Solve the system using a matrix.
2x – 4y + 2z = 16
-2x + 5y + 2z = -34
x – 2y + 2z = 4
([?],[],[]
ordered triple

9514 1404 393

Answer:

  d  2

Step-by-step explanation:

The system of equations can be written in augmented matrix form as ...

  [tex]\displaystyle\left[\begin{array}{cc|c}-\frac{1}{2}&3&-4\\-1&-1&-1\end{array}\right][/tex]

The value of x found by Cramer's rule is the ratio of two determinants. The numerator is the coefficient matrix with the x-column replaced by the constant column. The denominator is the coefficient matrix.

  [tex]\displaystyle x=\frac{\left|\begin{array}{cc}-4&3\\-1&-1\end{array}\right| }{\left|\begin{array}{cc}-\frac{1}{2}&3\\-1&-1\end{array}\right|}=\frac{(-4)(-1)-(-1)(3)}{(-\frac{1}{2})(-1)-(-1)(3)}=\frac{4+3}{\frac{1}{2}+3}\\\\\boxed{x=2}[/tex]

Using the Cramer's rule, the value of x in the system of equation is 2

The system of equation is given as:

-1/2x + 3y = -4

-x - y = -1

Represent the above equation as a matrix

[tex]\left[\begin{array}{cc}-1/2&3\\-1&-1\end{array}\right] \left[\begin{array}{c}-4&-1\end{array}\right][/tex]

Start by calculating the determinant of the matrix

|A| = -1/2 * -1 - 3 * -1

Evaluate

|A| = 7/2

To calculate x, we replace the first column by the last.

So, we have:

[tex]\left[\begin{array}{cc}-4&3\\-1&-1\end{array}\right][/tex]

Next, calculate the determinant of the matrix

|x| = -4 * -1 - 3 * -1

|x| = 7

The value of x is then calculated as:

x = |x|/|A|

This gives

x = 7 ÷ 7/2

Evaluate

x = 2

Hence, the value of x is 2

Read more about Cramer’s rule at:

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The question is incomplete. The complete question is :

A shipping container will be used to transport several 40-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 23000 kilograms. Other shipments weighing 7800 kilograms have already been loaded into the container. Which inequality can be used to determine cc, the greatest number of 80-kilogram crates that can be loaded onto the shipping container?

Solution :

Given data :

Weight of the crate = 40 kg

Greatest weight that the container can load = 23000 kg

Weight of the other shipments on the container = 7800 kg

So the greatest number of 40 kg crates = c

Therefore, the weight of the other shipment + weight of crate x number of crates ≤ greatest weight of the container

7800 + (40 x c) ≤ 23000

7800 + 40c ≤ 23000

40c ≤ 23000 - 7800

40c ≤ 15200

c ≤ 380

Hence, the maximum number of 40 kg crate is 380.

Answer: x > 2.5

Step-by-step explanation:

Since Mrs Gallegos burns 236 calories riding her bike each hour and she wants to burn more than 590 calories riding her bike at the same rate, the inequality that will represent the number of hours that she will use will be:

x > 590/236

x > 2.5

She must ride the bike for more than 2 1/2 hours to burn more than 590 calories.

Answer:

the answer is C ik its right because i did this two days ago so im sure its C

Step-by-step explanation:

Answer:

C. 264 cubic inches

Step-by-step explanation:

The formula for volume is Length times height times width. So you just multiply all of the numbers and you get your answer.

Answer:Mean and Normally distributed

Step-by-step explanation:

Answer:

2w + 2L is the answer I think, but see the discussion below.

Step-by-step explanation:

There are three possibilities.

One

| = 1

so you get 1 + w + 1 + w = 2 + 2w

Two

l = L

l + w + l + w

So you get 2l + 2w. Since the l is so confusing, I normally use L for l. It's not very pretty but it does work

In this instance, you would get 2L + 2w

Three

| could be an absolute value signal. If that is the case, you should use abs(+w+)

Of the three, I think two is what you intended.

answer:

4

explanation:

3x-6=19

3x=19-6

3x=13

3x÷3=13÷3

x=4

Answer:

Step-by-step explanation:

Two properties used are: [tex](a*b)^{m} = a^{m}*b^{m}\\[/tex]  and  [tex](a^{m})^{n}=a^{m*n}[/tex]

[tex](6a^{4})^{3}=6^{3}*(a^{4})^{3} = 216a^{4*3} = 216a^{12}[/tex]

Answer:

5 hours.

Step-by-step explanation:

800 wheels in 4 hours.

Half of 400 is 200.

Half one 2 is 1

So 1000 wheels. 5 hours.

Answer:

7 and -7

Step-by-step explanation:

7*-7 = -49

7+(-7)=0

Answer:

66.666666666666666666%

Step-by-step explanation:

Answer:

Perimeter = 87.2 m

Area = 470.4 square meters

Step-by-step explanation:

Formula to get the perimeter of a rectangle = 2(length + width)

                                                                         = 2(19.6 + 24)

                                                                         = 2(43.6)

                                                                         = 87.2 m

Similarly by using formula to get the area of the rectangle,

Area = Length × Width

        = 19.6 × 24

        = 470.4 m²

Answer:

The answer is 10,5

Step-by-step explanation:

can i have brainliest please

Answer:

See Explanation

Step-by-step explanation:

[tex] \csc \theta \: \cos \theta \: \tan \theta = 1 \\ \\ LHS = \csc \theta \: \cos \theta \: \tan \theta \: \\ \\ = \frac{1}{ \sin \theta} \: \times \cancel{ \cos \theta }\: \times \frac{ \sin \theta}{ \cancel{ \cos \theta }} \\ \\ = \frac{1}{ \cancel{ \sin \theta}} \: \times \cancel{ \sin \theta} \\ \\ = 1 \\ \\ = RHS \\ \\ hence \: proved[/tex]

Answer:

a) Only the first one is an identity.

Step-by-step explanation:

1). 8 cos O tan O csc O = 8   simplifies to:

cos O tan O csc O = 1

cos O * (sin O / cos O) * (1 /sin O)

=  cos O sin O / cos O sin O

= 1

So it is identity.

2) 13 sec^2 O/ cos^2 O - tan^2 O / cos^2O

= 13 sec^2 O - tan^2 O / cos^2 O

Now  sec^2 O = 1 + tan^2 O, so we have:

(13( 1 + tan^2 O) - tan^2 O) / cos^2 O

= (12 tan^2 O + 13) / cos^2 O

This is not always = 2 so its not an identity.

Step-by-step explanation:

Answer:

956

Step-by-step explanation:

Answer:

658

Step-by-step explanation:

Answer:

See explanartions below

Step-by-step explanation:

Given the coordinates A(-6,3) B(0,5) C(2,-1)

We first need to get the slope of AB, BC and AC

For AB;

A(-6,3) B(0,5)

Mab = 5-3/0-(-6)

Mab = 2/6

Mab = 1/3

For BC;

B(0,5) C(2,-1)

Mbc = -1-5/2-0

Mbc = -6/2

Mc = -3

For AC:

A(-6,3) C(2,-1)

Mac = -1-3/2-(-6)

MAc = -4/8

Mac = -1/2

Taking the product of Mab and Mbc

Mab * Mbc = 1/3 + -3

Mab * Mbc = -1

Since the product of Mab and Mbc is -1, hence AB abd BC are perpendicular showing that one of the angle of triangle ABC is 90 degrees

Answer:

Stefanie bought 10 erasers.

Step-by-step explanation:

Stefanie bought a package of pencils for $1.75 and some erasers that cost $0.25 each. She paid a total of $4.25 for these items.

Beind "x" be the number of erasers bought, you can express Stepanie's purchases by the equation:

1.75 + 0.25*x = 4.25

Solving:

0.25*x = 4.25 - 1.75

0.25*x = 2.5

x= 2.5÷ 0.25

x=10

Stefanie bought 10 erasers.

Answer:

10 erasers

Step-by-step explanation:

Answer:

yeah

Step-by-step explanation:

13 Dec 2020 — Multiply the divisors to find the lcm of 6, 12 and 18 ... given ratio: 5: 2: 8[tex]\frac{1245}{5+2+8}[/tex][tex]\frac{1245}{15}[/tex][tex]83[/tex]mango trees: 83 × 5

Answer:

90  

9

Step-by-step explanation:

Answer:

Step-by-step explanation:

so we see the two line of the same length of 14, which tells us that the lengths of 5x  and 7x-8  have to be the same length.  so we know we can set them equal to each other.  Often times that's the key to math problems , finding where you can set things equal.

5x = 7x-8  ( subtract 5x from both sides and then add 8 to both sides )

8 = 2x ( divide both sides by 2 )

4 = x

nice this looks right too  , both sides add to 20  :)

Answer:

x is greater or equal to 7

Step-by-step explanation:

Answer:

That's awesome have a wonderful day okay?

Step-by-step explanation:

Answer:

16.8 cm³

Step-by-step explanation:

Volume= length x width x height

length x width x height = Volume

 4       x 1.4       x    3      = 16.8 cm³

Answer:

16.8 cm

Rounded: 17 cm

Step-by-step explanation:

Use the Volume formula: V= W*L*H (width x length x height)

V= 4*3*1.4

V= 16.8

Answer:

cut it in half, your answer is 11

Answer:

GD: 3.5

Step-by-step explanation:

You said CE is 7, and GD is half the length of CE. So based off of your answer for CE, GD equals 3.5

Answer:

arc WVY = 265.4°

Step-by-step explanation:

arc XY = arc WX                because ZY = WZ

360° - 47.3° - 47.3° = 265.4°

Answer:

2 solutions

Step-by-step explanation: As we have seen, there can be 0, 1, or 2 solutions to a quadratic equation, depending on whether the expression inside the square root sign, (b2 - 4ac), is positive, negative, or zero. This expression has a special name: the discriminant.

A graph that shows the number of lawns you must cut to earn back the money spent on the lawn mower include the following: B. graph B (top right).

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Based on the information provided above, a linear equation that models the situation with respect to the rate of change is given by;

y = mx + c

y = 20x - 80

In conclusion, we can logically deduce that the slope is equal to $20 while the y-intercept is $80.

Read more on slope-intercept here: brainly.com/question/7889446

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Answer:

Discrete set

Step-by-step explanation:

A discrete consists of a fixed number of elements, such that each element or point in the set is a standalone point or isolated. This differs from a continous set which still consists of points in between each set of values. Therefore the property of isolated point is a characteristic of a discrete set. The can be written as a list. The values are isolated on a discrete set as opposed to that of a continuous set whereby values can take up any value within any two intervals in the set.

Answer: 7 ft

Step-by-step explanation: