Find the equation of a line parallel to y = x – 3 that contains the point (-2, 1).
Yeah
Answers
Answer:
The equation of a line parallel to y = x - 3 that contains the point (-2, 1) is:
[tex]y = x + 3[/tex]The graph of both the parallel equation is shown below to make you further understand the concept.
Step-by-step explanation:
The slope-intercept form of the line equation
[tex]y = mx+b[/tex]
where
[tex]m[/tex] is the slope[tex]b[/tex] is the y-interceptGiven the equation
[tex]y = x - 3[/tex]
comparing with the slope-intercept form of the line equation
Slope m = 1
Important Tip:
As the parallel lines never intersect, therefore, they have the same slopes.Thus, the slope of the parallel line is also 1.
As the parallel line contains the point (-2, 1).
so substitute m = 1 and (-2, 1) in the slope-intercept form of the line equation to determine the y-intercept of the parallel line
[tex]y = mx+b[/tex]
[tex]1 = 1(-2) + b[/tex] ∵ (x, y) = (-2, 1) and m = 1
[tex]1 = -2 + b[/tex]
switch sides
[tex]-2+b = 1[/tex]
add 2 to both sides
[tex]-2 + b + 2 = 1 + 2[/tex]
simplify
[tex]b = 3[/tex]
Thus, the y-intercept b of the parallel line is: b = 3
now substitute b = 3 and m = 1 in the slope-intercept form of the line equation to determine the equation of the parallel line
[tex]y = mx + b[/tex]
[tex]y = (1)x + 3[/tex]
[tex]y = x + 3[/tex]
Therefore, the equation of a line parallel to y = x - 3 that contains the point (-2, 1) is:
[tex]y = x + 3[/tex]The graph of both the parallel equation is shown below to make you further understand the concept.
From the graph:
The green line represents the equation y = x - 3 The black line represents the parallel equation y = x + 3It is clear that both lines are parallel.
Related Questions
PLEASE HELP ASAP I WILL GIVE YOU BRAINIEST!! Marcus is 14 years younger than twice Kimi's age. Marcus is 8 years old. How old is Kimi?
Answers
Answer: kimi is 22
Step-by-step explanation:
Answer:
Kimi is 11 years old
Step-by-step explanation:
We can read 'twice Kimi's age' as Kimi's age times 2 and
'14 years younger' as minus 14.
Our equation is
2(Kimi's age)-14= Marcus' age
Since Marcus is 8:
2(Kimi's age)-14= 8
Now we manipulate the equation so that it equals Kimi's age. Remember that whatever we do to the right side, we also do to the left.
First we add 14 to both sides
2(Kimi's age)-14(+14)= 8(+14)
2(Kimi's age)= 22
Then we divide by 2
2(Kimi's age)/2= 22/2
Kimi's age=11
Usually we would us X to represent our unknown, Kimi's age, but I left it as Kimi's age so that it is easier to follow.
On one day, 4 chefs and 5 helpers earned $650.
On another day working the same number of hours
at the same rate of pay, 5 chefs and 6 helpers
earned $800.
How much does a chef earn each
day?
Answers
5c + 6h = 800 where c are chefs, h are helpers
Start by finding an expression for c
4c + 5h = 650
4c = 650 -5h
c = (650- 5h)/4
Then substitute that into the second equation and solve for a number value for h
5 (650-5h)/4 + 6h = 800
(3250-25h)/4 + 6h = 800
Multiply both sides by 4
3250-25h + 24h = 3200
-h = -50
h = 50
Take that 50 and substitute it into the expression we have for c to get a number value for c
C= 650-5(50)/4
C = 650-250/4
C = 400/4
C= 100
Check your first equations, substituting $50 for the helpers and $100 for the chefs.
4 (100) + 5(50) =
400 + 250 = 650
5(100) + 6(50) =
500 + 300 = 800
calculate the area of a circle with a diameter of 3m?
with Solution =
Answers
Answer:
Area of circle = pie r²
= 3.14 × 2.25
=7.065
Answer: 7.07cm²
Step-by-step explanation: diameter=3
radius=d/2
=3/2
=1.5cm
area=πr²
=22/7 x 1.5 x 1.5
=22/7 x 2.25
=99/2 ÷ 7
=99/2 x 1/7
=99/14
Sherbrooke, Quebec is 210 miles from Boston, MA. A train leaves Boston at noon and arrives in Sherbrooke at 4:40 PM. On the return trip to Boston, the train travels 50.4 mph. How many times greater (or less) is the train’s speed on the return trip to Boston than on the trip to Sherbrooke?
Answers
9514 1404 393
Answer:
1.12 times as great
Step-by-step explanation:
The speed from Boston is ...
(210 mi)/(4 2/3 h) = 45 mi/h
Then the speed to Boston is ...
50.4/45 = 1.12 . . . times as great
__
The speed on the return trip is 1.12 times as great, or 12% greater than on the trip to Sherbrooke.
9514 1404 393
Answer:
1.12 times as great
Step-by-step explanation:
The speed from Boston is ...
(210 mi)/(4 2/3 h) = 45 mi/h
Then the speed to Boston is ...
50.4/45 = 1.12 . . . times as great
__
The speed on the return trip is 1.12 times as great, or 12% greater than on the trip to Sherbrooke.
Factor 3n^2 + 5n - 2
PLZ HELP
Answers
Answer:
(3n - 1)(n + 2)
Step-by-step explanation:
Use the rule 2 + 3 to find the missing number on the table.
X Y
0 3
3 6
11
7 10
9 12
Answers
Answer:
14
Step-by-step explanation:
11 + 3 = 14
Hope it helps!
Thanks!
Ten more than four times a number is equal to the difference between 73 and three times the number. Find the number.
Answers
Answer:
let x be the number then,
according to question ,
10+4x=73-3x
or, 4x+3x=73-10
or, 7x= 63
or, x= 63÷7
or,x=9 ans
hence , the number is 9
Which set of numbers below DO NOT make a triangle?
0 7,7,7
O 6,3,3
0 3,4,5
O 5, 11,7
Answers
Answer:
3,4,5
Step-by-step explanation:
All you have to do is use the Triangle Inequality Theorem, which states that the sum of two side lengths of a triangle is always greater than the third side. If this is true for all three combinations of added side lengths, then you will have a triangle therefore 3,4,5 is not triangle.
Tanner had $42.80 and spent 20% of his money on a book including tax. If he paid with a $10 bill, how much change did Tanner get back?
A. $7.28
B. $6.24
C. $1.44
D. $17.54
Answers
42.8 x 0.2 = 8.56
10 - 8.56 = 1.44
Please please give answer
Answers
Answer:
Then the total area is 116 cm^2 which agrees with answer D
Step-by-step explanation:
Notice we need to calculate the area of two rectangles (one larger at the bottom and a smaller one on top)
The Area of a rectangle is the product: base x height
In our case :
Area of Big rectangle = 12 cm x 7 cm = 84 cm^2
Area of smaller rectangle = 8 cm x 4 cm = 32 cm^2
Then the total area is: 84 cm^2 + 32 cm^2 = 116 cm^2
28% of what number is 7? Round your answer to the nearest tenth.
Answers
Answer:
25
Step-by-step explanation:
hope i helped, if u have any additional questions feel free to reply here or msg me on ig (/craxzyx) !! <3
25 iS THE ANSEWR SO NOW JUST ROUND
math help ohh yup #5 in the middle
Answers
Answer:
m<7 = 49°
m<8 = 41°
m<9 = 49°
m<10 = 41°
Step-by-step explanation:
Given :
m<7 ≅ m<9
m<8 = 41°
m<7 = 90° - m<8 (complementary angles)
m<7 = 90° - 41° (substitution)
m<7 = 49°
m<9 = m<7 (m<7 ≅ m<9)
m<9 = 49° (substitution)
m<10 = 90 - m<9
m<10 = 90 - 49
m<10 = 41°
find the measure of the angel x
Answers
Answer:
80°+30°=180°
=110=180
x=70°
answer
Answer:
80 - 30 = 50
Step-by-step explanation:
bcz sum of two interior angle is equal to one exterior angle
Count box lengths to identify the base and height. Then, find the area of the triangle.
How many square units is this triangle?
Answers
Answer:
14 units²
Step-by-step explanation:
1/2(7)(4)=14 units²
Answer:
14 square units
Step-by-step explanation:
NEED HELP W GEOMETRY
In △
ABC, ∡A
is 2 more than twice ∡B
, and ∡C
is 7 less than twice ∡B
. What is the measure of each angle in △
ABC and what is its classifications?
Answers
Answers:
Angle A = 76Angle B = 37Angle C = 67Triangle ABC is an acute triangle. It's also a scalene triangle.
====================================================
Work Shown:
x = measure of angle B
2x+2 = measure of angle A, since we're told its "2 more than twice angle B"
2x-7 = measure of angle C, for similar reasoning
The three angles add to 180. This is true for any triangle
A+B+C = 180
(2x+2)+(x)+(2x-7) = 180
5x-5 = 180
5x = 180+5
5x = 185
x = 185/5
x = 37
This means angle B is 37 degrees. The other two angles are
A = 2x+2 = 2*37+2 = 74+2 = 76
C = 2x-7 = 2*37-7 = 74-7 = 67
----------------
In summary, we have these three interior angles
A = 76B = 37C = 67As a way to check, note how A+B+C = 76+37+67 = 180. This confirms the answer. All three angles mentioned are smaller than 90 degrees, so this triangle is acute.
Furthermore, because all three angles are different measures, this means all three sides are different lengths. This leads to triangle ABC being scalene.
Sasha ran 2/3 of a 27km race before she stopped to walk. How
many kilometers had she run at that point?
Answers
Answer:
2/3 of 27=18 km
Step-by-step explanation:
Marisol buys 3 notebooks that each cost the same amount and 1 calculator that costs $9. The total cost is $21. How much does each notebook cost?
Answers
Answer: 4 dollars for each notebook
Step-by-step explanation:
21-9= 12
12/3=4
each notebooks costs 4 dollars
Answer:
$4
Step-by-step explanation:
D'Andre earns some money by helping people with their yards. It takes him an average of 2 hours to weed a flowerbed and an average of 1.5 hours to mow and edge a lawn. He can work no more than 6 hours a day. He charges $60 to weed a flowerbed and $75 to mow and edge a lawn. He needs to cover his expenses of $150 to make a profit. Write a system of inequalities that would help determine how many flowerbeds and lawns he could complete on a given day.
______________________________
plz help its due like rn so I'll give brainliest
Answers
Answer:
3 flowerbeds and 5 lawns.
Step-by-step explanation:
I promise.
Can someone help me with this problem and help me understand it better
Answers
Answer:
Proved
Step-by-step explanation:
Given
The attached table
Required
Prove that Lydia is incorrect
Firat, calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where:
[tex](x_1,y_1) = (5,19)[/tex]
[tex](x_2,y_2) = (4,15)[/tex]
So, we have:
[tex]m = \frac{15 - 19}{4 - 5}[/tex]
[tex]m = \frac{-4}{-1}[/tex]
[tex]m=4[/tex]
The equation is then calculated using:
[tex]y - y_1 = m(x-x_1)[/tex]
Where:
[tex](x_1,y_1) = (5,19)[/tex] and [tex]m=4[/tex]
This gives:
[tex]y - 19 = 4(x-5)[/tex]
[tex]y - 19 = 4x-20[/tex]
Make y the subject
[tex]y = 4x-20+19[/tex]
[tex]y = 4x-1[/tex]
The above shows the equation. Hence, the Lydia is correct
Helpppp!!!!!! After a few rides, your friends are ready for some ice cream! You stop into Scoops to You for some ice-cream. Which is the better deal?
3 scoops for $3.69
2 scoops for $2.69
1 scoop for $1.79
Answers
Answer:
3 scoops for $3.69 is better deal.
Step-by-step explanation:
Given that,
There are 3 deals to buy icecram.
3 scoops for $3.69
2 scoops for $2.69
1 scoop for $1.79
We can find the cost of 1 scoop for each deal. So,
First deal,
1 scoop = 3.69/3 = $1.23
Second deal,
1 scoop = 2.69/2 = 1.345
We can see that the cost of 1 scoop for deal 1 is less than others. It means first deal is best.
Helpppop meeeee plzzzzz
Answers
Answer:
7.4
Step-by-step explanation:
solve for side a in first triangle:
[tex]10^2-6^2=y^2[/tex]
100-36=[tex]\sqrt{64}[/tex] (take square root of 64)
y=8
then use 8 to solve for x:
[tex]8^2-3^2=x^2[/tex]
64-9=[tex]\sqrt{55}[/tex] (take square root of 55)
x=7.4
what is the answer to solve for n
Answers
Step-by-step explanation:
According to pythagoras theorem the square length of hypotenuse is equal to sum of other two sides
n^2 + 19^2 = 15^2
n^2 + 361 = 225 if we subtract 361 from both sides
n^2 = -136 but the root of square cannot be negative
I believe there's a mistake in this question so you should ask your teacher.
True and false
Urgent!!! Please help man!
Answers
Answer:
True
Step-by-step explanation:
Because I did this.
Your teacher tells you that the hour hand on
an analog cl o ck will ro t ate 45 while yo u
w rite a math quiz. If the quiz starts at 9:00,
wh at time does it end? Wh at is the angle
b e t ween the starting and ending positions
of the minute hand?
Answers
That is a right angle.
Which of the I-values are solutions to both of the following inequalities?
81> I and I > 68
Answers
Answer:
Option (C)
Step-by-step explanation:
Given inequalities are,
81 > x and x > 68
Therefore, 81 > x > 68 is the inequality representing the solution area for x.
Out of x = 88, 85 and 80,
x = 80 will lie between the range of x = 68 and x = 81.
Therefore, Option (C) will be the correct option.
Please help marking brainliest if correct, serious answers only, thank you.
Answers
cuz they’re on the inside of the lines
and they’re not on the same side of the line that crosses
The cost of a skateboard c after a 15% discount can be represented by the expression c−0.15c . Simplify the expression.
Answers
Answer:
0.85c
Step-by-step explanation:
To simplify the expression, subtract like terms:
c - 0.15c
= 0.85c
So, the simplified expression is 0.85c
What is the area of a rectangle
7 inches long and 3 inches wide?
Answers
Answer:
21
Step-by-step explanation:
you do 7x3
Given the set of ordered pairs, do the following.
a. mapping
b. table
c. graph
1. {(0, 0), (1, -1), (1, 1), (4, -2), (4, 2)}
2. {(10, 0), (10, 2), (10, 4), (10, 6), (10, 8)}
Answers
X | 0, 1, 1, 4, 4
Y | 0,-1,1,-2,2
X | 10,10,10,10,10
Y | 0,2,4,6,8
¿Cómo se dice 80 en números romanos?
Answers
Answer:
PLEASE MARK ME BRAINLEST...
Step-by-step explanation:
Para leer y escribir correctamente el número 80 como número romano LXXX, debe leerse y escribirse de izquierda a derecha, y de mayor a menor número.
Answer:
Guessing that Romanos means Roman Numerals = LXXX
Step-by-step explanation:
L=50
X=10
10X3= 30
30+50=80
