A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 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)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ______ second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is ______feet.
(Simplify your answer.)

Answer: x=-1 & y=2

Step-by-step explanation:

x = -3y+5

^^^substitute this equation into x in the second equation

(-3y+5)+9 = 4y

-3y+14 = 4y

Add +3y on both sides

14 = 4y+3y

14 = 7y

divide both sides by 7

y = 2

substitute y into either equation (I'm doing the first one)

x = -3(2)+5

x = -6+5

x = -1

Using multiplication law of logarithm the value of logb 50 is 2.085

The logb 50 is rewritten in the multiples of 2, and 5 then laws of logarithm is applied to find the final answer

logb 50

= logb (2 * 5 * 5)

applying multiplication law of logarithm

= logb 2 + logb 5 + logb 5

= 0.401 + 0.842 + 0.842

= 2.085

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Answer:

you go <left 5 times and then go down 3 times

The variable g has its value to be -4 on the given coordinate point

From the question, the points are given as

(g, -1) and (2, 5)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (g, -1) and (2, 5)

The slope of the line is given as

Slope = 3/2

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (g, -1) and (2, 5)

Substitute the known values in the above equation

So, we have the following equation

3/2 = (5 + 1)/(2 - g)

Evaluate the sum in the equation

This gives

3/2 = 6/2 - g

Cross multiply

So, we have

2(2 - g) = 12

Divide by 2

2 - g = 6

Make g the subject of the formula

g = 2 - 6

Evaluate the like terms

g = -4

Hence, the value of g of the line is -4

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Answer:

-2

Step-by-step explanation:

Answer:

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

Twice a number n is no less than 10 units from −1:

The inequality becomes an absolute value and translates as:

Answer:

5 mins and 30 seconds

Step-by-step explanation:

find out how many sets of 24copies/min

132 ÷ 24 = 5.5

5.5min = 5mins and 30seconds

The component form of the resultant vector is <5, -4>

Let vector u be a displacement AB on the graph and let vector v be a displacement BC on the graph such that the sum of displacement AB and BC is equivalent to a single displacement AC on the graph. We can write this as:

AB + BC = AC

or writing the vector sum with small letters given,

u + v = w (Note: w = AC)

Given: vector u = <2, -5> and vector v (3, 1)

u + v = w

<2, -5> + <3, 1> = <2+3, -5+1> = <5, -4>

u + v = <5, -4>

Thus, the coordinates of the vector sum on the graph will be (5, -4)

Therefore, the resultant vector in component form is <5, -4>

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The complete square of the given expression is x² + x + 1/4 = (x + 1/2)².

An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that all are constrained and create an equation.

In other meaning, expression is very useful to determine the end or root value of constraint.

As per the given

x² + x + (__) = (____)²

Let's say the square is (x + a)²

Then, (x + a)² = x² + 2xa + a²

Compare x² + x + (__) with  x² + 2xa + a²

2xa = x → a = 1/2

So, (x + 1/2)² = x² + 2x(1/2) + (1/2)²

⇒ x² + x + (1/4)

Hence "The complete square of the given expression is x² + x + 1/4 = (x + 1/2)²".

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Given question is incomplete and incorrect, correct question is attached below;

The complete square of the given expression is x² + x + 1/4 = (x + 1/2)².

An expression has been defined as the combination of some mathematical symbol such that an arithmetic operator and variable such that all are constrained and create an equation.

In other meaning, expression is very useful to determine the end or root value of constraint.

As per the given

x² + x + (__) = (____)²

Let's say the square is (x + a)²

Then, (x + a)² = x² + 2xa + a²

Compare x² + x + (__) with  x² + 2xa + a²

2xa = x → a = 1/2

So, (x + 1/2)² = x² + 2x(1/2) + (1/2)²

⇒ x² + x + (1/4)

Hence "The complete square of the given expression is x² + x + 1/4 = (x + 1/2)²".

Therefore, An expression has been defined as the combination of some mathematical symbol such that an arithmetic operator and variable such that all are constrained and create an equation. "The complete square of the given expression is x² + x + 1/4 = (x + 1/2)²".

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The  expression G  is an integer when it's evaluated.

What is an integer?

A full number, not a fraction, that can be positive, negative, or zero is called an integer (pronounced IN-tuh-jer). Integer examples include: -5, 1, 5, 8

Negative numbers and all entire numbers are both considered integers. Accordingly, a set of integers can be formed by adding negative numbers as well as whole numbers.

Consider 9+(-3).

9+(-3)

Remove parenthesis

=9-3 = 6

6 is an integer.

So,  the  expression G  is an integer when it's evaluated.

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A) An equation to determine how long it will take for you to save enough for the new digital camera is 23.5w + 25.75 = 329.99.

B) It will take you 13 weeks to save sufficiently for the new digital camera.

An equation is a mathematical statement that equates two algebraic expressions.

Equations combine constants and variables with the equation symbol (=).

Equations establish that two or more mathematical expressions are equivalent or equal.

In this situation, to determine the amount that needs to be saved, we deduct the amount already saved from the total requirement, and then divide the difference by the weekly savings.

The price of the digital camera = $329.99

The amount you have saved so far = $25.75

The amount you can save each week = $23.50

Let w = the number of weeks to complete the required amount.

25.75 + 23.5w = 329.99

23.5w + 25.75 = 329.99

23.5w = 329.99 - 25.75

23.5w = 304.24

w = 12.95

w = 13 weeks

Thus, we can establish from equation 23.5w + 25.75 = 329.99 that it will take a saver 13 weeks, saving $23.50 every week to save enough to purchase the new digital camera price at $329.99, given the constants and variables.

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The cost of each ream of paper is $4.5 and that of DVD is $5.

A system of linear equations is a group of  equations having same number of variables and degree.

For the n number of variables n number of equations are required.

On the basis of number of solutions a system of equations can be classified as consistent and inconsistent.

Given that,

The price for 17 reams of paper and 12 DVDs is $136.50.

And, the price for 8 reams of paper and 21 DVDs is $141.

Suppose the cost of each ream of paper be x.

And, the cost of each DVD be y.

THen, the following equations can be made for the two cases,

17x + 12y = 136.50      (1)

8x +  21y = 141            (2)

Solve these equations by multiplying equation (1) by 7 and (2) by 4 and then subtracting them as,

7(17x + 12y) - 4(8x +  21y) = 7 × 136.50 - 4 × 141            

=> 87x = 391.5

=> x = 4.5

Substitute x = 4.5 in equation (1) to get,

17 × 4.5 + 12y = 136.50

=> 12y = 136.50 - 76.50

=> 12y = 60

=> y = 5

Hence, the cost of each ream of paper and each DVD are $4.5 and $5 respectively.

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Answer:

Step-by-step explanation:

Used properties:

Answer:

64

Step-by-step explanation:

Given expression:

[tex]5^{3 \log_54}[/tex]

Apply log rules to find the value of the given expression.

[tex]\textsf{Apply the log power law}: \quad n\log_ax=\log_ax^n[/tex]

[tex]\implies 5^{\log_54^3}[/tex]

[tex]\implies 5^{\log_564}[/tex]

[tex]\textsf{Apply\:the\;log\:rule}:\quad \:a^{\log _a\left(b\right)}=b[/tex]

[tex]\implies 5^{\log_564}=64[/tex]

The rocket reaches its maximum height of 88 feet at 2.25 seconds after launch

The time

The function is given as

h(t) = -16t² + 72t + 7

To start with, we need to differentiate the function

h'(t) = -32t + 72

Next, we set the differentiated function to 0

-32t + 72 = 0

Next, we solve for the variable t

t = 2.25

This means that the time is 2.25 seconds

The maximum height

Recall that we have the value of t to be:

t = 2.25

Also, we have the equation to be

h(t) = -16t² + 72t + 7

So, we have

h(2.25) = -16(2.25)² + 72(2.25) + 7

Solve the expressions

h(2.25) = 88

This also means that the maximum height is 88 feet

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Assuming you meant to say [tex]\text{y} = (8/7)\text{x}[/tex] or [tex]\text{y} = \frac{8}{7}\text{x}[/tex], then yes this is a proportional equation.

This is because it is of the form y = kx where k = 8/7 is the constant of proportionality.

By solving a system of equations we will see that the exponential function is:

g(x) = 122.347*(0.589)^x

We know that our function is of the form:

g(x) = a*(b)^x

We also know that g(3)=25 and g(7)=3, then we can write:

a*(b)^3 = 25

a*(b)^7 = 3

So we have a little system of equations.

Taking the quotient between the second and first equations we get:

(a*(b)^7)/(a*(b)^3) = 3/25

b^4 = 3/25

b = (3/25)^(1/4) = 0.589

Replacing that in the first equation we get:

a*(b)^3 = 25

a*(0.589)^3 = 25

a = 25/(0.589)^3 = 122.347

The exponential function is:

g(x) = 122.347*(0.589)^x

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[tex]\sqrt{18}\implies \sqrt{9\cdot 2}\implies \sqrt{3^2\cdot 2}\implies 3\sqrt{2}[/tex]

The recursive formula for the given Explicit formula is a₁ = 16 and aₙ = -90aₙ₋₁  , the correct option is (c) .

In the question ,

an explicit formula for the geometric sequence is given

that is aₙ = 16(-90)ⁿ⁻¹  ,

we know that the general explicit formula for the geometric sequence is given by

aₙ = a₁(r)ⁿ⁻¹

where aₙ is the nth term , r is the common ratio, a₁ is the first term of the sequence .

On comparing the given explicit formula with the general formula ,
we get ,

a₁ = 16

r = -90

So , the recursive formula is a₁ = 16 and aₙ = -90aₙ₋₁ .

Therefore, The recursive formula for the given Explicit formula is a₁ = 16 and aₙ = -90aₙ₋₁  , the correct option is (c) .

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The largest possible volume V is  4000[tex]cm^3[/tex]

Given,

Volume of a box = length × breadth × height= l× b× h

In this case the box have a square base. i.e.,  l = b

Volume V = [tex]l^2[/tex] × h

We using the formula of Surface area

The surface area of a square box

S = 2(lb +lh+ bh)

S = 2([tex]l^2[/tex] + lh + lh) since l=b

S = 2([tex]l^2[/tex] + 2lh)

Also, Given that the box is open top.

S = [tex]l^2[/tex] +4lh

And Surface Area of the box is 1200cm^2

1200 = [tex]l^2[/tex] + 4lh ....1

Making h the subject of formula

h = (1200 - [tex]l^2[/tex])/4l .....2

Volume is given as

V = [tex]l^2[/tex] × h

V = [tex]l^2[/tex] ×(1200 - [tex]l^2[/tex])/4l

V = (1200l - [tex]l^3[/tex])/4

the maximum point is at dV/dl = 0

dV/dl = (1200 - [tex]31^2[/tex])/4

dV/dl = (1200 - [tex]31^2[/tex])/4 = 0

[tex]31^2[/tex]= 1200

[tex]l^2[/tex] = 1200/3 = 400

l = √400

I = 20cm

Since,

h = (1200 - [tex]l^2[/tex])/4l

h = (1200 - [tex]20^2[/tex])/4×20

h = (800)/80

h = 10cm

Hence, The largest possible volume V is ;

V = [tex]l^2[/tex] × h

V = [tex]20^2[/tex] × 10 = 4000[tex]cm^3[/tex]

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The linear equation which represents this situation would be 0.05A - 0.03B = 375.

What is a linear function?

A linear function has a positive relationship, so increasing one variable (input variable) causes an increase in the other variable (output variable), implying that the variables are directly proportional. As a result, the graph of a linear function is a straight line with a constant slope.

Similarly, a linear equation is a first-order algebraic equation with two variables and terms with exponents of one.

In general, a system of two linear equations must have at least two solutions.

Given Elisa earned a total of $375 profit at the end of the first year.

Also, she suffered a profit of 5% in fund A and a loss of 3% in fund B

So we can write the equation as

                   Total profit = Profit - Loss

                       375 = 0.05A - 0.03B

Hence, the linear equation which represents this situation would be

   0.05A - 0.03B = 375.

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By using the exponential function The number of computer affected in 1 hour is 10000

What is exponential function?

A mathematical function with the formula f (x) = a^x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, which equates to roughly, is the exponential-function base that is most frequently encountered.

We are given a function V(t) = 100e^4.6052t,

We are asked to find the number of computer affected after one hour

To find that we have to substitute t =1 in the equation we get

V(t) = 100e^4.6052

V(t) = 10000

There will be approximately 10000 computers affected by the virus in one hour.

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It takes 2 hours to complete with all three machines working.

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

Let total time taken by all machines be x hours.

Set up the equation as below:

1/3+1/14+1/10.5=1/x

Solve for x

Multiply both the sides by x

x/3+x/14+x/10.5=x/x

0.5x=1

x=2

So, It takes 2 hours to complete with all three machines working.

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Answer: x = 66

Step-by-step explanation:

All angles of a triangle equal 180 degrees.

This means we need to find out how many degrees we need.

48 + 63 = 111

180 - 111 = 69 (nice)

Now we need to subtract 3 from 69.

69 - 3 = 66.

This means x = 66

Answer:

x = 66°

Step-by-step explanation:

Formula we use,

→ A + B + C = 180°

Now the value of x will be,

→ 63° + 48° + (x + 3°) = 180°

→ 114° + x = 180°

→ x = 180° - 114°

→ [ x = 66° ]

Hence, the value of x is 66°.

In dollars and cents, the total projected insurance for three years would be $555.00.

In this exercise, you are required to calculate the total projected insurance for a V-8 sedan that was driven 15,000 miles each year, from the first through the third year (three years). Therefore, we would determine the projected insurance for each year in dollars and cents as follows:

For the first year, we have:

The projected insurance for first year = Insurance cents per miles × miles driven

The projected insurance for first year = 1.1/100 × 15,000

The projected insurance for first year = 0.011 × 15,000

The projected insurance for first year = $165.00.

For the second year, we have:

The projected insurance for second year = Insurance cents per miles × miles driven

The projected insurance for second year = 1.2/100 × 15,000

The projected insurance for second year = 0.012 × 15,000

The projected insurance for second year = $180.00.

For the third year, we have:

The projected insurance for third year = Insurance cents per miles × miles driven

The projected insurance for third year = 1.4/100 × 15,000

The projected insurance for third year = 0.014 × 15,000

The projected insurance for third year = $210.00.

Therefore, the total projected insurance for three years is given by:

Total projected insurance = $165.00 + $180.00 + $210.00

Total projected insurance = $555.00

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Therefore:

[tex](30+5x)^o+(15+10x)^o=180^o\\\\45^o+(15x)^o=180^o\\\\(15x)^o=135^o\\\\15x=135\\\\\large\text{$\bold{x=9}$}[/tex]

Answer:

Answer B is correct

Step-by-step explanation:

In a parallelogram opposite sides are parallel to each other.

AB // CD

Therefore, Co interior angles are added up to 180°.

<BAD + <CDA = 180

That is,

30 + 5x + 15 + 10x = 180

And now, solve the expression and find the value of x.

First, combine like terms.

45 + 15x = 180

Subtract 45 from both sides.

15x = 180 - 45

15x = 135

Divide both sides by 15.

x = 9

Answer:

A would save Brenda the most money

Step-by-step explanation:

Answer:

Option 3

Step-by-step explanation:

[tex]-\frac{7}{5} =-\frac{14}{10} =-1.4[/tex]

[tex]-1\frac{3}{10} = -\frac{13}{10}=-1.3[/tex]

∴ ascending order of these rational numbers

[tex]=-1.5, -1.4, -1.3, -1.2[/tex]

[tex]= -1.5,-\frac{7}{5}, -1\frac{3}{10}, -1.2[/tex]

The equation of the parabola which is as given in the task content is; f (x) = -3 (x - 5)² + 9.

It follows from the task content that the equation of the parabola which has the same shape as f(x)=-3 x² but with vertex (5,9) in the form f (x) = a (x-h)² + k be determined.

Recall that the vertex of a quadratic equations of the given form is defined by the coordinates (h, k).

On this note, the required equation of the parabola by substitution of h and k is;

f (x) = -3 (x - 5)² + 9.

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Answer: The correct answer is C) 30 gallons of gas

Step-by-step explanation:

Storage Tank Volume = 1680 Gallons

25 cars x 24 gallons = 600 gallons

35 trucks x 30 gallons = 1,050 gallons

Total gallons used = 1,050 + 600 = 1,650

Remaining gas = 1,680 - 1,650 = 30 gallons

Option C: 30 gallons of gas

Please remember to vote the answer as Brainliest if I earned it!

Answer:

C) 30 gallons of gas

Step-by-step explanation:

Total gallons of gas used by the cars:

⇒ 25 × 24 = 600 gallons

Total gallons of gas used by the trucks:

⇒ 35 × 30 = 1050 gallons

Total gallons of gas used by the cars and trucks:

⇒ 600 + 1050 = 1650 gallons

If the storage tank contained 1680 gallons of gas, then the number of gallons of gas left in the tank after the cars and trucks have filled their tanks is:

⇒ 1680 - 1650 = 30 gallons

The volume of the droplets in cubic meters would be = 1×10^-7 cubic meters.

Water droplets can be defined as the formation of small ball like structures with water due to the action of surface tension of liquid.

To convert cubic centimetres to cubic meters the following is carried out;

1 cubic meter = 1,000,000 cubic centimetres.

X cubic meters = 0.1 cubic centimetres

Make X cubic centimetres the subject of formula;

X cubic meters = 0.1× 1/1,000,000

X cubic meters = 1×10^-7.

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Answer:

Step-by-step explanation:

The value of x is equal to 10 and the exterior angle to angle d is equal to 141 degrees.Exterior AnglesTo solve this problem, we have to recall that the sum of angles in a triangle is equal to 180 degrees.Applying that formula here;But the exterior angle to angle D can be found assuming the angle lies on a straight line, then the sum of angle D and it's exterior angle would be equal to 180 degrees.Let y = exterior angleThe value of the exterior angle to d is equal to 141 degrees.Learn more on exterior angles here;brainly.com/question/17972372