14cm faces: Area = 6cm × 14cm = 84cm². Since there are two such faces, their combined area is 2 × 84cm² = 168cm².

For the 6cm by 5cm faces: Area = 6cm × 5cm = 30cm². Since there are two such faces, their combined area is 2 × 30cm² = 60cm².

For the 14cm by 5cm faces: Area = 14cm × 5cm = 70cm². Since there are two such faces, their combined area is 2 × 70cm² = 140cm².

Adding up all these areas gives us the total surface area of the prism:

Total Surface Area = 168cm² + 60cm² + 140cm² = 368cm²

Therefore, the surface area of the right rectangular prism is 368cm².

Answer:

Step-by-step explanation:

B on edge

Final answer:

The equation of the plane parallel to the given plane 9x - y - z = 7 and passing through the point (3, -8, -2) is 9x - y - z = 37.

Explanation:

The question involves finding an equation for a plane that is parallel to a given plane and passes through a specific point. Since the planes are parallel, they will have the same normal vector, and thus the same coefficients for x, y, and z. The given plane's equation is 9x - y - z = 7, so the normal vector is (9, -1, -1). Our plane must also have this normal vector, meaning our plane's equation will have the form 9x - y - z = D, where D is a constant we need to find such that the plane passes through the point (3, -8, -2).

Substituting this point into the equation gives us 9(3) - (-8) - (-2) = D, which simplifies to 27 + 8 + 2 = D. Therefore, D = 37 and the equation of our plane is 9x - y - z = 37.

Final answer:

The value of x for which the square of the binomial 3x+1 is 9 times greater than the square of the binomial x−2 is obtained by equating (3x + 1)² to 9(x − 2)², which simplifies and solves to x = 5/6.

Explanation:

To find the value of x for which the square of the binomial 3x+1 is 9 times greater than the square of the binomial x−2, we need to formulate and solve an equation based on the given conditions:

(3x + 1)² = 9(x − 2)²

Expanding both sides gives us:

9x² + 6x + 1 = 9x² − 36x + 36

Now, by simplifying and solving for x, we find:

42x = 35

x = 35 / 42

x = 5 / 6

Therefore, the value of x is 5/6.

Answer:

62.50

Step-by-step explanation: im smart

The statement "If [tex]\( A \subset B \)[/tex], then [tex]\( A \cap B = A \cup B \)[/tex]" is not always true; it holds only if A = B.

The statement "If [tex]\( A \subset B \)[/tex], then [tex]\( A \cap B = A \cup B \)[/tex]" is not always true.

If [tex]\( A \subset B \)[/tex], it means that every element in set A is also in set B.

Now, consider the intersection of A and B [tex](\( A \cap B \))[/tex]. This intersection contains all elements that are common to both sets A and B.

On the other hand, the union of A and B [tex](\( A \cup B \))[/tex] contains all elements that are in either set A or set B, or both.

Since A is a subset of B, all elements in A are already in B, which means [tex]\( A \cap B = A \)[/tex]. However, [tex]\( A \cup B \)[/tex] would just be B, because all elements in A are also in B, so [tex]\( A \cup B \)[/tex] is simply B.

Therefore, the statement "If [tex]\( A \subset B \)[/tex], then [tex]\( A \cap B = A \cup B \)[/tex]" is not true in general; it is true only if A = B .

Answer:

The Edg answer is as follows -

The statement is not true for all real numbers. It is only true for decimal or fractional values of x .

If x is an integer, then the ceiling function returns x when the input is x . But, the flooring function returns x + 1 when the input is x + 1.

Since x does not equal x + 1 when x is an integer, the expressions are not equal when x is an integer.

Step-by-step explanation:

Real numbers are set of numbers that include rational and irrational numbers.

[x]=[x+1] is not true for all real numbers

Assume that: x is an integer

And x = 5

So, the equation becomes

[tex]5 = 5 + 1[/tex]

[tex]5 = 6[/tex]

The above equation is not true, because:

[tex]5 \ne 6[/tex]

Hence, [x]=[x+1] is not true for all real numbers

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The surface area of the cube is 2,400 square feet.

To find the surface area of a cube, one must use the formula:

[tex]\[ \text{Surface Area} = 6 \times (\text{side length})^2 \][/tex]

Given that the width of the cube is 20 feet, we can assume that all sides of the cube are equal, since a cube has all sides of equal length. Therefore, the side length of the cube is 20 feet.

Now, we can substitute the side length into the formula:

[tex]\[ \text{Surface Area} = 6 \times (20 \text{ ft})^2 \] \[ \text{Surface Area} = 6 \times 400 \text{ ft}^2 \] \[ \text{Surface Area} = 2,400 \text{ ft}^2 \][/tex]

Thus, the surface area of the cube is 2,400 square feet.

It says to check if [tex] \frac{3}{8} [/tex] satisfy each equation or not.

Checking first equation :-

96 x [tex] \frac{3}{8} [/tex]

⇒ [tex] \frac{96 * 3}{8} [/tex]

⇒ [tex] \frac{288}{8} [/tex] = 36

⇒ 36 = 36. First equation is "YES".

Checking second equation :-

38 x [tex] \frac{3}{8} [/tex]

⇒ [tex] \frac{38 * 3}{8} [/tex]

⇒ [tex] \frac{114}{8} [/tex] = [tex] \frac{57}{4} [/tex]

⇒ [tex] \frac{57}{4} [/tex] ≠ 14. Second equation is "NO".

Checking third equation :-

16 x [tex] \frac{3}{8} [/tex]

⇒ [tex] \frac{16 * 3}{8} [/tex]

⇒ [tex] \frac{48}{8} [/tex] = 6

⇒ 6 = 6. Third equation is "YES".

Checking fourth equation :-

56 x [tex] \frac{3}{8} [/tex]

⇒ [tex] \frac{56 * 3}{8} [/tex]

⇒ [tex] \frac{168}{8} [/tex] = 21

⇒ 21 = 21. Fourth equation is "YES".

The probability that none of the 7 calls reaches a person is approximately 0.1967.

To find the probability that none of the 7 calls reaches a person, we need to calculate the probability that each individual call does not reach a person and then multiply those probabilities together.

The probability that a call reaches a live person is 0.15, so the probability that a call does not reach a live person is 1 - 0.15 = 0.85.

Therefore, the probability that none of the 7 calls reaches a person is 0.857 ≈ 0.1967.

Answer:

sample response:  None of the roots can have multiplicity because the polynomial is cubic and 3 roots are given. Write each root as a linear factor, then multiply the three factors to get the expression for the function.

Step-by-step explanation:

Answer:

Solution: {Heads, Tails}.

Step-by-step explanation:

Solution: {Heads, Tails}.

Sample space is a list of all the possible outcomes for the event. For flipping a coin the outcomes are {Heads, Tails}.

Answer:

163,380.48

Step-by-step explanation:

First find the average of the first 4 months' figures.

To do this, find the sum of the first 4 values and then divide by 4, the number of data points:

(14889.51+22936+9856.88+6777.77)/4 = 54460.16/4 = 13615.04

It costs on average £13615.04 per month to run the arena.

This means the estimated running costs for 12 months will be

13615.04(4) = £163,380.48

Answer:

12

Step-by-step explanation:

Jensen stopped at A and planned to stop at B next. He has a map with a scale of 1 inch to 35 miles.

It is clear that 1 inch on map corresponds to 35 miles in actual.

From the map he has, we can see that both places A and B are 2.5 inches apart on map.

Let's assume those are "X" miles away in actual. Then we can use proportions to solve this problem.

1 inch to 35 miles would be same as 2.5 inches to X miles. Mathematically, we can write it as follows :-

[tex] \frac{1 \;inch}{35 \;miles} =\frac{2.5 \;inches}{X \;miles} \\\\
\frac{X \;miles}{35 \;miles} =\frac{2.5 \;inches}{1 \; inch} \\\\
\frac{X}{35} =\frac{2.5}{1} \\\\
Cross \;\;multiplying \\\\
X = 35*2.5=87.5 \;miles [/tex]

Hence, actual distance between A and B is 87.5 miles.

The perimeter of the isosceles trapezoid is 36cm.

An isosceles trapezoid is a quadrilateral with two parallel sides of unequal length. To find the perimeter of an isosceles trapezoid, we need to add the lengths of all its sides. In this case, the two bases have lengths of 10cm and 16 cm, and one of the side lengths is 5cm. Since the two bases are parallel, the other side length is also 5cm.

The perimeter is calculated by adding the lengths of the bases and the two side lengths: 10cm + 16cm + 5cm + 5cm = 36cm.

The circumference and the area of the circular bed are 14π feet = 43.9823 feet and 49π feet² = 153.9380 feet² respectively.

The circumference is the total length covered by the boundary of an object.

To calculate the circumference of a circle with radius r units, we use the formula: Circumference = 2πr units.

The area of an object is the space its planar face or two-dimensional face covers.

To calculate the area of a circle of radius r units, we use the formula: Area = πr² sq. units.

In the question, we are asked to find the circumference and the area of the circular flower bed that a gardener makes, having a diameter of fourteen feet.

We know that radius = diameter/2 = 14/2 = 7 feet.

To calculate the circumference of the circular bed, we will use the formula 2πr, where r is the radius.

Substituting the radius, r = 7 feet in the above formula, we get:

Circumference = 2(π)(7) feet = 14π feet = 43.9823 feet.

To calculate the area of the circular bed, we will use the formula πr², where r is the radius.

Substituting the radius, r = 7 feet in the above formula, we get:

Area = (π)(7)² feet² = 49π feet² = 153.9380 feet².

Thus, the circumference and the area of the circular bed are 14π feet = 43.9823 feet and 49π feet² = 153.9380 feet² respectively.

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Let's find out the area of the two parts separately to see which part is smaller.

Area of rectangle is given by Length * Width

Area of Part 1

Width of Part 1 is 16'

Length of Part 1 is 16-12 = 4'

So area of Part 1 is 16*4 = 64' square

Area of Part 2

Width of Part 2 is 8'

Length of Part 2 is 8'

So area of Part 2 is 8*8 = 64' square

So area of both the parts is same . Hence Jeremy may choose any of the parts.

Hope it helps ..!!

The statements that can be inferred to be true regarding the regular dodecagon include:

A dodecagon simply means a twelve-sided star polygon that encloses space. It can be regular when all the interior angles and sides are equal.

It should be noted that the smallest angle of rotational symmetry for the dodecagon is 30° and it has a rotational symmetry of 180.

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The number of hours does Eric's father work each afternoon is 5 hours.

Given that,

Based on the above information, the calculation is as follows:

[tex]= (40 - (3\times 5)) / div 5\\\\= (40 - 15) \div 5\\\\= 25 \div 5[/tex]

= 5

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