Find the distance between (−4, −3) and (−2, 0). Round your answer to the nearest tenth.
Answers
Answer:Given the two points you entered of (-4, -3) and (-2, 0), we need to calculate 8 items:
Item 1: Calculate the slope and point-slope form:
Slope (m) = y2 - y1
x2 - x1
Slope (m) = 0 - -3
-2 - -4
Slope (m) = 3
2
Calculate the point-slope form using the formula below:
y - y1 = m(x - x1)
y - -3 = 3/2(x + 4)
Item 2: Calculate the line equation that both points lie on.
The standard equation of a line is y = mx + b where m is our slope, x and y are points on the line, and b is a constant.
Rearranging that equation to solve for b, we get b = y - mx. Using the first point that you entered = (-4, -3) and the slope (m) = 3/2 that we calculated, let's plug in those values and evaluate:
b = -3 - (3/2 * -4)
b = -3 - (-12/2)
b = -6
2
-
-12
2
b = 6
2
This fraction is not reduced. Using our GCF Calculator, we see that the top and bottom of the fraction can be reduced by 6
Our reduced fraction is:
1
0.33333333333333
Now that we have calculated (m) and (b), we have the items we need for our standard line equation:
y = 3/2x + 3
Item 3: Calculate the distance between the 2 points you entered.
Distance = Square Root((x2 - x1)2 + (y2 - y1)2)
Distance = Square Root((-2 - -4)2 + (0 - -3)2)
Distance = Square Root((22 + 32))
Distance = √(4 + 9)
Distance = √13
Distance = 3.6056
Item 4: Calculate the Midpoint between the 2 points you entered. Midpoint is denoted as follows:
Midpoint =
x2 + x1
2
,
y2 + y1
2
Midpoint =
-4 + -2
2
,
-3 + 0
2
Midpoint =
-6
2
,
-3
2
Midpoint = (-3, -3/2)
Item 5: Form a right triangle and calculate the 2 remaining angles using our 2 points:
Using our 2 points, we form a right triangle by plotting a 3rd point (-2,-3)
Our first triangle side = -2 - -4 = 2
Our second triangle side = 0 - -3 = 3
Using the slope we calculated, Tan(Angle1) = 1.5
Angle1 = Atan(1.5)
Angle1 = 56.3099°
Since we have a right triangle, we only have 90 degrees left, so Angle2 = 90 - 56.3099° = 33.6901
Item 6: Calculate the y intercept of our line equation
The y intercept is found by setting x = 0 in the line equation y = 3/2x + 3
y = 3/2(0) + 3
y = 3
Item 7: Determine the parametric equations for the line determined by (-4, -3) and (-2, 0)
Parametric equations are written in the form (x,y) = (x0,y0) + t(b,-a)
Plugging in our numbers, we get
(x,y) = (-4,-3) + t(-2 - -4,0 - -3)
(x,y) = (-4,-3) + t(2,3)
x = -4 + 2t
y = -3 + 3t
Calculate Symmetric Equations:
x - x0
z
y - y0
b
Plugging in our numbers, we get:
x - -4
2
y - -3
3
Step-by-step explanation:
The distance between (-4, -3) and (-2, 0) rounded to the nearest tenth is approximately 3.6 units.
What is coordinate geometry?A coordinate plane is a 2D plane created by the junction of the x-axis and y-axis, two perpendicular lines. A coordinate system in geometry is a way to use one or more integers or coordinates to determine the positions of the points.
The distance between two points (x1, y1) and (x2, y2) in a 2-dimensional plane is given by the distance formula:
D = √ [ ( y₂ - y₁ )² + ( x₂ - x₁ )² ]
Using this formula, we can find the distance between (-4, -3) and (-2, 0) as follows:
D = √ [ ( 0 + 3)² + (-2 + 4 )² ]
D= √(2² + 3²)
D = √(13)
D ≈ 3.6
Therefore, the distance between (-4, -3) and (-2, 0) rounded to the nearest tenth is approximately 3.6 units.
To know more about coordinate geometry follow
https://brainly.com/question/7243416
#SPJ3
Related Questions
I really really need help pls
Answers
Answer:
(c) r units right
Step-by-step explanation:
The translation transformations are ...
g(x) = f(x -h) +k . . . . . . . shifts h units right and k units up
Your transformation has h=r and k=0, so the graph is shifted r units right and no units vertically.
_____
Additional comment
This in not terribly mysterious. Suppose you have f(1) = 6. This means the point (1, 6) is on the graph.
Now, suppose you transform this to ...
g(x) = f(x -2)
When the value of x is 3, the value of g(x) is f(3-2) = f(1) = 6. That means the point (3, 6) is on the graph of g(x).
It is the same as the point (1, 6) on the graph of f(x), but shifted 2 units to the right.
__
You can shift a function r units right by replacing x with (x-r), as we just discussed. You can shift a function u units up by replacing y with (y-u). When we write equations in "functional form", the "u" gets "moved."
y-u = f(x) . . . . . graph of f(x) shifted u units up
y = f(x) +u . . . . graph of f(x) shifted u units up. (u added to both sides of the above equation)
Can you help me this
Answers
Answer:It’s A: Population.
Step-by-step explanation:
can I have help pls
Answers
Answer:
1. b
2. a
3. a
Step-by-step explanation:
1. the answer is x=7
2 and 3 answer is x = R which isn't really a real solution
Answer: it is right same exact test i did
What is the combined weight if the 3/4 lb bags
Answers
The function y = 2 • 1.5n models the value of a certain stock after n years. What is the recursive formula that models the situation?
Answers
Answer:
aₙ= 1.5aₙ₋₁ with a₁= 3
Step-by-step explanation:
recursive formula is represented by aₙ=b· aₙ₋₁
−3 and 7/10 / 2 and 1/4
Answers
Answer:
Step-by-step explanation:
(7/10 + -3)/(2 + 1/4)
(7/10 - 30/10)/(8/4 + 1/4)
(-23/10)/(9/4)
-2.3/2.25
-0.46/0.45 or -1.02 approximately
Answer:
Reduce the expression, if possible, by cancelling the common factors.
Exact Form:
[tex]\frac{74}{45}[/tex]
Decimal Form:
−1.64
Mixed Number Form:
−1 [tex]\frac{29}{45} \\[/tex]
Step-by-step explanation:
branliest
f(x)=12x-8. evaluate f(-7)
Answers
f(x)=12x-8
f(-7)=12(-7)-8
f(-7)= -84-8
f(-7)= -92
Select the expressions that are equivalent to 2q + 8q.
q • 10
10q
q +9q
q + q+ 8q
Answers
Answer:
10qq +9qq + q+ 8qStep-by-step explanation:
We know that, when combining 2q + 8q we'll get → 10q
1) q • 10 (Nope)
2) 10q (yes, It's equivalent)
3) q +9q (combine) → 10q (yes, It's equivalent)
4) q + q+ 8q (combine) → 10q ( yes, It's equivalent)
So therefore, 10q , q +9q, q + q+ 8q are expressions equivalent to 2q + 8q..
~
Hope this helps!
please help me with rhis question
Answers
Answer:
He is correct!
Step-by-step explanation:
one quarter of 9 is 2.25 cause if u divide 9 by 2, you get 4.50 which is one half, so if you divide 4.50 by 2 you get 2.25 which is one quarter of 9
4. Emily's house has a chimney. What is the
volume of her chimney?
4 in.
9 in.
12 in.
3 in.
4 in.
6 in.
Giving brainliest! Tysm!
Answers
Answer:
130 in will be the correct answer
(Show in number line): 2x<x+7
Answers
x
x
by simplifying both sides of the inequality, then isolating the variable.
Inequality Form:
x
<
7
x
<
7
Interval Notation:
(
−
∞
,
7
)
Can anyone help in this question, thanks
Answers
Answer:
Sorry I can only help you in 5a. The answer is 70 degrees because it is a central angle. The measure of an arc and a central angle is the same.
Step-by-step explanation:
What are the coordinates of vertex N after this translation? * Quadrilateral LMNP is translated 4 units up and 2 units right.
Answers
Answer:
A
Step-by-step explanation:
because
Evaluate each expression.
Answers
Answer:
Evaluate each expression:
Answer:
5 = 10
6 = 13
7 = 5
8 = 17
Step-by-step explanation:
5.
1: simplify
[tex]\sqrt{8^2+6^2}[/tex]
2: take both to power
[tex]\sqrt{64+36}[/tex]
3: sqrt
[tex]\sqrt{100} = 10[/tex]
6.
1: simplify
[tex]\sqrt{5^2+12^2}[/tex]
2: take both to power
[tex]\sqrt{25+144}[/tex]
3: sqrt
[tex]\sqrt{169} = 13[/tex]
7.
1: simplify
[tex]\sqrt{4^2+3^2}[/tex]
2: take both to power
[tex]\sqrt{16+9}[/tex]
3: sqrt
[tex]\sqrt{25} = 5[/tex]
8.
1: simplify
[tex]\sqrt{15^2+8^2}[/tex]
2: take both to power
[tex]\sqrt{225+64}[/tex]
3: sqrt
[tex]\sqrt{289} = 17[/tex]
If 600 people were surveyed in order to make this pie chart, how many people say they take the bus? 20 points
Answers
Answer:
if 600 people were surveyed it means that 10% equals 60 since 60x10=600. Since we now know that 10% is 60, this would mean that 20% is 120. meaning that 120 people took the bus
Simplify each and write it as a mix number
12/14
27/90
Answers
Step-by-step explanation:
Divide 12/14 by 2:
[tex]\frac{12 \div 2}{14 \div 2} =\frac{6}{7}[/tex]
Simplified. Can't be a mixed number, less than 1.
Divide 27/90 by 9:
[tex]\frac{27 \div 9}{90 \div 9} =\frac{3}{10}[/tex]
Simplified. Can't be a mixed number, less than 1.
3x + 5y = 4 2x + 3y = 4 solve in elimination
Answers
Answer:
y=-4, x=8
Step-by-step explanation:
1)3x+5y=4
2)2x+3y=4
Make 1 and 2 have the same co-efficient of x or y (i chose x as it is easier to get to 6 then 15)
Label the 2 new equations as 3 and 4
3)6x+10y=8
4)6x+9y=12
Now we can take away to give
y=-4
Now we substitute this into 1 or 2
I chose 2:
2x+3(-4)=4
2x=4+12
2x=16
x=8
Answer:
x = 8
y = -4
Step-by-step explanation:
Multiply the first equation by 2:
⇒ 3x + 5y = 4 ⇒ 6x + 10y = 8
(we will call this equation 3)
Multiply the second equation by 3:
⇒ 2x + 3y = 4 ⇒ 6x + 9y = 12
(we will call this equation 4)
Subtract equation 3 from equation 4 to eliminate the x variable:
6x + 9y = 12
- 6x + 10y = 8
-y = 4
Therefore, y = -4
Substitute y = -4 into one of the equations and solve for x:
3x + (5 x -4) = 4
⇒ 3x - 20 = 4
⇒ 3x = 24
⇒ x = 8
Joy and Willa left $3 each for a tip on a $44 restaurant bill. They are sharing the bill. How much does each person owe??
Answers
44-6= 38/2= 19
They each owe $19 if they each pay $3 tip.
We minus total by the tip and divide this by 2.
Hope this helps!
8. How tall do the people in your immediate
and extended family tend to be?
Answers
Answer:
maybe 5,5-6 foot. don't really keep track I just know they are almost as tall as me
Identify the parent function of f(x)=-3x^3-3
Answers
Answer:
f(x) = x^3
Step-by-step explanation:
To identify the parent function, replace any added constants with 0, and replace any constant multipliers with 1. Doing that gives you ...
f(x) = 1·x^3 -0
f(x) = x^3 . . . . . . the parent function
Using the unpaid balance method, find the current months finance charge on a credit card account having the following transactions.
Last month’s balance: $385
Last payment: $250
Annual interest rate: 21%
Purchases: $303
Returns: $158
(It would be great if you could tell me how to use the formula I=Prt where previous months balance + finance charge + purchases made - returns - payments)
Answers
Answer:
$5.02
Step-by-step explanation:
The unpaid balance method is a common method used by credit card companies to calculate finance charges. It determines the finance charge based on a portion of the previous balance you have not yet paid.
Equations to use:
[tex]\boxed{\begin{minipage}{9.7cm}\phantom{w}\\Periodic (monthly) rate = annual interest rate $\div$ 12\\\\Finance Charge = previous balance $\times$ periodic rate\\\\Unpaid Balance = previous balance + finance charge +\\\phantom{wwwwwwwwwww} new purchases - returns - payments\\\end{minipage}}[/tex]
The periodic rate is the interest rate charged over a certain number of time periods. The interest on a credit card is usually calculated monthly, so if the annual interest rate is 21%, then the periodic (monthly) rate is:
[tex]\text{Periodic Rate}=\dfrac{21\%}{12}=1.75\%=0.0175[/tex]
The unpaid balance is "last month's balance", which is $385.
Calculate the finance change by multiplying the previous balance (last month's balance) by the periodic rate:
[tex]\begin{aligned}\text{Finance change} &=\rm previous\; balance \times periodic\;rate \\&=\$385 \times 0.0175 \\&= \$6.7375\end{aligned}[/tex]
Calculate the unpaid balance by subtracting the returns and payments from the sum of the previous balance, finance charge and new purchases:
[tex]\begin{aligned}\rm Unpaid \; Balance &= \rm previous\; balance + finance\;charge +new \;purchases\\&\phantom{=w}\rm - returns - payments\\&= \$385 + \$6.7375 + \$303 - \$158 - \$250 \\&= \$286.7375\end{aligned}[/tex]
Finally, to calculate the current month's finance charge, multiply the unpaid balance by the periodic rate:
[tex]\begin{aligned}\text{Current month's finance charge}&=\rm unpaid \;balance\times periodic \;rate\\&=\$286.7375 \times 0.0175 \\&= \$5.02\; \text{(nearest cent)}\end{aligned}[/tex]
Therefore, the current month's finance charge is $5.02 to the nearest cent.
Mai got a prepaid debit card with 30 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 23 cents per yard. If after that purchase there was 27.01 left on the card, how many yards of ribbon did Mai buy?
Answers
Answer:
The answer I got was 13.
Step-by-step explanation:
I first did 30-27.01 to get 2.99.
I then divided 2.99 by 0.23 or 2.99/0.23 to get 13.
Hope this helped any!
sophia has 7m of ribbon to help decorate a room. she will cut pieces of ribbon that are each r inches long. (1in.=2.54cm) which expression can help find the number of pieces of ribbon that she will have
Answers
Step-by-step explanation:
1 m (meter) is 100 cm (centimeters).
so, 7 m is 700 cm.
each piece is r × 2.54 cm long (as every inch is 2.54 cm).
so,
number of pieces = 700 / (r × 2.54)
The number of species can find by expression is
700 / (r × 2.54)
We have given that
Sophia has 7 m of ribbon
she will cut pieces of ribbon that are each r inches long.
We have to calculate the number of pieces of ribbon that she will have
What is the value of 1 meter in cementer?
1 (meter) =100 (centimetres).........(1)
multiply both side by 7
7 m is 700 cm.
each piece is
r × 2.54 cm long ..................(as 1 inch is 2.54 cm).
so,
[tex]number of pieces = 700 / (2.54r)[/tex]
Therefore the number of species can find by expression is
700 / (r × 2.54)
To learn more about the expression visit:
https://brainly.com/question/723406
I need help on a question i don't know!
Answers
Answer:
20:4
Step-by-step explanation:
got it for u
log(8(1 + 3x))
I need help, I have looked at multiple examples and going off of that I get log(2)+log(1+3x)
Answers
Two right triangles are proportional. The shortest leg of the small triangle is 4 in and the hypotenuse is 12 in. The shortest
leg of the large triangle 8 in. Find the length of the hypotenuse of the large triangle.
A.12
B.21
C.20
D.24
Answers
Answer:
D) 24
Step-by-step explanation:
scale factor is 2
since 4 x 2 is 8 then 12 x 2 is 24
I need help finding the area for the given shape.
Answers
Step-by-step explanation:
a = ½bh
a = ½ × 3 × 6
a = ½ × 18
a = 9 in²
Answer:
18in
Step-by-step explanation:
6×3=18
hope its help
8.91203 to the nearest whole number =
Answers
URGENT PLEASE HELP
Assume the graph of a function of the form y = acos(k(x-b)) is given below.
Which of the following are possible values for a, k, and b?
-4
F3
-
he
T
이
3x
4
4
2.
-1
12
O A. a = 4, k= 2, and b = -
4
O B. a = 2, k = 4, and b = ?
4
O c. a = 4, k = 2, and b =
4
O D. a = 4, k = 2, and b = ?
4
Answers
The possible values of for a, k, and b from the graph of the function will be D. a=4, k=2, b= pi/4.
What is a function?A function simply means a relation between the set of inputs and the outputs.
A function from set X to set Y assigns each element of X to Y. In this case, the set X is the domain while the set Y is the codomain.
From the graph attached, it can be seen that the values of for a, k, and b from the graph of the function will be a=4, k=2, b= pi/4.
Learn more about functions on:
https://brainly.com/question/25841119
Im back again... and i need help. sorry but im doing a second attempt for math and its on geometery and i hate geometery
Answers
Answer: 1/3
Step-by-step explanation:
The scale factor is 1/3 because each side of figure B is 1/3 the magnitude of figure A.