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The expression which relates the total time taken and the time taken for the trip is [15s + 15(s+2)] / s² + 2s and 2.32 hours respectively.

Travel time = distance ÷ speed

Second half of the trip :

Time taken for second half of trip :

Time taken = 15 / s

First half of the trip :

Time taken for first half of trip :

Time taken = 15 / (s+2)

Total time taken :

First half + second half

15/(s+2) + 15/s = [15s + 15(s+2)] / s² + 2s

B)

If s = 12

Substitute s = 12 into the expression :

[15(12) + 15(12+2)] / 12² + 2(12)

[180 + 210] / 144 + 24

390 / 168

= 2.32 hours

Therefore, the total time taken is 2.32 hours.

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The equivalent expression of the different of two square is -1

Given the following expressions

a cot α = 1

a = 1/cot α = sinα/cosα

b = 1/cos α

We are to find the expression a² - b²

According to difference of two squares;

a² - b² =  (a + b) (a - b)

Substitute the given expressions into the formula as shown:

[tex]a^2 - b^2 = (\frac{sin \alpha}{cos \alpha} )^2 - (\frac{1}{cos \alpha} )^2\\a^2 - b^2=\frac{sin^2 \alpha}{cos^2 \alpha} -\frac{1}{cos ^2 \alpha}\\a^2 - b^2=\frac{sin^2 \alpha-1}{cos^2\alpha}\\a^2 - b^2=\frac{-(1-sin^2\alpha)}{cos^2\alpha} \\a^2 - b^2=\frac{-os^2 \alpha}{cos^2 \alpha}\\a^2 - b^2 = -1[/tex]

This shows that the equivalent expression of the difference of two squares is -1

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Answer:

i dont know if i did this right buut

Step-by-step explanation:

Answer:

If you were to create a scatterplot using sample ages such as : (30,32),(33,35),(47,49), etc. You will begin to see a perfect linear relationship, which would mean the correct correlation is 1.

(hope it helps! <3)

Answer:

...

Step-by-step explanation:

Answer:

Step-by-step explanation:

A) ∠1 =  ∠2   {Alternate angles are equal}

6x + y - 4 = x - 9y  + 1

6x + y      = x - 9y + 1 + 4

6x + y      = x - 9y + 5

6x - x  + y + 9y = 5

  5x  + 10y = 5

Divide the entire equation by 5

  x  + 2y = 1 -------------(I)

∠2 + ∠3 = 180       {Linear pair}

x - 9y + 1 + 11x + 2 = 180

x + 11x - 9y   = 180 - 2 - 1

          12x - 9y = 177

Divide the whole equation by 3

       4x - 3y  = 59    -------------(II)

B) Multiply equation (I) by 3 and multiply equation (II) by 2. Thus y will be eliminated and we can find the value of x.

(I)* 3           3x + 6y = 3

(II)*2           8x - 6y =  118    {Now add}

                  11x        = 121

                            x = 121/11

x = 11

Plugin x = 11 in equation (I)

                            11 + 2y = 1

                                  2y = 1 -11

                                  2y = -10

                                   y = -10/2

y = -5

C) ∠1 = 6x + y - 4

         = 6*11  - 5 - 4

          = 66 - 5 - 4

           = 57

∠2  = x - 9y + 1

        = 11 -9*(-5) + 1

         = 11 + 45 + 1

          = 57

∠3 = 11x + 2

      = 11*11 + 2

      = 121 + 2

      = 123

Answer:

B is the answer

Step-by-step explanation:

Answer: The front face has an area of 30 ft2. , The top face has an area of 40 ft2. ,

Step-by-step explanation: SOrry if im wrong

Answer: A, C, D

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Given is an isosceles triangle and so:

3x + 20 = 5x export like terms to the same side of the equation

20 = 5x - 3x

20 = 2x divide both sides by 2

10 = x

Answer:

$16.25

65% = 0.65

0.65 x $25 = $16.25

Hope this helps! (And I think thats what the question was)

Please find attached photograph for your answer.

Hope it helps

ray4918 here to help.

Amount of tax paid = 43-40 = 3

Tax rate = 3/40 = 0.75

0.75 x 100 = 7.5%

Tax rate = 7.5%

Answer:

[tex]\sqrt{18} + \sqrt{32} - 3 \sqrt{8} = \\ = \sqrt{9 \times 2} + \sqrt{16 \times 2} - 3 \sqrt{4 \times 2} \\ =3 \sqrt{2} + 4 \sqrt{2} - 3 \times 2 \sqrt{2} \\ = 3 + 4 - 6 \sqrt{2} \\ = 7 - 6 \sqrt{2} \\ = 1 \sqrt{2} [/tex]

Semoga membantu

Answer:

[tex]\sqrt{18} + \sqrt{32} - 3 \sqrt{8} = 1 \sqrt{2} [/tex]

Answer:

a regular pentagon has 72 degrees

Step-by-step explanation:

Answer:

y=2x-6

Step-by-step explanation:

The intercept is -6 so -6 and you take two points on the line e. g. (3,0) and (2,-2) You would do -2-0 to get -2 and 2-3 to get -1. -2 divided by -1 equals 2. The slope is two.

Answer:The area of the field is 57600 square feet.

Step-by-step explanation:

Answer:

57600 square feet.

Step-by-step explanation:

360 x 160 = 57600.

Answer:21600

Step-by-step explanation:

Multiply 60 by 2, then by 3. Add 120 and 180 to get 21600.

Answer:

43.57

Step-by-step explanation:

Line up the decimal points.

Add a 0 for 1.07 so the numbers have the same length.

01 . 0 7

42. 5 0

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

43.57

Answer:

1.07+42.5

=1.07+42.5

=43.57

Step-by-step explanation:

Add the numbers

Make 42.5 equal to 42.50 for better understanding when calculating

Step-by-step explanation:

Total amount is:

If the numbers are correct ₱500 won't be enough as the total amount exceeds it.

Mother bought 3 cans of sardines at ₱17.80 each, 5 cans of milk at ₱38.85 each, 3kg sugar at ₱60.50 each, and 2 cans of corn beef at ₱78.85 each. Find the total amount bought. If she paid ₱500 bill, find her change.

Mother bought 3 cans of sardines at ₱17.80 each, 5 cans of milk at ₱38.85 each, 3kg sugar at ₱60.50 each, and 2 cans of corn beef at ₱78.85 each.

The total amount for which she had brought the items

= ₱ (3×17.80 + 5×38.85 + 3×60.50 + 2×78.85)

= ₱ (53.40 + 194.25 + 181.50 + 157.70)

= ₱ 586.85

The total amount for which she had brought the items is ₱ 586.85.

I cannot solve the second part of the sum because the amount exceeds ₱ 500.

Hope it helps

Answer:

AHHHH I LOVE YOUR PROFILE PICTURE GOKU IS THE BEST <3 :D

Answer:

1) 1085 ÷ 7

7 )1085(155

- 7

38

- 35

× 35

- 35

0

1085 ÷ 7 = 155

2) 7104 ÷ 32

32 )7104(222

- 64

× 70

- 64

×64

- 64

××

7104 ÷ 32 = 222

3) 2244 ÷ 51

51)2244(44

- 204

×244

- 244

×××

2244 ÷ 51 = 33

4) 1584 ÷ 12

12)1584(132

- 12

×38

- 36

×24

- 24

××

1584 ÷ 12 = 132

5) 1467 ÷ 9

9)1467(163

- 9

56

- 54

27

- 27

××

1467 ÷ 9 = 163

6) 2830 ÷ 28

28)2830(101

- 28

××3

- 0

30

- 28

×2

2830 ÷ 28 = 101 with the remainder 2

7) 9090 ÷ 45

45)9090(202

- 90

××9

- 0

90

- 90

××

9090 ÷ 45 = 202

8) 7000 ÷ 62

62)7000(112

- 62

×80

- 62

180

- 125

×55

7000 ÷ 62 = 112 with the remainder 55

9) 1150 ÷ 15

15)1150(76

- 105

×100

- 90

10

1150 ÷ 15 = 76 with the remainder 10

Hope that my answer is right and helpful to you

Answer:

If the two random variables are independent, the covariance will be zero. It means they don't have any linear relationship.

Step-by-step explanation:

Answer:

C and B

Step-by-step explanation:

(6)

[tex]\frac{3x-7y}{8}[/tex] × [tex]\frac{6}{3x-7y}[/tex] ← cancel 3x - 7y on numerator and denominator

= [tex]\frac{1}{8}[/tex] × [tex]\frac{6}{1}[/tex] = [tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex] → C

(7)

[tex]\frac{6x}{x^2-9}[/tex] ÷ [tex]\frac{8}{4x-12}[/tex]

Factorise the denominators of both fractions

x² - 9 = x² - 3² = (x - 3)(x + 3) ← difference of squares

4x - 12 ← factor out 4 from each term

= 4(x - 3)

Then rewrite as

[tex]\frac{6x}{(x-3)(x+3)}[/tex] ÷ [tex]\frac{8}{4(x-3)}[/tex] ← cancel 8 and 4 by 4

= [tex]\frac{6x}{(x-3)(x+3)}[/tex] ÷ [tex]\frac{2}{x-3}[/tex]

• leave first fraction, change ÷ to × , turn second fraction ' upside down'

= [tex]\frac{6x}{(x-3)(x+3)}[/tex] × [tex]\frac{x-3}{2}[/tex] ← cancel x - 3 on numerator and denominator

= [tex]\frac{6x}{x+3}[/tex] × [tex]\frac{1}{2}[/tex] ← cancel 2 and 6 on numerator and denominator

= [tex]\frac{3x}{x+3}[/tex] → B

Answer:

17

Step-by-step explanation:

[tex]perimeter = 2(length + breadth) \\ breadth = (perimeter \div 2) - length[/tex]

[tex]72 \div 2 = 36 \\ 36 - 19 = 17[/tex]

Answer:

y is 17 mm

Step-by-step explanation:

perimeter formula is p= 2l +2w

19 is width

19+19 = 38

72-38=34

34/2= 17

17 is length

I hope it is right:)

Answer:

y=−11x+77/2

Step-by-step explanation:

The procedure for solving simultaneous linear equations now called Gaussian elimination appears in the ancient Chinese mathematical text Chapter Eight: Rectangular Arrays of The Nine Chapters on the Mathematical Art. Its use is illustrated in eighteen problems, with two to five equations.[4]

Systems of linear equations arose in Europe with the introduction in 1637 by René Descartes of coordinates in geometry. In fact, in this new geometry, now called Cartesian geometry, lines and planes are represented by linear equations, and computing their intersections amounts to solving systems of linear equations.

The first systematic methods for solving linear systems used determinants, first considered by Leibniz in 1693. In 1750, Gabriel Cramer used them for giving explicit solutions of linear systems, now called Cramer's rule. Later, Gauss further described the method of elimination, which was initially listed as an advancement in geodesy.[5]

In 1844 Hermann Grassmann published his "Theory of Extension" which included foundational new topics of what is today called linear algebra. In 1848, James Joseph Sylvester introduced the term matrix, which is Latin for womb.

Linear algebra grew with ideas noted in the complex plane. For instance, two numbers w and z in {\displaystyle \mathbb {C} }\mathbb {C}  have a difference w – z, and the line segments {\displaystyle {\overline {wz}}}{\displaystyle {\overline {wz}}} and {\displaystyle {\overline {0(w-z)}}}{\displaystyle {\overline {0(w-z)}}} are of the same length and direction. The segments are equipollent. The four-dimensional system {\displaystyle \mathbb {H} }\mathbb {H}  of quaternions was started in 1843. The term vector was introduced as v = x i + y j + z k representing a point in space. The quaternion difference p – q also produces a segment equipollent to {\displaystyle {\overline {pq}}.}{\displaystyle {\overline {pq}}.} Other hypercomplex number systems also used the idea of a linear space with a basis.

Arthur Cayley introduced matrix multiplication and the inverse matrix in 1856, making possible the general linear group. The mechanism of group representation became available for describing complex and hypercomplex numbers. Crucially, Cayley used a single letter to denote a matrix, thus treating a matrix as an aggregate object. He also realized the connection between matrices and determinants, and wrote "There would be many things to say about this theory of matrices which should, it seems to me, precede the theory of determinants".[5]

Benjamin Peirce published his Linear Associative Algebra (1872), and his son Charles Sanders Peirce extended the work later.[6]

The telegraph required an explanatory system, and the 1873 publication of A Treatise on Electricity and Magnetism instituted a field theory of forces and required differential geometry for expression. Linear algebra is flat differential geometry and serves in tangent spaces to manifolds. Electromagnetic symmetries of spacetime are expressed by the Lorentz transformations, and much of the history of linear algebra is the history of Lorentz transformations.

The first modern and more precise definition of a vector space was introduced by Peano in 1888;[5] by 1900, a theory of linear transformations of finite-dimensional vector spaces had emerged. Linear algebra took its modern form in the first half of the twentieth century, when many ideas and methods of previous centuries were generalized as abstract algebra. The development of computers led to increased research in efficient algorithms for Gaussian elimination and matrix decompositions, and linear algebra became an essential tool for modelling and simulations.[5]

Vector spaces

Main article: Vector space

Until the 19th century, linear algebra was introduced through systems of linear equations and matrices. In modern mathematics, the presentation through vector spaces is generally preferred, since it is more synthetic, more general (not limited to the finite-dimensional case), and conceptually simpler, although more abstract.

A vector space over a field F (often the field of the real numbers) is a set V equipped with two binary operations satisfying the following axioms. Elements of V are called vectors, and elements of F are called scalars. The first operation, vector addition, takes any two vectors v and w and outputs a third vector v + w. The second operation, scalar multiplication, takes any scalar a and any vector v and outputs a new vector av. The axioms that addition and scalar multiplication must satisfy are the following. (In the list below, u, v and w are arbitrary elements of V, and a and b are arbitrary scalars in the field F.)[7]

Question 8 measurements. Angle H (acute) Angle M (obtuse) Angle K (acute)

Question 9 measurements. Angle P (right) Angle Q (obtuse) Angle R (acute) Angle S (obtuse) Angle T (right)

Any angle that is visibly smaller than 90° in shape is an acute angle.

Any angle that has a square denoted inside the angle means that it is a 90° angle, therefore implying that it is a right angle.

Any angle that is visibly bigger than 90° in shape is an obtuse angle.

Note that in the Q.8, the total summation of the interior angles for a triangle is  180°. In this case, ∠H & ∠K can be safely assumed to be smaller than right angles, which means that ∠M would be either a right angle or obtuse. However, it is not given that ∠M is a right angle, and so the answer is obtuse.

a. Angle H: acute angle

b. Angle M: obtuse angle

c. Angle K: acute angle

It is given that angles P & T are right angles (as denoted by the squares). Therefore, angle Q & S are obtuse, and angle R is acute, based on visible differences:

a. angle P: Right angle.

b. angle Q: Obtuse angle.

c. angle R: Acute angle.

d. angle S: Obtuse angle.

e. angle T: Right angle.

Usually you will not be using visibility to solve the angle measurements, but in this case, it is not stated that shapes are not drawn to scale. Therefore, you can safely assume based on what the angles look like to answer.