A toy rocket is shot vertically into the air from a launching pad 6 feet above the ground with an initial velocity of 88 feet per second. The height​ h, in​ feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=−16t*2 + 88t +6. How long will it take the rocket to reach its maximum​ height? What is the maximum​ height?
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Part 1
The rocket reaches its maximum height at ? ​second(s) after launch.

Answer:

22 meters

Step-by-step explanation:

Let x = width of the rectangle

Let y = length of the rectangle

Equation 1

If the length of the rectangle is 6 meters shorter than four times the width then:

⇒ y = 4x - 6

Equation 2

Perimeter of a rectangle = 2(width + length)

If the perimeter is 58 inches, then:

⇒ 58 = 2(x + y)

Solve by substitution

Substitute Equation 1 into Equation 2 and solve for x:

⇒ 58 = 2(x + 4x - 6)

⇒ 58 = 2(5x - 6)

⇒ 58 = 2 · 5x - 2 · 6

⇒ 58 = 10x - 12

⇒ 58 + 12 = 10x -12 + 12

⇒ 10x = 70

⇒ 10x ÷ 10 = 70 ÷ 10

⇒ x = 7

Substitute found value of x into Equation 1 and solve for y:

⇒ y = 4(7) - 6

⇒ y = 28 - 6

⇒ y = 22

Conclusion

The dimensions of the rectangle are:

Therefore, the length of the longer side is 22 meters

The length of the longer side is 22 meters.

Let, one side of the rectangle is x meters.

According to the problem, the other side is 6 meters shorter than four times this side, which means the length of the second side is (4x - 6) meters.

The perimeter of a rectangle is given by the formula:

Perimeter = 2 * (length + width)

In this case, the perimeter is 58 meters:

58 = 2 * (x + 4x - 6)

Now, let's solve for x:

58 = 2 * (5x - 6)

58 = 10x - 12

Add 12 to both sides:

58 + 12 = 10x

70 = 10x

Now, divide both sides by 10 to isolate x:

x = 70 / 10

x = 7

So, one side of the rectangle is 7 meters.

Now, we can find the length of the longer side:

Length of the longer side = 4x - 6

Length of the longer side = 4 * 7 - 6

Length of the longer side = 28 - 6

Length of the longer side = 22 meters

Therefore, the length of the longer side is 22 meters.

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Answer:

1. 5² is 25 yards

2. 7² is 49m

3. 8² is 64cm

4.draw a square, make one side 6 feet then do 6² which is 36feet

5. do the same thing then write 10 inches on one side and 10² is 100 inches.

6. 7x3= 21 ft

7. 5x4= 20 in.

8. 2x8= 16 yd

Step-by-step explanation:

common sense

Answer:

123 save some for me

Step-by-step explanation:

:0

Answer: 123

Step-by-step explanation: I did the math- lol-

Answer:

Step-by-step explanation:

D∩L={f}

D∪L={a,f,g,j,k}

Primeter=10 + 4 +10 +7 = 31 ft

AnswEr :

Let's assume , three Consecutive integers be x , ( x +1 ) & ( x+2 ) , such that , x < ( x +1 ) < ( x +2 ) .

⠀⠀⠀⠀⠀⠀[tex]\underline {\boldsymbol{\star\: According \: to \: the \: Given \: Question \::}}\\[/tex]

⠀⠀⠀⠀⠀— The product of three consecutive integers is 30 times the smallest of the three integers.

[tex] \sf \dashrightarrow \:30\: \bigg\{ \: Smallest_{(\:integer\:)}\:\bigg\}\:\:=\: \:\bigg\{ \: I^{st} \:Integer\:\bigg\}\: \:\bigg\{\: II^{nd}\:Integer\:\bigg\}\: \:\bigg\{ \: III^{rd} \:Integer\:\bigg\}\:\:\: \\\\\sf \dashrightarrow \:30\: \bigg\{ \:x\:\bigg\}\:\:=\: \:\bigg\{ \: x\:\bigg\}\: \:\bigg\{ \: x + 1\:\bigg\}\: \:\bigg\{ \: x +2 \:\bigg\}\:\:\: \\\\ \sf \dashrightarrow \:30\: \:\:=\: \:\bigg\{ \: x + 1\:\bigg\}\: \:\bigg\{ \: x +2 \:\bigg\}\:\:\: \\\\ \sf \dashrightarrow \:30\: \:\:=\: \:x^2 + 3x + 2 \:\:\: \\\\ \sf \dashrightarrow \:x^2 + 3x - 28 \:= \:0\: \\\\ \sf \dashrightarrow \:\:\bigg\{ \: x - 2 \:\bigg\}\:\:\bigg\{ \: x + 7 \:\bigg\}\: \:= \:0\: \\\\ \pmb {\underline {\boxed {\purple {\:\frak{ \:x\:\:=\:-7\: \&\:2\:}}}}}\:\bigstar \: \\\\\\[/tex]

Therefore ,

When , x = 2 ,

When , x = –7 ,

Answer:

Hi,

Step-by-step explanation:

If the "is" means is equal to

Let's say a-1, a, a+1 the 3 consecutive integers.

[tex](a-1)*a*(a+1)=30*(a-1)\\\\(a-1)*(a*(a+1)-30)=0\\\\(a-1)(a^2+a-30)=0\\\\(a-1)(a^2+6a-5a-30)=0\\\\(a-1)(a(a+6)-5(a+6))=0\\\\(a-1)(a+6)(a-5)=0\\\\a=1\ or\ a=-6\ or\ a=5\\[/tex]

[tex]\begin{array}{|c|c|c|c|c|}a&a-1&a+1&Prod&30*(a-1)\\---&----&----&----&--------\\1&0&2&0&30*0=0\\5&4&6&120&4*30=120\\-6&-7&-5&-210&30*(-6)=-180\end{array}\\[/tex]

The two sets are : (0,1,2) and (4,5,6).

Explanation:

Pick any term. Subtract off the previous one to find the common difference.

And so on. You only need to pick one of those to show as your steps to your teacher. However, doing all three subtractions is a good way to get practice in seeing how we have an arithmetic sequence. The common difference must be the same each time.

We subtract 7 from each term to get the next term, i.e. we add -7 to each term to get the next one.

Hi student, let me help you out! :)

.  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We need to translate "five times the sum of a number and -23" into an algebraic expression.

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

So in this case we should add a number (let it be x) and -23:

[tex]\star~\large\pmb{x+-23}[/tex]

Which is the same thing as

[tex]\star~\large\pmb{x-23}[/tex]

Now we multiply this little expression by 5, which gives us

[tex]\star~\large\pmb{5(x-23)}[/tex]

The parentheses around the  expression indicate that we multiply 5 by the entire expression, and not just one term.

Hope it helps you out! :D

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

Answer:

60°

Step-by-step explanation:

Arc BC and Angle BWC are the same number of degrees.

When the vertex of an angle is at the center of a circle, its called a Central Angle. A central angle and the arc it "cuts off" have the same number of degrees.

Angle AWB and Angle BWC lay together on a straight line, so they add up to 180°.

180° - 120° is 60°

Angle BWC is 60° so Arc BC is 60°

I'll focus on question 10 only. Let me know if you need me to answer the others.

We have the population with this set of numbers: {2,4,6,8,10}

There are 5 values in that set.

Now consider having slots labeled A,B and C to represent the three placeholders for the numbers.

There are 5*4*3 = 20*3 = 60 permutations and 60/(3*2*1) = 60/6 = 10 combinations.

Therefore, we have 10 different subsamples of 3 items.

Step-by-step explanation:

4a(a-x)+x(a-x)

[4a]2-4ax+ax-(x)2

(4a)2-3ax-(x)2

1. If the mean is used to determine Nathan's salary, he should choose Company A.

2. If the median is used to determine Nathan's salary, he should choose Company A.

3. The center of the data for Company B is more accurately described by the Median because the data is not uniformly scattered and has extreme values or outliers.

The Mean is the average value obtained after adding up a set of values and dividing the result by the number in the set.

The Median represents the middle value in an ordered list from smallest to largest.

Salaries   Company A   Company B

Year 1                10                   10

Year 2              20                  20

Year 3              30                  70

Year 4              40                  30

Year 5              50                  40

Year 6              60                  50

Year 7              70                  60

Total             280                280

Mean              40                  40

Median           40                  35 (30 + 40)/2

Thus, Nathan should choose Company A whether the Mean or the Median is used to determine Nathan's salary.

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Answer: Company B

Company A

Median

Skewed Right

Step-by-step explanation:

Answer:

10 m

Step-by-step explanation:

opposite = sin30° × 20 = [tex]\frac{1}{2}[/tex] × 20 = 10 m

Answer:

4x^2 - 4x - 3

Step-by-step explanation:

f(x) = 2x - 1

g(x) = x^2 - 4

g(f(x)) = ?

[substitute the x of g(x) with f(x)]

g(x) = x^2 - 4

g(f(x)) = (2x - 1)^2 - 4

[solve]

[binomial * binomial = quadratic equation]

[use FOIL method (first, outer, inner, last)]

g(f(x)) = (2x - 1)(2x - 1) - 4

g(f(x)) = (2x*2x) + (-2x) + (-2x) + (1) - 4

[combine like terms]

g(f(x)) = 4x^2 - 2x - 2x + 1 - 4

g(f(x)) = 4x^2 - 4x - 3

Answer:

1 28/99

Step-by-step explanation:

When a number with 1-2 digits is divided by 99, it gets repeated with two digits. For example, 2/99=0.0202020202...

Another example would be 18/99=0.18181818...

Using this information, we can determine that 1.28282828 repeating would be 1 28/99

Let me know if you have any questions! :)

The inverse function of f(x) = 3x + 3 is f-1(x) = 1/3x - 1

The equation is given as:

f(x) = 3x + 3

Express f(x) as y

y = 3x + 3

Swap the positions of y and x

x = 3y + 3

Make y the subject

3y = x - 3

Divide by 3

y = 1/3x - 1

Replace y with the inverse function

f-1(x) = 1/3x - 1

Hence, the inverse function of f(x) = 3x + 3 is f-1(x) = 1/3x - 1

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Answer:

There are 0 solutions to this problem because it cannot be re-arranged logically enough to come to a new conclusion.

Answer:

0

Step-by-step explanation:

If we try to solve this question, we get no solutions:

First we subtract 5 from both sides :

9x = 9x + 2

Now we subtract 9x from both sides :

0 = 0 +2

0 = 2 ❌

This is why this equation has no solutions

Hope this helped and have a good day

The decimal degree of the angle 12' 8" is 0.2022

The angle measure is given as:

Angle = 12' 8"

As a general rule;

Where:

' represents minutes and " represents seconds.

So, we have:

Angle = 12/60 + 8/(60 * 60)

Evaluate the expression

Angle = 0.2022

Hence, the decimal degree of the angle 12' 8" is 0.2022

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Answer:

a=11,b=7 Is the correct answer

Please mark me as brainliest

Answer:

a = 11 and b = 7

Step-by-step explanation:

Multiply numerical values 5 x (-4) then add exponents of like terms x⁷(x⁴) = x¹¹ then y²(y⁵) = y⁷

Answer:

Step-by-step explanation:

1. To find f(0.5), substitute the x value in the function f(x) with 0.5

            f(x) = 30x + 5

          f(0.5) = 30*0.5 + 5

                    = 15 + 5

                    = 20

At 0.5 gigabytes of data used, the cost is  $20

2)  g(x) = 10x + 20

g(0.5) =  10*0.5 + 20

           = 5 + 20

           = 25

At 0.5 gigabytes of data used, the cost is $ 25.

3)          f(x) = 50

    30x + 5  = 50

Subtract 5 from both sides

            30x = 50 - 5

            30x = 45

Divide both sides by 30

                x = 45/30

             x = 1.5

If she chooses plan 'f', she could use 1.5 gigabytes.

         g(x) = 50

   10x + 20 = 50

            10x =50- 20

            10x = 30

                x = 30/10

              x = 3

If she chooses plan 'g', she could use 3 gigabytes.

4) Function 'g' would be better for a $50 monthly budget as she could get more gigabytes than function 'f'

Answer:

good and right and keep trying your best

Answer: Commutative property

Answer:

z = 30

Step-by-step explanation:

All angles of a triangle add up to 180:

z + 120 + 30 = 180

z + 150 = 180

z = 180 - 150

z = 30

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6000\\ P=\textit{original amount deposited}\\ r=rate\to 9.5\%\to \frac{9.5}{100}\dotfill &0.095\\ t=years\dotfill &2 \end{cases} \\\\\\ 6000=P[1+(0.095)(2)]\implies \cfrac{6000}{1.19}=P\implies 5042.02\approx P[/tex]

The domain is [tex]x \le 5[/tex] and the range of the function is [tex]f(x) \ge - 3[/tex]

The function is given as:

[tex]f(x) = \sqrt{5 - x} - 3[/tex]

The radicand must be at least 0.

So, we have:

[tex]\sqrt{5 - x} \ge 0[/tex]

Square both sides

[tex]5 - x \ge 0[/tex]

Rewrite as:

[tex]5 \ge x[/tex]

Solve for x

[tex]x \le 5[/tex]

This means that the domain is [tex]x \le 5[/tex]

For the range, we have; [tex]\sqrt{5 - x} \ge 0[/tex]

This means that:

[tex]f(x) \ge 0 - 3[/tex]

[tex]f(x) \ge - 3[/tex]

Hence, the range of the function is [tex]f(x) \ge - 3[/tex]

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If the diameter is d = 8, then we divide that in half to get the radius of r = 4.

If the radius is r = 9, then we double it to get the diameter of d = 18

The formulas are:

I'll let you determine the others.

Answer:

Step-by-step explanation:

Diameter is twice the radius.  d = 2*r

Radius is half the diameter r = d÷2

 1) d = 8

      r = 8÷ 2

      r = 4

2) r = 9

   d = 2*r

       = 2*9

   d = 18

3) r = 24

   d = 24*2 =48

4) d = 36

   r = 36 ÷2 = 18

5) d = 52

      r = 52÷2 = 26