Answer:
Step-by-step explanation:
Here we need to write the equations that passes through the point (4 , 3) and is parallel to the given line and perpendicular to it. So lets get started,
a)
First we calculate the slope of the given line by using any two points on the given line by the help of the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
we take the points (1 , 6) and (2 , 2) i chose these two you can choose any other two doesn't matter so now we calculate the slope,
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{2-6}{2-1}\\\\m=\frac{-4}{1}\\\\m=-4[/tex]
now since our slope is -4 and the line is parallel to the given line so the line that we need in part a would also have the same slope by the law parallel lines have same slope/gradient.
[tex]m_1=m_2[/tex]
so the slope/gradient of our new line that we need which passes through the point (4,3) is -4
Now using the point slope form formula:
[tex]y-y_1=m(x-x_1)[/tex]
we have our point (4,3) which corresponds to [tex](x_1,y_1)[/tex] and m which corresponds to -4 , so now
[tex]y-y_1=m(x-x_1)\\y-3=-4(x-4)\\y-3=-4x+16\\y=-4x+19[/tex]
sow our new line in part a is
[tex]y=-4x+19[/tex]
b)
In this part we need a line that is perpendicular to the given line which means we use the formula to calculate the slope of the perpendicular line which is:
[tex]m_1m_2=-1[/tex]
where [tex]m_1=-4[/tex] the slope of our given line so the slope of the perpendicular line is,
[tex]m_1m_2=-1\\-4m_2=-1\\\\m_2=\frac{1}{4}[/tex]
so using the point (4,3) and the new slope 1/4 we find the equation of the perpendicular line again by using the point-slope form formula:
[tex]y-y_1=m(x-x_1)\\y-3=\frac{1}{4}(x-4)\\\\4y-12=x-4 \\4y=x+8\\\\y=\frac{x+8}{4}\\\\y=\frac{x}{4}+2[/tex]
I have attached of the graphs as well you can check it out for better understanding.
Please help UwU
also hope your day is going GREAT
Answer:
Answer: B. XY
Step-by-step explanation:
Lines and Circles
There are four lines in the figure:
OB =Radius: A segment from the center to the circumference
XY = Secant: A line that intersects the circle in two points
EF = Chord: A line segment that joins two points on the circle
XV and XB = Tangent: A line that touches the circle on one point and is perpendicular to the radius.
Answer: B. XY
TIMED EXAM!!!!!
What is produced during the replacement reaction of Cu(NO3)2 and Zn?
ZnNO3 + Cu
Zn + Cu(NO3)2
ZnCu + 2NO3
Zn(NO3)2 + Cu
Answer:
The answer would be (D) Zn(NO3)2 + Cu
Step-by-step explanation:
For everyone else who needs the answer
Answer:
D
Step-by-step explanation:
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD:D
2 - 3x = -x - 8 Solve for X
Answer:
X=5
Step-by-step explanation:
(step 1) 2 - 3x = -x - 8
-3x + 2 = -x -8
(step 2)
-3x + 2 = -x - 8
-3 + 2 - 2 = -x -8 -2
(step 3)
-3x = -x- 10
(step 4)
-3 + x = -x -10 +x
(step 5)
-2x = -10
Answer
x = 5
Please please please help big grade please help
Answer:
2
Step-by-step explanation:
the scale factor is 2 because all the sides dubled
bruh do those mean i’ll give you a cookie :>
Answer:
SAS
And I don’t know if your going to give me a cookie. We need to social distance you know ;)
On my farm there are 10 brown horses and 8 mares(female horses).Can you conclude that there are 18 horses on my farm
Answer:
Yes
Step-by-step explanation:
You can conclude there are 18 horses because although some of the mares might be brown horses, the conjunction "and" implies the mares are in addition to the brown horses.
ILL GIVE BRAINLIEST!! PLS HELP!!! Ten students are taking both algebra and drafting. There are 24 students taking algebra. There are 11 students who are taking drafting only. How many students are taking algebra or drafting but not both?
Answer:
15 students
Step-by-step explanation:
from the algebra = 24 - 10 = 14
from the draft = 11 - 10 = 1
14 + 1 = 15
the total students that are taking algebra or drafting but not both is 15 students
Answer:
algebra:34 drafting:21 (use only one answer)
Step-by-step explanation:
10 + 24 =34 for algebra
10 + 11 = 21 for drafting
i need a step-by-step explanation please
Answer:
18x-16
Step-by-step explanation:
expression: (11x-8)+7(x-1)
ok so what you want to do is combine like terms
but first you are going to distribute
(11x-8)+(7x-8) you distribute the 7
they you can subtract 8 from -8 and that will give you -16
you will then add 11x and 7x which will get you 18x
the final expression will be 18x-16
The length of a rectangle is 2 more than twice the width. The area of the
rectangle is 60. Find the dimensions of the rectangle. What is the length of
the rectangle?
Answer: w=5 , L= 2+2(5)=12
Step-by-step explanation:
L=2+2W
A= 60
LxW=60, now we will replace the L
(2+2W)(W)=60 we multiply
2w^2+2w=60
2w^2+2w-60=0 we divide by 2 the equation so we can work easier
w^2+w-30=0
find out w using the quadratic equation
we will get 2 solution,
w=5 and another solution is -6, which is not valid, as the side can not be negative
The general form of a hyperbola is 9x2−5y2−54x−10y+31=0.
What is the standard form of this hyperbola?
Answer:
The standard form of this hyperbola is [tex]\frac{(x-3)^{2}}{5}-\frac{(y+1)^{2}}{9} = 1[/tex].
Step-by-step explanation:
From Analytical Geometry, the standard form of the hyperbola is defined by the following expression:
[tex]\frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{b^{2}} = 1[/tex] (1)
Where:
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
[tex]a, b[/tex] - Semiaxis lengths, dimensionless.
[tex]h, k[/tex] - Coordinates of the center, dimensionless.
Let the hyperbola be defined by [tex]9\cdot x^{2}-5\cdot y^{2}-54\cdot x -10\cdot y +31=0[/tex], we proceed to derive the standard form by algebraic means:
1) [tex]9\cdot x^{2}-5\cdot y^{2}-54\cdot x -10\cdot y +31=0[/tex] Given
2) [tex](9\cdot x^{2}-54\cdot x)+(-1) \cdot (5\cdot y^{2}+10\cdot y)+31 = 0[/tex] Commutative and associative properties/[tex](-1)\cdot a = -a[/tex]
3) [tex](9\cdot x^{2}-54\cdot x + 81)+(-81)+(-1)\cdot (5\cdot y^{2}+10\cdot y +5)+(-1)\cdot (-5)+31 = 0[/tex] Modulative, distributive and associative properties/[tex](-1)\cdot a = -a[/tex]/Existence of the additive inverse
4) [tex](3\cdot x-9)^{2}+(-1)\cdot (\sqrt{5}\cdot y +\sqrt{5})^{2}+(-81)+5+31 = 0[/tex] Perfect trinomial square/[tex](-a)\cdot (-b) = a\cdot b[/tex]/Commutative property
5) [tex]9\cdot (x-3)^{2}+(-1)\cdot (5) \cdot (y+1)^{2}-45 = 0[/tex] Distributive property/[tex](a\cdot b)^{c} = a^{c}\cdot b^{c}[/tex]/Definition of addition and subtraction.
6) [tex]9\cdot (x-3)^{2}-5\cdot (y+1)^{2}= 45[/tex] [tex](-1)\cdot a = -a[/tex]/Compatibility with addition/Existence of additive inverse/Modulative property.
7) [tex]\frac{(x-3)^{2}}{5}-\frac{(y+1)^{2}}{9} = 1[/tex] Compatibility with multiplication/Definition of division/Distributive property/Result.
The standard form of this hyperbola is [tex]\frac{(x-3)^{2}}{5}-\frac{(y+1)^{2}}{9} = 1[/tex].
Write the equation for the following graph (Hint: y= mx + b) Write the slope as a simplified fraction, not a decimal. Please Help
Answer:
y = (-5/2)x + 1
Step-by-step explanation:
We can see that the line intersects (0,1) and (2, -4). We use these points to find the slope: m = (-4-1)/(2-0) = -5/2. Also, the y-intercept is (0,1), so b = 1. Substituting these values into y=mx +b, we get y = (-5/2)x + 1.
I hope this helps! :)
Select the correct answer.
Simplify.
(m3)6 ./.m 18
HELP PLASEEEEEEEE!! amazing
Answer:
b
Step-by-step explanation:
Answer:
It would get MUCH hotter
Step-by-step explanation:
without water vapor to keep to plantet at an equilibrium it would get hotter which would boil the oceans making the earth more like venus
Find the value of f(3) for the function.
f(x) = - 7(x + 2)
Answer:
f(3) = -35
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
f(x) = -7(x + 2)
f(3) is x = 3
Step 2: Evaluate
Substitute: f(3) = -7(3 + 2)Add: f(3) = -7(5)Multiply: f(3) = -35the scale on a map of new york city is 6 centimeters = 2 kilometers on the map two friends is 15 centimeters apart how may kilometers apart do the two friends live
Answer: 5 kilometers
Step-by-step explanation: 6:2 = 3:1 = 15:5
WILL GIVE BRAINLIEST but you have to show your work
Answer:
x=-3
Step-by-step explanation:
[tex]\sqrt{x+7}-x=5\\\sqrt{x+7}=5+x\\x+7=x^2+10x+25\\x^2+9x-18=0\\(x+3)(x+6)=0\\x=-3, x=-6\\\sqrt{-3+7}-(-3)=5\\\sqrt{-6+7}-(-6)=7=5[/tex]
x=-6 is extraneous because 7 does not equal to 5
x=-3 is the answer because 5=5
steve has received $200 in the form of a dividend. What type of income is this.
Answer:
passive income
Step-by-step explanation:
Lucy recently emptied her coin jar and counted the coins. 25% gold coins, 35% silver coins, 40% copper coins. If there were 80 coins in all, how many more silver coins than gold coins were there in the jar?
Answer:
There were 8 more silver coins than gold coins in the jar.
Step-by-step explanation:
Given that:
Total coins in the jar = 80 coins
Gold coins = 25% of total coins
Number of gold coins = [tex]\frac{25}{100}*80[/tex]
Number of gold coins = 20
Silver coins = 35% of total
Number of silver coins = [tex]\frac{35}{100}*80[/tex]
Number of silver coins = 28
Copper coins = 40% of total
Number of copper coins = [tex]\frac{40}{100}*80=32[/tex]
Difference between silver and gold coins = No. of silver coins - No. of gold coins
Difference = 28-20 = 8
Hence,
There were 8 more silver coins than gold coins in the jar.
Answer:
jjjhvgfxzeAWQ2
Step-by-step explanation:
JUGFHHHGFDFGHFDFGHG
Solve equation by completing the square.
Simplify the following expression: (3x+4)(x-1)(x-3)
Answer:
3x³ - 8x² - 7x + 12
Step-by-step explanation:
We multiply these terms, (so expand the brackets). Referring to the diagram attached, we multiply the first terms, outer terms, inner terms, and last terms.
Let's first look at the first two (we will do something about the third brackets later):
(3x+4)(x-1)
Firsts:
3x²
Outer:
-3x
Inner:
4x
Last:
-4
Now we combine:
3x² - 3x + 4x - 4
= 3x² + x - 4
So from the whole equation, we now have this:
(3x² + x - 4)(x - 3)
We do a similar thing here.
3x³ - 9x² + x² - 3x - 4x + 12
Simplify:
3x³ - 8x² - 7x + 12
Pls answer I will mark
A ski hat is priced at $19.50 and a pair of ski boots are priced at $85.50. If the sales tax rate is 7%, then what is the total cost of the ski hat and ski boots ?
Answer:
The total cost of the ski hat and the ski boots is $112.35.
Step-by-step explanation:
First, we need to add the prices of the ski hat and the ski boots.
85.50 + 19.50 = $105
Now, we need to find 7% of $105, and then add it to the total.
105 x 0.07 = $7.35
105 + 7.35 = $112.35
Therefore, the total cost of the ski hat and the ski boots is $112.35.
Hope this helps! :D
The number of ice cubes in a drink and the temperature of the drink, what kind of association is that
Answer:
An unary association
Step-by-step explanation:
1/2 s + 3/4 s + 1/4 s + 4
1/2 s + 3/4 s + 1/4 s + 4
((2+3+1)/4)s +4
6/4 s + 4
3/2 s + 4
Answer:
3/2 + 4
Step-by-step explanation:
1/2+3/4+1/4= 3/2s
3/2s+4
Nick prepared 24 kilograms of dough after working 6 hours. How much dough did Nick prepare if he worked for 10 hours? Assume the relationship is directly proportional.
40kg of dough
Step-by-step explanation:
24 kg dough...........................6 hours
? dough.........................10 hours
x=(24*10)/6=240/6=40
If you take the square root of a positive number then the result will be a real Integer (non decimal or fraction).
Always
Sometimes
Never
Answer:
sometimes
Step-by-step explanation:
the square root of 49 is 7, but the square root of two is 1.4142135623730951
PLEASE SERIOUSLY, I REALLY NEED HELP WITH THIS, I ASK YOU PLEASE
Answer:
right now if you were to have a coke depending on the weather is from where you are standing effect how long it will take to melt
Step-by-step explanation:
If 6 is added to 2 times a certain number, the result is 14. Find the number. Please answer!!
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
Mia made three times as many baskets in yesterday’s basketball game as she did last Saturday. She scored a total of 24 baskets for both games. How many baskets did Mia score last Saturday?
Based on the information presented, it can be inferred that Mia made 8 baskets last Saturday.
How to calculate how many baskets Mia made last Saturday?To calculate the number of baskets Mia made last Saturday we must take into account the following information:
Yesterday she made 24 baskets.Last Saturday she made 3 times fewer baskets than yesterday.To calculate the number of baskets Mia made, we must divide 24 by 3 to find the number of baskets she made last Saturday.
24 ÷ 3 = 8So, it can be inferred that Mia made 8 baskets last Saturday.
Learn more about division in: https://brainly.com/question/369266
Arianna bought 16 postcards during 4 days of vacation. How many days will Arianna have to spend on vacation before she will have bought a total of 20 postcards? Assume the relationship is directly proportional
Answer:5 days
Step-by-step explanation:
16 divided by 4=4 postcards a day
20 divided by 4=5
5 days in total
hope this helps . Please mark brainliest