All categories

2 years ago

X =4 x+y=-6 4x - 3y + 2z = 26

Mathematics

1 answer:

slega [8]2 years ago

6 0

Answer:

x = 4 ,y = -10 , z = -10

Step-by-step explanation:

Solve the following system:

{y + 4 = -6 | (equation 1)

16 - 3 y + 2 z = 26 | (equation 2)

Express the system in standard form:

{y+0 z = -10 | (equation 1)

-(3 y) + 2 z = 10 | (equation 2)

Swap equation 1 with equation 2:

{-(3 y) + 2 z = 10 | (equation 1)

y+0 z = -10 | (equation 2)

Add 1/3 × (equation 1) to equation 2:

{-(3 y) + 2 z = 10 | (equation 1)

0 y+(2 z)/3 = (-20)/3 | (equation 2)

Multiply equation 2 by 3/2:

{-(3 y) + 2 z = 10 | (equation 1)

0 y+z = -10 | (equation 2)

Subtract 2 × (equation 2) from equation 1:

{-(3 y)+0 z = 30 | (equation 1)

0 y+z = -10 | (equation 2)

Divide equation 1 by -3:

{y+0 z = -10 | (equation 1)

0 y+z = -10 | (equation 2)

Collect results:

Answer: y = -10 , z = -10

You might be interested in

Richie and his brother have a paper route. Together they can deliver all of the papers in 40 minutes, and Richie can do it alone

Tcecarenko [31]

Answer

30 minutes

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

QUESTION IS DOW BELOW 30 POINTS EACH PLEASE HELP PLEASE HELP PLEASE HELP

ivann1987 [24]

The required solution is ∠RQT = 202° and ∠QTS = 51°

<h3 />

<h3>What is a cyclic quadrilateral?</h3>

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. It is also called as inscribed quadrilateral.

Its main property is that the sum of opposite angles of inscribed quadrilateral is always 180 degrees.

Now, the given circle has a cyclic quadrilateral QRST in which it is given that ∠RQT = 202° and ∠QRS = 129°

Since,sum of the opposite angles of a cyclic quadrilateral = 180°

⇒∠QTS + ∠QRS = 180°

⇒ ∠QTS + ∠129° = 180°

⇒ ∠QTS = 180° - ∠129°

⇒ ∠QTS = 51°

Hence,the requires angles are ∠RQT = 202° and ∠QTS = 51°.

More about cyclic quadrilateral :

brainly.com/question/14323008

#SPJ1

5 0

1 year ago

How do you find the first five terms of a sequence defined recursively

Blizzard [7]

Interesting question. Good to know for computer science.
Suppose you have a function like
an = 3x - 2 Try the first couple
a1 = 3(1) - 2
a1 = 3 - 2
a1 = 1

a2 = 3(2) - 2
a2 = 6 - 2
a2 = 4 So each term differs by 3
a2 - a1 = 3

an = a_(n - 1) + 3
a3 = a2 + 3
a3 = 4 + 3
a3 = 7

a4 = a3 + 3
a4 = 7 + 3
a4 = 10

a5 = a4+ 3
a5 = 10 + 3
a5 = 13

I'll do one more and then check it.
a6 = a5 + 3
a6 = 13 + 3
a6 = 16

a6 = 3x -2
a6 = 3*6 - 2
a6 = 18 - 2
a6 = 16 which checks.

So the general formula is
an = a_(n - 1) * k if you were multiplying or
an = a_(n - 1) + k if you were adding. The key thing is that you are working with the previous term.

6 0

2 years ago

Help and explain ///////////////////////////

Ilia_Sergeevich [38]

Hello,

First, you must understand that

(f-g)(x) means f(x)-g(x) it is the difference of two functions :

f(x)=2x+4 and g(x)=3x-7

f(5)=2*5+4=10+4=14

g(5)=3*5-7=15-7=8

So, (f-g)(5)= f(5)-g(5)=14-8<u>=6</u>

Answer A: none of the choices are correct.

An other way to do it:

(f-g)(x)=f(x)-g(x)=2x+4-(3x-7)= 2x-3x+4+7=-x+11

if x= 5 then (f-g)(5)=-5+11<u>=6</u>

4 0

2 years ago

Find the area of the region that lies under the parabola y=5x - x^2, where 1≤x≤4. I would definitely like to see some work :)

Elena L [17]

Answer:

16.5 square units

Step-by-step explanation:

You are expected to integrate the function between x=1 and x=4:

$\displaystyle\text{area}=\int_1^4{(5x-x^2)}\,dx=\left.\left(\dfrac{5}{2}x^2-\dfrac{1}{3}x^3\right)\right|_{x=1}^{x=4}\\\\=\dfrac{5(4^2-1^2)}{2}-\dfrac{4^3-1^3}{3}=37.5-21=\boxed{16.5}$

<em>Additional comment</em>

If you're aware that the area inside a (symmetrical) parabola is 2/3 of the area of the enclosing rectangle, you can compute the desired area as follows.

The parabolic curve is 4-1 = 3 units wide between x=1 and x=4. It extends upward 2.25 units from y=4 to y=6.25, so the enclosing rectangle is 3×2.25 = 6.75 square units. 2/3 of that area is (2/3)(6.75) = 4.5 square units.

This region sits on top of a rectangle 3 units wide and 4 units high, so the total area under the parabolic curve is ...

area = 4.5 +3×4 = 16.5 . . . square units

4 0

2 years ago