For the given Augmented Matrix ,the correct option is :
A) The solution set has exactly one element.
The exact solution is x = -25 , y = 2 and z = 2.
Augmented Matrix:
An augmented matrix is a means of solving simple linear equations. Coefficients and constant values of linear equations are represented as matrices called augmented matrices. Simply put, an augmented matrix is a combination of two simple matrices along columns. If the first matrix has m columns and the second matrix has n columns, then the augmented matrix has m + n columns.
Now, as given the Augmented matrix:
[1 7 3 -5]
[0 0 0 3]
[0 0 1 2]
[0 1 -1 4]
From this system we get:
y - z = 4 --------------------------- (1)
z = 2
and, z = 3
and, x + 7y + 3z =-5 ---------------- (2)
Now, Solving the equation with z = 2,
y - 2 = 4
⇒ y = 6
and, putting y = 6 and z = 2
x + 7× 6 + 3×2 = -5
⇒ x + 42 + 6 = -5
⇒ x +48 = -5
⇒ x = -53
Therefore, x = -53, y=6 and z =2
Now, for z = 3 in equation (1)
y - 3= 4
⇒ y = 7
Putting y =7 and z =3, we get:
x + 7 × 7 + 3×3 = -5
⇒ x + 49 + 9 =-5
⇒ x + 58 = -5
⇒ x = -63
Therefore, x = -63, y =7 and z =3
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V=S3
S = 20
Give your answer in simplest form.
Enter
simplest form of equation V= 60
Simplifying a fraction means reducing a fraction to its simplest form. A fraction is in its simplest form if its numerator and denominator have no common factors other than 1.
A 'Simplest Form Calculator' is a free online tool that reduces a fraction to its simplest form. In this calculator, you can enter value and find its simplest form within a few seconds.
V=S3
S = 20
Give your answer in simplest form.
V = S3
V = S× 3
S = 20
Therefor
V = 20 × 3
V= 60
simplest form V= 60
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Do the values in the table represent a proportional relationship?
x 2 3 4 5
y 5 6 7 8
Select from the drop-down menu to correctly complete the statement.
All of the y-values
Choose.
a constant multiple of the corresponding x-values, so the relationship
Choose
Values of x and y in table does not represent a proportional relationship.
From the table x values 2, 3, 4 and 5 corresponds to values of y 5, 6, 7 and 8 respectively. The ratio of x value and y value is
2/ 5 = 0.4
3/ 6 = 0.5
4/ 6 = 2/ 3 ≈ 0.67
5/ 8 = 0.625
As the ratio is not constant, the values in table does not represent a directly proportional.
The value of xy is
2×5 = 10
3×6 = 18
4×7 = 28
5×8 = 40
Again as the value of xy is not constant, so they are not inversely proportionally.
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Gregory(g) is 20 years older than his cousin Mark(m). Mark is 6 years younger than his
sister Louanne(L). Write an expression to represent the sum of their ages.
Answer:
Step-by-step explanation:
Let's make Mark x as he is in both equations.
For Gregory in Marks view = x+20
For Marks's sister Louanne = x-6
Now you just add everything!
> x+x+20+x-6
> 3x+14
The sum of their ages is 3x+14
Hope that helped!
There are 80 oranges and apples, and 5% of them are apples. William takes out some of the oranges, so apple make up 20% of the remaining pieces of fruit. How many oranges did he take out
9y -2x=1 solve for Y
Answer:
y = 1/9 + 2/9x
Step-by-step explanation:
9y - 2x = 1
9y = 1 + 2x (get rid of x)
y = 1/9 + 2/9x (divide 9 on both sides)
the swim team trains 4 days every week. Mon, Tues, and Thurs, the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. how many hours per week does the team train?
The number of hours that the team trains per week is 17 hours.
How to illustrate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
Since the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. The number of hours will be:
( 1 1/4 + 1/2 + 2 1/2) × 4
= 4.25 × 4
= 17 hours.
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Why are 3 4 5 and 5 12 13 Pythagorean triples?
A Pythagorean triple is a set of three positive integers a, b, and c that satisfies the equation a2 + b2 = c2.
In this case, the triple is (3, 4, 5) and (5, 12, 13).
The equation for the first triple is 32 + 42 = 52.
3² = 9
4² = 16
9 + 16 = 25
25 = 25
The equation for the second triple is 52 + 122 = 132.
5² = 25
12² = 144
25 + 144 = 169
169 = 169
Therefore, both sets of numbers are Pythagorean triples because they both satisfy the equation a2 + b2 = c2.
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2 Lauren is using 10 pink beads and 5 black a bracelet. Which beads to decorate ratio compares the number of black beads to the total number of beads She is using?
When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio.
What is ratio?A comparison between two items by means of a number. (arithmetic) comparing two quantities' relative magnitudes (usually expressed as a quotient).
When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls) 40% are girls, and 14% are boys.
Comparing two numbers by dividing them is how ratios work. Your formula would be A/B if you were contrasting one data point (A) with another data point (B). By doing so, you are multiplying information A by information B. Your ratio will be 5/10, for instance, if A is 5 and B is 10.
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If the amount of space between support towers is between 200 and 300 feet, determine the number of towers you will use.
SHOW ALL WORK TO EARN CREDIT.
How do I solve x-5(x-1=x-(2 x-3)
Answer:
x = 2/3
Step-by-step explanation:
x - 5(x - 1) = x - (2x - 3)
x - 5x + 5 = x - 2x + 3
-5x + 5 = -2x + 3
-3x = -2
x = 2/3
According to a Harris poll, 5% of U.S. adults admitted to having spent money gambling online. If a U.S. adult is selected at random, what is the probability that he or she has never spent any money gambling online
If a U.S. adult is selected at random, the probability that he or she has never spent any money gambling online is 95.
What is gambling?Gambling, the betting or staking of something of value, with consciousness of risk and hope of gain, on the outcome of a game, a contest, or an uncertain event whose result may be determined by chance or accident or have an unexpected result by reason of the bettor’s miscalculation.
Given that there was a 5 probability of U.S. adults admitted to having spent money gambling online.
We have to find the probability of a U.S. adult selected randomly that he or she has never spent any money gambling online.
We will assume the probability of the outcome which is known as P(E) and the probability of the outcome which we need to know as , P(E) since both are the complement of each other. Then we will substitute the value of P(E) in the formula compliment of P(E)= 1-P(E) so as to obtain compliment of P(E)
Given that there was a 5 probability of U.S. adults admitted to having spent money gambling online, therefore
P(E) =5
P(E)= 5/100
=0.05
The probability of a U.S. adult selected randomly that he or she has never spent any money gambling online will be given as compliment of P(E) , such that
compliment of P(E)= 1-P(E)
=0.95
= 0.95/100
=95
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Find three consecutive positive integers such that the product of the median and largest integer is 8 times the sum of the smallest and largest interger.
The positive integers are 14, 15 and 16
What is an algebraic expression?
An algebraic expression can be defined as an expression that is made up of coefficients, terms, variables, factors and constants.
From the given information, we have that;
Let the consecutive integers be;
x, x+ 1, x+ 2
This can be represented as;
(x+1)(x+2) = 8(x + x+ 2)
Now, expand the bracket
x² + 2x + x + 2 = 8(2x + 2)
x² + 3x + 2 = 16x + 16
collect like terms
x² + 3x - 16x + 2 - 16 = 0
Add or subtract like terms
x² - 13x - 14 = 0
Solve the quadratic equation
x² -14x + x - 14 = 0
factor in pairs
x(x- 14) + 1(x -14) = 0
Then,
x = -1
x = 14
Take 'x' as 14
smallest integer = 14
Median = 14 + 1 = 15
Largest integer = 16
Hence, the values are 14, 15 and 16
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How do you know if 3 measures can make a triangle?
To determine if three measures can make a triangle, use the Triangle Inequality Theorem. This theorem states that the sum of any two sides of a triangle must be greater than the measure of the third side.
for example
side 1 = 6
side 2 = 8
side 3 = 10
6 + 8 = 14 > 10,
therefore the three sides can make a triangle.
1. Gather the three measures of the triangle.
2. Add the two smallest side lengths together.
3. Compare the sum of the two smallest sides to the longest side.
4. If the sum of the two smallest sides is greater than the longest side, then the three measures can make a triangle.
5. If the sum of the two smallest sides is not greater than the longest side, then the three measures cannot make a triangle.
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Does 4 8 and 12 make a triangle?
No, 4, 8, and 12 are not valid side lengths for a triangle. So 4, 8 and 12 does not make a triangle.
In order for a shape to be a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality theorem.
If a triangle has sides of length 4, 8, and 12, then the triangle inequality theorem would be:
8 + 12 > 4 (true, as 8+12 =20)
12 + 4 > 8 (true, as 4+12=16)
4 + 8 > 12 (false, as 4+8 =12)
Since 4 + 8 = 12, and 12 is not greater than 4 or 8, a triangle cannot be formed with sides of length 4, 8, and 12.
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Decompose one number to subtract 726-340
The subtraction of the given number would be = 386
What is subtraction?Subtraction is defined as one of the major arithmetic operations that is used to remove a value from another given values.
The subtraction of the value 340 from 726 would be = 386.
That is; 726 - 340 = 386
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For the interval estimation of μ when σ is assumed known, the proper distribution to use is the_____. a. standard normal distribution b. t distribution with n degrees of freedom c. t distribution with n − 1 degrees of freedom d. t distribution with n − 2 degrees of freedom
When estimating a population mean (μ) with a known population standard deviation (σ), the proper distribution to use is the standard normal distribution. So, correct option is A.
This is because the sampling distribution of the sample mean follows a normal distribution when the population standard deviation is known. The central limit theorem guarantees that the sample mean will be normally distributed with mean μ and standard deviation σ/√n, where n is the sample size.
The formula for constructing a confidence interval for μ when σ is known is:
CI = x' ± zα/2 * (σ/√n)
where x' is the sample mean, zα/2 is the z-score corresponding to the desired confidence level (α), σ is the population standard deviation, and n is the sample size.
Since the standard normal distribution has a mean of 0 and a standard deviation of 1, we can use z-scores to find the appropriate values for zα/2. This is why the standard normal distribution is used for interval estimation when σ is known.
In summary, the standard normal distribution is used for interval estimation of μ when σ is known because the sampling distribution of the sample mean is normally distributed when the population standard deviation is known.
So, correct option is A.
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Help with these questions pls
The description of isometry and transformations is as follows,
isometry mean A distance-preserving transformation between metric spaces is known as isometry, congruence, or congruent transformation.
What is transformations?The transformation, or f, is a function that maps to itself: X X. Following the transformation, the pre-image X transforms into the image X. Any or all of the operations like translation, rotation, reflection, and dilation can be used in this transformation. A function is translated by moving it in a particular direction, rotated by spinning it about a point, reflection by reflecting the function, and dilation by scaling it.
Isometry: If two distinct points, a and b, were to be mapped to the same point, then the coincidence axiom of the metric d would be violated. This proof is similar to the proof that an order embedding exists between partially ordered sets. Clearly, a topological embedding exists for each and every isometry between metric spaces.
A bijective isometry is a global isometry, isometric isomorphism, or congruence mapping. A global isometry, like any other bijection, has a function inverse. A global isometry is also the inverse of a global isometry.
Types of transformations;
Transformation of Reflection: The term "reflection" refers to the kind of transformation that takes place when every point in the shape is reflected over a line. The image is on the opposite side of the line from the pre-image but at the same distance from the line when the points are reflected over it. An image point (q,p) is reflected from each point (p,q).
Transformation of Rotation: Rotation is the transformation that rotates each point of the shape by a predetermined number of degrees around that point. When the number of degrees is positive, the shape rotates counterclockwise, and when the number of degrees is negative, the shape rotates clockwise.
Transformation of Translation: Sliding occurs when a 2-d shape is translated. Let's look at how the vertices of the blue and red figures are positioned in relation to one another in order to describe their relative positions. By comparing its position to the positions of A, B, and C, we must determine their positions.
Hence the basic description of transformation is as follows.
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Julia needs to order some new supplies for the restaurant where she works. The restaurant needs at least 316 glasses. There are currently 286 glasses. If each set on sale contains 6 glasses, use the drop-down menu below to write an inequality representing ss, the number of sets of glasses Julia should buy.
The inequality representing s, the number of sets of glasses Julia should buy is 286 + 6s ≥ 316.
How to illustrate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
Since Julia needs to order some new supplies for the restaurant where she works. The restaurant needs at least 316 glasses. There are currently 286 glasses. If each set on sale contains 6 glasses, the number of sets will be:
286 + 6s ≥ 316
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he distance traveled is three times the number of hours I have hiked. The independent variable is hours. The dependent variable is distance.b.The distance traveled is three times the number of hours I have hiked. The independent variable is distance. The dependent variable is hours..c.The hours I have hiked is three times the distance. The independent variable is distance. The dependent variable is hours.d.The hours I have hiked is three times the distance. The independent variable is hours. The dependent variable is distance.
The option a "The distance traveled is three times the number of hours I have hiked. The independent variable is hours. The dependent variable is distance." is correct.
In the given question, we have to write a statement that describes how the distance that you travel is determined. Then identify the independent and dependent variables of this function.
As we know that the distance formula is the multiplication of of speed and time.
So, the distance traveled is three times the number of hours I have hiked. The independent variable is hours. The dependent variable is distance.
So the option a is correct.
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The complete question is:
The distance you travel while hiking is a function of how fast you hike and how long you hike at this rate. You usually maintain a speed of three miles per hours while hiking. Write a statement that describes how the distance that you travel is determined. Then identify the independent and dependent variables of this function.
a. The distance traveled is three times the number of hours I have hiked. The independent variable is hours. The dependent variable is distance.
b. The distance traveled is three times the number of hours I have hiked. The independent variable is distance. The dependent variable is hours.
c. The hours I have hiked is three times the distance. The independent variable is distance. The dependent variable is hours.
d. The hours I have hiked is three times the distance. The independent variable is hours. The dependent variable is distance.
Write an equation for the nth term of the geometric sequences. Then Find a6
A. 2, 8, 32, 128,.
B. 0. 6, -3, 15, -75,.
C. -1/8, -1/4, -1/2, -1,.
D. 0. 1, 0. 9, 8. 1, 72. 9,
We want to find an equation and the sixth term of the given geometric sequence.
The equation is: [tex]a_{n} = 4*a_{n}-1[/tex] and the sixth term is equal to 512
What is Geometric sequence?In a geometric sequence, each term is a constant times the previous term, so the general relation is:
[tex]a_{n} = k*a_{n}-1[/tex]
Here we can use any pair of consecutive terms to find the value of the constant, for example, if we use the first two, we have:
[tex]8 = k*2\\8/2 = 4 = k[/tex]
Now we know the value of the constant, then the general formula is: [tex]a_{n} = 4*a_{n}-1[/tex]
Now we can use this to get the sixth term:
[tex]a_{6} = 4*a_{5}-1=4*128 = 512[/tex]
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Find the slope from the pair of points (-4,-5) and (4,5)
Daria chooses a paint color from 5 shades of blue, 2 shades of yellow, and 2 shades of purple to paint her room. She can choose either carpet or wood flooring. If each choice is equally likely, how much greater is the probability of her choosing a shade of blue and carpet than the probability of choosing a shade of yellow and wood flooring?
The probability of choosing a shade of blue and carpet is 1/6 greater than that of choosing a shade of yellow and wood flooring.
The total number of possible paint colors Daria can choose is 5 shades of blue + 2 shades of yellow + 2 shades of purple = 9 shades
The total number of flooring options Daria can choose from is carpet or wood = 2 options
The probability of choosing a shade of blue is 5/9 and the probability of choosing carpet is 1/2. So, the probability of choosing a shade of blue and carpet is (5/9) * (1/2) = 5/18.
The probability of choosing a shade of yellow is 2/9 and the probability of choosing wood flooring is 1/2. So, the probability of choosing a shade of yellow and wood flooring is (2/9) * (1/2) = 2/18
The probability of choosing a shade of blue and carpet is 5/18, and the probability of choosing a shade of yellow and wood flooring is 2/18. So, the probability of choosing a shade of blue and carpet is (5/18) - (2/18) = 3/18 or 1/6 greater than the probability of choosing a shade of yellow and wood flooring.
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Find the missing length and area of each figure
LM = √(8² + 6²) = √(64 + 36) = √100 = 10 yd
Area = 2 × (1/2) × 6 × 8 = 48 yd²
Which triangle is triangle MNO similar to and why?
Answer:
triangle GHK
Step-by-step explanation:
angles add up to 180
angle N + angle M + angle O = 180
79 + 22 + angle N = 180
180 - 79 -22 = angle N = 79
triangle GHK has 2 of the same angles (79 and 79), so that is our answer
5. QRST is a Rhombus. The diagonals intersect at point 0. mZROS = 7x1, mzSTO= 4x - 22, QT = 4y + 2, ST = 8y-8 R T S X= y = mZTOQ = mzQRS = Perimeter QRST=_
The value of x is 18.45°.
The value of y is 2.5 units.
The measure of the angle TOQ is 128.15°.
The measure of the angle QRS is 90°.
The perimeter of QRST is 36 units.
What is a rhombus?A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal.
Given, m∠ROS = 7x - 1, m∠STO= 4x - 22.
We know the sum of linear pair of angles is 180°.
Therefore,
7x - 1 + 4x - 22 = 180.
11x = 203.
x = 203/11.
x = 18.45°.
Also given that line segment QT = 4y + 2 and ST = 8y - 8.
We know the sides of a rhombus are of equal length.
Therefore,
4y + 2 = 8y - 8.
- 4y = - 10.
4y = 10.
y = 10/4.
y = 2.5.
We know vertically opposite angles are equal hence m∠ROS = m∠TOQ.
= 7(18.45) - 1.
= 128.15°.
m∠QRS is 90° as all four interior angles of a rhombus are right angles.
The perimeter of QRST is 4×(QT).
= 4×(10 + 2).
= 4×12.
= 36 units.
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Angle AOB is a central angle with a measure of 110 degrees.
What is the measure of its arc AB?
The most accurate value for AB is 37.699111843077516 (approximately)
How to measure arc?The measure of an arc is directly related to the measure of the central angle that intercepts it. The measure of an arc is equal to the measure of its central angle, multiplied by the radius and divided by the degree of the circle.
Since, radius is not given let's assume it 20.
In this case, the central angle AOB has a measure of 110 degrees, and the radius of the circle is 20. Therefore, the measure of the arc AB is:
AB = (110/360) * 20 * 2 * π
or
AB = (110/360) * 20 * π
where π is the mathematical constant (approximately equal to 3.14).
So, the measure of the arc AB is (110/360) times the circumference of the circle, or (110/360) of the total length of the circumference.
The most accurate value for AB is 37.699111843077516 (approximately)
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Find the area of the fairway between two streams on a golf course.
Area =
yd2
Question 2
Explain how the fairway could be separated into figures whose areas you can find using formulas.
You could separate the figure into a trapezoid and a _____
A. Triangle
B. Square
Please do a step by step explanation
Question 1
The area of the fairway between two streams on a golf course cannot be determined without additional details such as the dimensions or measurements of the fairway and the streams.
Question 2
A. Triangle
THE FAIRWAYTo find the area of the fairway, you could separate it into figures whose areas you can find using formulas.
Step 1: Draw a diagram of the fairway, including the two streams and any other relevant features such as bunkers or trees.
Step 2: Divide the fairway into two sections, one on either side of the streams.
Step 3: Measure the width and length of each section of the fairway.
Step 4: Use the formula for the area of a rectangle to find the area of each section. (Area = width x length)
Step 5: Add the areas of the two sections together to find the total area of the fairway between the two streams.
THE TRAPEZOIDThe base of the trapezoid would be the width of the fairway and the width of the stream, and the height would be the distance between the fairway and the stream. The area of a trapezoid is (a+b)h÷2, where a and b are the lengths of the bases and h is the height. The triangle would be formed by the side of the trapezoid that is the distance between the fairway and the stream, and the width of the stream. The area of a triangle is base×height÷2.
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The two smaller angles of a right triangle have equal measures. find the measure of all three angles.
Answer:
Step-by-step explanation: Because all three angles of the triangle must equal to 180 degrees, the two smaller angles of the right triangle must be 45 degrees. This is because a right angle always is 90 degrees and because you know that the other two angles are the same, and it must all equal to 180, the angles must be 45 degrees, 45 degrees, and 90 degrees.
Angle 1: (right angle) 90 degrees
Angle 2: 45 degrees
Angle 3: 45 degrees
A figure made by two intersecting lines or two rays extending from the same point.
A figure made by two intersecting lines or two rays extending from the same point is called an angle.
What is an angle?
Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays. Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.
A figure made by two intersecting lines or two rays extending from the same point is called an angle.The character ∠ is used to represent it. Angles are frequently expressed in degrees and radians, a unit of circularity or rotation. We encounter angles frequently in life.
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a survey was given to people who own a certain type of car. what percent of the people surveyed were completed satisfaction with the car?
The percent of the people surveyed who were completed satisfaction with the car will be 48%.
How to calculate the percentage?A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100. The percentage then refers to a component per hundred. The word percentage simply means per 100 and it is represented by %.
In this case, a survey was given to people who own a certain type of car. 24 out of 50 stated that they were satisfied with the car.
The percent of the people surveyed were completed satisfaction with the car will be:
= 24 / 50 × 100
= 48%
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Complete question
A survey was given to people who own a certain type of car. 24 out of 50 stated that they were satisfied with the car. what percent of the people surveyed were completed satisfaction with the car?