f) Find the area of one small triangle

[tex](4x+1)(2x^2 -2) \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{llll} 2x^2-2\\ \times ~~ 4x\\\cline{1-1} 8x^3-8x \end{array}~~ + ~~ \begin{array}{llll} 2x^2-2\\ \times ~~ 1\\\cline{1-1} 2x^2-2 \end{array}\qquad \implies \boxed{8x^3+2x^2-8x-2}[/tex]

The polynomial function is obtained to be h(x) = -2 (x - 4)(x - 1)²(x + 2), with the values a = -2, b = -4, c = -1 and d = 2.

What is a polynomial?

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

The characteristics of the polynomial are -

The zeros are located at 4, 1 (multiplicity of 2) and-2

The end behavior is as follows -

As x reaches negative infinity, f(x) reaches negative infinity.

As x reaches infinity, f(x) reaches negative infinity.

The y-intercept of the function is (0, 16)

The equation of h(x) can be written as -

h(x) = a(x+b)(x+c)²(x+d)

The zeroes of the polynomial can be written as -

x = 4 ⇒ (x - 4)

x = 1 ⇒ (x - 1)

x = 1 ⇒ (x - 1)....Since the multiplicity is 2 so write it two times.

x = -2 ⇒ (x + 2)

So, the equation will be -

y = a (x - 4)(x - 1)(x - 1)(x + 2)

The y-intercept is given as (0,16).

So, substitute the values of x and y with 0 and 16 respectively.

y = a (x - 4)(x - 1)(x - 1)(x + 2)

16 = a (0 - 4)(0 - 1)(0 - 1)(0 + 2)

16 = 2a(-4)(-1)(-1)

16 = 2a × -4

16 = -8a

a = -2

Hence, the equation becomes y = -2 (x - 4)(x - 1)(x - 1)(x + 2).

On graphing the equation it can be seen that -

As x → -∞, f(x) x → -∞

As x x → ∞, f(x) x → -∞

Therefore, the polynomial equation is h(x) = -2 (x - 4)(x - 1)²(x + 2).

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Therefore , we can conclude from the answer to the above problem that the equation for a reflection from across y-axis is - (x,y) -> (x,y).

The x-axis and y-axis are the coordinate plane two crucial axes. In contrast to the x-axis, which is a horizontally number line, the y-axis is vertical. Its two orthogonal axes make up a coordinate plane. The ordinate refers to the y-axis, whereas the abscissa refers to the x-axis.

Here,

The Y-axis is the line that runs vertically along the graph from bottom to top. The measurement coordinates are parallel to the this axis.

The numbers on the y-axis are known as y-coordinates.

When expressing following result, the x-coordinate and y-coordinate go in parentheses in that order.

(x, y).

A' ( -1, 1 ) => A"(-1, -1) (-1, -1)

B' (-2, 2) => B"(-2, -2) (-2, -2)

C' (-2, 3) => C"(-2, -3) (-2, -3)

and D' (-1, 4) =>  D " (-1, -4)

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Answer:   [tex]11\text{x}^{3}\text{y}^{4}[/tex]

=====================================

Work Shown:

[tex]\left(121\text{x}^6\text{y}^8\right)^{1/2}\\\\\left(121\right)^{1/2}*\left(\text{x}^6\right)^{1/2}*\left(\text{y}^8\right)^{1/2}\\\\\sqrt{121}\text{x}^{6*(1/2)}\text{y}^{8*(1/2)}\\\\11\text{x}^{3}\text{y}^{4}\\\\[/tex]

Therefore,

[tex]\left(121\text{x}^6\text{y}^8\right)^{1/2}=11\text{x}^{3}\text{y}^{4}\\\\[/tex]

--------------

Explanation:

The exponent of 1/2 represents a square root. This is how [tex](121)^{1/2}[/tex] turned into [tex]\sqrt{121}[/tex] which then simplified to 11.

As for the variable terms, we multiply that outer exponent 1/2 with each exponent inside the parenthesis. Think of it like the distribution rule. It's not really distribution, but similar.

Recall that [tex](a^b)^c = a^{bc}[/tex]

The product of 4 x 5 is 20.

The term product in math is defined as product of two numbers is the result you get when you multiply them together.

Here we need to identify the product of 4 x 5.

As per the definition we all know that the product also known as multiplication is the process of multiplying it by another number.

Here we all know that the multiplication table is used for this onw,

So, here we have to write the multiplication table, that is

=> 4 x 1 = 4

=> 4 x 2 = 8

=> 4 x 3 = 12

=> 4 x 4 = 16

And then the value of

=> 4 x 5 = 20.

Complete Question:

What is the product of 4 x 5?

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The width that is left on each side of the mirror is 13 1/4 inches.

Mirrors, due to their size, weight, and combination of robustness and fragility present a challenge for drywall and plaster walls.

The mounting gear for most new mirrors is already included, but it is important to take great consideration when choosing the anchors, screws, and bolts that will connect the mirror to the wall.

Use the following guidance on how to hang a heavy mirror safely so you may update your space while safeguarding your walls and decor after deciding what kind of wall you have and selecting the appropriate materials.

25 - 12 3/4 = 13 1/4

5 1/8 inches broad on each side of the mirror when 13 1/4 are split by two.

5 1/8 + 5 1/8 + 14 3/4 = 25.

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Factor the radicand: If the radicand is not already in the form of a perfect square, you can factor it into its prime factors and pull out any perfect squares from the radicand.

For example, √(36) can be simplified to √(49) = √4 * √9 = 23.

Simplify the exponent: If the radical has an exponent (such as cube root), divide the exponent by the index of the radical. Example ∛64 = ∛(4^3) = ∛4 * ∛4 * ∛4 = 4 *4 *4 =4

Combine like factors: If there are any factors in the radicand that match the exponent, you can combine them and simplify the radical further. For example, √(2235) = √(2^235) = 2√(35) = 2√15 = 2*3 = 6.

It is important to note that not all radicals can be simplified to a whole number or a fraction. In some cases, the radical will be in its simplest form when it is left as an irrational number.

For Example, √2 cannot be simplified further.

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The nature of the roots of the quadratic equation 9x2 12x + 4 is that it has one root, which is equal to -4.

The nature of the roots of a quadratic equation is determined by its discriminant (b2 – 4ac). The discriminant of the given equation 9x2 12x + 4 is (12)2 – 4(9)(4) = 144 – 144 = 0.

Since the discriminant is equal to zero, the equation has two equal (or identical) roots. This indicates that the equation has one root since its roots are equal. We may apply the quadratic formula to get the equation's root.

The quadratic formula states that the roots of a quadratic equation can be found by solving the equation:

x = (-b ± √(b2 – 4ac))/2a

When we apply the formula to the given equation, we get:

x= (-12 ± √(0))/2(9)

Since the discriminant is equal to zero, the equation has one root. The root of the equation is x = -4.

Therefore, the nature of the roots of the quadratic equation 9x2 12x + 4 is that it has one root, which is equal to -4.

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The distance between the building and the base of the ladder is 4 feet.

The trigonometric functions are functions that can be applied to determined the side or measure of internal angle of a given triangle. Given that some required properties are given.

Given that the ladder is 8 feet long, let the distance between the building and the base of ladder be represented by t.

So that;

Cos θ = adjacent/ hypotenuse

Cos 60 = x/ 8

x = 8*Cos 60

  = 8*0.5

x = 4

Thus, the building is 4 feet far to the base of the ladder.

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(5a - 6)(5a + 6)

The correct answer is D

The types of solutions for an equation depend on the type of equation, but in general, the most common types of solutions are: single solution, no solution and infinite solutions.

In mathematics, particularly in algebra, a solution of an equation is a value or a set of values that, when substituted into the equation, makes it a true statement.

Single solution: An equation has a single solution when it has exactly one value that satisfies the equation. This solution is unique and it can be found by solving the equation for the variable.

No solution: An equation has no solution when it is impossible to find a value that satisfies the equation. This happens when the equation is contradictory or inconsistent. For example, the equation "2x = 5x + 1" has no solution because no value of x can make the equation true.

Infinite solutions: An equation has infinite solutions when any value of the variable satisfies the equation. This happens when the equation is an identity, meaning it is true for all values of the variable. For example, the equation "2x + 0 = 2x" has infinite solutions because any value of x will make the equation true.

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Answer: 3x^4*sqrt(3x) is the answer

Step-by-step explanation:

Factor 27 into its prime factors

          27 = 33

To simplify a square root, You take the square factors, or factors that are raised to an even exponent.

Factors which will be taken are:

          9 = 32

Factors which will remain inside the root are:

          3 = 3

To finish this we take the square root of the factors that were taken out. This can be done by dividing their exponents by 2 :

          3 = 3

I hope this helps!

Therefore, the real and unequal roots of the quadratic equation. The roots are uneven and real when the discriminant is bigger than zero. The roots are equal and real when discriminant is equal to zero.

When a, b, and c are real integers and the discriminant is bigger than zero (b2 - 4ac > 0), the roots of the quadratic equation ax2 + bx + c = 0 are real and unequal.

In this situation, we say that the roots are hypothetical. Ax2 + bx + c = 0 has real, rational, and unequal roots when a, b, and c are real numbers, a 0, and the discriminant is positive and perfect square.

D=b \s2 \s −4ac=42 \s −4×2×(−7)=16+56=72>0.

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Full Question = What will be the nature of roots of quadratic equation 2x 2 +4x−7=0?

One must first divide a compound inequality into two other inequalities before solving it.

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Yes, it is possible to draw a triangle.

This will be done by the property: the sum of two sides of a triangle should be more than the third side.

(4.6cm + 6.8cm) =10.2cm

11.4cm = 10.2cm

LHS>RHS

A triangle is possible.

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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Three points can define the two distinct vectors AB and AC (A, B, and C). The two vectors' cross product, which they both lie on, may be utilized as the plane's normal.

It is logical to assume that this is the case since a plane contains precisely two linearly independent vectors since it has a dimension of two. If the three points were collinear, there wouldn't be two linearly independent vectors; instead, the origin and tips of the two vectors are the three points.

The three points that make up a plane in a three-dimensional space can be used to define it as long as they are not on the same line. On a plane, there exist at least three non-collinear points. A line that connects any two locations in a plane is also considered to be a part of the plane. A line is created at the place of intersection when two planes clash.

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The odd one out is the furthest to the right. the Nickels.

The first square is 25 cents. The second square is 25 cents. The third square is 15 cents.

I hope this helps you :D

Answer:

the domain is x ≥ -4

Step-by-step explanation:

on the x-axis, the graph does not extend below -4. the point on the graph is filled in, which makes the domain greater than or equal to -4.

hope this helped, good luck!

The cab ride will cost you $14.

Cost is the quantity of money spent by a business or work to produce or create goods or services. It excludes the profit margin markup. Cost is the sum of money spent on making a good or product, as seen from the seller's perspective.

as stated in the inquiry, Meena I'm using an online taxi service to order a taxi.

The cab bills $3.50 for the pickup alone, plus an extra $1.75 for each subsequent mile driven.

The original taxi fare plus the number of kilometres multiplied by the 1.75-cent-per-kilometer cost of the additional drive equals 3.50 + 6 (1.75), which equals $14.

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Step-by-step explanation:

(f○g)(x) = f(g(x))

it simply means that we put the expression of g(x) into ask places of x in f(x).

(f○g)(x) = g(x)² + 3

therefore,

g(x)² + 3 = 9x² - 12x + 7

g(x)² = 9x² - 12x + 4 = (a + b)² = a² + 2ab + b²

9x² = a² tells us that a = ±3x

4 = b² tells us that b = ±2

which signs of a and b do we need ?

-12x = 2ab gives us the answer

-6x = ab

that means the signs need to be opposite and we have 2 possible solutions

g(x) = 3x - 2

or

g(x) = -3x + 2

First, solve the equation for one of the variables in the pair of equations to be solved using substitution method x = 2/13, y = 52

The substitution method is one algebraic approach to solving a linear system. By substituting one y-value for another, the substitution method works. We will illustrate this with an example. Since y = y, we can use y in the first equation instead of the second one.

                                      4x+2y=10⋅2x=26+2y

Take the first equation, for example. For a result of 20, multiply 10 by 2.

                                     4x+2y=20x

20 x both sides should be subtracted.

                                    4x+2y−20x=0

Get 16x by combining 4x and 20x.

                                  −16x+2y=0

The second equation is an example. For a result of 20, multiply 10 by 2.

                                      20x=26+2y

From both sides, subtract 2y.

                                          20x−2y=26

First, solve the equation for one of the variables in the pair of equations to be solved using substitution. Replacing that variable in the other equation with the result follows.

                                       −16x+2y=0,   20x−2y=26

By placing x on the left side of the equal sign, isolate x from one of the equations and solve it for x.

                                                −16x+2y=0

In the equation, deduct 2y from both sides.

                                     −16x=−2y

Subtract 16 from both sides.

                                          x= − 16/ 1(−2)y

16 divided by 2y is the answer.

                                         x= 8  / 1 y

The second equation, 20x2y=26, should now read 8 y instead of x.

                                  20×( 8 /1  )y−2y=26

multiply 20 times 8 y.

                          2  / 5 ​ y−2y=26

Boost 2y by 2.5 years.

                                 2 /1  y=26

2 times both sides will give you y=52.

In the formula x = 81y, change y to 52. You can solve for x directly because the resulting equation only has one variable.

                                        x= 8 /1  ×52

52 x 8 /1 is the multiplication.

                                   x= 2 /13

The system has now been resolved substitution equation are

x = 2/13, y=52

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The letter on the number line that represents the given number is B.

A number line is a straight line which extends from -∞ to -∞, on which the position or location of all directed numbers can be identified.

Directed numbers are numbers which have either a negative or positive sign. Examples include; -4, -1 2/3. 9 etc. Therefore all numbers can be located on a number line.

Considering the given question, to locate the position of 1 85/100. The whole number make us to understand that its position falls between 1 and 2. And the fraction part shows that the number is closer to 2 more than 1.

Therefore, the letter on the number line that represents 1 85/100 is B.

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To determine the amount of work done by the person in the wheelchair going up the ramp, you can use the formula for work:

work = force x distance x cos(theta)

where force is the force exerted by the person (25 N), distance is the distance traveled (10 m), and theta is the angle between the force and the displacement.

The angle between the force and the displacement is 90 degrees because the force is perpendicular to the displacement.

The force exerted by the person is to overcome the force of gravity on the person and wheelchair weight (60 N).

work = force x distance x cos(90)

work = (25 N + 60 N) x 10 m x cos(90)

work = 85 N x 10 m x 0

work = 0 J

It's impossible to do work when the angle between the force and the displacement is 90 degrees because the force and the displacement are perpendicular to each other.

The height of the ramp (3 m) is not used in this calculation, as it is not related to the force or distance.

The work done by the person in the wheelchair is 0 J because the force exerted by the person is perpendicular to the displacement. However, the person will be expending energy to overcome the force of gravity and move the wheelchair up the ramp.

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4 less than the product of 1 and x is x - 4.

An algebraic expression is a variable expression described using its terms, and operations on the terms.

In other words, algebraic expression are mathematical expressions where variables and constant are combined using operations such as subtraction, addition, multiplication etc.

Therefore, let's express the word expression in algebraic expression,

Hence, 4 less than the product of 1 and x is represented as follows:

(1 × x) - 4

x - 4

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Yes, thirty-six is a rational number. It is represented as a fraction of integers, so it is called an integer and a whole number.

A rational number is defined as the number that can be expressed as a fraction, P/Q and assuming that the denominator of the fraction is not zero, i.e., Q ≠0, and that both the numerator and denominator are integers. In case of an irrational numbers, they cannot be expressed as a fraction. We can identify a number is rational or irrational :

Now, we have a number say, x = 36 and we have to check it is rational or irrational number. Number 36 can be written as 36/1 = P/Q and 1 ≠0 like Q ≠ 0. So, x is a rational number because it can be expressed as the quotient of two integers.

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Complete question:

Is 36 is a rational or irrational?

Answer:

The value of the expression when x=3 is:

7^(3/2) + 9x - 3

We can simplify it as:

49 + 9*3 - 3

= 49 + 27 -3

= 73

So the final value of the expression is 73.

Given expression y=7x²+9x-3

Given value of x=3

We want to find the value of y.

Substitute the value of x=3 in y expression

y=7(3²)+9(3)-3

y=7*9+9*3-3

y=63+27-3

y=87

Therefore, the value of given expression is 87

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Complete question

What is the value of the expression below when x=3,

y=7x²+9x-3

The construction site area is 2025 square meters, calculated by finding the area of a square with side length 45m.

What is square ?

A square is a two-dimensional geometric shape that has four equal sides and four right angles. It is a type of rectangle where all sides are equal in length and opposite sides are parallel. It can also be defined as a polygon with four sides and four angles, all of which are right angles.

The construction site is in the shape of a square and the wooden wall surrounding it is 2m high and has a length of 45m.

Since the wall encloses a square, the length of one side of the square is equal to the length of the wall (45m).

Therefore, the area of the construction site can be calculated by finding the area of a square with side length 45m.

The formula for the area of a square is side length squared (s^2).

area = 45m x 45m = 2025 square meters.

So , The construction site area is 2025 square meters, calculated by finding the area of a square with side length 45m.

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Answer:

37.5%

Step-by-step explanation:

We take

12 divided by 32, then times 100% = 37.5%

So, 37.5% of Jayden's rabbits are male

Grams per cubic centimeter to kilograms per cubic meter is 1000.

1 g/cm³ = 1000 1 kg/m³

The conversion value:

Find the conversion from grams per cubic centimeter to kilograms per cubic meter!

Multiply the number with the each conversion value!

See that the cubic centimeter is as a denominator. So, we reverse the fractional value.

1 g/cm³

= 1 × 1/1000 × 1000000/1 kg/m³

= 1000 kg/m³

Hence, the conversion value from grams per cubic centimeter to kilograms per cubic meter is 1000.

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No, All 30-60-90 triangles are right triangles, but not all right triangles are 30-60-90 triangles.

No, not all right triangles are 30-60-90 triangles. A right triangle is a type of triangle that has one right angle (90 degrees) and two acute angles. The other two angles in a right triangle can have any measurement, they don't have to be 30-60-90 degrees.

A 30-60-90 triangle is a special type of right triangle that has specific angle measurements: one angle is 90 degrees (the right angle), one angle is 30 degrees, and one angle is 60 degrees. The ratio of the sides in a 30-60-90 triangle is also fixed, the longest side is opposite the 90-degree angle and it is always twice the length of the shortest side and the medium side is opposite the angle of 60 degrees and it's always the square root of 3 times the length of the shortest side.

For example, if a right triangle has angles of 45 degrees, 45 degrees, and 90 degrees, it is not a 30-60-90 triangle. The angles do not fit the pattern of 30-60-90 degrees.

Therefore, In short, all 30-60-90 triangles are right triangles, but not all right triangles are 30-60-90 triangles. A 30-60-90 triangle is a special type of right triangle with specific angle measurements and side ratios.

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