Which of these ordered pairs is a solution to the inequality y - 2x < -3? ( (2,4) (-2, 3) (3, 4) (1,-1)​

The volume of the prism in cubic inches is 6912 inch³.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Volume of Cuboid = length x width x height

Given:

length =  3 feet = 36 inch

width = 8 inch

height = 2 feet = 24 inch

So, Volume of cubic prism

= length x width x height

= 36 x 8 x 24

= 6912 inch³

Hence, the volume is 6912 inch³

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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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The probability that it is a large, blue fish is 21%.

Probability is the mathematical study of outcomes in uncertain situation. It is used to describe the likhood of an event occurring and it can be expressed as a number between 0 to 1. Probability is used to quantify the uncertainty associated with any given event it helps us understand how likely it is that something will happen and it can be used to make prediction about futures even probability theory is it cornerstone of modern statistic and is widely used in field such as finance economics and science.

Here we have to use the definition of a simple probability, wherever all fishes has the same Probability to be chose.

So, we have to divided the possible of outcomes with the total of outcomes. The possible outcomes refer to the number of large-blue fishes, and the totals numbers of outcomes represent the total number of fishes. So

Therfore, there's 21% of chances to selected one fish randomly and be a large, blue fish.

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The solutions of the given equation  are given below:

(i) 3x+4y =7

(ii) x=6y

(iii) x+πy =4

(iv) x-y =4

All these equations are having infinitely many solution.

Infinitely Many solution:

An equation can have an infinite number of solutions if certain conditions are met. If the lines are coincident and have the same y-intercept, the system of equations has infinitely many solutions. If two lines have the same y-intercept and slope, they are really on the same line.

(i) Given :

3x + 4y = 7                        --------------------------- (1)

On putting x = 0 in equation 1

3x + 4y = 7

⇒ 3 × 0 + 4y = 7

⇒ 0 + 4y = 7

⇒ 4y = 7

⇒ y = 7/4

Therefore, ( 0, 7/4) is a solution of given equation.

On putting y = 0 in equation 1

3x + 4 × 0 = 7

⇒ 3x + 0 = 7

⇒ 3x = 7

⇒ x = 7/3

Thus, (7/3, 0) is a solution of given equation.

Hence, 2 out of the infinitely many solutions of the given equation are(0,7/4), (7/3,0).

(ii) x = 6y

Let x = 0

⇒ x = 6y

⇒ 0 = 6y

⇒ y = 0/6

⇒ y = 0

(0,0) is the solution.

Let x = 1

⇒ x = 6y

⇒ 1 = 6y

⇒ y = 1/6

(1,1/6) is the solution.

Hence, 2 out of the infinitely many solutions of the given equation are (0,0), (1,1/6).

(iii) x + πy = 4

let x = 0

⇒ x + πy = 4

⇒ 0 +  πy = 4

⇒ πy = 4

⇒ y = 4/π

(0, 4/π) is the solution.

Let y = 0

⇒ x + πy = 4

⇒ x + 0(y) = 4

⇒ x  + 0 = 4

⇒ x = 4

(4, 0) is the solution.

Hence, 4 out of the infinitely many solutions of the given equation are (0, 4/π), (4, 0).

(iv) x - y = 4

Let x = 0

⇒ x - y = 4

⇒ 0 - y = 4

⇒ -y = 4

⇒ y = - 4

(0,- 4) is the solution.

Let x = 1

⇒ x - y = 4

⇒ 1 - y = 4

⇒ -y = 4 - 1

⇒ -y = 3

⇒ y = - 3

(1,- 3) is the solution.

Hence, 4 out of the infinitely many solutions of the given equation are(0,- 4), (1,- 3).

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Step-by-step explanation:

either x=-1/2

or x=-3

compare with ax²+bx+c=0

Right angles, isosceles triangles, acute angles, obtuse triangles, scalene triangles, and equilateral triangles are some of the several types of triangles.

The term "trigon" is frequently (though not usually) used to refer to a triangle, a 3-sided polygon. Every triangle consists of a set of three angles and three sides, of which some might be the same. Three points and three sides make up a triangle, which is a polygon. The three angles of the triangle sum up to 180 degrees. With three sides & three vertices, triangles are a specific type of polygon in geometry. The two-dimensional figure displayed here has three straight sides. A triangle is a type of 3-sided polygon.

Here ,

are a number of triangles.

Triangular Scalene. a triangle that doesn't have adjacent sides.

a triangle where each of a three angles is far less than 90° degrees is referred to as a sharp triangle.

Straight triangle a triangular including one angle that extends beyond 90 degrees.

Isosceles, right, and equilateral triangles are examples of triangles.

Right angles, isosceles triangles, acute triangular, obtuse triangles, scalene triangles, and equilateral triangles are some of the several types of triangles.

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The present value of $5000 to be received in 2 years at a 12% interest rate compounded continuously is $6356.25. This can be calculated by using the formula PV = FV/(1 + r)^t, where PV is the present value, FV is the future value, r is the interest rate, and t is the time period. Therefore, PV = 5000/(1 + 0.12)^2 = $6356.25.

Answer:

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

Use the continuous compound equation:

Substitute and calculate:

The matching choice is C.

Since the distribution of the 10 distances is not uniform, Raul should use the median to determine his total performance.

The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory.

It could be referred to as "the middle" value for a data set.

The fundamental difference between the mean and the median when describing data is that the median is more representative of the "normal" value because it is not skewed by a tiny fraction of exceptionally big or small values.

Due to the fact that income distribution can be very skewed, the median income, for instance, might be a better indicator of what is considered a "normal" income.

Given that it is the most resilient statistic, the median is crucial to strong statistics.

According to our question-

The home run is an outlier in the data set even if nine lengths are grouped together.

The median is the most accurate indicator of the middle of a data collection including outliers.

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No, 3(5a + 9) + 5a and 4(5a+6) are not equivalent

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).

To know if 3(5a + 9) + 5a and 4(5a+6) are equivalent, we simplify both expressions and see if they will have result

simplifying 3(5a + 9) + 5a;

by opening the parentheses

15a+27+5a

collecting like terms

20a+27

simplifying 4(5a+6);

by opening the parentheses,

20a + 24

Therefore 20a + 27 is not thesame as 20a+24. This means 3(5a + 9) + 5a is not equal to 4(5a+6).

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An equation in algebra is a mathematical statement that proves the equality of two mathematical expressions.

An equation in algebra is a mathematical statement that proves the equality of two mathematical expressions. Take into consideration the equation 3x + 5 = 14, in which 3x + 5 and 14 are two expressions that are separated by the word "equal." The standard form, slope-intercept form, and point-slope form are the three primary formats for linear equations. In a mathematical expression known as an equation, the equals sign appears. Algebra is used in a variety of equations. When you don't know how much to compute in math, you use algebra to approximate the answer.

given

Take into consideration the equation 3x + 5 = 14, in which 3x + 5 and 14 are two expressions that are separated by the word "equal."

The standard form, slope-intercept form, and point-slope form are the three primary formats for linear equations.

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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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We can rewrite the expression by using a rational exponent as:

[tex]\sqrt{6} = 6^{1/2}[/tex]

We know that all roots can be written as exponents, such that:

[tex]\sqrt[n]{x} = x^{1/n}[/tex]

Particularly, if there is no upper index on the root, then it is a square root, and the exponent corresponding to the square root is 1/2.

Here we want to rewrite the expression:

[tex]\sqrt{6}[/tex]

Using what we saw above, we can rewrite this as:

[tex]\sqrt{6} = 6^{1/2}[/tex]

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Answer: Any number that is to the right of it, hence greater/bigger.

-8,-7,-6,-5.....

Step-by-step explanation:

Example: If you have -8 vs -9 vs -10 dollars, You have more with -8 vs -9 or -10.

Hence anything to the right of a give number on the number line is greater.

Also, think of the opposite with negatives.

For example with positive numbers, the larger the number the greater, but with negative numbers its the other way around, the smaller the number the greater.

Answer:

3/8 cup

Step-by-step explanation:

1 cup water = 2/3 cup water * 3/2

x = 1/4 cup grape juice * 3/2

1/4 * 3/2 = 3/8

Answer:

1. t*y

2. 365*t*y

Step-by-step explanation:

Identify variables

T (time) seconds

Y amount of times per day

T * Y = amount of time you would spend carrying water in a day, 24 hrs

365 * t * y = 365 (amount of days per year, multiplied by the amount of time you carry water per day.)

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 right answer is SSS since two triangles are said to be congruency when each of their three sides and Mario is correct.

Triangles are said regarded as being congruent if their size and shape actually match exactly. The word "congruent" contains the sign. When a triangle's three sides and three angles match those of a another triangle's three sides and three angles, two triangle are said to be congruent.

Here,

begin by writing the names of the triangles' vertices, beginning with triangles DAB and BCD, as shown below.

AB = CD

DA = BC

In both triangles, side BD is the same, therefore

BD = BD

We can infer that the triangles DAB & BCD are congruent that use the SSS feature of a congruence triangle because they have the same number of sides on each side.

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Some types of inequalities that are commonly discussed include economic inequality, educational inequality, social inequality and, racial and ethnic inequality.

Economic inequality: This refers to the unequal distribution of wealth, income, and resources among individuals or groups within a society. It often results in a small group of individuals or families owning a disproportionate amount of wealth and controlling the majority of resources.

Educational inequality: This refers to the unequal access to quality education among individuals or groups within a society. It can result in a lack of educational opportunities for those from lower socio-economic backgrounds, which can limit their chances for higher-paying jobs and career advancement.

Healthcare inequality: This refers to the unequal access to quality healthcare among individuals or groups within a society. It can result in poorer health outcomes and increased health disparities for those from lower socio-economic backgrounds.

Social inequality: This refers to the unequal distribution of social status, power, and privilege among individuals or groups within a society. It can result in discrimination, prejudice and bias against certain groups, leading to reduced opportunities and access to resources.

Racial and Ethnic inequality: This refers to the unequal distribution of resources and opportunities among individuals or groups based on their race or ethnicity. It can result in discrimination and racism, leading to reduced opportunities and access to resources.

It's important to note that these types of inequalities often overlap and interact with one another, creating complex and interconnected forms of disadvantage.

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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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Therefore , the solution of the given problem of expression comes out to be 794.0481.

combinations of numbers, symbols, and operations (such + and) that show how much something is worth. Examples: • 2 + 3 is the formula.

Here,

3 x/2 variable  is another formula.There is no equals sign in the expression. A mathematical expression is a sentence made up of variables, numbers, or both. There is never an equal symbol in an expression. These expressions are examples. An equation is a mathematical statement proving the equality of two expressions.

Given : 5 +

=> 5 + (5.3)*(5.3)*(5.3)*(5.3)

=> 789.0481 + 5

=> 794.0481

Therefore , the solution of the given problem of expression comes out to be 794.0481.

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On solving the provided question, we can say that a rectangle ABCD on a coordinate plane, point A is in Quadrant Il with coordinates (-a, b), the distance from point A to point B is 3a

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

a rectangle ABCD on a coordinate plane,

point A is in Quadrant Il with coordinates (-a, b).

the distance from point A to point B is 3a

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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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The four main types of Exponents that can be written are Positive Exponents , Negative Exponents , Zero Exponents and Rational Exponents .

What are Exponents ?

The Exponents are defined as a method to express large numbers in terms of powers which means, that exponent refers to how many times the number is  multiplied by itself.

The Four Main types of Exponents are listed below :

(i) Positive Exponents : The Positive exponents tell us about how many times we multiply the base by itself. The result of the positive exponent is generally a very large number. For Example : [tex]x^{82} , x^{9}[/tex] .

(ii) Negative Exponent : The Negative exponents tell us about how many times to divide the base by itself. The result of the negative exponent is generally a very small number. For Example : [tex]x^{-82} , x^{-9}[/tex] .

(iii) Zero Exponent :  The Zero Exponent is the expression in which the power is 0 , and the result of the zero exponent is always 1 . For Example : [tex]x^{0}=1[/tex] .

(iv) Rational Exponent : The Rational Exponent means that there is a fraction present in the exponent. For Example : [tex]x^{\frac{1}{2} } ,y^{\frac{2}{3} }[/tex] .

The given question is incomplete , the complete question is

How do you write the 4 types of Exponents ?

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1. The graph will represent a proportional relationship if these two following statements are correct.

2. The coordinate (x,y) represents the amount of money y earned for washing x cars.

A proportional relationship is a linear function with an intercept of zero modeled as follows:

y = kx.

In which k is the constant of proportionality.

The input and output variables for this problem are given as follows:

Hence the coordinate (x,y) represents the amount of money y earned for washing x cars.

The problem is incomplete, hence the answer is given in general terms using concepts of proportional relationships.

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The equation in slope-intercept form of the line that passes through the points is f(x) = 2x + 2

From the question, we have the following parameters that can be used in our computation:

f(0) = 2 , f(-2) = -2

A linear equation can be represented as

f(x) = mx + c

Substitute the known values in the above equation, so, we have the following representation

m * 0 + c = 2

m * -2  + c = -2

Solving 0 * x + c = 2, we have

c = 2

So, we have

m * -2 + c = -2

This gives

-2 * m + 2 = -2

Evaluate the like terms in the above equation

So, we have the following representation

-2m = -4

Divide both sides of the equation by -2

So, we have

m = 2

Substitute the known values in the equation f(x) = mx + c, so, we have the following representation

f(x) = 2x + 2

Hence, the function is f(x) = 2x + 2

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Complete question

Write an equation in slope-intercept form of the line that passes through the points: f(0) = 2 and f(-2) = -2

The Positive co-terminal angle is 471° and negative co-terminal angle is -249°.

Co-terminal angles have different degrees, but they all have their initial side on the positive x -axis (it goes this way →) and share the same terminal side  hence the term "co-terminal." Co-terminal angles differ by 360°. Therefore, we only need to add/subtract 360° to get our positive/negative co-terminal angle measures.

Here the given angle is ,

=> 111°

Positive co-terminal angle:

=> 111°+360°=471°

Now negative co-terminal angle is ,

=> -(360°-111°)

=> - 249°

Hence the Positive co-terminal angle is 471° and negative co-terminal angle is -249°.

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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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Change of base formula is used to rewrite a logarithmic operation as a ratio of two logarithms each with the same base that is different from the base of the original logarithm, for example, log₆₄8 = log 8 / log 64.

Logarithm is the inverse function of an exponential. The logarithm of x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.

Change of base formula is used to rewrite a logarithmic operation as a ratio of two logarithms each with the same base that is different from the base of the original logarithm. It can be written as follow:

[tex]Log_{b} a = \frac{Log_{d} a}{Log_{d} b}[/tex]

For example:

We want to find the value of log₆₄8 using the change of base formula.

log₆₄8 = log 8 / log 64

          = log 8 / log 8²

          = log 8 / 2 log 8

          = 1/2

Thus the log₆₄8 is 1/2

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Answer:

Step-by-step explanation:

Idl

By solving the given expression we get the value of M is 87.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

7(0.06m+ 25.80 +0.10 (25.80))

7(0.06m+ 25.80 + 2.58)

7(0.06m+ 28.38)

7(0.06m+ 28.38)

7 0.06m+ 7·28.38

0.42m+ 198.66

In this case, we need to get the value for m

235.20=0.42m+ 198.66

If we place the m value of 87,

=0.42×87+198.66

= 235.20

When an equation is solved symbolically, expressions can be employed to represent the solutions.

For example, the phrase x = y + 1 solves the equation x + y = 2x – 1 for the unknown x, since substituting y + 1 for x in the equation results in (y + 1) + y = 2(y + 1) – 1, which is a true assertion.

Therefore, the value of M is 87.

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Answer:

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

Step-by-step explanation:

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