Tommy and Zach are starting out at the same position. Tommy runs north at 3 miles per hour and Zach starts to run east 2 hours later at the rate of 4 miles per hour. How long until Tommy and Zach are 8 miles apart?

Answers

Answer 1
Okay, Tommy runs in a positive y direction at 3mph, and his position can be expressed as:

T=3t

Then Zach starts running two hours later at 4mph and his position can be expressed as:

Z=4(t-2)=4t-8

The distance between Tommy and Zach can be expressed as the hypotenuse length of a right triangle with the distances for Tommy and Zach being the lengths of the sides...

d^2=T^2+Z^2

d^2=(3t)^2+(4t-8)^2

d^2=9t^2+16t^2-64t+64

d^2=25t^2-64t+64, and we want to know when they are 8 miles apart

25t^2-64t+64=8^2

25t^2-64t+64=64

25t^2-64t=0

25t(t-2.56)=0

So 2.56 hours after Tommy started running they will be 8 miles apart.

To be clear though, this is the time Tommy spent running, or the time that elapsed since Tommy started running.  Zach has only been running for 0.56 hours.  So if they are looking for the time Zach ran it is 0.56 not 2.56 hours.
Answer 2

Zach=2 hours Tommy= 3 1/2 hours


Related Questions

Find the sum. And simplify 1 4/9 + 3 1/3

Answers

Convert into improper fractions
1=9/9
9+4=13
13/9

3=9/3
9+1=10
10/3

To add fractions, we must find a common denominator.
3*3=9
9*1=9
13/9 *1/1 = 13/9
10/3 *3/3= 30/9
13+30=43
43/30
or 1 13/30

Hope this helps! A thanks/brainiest answer would be appreciated :)


write and expression with an exponent that has a value between 0 and 1

Answers

x^(0.5)+2x+0.5 can be your answer - x^(0.5) means square root of x

How much larger is one cubic foot than one cubic inch

Answers

One cubic foot is 12 times higher, wider and thicker. So its 1728 larger.

A high school student volunteers to present a report to the administration about the types of lunches students prefer. He surveys members of his class and records their choices. What type of sampling did the student use? systematic random sampling

Answers

Convenience Sampling. This hath been an answer given by the GREAT SHU SHAOSHU!

Answer:

the answer is convenience sampling

Step-by-step explanation:

Which equation can be used to find x,the length of the hypotenuse of the right triangle

Answers

a^2 + b^2 = c^2...a and b are the legs and c is the hypotenuse
18^2 + 24^2 = x^2 <==

** the hypotenuse is always the longest side..it is the side opposite the right angle

Answer:

[tex]x^{2}=24^{2}+18^{2}[/tex]

Step-by-step explanation:

we know that

The Pythagoras Theorem states that in a right triangle

[tex]c^{2}=a^{2}+b^{2}[/tex]

where

c is the hypotenuse

a,b are the legs of the right triangle

In this problem we have

[tex]a=24\ units, b=18\ units, c=x\ units[/tex]

substitute

[tex]x^{2}=24^{2}+18^{2}[/tex]


Zayed is helping his classmates get ready for their math test by making them identical packages of pencils and calculators. He has 72 pencils and 24 calculators and he must use all of the pencils and calculators. If Zayed creates the greatest number of identical packages possible, how many pencils will be in each package?

Answers

Answer:

3 pencils

Step-by-step explanation:

We are given Zayed is helping his classmates get ready for their math test by making them identical packages of pencils and calculators.

Number of pencils=72

Number of calculators=24

If Zayed creates the greatest number of identical packages

Then , we find GCF of 72 and 24

[tex]72=2\times 2\times 2\times 3\times 3[/tex]

[tex]24=2\times 2\times 2\times 3[/tex]

GCF=[tex]2\times 2\times 2\times 3[/tex]

Hence, Zayed creates 24 packages.

Number of pencils in each package=[tex]\frac{72}{24}=3[/tex]

Hence, 3 pencils and one calculator will be in each package .

Answer:

3 pencils

Step-by-step explanation:

what number is greater than 535 but rounded to the nearest 100 is 500?
which one?

523 535 545 550

Answers

Answer: 545

This is because in rounding, numbers are rounded up when they are past the halfway mark, but down when they are below the halfway mark. If the number is exactly the halfway point, then it is also usually rounded up.
In this case, the halfway point is 550. 545 is less than 550, so if it is rounded to the nearest 100, it is rounded down to 500.
545 because the 45 is more than 35 and the answer is still 500 when rounded off

Why is 3 + (−5) equal to −2?

Answers

since the 5 is a negative you are actually subtracting it from 3

 so 3 +(-5) is actually 3-5. which = -2

Answer:

-2

Step-by-step explanation:

pls mark me brainlyest

A soccer team played 160 games and won 65 percent of them. How many games did it win ? Please show work

Answers

To find the percent of games the soccer team won, you would do 160 multiplied by 0.65, because if you were to convert the 65% into a decimal, you would get 0.65. Notice the key word, "of". This refers to multiplication. So when doing 160*0.65, you get 104 games won. Therefore the soccer team won 104 of their games.

Hope this helps! :D Feel free to ask more questions, or ask me questions about my explanation.

The number of games won is 104.

What is a percentage?

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Number of games = 160

Percentage of games won = 65%

Now,

The number of games won.

= 65% of 160

= 65/100 x 160

= 104

Thus,

The number of games won is 104.

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Which decimal is equal to 4/20

Answers

To find the decimal value of a fraction, you simply divide the numerator by the denominator. In this case, we are dividing 4 by 20, which is equal to .2. Therefore, the decimal value that is equal to 4/20 is 0.2.
Just divife them by two it equals 2/10 when that is in decimal it is turned into 0.20

A construction company was contracted to build a cylindrical storage tank with a diameter of 48 feet and height of 25 feet. Just before construction was to begin, it was learned that a new law allows tanks to be a maximum of 9 feet in height. If the tank is redesigned to meet the law, but has the same volume, what is its new diameter?

Answers

v=hpir^2
d/2=r

so, at first, diameter is 48ft
48/2=24ft is radius
height is 25ft

so volume=25pi24^2 or 14400pi cubic feet

max of 9ft

if we want 9ft height
find r
hmm

14400pi=9pir^2
divide both sides by 9pi
1600=r^2
sqrt both sides
40=r
2r=d
2(40)=80=d

the new diameter is 80ft

A plant is already 11.50 meters tall, and it will grow 9 centimeters every month. The plant's height, H (in meters), after x months is given by the following function.

H (x) = 0.09x + 11.50

What is the plant's height after 15 months?

Answers

h(15)=0.09(15)+11.5
h(15)=1.35+11.5
h(15)=12.85
Final answer: 12.85m

The plants height after 15 months is:

What are linear equations?

"A linear equation in one variable is an equation in which there is only one variable present. It is of the form Ax + B = 0, where A and B are any two real numbers and x is an unknown variable that has only one solution."

Given the function is

[tex]H(x)= 0.09x + 11.50[/tex]

Also given,

Number of months are 15

[tex]\(H(x)= 0.09*15 + 11.50 \\H(x)= 1.35 + 11.50 = 12.85[/tex]

Hence, the plant's height after 15 months is 12.85 meters.

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Numbers that are divisible by 2,4,6,8,10 have to be.

Answers

The numbers have to be even

Identify each expression as a monomial, binomial, trinomial, or none of the above.

1) 24x²y

2) 9q + 4q/5p - 3p²

Answers

you can identify an expression by the number of the terms in the expression.

monomial = one term
binomial = two terms
and so on.

[tex]24x^{2}[/tex]y contains only one term, so it is a monomial.

9q +  [tex] \frac{4q}{5p} [/tex] - [tex]3p^{2} [/tex] contains three terms, so it is a trinomial.

solve the inequality 2(p – 7) > 8

Answers

2(p – 7) > 8
2p - 14 > 8
2p > 22
p > 11

The solution to the given inequality 2(p – 7) > 8 is p > 11.

What is inequality?

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The inequality is given in the question following as:

2(p – 7) > 8

We have to determine the solution to the given inequality.

As per the question, we have

2(p – 7) > 8

Open the parentheses and apply the distributive property of multiplication,

2p - 14 > 8

Add 14 both sides of the above in inequality,

2p - 14 + 14 > 8 + 14

2p > 22

Divided by 2 into both sides of the above in inequality,

p > 11

Therefore, the solution to the given inequality is p > 11.

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Connor is asked to find the probability of rolling a prime number on a die. He states that this is a simple event. True or false? A. True B. False

Answers

The correct answer is true

During one day on the stock market, an investor lost $2500 on one stock, but gained $1700 on another. At the end of trading that day, the investor's holdings were worth $52500. What were they worth when the market closed that day?

Answers

Let x and y represent the two holdings.

Before trading day:
The holdings were worth x + y.

At the end of the trading day:
Holding x  changes to x - 2500 because of loss.
Holding y changes to y + 1700 because of gain.

The holdings are worth $52500 at the end of trading, therefore
(x - 2500) + (y + 1700) = 52500
x + y - 800 = 52500
x + y = 53300

Answer:
Before the trading day, the holdings were worth $53,300.
At the end of the trading day, the holdings were worth $52,500.

Max is observing the velocity of a runner at different times. After one hour, the velocity of the runner is 5 km/h. After two hours, the velocity of the runner is 3 km/h. Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used. (5 points) Part B: How can you graph the equations obtained in Part A for the first 4 hours? (5 points)

Answers

Given:
Velocity = 5 km/h after 1 hour
Velocity = 3 km/h after 2 hours

Part A.
Let 
v = a + bt
where
v = velocity, km/h
t = time, hours

Because v=5 when t=1, therefore
a + b = 5             (1)
Because v=3 when t=2, therefore
a + 2b = 3            (2)
Subtract (1) from (2).
a + 2b - (a + b) = 3 - 5
b = -2
From (1), obtain
a - 2 = 5
a = 7

Answer:  v = 7 - 2t

Part B.
To graph the equation for 0<=t<=4, create a table.
  t       v
---  -----
 0      7
 1       5
 2      3
 3      1
 4     -1   (gnore negative speed)

The graph is shown below.

Answer:

thx for free 50

lol

Step-by-step explanation:

A carnival ride has a sign at the beginning of the line that says "Must be at least 48 inches tall to ride." Which of the following inequalities best represents the allowable height of riders?

h > 48
h < 48
h ≥ 48
h ≤ 48

Answers

H is equal to and greater than 48 the last one because you must be equal to 48 inches or greater than 48 inches so = would be equal to and < would mean that you must be greater than

Answer: h ≥ 48

Step-by-step explanation: h ≥ 48

I just took test got it right

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4−x and y = 8−x−1 intersect are the solutions of the equation 4−x = 8−x−1. (4 points)

Part B: Make tables to find the solution to 4−x = 8−x−1. Take the integer values of x between −3 and 3. (4 points)

Part C: How can you solve the equation 4−x = 8−x−1 graphically? (2 points)

Answers

Part A: Y=4-x and Y=8-x-1 is just a fancy way of showing the point of intersection, or where both slopes meet,  so to figure out x is the point where the x meets.
Part B: Just plug in number between -3-(3) for x
Part C: Solve the equation by drawing the slope of both equations and find where both lines intersect

A boy moves 4 miles south. Then he turns 90 degrees to the left. He moves forward 6 miles. H turns 90 degrees to the left. He moves forward 4 miles. How far is he now than from his starting point?

Answers

y1=-4

x1=6

y2=4

y1+y2=0

So he is just his x displacement from where he started, 6 miles.

Every day, the number of network blackouts has a distribution (probability mass function)
x | 0 | 1 | 2
P(x)| 0.7| 0.2| 0.1
A small internet trading company estimates that each network blackout results in a $500
loss. Compute expectation and variance of this company’s daily loss due to blackouts.

I computed this E(x)= .4 , varX= .44, but I don't know how i can find the answer?

The answer is
E(Y ) = 200 dollars,
Var(Y ) = 110, 000 squared dollars.


Answers

Final answer:

The expected daily loss of the company due to blackouts, E(Y), can be calculated by multiplying each possible loss (which is the number of blackouts times 500) by the probability of that loss occurring, and summing these products. The variance, Var(Y), is found by first finding the expected value of the square of the loss, E(Y^2), which is done in a similar way to finding E(Y), but by squaring each loss before multiplying by its probability. The variance is then given by E(Y^2) - [E(Y)]^2, resulting in a variance of $110,000.

Explanation:

The expectation (or mean) of a random variable Y can be computed by multiplying each outcome by its probability and summing all these products. The random variable Y here is the daily loss corresponding to x blackouts, which is given by 500*x, where x is the number of blackouts. Hence to find the expected daily loss, E(Y), you need to calculate:

E(Y) = 0*0.7 + 1*500*0.2 + 2*500*0.1 = $200

The variance of a random variable is found by taking the expected value of the squared variation of that variable from its mean. In this case, you'll calculate:

Var(Y) = E(Y^2) - [E(Y)]^2.

To find E(Y^2), you'll calculate:

E(Y^2) = 0*0.7 + (1*500)^2*0.2 + (2*500)^2*0.1

Substitute E(Y) and E(Y^2) into the variance formulas to get Var(Y) = 110,000.

So, the expectation and variance of the company's daily loss due to blackouts are $200 and $110,000 respectively.

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A dance competition on television had five elimination rounds. After each elimination, only one-fourth of the contestants were sent to the next round. The table below shows the number of contestants in each round of the competition: x 1 2 3 4 5 f(x) 512 128 32 8 2 Compute the average rate of change of f(x) from x = 2 to x = 4 and describe what it represents.

−60 contestants per round, and it represents the average rate at which the number of contestants changed from the second round to the fourth round

−120 contestants per round, and it represents the average rate at which the number of contestants changed from the second round to the fourth round

−60 contestants per round, and it represents the number of contestants who will reach the final round

−120 contestants per round, and it represents the number of contestants who will reach the final round

Answers

When x =2, f(x) = 128
When x = 4, f(x) = 8

The changing rate is [tex] \frac{8-128}{4-2}= \frac{-120}{2}=-60 [/tex]

This changing rate represents the decrease of the number of contestants as the competition approaches the final.

Correct option is the first option

−60 contestants per round and it represents the average rate at which the number of contestants changed from the second round to the fourth round 

Answer:

A

Step-by-step explanation:

Which of the following approaches can be used to construct a parallelogram? Select one: a. Measure equal segments on parallel lines, then join the endpoints of these segments. b. Construct two congruent angles, then bisect them. c. Construct the perpendicular bisector of a segment, then bisect two of the right angles. d. Construct two perpendiculars to a parallel line.

Answers

Final answer:

The correct approach to constructing a parallelogram is to measure equal segments on parallel lines and then join the endpoints of these segments, which ensures opposite sides are equal and parallel.

Explanation:

The student has asked which of the following approaches can be used to construct a parallelogram. The correct approach is Measure equal segments on parallel lines, then join the endpoints of these segments, which corresponds to option a. This method utilizes the properties of parallelograms, where opposite sides are equal in length and parallel to each other. The Euclidean Geometry postulates that relate to this method include E1 Two points determine a line, E2 Line segments can be extended, and the Parallel postulate: Given a line and a point not on the line, no more than one line can be drawn through the point and parallel to the given line.

To construct a parallelogram, you can follow these simplified steps:

Select any two parallel lines.

Measure and mark equal length segments on each of the lines.

Join the corresponding endpoints of these segments to form the parallelogram.

Dorothy types 120 words per minute .How many words does Dorothy type in 1.75 minutes ?

Answers

D. 210 Words is the correct answer.
The correct answer is D.) 210. If you think of it this way, half of 120 is 60. Dorothy types 120 words per minute, so she types 60 words per 30 seconds. Divide that by half again to get 30 words in 15 seconds. at them together, you get 90 words in that .75 of a minute. 120 + 90 = 210. Hope this helped you out, I would appreciate if you rated me the "brainliest answer" if I did!

Which are correct representations of the inequality 6x ≥ 3 + 4(2x – 1)? Check all that apply.
A=1 ≥ 2x
B=6x ≥ 3 + 8x – 4
and on a graph
.5 shaded to the left
- .5 shaded to the right
.5 shaded to the right

Answers

checking all that apply the correct answers would be A B and C

The correct answers are:

A) 1 ≥ 2x ; B) 6x ≥ 3 + 8x – 4 ; and .5 shaded to the left

Explanation:

Our inequality given is 6x ≥ 3 + 4(2x - 1). First we use the distributive property:

6x ≥ 3 + 4(2x) + 4(-1)

6x ≥ 3 + 8x - 4

This means A is correct.

Next we can subtract 8x from each side:

6x-8x ≥ 3+8x-4-8x

-2x ≥ 3-4

-2x ≥ -1

Divide both sides by -1 (remember to flip the inequality symbol):

-2x/-1 ≥ -1/-1

2x ≤ 1

This can also be written as 1 ≥ 2x, so B is correct.

To finish solving this, divide both sides by 2:

2x/2 ≤ 1/2

x ≤ 0.5

To graph this, we circle 0.5 and fill it in (since it is less than or equal to), and shade to the left (since it is less than).

A building contractor has a piece of crown molding that is 48 1/2 inches long he cuts off one piece measuring 10 1/4 inches and another piece 2 feet 1/8 inch how much does he have left

Answers

Well, lets first start with 48 1/2 - 10 1/4. We can turn 48 1/2 to 48 2/4. 48 2/4 - 10 1/4 = 38 1/4. Next, we have to convert 2 feet and 1/8 inches to inches, which would be 24 1/8 inches. Turn 38 1/4 to 38 2/8. Last of all, 38 2/8 - 24 1/8 = 14 1/8. He has 14 1/8 inches left.

Ravi and Tikiera are making Halloween Pencil Toppers to raise money for the Math Club. Ravi can make one pencil topper in 10 minutes and Tikiera can make one pencil topper in 9 minutes. If they work together, how quickly can they make one pencil topper? Round your answer to the nearest tenth of a minute.

Answers

You have to solve the following equation:

[tex] \frac{t}{9}+ \frac{t}{10} =1[/tex]

The answer you get is [tex]t= \frac{90}{19} [/tex] which is about 4.7 minutes!

How do you convert from a radical expression to a rational exponent?

Im just a little confused so if someone could explain this to me, thatd be great!

Answers

 The denominator of the raised fraction is what goes on the outside of the square root. So if you had 2 raised to 1/3, you'd put the 3 raised outside to the left of the radical and the 2 inside. They give the same answer, so if you know one, you can always play with the other until you get the same answer. My teacher told us in Calculus a funny/weird way to remember it is the "bottom (of the raised fraction) goes in the crack (of the radical)." Does this help??
Final answer:

To convert a radical expression to a rational exponent, identify the root index of the radical as this will be the denominator of the rational exponent. The base remains unchanged. The rational exponent is 1 over the root index.

Explanation:

To convert a radical expression to a rational exponent, you need to understand the connection between them. In mathematics, the 'nth root of a' can be written as a radical expression or as a to the power of 1/n, which is the rational exponent form.

For example, if we have √a (square root of a), which is a radical expression, it can be written as a^(1/2) in rational exponent form. Similarly, the cube root of a (3√a) translates to a^(1/3).

Here are the steps for conversion:

   

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Consecutive terms are __________________. A. even B. terms that are next to each other C. terms added together D. the Fibonacci sequence

Answers

terms that are next to each other


B. terms that are next to each other 
Hope this helped
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