The equation for the plane that contains the line and is perpendicular to the plane 2 · x + y - 3 · z = - 4 is - 10 · x + 17 · y - z = 76.
How to find the equation of a plane that contains a line and is perpendicular to another plane
From the equation of the plane 2 · x + y - 3 · z = - 4 we know that its normal vector is (2, 1, - 3). Hence, we have found two direction vectors and already know a point, which are part of this parametric equation:
(x, y, z) = (- 3, 4, 5) + t · (3, 2, 4) + u · (2, 1, - 3) (1)
The normal vector of the plane is equal to the cross product of the direction vectors of (1):
[tex]\vec n = (3, 2, 4) \,\times\,(2, 1, -3)[/tex]
[tex]\vec n = \left|\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\3&2&4\\2&1&-3\end{array}\right|[/tex]
[tex]\vec n = (-6-4,8+9, 3-4)[/tex]
[tex]\vec n = (-10, 17, -1)[/tex]
Since the plane contains the point (x, y, z) = (- 3, 4, 5), then we find that the independent constant of the equation of the plane is:
- 10 · x + 17 · y - z = k
- 10 · (- 3) + 17 · 4 - 5 = k
30 + 51 - 5 = k
k = 76
The equation for the plane that contains the line and is perpendicular to the plane 2 · x + y - 3 · z = - 4 is - 10 · x + 17 · y - z = 76.
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40 cm
42 cm
What is the length of the hypotenuse?
Answer:
by Pythagoras theorm
H² = B² + P²
H². = 40² + 42²
= 1600 + 1764
= 3364
= 58²
H = 58
hope it helps
Find the length of BC.
Step-by-step explanation:
sin 60 = perpendicular / hypotenuse
sin 60 = BC / AB
sin 60 =. BC / 10
√3 / 2 = BC/ 10
BC = 5√3
plz mark my answer as brainlist plzzzz.
hope this will be helpful to you .
What is the value of the expression below?
13 - (-9)
AAAHHHHH!!!!!!! SOMEONE HELP!!!!
Answer:
43.10
Step-by-step explanation:
Je parle une ciart mwoa
if
sin150°=1/2 fiind sin75°
Answer:
thank u for free points
Step-by-step explanation:
......
Find the length of JL.
4.5 units is the value of the length of JL
Given m∥n, find the value of x.
Answer:
53°
Step-by-step explanation:
Of the two lines are parallel then x = 53°
Divide 110 between two friends so that one gets 16 more than the other. solve the equation
Answer:
47 and 63
Step-by-step explanation:
Let x be the number one friend gets.
This means the second friend will get x + 16
x + x + 16 = 110
2x + 16 = 110
2x = 94
x = 47
One friend gets 47, and the other gets 63
Find the number that belongs
in the green box.
Round your answer to the nearest tenth.
Answer:
24.2
Step-by-step explanation:
There is but one answer to this. It appears below.
Let's try it out and see what happens. We'll do it the way it sits.
Sin 40/8 = sin(x) / 7 Multiply both sides by 7
7* Sin(40) / 8 = sin(x)
Sin(40) = 0.6428
7 * 0.6428 / 8 = sin(x)
.56245 = sin(x)
x = sin-1(0.56245)
x = 34.23
Rounded to the nearest tenth, it is 24.2
Answer: 34.2
Step-by-step explanation:
Hope this helps!
24 divided by 4 times d
Answer:
i think 6 not sure tho sorry if its worng
Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (negative 4) = 7
Negative 5 + x = negative 2
69
Step-by-step explanation:
2+ x = 5
x + 1 = 4
9 + x = 6
x + (negative 4) = 7
Negative 5 + x = negative 2
Enter
31/100 as a money amount and as a decimal in terms of dollars.
Answer:
It would be .31 cents, I believe
Step-by-step explanation:
Just divide 31 by 100 and you'll get your answer.
:)
Which equation represents the line through the points (3,2) and (-9,6) ?
x + 3y = 9
3x - y = -9
O x - 3y =9
3x + y =9
Answer:
Step-by-step explanation:
(3,2),(-9,6)
slope = (6 - 2) / (-9 - 3) = -4/12 = -1/3
y = mx + b
slope(m) = -1/3
use either of ur points...(3,2)....x = 3 and y = 2
now we sub into the formula and find b, the y int
2 = -1/3(3) + b
2 = -1 + b
2 + 1 = b
3 = b
so ur equation is : y = -1/3x + 3 <==
Substitutions can have different
values
A. True
B. False
1Answer:
Step-by-step explanation:
f(x) = 3sinxº
Find f(22)
Give your answer correct to 3 significant figures.
Answer:
f(22) = 1.12
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) = 3sinx°
f(22) is x = 22
Step 2: Evaluate
Substitute in x: f(22) = 3sin22°Trig: f(22) = 3(0.374607)Multiply: f(22) = 1.12382Round: f(22) = 1.12please HELP ITS A GRADE AND TIMED I WILL MARK BRAINLIEST
Answer:
Domain: All Real Numbers
Range: y<0
Step-by-step explanation:
Looking at the graph, you can tell that the variable y has a lower point.
( I'm not sure how accurate this is I'm doing the same test right now. ;-;)
THURSDAY Draw this model on a piece of 1 peper. Hank cut his pizza into 10 pieces and ate 6 of the pieces. Rose cut her pizza into 5 pieces and ate the same amount as Hank Show this on the drawing
Answer:
Rose: 6/5 or 1.2
Hank: 6/10 ÷ 6 = 0.1
Step-by-step explanation:
89% out of 100 that this is correct
..
There is a 15% off sale on a
PlayStation 5. If the original
cost is $700, what is the
sale price of the
PlayStation?
Answer:
$595
Step-by-step explanation:
When finding the volume of a rectangle shaped 3D box, what formula do you use?
Answer:
length x width x height
l x w x h
(5,1) (3,2) Write the equation in point-slope form
Answer: y-1=-1/2(x-5)
Step-by-step explanation:
[tex]\frac{2-1}{3-5}[/tex]
-1/2 slope
y-[tex]y_{1}[/tex]=m([tex]x-x_{1}[/tex])
y-1=-1/2(x-5)
y-1=-1/2x +5/2
y=-1/2x+7/2
is the ordered pair (1, -3) a solution to
3x + 5y = -8?
Answer:
Yes give Brainliest
Step-by-step explanation:
To find y place the other terms in the equation to the right
hand side of the equation.
Thus : 5y = 7 - 3x
( now divide both sides by 5 )
⇒ 5y5=7−3x5=15(7−3x)
now will you give brainliest?
solve and receive brain list
Answer:
it is called COLD DRANK
Step-by-step explanation:
REAPEAT AFTER ME COLD DRANK OK C-O-L-D D-R-A-N-K
Answer:
Step-by-step explanation:
6x + 26 = 8x - 12 ( 1 - 3x )
6x + 26 = 8x - 12 + 36x
Doing like terms on one side,
6x -8x -36x = -12 -26
-38x = -38
x = -38 / -38
x = 1
Hope this helps you. Do vote my answer.
Thanks
Question
What is the height of a triangle with an area of 893 square inches and a base of 38 inches?
Answer:
the height of the triangle is 47 inches
en un día de trabajo una pastelería ha producido 100 pasteles, de los cuales (2/5 en fracciones) tienen crema y (1/4 en fracciones) de la producción de pasteles no tiene crema y el resto son díbeticos ¿cuantos pasteles hay para diabéticos?
tfyhgbuhbj tctf ybubbimihbighv no
Step-by-step explanation:
tdcvyvj j ct ruv yo bb. v
I have to turn this in at 5:00
Answer:
1/8
Step-by-step explanation:
Multiply the chance of getting heads (1/2 or .5) by the chance it takes to get green (1/4 or .25)
.5*.25=.125 or 1/8
Please help I am giving brainliest!
Answer:
6.3 in.^2
Step-by-step explanation:
The diameter of the circle is 4 in., so the radius of the circle is 2 in.
[tex] A_{sector} = \dfrac{n}{360^\circ} \pi r^2 [/tex]
The two central angles have a total measure of 60 deg + 110 deg = 170 deg.
The central angle of the shaded sector is 360 deg - 170 deg = 190 deg.
We will use n = 190 deg in the area formula.
[tex] A_{sector} = \dfrac{190^\circ}{360^\circ} \pi (2~in.)^2 [/tex]
[tex] A_{sector} = 6.3~in.^2 [/tex]
James was putting the table cloth back on the table after dinner. The table is 25 inches long and 10 inches wide. If the table cloth hangs 5 inches off each side, what is the area of the table cloth?
Answer:
3000
Step-by-step explanation:
Answer: 700 square inches
===============================================================
Explanation:
The dimension 25 bumps up to 25+5+5 = 35 since we add two copies of 5 onto it. This is done to account for the portions that hang off the edge.
Similarly, the 10 inch dimension bumps up to 10+5+5 = 20 inches.
The table cloth is 35 inches by 20 inches to give an area of 35*20 = 700 square inches.
Side note: 700 square inches is approximately equal to 4.861 square feet (divide by 144 to convert from square inches to square feet).
The rectangle is rotated 180º counterclockwise about the origin. Which of the following ordered pairs is a vertex of the rectangle’s image?
A.
(-5, 1)
B.
(-4, -1)
C.
(4, -5)
D.
(4, 4)
The ordered pair is a vertex of the rectangle’s image will be (-4, -1). Then the correct option is B.
What is a transformation of a shape?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the structure and/or location of the object.
From before the refers to the object's initial condition, and Picture, after transformation, refers to the object's ultimate structure and location.
Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.
The rectangle is in the first quadrant then the coordinate of the vertices of a rectangle will be positive (x, y).
The rectangle is rotated 180º counterclockwise about the origin.
The rectangle will be in the third quadrant then the coordinate of the vertices of the rectangle will be negative (-x, -y).
Thus, the ordered pair is a vertex of the rectangle’s image will be (-4, -1). Then the correct option is B.
More about the transformation of the shape link is given below.
https://brainly.com/question/27224339
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5. A length of rope is 20m long. If I cut it into 10 equal length pieces, how long is
each piece? *
what is given
Answer:
each piece is = 3 m long
Step-by-step explanation:
20 /10= 2
combine like terms to create an equivalent expression
3.26d + 9.75d - 2.65
Answer:
13.01d - 2.65
Step-by-step explanation:
DON'T IGNORE THIS PART!!!
Hmmm... in order to be able to solve these type of expressions and more complex ones, we need to know what like terms are in the first place.
Well, the best definition of like terms is: Terms that have the same exact variables.
Let's see the terms that have the same exact variables! They are 3.26d and 9.75d.
By the way, before we continue--I would like to mention something extremely important: 3.26d and 9.75d are positive, whereas -2.65 is negative (you know, the negative sign appears right before it).
Now, let's add 3.26d and 9.75d. It equals 13.01d.
TIME TO COMBINE!!!
13.01d - 2.65