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The table shown below, which has some values for functions f(x) and g(x). What is/are the solution(s) when f(x) = g(x)? Explain your answer(s).

a. Solution(s): _____

b. Explanation (how did you know they were the answer): ______

The value 750 in equation 300x + 750 = 23,250 represents the initial amount in the club account.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 9 is an equation.

We have,

Initial amount in the club account = m

Amount raised by each member = n

All members raised the same amount.

Number of members = x

The total amount raised by all the members = p

nx + m = p

This is similar to the equation 300x + 750 = 23,250

So,

n = 300

m = 750

p = 23,250

Now,

m = 750 is the initial amount in the club account.

Thus,

750 represents the initial amount in the club account.

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The solution to the given system of linear equations is x = -4, y = -10

From the question, we are to solve the given system of linear equations.

The given system of linear equations is

y = 2x - 2          ------------ (1)

-4x - y = 26     ------------ (2)

Substitute equation (1) into equation (2)

-4x - y = 26

-4x - (2x - 2) = 26

- 4x - 2x + 2 = 26

-6x + 2 = 26

-6x = 26 - 2

-6x = 24

x = 24/-6

x = -4

Substitute the value x into equation (1)

y = 2(-4) - 2

y = -8 - 2

y = -10

Hence, the x = -4, and y = -10

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Answer:

We do not consider 21 as a prime number, because it can be written as a product of two smaller natural numbers

Step-by-step explanation:

The roots of the equation 25x² + 60x + 37 = 0 in simplest form will be - 6/5 + 100i and - 6/5 - 100i.

Let the equation be ax² + bx + c = 0.

Then the roots of the equation will be

[tex]\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}[/tex]

The equation is given below.

25x² + 60x + 37 = 0

The roots of the equation is given as,

x = [- 60 ± √{(60)² - 4 × 25 × 37}] / (2 × 25)

x = [- 60 ± √(-100)] / 50

x = [- 60 ± 100i] / 50

x = - 6/5 ± 100 i

x = - 6/5 + 100i, - 6/5 - 100i

The roots of the equation 25x² + 60x + 37 = 0 in simplest form will be - 6/5 + 100i and - 6/5 - 100i.

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Area of the triangle DEF = 35 square unit.

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.

Given,

Vertices of triangle

D(4, -3), E(-2, 1), and F(-9. -6)

   x₁  y₁      x₂ y₂              x₃ y₃

Area of triangle S = 1/2[x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)]

Area of triangle DEF = 1/2[4(1 - -6) + -2(-6 - -3) + -9(-3 - 1)]

                                  = 1/2 [4(7) -2(-3) -9 (-4)]

                                  = 1/2[28 + 6 + 36]

                                  = (1/2) (70)

Area of triangle DEF = 35 square unit

Hence, 35 square unit is the area of triangle DEF.

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The measure of the angle is 30.00 degrees

Trigonometry is the branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly right triangles. It is concerned with the measurement of angles and the calculation of sines, cosines, and tangents of those angles.

These ratios are known as trigonometric functions and they are used to relate the ratios of the sides of a right triangle to the angles opposite or adjacent to the right angle.

Since sin 30° = 0.5

Thus, sin⁻¹(0.5) = 30.00 degrees

Note: Angle 30° is one of the special angles and trigonometric are very easy recall.

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Answer: $31

8(15)+6(8)=168

she needs 31 more to reach 199

Using Trigonometric identities, the value of y = 11.49.

Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence.

These are identities that, geometrically speaking, involve certain functions of one or more angles.

They are not to be confused with triangle identities, which are identities that may involve angles but may also involve side lengths or other lengths of a triangle.

Using Trigonometric Identities,

Cos θ = Base / Hypotenuse

Cos 29 = 10 / y

0.87 = 10 / y

y = 10 / 0.87

y = 11.49

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Answer:

122°

Step-by-step explanation:

All triangles have a total of 180°.

Angle 1 will be X

Angle 2 will be Y

Angle 3 will be z

180 - (x + y) = z

The required graph is attached below.

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates,

Given here: The points (0,-2) (-1,2) Also the given equation is

y=-4x-4+2

y=-4x-2

Thus this is linear graph with y intercept at -2 and using the equation we plot the two points from Table 2.

Hence, The points are plotted.

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In order to find the y− intercept of a parabola in factored form, plug in 0 for x and find the corresponding y− value

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Vertical lines known as longitudes are used to determine the west or east of the meridian in Greenwich, England. Latitude and longitude work together to help cartographers, geographers, and others find specific locations on the globe.

Distance from the primary meridian is measured in terms of longitude. Longitude lines, often known as meridians, are fictitious lines that divide the Earth. They sprint from pole to pole from north to south, but they gauge the distance in either an east or west direction. The units of longitude are degree, minute, and second.

The North and South Poles serve as the meeting points for imaginary lines that circle the globe vertically (up and down) and are used to calculate longitude. Meridians are the name for these lines. One arc degree of longitude equals one meridian. There are 360 degrees in an orbit around the Earth.

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(3,2) is the required solution of an equation and This is a straight line and has infinite number of solutions.

the solution is explained as :

y=2

x=7−2(2) =3

Hence, (5,1) is one of the solution of the given equation.

A straight line is an infinite length of an  line that does not have any curves on it. A straight line in which it can be formed between two given points and also but both the ends extend to infinity. A straight line is  formed when two points A (x1, y1) and B (x2, y2) are connected with the shortest distance between them and the line  that ends are extended to infinity.

In the given representation shown below, a straight line between two points A and B is shown. A straight line AB is represented by:

←→

A B

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Answer:

Calculus in baseball. In baseball, calculus can be used to optimize the pitcher’s throw to achieve maximum efficiency. Also, calculus can be used to calculate the projectile motion of baseball’s trajectory and to predict if runners can make it to the next base on time given their running speed and the speed of a hit ball.

Step-by-step explanation:

Answer:

A linear equation can be used to represent the situation where a fixed amount is added to the original balance each month. The equation would have the form:

y = mx + b

where x is the number of months, y is the balance in the bank account, m is the monthly deposit amount, and b is the initial balance. In this case, we have:

y = 60x + 575

This equation can be read as: "The balance in the bank account (y) is equal to 60 dollars (m) added to the account each month (x), plus the initial balance of 575 dollars (b)."

An exponential equation can also be used to represent the situation where the balance in the bank account increases by a fixed percent each month, it would be:

y = a(1+r)^x

Where a is the initial amount, r is the interest rate and x is the number of months.

Step-by-step explanation:

The equations that form the system that models this situation are:

B. x² = y + 16  

F. 4y - 1 = 7x

The solution of the system of equations is: A. (5, 9).

In this scenario, the relationship between two numbers, where x represents the first number and y represents the second number is given by the following word description:

"The square of the first number is equal to the sum of the second number and 16."

"The difference of 4 times the second number and 1 is equal to the first number multiplied by 7."

Next, we would translate the word problem into an algebraic equation:

x² = y + 16    .......equation 1.

4y - 1 = 7x      .......equation 2.

Next, we would use an online graphing calculator to plot the given system of equations in order to determine its solution.

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The five rules for factoring are taking the difference grouping the numbers, dividing, multiplying, taking the greatest common factor and by taking the LCM.

There are certain times when we encounters such kind of problems which includes the factoring of the components of the polynomial.

Ine Sach kind of cases there are several methods for factoring the components of the polynomial like taking the greatest common factor or finding the LCM of the components in order to make the polynomial more simplified.

Also we can take out the most common digit or the number from the whole polynomial which comes under the category of grouping.

Also we can use the method of taking the differences or like taking the division and multiplication of certain digit into the polynomials in order to do the factoring.

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Although every complex number is a real number, not all complex numbers are real numbers.

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Hence he need to sell $55 on the last day to meet his quota for this

week.

What is average ?

average can be defined as the ratio of the sum of observations and total number of observations.

Given,

To meet your sales quota at work, you need to average $125 per day.

So far he  sold $150, $175, $90, and $155.

so ,

let last day he need to sell be x .

average = 150+175+90+155+x/ 5

125 = 570+x / 5

625 = 570 + x

x = 55

Hence he need to sell $55 on the last day to meet your quota for this

week.

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Answer:

210 minutes a week

Step-by-step explanation:

840 minutes/4 weeks

The number of zeros in a polynomial equation is determined by the number of degrees it has, which is n.

Polynomial

A polynomial is a mathematical equation made up of variables, constants, and exponents that are mixed using addition, subtraction, multiplication, and division.

Bi-quadratic Polynomial

(Not comparable) Biquadratic (mathematics) x4 + 3x2 + 2 is an example of a polynomial expression that only uses a variable's zeroth, second, and fourth powers. When used in the form x4 4x3 + 3x2 x + 1, it is sometimes extended to any expression containing the biquadrate or fourth power (but not higher powers).

What is a Polynomial Equation?

Polynomial equations are those created by combining variables, exponents, and coefficients. The greater of its possible exponents is referred to as the equation's degree.

Among all possibilities, the linear polynomial p(x) = 2x+3 is a polynomial of degree 1. Consequently, there is just one zero in it.

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Answer:

9 and 10

Step-by-step explanation:

66 divided by 7 would be 9.4 which lies between 9 and 10.

With sides that are 4 cm, 3 cm, and 7 cm long, a triangle cannot be built. Because the sum of the other two sides does not exceed that of the third side.

A triangle is referred to as a three-sided polygon that has three vertices. The connection of the three sides ends to end at a single point forms the angle of the triangle. The sum of these angles adds up to 180 degrees.

The triangle's three sides are specified as being 4 cm, 3 cm, and 7 cm. Add the two sides together and see if the result exceeds the third side to determine whether these sides constitute a triangle.

Here, the sum of two sides 4 cm and 3 cm is calculated as,

A+B = 4+3

=7 cm

This sum is equal to the third side C = 7 cm.

Therefore,  [tex]A+B\ngtr C[/tex]. So, the given sides don't form a triangle.

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Answer:

x=1

Step-by-step explanation:

Answer:

A) [tex]x>-2[/tex]

Step-by-step explanation:

[tex]x+4>-x \\ \\ 2x+4>0 \\ \\ 2x>-4 \\ \\ x>-2[/tex]

A mathematical equation can be defined in a variety of ways.

A mathematical equation can be defined in a variety of ways. The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.

Equation that is linear.

A quadratic equation.

Cubic Formula.

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A polynomial is a kind of algebraic expression in which the exponents of all variables should be a whole number.

The Power of the variables in any polynomial has to be a non-negative integer. A polynomial consists of constants and variables, but we cannot perform division operations by a variable in polynomials.

The example of polynomial is: 3x^2 + 5.

given the equation is x^3+3^2+3x.=0

                              (x³-x) +(3x²-3) =0

                              = x (x²-1) +3(x²-1)

                               = (x²-1) (x+3) = 0

                               (a² + b²) = (a+b) (a-b)

                               (x²-1) = (x+1) (x-1)

                              ⇒(x+1) (x-1) (x+3) =0

                               x =- 3, -1, 1

So, the required zeros are -3, -1,1.

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Note that the area of the above triangle is given as: 42.

This is solved using the SOH CAH TOA Rule and the Formula of the Right Angled Triangle

The hypotenuse is the longest side of a right triangle, a "opposite" side is the one across from a given angle, and a "adjacent" side is the one close to a given angle. Right triangle sides are described using specific terminology. A right triangle's hypotenuse is always the side opposite the right angle.

To find the area of the triangle we must obtain, the Base and the Height, that is FD and A F.

Note that we have

∠F = 90°

∠D = 30°

Since the sum of angles in a Δ = 180°,

∠A = 180 - (90 + 30)

∠A = 60°

To find the area of the triangle we must obtain, the Base and the Height, that is F D and A F.

To obtain F D, we must use the Sine rule which states:
Sine θ = O/H; that is

Sin ∠A = F D/AD

Sin 60° = F D/14

0.86602540378 = FD/14

F D = 14 * 0.86602540378

F D = 12.1243556529

F D [tex]\approx[/tex] 12. 12

Using the above Cos Rule (CAH) we can find the Adjacent Side (that is height). Thus

Cos A = A F/AD

Cos 60° = A F/14

0.5 = A F/14; multiply both sides by 14

A F = 0.5 * 14

A F = 7

Now we have Adjacent Side  (Height) = 7; and the Opposite Side (Base) = 12.12

The area of the Triangle according to the Pythagorean Rule is:

1/2 B * H

= 1/2 * 12.12 * 7

= 42.42

Thus the Area of the above triangle [tex]\approx[/tex] 42

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Simplified form of -5⁷÷ 5² is -5⁵.

The correct option is C.

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division.

Given expression,

-5⁷÷ 5²

Above expression can be written as

-5⁷/5²

= -1(5⁷)/5²

= -1(5⁵.5²)/5²

= -1(5⁵)

= -5⁵

Hence, -5⁵ is the simplified form of expression -5⁷÷ 5².

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