the difference between 2 numbers is 12. the larger number is 3 times the smaller. what are the numbers

Answer:

1) 43/40

2) 35/6

3) 43/40

4) -5/3

5) 1/6

Step-by-step explanation:

1)  -1 4/5 = -(1*5 +4)/ 5= -9/5

or          1= 5/5  so -1 4/5= -( 5/5+ 4/5)=-9/5

-2 7/8= -(2*8+7)/8=-23/8

=> -9/5 - ( -23/8)= -9/5 + 23/8 = (( -9*8)+(23*5))/40= (-72+ 115)/40

                                                                                =  43/40

2) 4 3/4= (4*4+3)/4= 19/4

-1 1/12= -(1*12+1)/12= -13/12

=> 19/4 - (-13/12)= 19/4 + 13/12 = ((19*3)+13)/12= (57+13)/12= 35/6

3) same like 1)

4) 3 1/3 = (3*3+1)/3= 10/3

=> 10/3 -5= (10- 3*5)/3= (10-15)/3= -5/3

5) -1/3 + 1/2= ((-1*2)+(1*3))/6 = (-2+3)/6= 1/6

Answer:

Step-by-step explanation:

3x = 18

Divide both sides by 3 and simplify

x=6

Answer:

Step-by-step explanation:

assuming  that you need to find the value of x

3x = 18

-divide both sides by 3

3x/3 = 18/3

-use the facts that 3/3 =1 and 18/3 = 3*6/3 = 6

x = 6

Answer:

11. [tex]x^{5}[/tex]

12. 5*[tex]x^{2}[/tex]

13. x+21

14. 2x-8

Step-by-step explanation:

Answer:

Anything to a negative power is always the reciprocal. An example might be 2⁻² can be written as 1/4

Step-by-step explanation:

Answer:

1.36

Step-by-step explanation:

9.52/7

1.36 is the length of one of the 7 equal pieces

Patterns are set of rules that guide the creation of a dataset. The observation from the first three designs are as follows:

The pattern

The first three design show that, as the design number increases (i.e. 1, 2, 3), the number of tiles used also increases (i.e. 7, 12, 19)

The expressions for the number of tiles

The design number and the number of tiles is represented as follows

[tex]1 \to 7[/tex]

[tex]2 \to 12[/tex]

[tex]3 \to 19[/tex]

From the designs, we observe that some tiles are at the middle, while other tiles are at the sides.

Design 1 has 1 tile at the center and 6 tiles at either sides.

So, we have:

[tex]1 \to 1 + 6[/tex]

[tex]2 \to 4 + 8[/tex]

[tex]3 \to 9 + 10[/tex]

Expand

[tex]1 \to 1^2 + 6 \to 1^2 + 2 \times 3 \to 1^2 + 2 \times (1 + 2)[/tex]

[tex]2 \to 2^2 + 8 \to 2^2 + 2 \times 4 \to 2^2 + 2 \times (2 + 2)[/tex]

[tex]3 \to 3^2 + 10 \to 3^2 + 2 \times 5 \to 3^2 + 2 \times (3 + 2)[/tex]

Notice the pattern,

The number of tiles in design n will be:

[tex]Tiles = n^2 + 2 \times (n + 2)[/tex]

Open bracket

[tex]Tiles = n^2 + 2n + 4[/tex]

Hence, the expressions for number of tiles in design n are:

[tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex]

Technology to prove that both expressions are equivalent

To prove that [tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex] are equivalent using technology, the graphs of [tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex] can be plotted and then compared

The table and graph for the first 6 designs

The table entry for the first 6 designs is calculated as follows:

[tex]n = 1\ \ \ \ \ Tiles = 1^2 + 2 \times 1 + 4 = 7[/tex]        

[tex]n = 2\ \ \ \ \ Tiles = 2^2 + 2 \times 2 + 4 = 12[/tex]        

[tex]n = 3\ \ \ \ \ Tiles = 3^2 + 2 \times 3 + 4 = 19[/tex]        

[tex]n = 4\ \ \ \ \ Tiles = 4^2 + 2 \times 4 + 4 = 28[/tex]        

[tex]n = 5\ \ \ \ \ Tiles = 5^2 + 2 \times 5 + 4 = 39[/tex]        

[tex]n = 6\ \ \ \ \ Tiles = 6^2 + 2 \times 6 + 4 = 52[/tex]        

So, we have:

[tex]\begin{array}{cc}Design & {Tiles} & {1} & {7} & {2} & {12} & 3 & {19} & {4} & {28} & {5} & {39}& {6} & {52} \ \end{array}[/tex]

See attachment for the graph of the above table

All the points on the curve make sense in this scenario because all values are positive.

The pattern type

We have:

[tex]Tiles = n^2 + 2n + 4[/tex]

When an equation has a degree of 2, the equation is quadratic.

Hence, the pattern is quadratic.

The largest design that an empty sign of 10ft by 12ft can contain.

From the first three designs:

The number of tiles on a complete row and column are always the same.

Design 1 has 3 tiles in its complete row and column

Design 2 has 4 tiles in its complete row and column

Design 3 has 5 tiles in its complete row and column

The relationship between the design number (d) and the number of complete tiles (t) is:

[tex]d = t - 2[/tex]

For the 10ft by 12ft empty sign

[tex]t = 10[/tex] because [tex]10 < 12[/tex]

So, we have:

[tex]d = t - 2[/tex]

[tex]d = 10 - 2[/tex]

[tex]d = 8[/tex]

Hence, the largest design number is design 8

Read more about patterns at:

https://brainly.com/question/13382968

Answer:

92% of Income is  Rs 18400

Step-by-step explanation:

I = 18400/.92 = Rs 20000

Let the small , medium and large baskets be denoted by s,m & l

Formulating the equations

s+m+l= 80--------- equation1

$15.75s+ $25 m + $32.5l = $2086.25------equation2

2s=l---------equation 3

Using the technology  s=15, m=35 and l= 30

15+35+30= 80--------- equation1

$15.75(15)+ $25 (35)+ $32.5 (30) = $2086.25------equation2

2(15)=(30)---------equation 3

Yes because multiple variables can be easily calculated through matrices using technology

In Matrix form

[tex]\left[\begin{array}{ccc}1&1&1\\15.75&25&32.5\\-2&0&1\end{array}\right][/tex] [tex]\left[\begin{array}{c}s\\m\\l\end{array}\right][/tex]     = [tex]\left[\begin{array}{c} 80\\2086.25\\0\end{array}\right][/tex]

Let A= [tex]\left[\begin{array}{ccc}1&1&1\\15.75&25&32.5\\-2&0&1\end{array}\right][/tex]

Z= [tex]\left[\begin{array}{c}s\\m\\l\end{array}\right][/tex]    

B = [tex]\left[\begin{array}{c} 80\\2086.25\\0\end{array}\right][/tex]

Z= A⁻¹ B

A⁻¹= A mod/ det A

det A= -1

Using the technology  s=15, m=35 and l= 30

15 small baskets,

35 medium baskets

30 large baskets were sold.

Part C:

15+35+30= 80--------- equation1

$15.75(15)+ $25 (35)+ $32.5 (30) = $2086.25------equation2

236.25+ 875+ 975=$2086.25

$2086.25=$2086.25

2(15)=(30)---------equation 3

Answer 2:

Yes because multiple variables can be easily calculated using technology.

N.B There is a typing error in question its $2086.25 not 52086.25

Answer:

Factors of 15: 1, 3, 5 and 15.

Factors of 17: 1 and 17.

Factors of 26: 1, 2, 13 and 26

Factors of 80: 1, 2, 4, 8, 10, 20, 40, and 80.

Actually you can find all the answers in the Internet.

Answer:

x > 2

Step-by-step explanation:

Distribute and cross-simplify 1/2 with parenthesis

4x + x + 2 > 12

Solve left side

5x + 2 > 12

Subtract 2 from both sides

5x > 10

Divide both sides by 5

x > 2

Answer:

1st box is "a 90°clockwise rotation about the origin

2nd box is "a 180° rotation about the origin

3rd box is "a 90° counterclockwise rotation about the origin

Answer:

Step-by-step explanation:

7/8 + 3/4

7/8 + 6/8

13/8 = 1 5/8

Step-by-step explanation:

17x-4(4x-4)

17x-16x+8

X+8

Answer:

x + 12

Step-by-step explanation:

17x - 4(4x - 3)

17x - 16x + 12

x + 12

Answer:

150.333

Step-by-step explanation:

The three is repeated

Answer:

9 ufh fcnbscbhbvxdfhbbhukkkocd

Answer:

3/2

Step-by-step explanation:

Csc(theta) = 1/Sin(theta)

So we have to find the side opposite theta.

a = 3*sqrt(5)

b = ?

c = 9

a^2 + b^2 = c^2

(3sqrt(5)) ^2 + b^2 = 9^2

9*5 + b^2 = 81

b^2 = 81 = 45

b^2 = 36

sqrt(b^2) = sqrt(36)

b = 6

Sin(theta) = 6/9

Csc(theta) = 1 / sin(theta) = 9/6

Csc(theta = 3/2

Problem 3

=====================================================

Explanation:

Use the pythagorean theorem to find the length of the missing side.

[tex]a^2 + b^2 = c^2\\\\a^2 + (3\sqrt{5})^2 = 9^2\\\\a^2+3^2*(\sqrt{5})^2 = 9^2\\\\a^2 + 9(5) = 81\\\\a^2 + 45 = 81\\\\a^2 = 81-45\\\\a^2 = 36\\\\a = \sqrt{36}\\\\a = 6\\\\[/tex]

This is the length of the missing vertical side. This side is opposite the angle theta.

[tex]\csc = \text{cosecant}\\\\\csc(\theta) = \frac{\text{hypotenuse}}{\text{opposite}}\\\\\csc(\theta) = \frac{9}{6}\\\\\csc(\theta) = \frac{3*3}{3*2}\\\\\csc(\theta) = \frac{3}{2}\\\\[/tex]

Alternatively, you can compute it like this

[tex]\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\theta) = \frac{6}{9}\\\\\sin(\theta) = \frac{2}{3}\\\\\csc(\theta) = \frac{1}{\sin(\theta)}\\\\\csc(\theta) = 1 \div \sin(\theta)\\\\\csc(\theta) = 1 \div \frac{2}{3}\\\\\csc(\theta) = \frac{3}{2}\\\\[/tex]

Answer:

see explanation

Step-by-step explanation:

Since AL bisects ∠ KAT then ∠ 1 = ∠ 2

(30)

7x + 3 = 6x + 7 ( subtract 6x from both sides )

x + 3 = 7 ( subtract 3 from both sides )

x = 4

(32)

SAT is a straight line , then

∠ 1 + ∠ 2 + ∠ 3 = 180° , then

x + x + 4x = 180

6x = 180 ( divide both sides by 6 )

x = 30

(34)

Similar to (32)

x + 12 + x + 12 + 6x - 20 = 180 , that is

8x + 4 = 180 ( subtract 4 from both sides )

8x = 176 ( divide both sides by 8 )

x = 22

Answer:

30) x= 4

32) x=30

33) x=22

Step-by-step explanation:

All step by step explainations are in pic below

Answer:

[tex] {3}^{2} \times {3}^{ - 6} \\ = {3}^{2 + ( - 6)} \\ = {3}^{2 - 6} \\ = {3}^{ - 4} [/tex]

5^4 /5

Use the exponent rule x^a/x^b = x^a-b

5^4/5 = 5^4-1 = 5^3

Answer as a positive exponent is 5^3

Answer:

I don't know where can you find this question's answer.

Answer:

2999

Step-by-step explanation:

a + 1 = 3000

=> Subtracting 1 from both sides,

=> a + 1 - 1 = 3000 - 1

=> a = 2999

Answer:

The choose B. 2(2m-1)-8m

Step-by-step explanation:

2(2m-1)-8m = 4m-2 + (-8m)

I hope I helped you^_^

Step-by-step explanation:

We are dealing with theoretical probability. This means that our probability of said outcome is

[tex] \frac{x}{y} [/tex]

where x is the outcome we want, and y is the total number of outcomes possible.

28. There is 3 triangles out of 6 polygons so the probability is 1/2.

29.There is 1 Pentagon so the probability is 1/6.

30. This is a complement to question 28. A complement is the inverse of the problem. A complement and its original add to 1 so the probability of both getting a triangle is 1/2.

31. There is 4 non quadraletrial so the probability is 2/3.

32. There is 3 figures that has more sides than three so 1/2 is the probability.

33.There is only multi right angles figures so 1/2 is the probability.

34. There is 30 days in April so the probability it's the 29th is

[tex] \frac{1}{30} [/tex]

35. There is 31 days in July and 15 days after the 16th. So the probability

is

[tex] \frac{15}{31} [/tex]

Step-by-step explanation:

Answer-

b) 1

Answer:

I hope it will helpful.

Step-by-step explanation:

I hope it will help you.

Answer:

31.1011905%

Step-by-step explanation:

Take the new price and subtract the original price

8.81 - 6.72

2.09

Divide by the original price

2.09/6.72

.311011905

Change to percent form

31.1011905%

Percent of increase in average movie theatre ticket price will be 31.1%

    Given prices of the ticket in two different years are,

To calculate the percent increase in the price of an object expression to be used,

Percent increase = [tex]\frac{\text{Final price - Initial price}}{\text{Initial price}}\times 100[/tex]

                             = [tex]\frac{8.81-6.72}{6.72}\times 100[/tex]

                             = [tex]0.311\times 100[/tex]

                             = [tex]31.10[/tex]%

          Therefore, percent of increase in the price of the ticket will be 31.1%

Learn more,

https://brainly.com/question/11265758

Hi ;-)

[tex]x=(180^o-70^o):2=110^o:2=\boxed{55^o}\\\\y=180^o-55^o=\boxed{125^o}[/tex]