Which of the following triplets cannot be the angles of a triangle?
a. 67°, 51°, 62°
b. 70°, 83°, 27°
c. 90°, 70°, 20°
d. 40°, 132°, 18°

Answer:

x = 2, y = 2

x = 4, y = 4

x = , y = 0

x = 4, y = 4

Step-by-step explanation:

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 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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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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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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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:

Combining like words, leveraging the sequence of operations, using the distributive principle, and factoring are the methods for simplifying an equation.

Adding or removing phrases with the same variables raised to the same powers is known as combining like words. The order of operations, commonly referred to as PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction), is a set of guidelines that specify the sequence in which mathematical operations must be carried out. By multiplying each phrase inside the parenthesis by the term outside the parentheses, you may apply the distributive principle to multiple a single term as well as the sum or difference of two or more terms. Finding common factors in an expression and separating them out is the process of factoring.

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Answer:

  100.0 feet

Step-by-step explanation:

You want to know the distance to a goalpost when the angle to the top of its 30 ft height is 16°42'.

The tangent relation is ...

  Tan = Opposite/Adjacent

Multiplying by Adjacent/Tan gives ...

  Adjacent = Opposite/Tan

In this problem, the distance to the goal can be modeled by the side "adjacent" to the acute angle 16°42' in a right triangle, and the "opposite" side will be the height of the goal.

  adjacent = 30'/tan(16°42') ≈ 99.995 ft

Rounded to the nearest tenth, the distance to the goalpost is 100.0 feet.

The required volume of the sphere is given as 33.49 cubic centimeters.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
Radius of sphere = 2 cm
The volume of the sphere = 4/3πr³
                                 = 4/3 × 3.14 × 2³
                                 = 33.49 cm³

Thus, the required volume of the sphere is given as 33.49 cubic centimeters.

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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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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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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 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.

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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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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The probability that these two spins added together would equal 7 is 1/25.

The probability that each spin will land on a specific number is 1/5. Since the spins are independent, we can multiply the probability of each spin landing on the desired number to find the probability of both spins landing on the desired numbers.

To get the sum 7, Charlie's spinner needs to land on 4, which is (1/5) and Libby's spinner needs to land on 3 which is also (1/5).

The probability of both spins landing on the desired numbers is (1/5) * (1/5) = 1/25.

It is important to note that the probability is low because the spins are independent events, meaning that the outcome of one spin does not affect the outcome of the other spin.

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The house must have 13 bedrooms.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

let the number of bedrooms be x.

As, the maximum number of people allowed is twice the number of bedrooms plus one .

So, max people ≤ 2x + 1

Now, we have number of people = 1 + 1 + 4 = 6

Then, the maximum bedrooms have

= 2 (6)+ 1

= 13

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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: Her neighbors paid her 28 dollars

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

[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]

For the triangles that are given, the congruency postulates are;Postulate of ASA Congruency ,the SSS congruency hypothesis,AAS congruency hypothesis, postulate for SAS Congruency,triangles cannot coexist.

Triangle congruency postulates include AAS, ASA, SSS, SAS, and RHS.

1) The congruency rule in this case is the ASA Congruency postulate because we have two corresponding angles and a congruent side included.

2) Since both triangles are furnished with three corresponding congruent sides, we can argue that the triangle congruence postulate in this case is the SSS congruency postulate.

3)In this case, the AAS Congruency postulate serves as the congruency rule because we are provided two related angles and the non-included congruent side.

4) The congruency rule in this case is the SAS Congruency postulate because we are given two congruent sides and an angle that also includes a congruent side.

5) The triangles are not congruent since we are provided three congruent angles but no information about any congruent sides.

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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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Answer: 4 3/4 OR 4.75

Step-by-step explanation:

Do the operations in the parentheses first.

5 1/2 + 2 3/4 = 8 1/4

Then, subtract.

8 1/4 - 3 1/2 = 4 3/4 OR 4.75

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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There are three ways to solve systems of linear equations in two variables graphing , substitution method ,elimination method.

What approach to solving a system of linear equations is the simplest?

Graphing. One of the most straightforward methods for resolving a set of linear equations is to use a graph.

                 You only need to graph each equation as a line and identify the point or points where the lines converge. Since these equations are already expressed in slope-intercept form, graphing them is simple.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

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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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Answer: 2.1

Step-by-step explanation: 5.88 divided by 2.80 = 2.1

Answer:

Step-by-step explanation:

3.08

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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Answer:

Step-by-step explanation:

is this college