Distance between the points (-3, 5, -7) and (2, -4, 6) is 5√11 units.
What is cartesian coordinate points?
The Cartesian coordinates of a point in three dimensions are the triple (x, y, z). The three numbers or coordinates give the signed distance from the origin along the x, y, and z axes respectively.
Solution:
Given, x1 = -3 , x2 = 2
y1 = 5 , y2 = -4
z1 = -7 , z2 = 6
The formula for finding the distance between two points on 3D graph is given below
Distance =√((x2-x1)²+(y2-y1)²+(z2-z1)²)
⇒Distance =√{(2-(-3))²+(-4-5)²+(6-(-7))²}
⇒Distance =√{(2+3)²+(-9)²+(6+7)²}
⇒Distance =√{5²+81+13²}
⇒Distance =√(25+81+169)
⇒Distance =√275
⇒Distance =5√11
Thus, the distance between (-3, 5, -7) and (2, -4, 6) is 5√11.
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According to the given information the distance between the points 16.58 units.
What is the distance formula, exactly?the algebraic phrase known as the distance formula, which provides the distances between two places in terms of respective dimensions (see coordinate system). The distance formulae for locations in rectangular coordinates in two- and two half Euclidean space are based upon that Pythagorean theorem.
How come we measure distance?We can determine an object's actual size by learning how far it is from us. The area that an object occupies in the sky may be measured. The distance to an object is then necessary to calculate its real size. An thing appears smaller the farther it is away.
Briefing:The distance between two points (x₁, y₁, z₁) and (x₂, y₂, z₂)
[tex]\begin{equation}d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2+\left(z_2-z_1\right)^2}\end[/tex]
x₁, y₁, z₁ = -3, 5, -7
x₂, y₂, z₂ = 2, -4, 6
[tex]\begin{equation}d=\sqrt{\left(2+3\right)^2+\left(-4-5\right)^2+\left(6+7\right)^2}\\\begin{equation}d=\sqrt{\left(5\right)^2+\left(-9\right)^2+\left(13\right)^2}\\\begin{equation}d=\sqrt{25+81+169}\\\begin{equation}d=\sqrt{275}\\[/tex]
= 16.58 units
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A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second.(Quadratic Word Problems (Profit/Gravity)
y=-16x^2+121x+83
Answer:
The rocket will hit the ground after about 8.20 seconds.
Step-by-step explanation:
The height of the rocket y, in feet, x seconds after launch is modeled by the equation:
[tex]y=-16x^2+121x+83[/tex]
We want to find the time at which the rocket will hit the ground.
If it hits the ground, the height of the rocket y will be 0. Thus:
[tex]0=-16x^2+121x+83[/tex]
We can solve for x. Factoring (if possible at all) or completing the square can be tedious, so we can use the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = -16, b = 121, and c = 83. Substitute:
[tex]\displaystyle x=\frac{-(121)\pm\sqrt{(121)^2-4(-16)(83)}}{2(-16)}[/tex]
Simplify:
[tex]\displaystyle x=\frac{-121\pm\sqrt{19953}}{-32}[/tex]
Divide everything by -1 and simplify the square root. The plus/minus will remain unchanged:
[tex]\displaystyle x=\frac{121\pm3\sqrt{2217}}{32}[/tex]
Therefore, our two solutions are:
[tex]\displaystyle x=\frac{121+3\sqrt{2217}}{32}\approx 8.20\text{ or } x=\frac{121-3\sqrt{2217}}{32}\approx -0.63[/tex]
Since time cannot be negative, we can ignore the second solution.
Therefore, the rocket will hit the ground after about 8.20 seconds.
Solve -4x + 6(x + 2) = 20.
Answer:
4
Step-by-step explanation:
-4x +6x +12 = 20
2x + 12 = 20
2x = 8
x = 4
Answer:
X=4
Step-by-step explanation:
-4x+6x+12=29
2x=8
x=4
Good luck .
which two ratios represent quantities that are proportional?
Answer:
C, because it equals in both sides
Answer:
The answer is C
Step-by-step explanation:
Note Figure is not drawn to scale.
If r= 2 cm and h = 2 cm, what is the surface area,
in terms of r?
Answer:
your answer is...
Step-by-step explanation:
50.265482457437
I used my calculator
Solve for x. Use the photo for the chord
Answer: x=3
Step-by-step explanation:
Mrs Fuller plants a 4 inch tomato plant in her garden. The tomato plant grows at a rate of 2 inches each week. Which equation can be used to determine h, the height of the tomato plant in inches after w weeks?
Answer: 4 + 2w
Step-by-step explanation:
The height of the tomato plant in inches after w weeks will be the value of the current height plus the weekly growth pee week. This can be represented in an equation as:
h = 4 + 2(w)
h = 4 + 2w
For example, the height of the tomato plant in inches after 5 weeks will be:
h = 4 + 2w
h = 4 + 2(5)
h = 4 + 10
h = 14 inches
which is the correct input-output table for the function g(x)=-1/2(4x+6)
Answer: The third choice.
Step-by-step explanation: To find the first output, start with your first input. In this case, it's -2, so your equation would be g(-2)= -1/2(4(-2)+6). Start by solving inside the parenthesis. 4x-2=-8 and -8+6=-2. -1/2x-2= 1, so your first output should be 1. The only choice that has this is the third one, so that is your answer. Hope I could help :)
need help asap i have 25minutes left
bac=57
Step-by-step explanation:
lmk=50
abc= 63 (if they are parallel)
I'LL GIVE YOU 5 STARES HELP. Find the area of the figures shown below and drop the correct result Into the appropriate blank. DRAG & DROP THE ANSWER 14 cm 55 cm 8 cm 11 36 m² 5 cm 38 cm 8 cm 58 cm 39 m2 8 m 40 m² 11 4 m 70 cm 10 m
What value of x makes the equation true?
3 - 14x = 17
A-1
B-1
C-28
D-2
Answer:
3 -14x =17
-14x = 17 - 3
-14x = 14
x = 14/-14 = 1/-1 = -1
∴ answer = -1
hope this answer helps you.....
please mark as brainliest... thank you!
I WILL NOT ACCEPT LINKS! AND WILL REPORT!!! Please help with this geometry question. An explanation would be nice!
ON=5.099
Hope it helps
Please help me with this
Answer:
x = 5
Step-by-step explanation:
Given
- 3x - 2 = - 17 ( add 2 to both sides )
- 3x = - 15 ( divide both sides by - 3 )
x = 5
-4(-2)+(-12)÷(+3)+-20+(+4)+(-6)
Answer:
-18
Step-by-step explanation:
[tex]-4(-2)+\frac{(-12)}{+3}-20+(+4)+(-6)=8-\frac{12}{3}-20+4-6=8-4-20+4-6=-18[/tex]
Answer:
-18Step-by-step explanation:
-4(-2)+(-12)÷(+3)+-20+(+4)+(-6). [B.E.D.M.A.S rule] (First bracket)
= 8 - 12 ÷ 3 - 20 + 4 - 6. (Then division)
= 8 - 4 - 20 + 4 - 6. (Then after addition)
= 8 + 4 - 4 - 20 - 6
= 12 - 30. (At last subtraction)
= -18 (Ans)
HELP PLEASE.
Area=
If there is no value under the square root enter a 1.
10^2+16^2=100+256=356^2
The first box should be 2 and the second should be 356
Plz help i don't wnat links i want you to show the answer on here i trust you will.
A=__in^2 i will give the brainlist 20 points btw
Answer:
a to L is 12 inches and a to n is 32 in Step-by-step explanation:
Plzzzz asappp help thanks
Answer:
I might not be right but try following the steps in the screen shot
Also the answer is in the screenshot
Step-by-step explanation:
I tried my best. :>
Find the circumference of the circle.
A. 11 cm
B. 44 cm
C. 22 cm
D. 33 cm
Answer:
The answer is 44 cm .
which is (B)
Module 19 - Reflections
Assignment Active
Practice working with reflections.
Assignment
y
M(-5, 4)
M'(5, 4)
What is the rule for the reflection?
ry-axis(x, y) - (x, y)
P'y-axis(x, y) - (x,-y)
* rx-axis(x, y) (-x, y)
Orx-axis(x, y) = (x,-y)
2
L(-6,2)
N(-3,2)
N'(3,2)
L'(6,2)
x
-2
2
-2
Answer:
R y-axis (x,y) to (-x,y)
Step-by-step explanation:
The rule for reflection is [tex]r_y[/tex] axis (x, y) -> (-x, y).
What is Transformation?A transformation is a broad phrase covering four distinct methods of changing the shape and/or position of a point, line, or geometric figure.
The original shape of the object is known as the Pre-Image, and the final shape and location of the object is known as the Image during the transformation.
As per the figure. the coordinates of Triangle LMN are
L(-6, 2),
M(-5, 4)
N(-3, 2)
and, the coordinates of Triangle L'M'N' are
L'(6, 2),
M'(5, 4)
N'(3, 2)
Here, the y coordinate is same only the sign of x coordinate change.
So, the rule for reflection is r y- axis (x, y) -> (-x, y).
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Please help!! I need answering
Answer:
B
Step-by-step explanation:
26x82=2132
2132/2=1066
3 3/4 x 4
Help me pas
Answer:
15 (C)
//msg added cus it was short//
PLEASE HELP ASAP ILL MARK BRAINLY IF U DO
Answer:
34.1 is the answer by Pythagoras thereom
how to do this question plz answer me step by step plzz plz please
Answer:
See the attached
Step-by-step explanation:
The solution and filled in Venn diagram is attached
What's the domain and range of the exponential growth function? (please help asappp no spam please or links or anything like that!!! will give brainliest)
Domain: All real numbers; Range: All real numbers
Domain: x > –2; Range: y > –2
Domain: x < –2; Range: All real numbers
Domain: All real numbers; Range: y > –2
Answer:
Domain: All real numbers; Range: y > –2
Step-by-step explanation:
Asymptote is y = -2 so all y-values have to be greater than -2. The asymptote is horizontal so x-values can be all real numbers.
A pattern of ordered pairs is shown.
(0, 1), (2,4), (4,7), (6, 10)
The pattern continues. What is the eighth ordered pair in the pattern?
A. (8,13) B. (14, 18). C. (14, 22) D. (16, 19)
Answer: C
Step-by-step explanation:
X’s are going by +2 and y’s by +3
After identifying the pattern, its eighth ordered pair is: (14, 22), option C.
--------------------------
The ordered pairs given are: (0, 1), (2,4), (4,7), (6, 10)
From them, we can see that for each new ordered pair, x increases by 2, and y increases by 3.Thus, the next ordered pairs are: (8, 13), (10, 16), (12, 19), (14, 22).The eighth ordered pair is given by (14,22), option C.A similar problem is given at https://brainly.com/question/16599038
Hello! Sorry about My last question! I was lying this is just a Homework assignment and it is completion Credit but if you do it I will still give you the brainliest!
To find the percent of something, turn the percent into a decimal and multiply (move the decimal place 2 places left, e.g. 53% = .53)
ANSWER CORRECTLY AND ILL MARK YOU AS BRAINIEST
Six containers have the following ounces in them: 6.2, 8.07, 9.4. 2.11, 5, 6.173 (Do not round your answer
Answer:
what is the question tho?
Answer:
Hi! The answer to your question is 36.953
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☆Brainliest is greatly appreciated!☆
Hope this helps!!
- Brooklynn Deka
solve for X
7x=49 (brainliest)
Answer:
7
Step-by-step explanation:
divide 7 to both side
7x/7=49/7
x=7
Question is in picture
Answer:
casino see v
Step-by-step explanation:
j:)
What does the y-intercept represent in the graph below?
hi, how can i graph the equation,
10i + 16p = t
?? thanks