Learning task 3

A. illustrate the following conditional statement in venn diagram

1. If it is a rectangle, it is a quadrilateral.

2. If you play violin, then you are a musician.

3. If frogs live in water, then they are amphibians.

4. If it is a fraction, then it is a rational number.

5. If it is an eagle, then it is a bird.

B. Interchange the conclusion and hypothesis with the resulting conditional statement true or false? Why?

Ex:
1. If it is an eagle then its a bird

If it's a bird then it's an eagle.

The resulting statement is not true since not all birds are eagle.

2.If it is an equiangular, then it's an equilateral.

3. If it is a rectangle then it is a quadrilateral.

m = 2.58 b is a linear function that models the scenario as stated.

A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph.

Given, At the bakery, loaves cost $2.58 each. The total money spent at the bakery (m) is equal to the product of 2.58 and the number of loaves of bread that were bought (b).

Linear Function for the given condition

(Since all money is spent on the loaves)

m = 2.58 b

Therefore, a Linear function that models the given situation is m = 2.58 b.

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We can find log without a calculator by using the some formula like:

log(a×b) = loga + logb

log(ab) = loga - logb

The power of 10 that must be raised in order to equal a given number is known as its logarithm. Simple illustrations:

[tex]10^2[/tex] = 100 , therefore log100 = 2

[tex]10^3[/tex] = 1000, therefore log1000 = 3

log200 = 2.301 (between log100 and log1000)

Mathematicians learn that the following are always true:

log(a×b) = loga + logb

log(ab) = loga - logb

Select a number that you can generate using factors whose logarithms you have learned, and that is very close to the original number.

Determine this estimated number's logarithm.

Determine the error percentage, multiply it by log1.01=0.00432 and then add or remove as necessary.

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150 pounds of candy priced at 45 dollar should be coupled with 200 pounds of candy priced at 80 dollar .

As different sweets are not distributed evenly, a mixture of various candies in a container is an example of a heterogeneous mixture. In addition, since the particles of various sweets do not interact, different candies are visible with the eye.

Let "x" stand for the number of pounds of candy costing 45 Dollar per pound, and "(350-x)" for the number of pounds of candy costing 80 Dollar per pound. The decimal equivalents of 45, 80, and 65 Dollar are 0.45, 0.80, and 0.65.

350*0.65=0.45x+(350-x)0.80

Solve it for x

x=150

350-150=200

Thus, 150 pounds of candy priced at 45 cents should be coupled with 200 pounds of candy priced at 80 cents.

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The value of a polynomial at a particular point is defined as the value that the provided function yielded at that moment.

As an illustration, consider the polynomial function (x) = x + 1.

When x = 1 for example, the polynomial at that point is given by P(1) = 1+1 = 2.

Consequently, the polynomial P(x) has a value of 2 when x equals 1.

'What are polynomials?'

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.

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The ratio in which the point (2,-3) divides the line segment joining the points (-1,3) and (4,-7) is 3:2  .

If the line segment that have the end points as [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] is divided by the point (x,y) in the ratio m:n , then the coordinate of the  point (x,y) is  [tex](\frac{mx_{2} +nx_{1} }{m+n} ,\frac{my_{2} +ny_{1}}{m+n} )[/tex] ;

the coordinate of the end points are given as : (-1,3) and (4,-7) ;

the point that divided the line segment is (2,-3) ;

On applying the above formula ,

we get ;

⇒ [tex]2 = (\frac{m\times 4 +n\times (-1) }{m+n} )[/tex] ;

⇒ 2(m+n) = 4m - n  ;

⇒ 2m [tex]+[/tex] 2n [tex]=[/tex] 4m - n ,

⇒ 4m - 2m = 2n + n ;

⇒ 2m = 3n ;

⇒ we get the ratio as m : n = 3 : 2  .

The given question is incomplete , the complete question is

What is the ratio in which the point (2,-3) divides the line segment joining the points (-1,3) and (4,-7) ?

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The right triangle shown in the figure is solved to get the dimensions as

c.

Angle B = 60 degrees, Side B C = 4 Start Root 3 End Root meters, Side A B = 8 Start Root 3 End Root meters

The dimension of the right triangle is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

Information from the question

opposite = a

adjacent = 12

hypotenuse = c

The opposite is calculated using tan, TOA

tan 30 = Opposite / Adjacent

tan 30 = a / 12

a = 12 * tan 30

a = BC = 4√3

The hypotenuse is calculated using cos, CAH

cos 30 = Adjacent / hypotenuse

cos 30 = 12 / c

c = 12 / cos 30

c = AB = 8√3

< A + < B + < C = 180 (sum of angles in a triangle)

30 + < B + 90 = 180

< B = 60

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The necessary information which is missing from this formula page is none of the above and is denoted as option D.

This is referred to as a sheet or page which helps a student recall formulas so that they can solve test items independently.

In the example given,  t-time V = d/t d-distance V = distance/time v-velocity and the meaning of their respective abbreviations were given for better explanation. We should note that a formula page lacks numerical values as only the formula for the parameter is given is contained which is why none of the above was chosen as the correct choice.

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Answer:

5 ft x 7 ft

Step-by-step explanation:

60/5 = 84/x

cross multiply to solve for x

60x = (84)(5)

60x = 420

x = 420/60 = 7

A right angle is an angle that measures exactly 90 degrees.

A right angle is an angle that is exactly equal to 90 degrees (or π/2) in measure.

We can see many real-life examples of the right angles in our daily life. For example, the corner of a book, edges of the cardboard, etc.

Any shape that is a square or a rectangle, will have its corners equal to 90 degrees or right angle.

A right angle is hence called a 90-degree angle.

In geometry, the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle is known as an angle.

Angles created by two rays lie in the plane that contains the rays.

The intersection of two planes also forms angles.

The angle is also used to designate the measure of an angle or a rotation.

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Answer: 43.96 [tex]m^{2}[/tex]

Step-by-step explanation:

Diameter = 14m

Circumference = D * pi = 14 * 3.14 = 43.96

Answer:

Step-by-step explanation:

To find the circumference of a circle, the formula is 2πr or πd.

So you have 14π or 43.96 meters

Answer:43.96 meters

Answer:he degree of the polynomial 3x 8 + 4x 3 + 9x + 1 is 8. We know that the polynomial can be classified into polynomial with one variable and polynomial with multiple variables

Step-by-step explanation:

The total number of seeds that Val is going to plant will be 5b + 8.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Val is going to plant b vegetable seeds in one garden and 4 b plus 8 vegetable seeds in another.

Then the total number of seeds that Val is going to plant will be calculated as,

⇒ b + 4b + 8

Simplify the expression, then we have

⇒ b + 4b + 8

⇒ 5b + 8

The total number of seeds that Val is going to plant will be 5b + 8.

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Answer:

The last one(D)

Step-by-step explanation:

-1×-1=1

1*3=3

____

9*1=9

12-9=3

Answer: hello person.

This is a system of equations problem that can be solved using substitution.

Let x be the number of pennies

Therefore the number of dimes is also x.

The number of quarters is 44 - 2x

The total value of the pennies is x * 0.01 = $0.01x

The total value of the dimes is x * 0.1 = $0.1x

The total value of the quarters is (44 - 2x) * 0.25 = $11 - 0.5x

Now we know that the total value is $0.01x + $0.1x + $11 - 0.5x = $3.59

So we can write the equation:

0.01x + 0.1x + 11 - 0.5x = 3.59

Now we can solve for x

0.6x + 11 = 3.59

0.6x = -7.41

x = -12.35

We know that x is the number of pennies and dimes. Since it is not a whole number, it is not possible.

We can think of another approach, assuming that x is the number of dimes and pennies, and y is the number of quarters.

x + y = 44

0.1x + 0.25y = 3.59

Now we can solve for x and y by substitution method.

x = 44 - y

0.1(44 - y) + 0.25y = 3.59

4.4 - 0.1y + 0.25y = 3.59

4.4 = 0.35y + 3.59

0.81 = 0.35y

y = 2.3

x = 44 - 2.3 = 41.7

We know that x and y must be whole numbers. Since x and y are not whole numbers it is not possible.

Hence, there is no possible number of coins for Carlos to have for the given scenario.

Step-by-step explanation:

So, the volume of the can in cubic centimeters is 61.99 cm^3. If we round to the nearest tenth, the volume of the can is 62 cm^3.

A can of soda can be modeled as a right cylinder, which is a three-dimensional geometric shape with two circular bases that are connected by a curved surface. The volume of a cylinder can be calculated using the formula:

V = πr^2h

Where V is the volume, π is a constant (approximately equal to 3.14), r is the radius of the base and h is the height of the cylinder.

Given that the radius of the can is 2.6 cm and the height is 9.2 cm, we can substitute these values into the formula:

V = π (2.6 cm)^2 (9.2 cm)

To get the area of the base we need to square the radius and multiply by π, and then multiply it by the height to get the volume.

V = π * 6.76 * 9.2 = 61.99 cm^3

So the volume of the can in cubic centimeters is 61.99 cm^3. If we round to the nearest tenth, the volume of the can is 62 cm^3. This means that the can can hold 62 cubic centimeters of liquid.

It's worth noting that this is an approximation and the real value of π is not 3.14. Also, this answer is based on the assumption that the can is a perfect cylinder with no other gaps or spaces.

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Answer:

The equation of a pair of straight lines parallel to a given pair of lines can be found by adding a constant multiple of the given equation to itself.

Given equation is x²+2xy+y²-2x-2y-15.

To find the equation of the pair of lines parallel to this equation, we can add a constant multiple of the equation to itself.

so adding k(x²+2xy+y²-2x-2y-15) to x²+2xy+y²-2x-2y-15, we get

(1+k)x²+(2+2k)xy+(1+k)y²-(2+2k)x-(2+2k)y-(15+15k) = 0

As these lines pass through the origin so the equation will be

(1+k)x²+(2+2k)xy+(1+k)y² = 0

This is the equation of the pair of lines parallel to the lines represented by the equation x²+2xy+y²-2x-2y-15 and passing through the origin.

Before the discount, the price of the table was $112.5.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the discount of 64% and the final sale price will be $72.

Assume the original price be {x}. Then, we can write -

72 = 64% of {x}.

72 = (64/100) x {x}

{x} = (72 x 100)/(64)

{x} = 7200/64

{x} = 112.5

Therefore, before the discount, the price of the table was $112.5.

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Standard form of polynomial  [g(x)-f(x)]  is   2[tex]x^{4}[/tex] -3/5[tex]x^{2}[/tex]+2x+7.

Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5. Finding both intercepts of the equation in this format is rather simple (x and y).

A polynomial example is 4 x 3 + 2 x 2 3 x + 1. There are four terms: 1, 4 x 3, 2 x 2, and 3 x. The coefficients are the numbers that are written in front of each variable in a phrase. Because those numbers appear in front of a variable, 4, 2, and -3 are coefficients.

polynomial [g(x)-f(x)] = 8+ 1/5[tex]x^{2}[/tex]+3x+2 -( -2[tex]x^{4}[/tex] -1 + 4/5[tex]x^{2}[/tex] -x )

                                   2[tex]x^{4}[/tex] -3/5[tex]x^{2}[/tex]+2x+7

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To see the steps of Solutions Using Substitution with Two Variables.

Now, According to the question:

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.

Linear Equations: Solutions Using Substitution with Two Variables

To solve systems using substitution, follow this procedure:

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If the computed upper deviation rate (sample deviation rate projected to the population and adjusted for sampling risk) exceeds the tolerable deviation rate during a compliance test that utilizes statistical sampling,

it means that the test results indicate, the population of items being tested is not in compliance with the standards or regulations.

There are several actions that the auditor could take in this situation, depending on the specific circumstances of the test and the nature of the non-compliance. These are:

Note that: the specific course of action will depend on the nature of the non-com pliance and the regulations or standards that apply. It is recommended that the debtor consults with legal or regulatory experts to ensure that they are taking the appropriate actions to address the non-compliance.

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The line crosses the Oy axis in A(0,  y), so x=0 and we have:

y + 4=11 ⇒ y = 7

Y is equal to 7 at the line's intersection with the y-axis.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

The point where the line crosses the y-axis is when x = 0. To find the value of y at this point,

we can substitute x = 0 into the equation and solve for y:

y + 4 = 6(0) + 11

y + 4 = 11

y = 11 - 4

y = 7

Therefore, the value of y at the point where the line crosses the y-axis is 7.

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Answer:

3060 US$

2,829.28 EU$ <—- I only added this because i live in EU.

Step-by-step explanation:

Answer: 530

Step-by-step explanation:

you need to put 4/5 then put 424/x then you multiply across and take 5x424 then devide your answer by 4 and get X=530

Answer: 7 and -5 OR -35 and 1

Also could you mark my answer as brainliest? It helps and doesnt hurt

To find the vertex in factored form, the easiest method is to find the axis of symmetry, substitute that in as x and solve for y. The axis of symmetry can be estimated by the formula: x = (r + s)/2. r and s are the zeros. x is the axis of symmetry that is the x-component in the vertex.

The axis of symmetry is a straight line that causes the shape of the object symmetrical. The axis of symmetry makes the exact reflections on each of its sides. It can be horizontal, vertical, or lateral. If we fold and unfold an object along the axis of symmetry, then the resulting two sides are identical.

The equation of the axis of symmetry can be expressed when a parabola is in two forms:

Standard form

The quadratic equation in standard form is, y = px² + qx + r

where p, q, and r are the real numbers.

The axis of the symmetry formula of the standard form is x = - q/2p.

Vertex form

The quadratic equation in vertex form is, y = a (x-p)² + q

where (p, q) is the vertex of the parabola.

The axis of the symmetry formula of the vertex form is p = q.

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No. The corresponding pairs of sides must also be marked  congruent to determine that the triangles are congruent.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

Explanation:

The arc markings tell us how the angles pair up, and which pairs are congruent. Eg: The double-arc angles are the same measure.

Despite knowing that all three pairs of angles are congruent, we don't have enough information to conclude the triangles are congruent overall. We can say they are similar triangles (due to the AA similarity theorem), but we can't say they are congruent or not. We would need to know if at least one pair of sides were congruent, so that we could prove the triangles congruent.

The list of congruent theorems is

SSS

ASA

AAS (or SAA)

SAS

HL

LL

Much of these involve an "S", to indicate "side" (more specifically "pair of sides). Both HL and LL involve sides as well. They are special theorems dealing with right triangles only.

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Answer:

Step-by-step explanation:

First, put the equation of the line given into slope-intercept form by solving for y. You get y = -2x +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6.

An exponential function is a function of the form y = ab^x, where a and b are constants, and x is the input variable.

In this case, the input variable is t, the number of years since the purchase, and the output variable is y, the resale value of the laptop computer.

We are given that the resale value decreases by 29% each year, so we can express the decrease as a decimal by dividing 29 by 100: 29/100 = 0.29

The relationship between y and t can be written as:

y = 1050(1 - 0.29)^t

In this function, 1050 is the initial value, 1-0.29 is the decreasing factor, and t is the number of years since the purchase. This function shows the relationship between y and t, that is the resale value of the laptop computer in relation to the number of years since the purchase.

The difference between a bar graph and a histogram is that of  b. a bar graph displays categorical data, while a histogram displays quantitative data.

A bar graph is majorly used to compare different categories or groups of data. It displays data in separate bars, each representing a different category. A histogram, on the other hand, is used to display the distribution of a continuous quantitative variable. It shows the frequency of different values within a range of values by using bars of different heights. The bars in a histogram are also adjacent to each other, with no space between them.

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The composite figure has an area of 26 square units.

In this question we find a composite figure formed by the sum of the areas of two right triangles and rectangles, whose area formulas are shown below:

Right triangle

A = 0.5 · w · l

Rectangle

A = w · l

Where:

Now we proceed to determine the area of the composite figure:

A = 0.5 · 3 · 1 + 3 · 1 + 0.5 · 3 · 1 + √10 · √40

A = 1.5 + 3 + 1.5 + 20

A = 26

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