In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
What is the best math equation?Euler's identity is considered to be "the finest of equations" in maths classes because it describes an unlikely combination of five mathematical constants. Euler's equation (published by Leonhard Euler in 1755) applies in the case of a perfect fluid.The basic operations involved in arithmetic are addition, subtraction, multiplication, and division. Arithmetic mean (average) = Sum of values/Number of values.In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.The forms commonly encountered are empirical, molecular, structural, and projection formulas. An empirical formula consists of symbols representing elements in a compound, such as Na for sodium and Cl for chlorine, and subscripts indicating the relative number of atoms of each constituent element.A General Rule for Solving Equations
Simplify each side of the equation by removing parentheses and combining like terms.Use addition or subtraction to isolate the variable term on one side of the equation.Use multiplication or division to solve for the variable.x= 9, y= 15
-4x +3y= 8 -----(1)
2x +5y=-3-----(2)
(1) ×2:
-8x +6y= 16 -----(3)
(3) -(2):
-4x +6y -(-8x +6y)= 16 -1
-4x +6y +4x -5y= 15
y= 15
Substitute y= 15 into (1):
-4x +3(15)= 8
-4x+45=8
4x+45-8
4x=37
x=37÷4
x=9
b = 2(9) + 5(15) + 3
b = 13 + 75 + 3 = 91
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Drag each interval to a box to show if the function shown is increasing, decreasing, or neither over that interval
Answer:
[tex]-10<x<-8[/tex]: Increasing[tex]-2<x>0[/tex]: Increasing[tex]8<x<10[/tex]: Neither[tex]3<x<7[/tex]: Neither[tex]-8<x<-5[/tex]: NeitherStep-by-step explanation:
A function is increasing if the graph is going up.
A function is decreasing if the graph is going down.
Four transformations of the function f(x) are given below. For each transformation, drag the graph that shows the result of that transformation into the box under it.
Answer:
g(x) = f(x) + 4 → Graph #5
h(x) = f(x + 4) → Graph #6
k(x) = f(x) - 4 → Graph #4
m(x) = f(x - 4) → Graph #3
Step-by-step explanation:
g(x) = f(x) + 4 → Graph #5
⭐ This transformation of f(x) means that to get g(x), you have to shift all of the y-values of f(x) up by 4.
⭐ Graph #5 exhibits this transformation because I took the point (0,1) and shifted it up 4 units to get (0,5). Graph #5 is the only graph that showed point (0,5).
h(x) = f(x + 4) → Graph #6
⭐ This transformation of f(x) means that to get g(x), you have to shift all of the x-values of f(x) by -4.
⭐ Graph #6 exhibits this transformation because I took point (0,1) and shifted it left 4 units to get (-4,1). Graph #6 is the only graph that showed point (-4,1).
k(x) = f(x) - 4 → Graph #4
⭐ This transformation of f(x) means that to get g(x), you have to shift all of the y-values of f(x) down by 4.
⭐ Graph #4 exhibits this transformation because I took point (0,1) and shifted it down 4 units to get (0,-3). Graph #4 is the only graph that showed point (0,-3)
m(x) = f(x - 4) → Graph #3
⭐ This transformation of f(x) means that to get to g(x), you have to shift all of the x-values of f(x) right by +4.
⭐ Graph #3 exhibits this transformation because I took point (0,1) and shifted it right 4 units to get (4,1). Graph #3 is the only graph that showed point (4,1).
(b)
(i) Factorise 1000x³-y³ completely.
(ii) Hence, without using a calculator, show that 124 is a factor of 992.
Answer:
i. (10-y)(100x^2 +10xy + y^2)
ii. See the explanation
Step-by-step explanation:
i. 1000x³-y³ =
10³x³ - y³ =
(10x)³ - y³ = ==> use formula: x³ - y³ = (x-y)(x^2+yx+y^2)
(10-y)((10x)^2 +10xy + y^2) =
(10-y)(10^2 * x^2 +10xy + y^2) = ==> simplify
(10-y)(100x^2 +10xy + y^2)
ii. 992/124=
(992-192)/(124-24)=
800/100 = 8
As a result, 8*124=992.
Hence, 124 (and 8) is a factor of 992
what does it mean when a company's corporate spread tightens
A corporate (or credit) spread is the extra interest a lender demands to make up for the extra risk they take on by financing the business.
Companies borrow money from their investors through the use of bonds, which are debt instruments. Better performance and low-risk perceptions for businesses cause bond spreads to narrow. The corporate spread decreases when people have favorable and low-risk impressions about the company issuing the bond since it is the extra interest paid over the interest from US Treasury bonds.
A bond is an IOU that specifies the amount of reward the IOU holder will get upon repayment of the borrowed funds. Basis points are typically used to calculate this interest rate. The matching government bond yield is typically considered for determining spread. The spread decreases as the danger increases.
Basis points are a standard unit of measurement for the corporate spread. These are "hundredths of a percent" more than the interest rate on Treasury bonds. Accordingly, a spread of 100 basis points is equal to 1% more than the yield on government bonds.
Spreads that are getting tighter indicate a company's assessment of risk is getting better. This is because investors have enough faith in the business to invest in it in exchange for reduced spreads. Strong financial statements, improved loan servicing, or a generally stable market impression could all be to blame for this.
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A bond is an IOU that specifies the amount of reward the IOU holder will get upon repayment of the borrowed funds. Basis points are typically used to calculate this interest rate. The matching government bond yield is typically considered for determining spread. The spread decreases as the danger increases.
Basis points are a standard unit of measurement for the corporate spread. These are "hundredths of a percent" more than the interest rate on Treasury bonds. Accordingly, a spread of 100 basis points is equal to 1% more than the yield on government bonds.
Pam need $6321 for her first year of college tuition each of her two grandfather said they would match what she saves she has seven years before she goes to college how much does Pam need to save on her own each year to have enough for her first year with the help of her two grandfathers Pam needs to save blank dollars each year
to have enough.
Pam needs to save $905 per year for seven years to have enough for her first year with the help of her two grandfathers.
How Much Money Must Be Saved Every Year?Pam needs to save $903 each year to have enough for her first year of college tuition with the help of her two grandfathers.
To calculate this, we first need to add up the total amount of money Pam's two grandfathers are offering to contribute:
Grandfather 1: $6321
Grandfather 2: $6321
Total Contribution: $12642
We then subtract this total contribution from the total cost of tuition for the first year:
Tuition: $6321
Total Contribution: -$12642
Total Amount Needed: $6321
Finally, we divide this total amount needed by the number of years Pam has to save:
Total Amount Needed: $6321
Years: 7
Amount Needed to Save Each Year: $903
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your class collected more than 410 cans of food for th eannual food drive in the first week, 185 cans were collected.how many cans c of food were colected in the second week?
The number of cans collected in the second week would be 225 cans.
A can of food is a container that holds a prepared food product, such as vegetables, fruits, beans, or soups. Canned foods are shelf-stable, meaning they can be stored for long periods of time without spoiling. They are often used as a convenient and easy-to-store source of food, especially in emergency situations.
To find out how many cans of food were collected in the second week, you need to subtract the number of cans collected in the first week from the total number of cans collected. In this case, the number of cans collected in the second week would be:
410 cans - 185 cans = <<410-185=225>>225 cans.
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How do you solve two parallel lines crossed by a transversal?
When two lines are crossed by a transversal, a number of angle pairs are formed. The sum of the measures of these angle pairs can be used to solve for unknown angles in the diagram.
Here are some of the angle pair relationships that hold for two lines crossed by a transversal:
Alternate Interior Angles: Alternate interior angles are pairs of angles on opposite sides of the transversal, but inside the two lines. These angles are congruent (have the same measure).Alternate Exterior Angles: Alternate exterior angles are pairs of angles on opposite sides of the transversal, but outside the two lines. These angles are congruent.Corresponding Angles: Corresponding angles are pairs of angles on the same side of the transversal, but on opposite sides of the two lines. These angles are congruent.Using these relationships, you can set up equations to solve for unknown angles in the diagram. For example, if you are trying to find the measure of angle A, you might use the fact that corresponding angles are congruent to set up the equation "m<A = m<D". Then, you can use other angle pairs to find the measures of the other angles, and solve the system of equations to find the measure of angle A.
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Are the whole numbers closed under division justify with example?
The division of the whole numbers is not closed under property as the division of whole number is not always a whole number.
A set has the closure property under a particular operation if the result of the operation is always an element in the set. If a set has the closure property under a particular operation then we say that the set is “closed under the operation.” The closure property of the division tells that the result of the division of two whole numbers is not always a whole number. Whole numbers are not closed under division that is a ÷ b is not always a whole number.
For example, 5 and 8 are whole numbers, but 5÷8 is not a whole number.
Therefore, closure property does not exist for division of whole numbers.
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A power company serves 17,000
customer's homes in a town. The
population of the town is decreasing by
about 3% every year. Which function
would represent the number of
homes,"H", the company will serve after
"n" years.
Answer:
2nd
Step-by-step explanation:
p=17000
r = -0.03
Hn)= p×(1+r)^n
H(n)= 17000(1+-0.03)^n
Which expression is equivalent to 18-(8* q) ? .
A (8q) - 18
B (18 - q) * 8
C (18 - 8) * c
D 18 - (0 * 8)
Answer:
the way you typed that is kinda confusing but the answer is
[tex]18 - 8q[/tex]
What are the factors of x³ 4x² 11x 30?
( x+2) , ( x-3 ) and ( x+ 5 ) are the roots of the equation .The function's zeros are frequently referred to as the function's roots, solutions, or x-intercepts.
what are roots in a equation ?The function's zeros are frequently referred to as the function's roots, solutions, or x-intercepts. These are all used across mathematics and have the same meaning as the zero concept. As a result, when a function y= or f(x)= is supplied, the zeros of the function are function values where y=0 or f(x)=0 f (x) = 0.
here ,
Since the sum of the coefficients is not zero , 1 is not a root
let x = -2
= -8 + 16 + 22 - 30 = 0
= -2 is a factor
dividing [tex]x^{3} + 4x^{2} -11x -30[/tex] by ( x + 2)
quotient = [tex]x^{2} + 2x -15[/tex]
= [tex]x^{2} +5x - 3x -15 =0[/tex]
= x(x + 5) - 3 ( x+ 5 ) =0
= ( x -3 ) ( x + 5 ) =0
other factors are ( x -3 ) and ( x+5 )
So , ( x+2) , ( x-3 ) and ( x+ 5 ) are the roots of the equation .
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the question is in the pic
I think it could be 1.5 kilometers.
The distance is 1,500 m but you have to convert it so probably 1.5 km.
What does congruent mean square?
Answer:
All the sides of the square are equalso the squares are congruent.. Are congruent shapes? Two shapes that are the same size and the same shape are congruent.
hope this helps
mark me brainliest
Step-by-step explanation:
Sheila is making accessories for the soccer team. She uses 675.22 inches of fabric on headbands for 46 players and 3 coaches. She also uses 443.44 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each
Answer:
232.88
Step-by-step explanation:
I used a calculator on this so it must be correct
The graph below represents the number of miles, y, that the satellite Space Explorer
flies in a hours. Find the rate of change.
Miles
90,000
85,000
80,000
75,000
70,000
65,000
60,000
55,000
50,000
45,000
40,000
35,000
30,000
25,000
20,000
15,000
10,000
5,000
Answer:
0
Space Explorer
Seve
(10,10000)
(5.5000)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Hours
miles per hour
Submit Answer
Answer:
1000
Step-by-step explanation:
answer is 1000 miles per hour
help please
- the line 5x-ay+26=0 and 3x-y+2=0 intersect on the y-axis. Determine the value of a.
The value of a if the lines 5x-ay+26=0 and 3x-y+2=0 intersect on the y-axis is; a = 13
How to solve the equation of a line?The general form of the equation of a line in slope intercept form is given as;
y = mx + c
where;
m is slope
c is y-intercept
We are given two equations of two lines as;
Line 1; 5x - ay + 26 = 0
Line 2; 3x - y + 2 = 0
Now, since they both intercept each other at the y-axis, it means that at the point of intersection, the value of x will be 0.
Thus, line 2 equation becomes;
3(0) - y + 2 = 0
y = 2
Putting 2 for y in line 1 equation gives;
5(0) - a(2) + 26 = 0
2a = 26
a = 26/2
a = 13
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What kind of sequence is 6 12 24?
As there is a common ratio between each term so this is a geometric sequence.
How geometric sequence is applied in real life?The idea of geometric progression can be used to determine how much money you will have in your account after a particular number of years if you deposit money in a bank that offers a fixed annual rate of interest.
What is the important property of geometric sequence?In a geometric progression or series, each term is equal to the one before it times the common factor, which is a fixed non-zero multiplier. The number of terms in a geometric series might be either finite or infinite.
Since in 6 12 and 24 the common ratio r=2. That is if we multiply the previous term by 2 we will get the next term so the given sequence is geometric sequence.
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3 3/8 T = ? lb
math question
Answer:
6,750 pounds
Step-by-step explanation:
3 3/8 tons = ? pounds
there are 2,000 pounds in 1 ton so:
3 3/8 * 2,000 = 6,750 pounds
Find the values of X and y in the diagram.
.Write an expression equivalent to -3 + 2/3y - 4 - 1/3y
Answer:
−7+y/3 is the same as that, but simplified.
Answer:
y/3-7
Step-by-step explanation:
The answer is the solved equation of -3+2/3y-4-1/3y.
Subtract 4 from -3 to get -7
= -7+2/3y-1/3y
Combine 2/3y and -1/3y to get 1/3y
-7+1/3, or just y/3-7.
does someone mind helping me with this? Thank you!
Answer:
[tex]y = 2x - 3[/tex]
Step-by-step explanation:
❗ The way I solved this problem doesn't involve me using point-slope form like the problem tells you to use❗
⭐ Perpendicular lines have a slope that is the opposite reciprocal of the slope of the line it is perpendicular to
⭐What does "opposite reciprocal" mean?
Opposite reciprocal: the slope of the perpendicular line is the reciprocal of the slope of the line it is perpendicular to and it has the opposite sign of the slope of the line it is perpendicular to.⭐What is slope-intercept form?
One way to write the equation of a line[tex]y = mx + b[/tex]m = the slopeb = the y-interceptWe can find the equation of the perpendicular line by:
Substituting the slope of the perpendicular line into the point-slope form equation using the opposite reciprocalSubstituting the given coordinate into the point-slope form equation to solve for b1. Substituting the slope into the point-slope form equation:
⭐ Perpendicular lines have a slope that is the opposite reciprocal of the slope of the line it is perpendicular to
The slope of the line the perpendicular like is perpendicular to is [tex]\frac{-1}{2}[/tex].
Therefore, the slope of the perpendicular line is [tex]2[/tex]
Substitute the slope into the point-slope form equation.
[tex]y = 2x + b[/tex]
Now, all we have to do is solve for b.
2. Substituting the given coordinate into the point-slope form equation:
We are given the coordinate (6,9).
[tex]y = 2x + b[/tex]
[tex]9 = 2(6) + b[/tex]
[tex]9 = 12 + b[/tex][tex]-3 = b[/tex]
Substitute "b" into the point-slope form equation.
[tex]y = 2x + 3[/tex]
What is a zero measurement?
The quantity or complete absence of the thing being measured is represented by the zero point.
Ex. Because the zero point is set arbitrarily and does not indicate the complete absence of temperature, the Fahrenheit scale is an interval scale.
What exactly is a random zero point?Zero degrees on either scale is not a "true" zero because it is an arbitrary number. The absence of temperature does not occur at the zero point; It's just a random number on the scale. Other examples of common interval scales include: Age and SAT scores (one is culturally determined).
Which scale has a point at zero?In addition, on a ratio scale, the distance between two variables is also the same. Furthermore, a proportion scale has a genuine zero point, meaning the worth of zero isn't erratic.
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What is the nth root theorem?
Answer:
The nth root theorem is a mathematical principle that states that, for any positive integer, it will have n nth roots!
An nth root of x is equivalent to saying [tex]\sqrt[n]{x}[/tex]. To elaborate, if you want to know how many 2nd roots that 1 has, through this theorem you will know it has 2 of these roots (-1 and 1). This applies for all numbers!
hope this helps :)
40 POINTS!
A system of equations is graphed on a coordinate plane.
Which coordinates are the best estimate of the solution to the system of equations?
A. (6, 0)
B. (0, 5)
C. (1, 4)
D. (1, 5)
The best estimate of the solution to the system of equations will be (1, 4). Then the correct option is C.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The system of the equations is given below.
2x + 3y = 12 ...1
4x + 2y = 10 ...2
Divide the equation 2 by 2, then we have
2x + y = 5 ...3
Subtract equation 3 from equation 2, then we have
2x + 3y - 2x - y = 12 - 5
2y = 7
y = 3.5
y ≈ 4
Then the value of 'x' is calculated as,
2x + 3.5 = 5
2x = 1.5
x = 0.75
x ≈ 1
The best gauge of the answer for the arrangement of conditions will be (1, 4). Then, at that point, the right choice is C.
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please help me with this problem
Answer:
0.84 m^2
Step-by-step explanation:
Long: 1200 millimeter = 1.2 meter
Wide: 700 millimeters = 0.7 meter
Area of rectangle: L x W
1.2 x 0.7 = 0.84 m^2
What form is used to inform the SSS of your illness or injury?
A sickness Notification Form is used to inform the SSS loan of your illness or injury.
The sickness benefit, according to SSS President and Chief Executive Officer Aurora C. Ignacio, is a daily cash payment made for each day a member is unable to work as a result of illness or accident.
In order to be eligible for the program, a member must have made at least three monthly contributions in the twelve months prior to the semester of illness or injury, be confined for at least four days in a hospital or at home, have used all of their current company sick days for the current year, and have informed their employer of their illness or injury.
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Write two inequalities to compare a and b how do you know?
To compare two numbers, a, and b, we can write two inequalities:
a < b when a is less than b
a > b when a is greater than b.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
We may write two inequalities to compare two numbers, a and b:
a < b
a > b
If a is less than b, then the first inequality is true and the second is false. If a is greater than b, then the first inequality is false and the second is true. Otherwise, if a and b are equal, then both inequalities are false.
We can determine which inequality is true by comparing the values of a and b and using the rules of inequality.
For example, if a=3 and b=5, then we can determine that a < b is true and a > b is false because 3 is less than 5.
On the other hand, if a=8 and b=2, then we can determine that a < b is false and a > b is true because 8 is greater than 2.
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How do I find a unique number in an array?
The simplest way to get unique number from an array is by putting all numbers of the array into hashmap's key and then print the keySet
How do we find a unique number in an array?an array is a collection of elements or numbers of the same data type.There are more than one way to find unique elements or number from an array:
1.By using hashing
2. By using nested loop
3. By using sorting
4. By putting all the elements in the hashmap's key
But the simplest way to get unique number from an array is the fourth method. And this is done by putting all the number from the array into the hashmap's key, we then print the key set.
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Help me pls I need this to be answered fast!!!-.-
Answer:
36 feet
Step-by-step explanation:
If one inch in the drawing equals 3 feet, then the 12-inch length of the wing would correspond to 12(3 feet). This means the final length of the wing will be 36 feet from tip to tip.
It reflects off the mirror and strikes a wall 9.5m away at point P. By what distance does the laser spot on the wall move if the mirror is rotated by 10??
As per the tangent formula, the distance does the laser spot on the wall move if the mirror is rotated by 10 is 2.9m
While we looking into the given question we have identified the following values,
Previous distance = 9.5
And the angle = 30 degrees
Rotated angle = 10 degrees
And the distance is considered as x.
Then as per the tangent formula, it can be written like the following,
=> tan 30/9.5 = tan 10/x
When we apply the tangent value, then we get,
=> 0.5773/9.5 = 0.1763/x
When we perform the cross multiplication, then we get,
=> 0.5773x = 9.5 x 0.1763
=> 0.5773x = 1.6749
Then the value of x is obtained as,
=> x = 1.6749/0.5773
=> x = 2.9012
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