The augmented matrix of a linear system has been reduced by row operations to the form shown. Continue the appropriate row operations and describe the solution set of the original system.
[1 7 3 -5]
[0 0 0 3]
[0 0 1 2]
[0 1 -1 4]
Select the correct choice below and; if necessary; fill in the answer boxes to complete your choice A: The solution set has exactly one element; (Type integers or simplified fractions B. The solution set has infintely many elements C. The solution set is empty:

The 40 50 90 triangle can be solved using Pythagoras theorem.

A triangle in which both legs are congruent, and the length of the hypotenuse is the length of a leg times the square root of 2.

Given:

We have 40 50 90 triangles.

A triangle with two equal legs whose hypotenuse measures one leg's length multiplied by the square root of two.

Because the length of the hypotenuse in the triangle above equals the length of one of its legs times sqrt(2), which is 3, the triangle is a 40-50-90 triangle.

So, Such type of Triangles can be solved using Pythagoras theorem.

Learn more about 40 50 90 triangle here:

https://brainly.com/question/29005645

#SPJ1

Answer:

27 students

Step-by-step explanation:

We know

1 student = $5

1 chaperone = $8.25

5 chaperon = $8.25 x 5 = $41.25

Let's solve

$176.25 -  $41.25 = $135

So, we know that the total amount Mrs. Rubio collected from students is $135, then we take

135 / 5 = 27 students

So, 27 students went on the field trip.

Answer:

8.25 × 5 = 41.25

176.25 - 41.25 = 135

5 × x = 135

x = 27

Therefore, 27 students went.

1287 combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter.

You win the jackpot if you match all six numbers. You receive a lesser fixed prize if you partially match some of the numbers.

Divide the number of winning lottery numbers by the total number of available lottery numbers to discover the probability of winning any lottery. Use the formula if the numbers are picked from a set and the order of the numbers is unimportant.

To find the winning combination we use the following formula

n !/ r!( n – r ) !

Where n = total number of to be drawn

r = the number which are drawn

In this question, n = 13, and r = 5

from the formula

13 !/5!( 13 – 5 ) !

= 13! / 5! 8!

= 13*12*11*10*9*8! / 5*4*3*2*1*8!

= 154,440 / 120

= 1287

To learn more about lottery possible to refer:

brainly.com/question/24245793

#SPJ4

The sum of squares of two sides is equal to the square of the third side.

Finding the Third Side of a Triangle with Two Sides

Let's assume that the triangle is right-angled, as the third side of a right-angled triangle can only be found when the other two sides are known.

A right-angle triangle is what?

This particular sort of triangle adheres to the Pythagoras theorem and may be calculated using the trigonometry tool.

We are aware that the right-angled triangle follows Pythagoras' Theorem.

According to the Pythagorean Theorem, the third side's square equals the sum of the first two sides' squares.

More about the right-angle triangle link is given below.

brainly.com/question/3770177

#SPJ4

The complete question should be:

What is the length of 3rd side of a triangle?

Answer:

[tex]\displaystyle x < \frac{12}{7}[/tex]

Step-by-step explanation:

This is an inequality, not an equation. Notice the sign is a "less than" sign and not an "equal" sign. You still solve it like a normal equation, however:

[tex]\displaystyle 7x-2 < 10\\\\\rightarrow 7x < 12\\\\\rightarrow x < \frac{12}{7}[/tex]

The side lengths measuring 4 units , 5 units and 6 units does not make a Right Triangle as they do not satisfy the condition of the Pythagoras Theorem that the square of the longest side is equal to the sum of square of other two side .

The Pythagoras Theorem states that the square of the lonest side (hypotnuse) is equal to the sum of the square of the other two sides ,.

The side lengths of the triangle are given as 4 units , 5 units and 6 units ,

According to the condition , [tex]6^{2} = 4^{2} + 5^{2}[/tex]

On simplifying ;

we get ;

[tex]36 = 16 + 25[/tex] ;

[tex]36 \neq 41[/tex]

that means the given side do not form a right triangle .

Therefore , the side 4 units , 5 units and 6 units do not make a right triangle .

Learn more about Right Triangle here

https://brainly.com/question/13054127

#SPJ4

The volume of the composite solid round to the nearest tenth is 83.7 inches³.

Volume of a three dimensional shape is the space occupied by the shape.

There are 2 hemispheres and a cylinder in the given composite solid.

Volume of hemisphere =  [tex]\frac{2}{3}[/tex] π r³, where r is the radius.

Volume of the cylinder = π r² h, where r is the radius and h is the height.

Here r = 2 inches and

h = 8 - 4 = 4 inches

Volume of hemisphere = [tex]\frac{2}{3}[/tex] π × 2³

                                      = [tex]\frac{16}{3}[/tex] π

There are two hemispheres.

Volume of two hemispheres = 2 × [tex]\frac{16}{3}[/tex] π =  [tex]\frac{32}{3}[/tex] π

Volume of the cylinder = π r² h

                                      = π × 2² × 4

                                      = 16 π

Volume of the composite Solid = [tex]\frac{32}{3}[/tex] π + 16 π

                                                    = [tex]\frac{80}{3}[/tex] π

                                                    = 83.7 inches³

Hence the volume of the composite solid is 83.7 inches³.

Learn more about Volume here :

https://brainly.com/question/1578538

#SPJ1

The required value of x is 17 for the given equation 11 = x - 6.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The equation is given in the question, as follows:

11 = x - 6

We can determine the value of x by adding 6 to both sides of the equation.

As per the question, we have

⇒ 11 = x - 6

⇒ 11 + 6 = x - 6 + 6

⇒ x = 11 + 6

Apply the addition operation, and we get

⇒ x = 17

Therefore, the required value of x is 17.

Learn more about the equation here:

brainly.com/question/10413253

#SPJ1

Answer:

Step-by-step explanation:

i don't know if this help :/

A triangle that is equilateral has three equal sides and three equal angles.

The angles are all 60 degrees each. Two 90-degree angles are formed when the height of an equilateral triangle is drawn to the base of the triangle, and the top angle is divided into two 30-degree angles. A triangle with sides of 30-60-90 always has sides that are 1:3:2.

The 30-60-90 triangle formula for sides y is also known as y3: 2y. The angles of the triangle are always 30, 60, and 90 degrees. Given that one of the angles is 90 degrees, this triangle is always a right triangle. These angles come together to form a right-angled triangle. Furthermore, the right angle is equivalent to the sum of two sharp angles, which will have the ratios of 1: 2 or 2: 1.

To learn more about two angles if angle P measures 30° refer to:

https://brainly.com/question/29305455

#SPJ1

Answer: 25cm²

Step-by-step explanation:

Ok, so I haven't actually learnt this in school so I'm going to give it my best shot. (Don't be surprised if I get this wrong though.)

So, Quadrilaterals A and B are similar. They have the same angles. Therefore, (I'm thinking that) Quadrilateral B is just a scaled-up version of Quadrilateral A.

Here comes my theoretical part:

If one side of Quadrilateral B is 5 times longer than the same side of Quadrilateral A...

(Quadrilateral A is 3cm, and Quadrilateral B is 15cm).

... then the area of the entire Quadrilateral B should just be 5 times bigger than Quadrilateral A.

Therefore, (I'm guessing), Quadrilateral B has an area of 25cm²

The fifth term of the given arithmetic sequence is 36.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d

Given that, in a sequence the first term of 4 and the common difference is 8.

Here, a=4 and d=8

Now, the fifth term is

a₅=4+(5-1)×8

= 4+32

= 36

Therefore, the fifth term of the given arithmetic sequence is 36.

To learn more about an arithmetic sequence visit:

https://brainly.com/question/10396151.

#SPJ1

Answer:

? = 74°

Step-by-step explanation:

• in a parallelogram, consecutive angles sum to 180° , that is

? + 106° = 180° ( subtract 106° from both sides )

? ( ∠ G ) = 74°

The domain of the equation is (A) All real numbers and the range of the equation is (A) y≥-4.

The range of values that can be plugged into a function is known as its domain. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range after we identify g's domain (y).

The domain of the equation is (A) All real numbers because the value of x is all real numbers.

and the range of the equation is (A) y≥-4, because the value of variable y is greater than and equal to -4 for all values of x.

To learn more about of domain and range of the equation visit:

brainly.com/question/29160910

#SPJ1

The difference in ages of Marcelle and Megan is 95/12 as an improper fraction and as a mixed number is 7 whole number and the fraction 11/12.

We shall convert the fractions to have similar denominators and simply apply subtraction for the numerators as follows:

Marcelle's age = 15 whole number, 1/2

Marcelle's age = 31/2

Megan's age = 7 whole number, 7/12

Megan's age = 91/12

LCM of 2 and 12 is 12 so;

Marcelle's age = 31/2 × 12/12

Marcelle's age = 186/12

difference in their age (186 - 91)/12

difference in their age = 95/12

Therefore, the difference in the ages of Marcelle and Megan is the fraction 95/12 or as a mixed number is 7 whole number and the fraction 11/12

Know more about fraction here:https://brainly.com/question/11562149

#SPJ1

Exact length of border required by Kristin is calculated to be 9.42 ft.

This question can be solved using the concept of circumference of a circle.

The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were expanded out and straightened out to a line segment, the circumference would be the length of the arc. The curve/arc length around any closed figure is more often referred to as the perimeter. The term "circumference" can also refer to the circle's actual location, which corresponds to a disk's edge. A sphere's circumference is equal to the length of any one of its great circles.

Circumference of a circle is given by 2πr.(r is the radius of the circle)

In the given question,

diameter= 3ft

radius= half times of diameter

radius= 1.5 ft.

Circumference= 2πr

= 2×3.14×1.5

=9.42 ft

Kristin will require 9.42 ft of border around the edge of the table.

We can learn more about circumference here:

https://brainly.com/question/4268218#

#SPJ4

Answer:

Submarine must descend by 12 feet in the fifth minute.Average of the data:Average of a data set is calculated by dividing the sum of terms by the number of the terms of the set.From the table given in picture,Let the distance descended by submarine in 5th minute = x feetAverage distance descended by the submarine =                                                                                 =                                                                                 =  feet per minuteStatement given in the question → "Submarine must descend at an average rate of at least 10 feet per minute"So the inequality for the statement will be,38 + x ≥ 50x ≥ 50 - 38x ≥ 12    Therefore, submarine must descend 12 feet in the 5th minute.

Step-by-step explanation:

Using trigonometric functions, we can  find a side length of a right triangle with an angle and a side.

Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.

Trigonometric ratios can be computed either using the provided acute angle or by calculating the ratios of the right-angled triangle's sides.

You can determine the hypotenuse by dividing the length of the side by sin(θ) if you have an angle and the side opposite to it. Alternatively, to find the length of the side next to the angle, divide the length by tan(θ).

To learn more about ratios visit:

https://brainly.com/question/1504221

#SPJ4

The difference in timing was greater since the silver medalists finished around 0.14 seconds ahead of the bronze medalists.

The unit technique is a strategy for addressing issues that entails first figuring out the value of a specific unit, then dividing that value to figure out the needed value. Simply put, the unit method is employed to derive a single system value from a multiple that is supplied. For example, 40 pens might cost 400 rupees, which is equal to the cost of one pen. This procedure could follow a regular procedure. a single nation. anything has a distinct identity. Its adjoint and reciprocal are equal in terms of mathematics, algebra, linear algebra, computational equations, or algebra of matrices or operators.

given

time separation of gold medalists by silver medalists is equal to 0.14 minus 0.2, or 0.11.

The difference in timing was greater since the silver medalists finished around 0.14 seconds ahead of the bronze medalists.

To know more about unitary method  visit:

https://brainly.com/question/28276953

#SPJ1

To find the flat fee for the annual golf pass, we need to find the y-intercept of the linear model. The y-intercept is the point at which the line crosses the y-axis, which in this case represents the flat fee for the annual golf pass.

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept.

We can find the slope of the line using the two points given: (25, 1,167) and (41, 1,407). The slope is (1,407 - 1,167) / (41 - 25) = 240 / 16 = 15.

Now that we know the slope, we can use either of the two points given to find the y-intercept. Let's use the point (25, 1,167). Plugging the values into the equation y = mx + b, we get 1,167 = 15 * 25 + b. Solving for b, we find that b = 1,167 - 15 * 25 = -300.

The y-intercept is -300, so the flat fee for the annual golf pass is $300. The correct answer is therefore D, $807.

Nate's car was filled with 16 gallons of gas.

The concept is used in this is equations. An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. An equation is the set of variables, constants, and mathematical operations like addition, subtraction, multiplication, or division balanced by an equal sign. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic, etc.

As gas is $2. 09 per gallon at the gas station.

$2. 09 → per gallon

and Nate filled up his car and spent $33. 44.

$33. 44 for fully filled → how many gallons ?

So,

33.44 / 2.09 = 16 gallons.

Therefore, Nate filled 16 gallons gas in his car.

To learn more about equations visit : brainly.com/question/1566730

#SPJ4

Answer:

x= 35⁰ - obtuse triangle

Step-by-step explanation:

since the sum of angles of the triangle = 180⁰

(3x-5) + (x+10) + (x) =180⁰

5x+5= 180

(subtracting 5 from both sides)

5x=180-5

5x= 175

(dividing by 5)

x= 35⁰

so the angles of the triangle are

(3x-5) = 105-5= 100⁰

(x+10) = 45⁰

(x) = 35⁰

then this triangle is an obtuse triangle

Answer:

70

Step-by-step explanation:

nk

The area of a square with a length of ((n ^ 3 * m ^ 4)/(nm)) ^ 2 inches is n^6*m^8/(nm)^4.

In geometry, a square is a flat shape with four equal sides and four right angles (90°). A square is an unique sort of parallelogram as well as an equilateral rectangle (an equilateral and equiangular one).

The general formula to find area of square is A=a^2 where is a is length of sides.

The area of a square is given by:

A= l^2 where l is the length

So l= n^3*m^4/(nm)^2

A=l^2= n^6*m^8/(nm)^4

So area of the square is n^6*m^8/(nm)^4.

To learn more about area of square visit the link:

https://brainly.com/question/25092270

#SPJ1

On solving the provided question, by properties of parallel lines we got to know that -  1 - A  2 - C  3 - B  4 - D

When two or more lines cross the intersection line, alternate exterior angles result. These angles are created on a number of sides outside the transverse lines. Any two parallel lines that cross one another create two angles with the horizontal line. In the area between the parallel lines, interior angles are formed, while alternate exterior angles are formed in the area outside the parallel lines.

Matches are -When two parallel lines cross one other, the horizontal line is divided into two angles. Interior angles develop between the parallel lines, whereas alternative outside angles develop outside the parallel lines.

1 - A

2 - C

3 - B

4 - D

To know more about alternate exterior angles visit:

brainly.com/question/2279752

#SPJ1

In 5 years the population will be fewer than 13000.

What is percentage ?

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. Percentage, a relative value showing hundredth parts of any amount, is a relative measure that indicates how many questions on a test you correctly answered out of 100 (75/100). Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified percentage.

20000( 1 - 9% )^5

≈ 12481

12481 < 13000

ie 5 years

To learn more about percentage from the given link  

https://brainly.com/question/24877689

#SPJ4

The margin of error is $148.89. The upper limit is $2215 and lower limit is $1914.

In statistics, confidence is another word for probability. If you create a confidence interval, for instance, with a 95% level of confidence, you can be sure that 95 out of 100 times, the estimate will fall between the upper and lower values indicated by the confidence interval.

First we need to name some of the variables we are given:

n = 38 the sample size

x = 6.88 the sample mean

= 1.86 the population standard deviation

We need to find a 90% confidence interval for the mean price per 100 lbs of watermelon:

= 1-.90 = .10

/2 = .05

z(/2) = -1.64

-z(/2) = 1.64

This can give us a probability expression:

P(-1.645 < z < 1.645) = .90

The margin of error is calculated with the formula: E = z(/2)(/√n)

E = 1.645(1.86/√38) = $.4963(300) = $148.89  

Then to calculate the upper and lower limit we add and subtract E from x:

lower limit = 6.88 - .4963 = $7.38(300) = $2214

upper limit = 6.88 + .4963 = $6.38(300) = $1914

To know more about probability visit:-

brainly.com/question/11234923

#SPJ4

The interquartile range of the data decreases when the eighth day's amount is included in the data is true.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Joanna set a goal to drink more water daily.

The number of ounces of water she drank each of the last seven days is

60, 58, 64, 64, 68, 50, 57

On the eighth day, she drinks 82 ounces of water.

Raw data:      [60,58,64,64,68,50,57,82],

Sorted data:  [50,57,58,60,64,64,68,82]

Sample size = 8 (even)

mean  = 62.875

median  = (60+64)/2 = 62

1st quartile   = (57+58)/2 = 57.5

3rd quartile  = (64+68)/2 =  66

IQR = 66 - 57.5 = 8.5

Data without the eight day's measurement.

Raw data:      [60,58,64,64,68,50,57]

Sorted data:  [50,57,58,60,64,64,68]

Sample size = 7 (odd)

mean            = 60.143

median         = 60

1st quartile   = 57

3rd quartile = 64

IQR = 64 -57 = 7

Hence, the interquartile range of the data decreases when the eighth day's amount is included in the data is true.

To learn more on Statistics click:

https://brainly.com/question/29093686

#SPJ1

Answer: It's just

The interquartile range of the data decreases when the eighth day's amount is included in the data.

Step-by-step explanation: The question asks you to select ALL correct answers, but there is only one correct answer.

The slope-intercept forms for the graphs 5, 6, 7, and 8 are - y = (-1/2)x + 6, y = 50x + 150, y = (10/3)x + 20, and y = 25x respectively.

What is slope-intercept form?

The line with m as the slope, m and b as the y-intercept is the graph of the linear equation y = mx + b. The values of m and b are real integers in the slope-intercept form of the linear equation.

First, find out the y-intercept(s).

The y-intercepts are the starting point of the lines in the graph.

For graph number 5, the starting point is 6.

For graph number 6, the starting point is 150.

For graph number 7, the starting point is 20.

For graph number 8, the starting point is 0.

Now find the slopes.

For graph number 5, the line goes down 1 unit and moves to the right 2 units, so the slope would be -1/2 (rise/run).

For graph number 6, the line goes up 100 units and moves to the right 2 units, so the slope would be 100/2 (rise/run) or 50.

For graph number 7, the line goes up 10 units and moves to the right 3 units, so the slope would be 10/3 (rise/run).

For graph number 8, the line goes up 25 units and moves to the right 1 unit, so the slope would be 25/1 (rise/run) or 25.

Then plug into the slope-intercept form : y = mx + b.

Where, m is slope and b is the y-intercept.

Graph 5: y = (-1/2)x + 6.

Graph 6: y = 50x + 150.

Graph 7: y = (10/3)x + 20.

Graph 8: y = 25x + 0 or y = 25x

Therefore, the equations are - y = (-1/2)x + 6, y = 50x + 150, y = (10/3)x + 20, y = 25x.

To learn more about slope-intercept form from the given link

https://brainly.com/question/19440459

#SPJ1

Answer:

9 ft

Step-by-step explanation:

assuming the 3 was a mistake T'T volume is l x w x h so if the base is l x w then 12 x 14 (168) is the base then divide the volume from the base (1512 / 168) the answer is 9 ft