A group of students is arranging squares into layers to create a project. The first layer has 5 squares. The second layer has 10 squares. Which formula represents an arithmetic explicit formula to determine the number of squares in each layer ?

Answer:

8 : 27

Step-by-step explanation:

Given the ratio of sides of 2 similar objects = a : b , then

ratio of volumes = a³ : b³

Here ratio of sides = 56 : 84 = 2 : 3 , then

ratio of volumes = 2³ : 3³ = 8 : 27

Given:

The height of a basketball is given by the function:

[tex]h(x)=-0.5x^2+3x+6[/tex]

where x is the horizontal distance from where it is thrown.

To find:

How far away from the basket should the player stand in order for the ball to go in the basket (10 feet high) on its way down.

Solution:

We have,

[tex]h(x)=-0.5x^2+3x+6[/tex]

Putting [tex]h(x)=10[/tex], we get

[tex]10=-0.5x^2+3x+6[/tex]

[tex]10+\dfrac{1}{2}x^2-3x-6=0[/tex]

[tex]\dfrac{1}{2}x^2-3x+4=0[/tex]

Multiply both sides by 2.

[tex]x^2-6x+8=0[/tex]

Splitting the middle term, we get

[tex]x^2-4x-2x+8=0[/tex]

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

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

[tex]x=2,4[/tex]

In the given function the leading coefficient is negative, so the given function represents a downward parabola. It means, first the function is increasing after that the function is decreasing.

So, the value of the function is 10 at [tex]x=2[/tex] (its way up) and at [tex]x=4[/tex] (its way down.

Therefore, the player should stand 4 units away from the basket in order for the ball to go in the basket (10 feet high) on its way down.

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

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:

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:

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

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 .

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

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

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:

brainly.com/question/24159063

#SPJ2

Answer:x=3

Step-by-step explanation:

4x+3=x+9

4x-x=(-3)+9

3x=6

x=6:3

x=2

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:

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:

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:

here's the answer to your question about

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

Learn more here: https://brainly.com/question/23531710

Answer:

5x10^-2 option B

Step-by-step explanation:

Answer:

5x10^-2

the second one.

Answer:

4/3

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:

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:

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]

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

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.

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:

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:

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:

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:

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