For each part, write the equation that represents the line in slope-intercept form (y = mx + b) and standard form (ax + by = c where a, b, and c are integers and a is not negative).
Answers
Answer:
Graph
[tex]y = -x+1[/tex] --- Slope intercept form
[tex]y +x= 1[/tex] --- Standard form
Points
[tex]y = 2x-2[/tex] --- Slope intercept form
[tex]y -2x=-2[/tex] --- Standard form
Step-by-step explanation:
Solving (a): The graph.
From the graph, we have:
[tex](x_1,y_1) = (1,0)[/tex]
[tex](x_2,y_2) = (0,1)[/tex]
First, calculate the slope
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
This gives:
[tex]m = \frac{1 - 0}{0 - 1}[/tex]
[tex]m = \frac{1 }{- 1}[/tex]
[tex]m = -1[/tex]
The slope intercept equation is:
[tex]y = m(x-x_1)+y_1[/tex]
So, we have:
[tex]y = -1(x-1)+0[/tex]
[tex]y = -1(x-1)[/tex]
[tex]y = -x+1[/tex]
In standard form:
[tex]y = -x+1[/tex]
Add x to both sides
[tex]y +x= x-x+1[/tex]
[tex]y +x= 1[/tex]
Solving (b): The points
From the graph, we have:
[tex](x_1,y_1) = (0,-2)[/tex]
[tex](x_2,y_2) = (3,4)[/tex]
First, calculate the slope
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
This gives:
[tex]m = \frac{4 - (-2)}{3 - 0}[/tex]
[tex]m = \frac{6}{3}[/tex]
[tex]m=2[/tex]
The slope intercept equation is:
[tex]y = m(x-x_1)+y_1[/tex]
So, we have:
[tex]y = 2(x-0)-2[/tex]
[tex]y = 2(x)-2[/tex]
[tex]y = 2x-2[/tex]
In standard form:
[tex]y = 2x-2[/tex]
Subtract 2x from both sides
[tex]y -2x= 2x-2x-2[/tex]
[tex]y -2x=-2[/tex]
Related Questions
solve for X: x + 2 (1.5x - 6) = 16 (IF YOU CAN PLEASE TELL ME HOW TO SOLVE QUESTIONS LIKE THIS)
Answers
Answer:
x=7
Step-by-step explanation:
You multiply the 2 with what is inside of the parenthesis so 3x-12
x+3x-12=16
then you add x +3x =4x
4x-12=16
then you add 12 to both sides
4x=28
then you divide by 4 on both sides
x=7
10. Write a rule for the function represented by the table.
Answers
Answer:
C) y=13+15x
Step-by-step explanation:
y=13+15x
The rule for the function represented by the table is: y = 15x + 13
Hence the correct option is A.
Given is a table showing the values of x and y:
x = 0, 1, 2, 3
y = 13, 28, 43, 58
Using this table we need to write a rule for the function represented by the table.
To determine a rule for the function represented by the table, let's examine the relationship between the values of x and y.
We notice that as x increases by 1, y increases by 15.
Based on this observation, we can create a linear equation to represent the relationship between x and y.
The equation will have the form:
y = mx + b
Where m is the slope of the line and b is the y-intercept.
To find the slope (m), we can calculate the difference in y-values divided by the difference in x-values:
m = (y₂ - y₁) / (x₂ - x₁)
Using the first two data points from the table (x₁ = 0, y₁ = 13 and x₂ = 1, y₂ = 28):
m = (28 - 13) / (1 - 0)
= 15 / 1
= 15
So, the slope of the line is 15.
To find the y-intercept (b), we can substitute the values of x and y from one of the data points into the equation and solve for b.
Let's use the first data point (x = 0, y = 13):
13 = 15(0) + b
13 = b
So, the y-intercept is 13.
Putting it all together, the rule for the function represented by the table is:
y = 15x + 13
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Brainly so you better do it right
Answers
Answer:
Step-by-step explanation:
what is 5/9 + 1/3? (please show your work)
Answers
Answer:
8/9
Step-by-step explanation:
First: Turn the 1/3 in 3/9 (You have to find the common denonminator or bottom number in a fraction)
Second: add (3/9 + 5/9= 8/9)
Answer: 8/9
(Brainliest??)
The value of the fractional expression 5/9 - 1/3 will be 17 / 3.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The numbers are given below.
5/9 and 1/3
Then the difference between the numbers 5/9 and 1/3 will be given by putting a minus sign between them. Then we have
⇒ 5/9 - 1/3
⇒ (5 - 3) / 9
⇒ 2 / 9
The value of the fractional expression 5/9 - 1/3 will be 17 / 3.
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I need this answer as soon as possible
Answers
Answer:
1) 1 2) 1/729 3) 1/27 4) -1/729
Step-by-step explanation:
plug them into calculator
Write a linear function f with the values f (3)= -4 and f (5)= -4
f(x)=
Answers
Answer:
Step-by-step explanation:
Find the missing value of x. Round to the nearest degree if necessary.
28 °
62 °
64 °
25
Answers
9514 1404 393
Answer:
(b) 62°
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relation between sides and angles. Here, the relevant relation is ...
Cos = Adjacent/Hypotenuse
cos(x) = 9/19
The inverse function is used to find the angle
x° = arccos(9/19) ≈ 61.73°
The missing value of x is about ...
x ≈ 62
Find the shaded area of the figure. Please help I am giving brainliest
Answers
Answer:
do u mean the degree? if u do then it would be 60
Step-by-step explanation:
Answer: 25pi/3 square units
=============================================================
Explanation:
If that point is the center, then we have two pizza slices that sweep out 60 degrees of a central angle.
The full circle has pi*r^2 = pi*5^2 = 25pi square units of area
We only want 60/360 = 1/6 of that for each slice, so 2*(1/6) = 1/3 of the full circle area is shown by the shaded region
(1/3)*(full circle area) = (1/3)*25pi = 25pi/3 square units is the shaded area
I need some help and can you please show your work? Thank you have a good day
Answers
Answer:
Step-by-step explanation:(4+7)-(1)
Warmup 2/16/21(create a table to compare the 2)
.
If you were babysitting, would you rather
Charge $5 for the first hour and $8 for each additional
hour?
bry
SY
.
Or
Charge $15 for the first hour and $6 for each additional
hour?
ebo...
Explain your reasoning.
ng
Answers
[] divided 1/3 =6/7.
Answers
Answer:
6/21
Step-by-step explanation:
Write an equation in slope intercept form given:
Slope = 1/2
y-intercept= -8
Answers
Answer:
y= 1/2x - 8
Step-by-step explanation:
a square yard is how many square feet
Answers
A school has an enrollment of 600 students. 270 of the students are girls. Express the fraction of students who are boys in lowest terms.
Answers
Answer:
11/20
Step-by-step explanation:
330/600 simplified = 11/20
Rounded to the nearest percent
Answers
Answer:50%
Step-by-step explanation: i think
A spice rack has ó shelves. Each shelf can display 15 spice jars. How many spice racks does a store need to display 2,250 spice jars?
Answers
Answer:
25
Step-by-step explanation:
Each spice rack can hold 90 jars. It will take 25 racks to hold 2,250 jars.
I hope this helps!
Do well!
Mark Brainliest!
Have to find the area of the figure please help!
Answers
Answer: Area = [tex]60\sqrt{2}[/tex]
============================================================
Explanation:
The triangle on the right side is a 45-45-90 triangle
The hypotenuse is 8, so the leg length is [tex]\frac{8}{\sqrt{2}} = \frac{8\sqrt{2}}{2} = 4\sqrt{2}[/tex]
This is the height of the parallelogram. The base is 15 which is always perpendicular to the height, and vice versa.
The area of this parallelogram is therefore, [tex]\text{base*height} = 15*4\sqrt{2} = 60\sqrt{2}[/tex]
Volume of the figures below?
Answers
answer 2: 198ft cubed
pls give brainlest pls & ty :)))
An Apple grower harvested 3280 green apples and 12220 Red apples in one day. Apples can be boxed at a rate of 500 apples per hour. Many minutes will it take to box all of the apples
Answers
Answer:
1860
Step-by-step explanation:
Find the Width of the Rectangular Prism.
Answers
Answer:
w = V/12 IN X= 840in then 840÷12 = 70in
A rectangular prism has 70in width having volume 840in³, length is 2in, and height 6in.
What is a rectangular prism?A rectangular prism or a cuboid is a three-dimensional closed figure which has volume along with surface area.
The volume of a cuboid is the product of its length, width, and height.
V = (l×w×h).
The total surface area of a cuboid is 2( lw + wh + wl) and the lateral surface area is 2(l + w)×h.
Given, A rectangular prism has a volume 840 in³, its length is 2 in and its height is 6in.
Assuming width to be w in.
∴ (l×w×h) = volume.
(2×w×6) = 840.
12w = 840.
w = 70 in.
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20 mountains and where they are found in the world
Answers
Answer:
20. Nuptse, Mahalangur Himalaya
It is located in the Mahalangur range in the Khumbu region and is one of the mountains surrounding Mount Everest.
19. Distaghil Sar, Hispar Karakoram
This peak is located in the Karakoram range of the Gilgit-Baltistan region of Pakistan. Dishtaghil Sar is almost three kilometers wide and 7884 meters in height.
18. Himalchuli, Manaslu Himalaya
The Himalchuli peak is a part of Nepal Himalayas and prevails south of Mount Manaslu, one of the world’s highest mountains. Himalchuli has the second-highest summit in its mountain range, i.e., Mansiri Himalaya, at the height of 7892 meters. Hisashi Tanabe of Japan was the first person to have climbed it in 1960.
17. Gasherbrum IV, Baltoro Karakoram
Gasherbrum IV is one of the peaks in the Gasherbrum mountain range, as the name suggests, and is located in Pakistan. It is at the north-east end of the Baltoro Glacier in the Karakoram range of the greater Himalayas. The rest of the three peaks located in the Gasherbrum range are well above 8000 meters, while this peak is about 7932 meters in elevation.
16. Annapurna II, Annapurna Massif
At 7934 m high, Annapurna II lies in the eastern ranges of the Annapurna range, and quite contrary to the common belief in people, it is an independent peak. The first ascent of this peak was made by Richard Grant, Chris Bonington, and Ang Nyima Sherpa in 1960 and has seen very few ascents since.
15. Gyanchung Kang, Mahalangur Himalaya
Gyanchung Kang lies between two of the tallest mountains globally, both of which are above 8000 meters, namely, Cho Oyu and Everest. It is part of Mahalangur Himalaya while it spreads between Nepal and Tibet Autonomous Region of China. It is 7952meters in height.
14. Shishapangma, Jugal Himal
All the mountains listed from here onwards are above an altitude of more than 8000 meters. It is located between Tibet and Nepal. It lies in the restricted area that foreigners are not permitted to visit on security grounds.
Mount Lhotse
13. Gasherbrum II or K4, Baltoro Karakoram
Gasherbrum II lies above Gasherbrum III, and as mentioned above, it is located in the Karakoram range. The 8035-meter peak was first climbed in 1956 by an Austrian climber.
12. Broad Peak or K3, Baltoro Karakoram
The broad peak at 8051 meters is the 12th highest mountain and is also popularly known as Falchan Kangri.
11. Gasherbrum I or Hidden Peak or K5, Baltoro Karakoram
The name was hidden peak due to the extreme remoteness in which it is located. Pete Schoning and Andy Kauffman, who were part of an eight-member American team, were the first to climb this 8080-meter peak in 1956.
10. Annapurna I, Annapurna Massif
The main peak of Annapurna I is the tenth tallest mountain in the world with an altitude of 8091 meters.
9. Nanga Parbat, Nanga Parbat Himalayas
It is also known by the name of “Killer Mountain” because it has one of the highest numbers of deaths and unsuccessful expeditions simultaneously; it has never been climbed during the winter. Located in the Diamer District of Gilgit-Baltistan, Pakistan, Nanga Parbat is the western anchor of the Himalayas.
8. Manaslu, Manaslu Himal
It lies in the Himalayas’ Gorkha district and is in very close proximity to the Annapurna range. Manaslu stands at 8163 meters. Located in the Diamer District of Gilgit-Baltistan, Pakistan, Nanga Parbat is the western anchor of the Himalayas.
7. Dhaulagiri I, Dhaulagiri Himal
It is the highest point in the Kali Gandaki river valley. This massif is bounded on the north and southwest by tributaries of the Bheri River and on the southeast by the Myagdi Khola.
6. Cho Oyu, Mahalangur range Himalaya
Cho Oyu is usually considered the easiest of the 8000-meter peaks due to the moderate slopes and passes nearby. Nepal (Province No. 1)–China (Tibet)
5. Makalu, Mahalangur range Himalaya
Despite being part of the Mahalangur range, Makalu is an isolated peak shaped like a four-sided pyramid. It is located in the Mahalangur Himalayas 19 km southeast of Mount Everest, on the border between Nepal and Tibet Autonomous Region, China.
4. Lhotse, Mahalangur Range Himalaya
Part of the Everest massif, Lhotse is connected to the latter peak via the South Col. Lhotse means "South Peak" in Tibetan
3. Kangchenjunga, Kangchenjunga Himalaya
In a section of the Himalayas called Kangchenjunga Himal delimited in the west by the Tamur River, in the north by the Lhonak Chu and Jongsang La, and in the east by the Teesta River.
2. K2 /Chhogori/Godwin Austen, Baltoro Karakoram
The Baltistan region of Pakistan is home to the highest point in both the Karakoram range and the nation in the form of K2.
1.Sagarmatha /Chomolungma/ Mount Everest /, Mahalangur Range Himalaya
Mount Everest or Sagarmatha, as it is called in Nepal, and Chomolungma is known in Tibet.
Step-by-step explanation:
Hope this helps :)
Louise buys 1 pack of pencils and 1 box of crayons for her son for $3.39. Elaine buys 7 packs of pencils and 8 boxes of crayons for her students for $25.88.
Answers
Answer:
Step-by-step explanation:
p+c=3.39, p=3.39-c
7p+8c=25.88, using p=3.39-c in this equation gives you
7(3.39-c)+8c=25.88
23.73-7c+8c=25.88
23.73+c=25.88
c=2.15, since p=3.39-c
p=3.39-2.15
p=1.24
So pencils cost $1.24 and crayons cost $2.15
Solve for X
B. X
X
152
Answers
Answer:
Step-by-step explanation:
180 - 152 = 28
2x + 28 = 180
2x = 152
x = 76
Question 2 (2 points)
(07.06)
Given the parent function f(x) = 2x, which graph shows f(x) + 1? (2 points)
a
exponential function going through point 0 2 and ending up on the right
b
exponential function going through point 0 0 and ending down on the right
c
exponential function going through point 0 0 and ending up on the right
d
exponential function going through point 0 1.5 and ending up on the right
Answers
Answer:
c
Step-by-step explanation:
Happy valentines dayyyy math suckss help pleaseeeeeee
Answers
On a single roll of a pair of dice, what are the odds against rolling a sum of 7? Please help ASAP!!! :(
Answers
A kid runs an ice cream stand for 14 days. In one day, he makes about 10.00. In those 14 days, about how much money will the kid make?
Answers
question 1: Multiply and simplify.
x^2⋅x⋅x^5
(I got x^8 but I was unsure.)
question 2: Multiply and simplify.
(3x+7)8x^2
Answers
Answer:
question 1 = x7 and question 2 = 24x^3+56x^2 I'm pretty sure
Thomas spends 37of his money on rent and 49of his money on food. Does he spend more money on food or rent?
Answers
Answer:
He spends more money on food
Step-by-step explanation:
Looking in the tens place, we have a 4 and a 3. 4 is greater than three and the 4 belongs to 49. Overall 49>37 so he spent more money on food.
At this weekend's soccer game, 20 out of the first 30 people who entered the
field were wearing a team jersey. If this sample is representative of the 240
people attending the game, about how many of them will probably be wearing
jerseys?
Answers
Answer:
160
Step-by-step explanation: