What is an intractable problem?

LM = √(8² + 6²) = √(64 + 36) = √100 = 10 yd

Area = 2 × (1/2) × 6 × 8 = 48 yd²

Number of students that do two subjects are 12.

Number of students that do only exactly one subject are;

For Art;

⇒ 14

For Chemistry;

⇒ 11

For Bio;

⇒ 8

Number of students that do at least two of the subjects are 15.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

In a class of 48 students, 24 of them do Arts, 22 do Chemistry and 20 do Biology.

All the students do at least one of the three subjects.

3 do all three subjects while 4 do Arts and Biology only, 3 do Arts and Chemistry only and 5 do Chemistry and Biology only.

Here,

Total students = 48

So, Number of students that do two subjects are = 4 + 3 + 5

                                                                            = 12

And, Number of students that do only exactly one subject are;

For Art;

⇒ 24 - (3 + 4 + 3)

⇒ 14

For Chemistry;

⇒ 22 - (3 + 5 + 3)

⇒ 11

For Bio;

⇒ 20 - (3 + 4 + 5)

⇒ 8

Number of students that do at least two of the subjects are;

⇒ 3 + 3 + 4 + 5

⇒ 15

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^answer:^

~10 cubic feet~

^step by step explanation:^

first, calculate the volume of the front “panel” of the shape. (5 cubic centimeters because 5 times 3 is 15 and 15 times 1/3 is 5. 5 times 2 is 10.

The factors of the given equation x³ - 2x² - 5x + 6 is (x - 1)(x + 2)(x - 3) with the help of synthetic division.

Let f(x) = x³ - 2x² - 5x + 6

Substitute x = 1

f(1) = (1)³ - 2(1)² - 5(1) + 6

⇒ f(1) = 1 - 2 - 5 + 6

⇒ f(1) = -1 + 1

⇒ f(1) = 0

As x = 1 is the root of the given equation therefore one of the factor of the given equation is (x-1)

Now use long division method, we get (x² - x - 6) as another factor.

⇒ f(x) = (x - 1)(x² - x - 6)

⇒ f(x) = (x - 1)(x² - 3x + 2x - 6)

⇒ f(x) = (x - 1)(x(x-3) + 2(x-3))

⇒ f(x) = (x - 1)(x - 3)(x + 2)

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if you dog like something

Equivalence Relation is a type of Relation that satisfies the property of Reflexive , Symmetric and Transitive , and an example of such relation is [tex][(1, 1), (1, 3), (2, 2), (2, 4), (3, 1), (3, 3), (4, 2), (4, 4)][/tex] .

What is an Equivalence Relation ?

A relation R on a set A is can be called as an equivalence relation if and only if the relation is reflexive, symmetric and transitive.

It is a relationship on the set which is represented by symbol “∼”.

(i) Reflexive: A relation is termed as reflexive, if [tex](a, a) \in R[/tex], for every [tex]a \in A[/tex].

(ii) Symmetric: A relation is termed as symmetric, if [tex](a, b) \in R[/tex] , then [tex](b, a) \in R[/tex] .

(iii) Transitive: A relation is termed as transitive if [tex](a, b) \in R[/tex] and [tex](b, c) \in R[/tex], then [tex](a, c) \in R[/tex] .

An Example of Equivalence Relation is [tex][(1, 1), (1, 3), (2, 2), (2, 4), (3, 1), (3, 3), (4, 2), (4, 4)][/tex] because ;

(i) [tex][ (1, 1),(2, 2), (3, 3), (4, 4) ] \in R[/tex] , So , R is Reflexive .

(ii) [tex](2,4) \in R[/tex] and [tex](4,2)\in R[/tex] , Thus ,  relation given by R is Symmetric .

(iii) [tex](3,1) \in R[/tex] and [tex](1,3) \in R[/tex] ⇒ [tex](3,3) \in R[/tex] , So R is Transitive .

Therefore , the Relation given by R is Equivalence Relation .

The given question is incomplete , the complete question is

What is Equivalence Relation and its Example ?

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Therefore , the solution of the given problem of triangle comes out to be  A'(1, 0) (1, 0) , B'(1, 2) (1, 2) and C'(3,-2) (3,-2).

The fact that a triangle has four segments or vertices qualifies it as a polygon. It is an elementary geometric form. The name given to a triangle with endpoints A, B, then C is Triangle ABC. A singular plane and square are obtained in Euclidean geometry when the edges are not collinear. Any triangle that has three sides and three corners is a polygon. The triangle's corners are the spots at which its three sides intersect. 180 degrees is the result of three triangle angles.

Here,

The image A'B'C' is formed by our transformation rule, (+3,y-2)

So:

1. Describe the updated coordinates for points A', B', and C'?

In order to locate these new positions, we have:

A' (-23, 2-2)  =>    A'(1, 0) (1, 0)

B' => (-23, 4-2)    =>   B'(1, 2) (1, 2)

C'=> (0+3,0-2) => C'(3,-2) (3,-2)

2. Explain the qualities that would emerge if the respective vertices were linked together by lines.

We can notice the two triangles on the First Figure if we look closely. The green one is A'B'C, while the red one would be the triangle ABC.

The equivalent vertices with in second figure have been joined together by line segments, as shown by the green lines.

Two things can be said about those three lines: first, they are parallel, and second, they are all the same length.

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Step-by-step explanation:

in an isoceles triangle (both legs have identical length) the height from the top corner to the baseline shots the baseline into 2 identical halves.

so,

6x + 6 = 9x - 15

6 = 3x - 15

21 = 3x

x = 21/3 = 7

many greetings to your teacher from me : he/ she made a formal mistake. the angles at Y have to be indicated as right angles. because if the line WY is not the height but could have any angle with the baseline, this cannot be solved.

Enlargements of the picture or reductions of the image are both types of dilations.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.

A dilation is a transformation that yields a different-sized picture with the same general shape as the original. Enlargements are dilations that result in a bigger picture. Reduction is the name for a dilatation that shrinks the picture. The initial figure is stretched or contracted by a dilatation.

The angles of the dilated picture relative to the pre-image stay constant, which is one of the primary characteristics of dilated images.

Even in the enlarged picture, parallel and perpendicular lines are still discernible.

A dilated image's side's midway matches the pre-exactly. image's

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The longer ladder can reach 3 8/7 feet higher than the shorter one.

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Using long division convert 1/4 to a decimal

To convert a fraction into a decimal, we'll just divide the numerator by the denominator:

4√1

we'll divide 1 by 4.

1 divided by 4 equals 0

0

4√1

To keep dividing, we'll add a decimal point and a zero after the 1, we'll also add a decimal point after the 0 on top

0.

4√1.0

Now we can divide 10 by 4, 10 divided by 4 equals 2.

0.2

4√1.0

Now we'll multiply 4 by 2, 4 times 2 equals 8. So we'll subtract 8 from 10.

0.2

4√1.0

-8

______

2

Since 2 is greater than 0, we're not finished dividing yet. We'll add another 0 after the decimal point and bring it down.

0.2

4√1.00

-8

________

20

20 divided by 4 equals 5.

0.25

4√1.00

-8

______

20

Now we'll multiply. 4 times 5 equals 20. When we subtract 20 from 20, we get 0. The 0 means we're done dividing.

0.25

4√1.00

-8

______

20

20

________

0

So 1/4 is equal to 0.25.

The answer is no, we would not be surprised if the sample mean housebroken age for the small breed dogs is at least 3 months more than the sample mean housebroken age for the large breed dogs, as the probability of this happening is very small, 2.28%.

    z = (3-2) / 0.5 = 2

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Therefore , the solution of the given problem of unitary method comes out to be total amount spent by Ria £129.58.

By multiplying the value about one unit by the quantity of units required, one can apply the unit technique to solve a problem. The unit procedure is used to separate a single entity integer from a given many, to put it simply. One pen, or 400 rupees, would be needed to purchase 40 needle. There might be a common way to verify this. only one nation. Anything has a unique feature. Algebra, grid logic, and its laminates and reverse are all identical terms used to describe mathematical analysis.

Here,

Given : Ria purchases 19 books for £6.82 apiece.

Thus,

Total cost of book = 19 * 6.82

=> 129.58

Therefore , the solution of the given problem of unitary method comes out to be total amount spent by Ria £129.58.

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On solving the provided question, we can say that - sequence (0.67,3-√4,√8,0.14) are the  rational, real, integer, irrational, irrational.

A sequence is a collection of numerals (referred to as "terms"), for example, 2, 5, 8. A specific pattern that some sequences follow may be leveraged to make them infinitely long. To continue the series, add 3 and use the example of 2,5,8. Formulas that show where to look for words inside a sequence can be found there. Informally, a sequence in mathematics is a collection of items that are in some order (or events). It has components, much like a set (also called elements or terms). The length of the sequence refers to the total, potentially unlimited number of ordered items. arranging two or more objects in a logical sequence. Chronological.

here,

the given sequence is (0.67,3-√4,√8,0.14)

as we can see that in the sequence we have a rational number, integer, real number and a irrational so,

the answer is  rational, real, integer, irrational, irrational.

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Step-by-step explanation:

please see the attachment

Two-way table showing meal pairings with frequency of salad, soup, chicken and fish.

Meal Pairing Salad Soup Chicken Fish

Frequency  46.          32.           ?. 35

To calculate the frequency of chicken, subtract the frequency of salad and fish from the total of 78 meals.

Frequency of chicken

= 78 - 46 - 35

= 27.

Meal Pairing Salad Soup Chicken Fish

Frequency 46.           32.            27. 35

The total number of meals served is 78. Of the 46 meals that included salads, 21 also included fish. This means that the frequency of fish is 35. The frequency of chicken can be calculated by subtracting the frequency of salad and fish from the total number of meals. The frequency of chicken is 27. The two-way frequency table representing this situation is as follows: Meal Pairing, Salad, Soup, Chicken, Fish; Frequency, 46, 32, 27, 35. This table shows that there were 46 meals with salad, 32 meals with soup, 27 meals with chicken, and 35 meals with fish.

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Answer:

Step-by-step explanation:

Given isosceles triangle ABC with AB≅AC, altitude AP, and AB=(2x+3), AC=(3y-1), BP=(y+1), and PC=(x+2), you want the values of x and y.

Corresponding parts of ∆ABP and ∆ACP are congruent, so we have ...

  2x +3 = 3y -1

  x +2 = y +1

Subtracting twice the second equation from the first gives ...

  (2x +3) -2(x +2) = (3y -1) -2(y +1)

  -1 = y -3 . . . . simplify

  2 = y . . . . . . add 3

Substituting into the second equation, we have ...

  x +2 = 2 +1

  x = 1 . . . . . . . .subtract 2

The values of x and y are 1 and 2, respectively.

Answer:

yes, it uses the Commutative Property

Step-by-step explanation:

The 3 types of terms in quadratic equation:

1) quadratic term,

2) linear term,

3) constant term.

We know that the second degree algebraic equation in x is a quadratic equation.

The standard form of quadrtic equation is ax^2 + bx + c = 0, where a, b, c are integers.

As thise is a quadratic equation, the value of a can not be zero. a ≠ 0

The term ax^2 is called the quadratic term.

From this term, the name given to the equation(quadrtic equation)

The term bx is called the linear term.

And the term c is called the constant term.

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Using the normal distribution and the central limit theorem, it is found that there is a 0.0901 = 9.01% probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50.

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Therefore, the sine of any angle can also only be between -1 and 1, inclusive.

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located.

Lines (line segments) and points make up the forms we perceive (vertices). To create a shape, these line segments are connected at their vertices. These lines' sides are what they are known as. The line segment that connects two vertices of a form or two-dimensional object is referred to as a side in geometry.

The sine of an angle can never be greater than 1 because the sine function maps an angle to the y-coordinate of the point on the unit circle that corresponds to that angle. The y-coordinate of any point on the unit circle is always between -1 and 1, inclusive. Therefore, the sine of any angle can also only be between -1 and 1, inclusive.

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No, the segments will not form a triangle based on the line segments provided.

For three line segments to form a triangle, they must satisfy the triangle inequality theorem. The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides of the triangle must be greater than the length of the third side.

This is because if the sum of the lengths of any two sides is less than or equal to the third side, it would not be possible to form a triangle with those side lengths, as the two shorter sides would not be able to reach the longer side to form the triangle.

In this case, the sum of the two shorter segments (12 units + 10 units) is 22 units, which is less than the measure of the longest segment (18 units). Therefore, the three segments will not form a triangle.

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In mathematics, a plane is a two-dimensional surface that can be enlarged indefinitely. In order to make a plane we need at least 3 points.

In order to make a plane we need at least 3 points. Let A, B and C are three points which can be defined by two particular vector AB and AC.

As the two vectors is located on the plane, we can use their cross product to define a normal vector on the plane.

As we see a triangle which is a two-dimensional geometric figure that is developed based on 3 points. Triangle is the smallest polygon. The other polygon needs more point for creation.

Therefore, it is proved that minimum three points is mandatory for plane formation.

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Linear graphs have the following form: y = mx + b, where m is the slope of the line and b is the y-intercept.

To calculate the slope, you can use the formula m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Exponential graphs have the following form: y = ab^x, where a and b are constants. To calculate the constants, you can use the formula y = a + b^x, where (x, y) are two points on the graph and a is the y-intercept.

Quadratic graphs have the following form: y = ax^2 + bx + c, where a, b, and c are constants. To calculate the constants, you can use the formula y = ax^2 + bx + c, where (x, y) are two points on the graph and c is the y-intercept.

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Answer:

50

Step-by-step explanation:

angleQPR=50

becauseQR=RP

so angleRQP=RPQ

x=50

Answer:

50

Step-by-step explanation:

angle QPR = 50 because QR= rp

The angle of elevation of the ramp is 28.6 degrees.

Tan = (Change in Height) / (Length of Ramp)

Therefore, using the given information, the angle of elevation of the 23-foot ramp is:

Tan = (6 feet) / (23 feet)

Tan = 0.26

= 14.5° (to the nearest tenth of a degree)

Therefore, the angle of elevation of the 23-foot ramp is 14.5°.

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Answer:

Step-by-step explanation:

(9a⁴b⁷) x (6a³b⁸)

(9 x 6) x (a⁴ x a³) x (b⁷ x b⁸)

54 x a⁷ x b¹⁵ = 54a⁷b¹⁵

Answer:

(9a⁴b⁷).(6a³b⁸)

=54a⁷b¹⁵

The constant term in the expression 2x + 3 is 3.

The term expression in math is called as the algebraic expression consists of unknown variables, numbers and arithmetic operators.

Here we have the expression 2x + 3.

Now, we have to find the constant term in the expression.

As per the definition of expression, we know that the expression has two part one is variable part and the remaining second part is the constant parts.

As the name suggest, the variable part contains the unknown value like x, y etc. that changes value of the expression depending upon the given value.

Another term is constant, where its value can't be changed.

While we looking into the given expression here we have identified that

=> 2x is the variable term because the value of the term is changed based on the value of x.

Therefore, the constant term is 3.

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Pam's piece rate is $16.67 for every pot she produces.

A rate is a type of ratio that compares two values with distinct units. A rate is expressed as a fraction.

Pam's piece rate is the amount of money she earns for each pot she makes. In this case, she earned $250 for making 15 pots, so her piece rate is:

$250 ÷ 15 pots = $16.67 per pot

Therefore, Pam earns $16.67 for each pot she makes. This is a way of calculating her pay based on the number of units she produces, rather than by the hour.

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Answer: x=-6

Step-by-step explanation:

[tex]\displaystyle\\2^{2x-1}*(\frac{1}{8} )^{1-x}=4^{3x+1}\\\\2^{2x-1}*8^{(-1)(1-x)}=(2^2)^{3x+1}\\\\2^{2x-1}*(2^3)^{x-1}=2^{2*(3x+1)}\\\\2^{2x-1}*2^{3*(x-1)}=2^{6x+2}\\\\2^{2x-1}*2^{3x-3}=2^{6x+2}\\\\2^{2x-1+3x-3}=2^{6x+2}\\\\2^{5x-4}=2^{6x+2}\\\\Hence,\\\\5x-4=6x+2\\\\5x-4-2=6x+2-2\\\\5x-6=6x\\\\5x-6-5x=6x-5x\\\\-6=x\\\\Thus,\ x=-6[/tex]

Answer:

Step-by-step explanation:

We have:

2^(2x-1) x [1/8]^(1-x) = 4^(3x+1)

2^(2x-1) x [1/2³]^(1-x) = 2²^(3x+1)

2^(2x-1) x 2^-3+3x = 2^6x+2

2^5x-4 = 2^6x+2

on comparing both sides we get :

5x-4 = 6x +2

x = -6