It has n-k basic variables. The basic variables are the variables that are not free variables, and they are the ones that can be solved for as part of the general solution.
The general solution of a system of m linear equations in n variables contains k free variables. This means that there are k variables that have no restrictions and can take on any value. The remaining n-k variables are the basic variables, which are the ones that can be solved for as part of the general solution. The basic variables are the ones that have restrictions and need to be solved for in order to determine the solution of the system. In other words, the number of basic variables is equal to the number of variables minus the number of free variables. Thus, the general solution of the system has n-k basic variables.
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use log. 16＾k ＋4＾（k＋1）＝1/4＾3
There are 47 page in walter book. He read 29 page how many more page are left to read ?
Answer:
18 pages
Step-by-step explanation:
47 pages in total - 29 pages read = 18 pages left
7/30 of (1/3 + 7/15) / (5/6 - 3/5)
Answer:
The answer of the fraction is 4/5
Answer:
b)
Step-by-step explanation:
= 7/30 (5/15 ₊ 7/15) ÷ (25/30 - 18/30)
= 7/30 (12/15) ÷ (7/30)
= 7/30 (12/15) ×(30/7)
= 12/15
= 4/5
On Monday, the balance in your checking account is -$149. The bank charges you a $15 fee for having a negative balance. The next day you make two deposits of $117 and $59. What is your new balance?
After making the deposits, your new balance will be $12
A produce tore offer red and green apple. In one morning they old 48 apple total. If 20 of the apple they old were red, what i the ratio of green apple old to red apple old?
The ratio of green apples sold to red apple old is:
7:5
If the store sold a total of 48 apples and 20 of them were red, then the number of green apples sold is:
48 apples - 20 red apples = 28 green applesTo find the ratio of green apples to red apples, we divide the number of green apples by the number of red apples and express the result as a fraction:
28 green apples / 20 red apples = 7/5So the ratio of green apples to red apples is 7:5, or written as a fraction, 7/5. This means for every 5 red apples sold, the store sold 7 green apples.
The ratio of green apples to red apples is a way of comparing the number of green apples to the number of red apples sold in a specific time period.
It provides a way to understand the proportion of green apples relative to red apples, and can be useful for the store to track the popularity of different types of apples.
Complete Question:
"A produce store offer red and green apple. In one morning they sold 48 apple total. If 20 of the apple they sold were red, what is the ratio of green apple sold to red apple sold?"
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Given :
ray TV bisects ZUTW
ray TV is an altitude in A TUW
Prove:
Δ TUW is isosceles
Answer:
To prove that triangle TUW is isosceles, we can use the fact that ray TV bisects angle ZUT and is an altitude in triangle TUW.
Since ray TV bisects angle ZUT, it splits the angle into two congruent angles, ZTV and TVU. This means that angle ZTV is congruent to angle TVU.
Since ray TV is an altitude in triangle TUW, it forms a right angle with the base of the triangle, which is line segment TU. This means that angle TVU is a right angle, and therefore, angle ZTV is a right angle as well.
Since angle ZTV and angle TVU are congruent right angles, we know that the two sides that form these angles, UT and TU, are congruent. This means that side UT is congruent to side TU, and therefore, triangle TUW is isosceles.
WHAT INQUANLITY DESCRIBES THE SOLUTION OF 2Y< 8
Reason: Divide both sides by 2. The inequality sign stays the same. The only time it flips if you divided both sides by a negative value.
The graph involves an open hole at 4 with shading to the left. The open hole means "exclude this value from the shaded solution set".
PLEASE HELP I will Mark Brainlist its A Math Question thank you
Answer:
The correct answer is the second alternative!
Is each biconditional statement true or false?
Select True or False for each statement.
An angle is a right angle if and only if the measure of the angle is 90°. True/False
An angle measures 120° if and only if the angle is an obtuse angle. True/False
An angle measures 180° if and only if the angle is a straight angle. True/False
As far as we are aware, a straight angle is defined as 180 degrees then the bi-conditional assertion is true.
What is meant by bi-conditional assertion?It combines the conditions "if two line segments are congruent then they are of equal length" and "if two line segments are of equal length then they are congruent." Only when both conditionals are true does a biconditional hold. The symbol "or" is used to denote bi-conditionals.
A statement with two conditions is one that has the form "p if and only if q." In other words, if p, then q and if q, then p. "P iff q" or "p q" are other ways to express the biconditional "p if and only if q."
Since we have given that
1) If and only if the angle's measurement is 90 degrees, it is a right angle : True.
As is common knowledge, one angle in a right-angled triangle must be 90 degrees.
2) If and only if an angle is obtuse, it measures 120 degrees : True
Obtuse angle is a term used to describe angles that are more than 90° but less than 180°.
And 90°<120°<180°
3) Only if the angle is a straight angle does it measure 180 degrees : True
As far as we are aware, a straight angle is defined as 180 degrees.
As a result, every bi-conditional assertion is true.
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4x+8y is less than or equal to 8, 5x+y is less than or equal to 10. Graph the solution set of the following inequalities (and fill in)
The graph of the set of inequalities is given in attachment.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
4x+8y is less than or equal to 8 and 5x+y is less than or equal to 10
4x+8y≤8
5x+y≤10
40x+8y≤80
40x+8y-4x-8y≤80-8
36x≤72
x≤72/36
x≤2
and now plug in x value
4(2)+8y≤8
8y≤0
y≤0
Hence, the graph of the set of inequalities is given in attachment.
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Please help I have a learning disablity and need help.
The Ramirez family drove 1,764 miles across the United States on their vacation. If it took a total of 28 hours, write a multiplication equation to find their average speed in miles per hour.
Use R
as the variable to represent their unknown average speed.
ANswer here_________________
Answer:
The answer is 63 miles per hour.
The distance (d) is multiplication of speed x and time (t):
d = x * t
d = 1,764 mi
t = 28 h
x = ?
1,764 mi = x * 28 h
x = 1,764 mi / 28 h
x = 63 miles per hour
Step-by-step explanation:
the x coordinate of the midpoint is the ____ the x coordinate of the end points
1) same as
2) difference between
3) average of
Fred has a recipe for 30 biscuits.
Here is a list of ingredients for 30 biscuits.
Self-raising flour:
230g
150g
100g
Butter:
Caster sugar:
Eggs:
2
Fred wants to make 45 biscuits.
(a) Complete his new list of ingredients for 45 biscuits.
Answer:
*1.5
Step-by-step explanation:
45/30＝1.5
use all ingredients *1.5 then get the ans
eg. 230g*1.5＝345g
150*1.5＝225
PLSSS HELP IF YOU TURLY KNOW THISS
Please help with this question
Answer:
352 inches squared
Step-by-step explanation:
The area of a triangle is 1/2 · base · height. There are 4 of the same triangles here, so it would be (1/2 · 8 · 18) · 4 to find the surface area of all 4 triangles, but you can't forget about the base. The area of a rectangle is length times width, so it would be 8 · 8. This means the formula for the entire surface area of this square pyramid is ((1/2 · 8 · 18) · 4) + (8 · 8). It can be simplified as follows:
((1/2 · 8 · 18) · 4) + (8 · 8)
((1/2 · 8 · 18) · 4) + 64
((4 · 18) · 4) + 64
(72 · 4) + 64
288 + 64
352
Given points F(3, 1), G( 8, 2), H(2, 4), and J(1, 6).
a. Find the slope of FG and the slope of HJ.
b. Explain if FG and HJ are parallel, perpendicular or neither.
The slope of FG is equal to 1/5 while the slope of HJ is equal to -2.
Lines FG and HJ are neither parallel nor perpendicular because their slopes are different and not an inverse of each other.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
For the slope of line FG, we have the following:
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (2 - 1)/(8 - 3)
Slope (m) of line FG = 1/5.
For the slope of line HJ, we have the following:
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (6 - 4)/(1 - 2)
Slope (m) of line HJ = -2/1.
Slope (m) of line HJ = -2.
In Mathematics, a condition that must be met for two lines to be perpendicular is given by m₁ × m₂ = -1 while m₁ = m₂ for an two lines that are parallel.
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Please help, I need the answer as soon as possible!!!!
the value of a in this expression will be 1/2.
What is a fraction?
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.4
The given expression [tex](\frac{m^{1/4} }{6m^{3/4} } )^-1[/tex]
=[tex](\frac{6m^{3/4} }{m^{1/4} } )[/tex]
=6 ([tex]m^{3/4-1/4}[/tex])
=6 ([tex]m^{1/2}[/tex])
a = 1/2
Hence the value of an in this expression will be 1/2.
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The solutions to a system of linear inequalities are located in the region where all the shaded regions of the inequalities overlap. What is the region of overlap called?
A. vertex
B. boundary line
C. intersection
D. test point
All the shaded regions of the overlap inequalities represents the located solution region of the system of linear inequalities , the overlap region is called intersection ( option C ).
Graph is attached.
Let us consider the system of linear inequalities are x + y > 1 and x -y <1.Represents both the system of inequality on the graph.Plot x + y > 1, region above x >1, y > 1 represents the inequality.Plot x - y < 1 region x < 1 , y > -1 represents the inequality.Shaded region of both the inequalities intersect each other represents the solution region of the system of inequalities.Solution region is the shaded region which get overlap.Graph is attached.
Therefore, the solution region is represented by the shaded region called (option C) intersection area of the system of linear inequalities.
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What is the value of 14 – ( 2) + 3 – 8 + 4?
Answer:
11
Step-by-step explanation:
12-5+4=12-1=11
how does each inverse function from part a relate to its original function? describe the relationship in terms of the context for each situation.
The inverse function is the reverse of the original function and relationship between the two functions is determined by the mapping between the inputs and outputs of the original function.
In mathematics, the inverse function is a inverse function of a function is the reverse of the original function.
To understand the relationship between an inverse function and its original function, consider the following example. Suppose we have a function that maps the height of an object to its weight.
The original function would take the height as an input and output the corresponding weight. The inverse function, on the other hand, would take the weight as an input and output the corresponding height.
It is important to note that not all functions have an inverse. A function is only considered to have an inverse if it is a one-to-one mapping, meaning that each input has a unique output.
In summary, If the original function is a one-to-one mapping, then it has an inverse function that can be found by swapping the inputs and outputs.
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a pool drained at a rate of 15 gallons every 2 minutes.How many cups of water drained out of the pool each second?
Answer: The answer is 0.125 cups.
Step-by-step explanation:
First, you need to find the unit rate of the draining.
7.5 gallons = one minute
Divide 7.5 by 60 seconds
After dividing, you should get 0.125 cups of water per second.
Therefore, the pool drained at a rate of 0.125 cups every second.
Hope this helps! :)
An art class is making a mural for their school which has a triangle drawn in the middle. The length of the bottom of the triangle is x. The other side is 13 more than 4 times the length of the bottom of the triangle. The last side is 8 more than the bottom of the triangle. Write and simplify an expression for the perimeter of the triangle.
Answer:
The perimeter of the triangle is the distance around the triangle.
We need to apply our ability to convert word problems in to mathematical expressions.
we were told that the bottom of the triangle is units.
From the diagram perimeter
Four times the length of the bottom will be .
12 more than 4 times the bottom will be
Hence another side of the triangle is
Finally we were told that the last side is 3 more than the bottom, that will be
Step-by-step explanation:
Are the two triangles similar? If so, how do you know
Answer:
Yes, through AA
Step-by-step explanation:
The angles of a triangle = 180
One angle is a right angle, which is 90. They give us an angle of 52.
Subtracting 180-90 = 90
Then subtracting 90-52 gives you 38
If you look at the other triangle... what's the given angle? It's 38
180-90=90
90-38 = 52
That 52 looks familiar
How do u draw the graph n wats the answer
y=2x-2 is the equation of the graph.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
From the given figure the points are (2, 2)(3,4)(4, 6)
m=6-4/4-3
m=2/1
slope =2
Now let us find the y intercept
4=2(3)+b
4=6+b
b=-2
y=2x-2
Hence, y=2x-2 is the equation of the graph.
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prove that sum of angles of a convex plygon of n sides is (n-2)pi, where n>3
The IH states that the sum of the angles in convex polygon C(which, by the IH, is (n - 2)·π) and the sum of the angles in triangle B (180°) is the same as the sum of the angles in A.
Using induction all convex polygons with n vertices have angles that add to (n - 2)·π, therefore let P(n) be that. We will demonstrate that P(n), where n≥3, holds for every n ∈ N. We demonstrate P(3), which states that any convex polygon with three vertices has an angle total of 180 degrees. Any triangle formed by such a polygon has angles that add up to 180°.
Assume that P(n) holds for some n ≥ 3 and that all convex polygons with n vertices have angles that add to (n-2) 180° for the inductive step. We demonstrate P(n+1), which states that each convex polygon with n+1 vertices has an angle sum of (n-1)·π. Let A represent any n+1-vertex convex polygon.
The IH states that the sum of the angles in convex polygon C (which, by the IH, is (n - 2)·π) and the sum of the angles in triangle B (180°) is the same as the sum of the angles in A. As a result, the total angle in A is (n-1) 180°. Thus, the induction is complete and P(n + 1) holds.
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Ernest measured a summer camp and made a scale drawing. The sand volleyball court is 4 centimeters wide in the drawing. The actual volleyball court is 8 meters wide. What is the drawing's scale factor?
The scale factor is greater than 1. The drawing scale factor is 200.
What are the measuring units?
A unit of measurement is a specific magnitude of a quantity that has been established and adopted by law or convention and is used as a benchmark for measuring other quantities of the same kind. A multiple of the unit of measurement can be used to express any other quantity of that type. A length, for instance, is a physical quantity.
Given that, the sand volleyball court is 4 centimeters wide in the drawing. The actual length of the volleyball court is 8 meters wide.
The sacle factor is the ratio of the actual length to new object.
The scale fator is
8 meter : 4 centimeters
= 800 centimeters: 4 centimeters
= 800 : 4
= 200 : 1
=200/1
= 200
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question 1what is the number of 6-card hands with three hearts and three spades?
The probability of a 6-card hand with three hearts and three spades is 0.001862, or 1/535
Probability is the mathematics of chance; it is the study of calculating the likelihood of certain outcomes in any given situation.
Here we have to find the probability of a particular 6-card hand consisting of three hearts and three spades is determined first by the fact that there are 13 hearts and 13 spades in a standard deck of 52 cards.
To calculate the probability of a 6-card hand consisting of three hearts and three spades, one must first consider that the order of the cards in a hand does not matter.
The total number of combinations of three hearts and three spades that can be drawn from a standard deck of cards is
=> 4,824.
This number can be calculated by an equation that uses the number of hearts, spades, and cards in a standard deck
=> (13 x 13 x 52).
Then the probability of a 6-card hand consisting of three hearts and three spades is calculated by dividing the number of combinations of three hearts and three spades
=> (4,824) / (2,598,960).
This equation yields a probability of 0.001862, or a 1 in 535 chance of getting a 6-card hand with three hearts and three spades.
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write a real world deseription for the Algebraic expression 4.95x + 3
Answer:
You are paying 3$ already for a drink and for each sandwich (x) you buy is 4.95$
Step-by-step explanation:
You are paying 3$ already for a drink and for each sandwich (x) you buy is 4.95$
So you pay 4.95x + 3 for your drink and x sandwiches
The algebraic expression 4.95x + 3 can be described as the total cost of a product that has a fixed price of 3 dollars, and an additional price of 4.95 dollars per unit of the product. In this case, x represents the number of units purchased, and the expression represents the total cost of the purchase.
tell whether each equation has one zero or infinitely many solutions.
2. 1/2n + 7 = (n+14)/2
Answer:
n/2 + 7 is always equal to (n + 14)/2
Step-by-step explanation:
Both equations are the same, re-written.
Simplify the following:
n/2 + 7
Put each term in n/2 + 7 over the common denominator 2: n/2 + 7 = n/2 + 14/2:
n/2 + 14/2
n/2 + 14/2 = (n + 14)/2:
Answer: (n + 14)/2
ms. losch has a piece of rope long that she cuts into pieces for an experiment in her first-grade class. each piece of rope is to be long. how many long pieces of rope can she cut from the original piece of rope?
Ms. Losch can cut the original piece of rope into as many pieces as she wants, provided that each piece is the same length as the original.
If the original piece of rope is 12 inches long, she can cut it into 12 one-inch long pieces, 6 two-inch long pieces, 4 three-inch long pieces, 3 four-inch long pieces, 2 six-inch long pieces, or 1 twelve-inch long piece.
It is important to note that the pieces of rope must all be the same length, so if she wants to make any combination of the lengths, she must make sure that the total length of the pieces of rope adds up to the original length.
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