The three planes given meet at a point. The planes are 3x+y-2z = 11, 4x-2y+z = -5, x+5y-4z = 33. The intersection is at what point? (Please explain.)

Answers

Answer 1

Answer:

(2, 7, 1)

Step-by-step explanation:

We have three equations, and using Gauss-Jordan Elimination, we can solve for x, y, and z

3x + y - 2z = 11

4x - 2y + z = -5

x + 5y - 4z = 33

We can start by taking out the z from all rows except one. To do this, we can work with the second row. I chose the second row because -5 is small and easy to add up with other numbers, and z has no coefficient in this row.

We can add 2 times the second row to the first row and 4 times the second row to the third row to get

11x - 3y = 1

4x - 2y + z = -5

17x -3y = 13

We then have the first and third rows having two variables. Since the y coefficients are the same, we can eliminate the y by adding the negative of the first row to the third row. Our result is then

11x - 3y = 1

4x - 2y + z = -5

6x = 12

From the third row, we can gather that x= 2. We can then plug that into the first row to get

22 -3y = 1

subtract 22 from both sides

-3y = -21

divide both sides by -3

y = 7

We can then plug our x and y values into the second row to get

4(2) - 2(7) + z = -5

8 - 14 + z = -5

-6 + z = -5

add 6 to both sides

z = 1

Our answer is thus (2, 7, 1)


Related Questions

What’s a converse in mathematics

Answers

Answer:

A converse is the result of reversing its two constituent statements.

Example, P-Q. Converse would be Q-P

In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication P → Q, the converse is Q → P. ... Either way, the truth of the converse is generally independent from that of the original statement.

which expression is equivalent to 1/2r + 8p - 3/4r -2p
A. 1/4r -6p
B. 1/4r +10p
C. 1/4r + 10p
D. 5/4r + 6p​

Answers

Answer:

D.5/4r+6p

Step-by-step explanation:

hula kong hahha

Can someone tell me which one it is?

Answers

Answer:

-16

Step-by-step explanation:

-16... using d = b²-4ac

Answer:

the discriminant is –16

hope this helps!

Somebody help i need to find the value of x and classify the sides and angles

Answers

Answer:

a) x=18

b) 36 (2*18)

c) 54 (3*18)

d) I'm not exactly sure what it's asking for, so I don't know

Step-by-step explanation:

triangle sum theorem means the sum of every triangle is 180 degrees

so we can make this equation: 180 = 90 + 2x + 3x

solve and you get 18.

14 is what % of 89 if you choose a random answer you will be reported

Answers

Answer:

15.73 %

Step-by-step explanation:

Given :-

14 is what % of 89 .

For finding% :-

→ 14/89 * 100

15.73 %

Answer:

15.73% to the nearest hundredth.

Step-by-step explanation:

14/89 = 0.157303

Now multiply  by 100

This gives 15.7303 %

Amelia is taking a road trip. She drove 250 miles the first day. If 250 is 40% of her total distance, how many miles is her roadtrip in all?

Answers

Answer: 625 miles

Step-by-step explanation:

100-40=60

so she has 60% for her distance so lets munis 40 from it and add 250 to 250

250+250=500

60-40=20

20 is half of 40 so whats half of 250? its 125

so she drove 625 miles for her road trip 2 and 1/2 a day

A• 3.7

B• 3.8

C• 5.3

D• 5.4

Answers

Answer:

D 5.4

Step-by-step explanation:

The pythagoras theorem states that a² + b² = c²

2² + 5² = ?²

4 + 25 = ?²

29=?²

? =

[tex] \sqrt{29} [/tex]

? = 5.4 rounded 2 sig fig one decimal place

What is the sale price for an item with an original price of 13.99 after applying a discount of 45%?

Answers

Answer:

7.69

Step-by-step explanation:

13.99 x 0.45 = 6.2955 or 6.3

13.99 - 6.3 = 7.69

How many four-digit integers contain only the digits 1, 2, 3, 4, and 5, with the property that no two consecutive digits are the same?

Answers

Answer:

120

Step-by-step explanation:

we solve this question by using permutation because the order matters

nPr

5P4 = 120

(04.02 MC)
4
What is the y-intercept of the line perpendicular to the line y = x + 1 that includes the point (4, 1)?

Answers

Answer:

The intercept of the line perpendicular to the line [tex]y = x + 1[/tex] is 5.

Step-by-step explanation:

The line [tex]y = x + 1[/tex] has a slope 1. By Analytic Geometry, the slope of the line perpendicular to the original line is determine by the following formula:

[tex]m_{\perp} = -\frac{1}{m}[/tex] (1)

Where:

[tex]m[/tex] - Slope of the original line.

[tex]m_{\perp}[/tex] - Slope of the line perpendicular to the original line.

If we know that [tex]m = 1[/tex], then the new slope is:

[tex]m_{\perp} = -\frac{1}{1}[/tex]

[tex]m_{\perp} = -1[/tex]

A line is defined by the following expression:

[tex]y = m\cdot x + b[/tex] (2)

Where:

[tex]x[/tex] - Independent variable.

[tex]y[/tex] - Dependent variable.

[tex]m[/tex] - Slope.

[tex]b[/tex] - Intercept.

If we know that [tex](x,y) = (4,1)[/tex] and [tex]m = -1[/tex], then the intercept of the line perpendicular to the original line:

[tex]b = y - m\cdot x[/tex]

[tex]b = 1+4[/tex]

[tex]b = 5[/tex]

The intercept of the line perpendicular to the line [tex]y = x + 1[/tex] is 5.

Which sequences are geometric? Check all that apply.

Answers

Step-by-step explanation:

A geometric sequence is when we multiply one number by a set rate to obtain the next number.

For the first one, we multiply 5 by 2 to get 10, 10 by 2 to get 20, and so on. This is geometric

Next, we multiply 3 by 4 to get 12, 12 by 4 to get 48, and so on. This is geometric

Next, we multiply 3 by 5 to get 15, 15 by 5 to get 75, and so on. This is geometric

Next, we multiply 8 by 15/8 to get 15, and 15 by 5 to get 75. 15/8 and 5 are not the same so this is not geometric

Next, we multiply 14 by 21/14 to get 21, and 21 by 28/21 to get 28. 21/14 and 28/21 are not the same so this is not geometric

Next, we multiply 17 by 20/17 to get 20, and 20 by 23/20 to get 23. 20/17 and 23/20 are not the same so this is not geometric.

Finally, we multiply 2 by 5 to get 10, 10 by 5 to get 50, and so on. This is geometric

HELPP!!!!!x
And thanks!

Answers

Answer:

7/10 > 17/25

Step-by-step explanation:

17/25  and 7/10

The common denominator is 50

17/25 *2/2 =34/50

7/10 *5/5 = 35/50

35 > 34 so

35/50 > 34/50

7/10 > 17/25

Subtract: (-137° + 6) - (-43°) Your answer should be in simplest terms. Enter the correct answer.​

Answers

Answer:

-9y⁹ + 6

Step-by-step explanation:

Subtracting a negative makes it positive

-13y⁹ + 6 + 4y⁹

combine like terms

-9y⁹ + 6

Find the circumference

Answers

Answer:

75.36 mi

Step-by-step explanation:

Given :-

Radius = 12 mi .

We know :-

→ Circumference = 2 π r

→ C = 2 * 3.14 * 12 mi

C = 75.36 mi

Answer:

Step-by-step explanation:

circumference of a circle=2πr

=2*3.14*12

=24*3.14

=75.36 mi

In trapezoid KLMN, solve for x ,then use that value to solve for

Answers

Answer:

Same side angles are supplementary

L+k=180

18x-18+72=180

18x=126

x=7

m∠18(7)-18

= 108°

---------------------

hope it helps...

have a grat day

HELP ME PLEASE ASAP I HAVE TO GET THIS DONE TODAY OR ILL FAIL

Answers

Answer:

(1,-8)

Step-by-step explanation:

this is be because a rectangle is parralel so opposite ends will have equal sides,  if you were to graph this, there would be a missing point in the spot (1,-8).  

Answer:

(1,-8)

Step-by-step explanation:

Each of the set of points; (-7,8) and (-7,-8) is reflecting over either the x or y-axis. So therefore the second set of points would be (1,8) and (1,-8).

asma is drawing a picture of a tree.she drawss a 15m tree as 3cm in her drawing book. if a fruit acctualy hangs from branch 3 m from the ground how high must asma draw it to keep the proportion correct?

Answers

Answer:

0.6 cm

Step-by-step explanation:

she divided the the height of the tree 500, so the same factor has to be applied to everything else

3m * 1/500 = 0.6cm

HELLPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP ASAP

Answers

Answer:

1 cm =5ft

2.7 cm =?

cross multiplying gives:

2.7 X 5= 13.5 ft

Can pls someone help I need help

Answers

a^2 + b^2 = c^2
9^2 + b^2 = 15^2
81 + b^2 = 225
225 - 81 = b^2
144 = b^2
square root of 144 = 12
b = 12

Solve each equation. Show your work or explain your method. Each explanation is worth 2 points. A. 2(x - 3) = 14 b. 12 (x + 10) = 24 c. 1/6(x + 6) = 11

Answers

Answer:

A. 3x+2=14. 3×+2-2=14-2. 3×=12

B. 12(×+10)=24. (12)(×)+(12)(10)=24. 12+120=24. 12×+120-120=24-120

C. 12×= -96. 12×/12. -95/12 x= -8

what is the volume of the following rectangular prism 9/5 units 2/3 units ​

Answers

Answer:

1.2

Step-by-step explanation:

9/5*2/3=1.2

simplify 26a+4a-10a​

Answers

Answer:

20a

Step-by-step explanation:

26a+4a-10a=30a-10a=20a

Answer:

20a

Step-by-step explanation:

26a+4a-10a

since they are like terms u can add and subtract them

=30a-10a

=20a

HELP ASAP- IF YOU ARE CORRECT I WILL MARK BRAINLY

Answers

The Answer is:

B) -3/2

Find the circumference of a circle with diameter,
d
= 3.2m.
Give your answer rounded to 2 DP.

Answers

Answer:

[tex]circumference = \pi \: d \\ = 3.14 \times 3.2 \\ = 10.05 \: m[/tex]

Answer:

circumference=10.05 m

Step-by-step explanation:

radius =diameter/2

=3.2/2

=1.6 m

circumference=2πr

=2*3.14*1.6

=10.048 m

=10.05 m

enlarge the triangle by a scale factor of -1.5 with centre of englargement (3,6)

Answers

The coordinates of the enlarged and reflected triangle are A'(x, y) = (6, 3),  B'(x, y) = (3, 3) and C'(x, y) = (6, 0).

How to enlarge a triangle on a Cartesian plane by rigid transformation

In this problem we find a triangle whose vertices have the following coordinates: A(x, y) = (1, 8), B(x, y) = (3, 8), C(x, y) = (1, 10), and we are asked to enlarge the triangle by a scale factor of - 1.5 and with a centre of enlargement at (3, 6). Please notice that the negative sign of the scale factor involves both enlargement and reflection. Then, the operation can be done by the following operation:

P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]            (1)

Where:

O(x, y) - Center of enlargementk - Scale factorP(x, y) - Original pointP'(x, y) - Resulting point

If we know that O(x, y) = (3, 6), k = - 1.5, A(x, y) = (1, 8), B(x, y) = (3, 8) and C(x, y) = (1, 10), then the coordinates of the resulting expression:

A'(x, y) = (3, 6) + (- 1.5) · [(1, 8) - (3, 6)]

A'(x, y) = (3, 6) + (- 1.5) · (- 2, 2)

A'(x, y) = (3, 6) + (3, - 3)

A'(x, y) = (6, 3)

B'(x, y) = (3, 6) + (- 1.5) · [(3, 8) - (3, 6)]

B'(x, y) = (3, 6) + (- 1.5) · (0, 2)

B'(x, y) = (3, 6) + (0, - 3)

B'(x, y) = (3, 3)

C'(x, y) = (3, 6) + (- 1.5) · [(1, 10) - (3, 6)]

C'(x, y) = (3, 6) + (- 1.5) · (- 2, 4)

C'(x, y) = (3, 6) + (3, - 6)

C'(x, y) = (6, 0)

The coordinates of the enlarged and reflected triangle are A'(x, y) = (6, 3),  B'(x, y) = (3, 3) and C'(x, y) = (6, 0).

To learn more on rigid transformations: https://brainly.com/question/1761538

#SPJ1

solve using the quadratic formula 2x^2+9x=5

Answers

Answer:

x = -1/2, x = -5    OR    x = -0.5 and x = -4

Step-by-step explanation:

I’ll just put a picture, I can’t fully explain digitally.    ;D

Question: Solve for x.

Answers

Answer:

x = 24

Step-by-step explanation:

(whole secant) x (external part) = (tangent)^2

(14+18)* 18 = x^2

32*18 = x^2

576 = x^2

Take the square root of each side

sqrt(576) = sqrt(x^2)

24 =x

What are the ordered pairs for all of the points

Answers

A (3,4)
B(-3,2)
C(-2,-4)
D(6,-3)

Answer:

A ( 3 , 4 )

B ( -3 , 2 )

C ( -2 , -4 )

D ( 6 , -3 )

E ( 0 , 0 )

Step-by-step explanation:

remember that x values go first and then y values ( x , y )

Lee ran a mile in 7 1/3 minutes. His friend Sam ran the same mile in 8 5/9 minutes. How many minutes faster did Lee run? (First answer will be the brainliest)

Answers

He ran the mile 1 and 3/9 minutes faster

solve for x round to the nearest tenth if necessary.

Answers

Answer:

20.4

Step-by-step explanation:

use trig relations with the angle 74˚

the sides we know are the hyp (74) and the adj side to 74˚ (x).

the trig function associated with hyp and adj is cos.

cos = adj/hyp.

cos 74˚ = x/74

0.27 = x/74

x = 20.39

x = 20.4

Answer:

20.4

Step-by-step explanation:

1. c = b · sin(C) / sin(B) = 20.39716

This is the equation to find x.

c = x

b = 74

C = ?

B = 90

2. C must be found. We know that A is 90 and B is 74.

3. 180 = 90 + 74 + C

According to the triangle sum theorem, the angles of every triangle would add up to equal to 180. This means we should add 90 and 74 first.

4. 180 = 164 + C

You must do 180 - 164 which equals 16.

5. C = 16

This means that 16 is what C equals. You can finally plug in the equation with all the gathered information

c = x

b = 74

C = 16

B = 90

4.  x = 74 · sin(16) / sin(90) =

You could use a calculator to find the answer.

5. The answer you would get is 20.39716, but you need to round to the nearest tenth. The 3 behind the decimal is the tenth place but there is a 9 behind it meaning the 3 must be rounded up to a 4. This means that your answer to this problem is 20.4 when rounded to the nearest tenth.

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