A cubic polynomial function f has a leading coefficient of 2 and a constant term of 5. When f(-1) = 2 and F(1) = 14, what is f(0.5)?
f(0.5) = ?
Explain your reasoning.

A regular solid shape is defined as a three-dimensional object that has all its faces congruent and all its vertices congruent. In other words, all faces have the same shape and size and all vertices have the same angle measures.

Among the options provided, only the cube is a regular solid shape. A cube is a three-dimensional object that has six equal square faces. Each face is a square and each vertex has the same angle measure. The edges of a cube are congruent and the shape is highly symmetrical.

The cylinder is not a regular solid shape because it has two congruent circular faces and one curved surface, which is not congruent to the other two faces. The vertices of a cylinder also have different angle measures.

The cuboid is not a regular solid shape because it has six rectangular faces, and the shape is not highly symmetrical. The vertices of a cuboid also have different angle measures.

In conclusion, a regular solid shape must have congruent faces and congruent vertices, and only a cube satisfies these conditions. It is important to note that not all regular shapes are regular solid shapes, for example, a sphere is a regular shape, but it is not a regular solid shape because it has no faces, vertices or edges.

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The ordered pair that lies on the inverse of the function is (25, 0)

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

g(x)=−(x−3)^3−2.

Set x = 0

So, we have the following representation

g(0) =−(0−3)^3−2.

Evaluate the expression

This gives

g(0) = 25.

So, the ordered pair of teh inverse is (25, 0)

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Answer: -3,4

Step-by-step explanation:

Answer:

x= 19

Step-by-step explanation:

6x+4+4x-14= 180

10x-10= 180

10x= 190

x= 19

Answer: 60

Step-by-step explanation:

(42/70) * 100

42/70 = 0.6

0.6 * 100 = 60

Answer :  70 - 42 = 28

then find out using percentage formula then will get answer  =

60%

The monthly payment is  $86.55. The result is obtained by using the formula for simple interest.

The simple interest of an amount of money can be counted by the following formula.

I = P × r × t

Where

A motocross company offers a loan to buy an ATV for $4,000. Loan Offer 9.3% Simple Interest.

If it is for 6 years, find the monthly payment!

We have

It is not mentioned that the simple interest apply per year or per month. We assume the simple interest is per year. It will be

I = P × r × t

I = $4,000 × 9.3% × 6

I = $2,232

The total money to be paid will be

A = P + I

A = $4,000 + $2,232

A = $6,232

The monthly payment is

MP = A/t

MP = $6,232/(6 × 12)

MP = $6,232/72

MP = $86.55

Hence, the person who borrows for $4,000 to buy an ATV should pay $86.55 each month for 6 years.

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1601000 students were awarded a bachelor’s degree in 2009.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

First, notice that the table is in thousands, remember that.

Now, we need to go to the part of the row of the table where we have "Bachelor".

There we can see that in 2009, a marginal total of 1,601 thousands got that degree.

Then we can conclude that in 2009, a total of:

1,601×100 = 1,601,000 students got a bachelor's degree.

Hence, 1601000 students were awarded a bachelor’s degree in 2009.

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Answer:

C. 1,601,000

Step-by-step explanation:

This is the correct answer.

Answer:

Step-by-step explanation:

In a triangle, the sides have a ratio of 3:7:10. If the perimeter is 210 feet, what is the length of the longest side in feet? (A) * 10.5 (B) 31.5 (C) (D) 105​

[210 : (3 + 7 + 10)] x 10 = 105 ft (your answer)

Step-by-step explanation:

the ratio tells us into how many units the total amount is split and then distributed among the different parts or members of the ratio.

3:7:10 means there are 3+7+10 = 20 units of length.

210 ft is the total of all lengths.

this is now split into these 20 units.

that means one unit of length for the ratio is

210/20 = 10.5 ft

the longest side is clearly the one with 10 units in the ratio.

so, it has

10×10.5 = 105 ft

Lines are not perpendicular .

What makes a line parallel?

Perpendicular lines are those that cross at a right angle when two non-vertical lines in the same plane.

                               Vertical and horizontal lines, or the axes of the coordinate plane, are perpendicular to one another. Two parallel lines' slopes are reciprocals with a negative sign.

  2x - 5y = -20

       5y = 2x + 20

      y = 2/5x + 20/5

      y = 2/5x + 4

    m₁ = 2/5

y = 2/5x - 1

 m₂ = 2/5

The product of the slopes of the two lines is

             2/5 * 2/5 = -1

                   4/25  =  -1

   the lines are not perpendicular .

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Answer:

I belive the answer is "5x+35"?

Answer:

x=29

Step-by-step explanation:

3x+15+2x+20=180; 3x+2x=145; 5x=145; x=29

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Answer:

0.43

Step-by-step explanation:

Rounding to 2 decimal places means keeping only 2 digits after the decimal point and adjusting the third digit, based on the rules of rounding. In this case, the number 0.4277 would be rounded to 0.43. This is because the third digit after the decimal point (7) is 5 or greater, so we round up the second digit (2) to 3. This gives us the rounded number 0.43, which has only 2 decimal places.

Answer:18

Step-by-step explanation:

Answer:18

Step-by-step explanation:

Answer: B,C,D

Step-by-step explanation:

Since the only requirement is that the width needs to be at least 50 yds. B, C,D all work.

The area of the shaded region is 84.82 cm².

The area of the shaded region is calculated by subtracting the area of the sector from the area of the entire circle.

Since the angle of the sector is 90 degrees, we can conclude that the entire circle is divided into four.

Area of the shaded region = πr² - 1/4(πr²) = 3/4πr²

where;

The area of the shaded region is calculated as;

A = 3/4πr²

A = 3/4 x π ( 6 cm )²

A = 84.82 cm²

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Los dos números dados en el conjunto de preguntas anterior son 32 y 160. Para resolver este problema, se puede establecer una ecuación con variables.

Sea x el número más pequeño, entonces el número más grande sería 5x. La suma de ambos es 192, por lo que

Al resolver esta ecuación simple, se obtiene que x = 32, y por lo tanto, 5x = 160. Estos son los dos números que cumplen con los requisitos dados en la pregunta.

En matemáticas, la sumatoria es la suma de una secuencia de cualquier tipo de números, llamados sumandos o sumandos; el resultado es su suma o total.

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A rocket is launched with height function h(t)= -16t²+88t for time 't' in seconds the rocket is in the air for the time t = 5.5 seconds.

A rocket launched with height function :

h(t)= -16t²+88t

't' represents the time in seconds

'h' is the height of rocket.

Time for which rocket is in the air given by :

When h(t) = 0

Substitute the value we get,

⇒  -16t²+88t = 0

⇒ -16t ( t - 5.5 ) = 0

⇒ -16 ≠ 0 or t ≠ 0 or ( t - 5.5 ) = 0

Time can never be zero.

hence,

( t - 5.5 ) = 0

⇒ t = 5.5 seconds

Therefore, the time of the rocket when it is in the air  is equal to 5.5 seconds.

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Answer:

Step-by-step explanation:

You want to know which functions have 5 in their domain, and what the function value is at x=5.

It is more convenient to do the second part first, as that tells you the answer to the first part:

f(5) = 5² -3·5 = 25 -15 = 10 . . . . 5 is in the domain

g(5) = (5 -5)/5 = 0/5 = 0 . . . . 5 is in the domain

h(5) = √(5 -10) = √(-5) . . . . UNDEFINED; 5 is not in the domain

Answer:

20 liters of white paint, 12 liters of red paint

Step-by-step explanation:

Let w = liters of red paint and r = liters of red paint

[tex] \frac{w}{r} = \frac{5}{3} [/tex]

[tex]w = \frac{5}{3} r[/tex]

[tex]w + r = 32[/tex]

[tex] \frac{5}{3} r + r = 32[/tex]

[tex] \frac{8}{3} r = 32[/tex]

[tex]r = 12[/tex]

[tex]w = 20[/tex]

The volume of the cedar canoe with a mass of 40 kilograms and a density of 400 kilograms per cubic meter is 0.1 cubic meters.

Density is expressed mathematically as;

p = m / v

Where m is mass and v is volume.

Given that;

To determine the volume, plug the given values into the above formula and solve for v.

p = m / v

v = m / p

v = 40kg / 400 kg/m³

v = 40kgm³ / 400 kg

v = 40m³ / 400

v = 0.1 m³

Therefore, the volume is 0.1 cubic meters.

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Answer:

a = 68°

Step-by-step explanation:

a and 112° are a linear pair and sum to 180° , that is

a + 112° = 180° ( subtract 112° from both sides )

a = 68°

Answer:2+n/7

Step-by-step explanation:

Simplify the expression

The equation representing the hanger is 3x - 2y = 0 and when x = 6, y = 9

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, the weight of the square is y

And, the weight of the triangle is x

Now, the equation according to the diagram is;

x + 3y = 4x + y

4x - x + 3y - y = 0

3x - 2y = 0

Now, when, x  = 6

So, y =

3x - 2y = 0

3x = 2y

3(6) = 2y

18 = 2y

y = 9

Hence, the equation representing the hanger is 3x - 2y = 0 and when x = 6, y = 9

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The length of one edge of the cube is 8 cm and the radius of the sphere is 9 cm.

What is the cube root?

The cube root of a number is a value that when multiplied by itself thrice or three times produces the original value. For example, the cube root of 27, denoted as 3√27, is 3, because when we multiply 3 by itself three times we get 3 x 3 x 3 = 27 = 33.

The surface area of a cube is given by the formula:

A = 6 * a^2

where A is the surface area and a is the length of one edge of the cube.

So, in this case:

384 = 6 * a²

Dividing both sides by 6:

64 = a²

Taking the square root of both sides:

a = 8 cm

So the length of one edge of the cube is 8 cm.

The formula for the volume of a sphere is:

V = (4/3) * π * r³

where V is the volume, π is Pi (approximately equal to 3.14), and r is the radius of the sphere.

So, in this case:

729 = (4/3) * π * r³

Dividing both sides by (4/3) * π:

729 / (4/3) * π = r³

Taking the cube root of both sides:

r = pow(729 / (4/3) * π, 1/3) = 9 cm

So the radius of the sphere is 9 cm.

The cube root of 729 is 9.

Hence, the length of one edge of the cube is 8 cm and the radius of the sphere is 9 cm.

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Answer:

90

Step-by-step explanation:

45+45=90

The standard form of the equation for the given p value and theta is equal to -x + y = 26√2.

Standard form of the equation is :

x cosθ + y sinθ = p

Here p = 26 and theta 'θ' = 3π /4

Substitute the value in the standard form we get,

x cos (3π/4 ) + y sin( 3π /4 ) = 26

⇒ x cos ( π - π/4 ) + y sin ( π - π/4 ) = 26

⇒ - x cosπ/4 + y sinπ/4 = 26

Substitute the value of cosπ/4 and sinπ/4 is equal to 1/√2 we get,

⇒ -x /√2 + y / √2 = 26

⇒ -x + y = 26√2

Therefore, the standard form of the equation is equal to -x + y = 26√2.

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Answer: Let's assume that there are "m" jokes written by male authors and "f" jokes written by female authors, such that m + f = total number of jokes in the magazine.

If a joke by a man is told first, there are (m - 1)! ways to arrange the remaining m - 1 jokes written by male authors and f! ways to arrange the jokes written by the female author. The total number of ways the jokes can be delivered is (m - 1)! * f!.

So, the answer is (m - 1)! * f! ways to deliver the jokes if a joke by a man is told first.

Step-by-step explanation:

A wheel of cheese has a radius of 7 inches and a height of 3 inches

The approximate surface area of this wheel of cheese is 458.4 square inches.

To get the surface area of a cylinder,  we have to calculate the area of the lateral surface and add the areas of the two circular end faces.

The lateral surface area of a cylinder is calculated as 2 * pi * r * h, where r is the radius and h is the height.

So the lateral surface area in this scenario would be: 2 * 3.14 * 7 * 3 = 150.52 square inches.

The area of the two end faces must then be calculated. we know, Pi * r^2, where r is the radius, gives the area of a circle.

So the area of each end face in this situation would be 3.14 * 7^2 = 153.94 square inches.

Total surface area= lateral surface area + end face area

=150.52 + 153.94 + 153.94 = 458.4 square inches (approximately)

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