You start out driving from your house to an old friend’s house in a different town, which is 280 miles away. After an hour and a half, you have gone 105 miles.

a) Assuming your speed is constant, find a linear function , which gives the distance from your house (in miles) as a function of time (in hours).

b) Find and interpret D(1).

c) Solve D(t)=280

d) Solve D(t)^3>=140 and interpret the result.

e) Considering the context of this function, what is the domain?

f) What is the range?

Answers

Answer 1

Part A:

Given that after an hour and a half, you have gone 105 miles and that your speed is constant, this means that the slope which represents the speed with which you are driving is given by

[tex] \frac{105}{1.5} =70 \ miles \ per \ hour[/tex]

At 0 hours, he has travelled 0 miles.

The equation of a straight line is given by y = mx + c, where m represent the slope and c is the y-intercept (the value of y when x is 0).

Therefore, a linear function , which gives the distance from the house (in miles) as a function of time (in hours) is given by D = 70t.

Part B:

D(1) is the value of D when t = 1.

D(1) = 70(1) = 70

This means that the distance traveled after 1 hour is 70 miles.

Part C:

D(t) = 280 means the time it takes you to travel 280 miles.

70t = 280

t = 280 / 70 = 4

t = 4.

Part D:

[tex]D(t)^3 \geq 140 \\ \\ \Rightarrow 70t^3 \geq 140 \\ \\ \Rightarrow t^3 \geq \frac{140}{70} =2 \\ \\ \Rightarrow t \geq \sqrt[3]{2} [/tex]

Part E:

The domain is a set of the possible values of the independent variable, from the context of the function, the independent variable is the time it took him for the journey.

Therefore, the domain of the function is [0, 4].

Part F:

The range is the set of the possible values of y, y in the context of the question is the distance travelled at each particular time.

Therefore, the range of the function is [0, 280].

Answer 2

a) D(t)=70t. To find this, consider that we traveled 105 miles in the first 1.5 hours. Since the speed is constant, we simply divide the 105 miles by the 1.5 hours. 105/1.5=70, which tells us we are going 70 mph. To express this as a function, we write the speed of travel (70) times the number of hours (t). Thus D(t)=70t. b) D(1)=70. This means that we traveled 70 miles after one hour. To find this, plug in 1 hour for t and simplify: 70(1)=70. c) t=4. To solve this, set 280=70t and solve for t. 280/70=4. d) t=.0741784872. To solve, take the cube root of both sides. This gives us D(t)=5.192494102. This can be written 70t=5.192494102. Dividing both sides by 70 we get that t=0741784872. e) Domain is t-interval [0,4]. To find this, consider that the trip is 280 miles and we are traveling at 70 mph. Dividing 280 by 70, we see that we will make the trip in 4 hours. Thus our trip starts at t=0 and ends at t-4. f) Range is the D-interval [0,280]. To find this, consider that the domain is [0,4]. d(0)=0 and D(4)=280. Thus the range is [0,280].

Related Questions

Please answer, , I need this by 10:00, thank you!

Answers

(2, 7) abd (5, 1)

Let m = slope

m = (1 - 7)/(5 - 2)

m = (-6)/(3)

m = -2

Use the slope and one of the points to plug into the point-slope formula.

I will use the point (5, 1).

y - 1 = -2(x - 5)

y - 1 = -2x + 10

The equation is

y = -2x + 11

Last week, 4.3 inches of rain filled a rain gauge. This week, another 3.375 inches of rain filled the gauge. What was the total amount of rain that filled the rain gauge in two weeks? Enter your answer in the box.

Answers

7.675 inches of rain was the total amount in the two weeks

The rain gauge collected a total of 7.675 inches of rain over the two-week period by adding last week's 4.3 inches to this week's 3.375 inches of rainfall.

This question demands basic understanding of mathematical operations and basic mathematical problem solving.

The question asks for the total amount of rain that filled a rain gauge over a two-week period. Last week, the rain gauge collected 4.3 inches of rain, and this week it collected an additional 3.375 inches. To find the total rainfall over the two weeks, we simply add these two amounts together:

4.3 inches (last week's rain) + 3.375 inches (this week's rain) = 7.675 inches

So, as per the above explaination, the rain gauge collected a total of 7.675 inches of rain over the two-week period.

10. Solve the equation for f. Show all of your work.
4f-5=7h+g

Answers

4f-5=7h+g
add 5
4f= 7h + g + 5
divide by 4 to get f by its self
f = 1/4g + 7/4h + 5/4

To different companies offer online gaming subscriptions. Company A charges $75 upfront and then $20 per month. Company B does not charge an upfront fee, but charges $35 per month. After how many months will the two companies charge the same amount?

Answers

Hello! To solve this equation, let's set it up like this: 75 + 20m = 35m. This is because Company B does not charge an upfront fee, so all you have to do is 35m and Company A charges $75 upfront and then $20 per month, so you do 75 + 20m. First, you subtract 20m from both sides. When you do, you get 75 = 15m. Now, you divide each side by 15 to isolate the m. When you do that, you get 5. Let's plug in the numbers to see what we get. 20 * 5 is 100 + 75 = 175. 35 * 5 =175. 175 = 175. There. The two companies will charge the same amount in 5 months. m = 5.

The number of months when the two companies charge the same amount is 5 months.

Let the number of months when the two companies charge the same amount be represented by x.

Therefore, based on the information given, the equation to solve the question will be:

75 + (20 × x) = 35 × x

75 + 20x= 35x

Collect like terms

35x - 20x = 75

15x = 75

Divide both side by 15

15x/15 = 75/15

x = 5

Therefore, the number of months when the two companies charge the same amount is 5 months.

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There are 3 times as many boys than girls. If there are 24 more boys than girls, how many students are there in total?

Answers

there are 8 girls total.

32 students in total bc if there is 8 girls u multiply by 3 equals 24 so if u add them in total its 32 students

Karla is given the equation 10x + 15 = 20 to solve. She says the solution is 1/2

Which reason justifies her solution?

A) Karla says that to solve the equation you first add 15 and then multiply by 10.

B) Karla says that to solve the equation you first multiply by 10 and then add 15.

C) Karla says that to solve the equation you first subtract 15 and then divide by 10.

D) Karla says that to solve the equation you first divide by 10 and then subtract 15.

Answers

the answer is c because you need to isolate the x

The answer is C.

you do the inverse of positive 15, which is negative 15. so put it on both side .

10x +15 =20
-15 =-15

to equal

10x =5

then divide 10 on both side

10x = 5
----- -----
10 10

x = 5/10 or 1/2

Susan is buying supplies for a party. If spoons only come in bags of 8 and forks only come in bags of 6, what is the least number of spoons and the least number of forks she can buy so that she has the same number of each? asap and tell my how you got the answer please

Answers

it would be 4 packs of spoons and 3 packs of forks. This is because if you multiply 6 times 4 you get 24 and 8 times 3 you will get 24 and then that would be even. If this needs to be further explained please ask me

Answer:

3 bags of spoon and 4 bags of fork.

Step-by-step explanation:

If Susan will buy 3 bags of spoon then, the total spoon is 3 × 8 = 24 spoons

and, If he will buy 4 bags of fork then, the total fork is 4 × 6 = 24 forks.

Thus, for getting equal numbers of spoon and fork he has to buy a minimum of 3 bags of spoon and 4 bags of fork.

Haji rows his canoe 10 mph in still water. He noticed one day that he could row 4 miles upstream in the same amount of time he could row 6 miles downstream. What was the approximate speed of the current that day?

Answers

so you see that he was rowing up stream and could go 4 miles an hour, but down stream, with the push of the current gave him an extra boost of 2 miles an hour

Answer:

2.0 mph

Step-by-step explanation:

A student received an 82$ on an exam if there were 50 questions on the exam which ratio would show the number of questions answered correctly

Answers

he answered 41 questions right.

41:50

Given the two expressions shown below:
A. square root of 3 + square root of 2
B. square root of 3 + square root of 6

Which statement best describes the two expressions?

A. both rational
B. both irrational
C. A is rational and B is irrational
D. A is irrational and B is rational

Plz help Thanks for Everything Guys

Answers

C. A is rational and B is irrational

If g( n ) = 3 n - 2, then what is the value of g(10)?

Answers

the correct answer is 28

is 640 ft or 0.5 mi greater?

Answers

0.5 a mile is greater because 1 mile is equal to 5,280 ft.

5,280 / 2 = 2,640 ft.

0.5 is bigger than 640 feet

A student answers
90%
of the questions on a math exam correctly. If
sheshe
answers
27
questions correctly, how many questions are on the exam?

Answers

So, we have the percentage she gets which is, 90% and the number of questions she answers correctly, which is 27

To find the number of questions in the exam, make an equation
(90% = [tex] \frac{90}{100} [/tex] = 0.9)
[tex] \frac{90}{100} [/tex] = [tex] \frac{27}{x} [/tex]
cross multiply and equate them
90x = 27 x 100
90x = 2700
divide by 90 on either sides to isolate x in order to find the answer
[tex] \frac{90x}{90} = \frac{2700}{90} [/tex]
90 and 90 cancels out
x = 30
So your final answer will be, there were 30 questions in the exam paper.

Final answer:

To find the total number of questions on the exam, set up a proportion 27 / x = 90% / 100%. Solve for x to find that there are 30 questions on the exam.

Explanation:

To find the total number of questions on the exam, we can set up a proportion. Let's represent the total number of questions on the exam as x.

The proportion would be:

Correctly Answered Questions / Total Questions = Percentage Correct

Substituting the given values:

27 / x = 90% / 100%

Cross multiplying:

27 * 100% = x * 90%

27 = 0.9x

Dividing both sides by 0.9:

x = 27 / 0.9

x = 30

Therefore, there are 30 questions on the exam.

math question down below

Answers

Average change in altitude per minute
216.12÷2.4
=90.05m

To find the average altitude, you divide. Get rid of the negative sign, (we'll need it later). 216.12 / 2.4 = 90.05. Bring back the negative sign.

You're answer is -90.05m

Hope this helps! ☺♥

What is 9.27 with a repiton bar over the 27 simplified to as a fraction?

Answers

That will be 3/11.

According to your question. It is incorrect. You meant repetitive.

https://socratic.org/questions/how-do-you-convert-0-27-27-repeating-to-a-fraction

This will prove my answer correct.

The answer to your problem is 3/11

At a pet shop there are 2100 cats and 210 dogs for a total of 2310 pets all together

Answers

That is correct. how did you come up with that.

There are 2100 cats and 210 dogs, totaling 2310 pets. Cats outnumber dogs 10 to 1.

To find the number of cats and dogs separately, let's set up a system of equations.

Let [tex]$ x $[/tex] represent the number of cats and [tex]$ y $[/tex] represent the number of dogs.

We're given two pieces of information:

1. There are 2100 cats and 210 dogs for a total of 2310 pets.

[tex]\[ x + y = 2310 \][/tex]

2. There are 2100 cats.

[tex]\[ x = 2100 \][/tex]

We can substitute the value of [tex]$ x $[/tex] from the second equation into the first equation:

[tex]\[ 2100 + y = 2310 \][/tex]

Now, let's solve for [tex]$ y $:[/tex]

[tex]\[ y = 2310 - 2100 \][/tex]

[tex]\[ y = 210 \][/tex]

So, there are 210 dogs.

To summarize:

- Number of cats [tex]($ x $):[/tex] 2100

- Number of dogs [tex]($ y $)[/tex]: 210

Jolene invests her savings in two bank accounts, one paying 4 percent and the other paying 11 percent simple interest per year. She puts twice as much in the lower-yielding account because it is less risky. Her annual interest is 4408 dollars. How much did she invest at each rate?

Answers

Its 23 200 at the 11% and 46400 at 4%

Jolene invested $46,378.95 at 4 percent and $23,189.47 at 11 percent to achieve her annual interest of $4408 by setting up and solving a system of equations based on her investment strategy.

Jolene invests her savings in two different bank accounts, one with a 4 percent interest rate and another with an 11 percent interest rate. She invests twice as much in the lower-yielding account. To determine how much she invested at each rate given her annual interest of $4408, we can set up a system of equations.

Let's denote the amount invested at 4 percent as x and the amount invested at 11 percent as y. Given that she puts twice as much in the account with 4 percent, we can say that x = 2y. Furthermore, the total interest earned from both accounts is $4408, so the equation for the total interest would be 0.04x + 0.11y = 4408.

Substitute x = 2y into the interest equation to get 0.04(2y) + 0.11y = 4408. After simplification, the equation becomes 0.19y = 4408. Dividing both sides by 0.19 gives us y = 23189.47. Since x = 2y, multiply y by 2 to find x = 46378.95.

Therefore, Jolene invested $46,378.95 at 4 percent and $23,189.47 at 11 percent.

A weed called the boomstar vine is known for growing at a very fast rate. It can grow up to 0.5 feet per day. How fast in inches per day can the boomstar vine grow up to? How fast in inches per hour can the boomstar grow up to?

Answers

It can grow 6in per day, and 0.25 inches per hour.

Final answer:

The Boomstar vine can grow up to 6 inches per day and 0.25 inches per hour, after converting from feet to inches and dividing by the number of hours in a day, respectively.

Explanation:

The Boomstar vine can grow up to 0.5 feet per day. To convert feet to inches, we multiply by the conversion factor of 12 inches per foot. Therefore, multiplying 0.5 feet by 12 gives us:

0.5 feet/day × 12 inches/foot = 6 inches per day.

Next, to find out how fast it grows in inches per hour, we divide the daily growth in inches by the number of hours in a day:

6 inches/day ÷ 24 hours/day = 0.25 inches per hour.

What is the measure of the angle 20x + 5= 24x - 1

Answers

4x=4
x=4/4=1
All the best

20x +5 = 24x -1

add 1 to each side

20x+6 = 24x

subtract 20x from each side

6 = 4x

divide both sides by 4

x = 6/4 = 1.5

measure of angle: 20(1.5) +5 = 30+5 = 35 degrees

24(1.5) - 1 = 36-1 = 35 degrees

Graph the line y=−1.5x. Using the graph, find:
The value of y corresponding to the value of x equal to 1; 0; 2; 3 problem.

If x = 1, y = .
If x = 0, y = 0.
If x = 2, y = .
If x = 3, y = .

Answers

x=0-> y=0
x=1-> y=-1.5
x=2-> y=-3
x=3-> y=-4.5

Gabriela works at a nearby electronics store. She makes a commission of 14%14, percent on everything she sells. If she sells a camera for $589.00dollar sign, 589, point, 00, how much money does Gabriela make in commission?

Answers

Good question I don’t know maybe ask you’re professor

Use exponents to write the number 64 three different ways

Answers

8^2
4^3
(the ^ means the number after is the exponent)

8 ^ 2

4^ 3

2^6

those are your three ways hope that helps

Write 10x10x10x10x10x10 as an exponent

Answers

it would be10 to the 6th power

The required answer for 10x10x10x10x10x10 as an exponent is 10⁷.

What is an exponent?

An exponent is a number or letter written above and to the right of a mathematical expression called the base.

Now the given expression is,
10 x 10 x 10 x 10 x 10 x 10

Using the property,

a^a . a^b = a^(a+b)

Thus,

10 x 10 x 10 x 10 x 10 x 10 = 10^(1+1+1+1+1+1)

⇒ 10 x 10 x 10 x 10 x 10 x 10 = 10^7

or, 10 x 10 x 10 x 10 x 10 x 10 = 10⁷

Thus, the required answer for 10 x 10 x 10 x 10 x 10 x 10 as an exponent is 10⁷.

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please help ❗️❗️❗️❗️❗️❗️

Answers

Pool A is filling up slower than Pool B because the slope of the graph for Pool A is less than that of the graph for Pool B.

The slope of the graph tells you the unit rate in gallons per minute. (gallons/minute)

_____
Side Note: Pool A starts with more water in the pool, so even though it is filling more slowly, it may be filled first.

Write the equations of three distinct lines that have the same y-intercept,-1.

Answers

Three possible answers are:
y = 2x-1
y = 5x-1
y = -3x-1

All of them have the same y intercept of -1. The slopes are the only thing that differ.

Any linear equation can be written in the form y = mx+b where
m = slope
b = y intercept

you have 33 marbles. Besides 1 group of 33 marbles, is it possible to divide the marbles into groups with the same number of marbles with no marbles left over

Answers

Yes you could have three groups of 11 with no marbles left over.

Yes hi could have 11 groups with 3

roberto needs to convert the equation 3x + y = -5 into slope-intercept form. why is able to add or subtract the variable term from either side of the equation?

Answers

3x + y = -5

-3x + 3x + y = -3x - 5

y = -3x - 5

The saving-borrowing-investing cycle generally begins with consumer borrowing to fund their purchases and for seed capital. They then use this capital to invest in their future, which then allows them to bring in more money. They then are able to use income to pay off their loans and to save.

Answers

The statements above are TRUE.
The saving borrowing investing cycle is used by people to achieve financial stability. They cycle is initiated when an individual borrow a sum of money to invest in a business. As time goes on the business begins to yield profits. Part of the profits will be used to repay the borrowed loan. After the repayment, the profits can then be reinvested into the business to generate more profits.

Simplify 0.4(−4.5)

help

Answers

you just multiply them together:
0.4 x -4.5 = -1.8

The answer to this question is -1.8

Find the value of x so that the function has the given value.

h(x)=−7x ; h(x)=63

Answers

Us x=-9

you get this by dividing 63/-7

The value of x for which the function h(x) = - 7x is h(x) = 63 is - 9.

What is a function?

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, h(x) = -7x and h(x) = 63.

∴ We can equate these two functions as h(x) = h(x) which is,

- 7x = 63.

- x = 63/7.

- x = 9.

x = - 9.

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