Find the quotient using long division

4x^2-11x+5/x-4

9514 1404 393

Answer:

  a) at t=12, Whitney is speeding up

  b) 13/48 = 0.2704833 . . . miles/min; not a good measure

Step-by-step explanation:

a) At t=12, Whitney's velocity is -0.2 miles/min and is decreasing. That is, the magnitude of her velocity (speed) is increasing. Whitney is speeding up at t=12.

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b) The (signed) area under the curve, divided by the time period (24 min) will give Whitney's average velocity. It can be found by using the formulas for area of a trapezoid and triangle.

  distance 0-11 = 1/2(11 +3)(0.8) = 5.6 miles

  distance 11-16 = 1/2(5)(-0.6) = -1.5 miles

  distance 16-24 = 1/2(8)(0.6 = 2.4 miles

Whitney's average velocity is ...

  (5.6 -1.5 +2.4)mi/(24 min) = 6.5 mi/(24 min) = (13/48) mi/min ≈ 0.270 mi/min

The laws of physics tell us that no work is being done if velocity is constant. Hence, the strenuousness of Whitney's pedaling depends on the acceleration she is maintaining. The average velocity measure tells nothing of that, so is a poor measure of how strenuously Whitney is pedaling.

Answer:

Part A) The distance between Whitney's house and Anh's house is 6.5 miles.

Part B) The total distance traveled by Whitney during the trip was 9.5 miles.

Step-by-step explanation:

Part A)

Notice that during Whitney's journey to Anh's house, her velocity was negative for some time. So, Whitney was travelling backwards. Hence, the total distance Whitney traveled will be greater than the actual distance from Whitney's house to Anh's.

So, instead, we can calculate Whitney's total displacement. Total displacement is given by:

[tex]\displaystyle \text{Displacement}=\int_a^bv(t)\, dt[/tex]

Where v(t) is the velocity function.

So, the displacement of Whitney when she traveled from her house to Anh's house will be:

[tex]\displaystyle \text{Displacement}=\int_0^{24}v(t)\, dt[/tex]

To calculate the integral, we can split it off at t = 11, t = 16, and t = 24.

The three regions represent three geometric figures, which we can use to calculate the area and then find the integral. Rewriting:

[tex]\displaystyle \text{Displacement}=\int_0^{11}v(t)\, dt+\int_{11}^{16}v(t)\, dt+\int_{16}^{24}v(t)\, dt[/tex]

Now, we can calculate the area of each figure.

The first figure is a trapezoid with a height of 0.8 and two bases of 11 and 3. So, its area is:

[tex]\displaystyle A_1=\frac{1}{2}(0.8)(11+3)=5.6\text{ miles}[/tex]

The second figure is a triangle with a height of 0.6 and a base of 5. So, its area is:

[tex]\displaystyle A_2=\frac{1}{2}(0.6)(5)=1.5\text{ miles}[/tex]

Lastly, the third figure is another triangle will a height of 0.6 and a base of 8. So, its area is:

[tex]\displaystyle A_3=\frac{1}{2}(0.6)(8)=2.4\text{ miles}[/tex]

However, notice that the second figure is below the x-axis. During that interval, Whitney was traveling backwards. Hence, we will subtract the second area from the rest of the areas.

Then the displacement will be:

[tex]\displaystyle \text{Displacement}=5.6-1.5+2.4=6.5\text{ miles}[/tex]

So, the distance between Whitney's house and Anh's house is 6.5 miles.

Part B)

The total distance differs from displacement in that it includes all the distances in both directions. It is given by:

[tex]\displaystyle \text{Distance}=\int_a^b|v(t)|\, dt[/tex]

In other words, all of our values are now positive. We will utilize the same strategy:

[tex]\displaystyle \text{Distance}=\int_0^{11}|v(t)|\, dt+\int_{11}^{16}|v(t)|\, dt+\int_{16}^{24}|v(t)|\, dt[/tex]

Substitute. The only difference is that we will add 1.5 instead of subtracting it. So:

[tex]\displaystyle \text{Distance} =5.6+1.5+2.4=9.5[/tex]

Therefore, in this instance, Whitney traveled a total of 9.5 miles to get to Anh's house.

Answer:

y = 1/2x + 10  

Step-by-step explanation:

I'm not sure if this is right but:

First you work out the gradient of the line which is the difference in y divided by the difference in x:  

Gradient = (14 - 11) ÷ (8 - 2) = 3 ÷ 6 = 1/2    

the gradient is 1/2 so you'd write that as: y= 1/2x + c

Then you need to work out the y-intercept ( c )  

You do this by substitution:

14 = 1/2(8) + c

14 = 4 + c

c = 10

So the y-intercept is 10 so you'd write that as:

y = 1/2x + 10

Answer:

1041.44

Step-by-step explanation:

A=2πrh+2πr^2

=2π6.5×19+2π6.5^2≈1041.43796

Answer:

1:3

Step-by-step explanation:

Given thatm

No. of cricket players = 40

No. of kabaddi players = 20

Total no. of players = 40 + 20

= 60

The ratio of kabaddi players to the total number of players is :

R = 20:60

R = 2:6

R = 1:3

Hence, the required ratio is 1:3.

Answer:

x = 0

Step-by-step explanation:

2^x = 1

The only way a number can equal one when there's an exponent is when the exponent is 0

x = 0

2^0 = 1

Answer: 0.40 2.576 √0.40(0.60)

——————

50

Step-by-step explanation:

Put a upside down T which is the Plus-minus sign in between .40 and 2.576

The 99% confidence interval for the proportion of songs on her phone that are by a female artist will be given below. Then the correct option is A.

[tex]0.4 \pm 2.58 \times \dfrac{0.4(1-0.4)}{50}[/tex]

It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.

Della has over 500 songs on her mobile phone, and she wants to estimate what proportion of the songs are by a female artist.

She takes an SRS of 50 songs on her phone and finds that 20 of the songs sampled are by a female artist.

The 99% confidence interval for the proportion of songs on her phone that are by a female artist will be

[tex]\rm x = 20\\\\n = 50 \\\\p = \dfrac{20}{50} = 0.4\\\\z= 99\% \ confidence\ interval = 2.58[/tex]

Then we know that

[tex]p\pm z \times \dfrac{p(1-p)}{n}\\\\0.4 \pm 2.58 \times \dfrac{0.4(1-0.4)}{50}\\\\0.4 \pm 2.58 \times \dfrac{0.4*0.6}{50}\\\\0.4 \pm 0.012384[/tex]

More about the normal distribution link is given below.

https://brainly.com/question/12421652

Answer:

x = ±8

Step-by-step explanation:

The given equation is :

[tex]3x^2-192=0[/tex]

We can use the Square root Property to solve it.

Adding 192 both sides,

[tex]3x^2-192=0\\\\3x^2=192[/tex]

Dividing both sides by 3.

[tex]x^2=64\\\\x=\sqrt{64} \\\\x=\pm 8[/tex]

So, the value of x is equal to +8 and -8.

Answer:

20

Step-by-step explanation:

12.50-8.00=3.00

The number of boxes of cookies that makes the cost equal is 6.

An equation is a mathematical statement containing two expressions on either sides which are connected with an equal to sign.

For the first store,

Cost for 5 boxes of cookies = $12.50

Cost for 1 box of cookie = 12.50 / 5 = $2.50

Cost for x box of cookies = 2.50x

For the second store,

Cost for 4 boxes of cookies = $8

Cost for 1 box of cookie = $8 / 4 = $2

Cost for x box of cookies = 2x

But you have to buy a gallon of milk for $3.00 to get that deal.

Total cost for x boxes of cookies = 2x + 3

Hence the cost model equations are :

C(x) = 2.50x and C(x) = 2x + 3

Cost will be equal when,

2.5x = 2x + 3

0.5x = 3

x = 6

Hence 6 boxes of cookies make both cost equal.

Learn more about Equations here :

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Answer:

76 sq. centimeters.

Step-by-step explanation:

Answer:

76 square centimeters

Step-by-step explanation:

Break it down into easier shapes.

There is one rectangle and one square. Both of them share the same formula for calculating area: length × width.

The rectangle is 6 cm long and 10 cm wide.

Plug this into the formula:

6 cm × 10 cm = 60 cm^2

The square is 4 cm wide. It does not directly say how long it is. Instead, notice how the rectangle below it is 6 cm long and adding the square to it totals to 10 cm long. This means the square is the difference between the total amount of cm and the rectangle's cm. Calculate the difference:

10 cm - 6 cm = 4 cm.

The square is 4 cm long and 4 cm wide.

Plug this into the formula:

4 cm × 4 cm = 16 cm^2

Add both areas together:

60 cm^2 + 16 cm^2 = 76 cm^2

Answer:

i think there is something wrong with this problem

Step-by-step explanation:

maximum sum of all exterior angles is 360°

3(50°) = 150

150° + 127° + 135° = 412°

Answer:

find common denominators

1. 19/15 or 1 4/15

2. 5/12

3. 29/24 or 1 5/24

4.1/6

5. 19/30

6. 13/18

7. 31/24 or 1 7/24

8. 11/20

Answer:

4.7months

Step-by-step explanation:

2.82÷0.6 = 4.7

Answer:

Number of bacteria when t = 10 min is 3,000

Step-by-step explanation:

Given:

Number of bacteria in a culture by equation

Q(t) = 2(729^t)

Value of t = 10 min = 10 / 60 = 0.1667 hour

where t is number of hours

Find:

Number of bacteria when t = 0.1667 hour

Computation:

Given equation

Q(t) = 2(729^t)

Put t = 0.1667

Q(10) = 2(729⁰'¹⁶⁶⁷)

We know that;

a⁰ = 1

So,

Q(0.1667) = 2(729⁰)

Q(0.1667) = 3

Number of bacteria when t = 0 is 3,000

Answer:

The total will be 200, I agree to this person bc i did the math, and he or she is correct

Step-by-step explanation:

Answer:

A,B,E or 1,2,5

if its letters or numbers.

Step-by-step explanat

The expressions that are the result of decreasing x by 80% will be (1 - 0.80)x, x - (80/100)x, and (20/100)x. Then the correct options are A, C, and E.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

The expressions that are the result of decreasing x by 80%.

We know that if something is decreased by a percentage p% then the percentage is written as (1 - p%). Then the expression is written as,

⇒ [(100 - 80) / 100]x

Then the expression can be written as,

⇒ [(100 - 80) / 100]x

⇒ x - (80/100)x

⇒ x - 0.80x

⇒ (1 - 0.80)x

⇒ 0.20x

⇒ (20/100)x

The expressions that are the result of decreasing x by 80% will be (1 - 0.80)x, x - (80/100)x, and (20/100)x. Then the correct options are A, C, and E.

More about the percentage link is given below.

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Answer:

it is D ithought sinse for x=0 y=0 and for x=4 y=-2 (-1/2 x4 =-2 )and others didnot give correct nbs

Answer:

45units²

Step-by-step explanation:

Triangle area = (1/2)(base length)(perpendicular height)

= (1/2)(6)(15)

=3(15)

=45units²

Answer:

A would be the answer

Step-by-step explanation:

Hope it was helpful .

Answer:

Ratios describe proportions. We can always multiply across ratios, or divide across them (as long as we do it to all of them). For example, the ratio 3 : 2 is the same as 6 : 4 and 300 : 200. Accuracy Tip.

Step-by-step explanation:

Answer:

f(-4)   =20

Step-by-step explanation:

f(-4) =  [tex](4)^{2}[/tex] +4 ( Insert -4 in)

f(-4) = 16+4

f(-4)   =20

Answer:

w < 7

Step-by-step explanation:

Since the inequality is an OPEN circle, that means the sign is < or >

Since the sign is going to the left that means it's < or ≤

The one that has both of these effects is <

Since the sign starts at 7, the inequality is w < 7

Answer: B. w<7

Step-by-step explanation:

9514 1404 393

Answer:

  KK KL KM KN KP LL LM LN LP MM MN MP NN NP PP

Step-by-step explanation:

Instead of starting with adjacent letters in the list, we start with the same letter. There are 15 possible pairs.

  KK KL KM KN KP LL LM LN LP MM MN MP NN NP PP

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Additional comment

We leave out pairs with letters previous, because you've said KL is the same as LK, and KL has already been listed. The problem with this list is that it misstates the probabilities of randomly obtaining a given pair. It is not 1/15, but is 2/25 for all but letter duplicates. For duplicates (KK), the probability is 1/25, not 1/15.

Answer:

[tex](x + 2)^2 + (y + 5)^2 = 1[/tex]

Step-by-step explanation:

Equation of a circle:

The equation of a circle with center [tex](x_0,y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

Center: (−2, −5); radius= 1

This means that [tex]x_0 = -2, y_0 = -5, r = 1[/tex]. So

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

[tex](x - (-2))^2 + (y - (-5))^2 = 1^2[/tex]

[tex](x + 2)^2 + (y + 5)^2 = 1[/tex]

This is the equation of the circle.

Answer:

they are the same because lxw is the b so all you need to do is bxh

Step-by-step explanation:

Answer:

0,0215

Step-by-step explanation:

Answer:

D. -2

Step-by-step explanation:

The zero of a function is always along the x-axis and in this case that's -2.

Hope this helps :)

Answer:

go make me a sandwhich you witch

Step-by-step explanation:

Answer:

X=8

Step-by-step explanation:

64 Divided by Eight equals Eight.

Because he worked eight hours that week and earned $64 so divide that up by eight then you got your answer.