A ball is thrown directly upward from height of 2 ft with an initial velocity of 24 ft/sec. The function is s(t)=-16 t^2+24t+2 give the height of the ball, in feet, t seconds after it has been thrown. Determine the time at which the ball reflects its maximum height and find the maximum height.

Answer:

16 x ^4  −  96 x^ 3  +  216 x ^2  −  216 x  +  81

Step-by-step explanation:

Use the binomial expansion theorem to find each term. ∑

∑The binomial theorem states ( a + b ) n = n ∑ k = 0 n C k ⋅ ( a n − k b k ) . 4 ∑ k = 0 4 ! ( 4 − k ) ! k ! ⋅ ( 2 x ) 4 − k ⋅ ( − 3 ) k

Expand the summation. 4 ! ( 4 − 0 ) ! 0 ! ⋅ ( 2 x ) 4 − 0 ⋅ ( − 3 ) 0 + 4 ! ( 4 − 1 ) ! 1 ! ⋅ ( 2 x ) 4 − 1 ⋅ ( − 3 ) + 4 ! ( 4 − 2 ) ! 2 ! ⋅ ( 2 x ) 4 − 2 ⋅ ( − 3 ) 2 + 4 ! ( 4 − 3 ) ! 3 ! ⋅ ( 2 x ) 4 − 3 ⋅ ( − 3 ) 3 + 4 ! ( 4 − 4 ) ! 4 ! ⋅ ( 2 x ) 4 − 4 ⋅ ( − 3 ) 4

Simplify the exponents for each term of the expansion. 1 ⋅ ( 2 x ) 4 ⋅ ( − 3 ) 0 + 4 ⋅ ( 2 x ) 3 ⋅ ( − 3 ) + 6 ⋅ ( 2 x ) 2 ⋅ ( − 3 ) 2 + 4 ⋅ ( 2 x ) ⋅ ( − 3 ) 3 + 1 ⋅ ( 2 x ) 0 ⋅ ( − 3 ) 4

Simplify each term.

= 16 x ^4  −  96 x^ 3  +  216 x ^2  −  216 x  +  81

Answer:

(x-3)^2+(y-5)^2=3^2

Step-by-step explanation:

Answer:

5.4

Step-by-step explanation:

Step 1: Take any two side lengths from the quadrilaterals (one from ABCD and one from PQRS)

Step 2: Divide the length you took from PQRS by the length you took from ABCD.

Step 3: Since CD and RS and corresponding sides, multiply 3 by 1.8

Therefore, x = 5.4.

Answer:

5.4

Step-by-step explanation:

Look at photo for explanation

Answer:

The answer is C.

Step-by-step explanation:

[tex] \: [/tex]

[tex] = 125[/tex]

Step-by-step explanation:

[tex]25 + 100 = ?[/tex]

[tex]25 + 100 = 125[/tex]

[tex] \: [/tex]

1. Commutative property of multiplication = G. 10x3=3x10

3. Associative property of Addition = K. (6+2) + 1 = 6 + (2 + 1)

4. Associative property of multiplication = F. (5x3)x4=5x(3x4)

5. Symmetric property = J. If 11 = y then y = 11

6. Reflexive property = A. 21=21

7. Transitive property = B. If k=15 and 5 = 3m. Then k = 3m

8. Zero property of multiplication = D. 9x0=0

9. multiplicative inverse = I. 8x1/2=1

10. Zero property of multiplication = L. 2+(2-)=0

11. Additive identity = E. 4+0=4

12. Multiplicative identity = H. 19x1=19

Hope this helps!

Answer:

Step-by-step explanation:

G. 10x3=3x10     1. Commutative property of multiplication

3. Associative property of Addition

F. (5x3)x4=5x(3x4)     4.Associative property of multiplication

J. If 11 = y then y = 11      5. Symmetric property

A. 21=21       6. Reflexive property

7. Transitive property

8. Zero property of multiplication

9. multiplicative inverse

D. 9x0=0    10. Zero property of multiplication

E. 4+0=4     11. Additive identity

H. 19x1=19   12. Multiplicative identity

B. If k=15 and 5 = 3m. Then k = 3m    This statement is not true.

This may be the transitive property, but this was written incorrectly. You have 15 in k = 15, but 5 in 5 = 3m.

C. 7+4=4+7      This is commutative property of addition, which is not listed above

I. 8x1/2=1     This statement is false. Maybe you meant 8 x 1/8 = 1. Then it is 9. Multiplicative inverse.

K. (6+2) + 1 = 6 + 2 + 1 This does not illustrate anything.

Maybe you missed the parentheses on the right side: 6 + (2 + 1). Then it is the associative property of addition.

L. 2+(2-)=0 If this were 2 + (-2) = 0, then it would be Additive Inverse, but I don't see this listed above.

Answer:

It is a geometric sequence and the common scale factor is [tex]\frac{2}{3}[/tex].

Step-by-step explanation:

In an arithmetic sequence, the difference between consecutive terms is always the same.

[tex]a_n=a_1+(n-1)d[/tex]

where aₙ is the nth term, a₁ is the first term, n is the index, and d is the common difference.

In a geometric sequence, each consecutive term was multiplied by some factor over the last.

[tex]a_n=ax^n^-^1[/tex]

where aₙ is the nth term, n is the index, and x is the scale factor.

In the given sequence, there is no common difference so it is not an arithmetic sequence. There is, however, a common scale factor applied to each consecutive term. Each term is multiplied by [tex]\frac{2}{3}[/tex] over the last.

The formula for this sequence would be:

[tex]a_n=a\frac{2}{3} ^{n-1}[/tex]

Answer:

r = [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

If the sequence is geometric then there will be a common ratio r between consecutive terms , that is

r = a₂ ÷ a₁ = a₃ ÷ a₂ = a₄ ÷ a₃

Then

a₂ ÷ a₁ = [tex]\frac{2}{9}[/tex] ÷ [tex]\frac{1}{3}[/tex] = [tex]\frac{2}{9}[/tex] × 3 = [tex]\frac{2}{3}[/tex]

a₃ ÷ a₂ = [tex]\frac{4}{27}[/tex] ÷ [tex]\frac{2}{9}[/tex] = [tex]\frac{4}{27}[/tex] × [tex]\frac{9}{2}[/tex] = [tex]\frac{2}{3}[/tex]

a₄ ÷ a₃ = [tex]\frac{8}{81}[/tex] ÷ [tex]\frac{4}{27}[/tex] = [tex]\frac{8}{81}[/tex] × [tex]\frac{27}{4}[/tex] = [tex]\frac{2}{3}[/tex]

Then sequence is geometric with common ratio r = [tex]\frac{2}{3}[/tex]

Answer:

slop = 2/3

Step-by-step explanation:

slope = rise/run

Start at the lower left point (-2, -1).

We need to go to the upper right point (4, 3) by going only vertically (rise) and horizontally (run).

First we go up 4. The rise is 4.

Then we go right 6. The run is 6.

slope = m = rise/run = 4/6 = 2/3

slope = 2/3

Answer:

2035

Step-by-step explanation:

2010=100g

2020=70

100-70=30

70-30=40

2030=40

Answer:

Somewhere in 2038

Step-by-step explanation:

In 2010 in there was 100g of a certain radioactive isotope

In 2020 now there’s 70g of a certain radioactive isotope

what changed,?

In 10 years they lost 30g of radioactive isotope

Therefore

Year 2030 there will be 50g

Year 2035 there will be 35g

Year 2040 there will be 20g

But we want to get 25g in how many years

1 year takes 3g

2 year takes 6g

3 year takes 9g

4 year takes 12g

But we need to take away 10g from 35 so it’ll be between somewhere between 2038 maybe half year..

Answer:

Step-by-step explanation:

System of equations according to given:

Substitute n into first equation and solve for s:

Equations are

EQUATION(2)× 30

[tex]\\ \sf\longmapsto 30x-30y=120--(3)[/tex]

Subtracting (1) and (3)

[tex]\\ \sf\longmapsto 80y=560[/tex]

[tex]\\ \sf\longmapsto y=7[/tex]

Answer:

1225

350/2=175

175 x 7 = 1225

Answer:

32

Step-by-step explanation:

Trust me its hard to explain.

Answer:

n = 8.

Step-by-step explanation:

The interior angle of a regular hexagon = 120 degrees.

So m < GAB = 360 - 120 - 105

= 135 degrees so the regular polygon has a total of 135n degrees.

Using the formula for the sum of interior angles of a polygon,

For the polygon with n sides:

Sum of interior angles = 180(n - 2)

135n = 180(n - 2)

135n = 180n - 360

45n = 360

n = 360/45 = 8.

Answer:

It is 0.8 + n = 4.5 that is the right answer

Answer: 0.8 plus n equals 4.5

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

For a line joining two points (x1, y1) and (x2, y2), it's slope is given as:

[tex] \boxed{ \mathsf{slope = \frac{ y_{2} -y _{1}}{ x_{2} - x _{1}} }}[/tex]

Here, the two points are (-1, 6) and (2, 3) in place of (x1, y1) and (x2, y2).

Solving for slope:

[tex] \implies \mathsf{ \frac{3 - 6}{2 - ( -1 )} }[/tex]

[tex] \implies \mathsf{ \frac{ - 3}{2 + 1 } }[/tex]

[tex] \implies \mathsf{ \frac{ - 3}{3 } }[/tex]

[tex] \implies \mathsf{ - 1 }[/tex]

Hence, the slope of the line joining the given points is -1.

Answer:

-1

Step-by-step explanation:

Answer:

so the answer is = 210 beacuse  u have multiply 5 times 6 times 7

Step-by-step explanation:

So, the area A of a triangle is given by the formula A=12bh where b is the base and h is the height of the triangle. Example: Find the area of the triangle. The area A of a triangle is given by the formula A=12bh where b is the base and h is the height of the triangle.

Answer:

5. 8 months

6. 13 pencils

Answer:

ΔY = 10

Step-by-step explanation:

Answer:

2.50

Step-by-step explanation:

If 4= $5.00

then divided 5.00 by 4=1.25

so 1 = 1.25

1.25x2=2.50

Therefore 2 tastykake snack cakes = $2.50

Answer:

The answer is 2.5

Step-by-step explanation:

5 divided by 4 = 1.25

1.25 times 2 = 2.5

brainliest :)

Step-by-step explanation:

4) total length of the journey is

1st hr = 74km 224m = 74224m

2nd hr = 74km 224m = 74224m

3rd hr = 58km 56m = 58056m

4th hr = 62km 8m = 62008 m

total distance (adding all) = 268512m = 268km 512m .

5) total weight = 22kg 200g = 22200g

mangoes weight = 14kg 750g = 14750g

apples weight = 5kg 80g = 5080g

total weight - fruits weight

(22200-14750-5080)g

= 2370g

= 2kg 370g.

hope this helps you.

Answer:

1.8

Step-by-step explanation:

-2 1/4 x -4/5 = 9/5

= 1 4/5

= 1.8

Answer:

-4, 2    (-4,0) (2,0)

Step-by-step explanation:

factoring in binomials

[tex](x+4)(x-2)=x^{2} +2x-8[/tex]

The zeros:

[tex]x+4=0\\x=0-4\\x_{1} =-4[/tex]

[tex]x-2=0\\x=0+2\\x_{2} =2[/tex]

I hope this help you

Answer:

- x - 16

Step-by-step explanation:

Answer:

439

Step-by-step explanation:

The denominator simplifies to 106/15

The question becomes

3+1/(106/15)=3+15/106=333/106

Therefore m+n=439

Answer:

4/7

Step-by-step explanation:

6 -2/2+5 = 4/7

thats it simple

Answer: 10

Step-by-step explanation:

6-x/x+5

6-(2)/(2)+5

Order of Operations

6-1+5

5+5

10