x² + 4x + 4, this is a perfect square trinomial, which is expressed as
(x + 2)²
What is trinomial?Trinomials are algebraic formulas that include three dissimilar terms, therefore the name "trinomial."
An algebraic expression called a trinomial contains three terms that are non-zero. Trinomial expression illustrations: The trinomial x + y + z has three variables: x, y, and z.
A trinomial is formed when three monomials are added together or subtracted from one another. A quadratic trinomial has the following form: ax² + bx + c, where a, b, and c are real, non-zero values.
Given that,
x² + 4x + 4
= (x)² + 2(2x) + 4
= (x)² + 2(x)(2) + 2²
This is similar to a² + 2ab + b² = (a + b)²
so, we can write:
= (x + 2)²
= (x + 2) (x + 2)
so, this is a perfect square trinomial.
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PLEASE HELP!!! WILL AWARD BRAINLIEST!!!
Use the box plots comparing the number of males and number of females attending the latest superhero movie each day for a month to answer the questions.
Top data set labeled males, minimum at 1, Q1 at 3, median at 11, Q3 at 14, maximum at 21, and an outlier at 30.
Bottom data set labeled females, minimum at 0, Q1 at 15, Median at 18, Q3 at 21.
Part A: Estimate the IQR for the males' data. (2 points)
Part B: Estimate the difference between the median values of each data set. (2 points)
Part C: Describe the distribution of the data and if the mean or median would be a better measure of center for each. (4 points)
Part D: Provide a possible reason for the outlier in the data set. (2 points)
Use the box plots comparing the number of males and number of females attending the latest superhero movie each day for a month to answer the questions
The estimated IQR for the males dataset is 24 , the estimated difference between median value of each dataset is 14.
What is median ?
The median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution in statistics and probability theory. It can be regarded as "the middle" value for a set of data.
When a dataset is ordered, the median value is the one that appears exactly in the middle of the dataset. Depending on whether you have an odd or an even number of data points, there are different processes to take when calculating the median.
In a collection of numbers, the median is the value in the middle. A series of numbers must first be sorted, or arranged, in value order from lowest to highest or highest to lowest in order to find the median value.
A. IQR for male dataset
The IQR is calculated as follows:
IQR = Q3 - Q1
=
For the male's data:
IQR = Q3 - Q1
= 25 - 1
= 24
Hence, the IQR of the male dataset is 24.
B. Difference in median values
We have:
median = 20 ----- Male dataset
median = 6 ----- Female dataset
So, the difference (d) is:
d = 20 - 6
= 14
Hence, the difference in median of both dataset is 14.
C. Best measure of center
The female box plot has an outlier. This means that the measure of center to use for the female dataset is the median.
The male box plot has no outlier; this means that the mean can be used as a measure of center for the male box plot
D. Reason for outlier
There are several reasons that could cause an outlier in a dataset. One of the reasons is human error during data entry.
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A rope is fixed between two trees that are 10 metres apart. When a child hangs on to the centre of the rope, it sags so that the centre is 2 metres below the level of the ends. Find the lenth of the rope.
The length of the rope is 2√29 meters.
What is an isosceles triangle?
An isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and skelos are the source of the name (leg). An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal.
Given that the distance between two trees is 2 meters. A boy hangs on a rope tied to the trees in the middle of the rope.
it sags so that the center is 2 meters below the level of the ends.
Thus it forms an isosceles triangle. △ACD and △BCD are two right triangles.
Since △ABD is isosceles triangle and AD = BD.
In △ACD, Hypotenouse = AD, Base = AC = 10/2 = 5 cm, Height = CD = 2 meters
Apply Pythagorean theorem on △ACD:
AD² = AC² + CD²
AD² = 5² + 2²
AD² = 29
AD = √29
Therefore, BD = √29
The length of the rope is AD + BD = 2√29 meters.
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janes is 2 mi offshore in a boat and wishes to reach a costal village 6 mi down a straight shoreine from the point nearest ht eboat
Jane should land 1.5 mi down the shoreline and walk the remaining 4.5 mi to the village to minimize her travel time.
Let x = distance travelled along the shore over water.
Then, 6 − x = distance travelled along the shore over land.
Let T = the total time taken to reach the destination.
T = distance/velocity = √(4 + x²)/3 + (6-x)/5 on [0, 6].
Note that T must be non negative and that x = 6 means the destination
is reached solely by rowing and without the benefit of faster land
travel. In actual fact, T is valid over [0, ∞) but [0, 6] is reasonable here.
T' = x/3√(4 + x²) - 1/5 = 5x - 3√(4 + x²) = 0
⇒5x = 3√(4 + x²)
⇒25x² = 9(4 + x²)
⇒16x² = 36
⇒x = ±6/4 = ±1.5
The negative x value is discarded since it does not belong to [0,6].
T(0) = 28/15 = 1.8667
T(1.5) = 1.733
T(6) = 2.1082
Therefore, Jane should land 1.5 mi down the shoreline and walk the
remaining 4.5 mi to the village to minimize her travel time.
Her minimum travel time will be T(1.5) = 1.733 hrs. or 1hr 44 min.
--The given question is incomplete, the correct question is
"Jane is 2 mi, offshore in a boat and wishes to reach a coastal village 6 mi, down a straight shoreline from the point nearest the boat. She can row at 3mph and can walk at 5 mph. Where should she land her boat to reach the village in the least amount of time?"--
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i don’t know this pls help
The perimeter of the right triangle is 228 inches
What is a right-angle triangle?
It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
The complete length of a shape's edge serves as its perimeter in geometric terms. Adding the lengths of all the sides and edges that surround a form yields its perimeter.
Since it is a right triangle,
c² = 57² +76²
c² = 3249 + 5776
c² = 9025
c= √ 9025 = 95
Perimeter is the sum of all sides
Perimeter = 57+76+95 = 228 inches
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If QS is the ANGLE bisector, solve for x
Question setup: x over 18 = 45 over 20
Solving for x in the angle bisector which resulted to the proportion x over 18 = 45 over 20 results to x = 40.5
What are angle bisectors as used in geometry?In geometry, a line that divides an angle into two equal angles is referred to as an angle bisector.
By definition, a bisector is something that divides an object or a shape into two equal parts. A ray is said to be an angle bisector if it divides an angle into two equal portions of the same measure.
The division from angle bisectors gave rise to the proportion which is given by
x / 18 = 45 / 20
cross multiplying
x = 18 * 45 / 20
x = 40.5
hence x is solved to get 40.5
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X denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose that for banner-tailed kangaroo rats, X has an exponential distribution with parameter λ = 0. 1342. (a) What is the probability that the distance is at most 100 m? At most 200 m? Between 100 and 200 m? (Round your answers to four decimal places. ) at most 100 m at most 200 m between 100 and 200 m (b) What is the probability that distance exceeds the mean distance by more than 2 standard deviations? (Round your answer to four decimal places. ) (c) What is the value of the median distance? Hint: Find a such that P(X≤a)= 0. 50 (Round your answer to two decimal places. ) m
The probability that the distance is at most 100m is 0.749926 and at most 200 m is 0.9375 between 100 and 200 m is 0.1876 and the probability that distance exceeds the mean distance by more than 2 standard deviations is 0.04979
What is Probability ?
probability can be defined as the ratio of the number of favourable outcomes and the total number of outcomes.
We are given with an exponential distribution with
λ=0.01386.
The probability distribution function is:
F(x)=λ * e power (−λx)
Cumulative distribution function is
F(x) = 1- e power (−λx)
The mean of the exponential distribution function
E(X) = 1 / λ
= 1/0.01386
= 72.15
Hence, E(X) = 72.15
The variance of the exponential distribution function
V(X) = 1 / λ ^{2}
= 1/0.01386*0.01386
= 5205.63
V(X) = 5205.63
Probability that the distance is at most 100m
P(X <= 100 ) = F (100)
= 1- e power (−λx)
= 1 - e power (-0.01386*100)
= 1- e power (-1.386)
= 1-0.25007
= 0.749926
Therefore, P(X<=100) = 0.749926
probability that the distance is at most 200m
P ( X<= 200) = F(200)
=1-e power (−λx)
=1-e power (-0.01386*200)
= 1 - e power (-2.772)
= 1-0.06253
= 0.9375
P(X<= 200) = 0.9375
Probability that the distance is between 100 and 200m
P(100<= X <= 200) = F(200) - F(100)
= 0.9375-0.7499
=01876
P(100 <= X <= 200) = 0.1876
Probability that the distance exceeds the mean distance by more than 2 standard deviation.
P( X + P>μ+2σ) = P(X>72.15+2√5205.63)
= P(X > 72.15 +144.3)
P(X>216.45)
= 1-P(X<= 216.45)
1 - (1- e power (-0.01386*216.45)
= e power (-2.9999)
= 0.04979
P( X + P>μ+2σ) = 0.04979
Hence , The probability that the distance is at most 100m is 0.749926 and at most 200 m is 0.9375 between 100 and 200 m is 0.1876 and the probability that distance exceeds the mean distance by more than 2 standard deviations is 0.04979
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How to find a side length of a right triangle with an angle and a side?
Using trigonometric functions, we can find a side length of a right triangle with an angle and a side.
What is the trigonometric ratio?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).
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Identify the term(s), coefficient(s), and
constant(s) in the expression
52 + 6 + ya.
Term(s) Coefficient(s) Constant(s)
In the expression 52 + 6 + ya,
"ya" is a term,The coefficient of "ya" is 1,"52" and "6" are constants.Describe Term(s), Coefficient(s), Constant(s).The terms are the individual parts of the expression that are being added together. The coefficient is the numerical factor that is multiplied by a variable in a term, and the constant is a term that has no variable.
Any expression with variables will either add or delete one or more variables. Any one of a variety of numbers to represent a generic idea. An absolute number is a constant. A constant is a number, whereas a coefficient is a number that is "in front of" a variable.
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What is the perimeter of ^AEB? 16.4 ft 18.5 ft 18.7 ft 22.9 ft
The perimeter of ΔAEB is 18.5 feet.
What is Triangle Proportionality theorem?A triangle's other two sides are divided in the same proportion if a line drawn parallel to either one of its sides intersects the other two sides at two different spots.
As, side AB║DF hence we will use Triangle Proportionality theorem to calculate the length of side AE.
Since, AE/AD = EB/ BF
AE/2 = 7.2/8.4
AE = 6.5 feet
So, the perimeter of ΔAEB is
= AE + EB + BE
=6.5+4.2+7.8
=18.5 ft.
Hence, the perimeter is 18.5 feet.
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Please help quickly
ES=____ units.
Round your answer to the nearest tenth.
ES is 8√2 units from the given graph.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The given two points from the graph are S(4, 4) and E(-4, -4)
We need to find ES which means the distance between two points in units.
The length along a line or line segment between two points on the line or line segment.
Distance=√(x₂-x₁)²+(y₂-y₁)²
√(-4-4)²+(-4-4)²
√(-8)²+(-8)²
√64+64
√64×2
8√2 units.
Hence, ES is 8√2 units from the given graph.
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Karina is designing a logo on a coordinate plane. The logo is a square whose area is 200200200 square units. She places a circle in the middle of the logo centered at (0,0)(0,0)(, 0, comma, 0, ). The circle passes through the point (6.3,1.6)(6.3,1.6)(, 6, point, 3, comma, 1, point, 6, ). Approximately what percentage of the logo does the circle cover
Approximately 66(2s f) percentage of the logo does the circle cover.
What is percentage?
A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.
To find the percentage we must first find the area of the circle:
We can find the radius of the circle using the distance formula;
⇒ [tex]d=\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]
⇒ [tex]r = \sqrt{(6.3-0)^2+(1.6-0)^2}[/tex]
⇒ r = 6.5
Now we calculate the area;
⇒ [tex]A = \pi r^2[/tex]
⇒ [tex]A = \pi (6.5)^2[/tex]
⇒ [tex]A = \frac{169}{4} \pi[/tex]
To get the percentage we divide the area of the circle by the square’s are and multiply by 100;
⇒ Percentage = [tex]\frac{42.25*\pi }{200}*100[/tex]
⇒ Percentage = 66(2s f)
Hence, approximately 66(2s f) percentage of the logo does the circle cover.
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A spinner is divided into 7 equal regions, numbered 9 through 15. An arrow is spun and lands on one of the numbers. Which of the following best describes the probability of the arrow landing on a number that is greater than 13?
A.
0.143
B.
0.286
C.
0.429
D.
0.571
Therefore , the solution of the given problem of probability comes out to be P =0.286(approx).
Define probability.Probability is the likelihood or potential for something to event. For instance, there is only one way to get a head and a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2. (a head or tail). P(heads) must equal 12. Classical: (equally likely results) (equally probable outcomes) S, the sample location (the collection of all distinct outcomes that could occur), Definition of Relative Frequency and Subjective Probability.
Here,
Given : S = {9,10,11,12,13,14,15}
If A is a subset of S, A could be {14,15}.
If a subset A represents the complement of spinning a number greater than 13, its sample space is A = {14,15}.
Thus,
To find the probability that it will land on number greater than 13
P = likelihood of event / total no of events
=> P = 2/7
=> P = 0.2857
=> P =0.286(approx)
Therefore , the solution of the given problem of probability comes out to be P =0.286(approx).
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20 workers can paint a building in 21 days. If work has to be finished in 15 days, find the number of extra workers required.
Step-by-step explanation:
20 workers finish work in 21 days.
the necessary work effort is 20×21 = 420 workdays.
the same effort is needed even if the overall time is shorter.
x workers in 15 days.
x × 15 = 420
x = 420/15 = 28 workers.
so, 28-20 = 8 additional workers are needed to finish the work in 15 days.
What type of line is Y 0?
If the value of y = 0, then it make the straight line on the graph.
The term graph in math is defined as the way that is used to represent a set of data to make it easier to understand and interpret statistical information.
Here we have the expression y = 0.
And here we know that the y coordinate is constant which is 0 for given equation and only x coordinate is variable.
Therefore it represent the x-axis.
Therefore, basically y=0 is the linear equation to denote the x - axis, here as all the points on the x- axis, then we have their y co-ordinate = 0.
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What is the domain and range of the function f/x )= log x?
The domain of the function f(x) = log x is (0, ∞). The value of x belongs to (0, ∞).
What is a logarithm?
The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.
The given function is f(x) = log x.
When the value of x is less than or equal to 0, then the value of log x is undefined.
The possible value of x where f(x) exists is the domain of a function.
In the given function the value of x must be greater than zero.
The domain of the function is (0,∞).
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Calculate the size of angle ABC
Therefore , the solution of the given problem of trigonometry comes out to be B = arcsin(9/14) - 180° = 140.0°.
Describe trigonometry.Correlations between triangles' angles and sides are studied in the branch of mathematics known as trigonometry. Since every straight-sided form may be reduced to a collection of triangles, trigonometry can be found throughout geometry. The relationships between trigonometry and other branches of mathematics, in particular calculus, real or complex, infinite series, logarithms, and infinite series, are astonishingly complicated.
Here,
There are two potential solutions because the supplied angle is opposite the given side that is the shortest.
Using the sine law,
B = b/asin(A)arcsin(9/7sin(30°))arcsin(9/14)
Angle B may take on the following values:
B is equal to arcsin(9/14) = 40.0°.
B = arcsin(9/14) - 180° = 140.0°
Therefore , the solution of the given problem of trigonometry comes out to be B = arcsin(9/14) - 180° = 140.0°.
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Choose the best description of the data used to generate this histogram (note that the horizontal axis has no scale, so you will make your choice based solely upon the histogram's shape): OSAT Math scores of 1,000 future engineers and scientists. O Results of rolling a six-sided die 1,000 times. Cholesterol levels of 1,000 adults. O Shoe sizes of 1,000 men and women. O Prices of 1,000 California homes. * That is not quite right. The bulk of the SAT Math scores of engineers and scientists would be high scores, since people interested in those fields are usually good at math. So that distribution would be skewed left. Please try again.
On solving the provided question we can say that so the value of the data from histogram graphs will be x [tex]\alpha[/tex] 0.123 * 125 / 100 = 0.15375
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle
the best way to describe the data that was used to create this histogram (keep in mind that there is no scale on the horizontal axis, so you must choose based simply on the appearance of the histogram graphs
so the value of the data from histogram graphs will be
z = 0.123
u = 100
x = 125
x [tex]\alpha[/tex] 0.123 * 125 / 100 = 0.15375
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Diaz has a company car that allows him to drive up to 1,500 miles each month. He averages 28 miles each day. The remaining miles for this month can be calculated using the formula m = 1500 - 28d where m is the remaining miles and d is the is the number of days driven this month. Which of the following statements is true?
The remaining miles are 660 miles.
This month, Diaz drives 28 miles each day using the car allotted to him by his company.
But the company allows him to drive up to 1500 miles each month by his car.
To calculate the remaining miles that Diaz has not traveled this month, we have to use the formula m = 1500 - 28d, where d is the number of days in that particular month.
A month general consists of 30 days.
So, this month Diaz has traveled 28×30 miles = 840 miles ( using multiplication)
Therefore, the remaining miles(m) that Diaz has not traveled this month comes to 1500 - 840 = 660 miles.
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The complete question is:
Diaz has a company car that allows him to drive up to 1,500 miles each month. He averages 28 miles each day. The remaining miles for this month can be calculated using the formula m = 1500 - 28d where m is the remaining miles and d is the number of days driven this month. What are the remaining miles?
Find an order pair (x,y)that is a solution to the equation
2x+y=3
Answer:
(2, -1)
Step-by-step explanation:
2(2)+ (-1) = 4-1 = 3.
The dollar value v(t) of a certain car model that is t years old is given by the following exponential function.
v (t)=20,000 (0.86)'
Find the value of the car after 4 years and after 10 years.
Round your answers to the nearest dollar as necessary.
Value after 4 years:
Value after 10 years:
Answer:
4 years: $10,94010 years: $4,426Step-by-step explanation:
Given the value function v(t) = 20000·0.86^t, you want the value after 4 years and 10 years.
EvaluationPut the value of t in the formula where t is, and do the arithmetic.
The attached calculator output tells us ...
value after 4 years: $10,940
value after 10 years: $4,426
__
Additional comment
When you are asked to do the same evaluation with different numbers, it is convenient to process them as a list, or using a spreadsheet.
Ash and her 2 friends went to dinner. If the bill was $124.72, and they left an 18% tip, how much did each person pay
Each person will pay $49.056. The value must be divided by the entire value, and the resulting number must then be multiplied by 100 to get the percentage.
Which percentage is it?A percentage, often known as percent, is a division by 100. Percentage, which meaning "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.
Amount of bill = $124.72
and tip they left = 18% of $124.72
total amount is =$124.72 + $124.72*18%=$147.1696
so, each person pay= $147.1696/3=$49.056
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what is the x and y of this equation 5x+7=6x+4
The value of x will be; x = 3
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given that the equation 5x+7=6x+4
Here, we need to solve for x;
5x+7=6x+4
combine the like terms;
5x - 6x = -7 +4
-x= - 3
x = 3
Therefore, the solution will be as;
x = 3
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Solve the following equation. Then place the correct number in the box provided 7x-2<10
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]
What is the domain of the function f/x )= log?
The domain of the given function would be x > 0.
What is a function?
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
The function f(x) = log is the natural logarithm function, also known as ln(x). The domain of this function is the set of all positive real numbers x such that x > 0, because the natural logarithm of a non-positive number is undefined.
Hence, the domain of the given function would be x > 0.
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The domain of the given function would be x > 0.
What is a function?
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
The function f(x) = log is the natural logarithm function, also known as ln(x). The domain of this function is the set of all positive real numbers x such that x > 0, because the natural logarithm of a non-positive number is undefined.
Hence, the domain of the given function would be x > 0.
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Find the x-intercept and y-intercept
from the following linear equation:
12x + 30y = 180
x - intercept = ()
y - intercept ()_
Answer:
x - intercept = (15, 0)
y - intercept = (0, 6)
Step-by-step explanation:
x-int. is when y = 0
y-int. is when x=0
Plug in y = 0 and x = 0 to get intercepts.
FOR X-INT.:
12x + 30(0) = 180
12x = 180
x = 15
x-int. is (15, 0)
FOR Y-INT. :
12(0) + 30y = 180
30y = 180
y = 6
y-int. is (0, 6)
What is the plotting method?
Plotting method is the graphical representation of mathematical expression.
What is mean by plotting?A plot is a graphical representation of a list of data. Besides, a plot is the graphical analysis of mathematical expressions and equations because plot can show the relationship between two or more variables. There are many plotting methods such as hand plotting method, computer aided plotting method and so on.
What are the steps of plotting method?At first, we need to choose the coordinate system by which we plot the point.
suppose we choose a XY coordinate plane. At first identify the horizontal or X axis and vertical or Y axis.
besides, we need to determine the required value that will be plotted on the plan.
if we have a list of X and Y value then find the value of X on the x axis and next find the value of Y on the Y axis.
we will notice some points for every pair of x and y value. Finally, we will join the points to achieve a required shaped graph.
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The surface area of a sphere with the radius r is 4 pi r^2. Including the area of its circular base, what is the total surface area of a hemisphere with the radius 6 cm? Express your answer in terms of pi.
The total surface area of the hemisphere is 108 pi cm^2.
Surface area is the amount of space covering the outside of a three-dimensional shape. We calculate the surface area for three dimensional objects. The surface area of a 3-D object is not same as its volume.
The surface area of a sphere with the radius r is 4 pi r^2
The surface area of a hemisphere with the radius r = 2 pi r^2 + pi r^2
where pi r^2 represents the area of the circular base of the hemisphere of radius r.
The surface area of a hemisphere sphere with the radius r is 3 pi r^2
For radius r=6cm
TSA of the hemisphere is 3 pi (6x6) cm^2
TSA = 108 pi cm^2
108 pi cm^2 is the total surface area of a hemisphere with the radius 6 cm.
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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:
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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how to solve x-y+x/2 (if x=10, y=1)
Find the x and y Intercept of x + 2y = -14
Answer:
Y-intercept: (0, -7)
X-intercept: (-14,0)
Step-by-step explanation:
To find the y-intercept, we need to put 0 in for x
0 + 2y = -14
2y = -14
y = -7
So, the y-intercept is located at (0, -7)
To find the x-intercept, we need to put 0 in for y
x + 2(0) = -14
x = -14
So, the x-intercept is located at (-14,0)
Step-by-step explanation:
To find the y-intercep, we need to put 0 in for x
0 + 2y= -14
2y = -14
y = - 7
So, the y - intercept is located at ( 0, - 7)