Calculate the average velocity of a motor cycle that travels 72km/hr in 20 seconds.
​

Answer:

G its G

Step-by-step explanation:

[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]

the given expression can be solved as follows ~

[tex] \frac{x}{13} - 1 = \frac{5x}{2} + \frac{1}{2} \\ [/tex]

taking LCM both the sides ,

[tex] \frac{x - 13}{13} = \frac{5x + 1}{2} \\ [/tex]

on cross multiplying ,

[tex](x - 13)2 = (5x + 1)13 \\ \\ \implies \: 2x - 26 = 65x + 13[/tex]

let's now gather the like terms at either sides of the equation ~

[tex]65x - 2x = - 26 - 13 \\ \\ \implies \: 63x = - 39 \\ \\ \implies \: x = \frac{\cancel{ - 39}}{\cancel{63}} [/tex]

on simplifying the equation ,

[tex] \implies \frac{-13}{21}\\[/tex]

hope helpful ~

Answer:

(-3, 13)

Step-by-step explanation:

The transformation that moves a point 4 left and 8 up is ...

 (x, y) ⇒ (x -4, y +8)

The transformation that reflects a point across the y-axis is ...

 (x, y) ⇒ (-x, y)

Applied after the translation, the transformation of ∆ABC becomes ...

 (x, y) ⇒ (-(x -4), y +8) = (4 -x, y +8)

Then point A gets moved to ...

 A(7, 5) ⇒ A'(4 -7, 5 +8) = (-3, 13)

Answer:

Step-by-step explanation:

The area of a square is 49 cm2. What is the perimeter, in cm, of the square?

first we use the inverse formula to find the side (√49 = 7), then multiply the side by 4 (7 x 4 = 28)

or you can use an expression

4 * √49 = 28

Answer: 10+17

Step-by-step explanation:

Distribute:

3(2+6)+4−1

6+18+4−1

Subtract the numbers:

6+18+4−1

6+17+4

Combine like terms:

6+17+4

10+17

solution:

10+17

Given the radius r and the tangent line AB, the length of the line OA is 24 units

The radius r and the tangent line AB meet at a right angle.

By Pythagoras theorem, we have:

AB² = OA² + r²

So, we have:

24² = OA² + 7²

Rewrite as:

OA² = 24² - 7²

Evaluate

OA² = 527

Take the square root of both sides

OA = 23

Hence, the length of OA is 24 units

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Answer:

1.

3.5 days

2.

6.75 minutes, 6 minutes 45 seconds, 6.8 minutes to 1 dp

Step-by-step explanation:

1.

With double the amount of tractors it will take half the time.

7 divided by 2 is 3.5

2.

This is an example of inverse proportion. The job that has to be done to to prepare the vegetables, That stays the same.

However, the more people there are to do the work, the quicker it will get done.

There is a constant to be found:

x multiplied by y equals k

3 x 45 = 135

For 20 people:

20 x y = 135

135 divided by 20 is:

6.75, or 6.8

Answer:

y = -x – 2

Step-by-step explanation:

Slope is ΔY/ΔX =  -1

plug this into the equation:

1=-(-3) +b

= -2=b

so we get; y = -x – 2

Answer: y = -x - 2

Step-by-step explanation:

     I will be writing this equation in slope-intercept form.

     First, we will find our m value, also known as the slope.

        [tex]\displaystyle \frac{\text{change in y}}{\text{change in x}} =\frac{1--4}{-3-2} =\frac{5}{-5}=-1[/tex]

     Now, we will find our b value, or the y-intercept.

-> The line intercepts the y-axis at (0, -2), so our y-intercept is -2.

     Lastly, we will write our equation.

y = mx + b

y = -x - 2

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Answer:

11

Step-by-step explanation:

11x=121

11x/11 = 121/11

x = 11

So, 11*11 = 121

I believe it is 312, hope this helps, sorry if it doesn't!:)

Answer:

The answer would be C, Both I and II.

Step-by-step explanation:

You can find an attached file which shows the scenarios incase your confused.

Hey there!

Do PEMDAS to solve.

PEMDAS simply means.

• Parentheses
• Exponents
• Multiplication
• Division
• Addition
• Subtract

Some people use this method to make PEMDAS easier to understand

• Please
• Excuse
• My
• Dear
• Aunt
• Sally

4 + 4(5 + 2^2)

= 4 + 4(5 + 2 * 2)

= 4 + 4(5 + 4)

= 4 + 4(9)

= 4 + 36

= 40

Therefore, the answer should be: 40

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

By using the Pythagorean theorem, we conclude that side x measures (5/2)*√3 units.

In the image, we can see that the equilateral triangle can be divided into two right triangles.

If each side of the equilateral triangle measures 5 units, then for the right triangles we will have that the hypotenuse measures 5 units, and the bottom side measures half of that: 2.5 units.

Now remember the Pythagorean theorem. It says that the sum of the squares of the cathetus is equal to the square of the hypotenuse.  Then we will have:

[tex]x^2 + 2.5^2 = 5^2[/tex]

[tex]x = \sqrt{5^2 - 2.5^2} = \frac{5}{2}\sqrt{3}[/tex]

Then we conclude that side x measures (5/2)*√3 units.

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Answer:

The solution is in the image

So values are

The rule is

Explicit formula

Equation here is

Answer:

[tex]f(x)=4^x[/tex] grows at a faster rate than the given quadratic function.

Step-by-step explanation:

Given table:

[tex]\large \begin{array}{| c | c |}\cline{1-2} x & y \\\cline{1-2} 0 & 0 \\\cline{1-2} 1 & 3 \\\cline{1-2} 2 & 12 \\\cline{1-2} 3 & 27 \\\cline{1-2}\end{array}[/tex]

First Differences in y-values:

[tex]0 \overset{+3}{\longrightarrow} 3 \overset{+9}{\longrightarrow} 12 \overset{+15}{\longrightarrow} 27[/tex]

Second Differences in y-values:

[tex]3 \overset{+6}{\longrightarrow} 9 \overset{+6}{\longrightarrow} 15[/tex]

As the second differences are the same, the function is quadratic.

The coefficient of [tex]x^2[/tex] is always half of the second difference.

Therefore, the quadratic function is:

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

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Therefore, the average rate of change for [tex]f(x)=3x^2[/tex] over the interval
0 ≤ x ≤ 3 is:

[tex]\textsf{Average rate of change}=\dfrac{f(3)-f(0)}{3-0}=\dfrac{27-0}{3-0}=9[/tex]

An exponential function that grows at a faster rate than [tex]f(x)=3x^2[/tex] over the interval 0 ≤ x ≤ 3  is [tex]f(x)=4^x[/tex]

[tex]\large \begin{array}{| c | c | c | c | c |}\cline{1-5} x & 0 & 1 & 2 & 3 \\\cline{1-5} f(x)=4^x & 1 & 4 & 16 & 64\\\cline{1-5} \end{array}[/tex]

[tex]\textsf{Average rate of change}=\dfrac{f(3)-f(0)}{3-0}=\dfrac{64-1}{3-0}=21[/tex]

As 21 > 9, [tex]f(x)=4^x[/tex] grows at a faster rate than [tex]f(x)=3x^2[/tex] over the interval 0 ≤ x ≤ 3.

Answer:

5 seconds and 488 ft

Step-by-step explanation:

(a)

given a quadratic in standard form

y = ax² + bx + c ( a ≠ 0 ), then

the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

y = - 16x² + 160x + 88 ← is in standard form

with a = - 16 and b = 160 then

[tex]x_{vertex}[/tex] = - [tex]\frac{160}{-32}[/tex] = 5

the maximum height is at the vertex, the turning point on the graph

then it takes 5 second to reach its maximum height

(b)

to find the maximum height substitute x = 5 into the equation

y = - 16(5)² + 160(5) + 88

  = - 16(25) + 800 + 88

 = - 400 + 888

 = 488

maximum height is 488 ft

Answer:

g(x) = 2ˣ⁻¹ + 3

Step-by-step explanation:

f(x) = 2ˣ

Translated 1 unit right

Translated 3 units up

Answer:

Well if its a translation on the x-axis  the formula would be g(x) = -2×

Although Functions are not my strong suit

I hope i got this right!

Answer:

[tex]7 \frac{2}{9} [/tex]

Step-by-step explanation:

here is your answer

Calculation steps:

[tex]11 \frac{6}{9} - 4 \frac{4}{9} [/tex]

[tex] = (14 - 4) + ( \frac{6}{9} - \frac{4}{9} )[/tex]

[tex] = 7 + \frac{6 - 4}{9} [/tex]

[tex] = 7 + \frac{2}{9} [/tex]

[tex]7 \frac{2}{9} [/tex]

[tex]11 \frac{6}{9} - 4 \frac{4}{9} [/tex]

[tex]11 \frac{6}{9} - 4 \frac{4}{9} [/tex]

[tex] = \frac{35}{3} - \frac{40}{9} [/tex]

[tex] = \frac{(35 \times 9) - (40 \times 30)}{3 \times 9} [/tex]

[tex] = \frac{315 - 120}{27} [/tex]

[tex] = \frac{195}{27} [/tex]

[tex] = 7 \frac{2}{9} [/tex]

Answer:

its A

Step-by-step explanation:

Answer:

Amelias salary increase by $12,000 every year so 12*20 = $240,000 salary in 20th year.

Using sampling concepts, it is found that the correct statement is given by:

c. the sample is 85 people. the population is 2,534 people.

It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.

In this problem, a group of 85 people, which is the sample, is taken from the entire population of 2,534 people, hence option c is correct.

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Answer:

c) 5

Step-by-step explanation:

we know that,

alpha + beta = -b/a

here, we are given that alpha is L and beta is M (roots of the quadratic equation)

therefore,

L+M = -b/a

L+M = -(-40)/8

L+M = 40/8

L+M = 5

HOPE IT HELPS!!

PLEASE MARK BRAINLIEST... ♡

Answer:

L + M are 5.122 and -0.122 so I am assuming the answer you want is 5 or c.

Step-by-step explanation:

SOME OF THIS I NEEDED TO RESEARCH BECAUSE I FEEL LIKE THIS IS OUT OF MY DEPTH BUT I GUESS HERE YOU GO

STEP

1

:

Equation at the end of step 1

 (23x2 -  40x) -  5  = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1     Factoring  8x2-40x-5

The first term is,  8x2  its coefficient is  8 .

The middle term is,  -40x  its coefficient is  -40 .

The last term, "the constant", is  -5

Step-1 : Multiply the coefficient of the first term by the constant   8 • -5 = -40

Step-2 : Find two factors of  -40  whose sum equals the coefficient of the middle term, which is   -40 .

     -40    +    1    =    -39

     -20    +    2    =    -18

     -10    +    4    =    -6

     -8    +    5    =    -3

     -5    +    8    =    3

     -4    +    10    =    6

     -2    +    20    =    18

     -1    +    40    =    39

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

2

:

 8x2 - 40x - 5  = 0

STEP

3

:

Parabola, Finding the Vertex:

3.1      Find the Vertex of   y = 8x2-40x-5

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 8 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C ,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   2.5000  

Plugging into the parabola formula   2.5000  for  x  we can calculate the  y -coordinate :

 y = 8.0 * 2.50 * 2.50 - 40.0 * 2.50 - 5.0

or   y = -55.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = 8x2-40x-5

Axis of Symmetry (dashed)  {x}={ 2.50}

Vertex at  {x,y} = { 2.50,-55.00}

x -Intercepts (Roots) :

Root 1 at  {x,y} = {-0.12, 0.00}

Root 2 at  {x,y} = { 5.12, 0.00}

Solve Quadratic Equation by Completing The Square

3.2     Solving   8x2-40x-5 = 0 by Completing The Square .

Divide both sides of the equation by  8  to have 1 as the coefficient of the first term :

  x2-5x-(5/8) = 0

Add  5/8  to both side of the equation :

  x2-5x = 5/8

Now the clever bit: Take the coefficient of  x , which is  5 , divide by two, giving  5/2 , and finally square it giving  25/4

Add  25/4  to both sides of the equation :

 On the right hand side we have :

  5/8  +  25/4   The common denominator of the two fractions is  8   Adding  (5/8)+(50/8)  gives  55/8

 So adding to both sides we finally get :

  x2-5x+(25/4) = 55/8

Adding  25/4  has completed the left hand side into a perfect square :

  x2-5x+(25/4)  =

  (x-(5/2)) • (x-(5/2))  =

 (x-(5/2))2

Things which are equal to the same thing are also equal to one another. Since

  x2-5x+(25/4) = 55/8 and

  x2-5x+(25/4) = (x-(5/2))2

then, according to the law of transitivity,

  (x-(5/2))2 = 55/8

We'll refer to this Equation as  Eq. #3.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x-(5/2))2   is

  (x-(5/2))2/2 =

 (x-(5/2))1 =

  x-(5/2)

Now, applying the Square Root Principle to  Eq. #3.2.1  we get:

  x-(5/2) = √ 55/8

Add  5/2  to both sides to obtain:

  x = 5/2 + √ 55/8

Since a square root has two values, one positive and the other negative

  x2 - 5x - (5/8) = 0

  has two solutions:

 x = 5/2 + √ 55/8

  or

 x = 5/2 - √ 55/8

Note that  √ 55/8 can be written as

 √ 55  / √ 8

Solve Quadratic Equation using the Quadratic Formula

3.3     Solving    8x2-40x-5 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     8

                     B   =   -40

                     C   =   -5

Accordingly,  B2  -  4AC   =

                    1600 - (-160) =

                    1760

Applying the quadratic formula :

              40 ± √ 1760

  x  =    ——————

                     16

Can  √ 1760 be simplified ?

Yes!   The prime factorization of  1760   is

  2•2•2•2•2•5•11

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 1760   =  √ 2•2•2•2•2•5•11   =2•2•√ 110   =

               ±  4 • √ 110

 √ 110   , rounded to 4 decimal digits, is  10.4881

So now we are looking at:

          x  =  ( 40 ± 4 •  10.488 ) / 16

Two real solutions:

x =(40+√1760)/16=5/2+1/4√ 110 = 5.122

or:

x =(40-√1760)/16=5/2-1/4√ 110 = -0.122

Answer:

see explanation

Step-by-step explanation:

(a)

calculate the gradient (slope) m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = O (0, 0 ) and (x₂, y₂ ) = A (- 5, 2 )

[tex]m_{OA}[/tex] = [tex]\frac{2-0}{-5-0}[/tex] = [tex]\frac{2}{-5}[/tex] = - [tex]\frac{2}{5}[/tex]

(b)

the angle between a tangent and a radius at the point of contact is 90°

given a line with slope m then the gradient of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{2}{5} }[/tex] = [tex]\frac{5}{2}[/tex]

(c)

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = [tex]\frac{5}{2}[/tex] , then

y = [tex]\frac{5}{2}[/tex] x + c ← is the partial equation

to find c substitute A (- 5, 2 ) into the partial equation

2 = - [tex]\frac{25}{2}[/tex] + c ⇒ c = 2 + [tex]\frac{25}{2}[/tex] = [tex]\frac{29}{2}[/tex]

y = [tex]\frac{5}{2}[/tex] x + [tex]\frac{29}{2}[/tex] ← equation of tangent

Answer:

Relative frequency for each discount :

10% - 0.4925, 20% - 0.3325, 40% - 0.175

Since only 33.25% of customers got 20% discount, it is not an appropriate method.

Step-by-step explanation:

relative frequency = number of frequency/total number of frequency

you can find out relative frequency for each number and add them up to get relative frequencies of discounts.

Answer:

13.125

Step-by-step explanation:

A percentage is a way to describe a part of a whole. The percentage increase in the number of tigers is 21.56%.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

The percentage change is given by the formula,

Percentage change = |(Intial Value - Final value)|/Initial Value × 100%

Percentage Change = |3200-3890|/3200 × 100% = 21.56%

Hence, the percentage increase in the number of tigers is 21.56%.

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