Using the matrix solver on your calculator, find the solution to the system of

equations shown below.

2x - 4y = 4

x - 2y = 8

Answers

Answer 1

Answer:

x = 5

y = - 3/2

Step-by-step explanation:

[tex]\left \{ {{2x-4y =4} \atop {x-2y=8}} \right.[/tex]

The augmented matrix is :

[tex]\left[\begin{array}{ccc}2&-4&4\\1&-2&8\\\end{array}\right][/tex]

Now; to Row operations

Swap row 2 to row 1

[tex]\left[\begin{array}{ccc}1&-2&8\\\\2&-4&4 \end{array}\right][/tex]

Multiply row 1 with 2 and add to row 2 ;

1(2) = 2

-2(2) = -4

8(2) = 16

2 +2  = 4

4 +(-4) = 0

16+ 4 =20

Now; we have:

[tex]\left[\begin{array}{ccc}1&-2&8\\\\4&0&20 \end{array}\right][/tex]

changing row 2 back to equation form:

4x + 0y = 20

4x = 20

x = 20/4

x = 5

substituting x = 5 in row 1

x - 2y = 8

5 - 2y = 8

-2y = 8 -5

-2y = 3

y = - 3/2


Related Questions

Maya is researching energy costs. She made a table of the cost for different numbers of gallons of gasoline. How much will 12 gallon cost?
A.$7.80

B.$23.40

C. $31.20

D. not enough information

Answers

Answer:

The answer is B

Step-by-step explanation:

BEcause I took the test

Answer:

B. $23.40

Step-by-step explanation:

1. You have to divided the cost by the number of gallons to get the the cost per gallon

2. multiply the number of gallons by the cost per gallon that you found

Then you have your answer!

Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number.
11.21 m
34 m
5 m
6 m

Answers

Answer:

755 m²; 785 m²

Step-by-step explanation:

In the picture attached, the prism is shown.

Lateral area = perimeter of base * height

The base is a right triangles, then its perimeter is:

perimeter: 5 + 6 + 11.21 = 22.21 m

Lateral area = 22.21*34 = 755 m²

Surface area = lateral area + 2 (Area of base)

The base is a right triangles, then its area is:

area of base = (1/2)*5*6 = 15 m²

Surface area = 755 + 2*15 = 785 m²

(x*y)*z=144
x = y*3
z = y*2

please help

Answers

Answer:

whats the question that u need help with

How do you find the height of this trapezoid?​

Answers

Answer:

Step-by-step explanation:

sin 60 = h/12

h = 12sin60

h = 12* √3/2 = 6√3 cm

ASAP PLS

How many cubic centimeters of water can this paper cone cup hold?
8 centimeters
192 cubic centimeters
1447 cubic centimeters
9 centimeters
216 cubic centimeters
487 cubic centimeters
Vcone =

Answers

Answer:

48π

Step-by-step explanation:

The radius is 4 and the height is 9

V=1/3*π 4^2*9

Simplify:

48π

Which of these graphs represents a function


A.w
B.x
C.y
D.z

Answers

the graph the represent a function is D.z because it shows an actual function

The correct option is D. The graph z is representing a quadratic function.

What is a quadratic function?

In algebra, a polynomial function with one or more variables in which the highest-degree term is of the second degree is known as a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic.

The general form of the quadratic functions is represented as below:-

y = ax² + bx + c

Where a,b, and c are the constants x and y are variables.

The graph of the quadratic functions will be parabolic on the x-y plane.

Therefore, the correct option is D. The graph z is representing a quadratic function.

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PLEASE HELP ON THIS QUESTION! I WILL MARK YOU BRAINLIEST IF CORRECT :) TYY

Answers

Answer:

no it's not a reflection

Step-by-step explanation:

a reflection would not be upside down like that, it would be the same thing rotated

find the missing letter N if the width is 2ft and the area equal 28 sq ft​

Answers

Answer:

Step-by-step explanation:

Area = 28 Sq.ft

length * width = 28

2 * n = 28

Divide both sides by 2

2n/2 = 28/2

n = 14 ft

What is the equation of a line with a slope of -2 that passes through the point (6, 8)?
A. 2x + y = 20
B. y-2x = 4
C. y-2x = 20
D. 2x + y = 4

Answers

Answer:

2x+y = 20

Step-by-step explanation:

The equation for a line is y = mx+b where m is the lope and b is the y intercept

y = -2x+b

substitute the point into x and y

8 = -2(6) +b

8 = -12+b

Add 12 to each side

20 =b

y = -2x+20

Add 2x to each side

2x+y = 20

Answer: 2x+y = 20

Step-by-step explanation:

The equation for a line is y = mx+b where m is the lope and b is the y intercept

y = -2x+b

substitute the point into x and y

8 = -2(6) +b

8 = -12+b

Add 12 to each side

20 =b

y = -2x+20

Add 2x to each side

2x+y = 20

Write the number in standard form. 6.45×10^−4

Answers

Answer:

.000645

Step-by-step explanation:

.0006.45

move the decimal place 4 places to the Left because it is a negative.  

The point P(x,y) lies on the terminal side of an angle theata = -60 degrees in standard position. What are the signs of the values of x and y

Answers

Answer:

a

Step-by-step explanation:

a

19. Alyse is writing down some notes to argue her case as to how the
body functions when riding a bike. Select the correct phrases below to
help finish these notes.

Answers

Answer: Bro write the question better

Step-by-step explanation:

What is the product of the binomials below?
(5x + 2)(4x +4)

Answers

You can use the FOIL method (First, Outer, Inner Last) as how most people prefer it.

5x*4x=20x^2

5x*4=20x

2*4x=8x

2*4=8

Combine them all together and you get 20x^2 + 28x +8

I hope this helps.

Answer:

20x^2 + 28x + 8

Step-by-step explanation:

you use the box method shown in the picture to multiply then combine like terms

Emma can run 4.5 miles in 36 minutes. How many miles can she run in 2 hours if she keeps a constant pace?

Answers

Answer:

13.34

Step-by-step explanation:

Answer:

15 miles is the answer, I hope this helps

Step-by-step explanation:

1. Set up a proportion

2. Convert 2 hours to 120 minutes

3. Cross multiply then divide the remaining number in the proportion

Dustin works in a department store. He earned $89.00 for working 10 hours last week. At this rate, how much would Dustin earn for working 38 hours?​

Answers

Answer:

$338.20

Step-by-step explanation:

Find out how much Dustin gets for one hour of work, since you are given how much Dustin earns in 10 hours, you divide it by 10 (the number of hours) to find one hour,

89/10=8.9

$8.9 per hour

So 38 hours would be

8.9 x 38= $338.20

Answer:

$338.20

Step-by-step explanation:

Need help with this

Answers

Answer:

5 to the power of -2

Step by Step explanation:

Because you are diving, you need to subtract the powers.

For example, you subtract 10 from 12 to get -2

The 5 remains the same so the answer should be 5 to the power of -2

Hope this helps

(1/3)^3 Evaluate the expression. This question is designed to test your intelligence.

Answers

Answer:

1/27

Step-by-step explanation:

That means

1/3 * 1/3 * 1/3

1/9 * 1/3

1/27

Answer:

1/27

Step-by-step explanation:

(1/3)^3

1/3*1/3*1/3

1/27

A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 35% salt and Solution B is 80%
salt. She wants to obtain 90 ounces of a mixture that is 40% salt. How many ounces of each solution should she use?
Solution A:
Solution B:

Answers

Answer:

80? bc yhu cant use solution a because it only has 35...i think

Step-by-step explanation:

if im wrong sorry

The requried scientist should use 80 ounces of Solution A (35% salt) and 10 ounces of Solution B (80% salt) to obtain a 90-ounce mixture that is 40% salt.

Let's assume the scientist uses x ounces of Solution A and y ounces of Solution B to obtain the desired mixture.

From the information given, we can set up the following equations:

Equation 1: The total amount of solution is 90 ounces, x + y = 90

Equation 2: The amount of salt in the mixture can be expressed as, 0.35x + 0.80y = 0.40 * 90

Simplifying Equation 2:
0.35x + 0.80y = 36

To solve these equations, we can use substitution or elimination. Let's use the substitution method.

From Equation 1, we can express x = 90 - y and substitute it into Equation 2:

0.35(90 - y) + 0.80y = 36

31.5 - 0.35y + 0.80y = 360

45y = 4.5y = 10

Substituting y = 10 back into Equation 1:

x + 10 = 90

x = 80

Therefore, the scientist should use 80 ounces of Solution A (35% salt) and 10 ounces of Solution B (80% salt) to obtain a 90-ounce mixture that is 40% salt.

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please help me please please please please​

Answers

Answer: [tex]2\frac{2}{3}[/tex]

Step-by-step explanation:

[tex]-2\frac{1}{3}-(-5)=[/tex]

Convert the mixed number to improper fraction. You can do this by multiplying the whole number times the denominator and adding the numerator; over the same denominator.

[tex]-\frac{2*3+1}{3} -(-5)=[/tex]

Solve;

[tex]-\frac{6+1}{3} -(-5)=[/tex]

[tex]-\frac{7}{3} -(-5)=[/tex]

Now, get rid of the two negatives by multiplying.

[tex]-\frac{7}{3} +5=[/tex]

Remember 5 has a 1 below; therefore, we can subtract these two fractions by getting both to a same denominator. Let's rewrite 5 as a fraction.

[tex]-\frac{7}{3}+\frac{5}{1} =[/tex]

To be able to convert 1 to 3, we have to multiply by 3. Remember that if you change the denominator, you have to change the numerator as well.

[tex]-\frac{7}{3}+\frac{5}{1} (\frac{3}{3} ) =[/tex]

Solve;

[tex]-\frac{7}{3}+\frac{15}{3} =[/tex]

Subtract numerators and keep the same denominator.

[tex]\frac{-7+15}{3}=\frac{8}{3}[/tex]

Convert to a mixed number. To do this, first, divide:

8/3=2

6

----

2

The 2 after the equal sign is the whole number, the two in the remainder is the numerator and the 3 is the denominator. Leaving our result as: [tex]2\frac{2}{3}[/tex]

The lowest point of elevation in the United States is at Death Valley National Park in California at 282 feet below sea level. The Dead Sea in Israel is 1,360 feet below sea level. Write a division expression that could be used to find how many times greater the Dead Sea lies below sea level than Death Valley. Then determine how many times greater. Round to the nearest whole number.

Answers

Answer:437

Step-by-step explanation:I took the test

PLEASE HELP ME
I NEED IT

Answers

Answer:

[tex]\sqrt{24}[/tex]

Step-by-step explanation:

[tex]4\frac{4}{9}[/tex] cannot be correct because it equals 4.4.

[tex]\sqrt{20}[/tex] cannot be correct because it equals 4.5.

480% is 480/100 which equals 4.8 which is also not correct.

Therefore, [tex]\sqrt{24\\}[/tex] is correct because it is greater than 4.8 and less than 5.0.

4) If z/3 = 6, what is z equal to?

Answers

Answer:

z/3 = 6

multiply both sides by 3

z/3 * 3 = 6*3

z = 18

Which ordered pair is a solution of the equation?
2x + 4y = 6x - y

a. only 4,5
b. only 5,4
c. both 4,5 and 5,4
d. neither

pls answer​
ill mark brainliest

Answers

You Answer is: 4x - 5y = 0

Answer:

b. only 5,4

Step-by-step explanation:

Which is the longest length?
a 1 yd. 20 in.
b 1yd. 1 ft.
С
40 in.
d 3 ft.

Answers

Answer:

a-1yd20in

Step-by-step explanation:

a-4ft 8in

b-4ft

c-3ft 4in

d-3ft

Answer:

it's A, one yard and 20 inches

Step-by-step explanation:

If you convert them all to inches,  a yard and a 20 inches are equal to 56 inches, so you can rule out the 40 inches answer. a yard and a foot are equal to 48 inches, so we can rule out that also. 3 feet is equal to 36 inches, because we know that a foot is equal to 12 inches. so you are left with A. 1 yard and 20 inches.

What is the value of x when 1/3x=9 1/3?
Helppp nowww

Answers

Answer:

x=28

Step-by-step explanation:

[tex]\frac{1}{3} x=9\frac{1}{3} \\\frac{1}{3} x=\frac{28}{3} \\x=28[/tex]

The value of x is 28.

What is mixed fraction?

A mixed fraction represented with its quotient and remainder is a mixed fraction.

How to convert a mixed fraction fraction into an improper fraction?

To convert a mixed fraction into improper fraction first we multiply the denominator of the proper fraction to the whole number attach with it then we add the numerator.

According to the question:

we have

[tex]\frac{1}{3}x =9\frac{1}{3}[/tex]

for finding the value of x

[tex]\frac{1}{3}x =9\frac{1}{3}[/tex]

⇒[tex]\frac{1}{3}x=\frac{28}{3}[/tex]

⇒[tex]\frac{3}{3} x= 3[/tex]×[tex]\frac{28}{3}[/tex]                      (multiply both the sides by 3)

⇒ [tex]x= 28[/tex]

The value of x is 28.

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Find the product of each sum and difference.
(21+9)(21-9)

Answers

30 12

Step-by-step explanation:

21 + 9 equals 30 21 - 9 equals 12

A cone and a cylinder have the same height and their bases are congruent circles

If the volume of the cylinder is 90 cm^3,
what is the volume of the cone?

Answers

Answer:

30 cm³

Step-by-step explanation:

Volume of cone is ⅓ of volume of cylinder , when they have same radius and height.

Volume of cone = ⅓ × 90 = 30 cm³

The chart below shows the distribution of weeds in a yard.

A circle graph titled Lawn weeds. The largest proportion is crab grass, then dandelion, then clover, then chickweed.

A lawn-care specialist chooses a random sample from the yard and determines the number of weeds in the sample. The results of the sample are shown in the table below.

Weed Type
Number
Dandelion
2
Clover
3
Crab Grass
2
Chickweed
2

Which explains whether or not this is a representative sample?
Yes, this is a representative sample because each type of weed is represented in the sample.
Yes, this is a representative sample because each type of weed is represented approximately the same number of times in the sample.
No, this is not a representative sample because each type of weed should be represented in proportion to the number of weeds actually present in the yard.
No, this is not a representative sample because each type of weed should be represented exactly the same number of times in the sample.

Answers

Answer:

Its c,No, this is not a representative sample because each type of weed should be represented in proportion to the number of weeds actually present in the yard.

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

there are 12 inches in 1 foot
write an equation to find the number of inches in any number of feet

Answers

Answer:

divide the number of inches by 12

Step-by-step explanation:

1/12=x/12 then you would cross multiply it

In quadrilateral PQRS, PQ = QR = RS = SP, PR = 14, and QS = 48. Find the perimeter of PQRS.

Answers

Answer:

100 units

Step-by-step explanation:

Lengths of diagonals:

PR = 14

QS = 48

Since all 4 sides are equal in length, it's a rhombus

Length of each side:

sqrt[(14/2)² + (48/2)²]

sqrt(625)

25

Perimeter = 4 × 25

= 100

The side length of the rhombus is 25 units. Then the perimeter of the rhombus PQRS will be 100 units.

What is the perimeter of the shape?

The complete stretch of a shape's border is referred to as the perimeter in geometry. A shape's periphery is calculated by summing the lengths of all of its sides and borders. Its dimensions are expressed in linear units like centimeters, meters, inches, and feet.

In quadrilateral PQRS, PQ = QR = RS = SP, PR = 14, and QS = 48. The diagonal of the rhombus intersect at a right angle. Then the side length of the rhombus is given as,

a² = (14 / 2)² + (48 / 2)²

a² = 49 + 576

a² = 625

a = 25

Then the perimeter of PQRS will be given as,

P = 4a

P = 4 x 25

P = 100 units

The side length of the rhombus is 25 units. Then the perimeter of the rhombus PQRS will be 100 units.

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