solve the system of equations using matrices and a calculator.
3x - 4y + 5z = -10
2x - y -2z = 12
x + y - z =15

Answers

Answer 1

(x, y, z) = (59/8, 6, -13/8)

Answer 2

Answer:

x = 59 / 8

y = 6

z = -13 / 8

Step-by-step explanation:

For this problem, you simply need to set up the augmented matrix for you to enter into the calculator.  Once entered into the calculator, you will be given the values for x, y, and z.  Here is the augmented matrix:

3x - 4y + 5z = -10

2x - y - 2z = 12

x + y - z = 15

3  -4  5  |  -10

2  -1  -2  |  12

1    1  -1   |  15

Input this augmented matrix into the calculator and you will get these values for x, y, and z:

x = 59 / 8

y = 6

z = -13 / 8

Cheers.


Related Questions

A bike shop rents bikes for $4.50 per hour, plus a $7.50 insurance charge. For how many hours can Peter rent a bike if he has $30?

Answers

Answer:

With $30, Peter can afford 5 hours

Step-by-step explanation:

Given

Insurance Charge = $7.5

Charges = $4.5 per hour

Required

Determine the number of hours $30 can afford

First, we need to determine the equation.

Total Charges = Charges per hour + Insurance Charge

Substitute values for Charges per hour and Insurance Charge

Total Charges = 4.5 per hour + 7.5

Let the number of hours be n;

So,

Total Charges = 4.5n + 7.5

To calculate Peter's; substitute 30 for total charges

[tex]30 = 4.5n + 7.5[/tex]

Subtract 7.5 from both sides

[tex]4.5n = 30 - 7.5[/tex]

[tex]4.5n = 22.5[/tex]

Divide both sides by 4.5

[tex]n = \frac{22.5}{4.5}[/tex]

[tex]n = 5[/tex]

Hence;

With $30, Peter can afford 5 hours

Solve the equation for x.
1/3 (6x - 15) = 1/2 (10x-4)

Answers

Answer:

x = - 1

Step-by-step explanation:

[tex] \frac{1}{3} (6x - 15) = \frac{1}{2} (10x - 4)[/tex]

Expand the terms in the bracket

That's

[tex] \frac{1 }{3} \times 6x + \frac{1}{3} ( - 15) = \frac{1}{2} (10x) + \frac{1}{2} ( - 4) \\ 2x - 5 = 5x - 2[/tex]

Subtract 5x from both sides

[tex]2x - 5x - 5 = 5x - 5x - 2 \\ - 3x - 5 = - 2[/tex]

Add 5 to both sides

[tex] - 3x - 5 + 5 = - 2 + 5 \\ - 3x = 3[/tex]

Divide both sides by - 3

[tex] \frac{ - 3x}{ - 3} = \frac{3}{ - 3} [/tex]

We have the final answer as

x = - 1

Hope this helps you

101) Nicole was 16 years old twelve years ago.
How old is she now?
help asap please!!!

Answers

Hey there! I think Nicole would be 28.

What is the arc length S what is shown below?
The angle in the image is a central angle în radians.

Answers

Answer:

  14 cm

Step-by-step explanation:

The applicable formula is ...

  s = rθ

  s = (7 cm)(2) = 14 cm

Which pair of fractions shows a correct comparison? A.2/3 = 5/10 B.2/3 1/9 D.1/3 = 3/10 E.1/3 > 5/6 F.1/3 < 4/12

Answers

Hand drawn did is d do did d didn’t d didn’t f didn’t be c did d d due r. Rjrnrrjrnene e event ebeir Brie r r firndbejr. Turn d their evens. Did d didn’t r rut brief. Ruffin t t

This equation shows how the total cost of visiting the art museum as a member is related to the number of visits. c = v + 11 The variable v represents the number of visits to the art museum, and the variable c represents the total cost of those visits. What is the maximum number of visits a member of the art museum can make for a total cost of $14?

Answers

Answer:

6

Step-by-step explanation:

C=9.2v + 21.2

76.4 = 9.2v + 21.2

76.4 - 21.2 = 9.2v

55.2 = 9.2v

v= 55.2 / 9.2 = 6

1/2a+6b/7 Verbal Expression?

Answers

Answer:

one half of a plus six times b divided by seven

Step-by-step explanation:

Solve 1. At a concert, a band sold t-shirts for $18 and hats for $12. They sold 60 t-shirts and hats combined for a total of $870. How many t-shirts did they sell? How many hats?​

Answers

Answer:

25 t-shirts and 35 hats were sold

Step-by-step explanation:

Here, we want to calculate the number of hats and the number of t-shirts sold.

Let the number of hats be h and the number of t-shirts be t

The sum of both is 60;

Mathematically;

h + t = 60 •••••••••••(i)

The total revenue from selling h hats at $12 per one is 12 * h = $12h

The total revenue from selling t t-shirts at $18 per one is 18 * t = $18t

So the addition of this gives the total;

12h + 18t = 870 ••••••••(ii)

From i, h = 60-t; substitute this into ii

12(60-t) + 18t = 870

720 -12t + 18t = 870

720 + 6t = 870

6t = 870 -720

6t = 150

t = 150/6

t = 25

From the substitution;

h = 60-t

h = 60-25

h = 35

Answer:

48 hats

Step-by-step explanation:

im not sure if this is the right answer but i hope this helps

- Suppose Q is the midpoint of PR. Use the information to find the missing value. PQ = 3x + 14 and QR = 7x - 10; Find x.​

Answers

Answer:

x =6

Step-by-step explanation:  Q is the midpoint of PR.

Therefore PQ = QR

3 x + 14 = 7 x -10

       -14          -14

3 x         = 7 x-24

-7x                 -7x

-4x     =      -24                             Divide both sides by -4

x = 6

The value of x for PQ = 3x + 14 and QR = 7x - 10 is 6 units.

What is midpoint of line segment?

The midpoint divides the line segment into two equal parts.

It is given that Q is the midpoint of PR which implies Q will divide PQ into two equal parts that is PQ (3x+14) equals QR (7x-10). now calculating x value  :

[tex]\begin{aligned}PQ&=QR\\3x+14&=7x-10\\7x-3x&=14+10\\4x&=24\\x&=6\end{aligned}[/tex]

Therefore, the value of x for PQ = 3x + 14 and QR = 7x - 10 is 6 units.

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Danny and 4 friend go to the movies. Each person buys a movie ticket for $10, a snack for $2 and a drink for $3. Write an expression which shows how much Danny and his friends spent.

Answers

8000647 dollars

Step-by-step explanation:

broggxtxycycuvuh8y7rtwh4w5iwutettixgdbf

Write a division expression with a quotient of 20^{5}

Answers

Answer:

3200000

Step-by-step explanation:

Can some one help me with my advanced math homework it’s due tomorrow

Answers

Answer:

1.) 88

2.) 196

3.) 63

4.) 90

5.) 367.142857143

6.) 695. 2 repeating

7.) 109.285714286

8.) 63.5593220339

Step-by-step explanation:

Write 8660 in scientific notation

Answers

Answer:

8.66 x 10^3

Step-by-step explanation:

8.66 * 1000 (10^3) = 8660

8.66 x 10^3
This is the answer

A thermometer comes with a guarantee that the stated temperature differs from the actual temperature by no more than 1.5 degrees Fahrenheit. Write an equation to represent the minimum and maximum actual temperatures when the thermometer states that the temperature is 87.4 degrees Fahrenheit.

Answers

Answer:

The equation is;

T = 87.4 ± 1.5

Maximum value of T = 88.9 °F

Minimum value of T = 85.9 °F

Step-by-step explanation:

We are given the stated temperature as 87.4 °F

Now, we are told that this stated temperature differs from the actual temperature by no more than 1.5 degrees Fahrenheit.

Thus, if the actual temperature is T, it means that T should either be 1.5 more than 87.4 or 1.5 less than 87.4.

Thus the equation is;

87.4 ± 1.5 = T

So maximum value of T = 87.4 + 1.5 = 88.9 °F

While minimum value of T = 87.4 - 1.5 = 85.9 °F

Georgette created a factor tree and wrote the prime factorization of 72 shown here. A factor tree of 72. 72 branches to 8 and 9. 8 branches to 2 and 4. 4 branches to 2 and 2. 72 = 23 × 9 What is Georgette’s error? A. Georgette should have started the factor tree with 2 × 36. B. Georgette did not complete the factorization; 9 is a composite number. C. Georgette should have expressed 4 as 4 x 1, not 2 x 2. D. Georgette should have expressed 8 as 4 × 4, not 2 × 4.

Answers

Answer:

Georgette did not complete the factorization; 9 is a composite number.

Step-by-step explanation:

9 can be broken down to 3x3

So it the prime factorization of 72 should be 2x2x2x3x3

Georgette’s error is Georgette should have expressed 8 as 4 × 4, not 2 × 4.

The correct option is D.

The correct prime factorization of 72 is 2³ × 3², which means it can be expressed as the product of prime numbers raised to their respective exponents.

Analyzing the factor tree provided by Georgette, we can see that she made an error when branching from 72 to 8 and 9.

The prime factorization of 8 should be 2³, not 2 × 4, and the prime factorization of 9 should be 3², not 2 × 2.

Therefore, Georgette's error is that she have expressed 8 as 2³ × 1 or 4 × 2, not as 2 × 4.

The correct factor tree for 72 would be:

    72

  /  \

2   36

    / \

   2   18

       / \

      2   9

          / \

         3   3

So, the prime factorization of 72 is 2³ × 3².

Learn more about Prime Factorization here:

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Find the common difference of the arithmetic sequence. 6, 9.4, 12.8, 16.2, . . .

Answers

Answer:

The answer is 3.4

Step-by-step explanation:

The sequence above is an arithmetic sequence

So in order to find the common difference subtract the previous term from the next term

So we have

Taking 9.4 and 6

That's

9.4 - 6 = 3.4

Taking 12.8 and 9.4

12.8 - 9.4 = 3.4

Taking 16.2 and 12.8

16.2 - 12.8 = 3.4

Since the common difference is the same for any of the terms taken , the common difference is 3.4

Hope this helps you

Answer:

3.4

Step-by-step explanation:

The transitive property of equality states that _____. if a = b, then b = a if a = b, then ac = bc if a = b and b = c, then a = c if a = b and c = c, then a + b = b + c

Answers

Answer:

If a = b and b = c, then a = c

Step-by-step explanation:

The transitive property of equality tells us that if we have two things that are equal to each other and the second thing is equal to a third thing, then the first thing is also equal to the third thing.

Answer:

If a = b and b = c, then a = c

Step-by-step explanation:

i got it right on a test

18 = 3(3x − 6) multi step equations show all steps pls

Answers

Answer:

x=4

Step-by-step explanation:

18 = 3(3x − 6)

Divide each side by 3

18/3 = 3( 3x-6)/3

6 = 3x-6

Add 6 to each side

6+6 = 3x-6+6

12 = 3x

Divide by 3

12/3 = 3x/3

4 =x

Answer: 4 = x

Step-by-step explanation: To solve this equation, we start by

distributing the 3 through the parenthses on the right side.

3(3x) is 9x and 3(-6) is -18.

So our equation now reads 18 = 9x - 18.

Our next step is to get the x term by itself on the right side.

So we add 18 to both sides to get 36 = 9x.

Now divide both sides by 9 to get 4 = x.

5. If median =137 and mean = 137.05, then find the value of mode. (2marks)

Answers

Answer:- 136.9

Step-by-step explanation:

3median=2mean+mode

3(137)=2(137.05)+mode

411=274.1+mode

411-274.1=mode

mode=136.9

Gym A charges $9.00 per hour of childcare. Gym B charges $0.75 per 5 minutes of childcare.

Answers

Answer:

$9.00

Step-by-step explanation:

0.75 times 12 equals 9

Answer:

the answer is they are both the same

Step-by-step explanation:

be i took the test

Solving the equation x + 2(x – 5) = 320
will need the following steps:
1. x + 2x + 10 = 320
II. 3x + 10 = 320
III.
3x = 310
310
IV.
x =
3
Which step above is incorrect?
A Step
B Step III
C Step IV
D All steps are correct
Lo

Answers

Answer:

   A.  Step I

Step-by-step explanation:

Appropriate application of the distributive property would give ...

  x +2x -10 = 320 . . . . . . . does not match step I

Further solution steps would be ...

  3x -10 = 320

  3x = 330

  x = 110

-3(-9v-4)-2(v-2)????

Answers

Answer: 25v+16
Solution: Distribute the -3 to the whole equation in the parenthesis. This will make the equation 27v+12-2(v-2). Do the same thing with the -2 and the other parenthesis. This will make the equation 27v+12-2v+4. Combine like terms. This will make the equation 25v+16.
Hope this helped

square root of 87 to the nearest 10th

Answers

Answer:

9.3

Step-by-step explanation:

Step 1: Calculate. We calculate the square root of 87 to be: √87 = 9.32737905308882.

Step 2: Reduce. 9.32.

Step 3: Round. Round 9.32 so you only have one digit after the decimal point to get the answer: 9.3.

True or False: Segment AB is congruent to segment BC. A B C -2 0 1 3 Select one: True False​

Answers

I believe it’s true not sure tho

Mrs. Kim spent $4.77 on her favorite imported cheese. She bought 9/10 of a pound. Find how much cheese cost per pound.

Answers

4.77x10= 47.7/9 = 5.30. 1 pound cost $5.30

5. What are the names of the segments ?
6. What are the names of the rays ?

Answers

DE +EF for segments
DF

Answer:

de ef     and  df

Step-by-step explanation:

-8 is a term. true or false

Answers

Answer:

false

Step-by-step explanation:

Write the equation of the line, with the given properties, in slope-intercept form.
Slope = -2, through (-4,6)

Answers

Answer:

y= -2x -2

Step-by-step explanation:

slope-intercept form:

y= mx +c, where m is the gradient and c is the y-intercept.

Given that the slope is -2, m= -2.

Susbt. m= -2 into the equation:

y= -2x +c

To find the value of c, substitute a pair of coordinates.

When x= -4, y= 6,

6= -2(-4) +c

6= 8 +c (expand)

c= 6 -8 (-8 on both sides)

c= -2 (simplify)

Thus, the equation of the line is y= -2x -2.

100 points! Find the slope of the image.

Answers

Answer:

5/2

Step-by-step explanation:

We can use the slope formula

m = (y2-y1)/(x2-x1)

A  has points ( -2,0) and (0,5) as points on the line

m = ( 5-0)/( 0 - -2)

     ( 5-0)/( 0 +2)

  = 5/2

The lines B and C are parallel so they have the same slope 5/2

Which situation represents a propertional relationship between the hours worked and the amount earned fir matt and jane?

Answers

I say girl why are you calling and math Is easy if you think about it it’s really cool
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