A car accelerates uniformly from 36 km/h to 72 km/h in 2 seconds. Calculate :a.The acceleration of the car b.The distance covered by the car in that time.

Answer:

m = -5/2

b = 3

Step-by-step explanation:

The equation is in y = mx +b form where m is the slope and b is the y-intercept.  This means that the slope is -5/2 and the y-intercept is 3.

Use the Pythagorean theorem:

c^2 = 2^2 + 2^2

c^2 = 4 +4

c^2 = 8

c = sqrt(8)

c = 2.8284

Rounded to nearest tenth = 2.8

Step-by-step explanation:

[tex]f( \frac{2}{3} x) = \frac{4}{9} {x}^{2} - 1 \\ \frac{4}{9} {x}^{2} - 1 = 0 \\ \sqrt{ {x}^{2} } = \sqrt{ \frac{9}{4} } \\ x = \frac{3}{2} \\ x = - \frac{3}{2} [/tex]

we have three points of the graph

(0,-1) min point

and those two values for x.

so:

There are 9,232,320 ways to split 14 people into seven pairs.

To split 14 people into seven pairs, we need to find the number of ways to arrange the people into those pairs.

Let's break down the process step by step:

1. Selecting the first pair: We have 14 people to choose from for the first person in the first pair. After selecting the first person, we have 13 people remaining to choose from for the second person in the pair. Since the order of selection doesn't matter, we divide by 2 to account for the fact that we have counted each pair twice (e.g., choosing A then B is the same as choosing B then A).

Therefore, the number of ways to select the first pair is (14 * 13) / 2 = 91.

2. Selecting the second pair: We have 12 people remaining after forming the first pair. Similar to the first pair, we have 12 choices for the first person and 11 choices for the second person in the second pair. Again, we divide by 2 to account for the order of selection.

The number of ways to select the second pair is (12 * 11) / 2 = 66.

3. Continuing this process, we select pairs until all 14 people are paired up. Each time, the number of remaining people decreases by 2.

So, the total number of ways to split 14 people into seven pairs is:

91 * 66 * 40 * 24 * 10 * 6 * 2 = 9,232,320.

Therefore, there are 9,232,320 ways to split 14 people into seven pairs.

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Answer: B or 1/2

Step-by-step explanation: not too sure if this is right if not sorry

Answer:

4 is the largest number that is common to both 32 and 44.  Factoring it out looks like this: 4(8 + 11) = 4(8 + 11).  That's weird to me but all textbooks begin that process just that same way.

Step-by-step explanation:

Greatest common factor of 32 and 44 is 4:

32/4 = 8

44/4 = 11

Factor 4 out of the equation 32 + 44 =

The factored form would be 4(8 + 11)

Answer:

hope its what you are searching for....

Answer:

2.5

Step-by-step explanation:

42/16.8=2.5

Answer:

w=A/I

2.5in

Step-by-step explanation:

This is the full answer

The perimeter of a rectangle is calculated by:

[tex]\boxed{P=width +width+length+ length}[/tex]

Remember: In a rectangle, opposite sides are equals.

If we know how much is the width, then it's just apply it to the expression:

[tex]P=width+width+length+length\\312 =68 + 68 + length + length\\312 = 136+(2\cdot length)\\312 - 136 = 2\cdot length\\2\cdot length = 176\\length = \frac{176}{2} \\length = 88[/tex]

Therefore, the length of the pool is 88m.

Answer:

7x^2 -28x +28

Step-by-step explanation:

7(x - 2)^2

7 ( x-2)(x-2)

Foil

7 ( x^2 -2x-2x+4)

Combine like terms

7( x^2 -4x+4)

Distribute

7x^2 -28x +28

Answer:

  [tex]\dfrac{1}{7x-14}[/tex]

Step-by-step explanation:

Perhaps you want to simplify ...

  [tex]\dfrac{x-2}{7(x-2)^2}=\dfrac{x-2}{x-2}\cdot\dfrac{1}{7(x-2)}=\boxed{\dfrac{1}{7x-14}}[/tex]

Answer:

y = x-1

Step-by-step explanation:

The slope intercept form is

y = mx+b where m is the slope and b is the y intercept

y= 1x -1

y = x-1

The slope intercept form is,

y = x -1

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Since, The slope intercept form is

y = mx + b

where m is the slope and b is the y intercept

Here, We have;

The slope of a line is 1, and the y-intercept is -1.

Hence, We get;

The slope intercept form is,

y = 1x -1

y = x - 1

Thus, The slope intercept form is,

y = x -1

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Answer:

130

Step-by-step explanation:

Answer:

A) 27.6

B) 978.3

C) 42.9

D) 9

Step-by-step explanation:

I'm pretty sure its suppose to b 1 answer but i didn't do this question.

Answer:

A)= 27.6 B)= 978.3 C)= 42.9 D=9

Step-by-step explanation:

Answer:

Lose $25, Gain $5, Gain $45, Stock ABC 40%, 15%, 45%, Stock JKL 15%

Step-by-step explanation:

sorry i don,t unerstan what u wn,t

Answer:

E. (x³/360)π square units

Step-by-step explanation:

The area of a sector has a formula.

θ°/360° × πr²

The radius is x units, the central angle of the sector is x°.

x/360 × πx²

x/360 × x² × π

x³/360 × π

The area of the sector is equal to (x³/360)π square units.

Answer:

1194

Step-by-step explanation:

Answer:

The answer is 1194

Step-by-step explanation:

It goes up by one point each so if you add all the numbers from 18 thru 52 you would get the answer.

Answer:

The equation that models how far from the tip of the saw is from the wood in terms of time is x(t) = 10×cos(2×π×t) + 17

Step-by-step explanation:

The given parameters are;

Length of the saw blade = 40 cm

Thickness of the wood across = 8 cm

Length of blade between wood saw handle with hand extended = 5 cm

Length of the tip from the wood at the above time = 40 - 8 - 5 = 27 cm

Length of blade between wood saw handle with saw pulled inwards = 25 cm

Length of the tip from the wood at the above time = 40 - 8 - 25 = 7 cm

Time for one complete cycle = 1 second

We note that the basic equation for oscillatory motion is of the form;

x(t) = A·cos(ωt) + d

Where:

A = Amplitude of the motion = (27 - 7)/2 = 10 cm

ω = Angular frequency = 2·π/T

ωt = Motion's phase

t = Time of the motion

d = The middle location = 27 - 10 = 17 cm

T = The time to complete a cycle = 1 s

Therefore;

ω = 2·π

Given that he stars with his arm extended out, we have;

27 = 10×cos(2×π×0) + 17

Therefore, the equation that models how far from the tip of the saw is from the wood in terms of time is x(t) = 10×cos(2×π×t) + 17.

Answer:41.7

Step-by-step explanation:let the unknown percent be x

X\100 of 48=20

X/100 x 48 =20

48x/100= 20

Cross multiply

48x =100 x 20

48x = 2000

Divide both sides by 48

X= 2000/48

X= 41.7

Answer:

-4/7

Step-by-step explanation:

When we simplify the fraction -64/112, we get -4/7.

Answer:

-4/7

Step-by-step explanation:

-64/112 is already a rational number.

Simplify the fraction.

= -4/7

Answer:

The ball is higher than 10 feet off the ground when the time is between 2 to 5 seconds

Step-by-step explanation:

In the above question, we are given the equation:

h(t) =-t²+7t.

We are asked to find the time (t) when the ball will be higher than 10 feet.

h(t) = height = 10 feet.

So we have:

10 = -t² + 7t

t² - 7t + 10 = 0

We have a quadratic equation hence we factorise.

t² - 5t - 2t + 10 = 0

(t² - 5t) +(2t - 10)= 0

t(t - 5) + 2 (t - 5) = 0

(t - 2) (t - 5) = 0

t - 2 = 0, t = 2

t - 5 = 0, t = 5

t = 5 and t = 2

Therefore, the ball is higher than 10 feet off the ground when the time is between 2 to 5 seconds.

Answer:

Step-by-step explanation:

First write the question as an equation

x+y = -5

2x+y = -2

From the given equations, we can create a third one.

x+y+2x+y = -7 or 3x+2y = -7

Use trial and error method for the possible values x and y

We know that at least one of these two have to be negative.

x can be 1, in which case y has to be 5.

Check this for

x+y ≠ -5

x can be -1

Try another one where x = -1 and y has to equal -2

Check this

X

x+y = -5

but,

2x+y ≠ -2

Another one,

Answer:

3 and -8

3 x 2 = 6

6 + -8 = 2

3 + -8 = 5

You have to find out which numbers add up to -5

Mainly trial and error

Step-by-step explanation:

Answer:

The constant rate of change would be considered slope. It would define the rate of change for the entire line, meaning it would show the constant change for infinity. The average rate of change would be the change between 2 data/set points. It would not be applied to infinite numbers, but only given points and numbers.

Answer:

Step-by-step explanation:

In arithmetic progression common difference is given by

d = nth term - (n-1)th term.

In geometric progression common ratio is given by

r = nth term / (n-1)th term.

Another thing  important to note is that in both AP and GP common difference and common ratio remains same for any two consecutive terms which can be calculated using above formula.

we will be using this concept to solve this problem.

________________________________

Let look at the problem

series

11, 6 ,1

Lets try to find common difference for this series

common difference of third and second term = 1-6 = -5

common difference of  second term and first term = 6 -11 = -5

Thus, we see that common difference is same in both case ,

hence it can be concluded that series is Arithmetic progression.

another way to validate this is

nth term of AP is given by

nth term = a + (n-1)d

where a is first term

lets try to find third term using this formula and using d = -5 and a = 11

3rd term = 11 + (3-1)-5 = 11 + 2*-5 = 11- 10 = 1

Thus, we see that third term calculated is same as given in series i.e 1

Hence series is Arithmetic progression validated as well.

______________________________________________

Problem is solved but lets see if the series is GP or not

common ratio of third and second term = 1/6 = 1/6

common ratio of  second term and first term = 6 /11

Thus, we see common ratio is not same for the two consecutive term in the series and hence series cannot be geometric progression.

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Answer:

Step-by-step explanation:

0.2(20)+6-4(1/2)=4+6-2=8

Answer:

0.2(20)+6-4(112)=4+6-2=8

Answer:

£21,600

Step-by-step explanation:

First thing I did was turn 10% into a decimal of .10 . I then went ahead to multiply that tax by 24, 000. Once I did that I got 2 400. I then went ahead to subtract that from her paycheck and got the outcome of 21 600.

Answer:

[tex] \frac{1}{8} [/tex]

Step-by-step explanation:

there are 8 numbers

we want one of them (number 4)

which is 1 in 8

that is:

[tex] \frac{1}{8} [/tex]

Answer:

-11

Step-by-step explanation:

You need to find the difference in y-coordinates and divide that difference into a 7:3 ratio. Then you add that to the y-coordinate of point J.

Difference in y:

-20 - 10 = -30

7 + 3 = 10

7/10 * (-30) = -21

Add -21 to 10:

10 + (-21) = -11

The y-coordinate is -11.

The diagram that will show possible angle measures of a triangle is. A triangle has angle lengths of 32 degrees, 115 degrees, and 33 degrees.

It should be noted that the sum of the angles that are in a triangle equals 180°. Therefore, in this situation, we'll need to add the values and the one that gives 180° is the right answer.

Therefore, when a triangle has angle lengths 32 degrees, 115 degrees, and 33 degrees, the sum will be:

= 32 + 115 + 33

= 180°

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Answer:

Step-by-step explanation:

It's B