what are the possible values of remainder r, when a positive integer 'a' is divided by 3​

An asymptote is a straight line that approaches a curve indefinitely but does not intersect at any point. There are asymptotes at t [tex]\dfrac{3}{2}\rm\ and\ \dfrac{-1}{3}[/tex].

An asymptote is a straight line that approaches a curve indefinitely but does not intersect at any point. In other words, when a curve approaches infinity, it approaches an asymptote line.

The function that is given to us is:

[tex]f(x)=\dfrac{x+1}{6x^2-7x-3}[/tex]

As in the function, there is a fraction therefore, the denominator should not be zero in order for the function to be defined. Therefore, there are asymptotes at

[tex]6x^2-7x-3 = 0\\[/tex]

Substituting the value in the formula of the quadratic equation we will get,

[tex]D=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\D = \dfrac{-(-7)\pm\sqrt{(-7)^2-4(6)(-3)}}{2(6)}\\\\D =\dfrac{-(-7)\pm\sqrt{11}}{12} = \dfrac{3}{2}, \dfrac{-1}{3}[/tex]

Thus, there are asymptotes at  [tex]\dfrac{3}{2}\rm\ and\ \dfrac{-1}{3}[/tex].

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If Mr. Goldsman runs for one and a half hours, Kirby runs for 37 minutes 30 seconds.

The first step is to determine how many minutes kirby would run for every minute Mr Goldsman runs

Rate = 5/12

The second step is to multiply the rate by the minutes run by Mr Goldsman.

5/12 x 90 = 37.5

= 37 minutes 30 seconds

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Answer:

  1

Step-by-step explanation:

The square of the value in the empty space is the constant in the expanded expression. That is ...

  [ ]² = 1

The value in the space is ...

  [ ] = √1 = 1

The filled-in equation is ...

  (3x -1)² = 9x² -6x +1

_____

The expansion of the square of a binomial is ...

  (ax -b)² = a²x² -2abx +b²

Above, we used the constant term to find 'b', but we could also have used the linear term:

  -6x = -2(3)bx . . . . . a=3 in this problem

  1 = b . . . . . . . divide by -6x

Answer:

C

Step-by-step explanation:

Volume = bhd

Volume = (x + 3)(x + 8)(x²)

start with (x + 3) and (x + 8), factor:

x² + 8x + 3x + 24

x² + 11x + 24

now bring x² back:

(x² + 11x + 24)(x²)

x⁴ + 11x³ + 24x²

Answer:

Domain: input values (x-values)

Range: output values (y-values)

Absolute value: remove negative sign → output becomes positive
eg. |-2| = 2

Squaring a number → output is always positive

[tex]a(x)=3|x|[/tex]

Domain = all real numbers

Range = all positive numbers and zero

[tex]b(x)=3x^2[/tex]

Domain = all real numbers

Range = all positive numbers and zero

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

The Distributive Property states the following:-

[tex]\longrightarrow\sf{a(b+c)=ab+ac[/tex]

Where

[tex]\longrightarrow\sf{a,~b,~and~c~can~be~either~constants~or~variables}[/tex]

Now, let's use this property to simplify our expressions.

The first one is

[tex]\bigstar{\underline{\boxed{{4(x+2)}}}[/tex]

Simplify by distributing 4:-

[tex]\longrightarrow\sf{4~times~x~+4~times~2}[/tex]

Add the products:-

[tex]\longrightarrow\sf{4x+8}[/tex]

[tex]\rule{250}{2}[/tex]

Solve the next one:-

[tex]\bigstar{\underline{\boxed{\sf{-5(9+x)}}}[/tex]

Distribute -5 & add the products:-

[tex]\longrightarrow\sf{-45-5x}[/tex]

[tex]\rule{250}{2}[/tex]

Solve the last one:-

[tex]\bigstar{\underline{\boxed{7(x-3)}}[/tex]

Distribute 7:-

[tex]\longrightarrow\sf{7x-21}[/tex]

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

Hope everything is clear; if you need any more explanation/clarification, kindly let me know, and I'll comment and/or edit my answer :)

Answer:

49.65-50.35

Step-by-step explanation:

0.7% of 50 is 0.35. We can find the range by first subtracting that from 50 which is 49.65, then adding it to get 50.35.

Hey there!

The first step in solving this equation is

2(7x-3)=9

14x-6=9

Now, add 6 to both sides:

14x=15

Divide both sides by 14:

x=15/14

Hope everything is clear.

Let me know if you have any questions!

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Answer:

Option 2 hope it helps pls mark as the brainliest

Answer:

[tex]\displaystyle 4536,4597918...\:cm.^2 = A[/tex]

Step-by-step explanation:

Split the diametre in half before proceeding:

[tex]\displaystyle \pi{r}^2 = A \\ \\ 38^2\pi = A \hookrightarrow 1444\pi = A \\ \\ \boxed{4536,4597918... = A}[/tex]

I am joyous to assist you at any time.

The number of cubes that will fit into the shoebox is 40 cubes

Volume is the measure of a substance an object contains

Volume of the box = length * width * height

Volume of the box = 5/4 * 1 * 1/2
Volume of the box = 5/8cubic unit

Determine the volume of the box

Volume of the box = l³

Volume of the box = (1/4)³ = 1/64 cubic units

Number of cubes = (5/8)/(1/64)
Number of cubes = 5/8 * 64/1
Number of cubes = 5 * 8
Number of cubes = 40 cubes

Hence the number of cubes that will fit into the shoebox is 40 cubes

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Answer:

(4,5) (4,8)(4,6)

Step-by-step explanation:

So now you're reflecting over the horizontal line that passes through the point (0,5)

:))

Step-by-step explanation:

(4,5),(4,6),(4,8)

the answer is this!

Answer:

J

Step-by-step explanation:

Start by labelling the sides of the triangle. The length of the ramp is the hypotenuse side, while the height of the ramp is the opposite side.

[tex]\textcolor{steelblue}{ \sinθ = \frac{opp}{hyp} }[/tex]

Let the length of the ramp be x.

[tex] \sin5° = \frac{3}{x} [/tex]

Multiply x on both sides:

x(sin5°)= 3

[tex]x = \frac{3}{ \sin5°} [/tex]

x= 34.4 (3 s.f.)

Thus, the length of the ramp is 34 ft. (nearest foot)

Answer:

Step-by-step explanation:

The expression "32 divided by 10-8 divided by 2-3" evaluates to -3.8.

To solve the expression "32 divided by 10-8 divided by 2-3," we follow the order of operations, which is often represented by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right).

32 divided by 10 equals 3.2.

Next, perform the second division which is 8 divided by 2 which equals 4.

Subtract the result of the second division (4) from the first division result (3.2): 3.2 - 4

= -0.8.

Finally, subtract 3 from the -0.8.

-0.8 - 3

= -3.8.

Therefore, the expression "32 divided by 10-8 divided by 2-3" evaluates to -3.8.

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Answers:

5.) [tex]\displaystyle \pm{8\sqrt{3}}[/tex]

4.) [tex]\displaystyle 3\sqrt[5]{3}[/tex]

3.) [tex]\displaystyle \pm{8\sqrt{5}}[/tex]

2.) [tex]\displaystyle 3\sqrt[3]{3}[/tex]

1.) [tex]\displaystyle \pm{3\sqrt{2}}[/tex]

Step-by-step explanations:

5.) [tex]\displaystyle \sqrt{27} + \sqrt{75} \hookrightarrow \pm{3\sqrt{3}} + \pm{5\sqrt{3}} \\ \\ \boxed{\pm{8\sqrt{3}}}[/tex]

4.) [tex]\displaystyle \sqrt[5]{3} + \sqrt[5]{96} \hookrightarrow \sqrt[5]{3} + 2\sqrt[5]{3} \\ \\ \boxed{3\sqrt[5]{3}}[/tex]

3.) [tex]\displaystyle \sqrt{45} + \sqrt{125} \hookrightarrow \pm{3\sqrt{5}} + \pm{5\sqrt{5}} \\ \\ \boxed{\pm{8\sqrt{5}}}[/tex]

2.) [tex]\displaystyle \sqrt[3]{3} + \sqrt[3]{24} \hookrightarrow \sqrt[3]{3} + 2\sqrt[3]{3} \\ \\ \boxed{3\sqrt[3]{3}}[/tex]

1.) [tex]\displaystyle \pm{\sqrt{2}} + \sqrt{8} \hookrightarrow \pm{\sqrt{2}} + \pm{2\sqrt{2}} \\ \\ \boxed{\pm{3\sqrt{2}}}[/tex]

I am joyous to assist you at any time.

Answer:

6/19

Step-by-step explanation:

2+4+7+6=19

dose not have an a=6

6/19

Answer:

5. 52+56 < 49x -46x

108< 3x

108/3< 3x/3

36

Given A room is half as long again as it is broad

Let the breadth of the room x m

length of the room x + x/2 = 3x/2m

Area of the room , x × 3x/2 = 3x²/2m

Given , cost of carpeting the room at Rs. 3.25m⁻²

So , total cost , 3x²/2 × 3.25

But , Total cost of carpeting is given as 175.50 so ,

let the height of the room H m

Area of the four wall = 2(L+ b)× h 2(6+9)× H

= 30H m²

Area of the of the one door and two window is 8m²

8m² Area to be prepared = Area of four wall - area of two window and 1 door = (30H - 8) m²

Given cost of preparing wall is Rs. 1.40m²

total cost of preparing wall is (30H - 8) × 1.40

Total cost of preparing wall is given as 240.80

comparing , (30H - 8 ) × 1.40 = 240.80

Hence, Dimensions of the room are lengths 9m , breadth 6m and height 6m

Answer:

r≈12mi

Step-by-step explanation:

mark brainiest and Im 100% correct

Answer:

1376.1 ft^3

Step-by-step explanation:

The volume of a sphere formula: V=4/3πr^3

r = 6.9 ft

V = 4/3 * π * (6.9^3) = 1,376.055

to the nearest tenth it's 1376.1 ft^3

Answer:

ezz multiply and see what it s if its wrong then txt me

Step-by-step explanation:

Percentage discount

[tex]\\ \rm\rightarrowtail \dfrac{2}{86.25}{100}[/tex]

[tex]\\ \rm\rightarrowtail 0.0232(100)[/tex]

[tex]\\ \rm\rightarrowtail 2.32\%[/tex]

Answer:

2.3% (nearest tenth)

Step-by-step explanation:

[tex]\sf percentage \ change =\dfrac{|final \ value - initial \ value|}{initial \ value} \times 100\%[/tex]

Given:

[tex]\sf \implies percentage \ change =\dfrac{|84.25-86.25|}{86.25} \times 100\%[/tex]

[tex]\sf \implies percentage \ change =\dfrac{2}{86.25} \times 100\%[/tex]

[tex]\sf \implies percentage \ change =2.3\% \ (nearest \ tenth)[/tex]

Using proportions, it is found that the value of a is of 3.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, a 180º angle has a measure of [tex]\pi[/tex] radians. What is the measure of a 540º angle? The rule of three is given by:

180º - [tex]\pi[/tex] rad.

540º - x [tex]\pi[/tex] rad.

Applying cross multiplication:

180x = 540.

x = 540/180 = 3.

The value of a is of 3.

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Using proportions, the value of a is 3.

Proportion is a mathematical comparison between two numbers.

When going from degrees to radians, 180 degrees is always going to equal π radians.

The conversion of angle from radian to degree;

[tex]\rm 180-\ 1 \\\\540-a[/tex]

The value of a is;

[tex]\rm \dfrac{180}{540}=\dfrac{1}{a}\\\\\dfrac{1}{3}=\dfrac{1}{a}\\\\1 \times a=1\times 3\\\\a=3[/tex]

Hence, the value of a is 3.

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Answer:

[tex]surface \: area \: ofa \: cube \: \\ area = \: 6 {a}^{2} \\ 6( {3}^{2} ) \\ 6(9) = 54[/tex]

Answer:

6x

Explanation:

A number is x. 6 x x is written as 6x

Answer:

6x or 6*x

Step-by-step explanation:

Represent the following sentence as an algebraic expression, where "a number" is the letter x.

6 is multiplied by a number

6x

6 * x

Hope this helps!

Answer:

Maurico started with more :)

Step-by-step explanation:

Mariah started with 150 while Maurico started with around 190 so he has more to start with :)

Have a great day!

Please rate and mark brainliest!

Answer:

Mauricio

Step-by-step explanation:

To find who started with more money in their savings account, we want to observe the savings in $ when time=0 years

So by looking at the table of Mariah's savings, we see that when t=0 she had S=150$

By looking at the graph which describes Muaricio's savings as a function of time, we can see that when time=0 or x=0, y=S=190$

In other words, the y-intercept is the initial amount of savings.

190>150

:P

Hope this helps, it would be appreciated if you made me brainliest.

Answer:

  -5 = log₄(0.0009765625)

  4 = log₄(256)

Step-by-step explanation:

Apparently, you want to express a number as a logarithm. That is, you want to find y for some value of x such that ...

  x = log₄(y)

Taking antilogs, this is ...

  y = 4^x

__

For x =-5, the log expression would be ...

  y = 4^-5 = 0.0009765625

  log₄(0.0009765625) = -5

__

For x = 4, the log expression would be ...

  y = 4^4 = 256

  log₄(256) = 4

Answer:

Myra swims for 3 miles.

Step-by-step explanation:

3/5 = 6/10

2 4/10 + 6/10 = 3

Answer: A

Step-by-step explanation:

If 2sinθ = 6/5, then the value of cos (90 - θ) will be 3/5. Then the correct option is A.

We can use the fact that:

sinθ = cos(90 - θ)

to convert the sine to cosine (but the angles won't stay the same unless it's 45 degrees).

If 2sinθ = 6/5.

Then the value of cos (90 - θ) will be

cos (90 - θ) can be written as sin θ

Then we have

cos (90 - θ) = sin θ

cos (90 - θ) = 3/5

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