solve each equation
20x-3/15=8

56.6 miles will he have to his destination after 68 minutes of driving.

A linear function is a mathematical expression involving variables that, when graphed, creates a straight line. Linear functions are used to model relationships between two variables, such as cost and revenue, price and demand, and distance and time. Linear functions can also be used to solve equations and are especially useful for predicting future outcomes.

The linear function representing Sam's distance to his destination can be expressed as:

Distance to Destination = 69 - (60 - Driving Time)

Therefore, after 68 minutes of driving, Sam will have 56.6 miles to his destination:

Distance to Destination = 69 - (60 - 68)
Distance to Destination = 56.6.

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ordered pair is in the solution set of the system of inequalities shown in the graph will be (1, 5)

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.

Set of such values is called solution set to the considered equation or inequality.

The shaded portion will be consider as the dashed line joining points

The portion affected by the two shadings would be the portion common to the right of the dashed line joining points

The ordered pair is in the solution set of the system of inequalities shown in the graph will be (1, 5)

Hence, ordered pair is in the solution set of the system of inequalities shown in the graph will be (1, 5)

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Part A: The value of π for circle A using the circumference is 3.14 and the value of π for circle B using the circumference is 3.14.

Part B: The value of π for circle A using the area is 3.14 and the value of π for circle B using the area is 3.14.

Part C: You can notice that pi's value remains constant in both circles, proving that it is a constant.

Circle A has a diameter of 7 inches, a circumference of 21. 98 inches, and an area of 38. 465 square inches.

The diameter of circle B is 6 inches, the circumference is 18. 84 inches, and the area is 28. 26 square inches.

Part A: Using the formula for circumference, solve for the value of pi for each circle.

Circumference formula of circle = 2πr

The diameter of circle A d = 7 inches

The radius of circle A r = 7/2 inches

The circumference of circle of A = 21. 98 inches

Now putting the values in the formula

2π×[tex]\frac{7}{2}[/tex] = 21. 98 inches

7π = 21. 98 inches

Divide by 7 on both side, we get

π = 3.14

The value of π for circle A is 3.14.

The diameter of circle B d = 6 inches

The radius of circle B r = 6/2 inches = 3 inches

The circumference of circle of B = 18.84 inches

Now putting the values in the formula

2π×3= 18.84 inches

6π = 18.84 inches

Divide by 6 on both side, we get

π = 3.14

The value of π for circle B is 3.14.

Part B: Use the formula for area and solve for the value of pi for each circle.

The area of circle = [tex]\pi r^2[/tex]

The radius of circle A r = 7/2 inches = 3.5 inches

The area of circle A = 38.465 square inches

Now putting the value

[tex]\pi (3.5)^2[/tex] = 38.465

π × 12.25 = 38.465

Divide by 12.25 on both side, we get

π = 3.14

The value of π for circle A is 3.14.

The radius of circle B r = 3 inches

The area of circle B = 28.26 square inches

Now putting the value

[tex]\pi (3)^2[/tex] = 28.26

π × 9 = 28.26

Divide by 9 on both side, we get

π = 3.14

The value of π for circle B is 3.14.

Part C: We have to explain what observation you can make about the value of pi for circles A and B.

You can notice that pi's value remains constant in both circles, proving that it is a constant.

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The largest possible value of D is  6.4.

The largest possible value of D is calculated by applying the following formula as shown below.

The largest possible value of D is obtained when the situation occurs;

let b = 3

a = 4

c = - 2

D = √ ( b²  - 4ac )

D = √ ( 3² - ( 4 x 4 x - 2 )

D = √ ( 9 +  32 )

D = √ ( 41 )

D = 6.4

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C 3.6  = 1.5 3.6x=1.53, point, 6, x, equals, 1, point,5.

An equation is a mathematical statement that states that two expressions are equal. It is composed of two expressions, one on each side of an equals sign, and can be used to solve for unknown values. Equations can involve numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. They are used to solve a wide variety of mathematical problems.

The equation to solve for the price of a box of generic cereal is 3.6/1.5 = x, where x is the price of the box of generic cereal. By dividing 3.6 by 1.5, the price of a box of generic cereal is determined to be $2.40.

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The elimination method  is another name for the addition method to solve a system of equations in two variables.

What is  The elimination method?

The elimination approach involves removing one of the variables from the system of linear equations by adding or subtracting, as well as multiplying or dividing the variable coefficients.

What are some instances of elimination methods?

Utilizing the addition property of equality, the elimination approach is used to solve systems of linear equations. Each side of an equation can be increased by the same amount.

                               You can therefore add x + y to the left side of the first equation and add 8 to the right side of the equation if your system is x - 6 = 6 and x + y = 8.

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The expression [tex]\sqrt[3]{8^{x} }[/tex] is equivalent to, [tex]8^{x/3}[/tex], So Option C is correct

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

An expression,  [tex]\sqrt[3]{8^{x} }[/tex]

equivalent expression = ?

⇒   [tex]\sqrt[3]{8^{x} }[/tex]

⇒  [tex]\sqrt[3][/tex]cube root can be written as 1/3 power of 8

So, expression will convert like this,

⇒   [tex]8^{x/3}[/tex]

Hence, the equivalent expression is  [tex]8^{x/3}[/tex]

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The SAS (side-angle-side) theorem of congruence states that if two sides and their included angle in one triangle are exactly equal to the corresponding two sides and their included angle in another triangle,

prove that the triangles are congruent using SSS or SAS?

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.

The value of x is, 18 and the measure of angle A is 110°.

Parallel lines are those lines that are equidistance from each other and never intersect each other.

We have to given that;

The values of angle A and B are,

⇒ ∠A = 5x + 20

⇒ ∠B = 9x - 92

Now, By figure,

Angles A and B are corresponding angles of parallel lines.

Hence, The sum of angles A and B are 180°.

So, We can formulate;

⇒ ∠A + ∠ B = 180°

⇒ (5x + 20) + (9x - 92) = 180

⇒ 14x - 72 = 180

⇒ 14x = 180 + 72

⇒ 14x = 252

⇒ x = 252 / 14

⇒ x = 18

Hence, The measure of angle A is,

⇒ ∠A = 5x + 20

⇒ ∠A = 5×18 + 20

⇒ ∠A = 90 + 20

⇒ ∠A = 110°

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The complete question is shown in figure.

Answer: Her neighbors paid her 28 dollars

Step-by-step explanation: if you add 4, 16, and 8 then you get 28

the measured angle S is 1/2((Arc XPQ-Arc XQ)).

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

The sum of all angles of the triangle = 180

The circle is within the triangle,

The arc XPQ is the total, arc XQ

So the measured angle S is 1/2((Arc XPQ-Arc XQ)).

0.5 (Arc XPQ-Arc XQ)

Hence the measured angle S is 1/2((Arc XPQ-Arc XQ)).

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The slope between the points (-6, 6) and (-6, -1) is -infinity.

The slope of a line is the change in the dependent variable with respect with the change in the independent variable.

Therefore, the slope is define as rise over run.

Hence let's find the slope between the points (-6, 6) and (-6, -1)

Therefore,

slope = y₂ - y₁ / x₂ - x₁

x₁ = -6

x₂ = -6

y₁ = 6

y₂ = -1

Therefore,

slope = -1 - 6 / -6 + 6

slope = -7 / 0

slope = - infinity

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We will have a Deficit balance of $30 at the end of the month.

"Unilateral transfer" is the term used to describe the balance of payments deficit's most obvious cause. For instance, Americans who contribute money to another country in the form of foreign aid do not receive anything in return (economically speaking). Few economists would argue that foreign aid-related balance of payment deficits are a "bad thing."

Weekly net income = $380

Monthly net income = $380 * 4 weeks = $1520.

Monthly expenses = $1550

Balance = Monthly income - monthly expenses = $-30.

The negative sign shows a deficit of $30 monthly

Therefore, We will have a Deficit balance of $30 at the end of the month.

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The slope 0/(-2) means, the line is coincident or parallel to the x-axis

We know that the slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate.

The slope of the line describes the steepness of a line.

Also,  if a line makes an angle θ with the positive direction of the x-axis, then the slope of the line will be tangent of angle θ

m = tan θ

Here we have been given a slope 0/(-2)

As we know 0/(-2) = 0

So, the slope is 0.

Let m = 0

From definition of slope of line,

m = tan θ

0 = tan θ

θ = arctan(0)

θ = (nπ)                where n = 0, 1, 2, . . .

This means, the slope 0/(-2) means for every two units of horizontal distance crosses there is no change of vertical distance.

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Answer: The production possibilities is a graph that shows all of the different combinations of output that can be produced given current resources and technology. Sometimes called the production possibilities frontier, the PPC illustrates scarcity and tradeoffs.

The product of these given polynomials will be

(4x^2+9-12x)(25x^2+36+60x)

What are polynomials?

Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable. An example of a polynomial with one variable is x^2+x-12. In this example, there are three terms: x^2, x and -12.

Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial.

Now

Given polynomial  ​ (2x−3)(5x+6)(2x−3)(5x+6)

After combining like terms

(2x-3)^2(5x+6)^2

(4x^2+9-12x)(25x^2+36+60x)    ( As (a+b)^2 = a^2 + b^2 + 2ab

                                                             (a-b)^2 =a^2 + b^2 - 2ab )

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To find f(-1) on a graph, you need to locate the point (-1, y) and then read off the value of y.

Begin by locating the point (-1, 0) on the graph. This point is located at the far left side of the x-axis. Then, draw a line from this point to the line representing the function. This line will intersect the line of the function at a point which is the coordinates (-1, y).

Now, read off the value of y at this point. This is the value of f(-1). To double-check your answer, make sure that the coordinates of the point you have located are (-1, y). If they are, then the value of y is the value of f(-1).

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Yes, the survey data is biased.

The survey data is biased because the sample group lacks inclusivity.

Bias is a statistical word that means a systematic deviation from the actual value. It is a sampling method that may show some serious problems for the researcher as a less increase cannot reduce in sample size.

In a biased sample, one or more parts of the population are favored over others, whereas in an unbiased sample, each member of the population has an equal chance of being selected. We also saw that a representative sample is a subset of the population that reflects the characteristics of the larger group.

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If the sum of the squares on a triangle's two shorter sides is more than the square on its longest side, the triangle is said to be acute.

A triangle is said to be acute if the sum of its two shorter sides' squares is larger than its longest side's square. The triangle is obtuse, though, if the squares added together of its two shorter sides are less than those added together of its longest side.

The Pythagorean Theorem's antithesis states that if the square of the length of a triangle's longest side equals the sum of the squares of its other two sides, then the triangle is a right triangle.

With the aid of Pythagoras' theorem, it is possible to establish whether a triangle has a right angle. A straight angle is present in a triangle if the squares of the two shorter sides equal the square of the hypotenuse.

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The factored form of a quadratic function is  (x + a)(x+ b).

In math the term quadratic function is defined as a polynomial function of degree 2.

Here we have to find the process to convert the quadratic equation into the factored form.

As per the definition of quadratic equation, we all know that the standard form of the quadratic equation s written as,

=> y = ax² + bx + c

As we all know that factorization of quadratic equations can be done using different methods such as splitting the middle term or by using the quadratic formula or by completing the squares, etc.

Here we spilt the middle term then the expression is written as,

=> (x + a) (x + b)

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[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{-3})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{7} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{ \cfrac{1}{7}}(x-\stackrel{x_1}{5}) \implies y +3= \cfrac{1}{7} (x -5)[/tex]

The properties of adjacent angles are

When an angle's vertex and side are shared by another angle, the two angles are said to be adjacent angles.

The vertex of an angle is the point where the rays come to a halt and create the sides of the angle. When two adjacent angles share a vertex and a side, they can be either complimentary or supplementary angles.

Angles are said to be adjacent when they lie side by side to each other.

hence we can conclude that adjacent angles have a common vertex and side

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Answer:

2. have a common side.

3. have a common vertex.

Step-by-step explanation:

1) A  perpendicular bisector in kite ABCD is; BD

2) An isosceles triangle in kite ABCD is; ΔABC

3) A right triangle in kite ABCD is; ΔABM

In geometry, a kite is defined as a quadrilateral with reflection symmetry across a diagonal.

1) A perpendicular bisector is defined as a line segment which bisects another line segment at 90 degrees.

Looking at the diagram, Line BD bisects Line AC and as such BD is the perpendicular bisector.

2) An Isosceles triangle is defined as a a triangle in which two sides have the same length.

In this case, in Triangle ABC, AB and BC have the same length and as such Triangle ABC is the Isosceles Triangle.

3) A right triangle is defined as a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle.

In this case if Mis the intersection of BD and AC, then the right angle triangle is ABM

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The perimeter of the triangle is given by an expression 18m³ + 2m² - m

Consider the following diagram.

In this question we have been given a triangle.

The sides of the triangles are represented by a mathematical expressions

(5m³ + 3m² - 2m), (8m³ - 4m² + 3m) and (5m³ + 3m² - 2m)

From given expression we can observe that, there are two sides with expression 5m³ + 3m² - 2m.

This means, the triangle must be an isosceles triangle.

We know that the formula for the perimeter of isosceles triangle.

P = 2a + b

where, a = side and b = base of isosceles triangle

Using above formula the perimeter of given triangle would be,

P = 2(5m³ + 3m² - 2m) + (8m³ - 4m² + 3m)

P = (10m³ + 6m² - 4m) + (8m³ - 4m² + 3m)

P = (10 + 8)m³ + (6 - 4)m² + (-4 + 3)m            .....(combine like terms)

P = 18m³ + 2m² - m

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Yes, it is possible to solve 30 60 90 triangles if only a hypotenuse is given. The 30, 60, and 90 are special right triangles.

30,60,90 special right triangles because there is a relation between height, base, and the hypotenuse

In this type of triangle, the hypotenuse is double of height.

Let's assume the hypotenuse given = [tex]x[/tex]

therefore, height = [tex]\frac{x}{2}[/tex]

and the base is [tex]\sqrt{3}[/tex] times the height

so, base = [tex]\frac{x}{2}\sqrt{3}[/tex]

Points to be noted:

the opposite side of [tex]30^o[/tex] is height, the opposite side of [tex]60^o[/tex] is base, and the opposite side of [tex]90^o[/tex] is the hypotenuse.

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The marked price when a customer gets a discount of 3250 (from graph) and the discount when the marked price is 2500

percentage, a relative value indicating hundredth parts of any quantity.

The relation between the market price and the discount is

y=0.5x

Which is the required relationship between the Marked Price and the Discount.

We have to find the marked price when a customer gets a discount of 3250

As discount is 3250

In the graph is represent the point F ( 3250, 0)

If we draw a line parallel to Y axis and passing through the point F( 3250, 0) then it intersects the line y = 2x at B( 3250 , 6500)

Accordingly we get the point A ( 3250, 6500)

Hence the Marked Price = 6500

Manually it can be checked

As discount is 3250

x = 3250

So y = 2 × 3250 = 6500

(2) We have to find the discount when the marked price is 2500

As marked price is 2500

In graph it represent the point C( 0, 2500)

If we draw a line parallel to X axis and passing through the point C( 0, 2500) then it intersects the line y = 2x at B( 1250 , 2500)

Accordingly we get the point B( 1250 , 2500)

Hence the discount = 1250

Manually it can be checked

As marked price is 2500

y = 2500

So x = 2500 ÷ 2 = 1250

Hence,  the marked price when a customer gets a discount of 3250 (from graph) and the discount when the marked price is 2500

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7.13 square inches is the area of the circle greater than the area of the square

area of a circle is pir^2 = pi*2.5^2

side of the square by Pythagoras

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

5^2 = 2x^2

x^2 = 12.5 = area of the square

area of circle = pi * 6.25 = 19.63

difference in areas = 19.63 - 12.5 = 7.13 sq ins

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Answer:

Step-by-step explanation:

is this college

Of the four variables, employee number, pay rate, hire date, and sex, the "Sex" variable is the best fit to use as a dummy variable.

The variable "Sex" is the best fit to use as a dummy variable. A dummy variable is used to represent a categorical variable with a numerical value, such as 0 or 1. In this case, "Sex" is a categorical variable with two categories (male and female) and can be transformed into a dummy variable with values 0 or 1 to represent the categories. The other variables, Employee Number, Pay Rate, and Hire Date, are not categorical variables and would not be appropriate to use as dummy variables.

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