You are 9 miles away from home. You start biking home at a speed of 6 miles per hour.
a. write an equation. in standard form that represents your distance from home y after x hours.
b. find the y-intercept of the graph. what does this represent?
c. find the x-intercept of the graph. what does this represent?

Answers

Answer 1

a) y=9-6x, standard form is ax+by=c so add 6x to both sides

6x+y=9

b) from the first, we had it in slope intercept form, mx+b where b is the y-intercept. y=-6x+9

So the y-intercept is the point (0,9) which represents the starting distance before you start biking. You start being 9 miles from your house.

c) The x intercept occurs when y=0 so:

y=9-6x, so if y=0

0=9-6x

6x=9

x=9/6

x=1.5

This represent the time when you will arrive home and the total time that has elapsed to get there.

Answer 2

The distance and speed are illustrations of linear equations

The standard form is [tex]\mathbf{6x + y = 9}[/tex]The y-intercept is 9The x-intercept is 1.5

The given parameters are:

[tex]\mathbf{Rate = 6}[/tex]

[tex]\mathbf{Initial = 9}[/tex]

(a) The standard equation

Because the distance reduces with time, the equation is:

[tex]\mathbf{y = Initial-Rate \times x}[/tex]

This gives

[tex]\mathbf{y = 9 - 6\times x}[/tex]

[tex]\mathbf{y = 9 - 6x}[/tex]

Add 6x to both sides

[tex]\mathbf{6x + y = 9}[/tex]

(b) The y-intercept

This is the initial distance away from home.

So, the y-intercept is 9

Set y to 0, to calculate the x-intercept

[tex]\mathbf{6x + y = 9}[/tex]

[tex]\mathbf{6x + 0 = 9}[/tex]

[tex]\mathbf{6x = 9}[/tex]

Divide both sides by 6

[tex]\mathbf{x = 1.5}[/tex]

This is the initial time away from home.

So, the x-intercept is 1.5

Read more about linear equations at:

https://brainly.com/question/11897796

Related Questions

The variable Z is directly proportional to X. When X is 3, Z has the value 54. Wha is the value of Z when X= 12

Answers

The variable Z is directly proportional to X
Z = kX (Where k is the constant of proportionality)
To find k
54 = k3

k = 54/3
k = 18

now find new Z

Z = 18X
Z = 18(12)
Z = 216

Suppose a youth organization wants to choose a president, vice-president and secretary for the upcoming year from its 35 person membership. In complete sentences, explain why this is a permutation. Determine how many different ways the youth board can be chosen.

Answers

P(n, r)=[tex] \frac{n!}{(n-r)!} [/tex]

is the formula which gives the total number of permutations of r objects out of n.

A permutation means an arrangement in a list, be it horizontally, or vertically.

So there is a first place, a second and so on.

Example: a, b, c and a, c, b are 2 different permutations.

with these in mind:

the problem described is a permutation problem, because the order is important.

We do not only care whether a certain person is chosen among the 3, we also care what position he/she will hold.

The total number of permutations of 3 objects out of 35 is calculated by the formula:

[tex]P(35, 3)=\frac{35!}{(35-3)!}=\frac{35!}{(32)!}= \frac{35*34*33*32!}{32!}=35*34*33=39,270[/tex]

Answer: 39, 270

A triangle has coordinates A (1, 5), B (-2, 1) and C (0, -4). What are the new coordinates if the triangle is dilated with a scale factor of 1/5?

Answers

IF you are dilating about the origin, which you didn't exactly state, the new coordinates are A' (1/5, 1), B' (2/5, 1/5), C' (0, 4/5). Dilation is all about distance, so you have to move the new coordinates to whatever the scale factor is times the x and y distance. For example, A is at (1, 5), so 1/5 of 1 is 1/5, and 1/5 of 5 is 1, hence your new coordinate for A. It is a fifth of the distance from the origin as its preimage is.

Let g(x) = 2x and h(x) = x2 + 4. Evaluate (g ∘ h)(3).

Answers

if g(x)=2x and h(x)=x^2+4 then:

(g○h)(x)=g(h(x))

(g○h)(x)=2(x^2+4)

(g○h)(x)=2x^2+8

(g○h)(3)=2(3^2)+8

(g○h)(3)=2(9)+8

(g○h)(3)=18+8

(g○h)(3)=26

There is a traffic light at the intersection of walnut street and Lawrence avenue. The traffic light in walnut street follows a cycle. It is green for 50 seconds, yellow for 10 seconds, and red for 30 seconds, as you travel along walnut and approach the intersection, what is the probability that the first color you see is red?

Answers

P(R)=30/(30+10+50)

P(R)=30/90

P(R)=1/3

Answer: The probability that the first color we see is red is 0.34.

Step-by-step explanation:

Since we have given that

Time taken by green color on the traffic light = 50 seconds

Time taken by yellow color on the traffic light = 10 seconds

Time taken by red color on the traffic light = 30 seconds

Total number of seconds = 50+10+30=90

So, Probability that the first color we see is red is given by

[tex]\dfrac{\text{Time alloted for red color}}{\text{Total number of seconds}}\\\\=\dfrac{30}{90}\\\\=\dfrac{1}{3}\\\\=0.3333...\\\\\approx 0.34[/tex]

Hence, the probability that the first color we see is red is 0.34.

Mike and adam left a bus terminal at the same time and traveled in opposite directions. mike’s bus was in heavy traffic and had to travel 20 mi/h slower than adam’s bus. after 3 hours, their buses were 270 miles apart. how fast was each bus going?

Answers

adam's bus speed = a
mike's bus speed = m
total distace = t

m = a - 20

after 3 hour:

3 * (m + a) = t
3 * (m + a) = 270
3m + 3a = 270
[ 3 * (a - 20) ] + [ 3 * a ] = 270
[ 3a - 60 ] + 3a = 270
3a - 60 + 3a = 270
3a + 3a = 270 + 60
6a = 330

their speed:
a = 55
m = 55 - 20 = 35

HELP If f(x)=1/7x-9,then f^-1(x)=?

Answers

The inverse of f(x) is 7x+63

Answer:

Plato/Edementum

Step-by-step explanation:

this is the correct answer if you are taking Inverse of a Function: Mastery Test just type in 7x+63 type it in like that and it will be correct

Table that organizes two categorical variables is called?
It says it has 13 letters

Answers

A table that organizes two categorical variables is called a two - way table. It is a table that examines the correlation between two categorical variables. values that are placed inside the table can be shown as relative frequencies or frequency counts or can be graphically shown as segmented bar chart. The rows represent a category and the columns represent another category. An example would be a question whether how many males or females in a class. Some will answer yes or no. So we will have rows that shows the gender and columns that shows the answer. The intersection between the rows and columns indicates their answer in a specific class. This is a two way table.

What is recorded in section 24 of cms-1500?

Answers

Procedures performed for a patient.

What is the y intercept of Y = 3x - 4?

Answers

in y = mx + b form, the y intercept can be found in the b position

y = mx + b
y = 3x + (-4)

so ur y intercept is -4

[tex]\bf \begin{array}{llll} y=&mx&+b\\ &\uparrow &\ \uparrow \\ &slope&y-intercept \end{array}\qquad \begin{array}{llll} y=&3x&-4\\ &&\ \uparrow \end{array}[/tex]

What is the correct name for this circle?

Answers

the circled is named for the letter in the center

so this one is named circle C

Given the following linear function sketch the graph of the function and find the domain and range.
F(x)=2/7x-2

Answers

Hopefully the picture loads, but the x-int is (7,0) and the y-int is (0,-2)

Domain and range are from negative infinity to positive infinity or all real numbers

What is the data path width for a dimm that supports ecc?

Answers

Normally, the data path width for DIMMs is 64 bits but for the DIMMs that support ECC, the data path is 72 bits.

To add, error checking uses the extra 8 bits. ECC memory is more reliable than non-ECC memory but it costs more than a non-ECC memory. Comprising the DIMMS are a series of dynamic random-access memory integrated circuits. Mounted on a printed circuit board, these modules are designed for use in personal computers, workstations and servers.

The most common kinds of internal data corruption are detected and corrected by a type of computer data storage called error-correcting code memory.

Simplify 12 to the 16th power over 12 to the 4th power

Answers

Hello there!

[tex] \frac{ 12^{16}}{12^{4} } [/tex]

Do solve for this, we actually just have to do one thing since our number is the same - subtract the exponents.

When you divide by exponents, you are subtracting them.

For example;

[tex] \frac{ x^{5} }{x^{2} } [/tex]

Subtract the exponents.

[tex] x^{3} [/tex] is your answer for this example.

Let's apply this to our current expression.

[tex] \frac{ 12^{16}}{12^{4} } [/tex]

Subtract the exponents.

[tex] 12^{12} [/tex] is your simplified expression with exponents.

I hope this helps!

Which is the slope of the line that connects points (3,17) and (7,25) ?

Answers

The slope of a line can be found with any two points on the line:

slope=(y2-y1)/(x2-x1) where (x1,y1) and (x2,y2) are any two points...

slope=(25-17)/(7-3)

slope=8/4

slope=2

this could easily be plotted on a graph.
8/4, reduced to 2/1.
2/1 is the correct answer.

Find the sum of the arithmetic sequence. 15, 17, 19, 21, ..., 33

Answers

as formula says:

sum = [tex] n *\frac{ a_{1} + a_{n} }{2} [/tex]

in our case n = 10, a1 = 15 and An = 33 so the answer will be:

sum = 10 * (33 + 15)/2 = 10 * 48 / 2 = 10 * 24 = 240

Answer:

240

Step-by-step explanation:

Hope this helps! :)

What is the problem to this

Answers

4:9
24:x
Set up a proportion
4/9=24/x
4x=216
x=54
a) 54 is your answer
hope this helps, and please give brainliest if it does!

The answer is: [A]: " 54 " .
__________________________
Given: "For every 4 people that made the team, 9 people did not make the team. 24 people made the team. How many did NOT make the team?

24 people made the team. How many groups of 4 people is that?

24 divided by 4 equals: "6".
__________________________
6 * 9 = 54 .
__________________________
The answer is: [A]: " 54 " .
__________________________

Find the solution of this system of equations.
Separate the x- and y-values with a comma.
x= 5 + y
28x – 9y= -12

Answers

x= 5 + y
28x – 9y = -12

substitute x= 5 + y into 28x – 9y = -12

28x – 9y= -12
28(5 + y) – 9y = -12
140 + 28y - 9y = -12
19y = -152
y = -8

x = 5 + y
x = 5 - 8
x = -3

solution (-3, -8)

What is the domain of y = tan x, where n is any integer?

Answers

now [tex]\bf tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}[/tex] so, if the cosine of the angle, ever becomes 0, the rational becomes undefined. so hmmm other than those points, the values the angle can take on are pretty much anything, positive or negative ones... and the cosine is 0 at [tex]\bf \frac{\pi }{2}\qquad \frac{3\pi }{2}\qquad \textit{on the range of }[0,2\pi ][/tex]

so.. one can say the domain of tangent, is all angles EXCEPT those where cosine turns to 0

[tex]\bf \{x|x\in \mathbb{R}; x\ne \frac{\pi }{2}\pm\pi n\}\qquad \textit{\underline{n} being an integer}[/tex]

Answer:

x is not equal to pi/2 + n*pi

Step-by-step explanation:

just got it right on a pex

Teh width of a rectangle is 2 cm less than 7 times the length. the perimeter is 60 cm. determine the length and the width of the rectangle

Answers

P=2(L+W)
60=P=2(L+W)
60=2(L+W)
divide by 2
30=L+W

given
W=-2+7L
subsitute
30=L+W
30=L-2+7L
30=8L-2
add 2
32=8L
divide by 8
4=L

sub back
W=-2+7L
W=-2+7(4)
W=-2+28
W=26

width is 26cm
length is 4cm

Determine whether the sequence converges or diverges. If it converges, give the limit. 60, 10, five divided by three, five divided by eighteen, ...

Answers

[tex]A_n = 60, 10, \frac{5}{3}, \frac{5}{18}[/tex]

Using geometric sequence form, we can rewrite it as:
[tex]A_n = a_1 \cdot r^{n-1}[/tex]
[tex]A_n = 60 \cdot \frac{1}{6}^{n - 1}[/tex]

Since r < 1, there exists a limit, and thus, it is said to converge.
[tex]\lim_{n \to \infty} 60 \cdot (\frac{1}{6})^{n - 1}[/tex]
[tex] = 0[/tex]

Since the ratio is still positive, as n tends towards infinity, the graph of the sequence will never go below the horizontal. Thus, we say that the limit of the function is zero, which means that as we increase the size of n, eventually after the infinite-th time, it will hit zero.

Suppose that 66% of people own dogs. if you pick two people at random, what is the probability that they both own a dog?

Answers

Final answer:

The probability of two people owning a dog when 66% of people own dogs is found by squaring the probability (0.66), giving us a result of 0.4356 or 43.56%.

Explanation:

The question asks to calculate the probability that both people picked at random own a dog when it is known that 66% of people own dogs. To find this probability, we can simply multiply the probability of the first person owning a dog by the probability of the second person owning a dog, assuming that these events are independent.

The probability that one person owns a dog is given as 66%, which is 0.66 in decimal form. Thus, the probability that both people own a dog is 0.66 × 0.66 (or 0.66 squared). Calculation yields:

0.66 × 0.66 = 0.4356

Therefore, the probability that both people own a dog is 0.4356, or 43.56%.

A student took a test which had 6 questions. He would score 8 points on the test if all his answers are correct. If y represents the student's score when he got x questions incorrect, which graph best represents this situation?

Answers

m=(y2-y1)/(x2-x1) so if we take the endpoints (0,0) and (6,8)

m=(8-0)/(6-0)

m=8/6

m=4/3, and since we know we have the point (0,0) we know the line is just:

y=mx, using m found above...

y=4x/3

So the graph that will match this line is one that has a point on the origin and has a positive slope of 4/3. So another point other than the origin that will be quite clear is the point (3, 4)

please help!!!! question is/.........

Answers

Area of circle = 3.14 x 6^2 = 3.14 x 36 = 113.04

1/2 circle = 113.04 / 2 = 56.52

Area of rectangle = 8 x 6 = 48

Area of figure = 48 + 56.52 = 104.52

answer
104.52 ft^2

On a blueprint, the scale indicates that 7 cm represent 16 ft. What is the length of a room that is 9.8 cm long and 5 cm wide on the blueprint?

Answers

7/16 =9.8/ x =156.8/7 = 22.4 feet long

7/16 = 5/x = 80/7 = 11.428 feet wide round to 11.43 or 11.4 feet

A bridge in the shape of an arch connects two cities separated by a river. The two ends of the bridge are located at (–7, –13) and (7, –13), and the center of the arch on the bridge is located at (0, 0). Find the equation of the arch of the bridge.

Answers

The equation of the arch is y = (-13/49)x².

The equation of an arch can be described by a parabola when one side of the arch mirrors the other side. This is the case for the bridge problem given.

The center of the bridge is at the origin (0, 0), and it is the vertex of the parabola. Since the arch is symmetrical and the x-coordinate of the vertex is 0, the parabola is a vertical one. Thus, the equation will be in the form y = ax². To find the value of a, we will use the fact that one end of the bridge is at (7, -13).

Since (7, -13) is a point on the parabola, by plugging these values into the equation y = ax², we get:

-13 = a(7²)

-13 = 49a

a = -13/49

Thus, the equation is y = (-13/49)x².

Find P(organic | oranges)
Find P(Non-organic | oranges)

Answers

Answer to part A: 0.63
Answer to part B: 0.37
Answer to part C: organic oranges

---------------------------------------------------------------------
---------------------------------------------------------------------

Work Shown:

Part A
P(Organic|Oranges) = P(Organic AND oranges)/P(Oranges)
P(Organic|Oranges) = 0.19/0.30
P(Organic|Oranges) = 0.63

Part B
P(Non-organic|Oranges) = P(non-organic AND oranges)/P(oranges)
P(Non-organic|Oranges) = 0.11/0.30
P(Non-organic|Oranges) = 0.37

Part C
The probability in part A is larger compared to the answer in part B, so it's more likely to have someone pick organic oranges rather than non-organic oranges. Melina should restock organic oranges for the next sale.

Solve using perfect square factoring patterns. x2 – 8x + 16 = 25

Answers

x^2 – 8x + 16 = 25
-25 both sides
x^2-8x-9=0
(x-9)(x+1)
x=9,-1

Find the fifth roots of 243(cos 240° + i sin 240°)

Answers

The best way to find a root is to get the root of the coefficient, then divide the angle by what root you want for the first one, then add 360/root to get each additional angle until you have all the roots. So for the fifth root, get the fifth root of 243, then divide 240 by 5 for your first angle. You then write the root in the same form as the original, just with your new numbers. Now take 360/5 to find that you will add 72 to the angle to get your next angle. Keep adding 72 to get another angle until you have five roots in all.

Apply De Moivre's Theorem

zⁿ = rⁿ(cos.n.Ф + i.sinn.Ф).

The 5th root, that means that n = 1/5 ↔↔↔ rⁿ = r¹/₅ = ⁵√r

zⁿ = ⁵√(243) [cos (240+2kπ)/5 +i.sin(240+2kπ)/5]
with k = 1,2,3,..,n-1. Note that ⁵√(243) = 3

1st root : for k=0 → 3[cos(240/5)+isin(240/5) = 3(cos48°+isin48°)
2nd root : for k=1→3[cos(240+360)/5)+isin(240+360)/5]=3(cos120°+isin120°)
3rd root : for k=2 →→ 3(cos192 + isin192)
4th root : for k=3→→3(cos264+isin264)
5th root : for k =4↔↔3(cos336+isin336)

A small school has 110 students who occupy three classrooms: a, b, and

c. after the first period of the school day, half the students in room a move to room b, one-fifth of the students in room b move to room c, and one-third of the students in room c move to room

a. nevertheless, the total number of students in each room is the same for both periods. how many students occupy each room?

Answers

There are 20, 50 and 30 in each room respectively.

What is equation?

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, there are 110 students in total in all the class.

According to question,

a+b+c = 110

After the room changes, we have

a/2 + c/3 = a

4b/5 + a/2 = b

2c/3 + b/5 = c

or,

a/2 = c/3

a/2 = b/5

b/5 = c/3 = a/2

so, substituting in,

a + 5a/2 + 3a/2 = 110

2a + 5a + 3a = 220

a = 22

b = 55

c = 35

Hence, there are 20, 50 and 30 in each room respectively.

For more references on equation, click;

https://brainly.com/question/29657992

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