with a head wind, it takes 7 hours to fly 2800 miles from miami to seattle. with a tailwind, and the same airspeed, it takes 5 hours to fly in the opposite direction, from seattle to miami. find the airspeed and the windspeed

Answer:

The given equation is H = -16t^2 + 64t + 60, where t is the elapsed time in seconds. This equation represents the height, H, of an object thrown upward from the ground with an initial velocity of 64 ft/s.    

Step-by-step explanation:

1. The term -16t^2 represents the effect of gravity on the object. Since the coefficient is negative, it indicates that the object is moving upward against the force of gravity. The square of the time, t^2, shows that the effect of gravity increases as time passes.  2. The term 64t represents the initial velocity of the object. The coefficient 64 indicates that the object was thrown upward with an initial velocity of 64 ft/s. The time, t, shows the effect of the initial velocity on the height.  3. The constant term 60 represents any additional height above the ground at the start. It could be the height from which the object was thrown or any elevation from the ground.  By plugging different values of t into the equation, you can find the corresponding heights at different times. For example, if you substitute t = 0, the equation becomes H = -16(0)^2 + 64(0) + 60 = 60. This means that at the start (t = 0), the object is at a height of 60 feet above the ground.  To find the maximum height reached by the object, we need to determine the vertex of the parabolic equation. The vertex is given by the formula t = -b/(2a), where a and b are the coefficients of t^2 and t, respectively.  In this case, a = -16 and b = 64. Substituting these values into the formula, we get t = -64/(2(-16)) = 2 seconds. This means that the object reaches its maximum height after 2 seconds.  To find the maximum height, substitute t = 2 into the equation: H = -16(2)^2 + 64(2) + 60 = 64 feet. Therefore, the object reaches a maximum height of 64 feet above the ground after 2 seconds.  I hope this explanation helps you understand the meaning of the given equation and how to interpret it in the context of elapsed time and height. Let me know if this helped!

Answer:

813 = 800 + 10 + 3 = (8 [tex]\times 10^{2}[/tex] ) + ( 1[tex]\times 10^1[/tex] ) + ( 3 [tex]\times 10^0[/tex] )  

Step-by-step explanation:

i) 813 = 800 + 10 + 3 = (8 [tex]\times 10^{2}[/tex] ) + ( 1[tex]\times 10^1[/tex] ) + ( 3 [tex]\times 10^0[/tex] )  

The circumference of a circle is the distance around the Outside of the circle.

The circumference of found by multiplying PI by the diameter of the circle.

Answer: I guessed on the second one

Step-by-step explanation:

The problem falls under mathematics, more specifically algebra, using a system of two equations to solve for the timing of the cardio and weighted workouts. The equations can be formed from the provided data and can be solved using substitution or the elimination method.

This problem is a system of equations questions in mathematics, specifically in the subset of algebra. To be able to solve this, you need to create two equations from the data provided on the table and then solve for both cardio and weighted workout timings. For instance, if I did 2 cardio workouts and 3 weighted workouts in week 1 for a total of 150 minutes and 3 cardio workouts and 1 weighted workout in week 2 for a total of 160 minutes, you can construct these two equations:

2*cardio + 3*weighted = 150 (Equation for week 1)

3*cardio + weighted = 160 (Equation for week 2)

Next, you solve this system of equations either by substitution or elimination- whatever you're more comfortable with. The results will give you the duration of each cardio and weighted workout.

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Answer:

Part 1) John’s situation is modeled by a linear equation (see the explanation)

Part 2)  [tex]y=100x+300[/tex]

Part 3) [tex]\$12,300[/tex]

Part 4) [tex]\$2,700[/tex]

Part 5) Is a exponential growth function

Part 6) [tex]A=6,000(1.07)^{t}[/tex]

Part 7) [tex]\$11,802.91[/tex]

Part 8)  [tex]\$6,869.40[/tex]

Part 9) Is a exponential growth function

Part 10) [tex]A=5,000(e)^{0.10t}[/tex]    or  [tex]A=5,000(1.1052)^{t}[/tex]

Part 11)  [tex]\$13,591.41[/tex]

Part 12) [tex]\$6,107.01[/tex]

Part 13)  Natalie has the most money after 10 years

Part 14)  Sally has the most money after 2 years

Step-by-step explanation:

Part 1) What type of equation models John’s situation?

Let

y ----> the total money saved in a jar

x ---> the time in months

The linear equation in slope intercept form

y=mx+b

The slope is equal to

[tex]m=\$100\ per\ month[/tex]

The y-intercept or initial value is

[tex]b=\$300[/tex]

so

[tex]y=100x+300[/tex]

therefore

John’s situation is modeled by a linear equation

Part 2) Write the model equation for John’s situation

see part 1)

Part 3) How much money will John have after 10 years?

Remember that

1 year is equal to 12 months

so

[tex]10\ years=10(12)=120 months[/tex]

For x=120 months

substitute in the linear equation

[tex]y=100(120)+300=\$12,300[/tex]

Part 4) How much money will John have after 2 years?

Remember that

1 year is equal to 12 months

so

[tex]2\ years=2(12)=24\ months[/tex]

For x=24 months

substitute in the linear equation

[tex]y=100(24)+300=\$2,700[/tex]

Part 5) What type of exponential model is Sally’s situation?

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex] 

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]P=\$6,000\\ r=7\%=0.07\\n=1[/tex]

substitute in the formula above

[tex]A=6,000(1+\frac{0.07}{1})^{1*t}\\ A=6,000(1.07)^{t}[/tex]

therefore

Is a exponential growth function

Part 6) Write the model equation for Sally’s situation

see the Part 5)

Part 7) How much money will Sally have after 10 years?

For t=10 years

substitute  the value of t in the exponential growth function

[tex]A=6,000(1.07)^{10}=\$11,802.91[/tex] 

Part 8) How much money will Sally have after 2 years?

For t=2 years

substitute  the value of t in the exponential growth function

[tex]A=6,000(1.07)^{2}=\$6,869.40[/tex]

Part 9) What type of exponential model is Natalie’s situation?

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex] 

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]P=\$5,000\\r=10\%=0.10[/tex]

substitute in the formula above

[tex]A=5,000(e)^{0.10t}[/tex]

Applying property of exponents

[tex]A=5,000(1.1052)^{t}[/tex]

 therefore

Is a exponential growth function

Part 10) Write the model equation for Natalie’s situation

[tex]A=5,000(e)^{0.10t}[/tex]    or  [tex]A=5,000(1.1052)^{t}[/tex]

see Part 9)

Part 11) How much money will Natalie have after 10 years?

For t=10 years

substitute

[tex]A=5,000(e)^{0.10*10}=\$13,591.41[/tex]

Part 12) How much money will Natalie have after 2 years?

For t=2 years

substitute

[tex]A=5,000(e)^{0.10*2}=\$6,107.01[/tex]

Part 13) Who will have the most money after 10 years?

Compare the final investment after 10 years of John, Sally, and Natalie

Natalie has the most money after 10 years

Part 14) Who will have the most money after 2 years?

Compare the final investment after 2 years of John, Sally, and Natalie

Sally has the most money after 2 years

Answer:

here is the answer, out of all my experience i'm not too good on these word problems. You should check number two but if you agree than yay.

Step-by-step explanation:

Answer:

-.15

Step-by-step explanation:

you first do whats in the parantheses (3/4 - 1) which equals -.25, then multiply by 2 which gives you -.5, now add .35 and your total is -.15

Answer:

0.85

Step-by-step explanation:

2(3/4-1)+0.35

=(1.5-1)+0.35

=0.5+0.35

=0.85

Answer:No

Step-by-step explanation:

B

Step-by-step explanation:

(1)Area of triangle= 1/2 x height (7cm) x base (8cm)

= 56/2

= 28

(2)Area of circle = (Pi)r^2

= (Pi)4cm^2

= 50.26548....

Since the circle is half divide the above by 2

= 25.132741.....

Round the answer to the nearest hundredth

= 25.13

(1) + (2)

28+25.13= 53.13

Hope this helps! :)

Answer:

[tex]f(3)=-60[/tex]

Step-by-step explanation:

[tex]f(3)=5(3)^2-7(4(3)+3)\\\\f(3)=5(3)^2-7(12+3)\\\\f(3)=5(3)^2-7(15)\\\\f(3)=5\times 9-7\times 15\\\\f(3)=45-105\\\\f(3)=-60[/tex]

In this problem, we use the Triangle Inequality Theorem to find that the minimum value for x, which would yield a valid triangle, is 27.67.

In this Mathematics problem, we're given a triangle with sides 9cm, 3x-20cm, 72cm, and 56cm. According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. By doing this, we can set up an inequality to solve for x:

So, the minimum value for x that would yield a valid triangle is 27.67.

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answer: 28: 4

21: 3

70: 10

step-by-step explanation:

divide 28 by 4, and of course, do to the bottom what you do to the top. 4 divided by 4 is 1, and 28 divided by 4 is 7.

7: 4.

then, multiply by the number of smoothies.

for 3, it's 21: 3.

for 10, it's 70: 10.

1) Turn everything into improper fractions: 10/3, 17/6, and 11/4

2) Find LCM of 3, 6, and 4: 12

3) Fix improper fractions to match the new denominator: 40/12, 34/12, and 33/12

4) Add them all up: 40/12+34/12+33/12=107/12=8 11/12

So your final answer is 8 11/12

Hope this helped and please mark as brainliest!

Answer:

Rita's answer in incorrect because the remainder that Rita got which is 23 is greater 17 which is the divisor. 17 can still go in 23 1time to have a remainder of 6. Hence Rita's answer is wrong with 34R6 being the correct answer.

Step-by-step explanation:

Quotient is the required answer if 584 is divided by 17

584 will be the dividend and 17 is the divisor.

To calculate 584/17, 17 will go in 58 3times with 7 as remainder. This remainder 7 will combine with 4 to make 74, 17 will also go in 74 4times with remainder of 6.

The final answer by combining the number of times 17 goes in 584 which is 34 with final remainder of 6. This means that;

584/17 = 34 remainder 6 i.e 34R6

This shows that Rita's answer in incorrect because the remainder that Rita got which is 23 is greater 17 which is the divisor. 17 can still go in 23 1time to have a remainder of 6. Hence Rita's answer is wrong with 34R6 being the correct answer.

Answer:

[tex]-16x^2[/tex]

Step-by-step explanation:

[tex](2x)^2 * -4\\=4x^2*-4\\=-16x^2[/tex]

Answer:

0

Step-by-step explanation:

An exponent multiply's that number by that amount of the exponent.

EX : 2^3 where ^ represents exponent

You would write it out like :2*2*2=8

Your problem asks us to multiply the number 2 by itself twice, equaling 4

and 4 subtracted by 4 is zero .

Answer:

b

Step-by-step explanation:

Answer:

The total number of fliers the volunteers gave out is 1,368: 756 in the first neighborhood and 612 in the second.

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Amount of fliers the volunteers gave for a political campaign = 21/38

Remaining 612 were given out in another neighborhood

2. What is the total number of fliers they gave out?

x = Total of fliers

21x/38 = Fliers given out in the first neighborhood

612 = Fliers given out in the second neighborhood

Let's solve for x, this way:

x - 21x/38 = 612

38x - 21x = 612 * 38 (38 is the Lowest Common Denominator)

17x = 23,256

x = 23,256/17

x = 1,368

The total number of fliers the volunteers gave out is 1,368: 756 in the first neighborhood and 612 in the second.

Answer:

14

Step-by-step explanation:

The revenue earned is represented by t(x)=5x. Since the equation asks for the profit after four seasons you fill in 4 for x and get 20. r(x)=(1.5)x is how much it costs to pay their employees each season so you fill in 4 for x. Now you take revenue earned and subtract it by the cost to pay employees and you get the profit.

5x - 1.5x = Profit

5(4) - 1.5(4) = Profit

20 - 6 = Profit

14 = Profit

Answer:

15

Step-by-step explanation:

Answer:7

Step-by-step explanation:

Answer:

Technically, since it's an improper fraction, turning it into a whole number is not possible.

Step-by-step explanation:

21/4 as a decimal is 5.25

5.25 as a mixed number would be 5 1/4. Therefore, the closest 21/4 can get to a "whole number" is 5.

Answer:

C(g) = 2.19g ; 2.5

Step-by-step explanation:

Question 1

Since the cost is $2.19 per gallon. For every gallon, the cost will increase by $2.19. Hence, the cost per gallon C(g) is 2.19g.

Question 2

f(1.5) = 3(1.5) - 2

= 4.5 - 2

= 2.5

Answer:

1. C(g) = 2.98g

2. 2.5

Step-by-step explanation:

1. 1 gallon cost $2.98

Therefore y gallon will cost = y2.98 ie C(g) = 2.98g

2. F(x) = 3x — 2

F(1.5) = 3x1.5 — 2 = 4.5 — 2 = 2.5

Answer:

Step-by-step explanation:

u had 11 and u spent 7

7/11 <=== the fraction of money u spent is 7 out of 11

Answer:

Step-by-step explanation:

D=rt

180miles = 45mph* times

180miles/45mph =time

Time = 4hours

Answer:

[tex]y=-1.5x[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

In this problem we have

y=15/2 when x=-5

Find the constant of proportionality k

[tex]k=\frac{y}{x}[/tex]

substitute the given values

[tex]k=\frac{(15/2)}{-5}=-1.5[/tex]

therefore

The linear equation that relates x and y is equal to

[tex]y=-1.5x[/tex]

Answer:

1*56 8*7 ECT

Step-by-step explanation:

56 one time=56. 7 8 times = 56

Answer:

The answer is figure a :-)

The reason why is because all sides of figure A are equivalent.

Answer:

_____________________________________________

Step-by-step explanation:

Answer:

We also know that If two angles are complementary then  their sum is equal to 90°. So, two angles ∠1 & ∠2 are complementary.

Step-by-step explanation:

As BA is perpendicular to BC. So, angle ∠ABC is 90°.

We also know that If two angles are complementary then  their sum is equal to 90°. As ∠ABC is the sum of the ∠1 & ∠2. In other words, ∠1 & ∠2 are complementary. So, two angles ∠1 & ∠2 are complementary.

Lets prove this.

Given: BA ⊥ BC

Prove: ∠1 & ∠2 are complementary.

Statement                                                       Reasons

1. ∠1 & ∠2 are complementary                      1. Given

2. ∠1 + ∠2 = 90°                                             2. Def. of complementary angles

Final answer:

Using an algebraic approach, we found out that if Barbara is 142 cm tall, which is 2 cm less than three times her birth height, then her height at birth was 48 cm.

Explanation:

The question asks us to determine Barbara's height at birth given that she is currently 142 cm tall and that this height is 2 cm less than three times her height at birth. To find her height at birth, we can construct and solve a simple algebraic equation based on this information.

Let h represent Barbara's height at birth. The problem states that:

142 cm = 3h - 2 cm

Adding 2 cm to both sides of the equation, we get:

144 cm = 3h

Dividing both sides of the equation by 3 so we can solve for h, gives us:

h = 144 cm / 3

h = 48 cm

Therefore, Barbara's height at birth was 48 cm.

Answer:5/8

Step-by-step explanation:

Answer:

Step-by-step explanation:

0.79 x 8 =

6.72

15.21 - 6.72 =

Answer =

8.49