What is the average rate of change for this quadratic function for the interval
from x = 3 to X = 5?

Answer:

Approximately 9.2

Step-by-step explanation:

For right triangle, if you know 2 sides, you can find the third using pythagorean theorem, a^2 + b^2 = c^2. 'a' and 'b' are the lengths of the legs, while 'c' is the hypotenuse. You can plug in what you know into this formula:

9^2 + 2^2 = c^2

81+4 = c^2

c = √85, or approximately 9.2

Answer:

Chukwu's share is of $57.

Step-by-step explanation:

This question is solved by a system of equations.

I am going to say that:

Chukwu's share is x.

Abdul's share is y.

Kunle's share is z.

Chukwu, Abdul and kunle are to share $142

This means that [tex]x + y + z = 142[/tex]

Abdul gets $11.00 less than Chukwu

This means that:

[tex]y = x - 11[/tex]

$7.00 more than Kunle.

This means that:

[tex]y = z + 7[/tex]

So

[tex]z = y - 7[/tex]

[tex]z = x - 11 - 7[/tex]

[tex]z = x - 18[/tex]

How much is Chukwu's share?

We want to find x, so:

[tex]x + y + z = 142[/tex]

[tex]x + x - 11 + x - 18 = 142[/tex]

[tex]3x - 29 = 142[/tex]

[tex]3x = 171[/tex]

[tex]x = \frac{171}{3}[/tex]

[tex]x = 57[/tex]

Chukwu's share is of $57.

Answer:

Given:- [tex]y=-5x^3+10x+20[/tex]

A parabola attain maximum height at the vertex: formula to find x-coordinate of vertex is, [tex]x=-\frac{b}{2a}[/tex]

plug in a=-5 and b=10

so, [tex]x=-\frac{10}{2(-5)} =-\frac{10}{-10} =1[/tex]

Now plug in x=1 to get maximum height,

[tex]y=-5(-1)^2+10(1)+20[/tex]

[tex]=-5+10+20[/tex]

[tex]=+25[/tex]

so, maximum heigh reached by the rocket was 25 yards

Rocket will hit the ground when y=0

[tex]0=-5x^2+10x+20[/tex]

[tex]0=-5(x^2-2x-4)[/tex]

[tex]\frac{0}{-5} =\frac{-5}{-5} (x^2-2x-4)[/tex]

So, [tex]x^2-2x-4=0[/tex]

quadratic formula is,

[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]

plug in a=1, b=-2,and c=-4

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

[tex]=\frac{2=-\sqrt{4+16} }{2}[/tex]

[tex]=\frac{2+-\sqrt{20} }{2}[/tex]

[tex]=\frac{2+-2\sqrt{5} }{2}[/tex]

[tex]=1+-\sqrt{5}[/tex]

[tex]=1-\sqrt{5} ,1+\sqrt{5}[/tex]

[tex]=1-5.236,1+2.236[/tex]

[tex]=-1.236,3.236[/tex]

So, it takes 3.2 seconds to hit the ground.

OAmalOHopeO

Area = Side^2

Area =( 4x + 2 )^2

Area = (4x)^2 + 2(4x)(2) + (2)^2

Area = 16x^2 + 16x + 4

Thus the correct answer is option B .

9514 1404 393

Answer:

  y = 4

Step-by-step explanation:

The given points are on the horizontal line ...

  y = 4

This is the standard-form equation of that line.

Answer:

Step-by-step explanation:

[tex]\frac{sinxcos^3x-cos xsin^3x}{cos^42x-sin^42x} \\=\frac{sin x cos x(cos^2x-sin ^2 x)}{(cis^2 2x+sin^2 2x)(cos^2 2x-sin ^22x)} \\=\frac{2sin x cos x cos 2x}{2(1)(cos 4x)} \\=\frac{sin 2x cos 2x}{2 cos 4x} \\=\frac{2 sin 2x cos 2x}{4 cos 4x} \\=\frac{sin 4x}{4 cos 4x} \\=\frac{1}{4} tan 4x[/tex]

Answer:

10

Step-by-step explanation:

ans is 10

because 2×5 is 10

Answer:

2x5= 10

Step-by-step explanation:

5, 10,15,20

five 2 times is 10

Answer:

17

Step-by-step explanation:

2f + 4f + 2 - 3 when f = 3

1) first we multiply 3 wherever f is

2 x 3 + 4 x 3 + 2 - 3 (solve)

6 + 12 + 2 - 3

18 + 2 - 3

20 - 3

17

Answer:

6+12+2-3=17

Step-by-step explanation:

Step-by-step explanation:

Asymptote: y = 2 y-intercept: (0,8)

Step-by-step explanation:

The given function is

f(x) = 6(0.5)^{x} + 2f(x)=6(0.5)

x

+2

This function is of the form:

f(x) = a {b}^{x} + cf(x)=ab

x

+c

where y=c is the horizontal asymptote.

By comparing , we have c=2 hence the horizontal asymptote is

y = 2y=2

To find the y-intercept, we put x=0 into the function to get:

f(0) = 6(0.5)^{0} + 2 = 6 + 2 = 8f(0)=6(0.5)

0

+2=6+2=8

Therefore the y-intercept is (0,8).

Answer:

32 newspapers

Step-by-step explanation:

6.4 / 0.2 = 32

Answer:

32 papers

Step-by-step explanation:

Take the total amount and divide by .20

6.40 / .20

Multiply the top and bottom by 10

64/2

32

Answer:

θ = 51.7

SOH-CAH-TOA

CAH: COS = ADJ/HYP   cos(θ) = 19.4/29.3

θ = 48.5

93.2 + 48.5 + x = 180

x = 38.3

90 + 38.3 + θ = 180

θ = 51.7

Step-by-step explanation:

Answer:

Step-by-step explanation:

I hope these are people in vehicles travelling toward each other.

80 mh * t + 40 mph * t = 420 miles

The two vehicles are going to travel a total of 420 miles. B will cover a lot more ground than A, but together they will make 420 miles

80t + 40t = 420

120t = 420

t = 420/120

t = 3.5

So after driving 3.5 hours, the two cars will meet.

Answer:3165

Step-by-step explanation:

Answer:

b = 2√3

a = 4

Step-by-step explanation:

Here taking 60 as reference angle

so

tan60 = p/b

[tex]\sqrt{3}[/tex]    = p/2

so p = 2√3

so

b = 2√3

so

[tex]h^2 = p^2 + b^2\\h^2 = (2\sqrt{3})^2 + 2^2\\h^2 = 12 + 4\\h^2 = 16\\h = \sqrt{16} \\h = 4[/tex]

a = 4

Answer:x=3

Step-by-step explanation:

4x+3=x+9

4x-x=(-3)+9

3x=6

x=6:3

x=2

Answer:

here's the answer to your question about

Answer:

The speed of the balloon is 0.16 m/s.

Step-by-step explanation:

CD = 300 m

Let AD = x

AB = y

time, t = 3 min

Triangle, ADC

[tex]tan 15 = \frac{AD}{BC}\\\\0.27 \times 300 = x \\\\x = 80.4 m[/tex]

Triangle, BCD

[tex]tan 20 = \frac{BD}{BC}\\\\0.36 \times 300 = x + y \\\\x + y = 109.2 m[/tex]

So, y = 109.2 - 80.4 = 28.8 m

Speed = 28.8/180 = 0.16 m/s

Answer:

11/43

Step-by-step explanation:

A local community college has 860 students

Out of this 860 students, 220students ride bikes

Therefore the fraction of bike riders to the number of students can be calculated as follows

= 220/860

= 11/43

Answer:

y = 1/2x + 5/2

Step-by-step explanation:

y = 1/2x + b

5 = 1/2(5) + b

5 = 5/2 + b

5/2 = b

If you can show that the following two items are true

then you have shown that triangle A'B'C' is a translated or shifted copy of triangle ABC. In other words, they are the same triangle.

Answer:

Mike had 72 stamps

Ken had 120 stamps

Step-by-step explanation:

Given

[tex]M \to Mike[/tex]

[tex]K \to Ken[/tex]

[tex]\frac{1}{5} * K = \frac{1}{3} * M[/tex]

[tex]K + 24 = 3 * ( M - 24)[/tex]

Required

Find K and M

Make K the subject in: [tex]K + 24 = 3 * ( M - 24)[/tex]

[tex]K = 3 * ( M - 24) - 24[/tex]

Substitute [tex]K = 3 * ( M - 24) - 24[/tex] in [tex]\frac{1}{5} * K = \frac{1}{3} * M[/tex]

[tex]\frac{1}{5} * [3 * ( M - 24) - 24] = \frac{1}{3} * M[/tex]

Open brackets

[tex]\frac{1}{5} * [3M - 72 - 24] = \frac{1}{3} * M[/tex]

[tex]\frac{1}{5} * [3M -96] = \frac{1}{3} * M[/tex]

Multiply both sides by 15

[tex]3* [3M -96] = 5 * M[/tex]

[tex]9M -288 = 5M[/tex]

Collect like terms

[tex]9M -5M= 288[/tex]

[tex]4M= 288[/tex]

Divide both sides by 4

[tex]M= 72[/tex]

Substitute [tex]M= 72[/tex] in [tex]K = 3 * ( M - 24) - 24[/tex]

[tex]K = 3 * (72 - 24) - 24[/tex]

[tex]K = 3 * 48 - 24[/tex]

[tex]K = 120[/tex]

Nate had $3000 at the beginning.

The percentage is defined as a ratio expressed as a fraction of 100.

Let the original amount of money is P

Nate spent 12 % of his paycheck on car repairs

⇒ 12% of P = 12P/100

And he spent 25 % of the remainder on food.

⇒  0.25(88/100)P

He gave $ 1,320 of the remaining money to his parents

⇒ 1320  

If the usual price of the computer was $ 825 and the discount was 20 %

⇒ 825 - 0.20(825) = 660

P = 12P/100 + 0.25(88/100)P + 1320 + 660

P - 34P/100 = 1980

100P - 66P = 198000

P = 3000

Hence, Nate had $3000 at the beginning.

Learn more about the percentages here:

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#SPJ2

Answer:

4/3

Step-by-step explanation:

Answer:

h=17.3 A=173

Step-by-step explanation:

Calculator

Answer:

height = 17.3 mm

area = 173 mm²

Step-by-step explanation:

all three sides are of the same length (20 mm).

so, the height actually splits the baseline in half

(2 × 10 mm) while hitting it at a 90 degree angle.

so, we use Pythagoras, where the full side opposite of this 90 degree angle is c (Hypotenuse), the height of the main triangle is one side, and half of the baseline is the other side.

c² = a² + b²

20² = 10² + height²

400 = 100 + height²

300 = height²

height = 17.3 mm

the area of the main triangle is baseline (20) times height divided by 2.

so,

At = 20×17.3/2 = 10×17.3 = 173 mm²

Answer:

380

Step-by-step explanation:

This is a bit nasty. It depends on how you read the 20 miles more and what you do with it. The best and most careful way to do it is do it a long way setting up the two equations carefully.

Second day

Let the time travelled = t

Let the speed travelled = 60 mph

d2 = 60*t

First Day

40*(t + 2) = d1

but d1 = d2 + 20 because he travelled 20 miles further on d1

40 * (t + 2) = d2 + 20

d2 however = 60*t

40*(t+2 ) = 60*t + 20          Remove the brackets

40t + 80 = 60t + 20           Subtract 20 from both sides

40t + 60 = 60t                   Subtract 40t from both sides

60 = 20*t                           Divide by 20

t = 60/20

t = 3 hours.

Day 2 = 60 + t = 180

Day 1 = 40*5  = 200

Total distance = 380

Where did that 20 miles go? It was just an observation about the difference in distance travelled between the 2 days.

The total distance the driver traveled in the two days is 260 miles

From the question, on the first day, the driver was going as a speed of 40 mph.

Let s be speed

∴ [tex]s_{1}= 40mph[/tex]

On the second day, he increased the speed to 60 mph

∴ [tex]s_{2}= 60mph[/tex]

From the statement- If he drove 2 more hours on the first day

Let time be t

Then

[tex]t_{1}= t_{2} + 2[/tex] hrs

and traveled 20 more miles

Let d be distance  

Then,

[tex]d_{1}= d_{2} + 20[/tex] miles

From the formula

Distance = Speed × Time

Then,

[tex]d = s \times t[/tex]

∴ [tex]d_{1} = s_{1} \times t_{1}[/tex]

From above,

[tex]d_{1}= d_{2}+20[/tex] miles

[tex]s_{1}= 40mph[/tex]

[tex]t_{1}= t_{2} + 2[/tex] hrs

Putting these into

[tex]d_{1} = s_{1} \times t_{1}[/tex]

[tex]d_{2} + 20 = 40\times (t_{2}+2)[/tex] ...... (1)

But,

[tex]Time = \frac{Distance}{Speed}[/tex]

∴ [tex]t_{2}= \frac{d_{2} }{s_{2} }[/tex]

From above, [tex]s_{2}= 60mph[/tex]

∴ [tex]t_{2}= \frac{d_{2} }{60}[/tex]

Put this into equation (1)

[tex]d_{2} + 20 = 40\times (t_{2}+2)[/tex]

[tex]d_{2} + 20 = 40\times (\frac{d_{2}}{60} +2)[/tex]

[tex]d_{2} + 20 = \frac{2}{3}d_{2} +80\\d_{2} = \frac{2}{3}d_{2} +80-20\\d_{2} = \frac{2}{3}d_{2} +60[/tex]

Multiply through by 3

[tex]3\times d_{2} = 3\times \frac{2}{3}d_{2} +3 \times 60\\3d_{2} = 2d_{2} + 120\\3d_{2} -2d_{2} = 120[/tex]

∴ [tex]d_{2} = 120[/tex] miles

∴The distance traveled on the second day is 120 miles

For the distance traveled on the first day,

Substitute [tex]d_{2}[/tex] into the equation

[tex]d_{1}= d_{2}+20[/tex] miles

∴ [tex]d_{1}= 120+20[/tex]

[tex]d_{1}= 140[/tex] miles

∴ The distance traveled on the first day is 140 miles

The total distance traveled in the two days = [tex]d_{1} + d_{2}[/tex]

The total distance traveled in the two days = 120 miles + 140 miles

The total distance traveled in the two days = 260 miles

Hence, the total distance the driver traveled in the two days is 260 miles

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Answer:

56.57

Step-by-step explanation:

See attached photo for steps

EDIT: I forgot to add 3.14, I am so sorry

Answer:

56.52

Step-by-step explanation:

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

Explanation:

HL stands for Hypotenuse Leg. This rule works only for right triangles.

So we must have two hypotenuses that are congruent, and we must have two legs that are congruent

The diagram shows that AB = DE are the congruent hypotenuses. So we have "H" taken care of. We just need the "L" portion.

We can see that only choice D works, which is AC = EC. If we knew that AC and EC were the congruent legs, then we have enough info to use HL.

Answer:

3596

Step-by-step explanation:

Use long multiplication to evaluate.

Answer:

3596

Step-by-step explanation:

(58*10) = 580

580*6 = 3480

58 * 2 = 116

3480 + 116 = 3596

Answer:

5x10^-2 option B

Step-by-step explanation:

Answer:

5x10^-2

the second one.