13
Calculate a, b and m so that the
polynomials P and Q defined by :
P(x) = (m - 2)x2 + (2a + 3)x +b +6 and
Q(x) = 3x2 - (m - 2)x + 2a - 3 , are equal.​

Step-by-step explanation:

[tex]2\mathbf{u}=\langle 10,6 \rangle \\ \\ 3\mathbf{v}=\langle -12, 0 \rangle \\ \\ 2\mathbf{u}-3\mathbf{v}=\langle 10,6 \rangle -\langle -12,0 \rangle =\langle 22,6 \rangle[/tex]

The shorter side of the triangle will be opposite to 30° angle and larger side will be opposite to 90° angle .

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

The side opposite the smallest angle is the one that is the shortest. The shortest side is opposite the angle that you already know to be the shortest.

The side opposite the right angle is always the hypotenuse of a right triangle. In a right triangle, it is the longest side.

So the shorter side will be opposite to 30° angle and larger side will be opposite to 90° angle .

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The lens formula is used in optics to calculate the position and size of the image formed by a lens.

A lens is a piece of glass or other transparent material that bends light to form an image. The lens formula relates the distance of the object from the lens, the distance of the image from the lens, and the focal length of the lens.

The lens formula is used to determine the position and size of the image formed by a lens in order to design and analyze optical systems. It is used in the design of camera lenses, telescopes, microscopes, and other optical devices.

It also allows us to determine the size and position of the image formed by a lens in a given situation, which is essential for the analysis and correction of optical aberrations.

The lens formula also allows us to determine the type of image formed by a lens, whether it is real or virtual, inverted or erect, and the size of the image compared to the object.

In conclusion, the lens formula is used in optics to calculate the position and size of the image formed by a lens. It is used in the design and analysis of optical systems such as camera lenses, telescopes, microscopes and other optical devices. It also allows us to determine the type of image formed by a lens and the size of the image compared to the object.

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Answer:

$3,040.00

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]

Given:

Substitute the given values into the continuous compounding formula and solve for P:

[tex]\implies 8441.60=Pe^{0.06 \times 17}[/tex]

[tex]\implies 8441.60=Pe^{1.02}[/tex]

[tex]\implies P=\dfrac{8441.60}{e^{1.02}}[/tex]

[tex]\implies P=3043.99824...[/tex]

Therefore, the amount of the initial investment is $3,040.00 (rounded to the nearest tens place).

Answer:

2880

Step-by-step explanation:

Answer:

x = 0.25y + 7/12

Step-by-step explanation:

12x - 3y = 7

12x = 3y + 7

x = 0.25y + 7/12

A polynomial is factored when it is broken down into the sum of two or more other polynomials. For instance, f (x) = x 2 + 5 x + 6 can be broken down into f(x) = (x+3)(x+2) and f(x) = x2 + 5 x + 6.

A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.

A polynomial is factored when it is broken down into the sum of two or more other polynomials. For instance, f (x) = x 2 + 5 x + 6 can be broken down into f(x) = (x+3)(x+2) and f(x) = x2 + 5 x + 6.

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The additive inverse of the expression is 4x + 8

From the question, the expression is given as

negative 4X -8

Express properly

So, we have the following representation

-4x -8

For an expression y, the additive inverse is -y

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

Additive inverse of -4x -8 = -(-4x -8)

Open the bracket

Additive inverse of -4x -8 = 4x + 8

Hence, the additive inverse is 4x + 8

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Therefore , the solution of the given problem of factor comes out to be

Ax²+Bx+C= (x-a)(x-b) is the formula for factor form.

It appears that a factor is a parameter that is combined by another to achieve an outcome. A product is the solution to a multiplication puzzle. Think of mixing the factors in an arithmetic problem to get the product. 8 has the elements 2 and 4, for instance: There could be just two parts to a number or many more.

Here,

Take a look at the generic form:

=>Ax²+Bx+C= (x-a)(x-b),

where a & b are the polynomial's roots.

Here, b=2 and a=1

(x+1)(x2) (x + 1)(x 2) is the factored form.

Therefore , the solution of the given problem of factor comes out to be

Ax²+Bx+C= (x-a)(x-b) is the formula for factor form.

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Answer:

C(x) = 25 + 1.5x

Step-by-step explanation:

A function is a mathematical equation that describes how two variables are related. To write a function that models the cost of having a carpet installed, we can use the information provided in the problem.

The cost of having a carpet installed is:

C(x) = 25 + 1.5x

Where C(x) represents the total cost of the carpet installation and x represents the number of square yards of carpet.

25 is a fixed cost for delivery , and $1.5 is cost per sq yard.

So, C(x) = 25 + 1.5x this function is representing the cost of having a carpet installed in x sq yard.

The area of a triangle can be calculated using the formula A=1/2*b*h, where b is the base of the triangle and h is the height.

The area of a triangle can be found by using the formula A = 1/2bh, where b is the base of the triangle and h is the height of the triangle. To find the area of a triangle in square units, you would need to multiply the base and the height of the triangle and then divide the result by 2.Once you have these two measurements, simply plug them into the formula and calculate the area.

To calculate the area, we need to first measure the base and the height. Once we have the measurements, we can calculate the area by multiplying the base by the height and then dividing by two. For example, if the base is 8 units and the height is 6 units, the area of the triangle will be 24 square units (A = 1/2*8*6 = 24).

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The expression "value of 3 exponent of 1" is denoted as 3¹ ,and the value of this expression is 3 .

The Exponent is defined as how many times to use that number in a multiplication .

It is written as a small number to right above the base of the number.

we have to find the value of the exponent expression " value of 3 exponent of 1" ,

the given expression can be represented as ⇒ 3¹ ,

we know that the value of any number with an exponent of 1 is the number itself .

So , the value of 3¹ is ⇒ 3 .

Therefore , the value of 3 exponent of 1 is  3   .

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You can only add or subtract radicals together if they are like radicals.

√28

Factor 4 out of 28.

√4(7)

Rewrite 4 as 22.

2 2.7

Pull terms out from under the radical.

217

The result can be shown in multiple forms.

Exact Form:

2√7

Decimal form:

5.29150262…

√63

Factor 9 out of 63.

/9 (7)

Rewrite 9 as 32.

Pull terms out from under the radical.

3√7

The result can be shown in multiple forms.

Exact form: 3√7

Decimal Form: 7.93725393...

Sqrt(24)

2√6

Pull terms out from under the radical.

√2^2.6

The result can be shown in multiple forms.

Exact Form:

2√6

Decimal Form:

4.89897948....

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The complete question is: Solve the following radicals:

a) 5 ± [tex]\sqrt{28}[/tex]

b) 4 ± [tex]\sqrt{63}[/tex]

c) 6 ± [tex]\sqrt{24}[/tex]

A polyhedron with 3 rectangular faces and triangular shaped bases is called a triangular prism. It is a three-dimensional shape with three side faces, two base faces, and edges connecting them to one another.

Nine different nets make up the pentahedron known as Triangular Prism. The bases are connected at their vertices and edges by three rectangular sides. The triangular prism's rectangular-shaped sides are joined to one another side by side.

Triangles have all cross-sections that are perpendicular to their base faces. In contrast to a triangular prism, a triangular pyramid has four triangular bases that are all congruent with one another and connected together.

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Equivalent expressio

When two expressions can be reduced to a single third expression or when one of the expressions can be written in the same way as the other, they are said to be equivalent. When values are replaced for the variable and both expressions yield the same result, you may also tell if two expressions are equal.

Because both expressions have the same value for any value of x, 3(x + 2) and 3x + 6 are identical expressions. 3x + 6 = 3 × 4 + 6 = 18. Algebraic equations with equivalent solutions or roots are called equivalent equations.

An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation. Expressions that are equivalent do the same thing even when they have distinct appearances. In the event when two algebraic expressions.

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I got a similar one too. It was 6(4.5x+1.5) ..

Step-by-step explanation:

An ordered pair is a pair of numbers that are usually represented in the form of (x, y) and it is used to indicate the position of a point in a coordinate system or a Cartesian plane.

Another example is an ordered pair (-2, 1) representing a point in the coordinate system located 2 units to the left of the y-axis and 1 unit above the x-axis.

In this way, any point in a coordinate system can be represented by an ordered pair.

In summary, the ordered pair is a way to represent a point in a coordinate system and it is made up of two numbers (x, y), where x represents the horizontal position and y represents the vertical position of the point in the coordinate system.

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Answer:

It equals one

Step-by-step explanation: Anything that has the exponent of 0 will always equal one

If the rectangular area has maximum area, the dimension of the rectangular area is 62.5 m×62.5 m. The area is 3,906.25 square meters.

To enclose a rectangular area with one side bordered by a stream, Farmer Mei can use the remaining 250 meters of fence to form the other three sides of the rectangle. Since the rectangle has two sides of equal length (the width and the height), we can set up the equation:

2L + 2W = 250

where L represents the length of the rectangle and W represents the width.

Solving for one variable in terms of the other:

W = 250/2 - L

The area of the rectangle is given by the formula:

A = L×W

Now, we can substitute the value of W from the above equation into this one to get:

A = L × (250/2 - L)

A = 125L - L²

To find the maximum area, we need to take the derivative of A with respect to L and set it equal to 0.

dA/dL = 250/2 - 2L = 0

Which gives us the value of L = 125/2 = 62.5m

Now, we can substitute this value of L back into the equation for W to find the width of the rectangle:

W = 250/2 - 62.5 = 62.5m

Therefore the dimensions of the rectangle is 62.5m x 62.5m and the maximum area that can be enclosed is 62.5m x 62.5m = 3,906.25 sq m.

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Triangle MNO with sides m = 20, n = 14 and angle m ∠ M = 51° can have two possible configurations.

In this problem we have the knowledge of two sides and an angle of triangle MNO, where angle M is opposite to side m. First, determine the possible values for angle N by law of sine:

n / sin (m ∠ N) = m / sin (m ∠ M)

14 / sin (m ∠ N) = 20 / sin 51°

sin (m ∠ N) = (14 / 20) · sin 51°

sin (m ∠ N) = 0.544

There are two possible values for angle N: m ∠ N₁ ≈ 32.957°, m ∠ N₂ ≈ 147.043°. The existence of two different angles indicates that two distinct triangles can be formed.

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Answer:

The third side of the triangle must be greater than 4 and less than 19. This follows from the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the third side, and the difference between any two sides of a triangle must be less than the third side. Therefore, the third side must be greater than 4 (5 + 4) and less than 19 (14 - 4).

The Factor Theorem states that if a polynomial is divided by (x-a) then the remainder is equal to zero if and only if (x-a) is a factor of the polynomial.

To solve the Factor Theorem, first you need to determine the polynomial and the value of (x-a).

Then you divide the polynomial by (x-a). To do this, use synthetic division. Synthetic division is a shorthand way of dividing a polynomial by a linear factor.

If the remainder is 0, then the polynomial is divisible by (x-a). If the remainder is not 0, then (x-a) is not a factor of the polynomial.

To summarize, the Factor Theorem states that if the remainder is 0 after dividing a polynomial by (x-a), then (x-a) is a factor of the polynomial.  The Factor Theorem can be solved by using synthetic division.

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The side lengths of a 45-45-90 triangle can be found using side ratios or the formula that the length of hypotenuse is root two times the length of each leg which is equal.

A 45-45-90 triangle is a special type of right triangle that has two angles that measure 45 degrees and one angle that measures 90 degrees. This triangle has a unique relationship between its side lengths.

The length of the hypotenuse (the side opposite the 90-degree angle) is equal to √2 times the length of one of the legs (the two sides that are congruent and form the 45-degree angles).

The length of each leg is equal to the length of the hypotenuse divided by √2.

For example, if the hypotenuse of a 45-45-90 triangle measures 8 units, then one leg measures 8/√2 = 8/1.4142 = 5.6568 units, and the other leg measures also 8/√2 = 8/1.4142 = 5.6568 units.

Another way to find the side lengths of a 45-45-90 triangle is to use the side ratios. The ratio of the sides in a 45-45-90 triangle is 1:1:√2, so if you know the length of one side, you can find the length of the other sides using these ratios.

It's important to keep in mind that a 45-45-90 triangle is a special type of triangle and its side lengths can be found using the formulas and ratios mentioned above. Regular triangles, such as a 30-60-90 triangle, have also similar relationships between their sides.

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The (2,1) is a solution of the system of equations is shown. A formula that expresses the connection between two expressions on either side of a sign. Typically, it has a single variable and an equal sign.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

2 + 3·1 = 5

5 = 5

1 = -2 +3

1 = 1

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Answer:

B.  x + 10 ≥ 70;  x ≥ $60

Step-by-step explanation:

Given:

The equation that models the given parameters is:

To solve for x, subtract 10 from both sides of the equation:

[tex]\implies x+10-10 \geq 70-10[/tex]

[tex]\implies x \geq 60[/tex]

Therefore, Kelvin needs to withdraw at least $60 from the bank.

The weight of a piece can be found through the letter because the diagram is made up of balanced hangers which means that the weight of one side is equal to the weight of the other side.

For diagram A = X+3 = 8

X = 8-3 = 5

The weight of the letter piece X = 5

For diagram B = 12= 2y

y = 12/2 = 6

The weight of the letter piece y = 6

For diagram C = 11 = 4z

z = 11/4 = 2.75

The weight of the letter piece z = 2.75

For diagram D = 13⅘ = w + 3⅘

w = 13⅘ - 3⅘ = 10

The weight of the letter piece w = 10

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Answer:

To have a positive balance of $15, Brittney will need to save an additional $25 - $10 = $15. Therefore, she will need to earn an additional $15 to meet her goal.

Answer: 13x + 5y - 3

Step-by-step explanation: 7x + 6x + 3y + 2y -2 -1
= 13x + 5y - 3

Answer:

No solution

Step-by-step explanation:

y=8x-2

y=8x+2

8x - 2 = 8x + 2

8x = 8x + 4

0x = 4

We know any number multiplied by 0 will be equal to 0.

So, there is no solution.

The area of a triangle with the base 4.8 cm and height 3.6 cm is 8.64 cm².

The area of a triangle can be easily calculated by keeping the values of base and height in the formula -

Area of triangle = 1/2 × base × height of triangle. We know the values of base and height which are in same units. Hence, directly keeping the values -

Area = 1/2 × 4.8 × 3.6

Performing division on Right Hand Side of the equation

Area = 2.4 × 3.6

Performing multiplication on Right Hand Side of the equation

Area = 8.64 cm²

Therefore, the area of triangle is 8.64 cm².

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