Solve the system by elimination 5x - 3y + 4z = - 16-4x + 2y - 3z = 12 - x + 5y + 7z =32 X = Y = Z =

Answer:

Triangle 2

Step-by-step explanation:

a^2+b^2=c^2

6^2+8^2=10^2

36+64=100

100=100

Gaussian Elimination and Gauss-Jordon Elimination are two methods of solving linear systems of equations.
A-x=3, y=2, z=-2,B-x=4, y=-2, z=15 C-x=2, y=-2, z=2.

An equation is a mathematical statement that states two expressions are equal. It consists of two expressions separated by an equals sign (=) and can use any of the operations of arithmetic such as addition, subtraction, multiplication, division and exponents. An equation can be solved to find the value of one or more variables that make the equation true.

Question 1:

Using Gaussian Elimination:

2x+y + 2z = 1

4x + 3z = -5

5y + 4z = 13

Step 1: Subtract 2 times the first equation from the second equation.

0x+3y+z=-6

Step 2: Subtract 5 times the first equation from the third equation.

0x+2y+3z=10

Step 3: Subtract 2 times the second equation from the third equation.

x+y=4

Step 4: Subtract 4 times the second equation from the first equation.

x=3

Step 5: Substitute x = 3 in the second equation.

3+2y+z=-6

Step 6: Subtract 3 times the fifth equation from the fourth equation.

y=2

Step 7: Substitute y = 2 in the fifth equation.

3+4+z=-6

Step 8: Solve for z.

z=-2

Answer: x=3, y=2, z=-2

Question 2:

Using Gauss-Jordan Elimination:

2x+y+z=13

x+2y+z= 11

x + 3y + 3z = 19

Step 1: Subtract 2 times the first equation from the second equation.

-x+3y=2

Step 2: Subtract x times the first equation from the third equation.

2y+2z=6

Step 3: Subtract 3 times the second equation from the third equation.

x=4

Step 4: Substitute x=4 in the second equation.

4+3y=2

Step 5: Solve for y.

y=-2

Step 6: Substitute y=-2 in the first equation.

2x+(-2)+z=13

Step 7: Solve for z.

z=15

Answer: x=4, y=-2, z=15

Question 3:

Using Gaussian Elimination:

-3x+2y-6z = 6

5x + 7y - 5z = 6

x + 4y = 2z = 8

Step 1: Subtract 5 times the first equation from the second equation.

2x+9y-z=0

Step 2: Subtract 2 times the third equation from the first equation.

-5x+2y-2z=-2

Step 3: Subtract 2 times the first equation from the third equation.

3x+7y=2

Step 4: Subtract 3 times the second equation from the third equation.

x=2

Step 5: Substitute x=2 in the second equation.

4+9y-z=0

Step 6: Solve for y.

y=-2

Step 7: Substitute y=-2 in the fifth equation.

2+(-2)-z=0

Step 8: Solve for z.

z=2

Answer: x=2, y=-2, z=2

Conclusion:

Gaussian Elimination and Gauss-Jordon Elimination are two methods of solving linear systems of equations. Both methods rely on manipulating the equations to create a triangular form, which allows for the easier determination of the variables. By using both methods, we were able to solve each of the three linear systems of equations given in the question.

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Work Shown:

9+15 = 24 students total

9 have glasses, so 9/24 = 0.375 = 37.5% of the class wears glasses.

Mr. Lloyd could use his credit card to buy the TV. Therefore, option  A is the correct answer.

Using a credit card to make a purchase requires that the buyer have a credit limit that is large enough to cover the amount of the purchase. Mr. Lloyd does not have enough money in his bank account to pay for the television, so he would not be able to use a credit card to make the purchase.

Options B, C, and D are all viable options for Mr. Lloyd. He could save up money and pay cash for the television at a later date, or he could use his debit card to make the purchase when he has enough money in his bank account. He could also save money and use his debit card at a later date when he has enough money in his bank account.

Therefore, option  A is the correct answer.

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Mr. Lloyd wants to buy a new television, but he does not have enough money in his bank account to pay for one. Which of these is NOT an option for Mr. Lloyd?

A) He can use his credit card to buy the television now.

B) He can save money and pay cash for the television at a later date.

C) He can use his debit card to buy the television now.

D) He can save money and use his debit card to buy the television at a later date.

Answer:

THE ANSWER IS 81/16 OR C

your right Step-by-step explanation:

The measure of TW from the given triangle TUV is 35 units.

The point in which the three medians of the triangle intersect is known as the centroid of a triangle. It is also defined as the point of intersection of all the three medians.

Given that, in triangle TUV, Y is centroid if YW=5b and TY=4b+14.

The centroid is positioned inside a triangle. At the point of intersection (centroid), each median in a triangle is divided in the ratio of 2:1.

Now, TY/YW =2/1

(4b+14)/5b =2/1

10b=4b+14

6b=14

b=14/6

b=7/3

Now, TW=YW+TY

TW=5b+4b+14

TW=9b+14

Substitute, b=7/3 in TW=9b+14, we get

TW=9×7/3+14

= 21+14

= 35

Therefore, the measure of TW is 35 units.

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Answer:

its A

Step-by-step explanation:

correct on edge

Answer:

103

Step-by-step explanation:

For any Triangle, The Sum of Interior Angles = 180°

So, For Triangle ABC ---> m∠A + m∠B + m∠C = 180°

By Substituting by the Givens m∠A =68 and m∠B=9

68 + 9 + m∠C = 180

77+ m∠C=180

Subtract 77 from both Sides

m∠C=180-77=103°

The exact value of sin(5π/12) is (√6 + √2)/4

From the question, we have the following parameters that can be used in our computation:

sin 5pi/12

Express properly

So, we have

sin(5π/12)

Convert the angle to degrees

This gives

sin(5π/12) = sin(5/12 * 180)

Evaluate

sin(5π/12) = sin(75)

The actual value of sin(75) is (√6 + √2)/4

This means that

sin(5π/12) = (√6 + √2)/4

Hence, the exact value of sin(5π/12) is (√6 + √2)/4

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The exact value of sin 5π/12 is (√6 + √2)/4

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Angle in trigonometry can be measured in either degree or radian.

π is a measurement in radian which is equivalent to 180° in degrees.

Therefore:

5π/12 = 5 × 180/12

= 75°

Therefore sin5π/12 = sin75°

sin75 = sin( 45+30) = sin45cos30+ cos 45sin30

= 1/√2 × √3/2 + 1/√2 × 1/2

= √3/2√2 + 1/2√2

= (√3+1)/2√2

rationalizing;

(2√6 + 2√2)/8

dividing through by 2

=(√6 + √2)/4

therefore tan75 =(√6 + √2)/4

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Answer:

what are you telling Id understand

Step-by-step explanation:

became

Answer:

6 hours

Step-by-step explanation:

Total time it will take to complete the trip = Total time spent on riding + Time taken for lunch break.

Distance to be covered = 60 miles.

D = 60

Speed of riding = 15 miles per hour

S = 15

Thus time taken to cover a distance 60 miles by riding at a speed of 15 mph:

T=D/S=60/15

T= 4hours

They will spend 4 hours on riding and 2 hour of lunch break.

Hence total time taken to complete the trip = 4 + 2 = 6 hours.

It will take 6 hours to complete the trip.

The number of hours taken by riders to complete the trip is 6 hours.

Given that, distance = 60 mile, speed = 15 mph and lunch break = 2 hours.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Using speed formula Speed=Distance/Time

Here, 15 = 60/Time

⇒ Time = 60/15

= 4 hours

Total time taken in the trip is 4+2 = 6 hours

Hence, the number of hours taken by riders to complete the trip is 6 hours.

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The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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9514 1404 393

Answer:

  Oscar

Step-by-step explanation:

On the face of it, you can see that the number of kilometers representing a given distance is greater than the number of miles. (152 > 95)

This means the constant of proportionality (a) in the equation ...

  k = am

must be greater than 1. You can find its value by solving this equation for 'a' and using the table entries for k and m:

  a = k/m = 152/95 = 8/5 = 1.6

The correct relation is ...

  k = 1.6m . . . . . Oscar wrote the correct equation

2) They tοgether will take 10.9 hours οr 120/11

3) jοsh will take 21/11 hrs οr 1.9 hrs

4) Tοgether they will take 36/13 οr 2.8 hrs

The place values οf the digits in a decimal number are displayed οn the decimal place value chart. We knοw that a digit in a number represents a numerical value οr place value.

Decimal place value charts are used tο determine the prοper placement οf each digit in a decimal number.

A decimal number cοnsists οf a whοle number and a fractiοnal cοmpοnent, separated by the decimal pοint, a dοt.

Fοr instance, the decimal number 4.37 has twο parts: an actual number pοrtiοn οf 4 and a fractiοnal pοrtiοn οf 37.

Sοlutiοns tο the abοve prοblem

2) Tοm takes = 12 hrs

Huck takes= 10hrs

We can aply unitary methοd

tοgether they will take= 1/12+1/10=2/t

11t=120;

t=120/11 οr 10.9 hrs

3) Tοgether Kim and jοsh can clean the hοuse tοgether in = 3 hrs

Kim takes = 7hrs

Jοsh will take= 1/7+1/x=2/3

3x+21=14x

21=11x

x=21/11 οr 1.9 hrs

4) Jack makes baseball grοunds in= 2 hrs

Mike takes= 3 hrs

Chris takes= 4 hrs

Tοgether they will take= 1/2+1/3+1/4=3/x

13x=36

x=36/13 οr 2.8 hrs

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After simplificatiοn οf the given expressiοn the factοr is 11. Thus, οptiοn b is cοrrect.

There is a need fοr mathematical οperatiοns like multiplying, splitting, adding, and even deleting. They wοuld result in the fοllοwing assertiοn if cοmbined: A mathematical fοrmula, sοme data, and an equatiοn A declaratiοn οf truth is made up οf values, elements, and mathematical οperatiοns like additiοns, erasures, algebraic expressiοns, and divisiοns. It is pοssible tο rate and analyze wοrds and sentences.

Here,

When we replace these in the statement, we get:

=\(\dfrac{(2^{10} \times 3^{10})(5^3 \times 11^3)(3^2 \times 5^2) }{(2^{10} \times 5^5)(3^{12})(11^{20})}\)

= \(\dfrac{(11 \times 15^2) } {15^2}\)

= 11

After simplificatiοn of the given expressiοn the factor is 11. Thus, οption b is correct.

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Answer:

2+4 6(8)

Step-by-step explanation:

pls give brainliest

Answer:

2+4=6/6×8=48

hope this helped

402.12÷0.01 per cubic inch is written as \(40212 inch^{-3\) οr \(2.4538868 \times109 m^{-3\)

Imperial units and US custοmary units bοth use the cubic inch as a measure οf capacity. The capacity οf a cube, which is equal tο 1/231 οf a US gallοn, has three lengths that are each οne inch lοng.

Given,

402.12÷0.01 per cubic inch

We can write the equatiοn as

40212 per cubic inch

Or \(40212/ inch{^3\)

Or, \(40212 inch^{-3\)

We knοw that 1 inch 0.0254 m

Then we can write the equatiοn as 2.4538868 × 109 m-3

Hence the cοrrect answer is \(40212 inch^{-3\) οr \(2.4538868 \times 109 m-3\)

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Three or more line segments that only intersect at their ends form closed, two-dimensional shapes known as polygons.

A polygon is a closed, two-dimensional shape with straight sides that is flat or plane. It has straight sides. Polygons are a different category that belongs to the category of two-dimensional figures because two-dimensional (2D) figures are flat because they lack volume.

Polygons are flat 2D shapes that have straight lines and all lines are closed, meaning that they don't have any disconnected lines. Polygons are a subcategory of 2D figures because they carry all traits of 2D figures but also have special ones of their own. Examples of polygons are squares, rectangles, and triangles. Examples of nonpolygons but still are 2D figures are circles, ovals, and any other flat shape.

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Complete question

How can polygons be considered a subcategory of two-dimensional figures?

Answer:

23x+250 and that would equal your total cost

Answer:

x = 10/√2 ≈ 7.07

Step-by-step explanation:

Comenzaremos por dividir el triángulo en dos partes y definir H, como en la figura adjunta.

Aplicando el teorema de Tales, sabemos que:

\(\dfrac{l/2}{H}=\dfrac{x/2}{h}\\\\\\\dfrac{l}{H}=\dfrac{x}{h}\)

También sabemos que, dado que el tirángulo menor es la mitad que el triángulo mayor, la relación entre áreas es:

\(\dfrac{A}{A_x}=\dfrac{lH/2}{xh/2}=\dfrac{lH}{xh}=2\)

Dado que formamos dos triángulos rectángulos, podemos despejar el valor de H como:

\((l/2)^2+H^2=l^2\\\\H^2=l^2-(l/2)^2=10^2-5^2=100-25=75\\\\H^2=\sqrt{75}\)

Podemos entonces despejar x de la siguiente manera:

\(h=\dfrac{H}{l}\cdot x=\dfrac{lH}{2x}\\\\\\2x^2\dfrac{H}{l}=lH\\\\\\2x^2=l^2\\\\\\x=\dfrac{l}{\sqrt{2}}=\dfrac{10}{\sqrt{2}}\approx7.07\)

The equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is: R(x) = 250000 + 375x - 2.5x²

Equations are mathematical statements with two algebraic expressionsοn either sideοf an equals (=) sign. It illustrates the equality between the expressions writtenοn the left and right sides. To determine the valueοf a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

N(x) = 625 + 2.5x

The revenue R(x) will be the productοf the numberοf students enrolled and the fee charged per student. The fee charged per student will be (400 - x) dollars. So, the revenue function can be represented as:

R(x) = (625 + 2.5x)(400 - x)

Simplifying the expression, we get:

R(x) = 250000 + 375x - 2.5x²

Therefore, the equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is:

R(x) = 250000 + 375x - 2.5x²

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Answer:

19 1/2 feet^2

Step-by-step explanation:

The formula is (1/2)bh.

So, (1/2)(4 7/8)(8)

You will get 19 1/2 feet^2.

Answer:

19 1/2 ft^2

Step-by-step explanation:

4 7/8 x 8 =39

39 ÷ 2 = 19 1/2

yan po yung correct answer.

Answer:

side 1^2 + side 2 ^2 = hypotenuse ^ 2

18^2 + 20^2 = hypotenuse^2

324 + 400 = 724

hypotenuse^2 = 724

hypotenuse = 26.9072480941474

hypotenuse = 26.9

Step-by-step explanation:

Answer:

The two angles that are directly across the intersection point from each other are called vertical angles. Vertical angles are always congruent.

Step-by-step explanation:

brainliest???

Vertical angles are two angles that are opposite of each other when two intersect. These angles are congruent.

Vertical angles are angles opposite to each other where two lines cross.

When two lines intersect, they naturally form two pairs of vertical angles. Vertical angles share the same vertex or corner, and are opposite each other.

These pair of angles are congruent which means they have the same angle measure.

Hence, Vertical angles are two angles that are opposite of each other when two intersect. These angles are congruent.

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The interpretation of the ratio is that there are 2 panthers for every 50 hogs in the swamp forest.

Here we know that the ratio of wild hogs to Florida panthers in a swamp forest 50:2.

For a ratio between elements A and elements B of the form:

a:b

Where a and b are real numbers.

Means that for each a elements of type A, there are b elements of type B

This means that in the swamp forest there are 50 hogs there are 2 panthers.

etc..

That is the interpretation of the ratio.

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25:1 is the value of the ratio and for every 25 wild hogs in the swamp forest there is 1 florida panthers is the interpretation

A ratio compares values. A ratio says how much of one thing there is compared to another thing. The trick with ratios is to always multiply or divide the numbers by the same value

Given: the ratio of wild hogs to florida panthers in a swamp forest 50:2

wild hogs : florida panthers = 50:2

Dividing both sides of the ratio by 2 gives:

wild hogs : florida panthers = 25:1

Therefore, the value of the ratio is 25:1 and the interpretation is that for every 25 wild hogs in a swamp forest there is 1 florida panther

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At the end of 2 years, Jackson's account balance is $700.40.

We have,

The formula for calculating simple interest is:

I = Prt

Where:

I is the interest earned

P is the principal amount

r is the interest rate

t is the time period

In this case,

Jackson invested $680.00 at an annual interest rate of 1.5% for 2 years. Therefore:

P = $680.00

r = 1.5% = 0.015

t = 2 years

Plugging these values.

I = Prt = $680.00 x 0.015 x 2 = $20.40

So,

Jackson earned $20.40 in interest over 2 years.

To find his total account balance at the end of 2 years, we need to add the interest earned to the initial principal:

Total balance

= $680.00 + $20.40

= $700.40

Therefore,

At the end of 2 years, Jackson's account balance is $700.40.

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Answer:

32 centimeters is the diameter of the large pizza.

Step-by-step explanation:

I hope this helps