Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effect of the other. The term "inverse" refers to the reciprocal of a number, i.e., x - 1 = 1 / x. One results from multiplying a number by its reciprocal, or inverse.
Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effect of the other. The term "inverse" refers to the reciprocal of a number, i.e., x - 1 = 1 / x. One results from multiplying a number by its reciprocal, or inverse.
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Which of the following points is a solution to the system of equations shown?
y - x = -1
x + y = -5
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[tex]\quad \qquad \huge \bf \dag \: Answer \: \dag[/tex]
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[tex] \underline{ \large \rm Solution} : [/tex]
[tex]\rm Given : [/tex]
Two equations are -
y - x = -1 (i)x + y = -5 (ii)[tex] \rm Procedure : [/tex]
Considering the equations as (i) and (ii) respectively
From equation (i) -
y = x - 1put this value of y in equation (ii) -
x + y = -5x + x - 1 = -52x = -5 + 12x = -4 x = -2Next thing to do would be to put value of x we got in equation (i) to get y
y - x = -1y - (-2) = -1 y + 3 = -1 y = -1 - 3 y = -4Values asked are :
[tex] \rightarrow \rm y = - 4[/tex]
[tex] \rightarrow \rm x= - 2[/tex]
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[tex] \large \bf hope \: \: it \: \: helps \: - dabI [/tex]
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what is the answer thank ya mate
Answer: The ship is going to another planet.
Step-by-step explanation:
I hate i-ready,
Your welcome mate
The tip of a minute-hand travels 103. 62mm in one hour. Find the length of the minute
hand
Using the concept of circumference of a circle, the length of the minute hand is 16.5mm.
What is circumference of a circle?
The measurement of the circle's perimeter, also known as the circle's boundary, is called its circumference . The radius of the circle is considered when applying the formula to determine the circumference of the circle.
Circumference of circle(C) = 2πR
where,
R represents the radius of the circle
π is a constant with an approximate value of 3.14
Now, it is given that the tip of a minute-hand travels 103. 62mm in one hour which means that the minute hand moves 360 degrees.
This means that C= 103.62
So, using the concept of circumference of a circle,
C= 2πR
103.62= 2*3.14*R
So, R= 103.62/6.28
R=16.5mm
Hence, the length of the minute hand is 16.5mm.
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Aisha has 50 chocolates she fills 3 boxes and has 2 left over How many chocolates does she have left? Write it as an equation
Aisha has 2 chocolates left. You can represent the problem as an equation as follows:
x = 3b + 2Where x is the total number of chocolates, b is the number of boxes filled and 2 is the remaining chocolates left.
Since we know that Aisha has 50 chocolates, we can substitute this value for x in the equation:
50 = 3b + 2
Solving for b, we find that b = 16. So, Aisha filled 16 boxes and had 2 chocolates left over. The equation is true, and Aisha has 2 chocolates left.
It's worth noting that this is a simple algebraic equation, we can use the same equation to find the number of chocolates given the number of boxes and remaining chocolates, or to find the number of boxes given the number of chocolates and remaining chocolates or to find the remaining chocolates given the number of boxes and the number of chocolates.
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You buy clothing at a sale. You buy sneakers at 2 3 of their original price of $60, a sweater at 7 10 of its original price of $35, and a jacket at 5 6 of its original price of $45. Answer each question and show all your work. How much money did you spend
We spent a total of 40.2 + 24.5+ 37.8 = $102.50
Explain about the fractions?A fraction is a metric unit for describing a piece or component of a whole. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator.
Fractions are used to represent the parts of an entity or collection of entities. The components of a fraction are two. The figure at the top of the line is the numerator. It provides information on how many equal sections from the total or collection were taken. The number that appears below the line is the denominator.
We multiply the initial price by the fractions' decimal conversions to determine how much we spent. The quantities are then combined.
You purchased sneakers for $60 and paid 2/3 of that amount, or $0.6666, for a total of $40.20, saving $19.80.
Sweater costs $35 and you paid $7.50 for it, saving you $10.50. 35(0.7)=$24.50.
You paid $45 for a jacket, and since 5/6=0.8333, 45(0.84)=$37.80, you made a $7.20 profit.
We spent a total of 40.2 + 24.5+ 37.8 = $102.50
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The figure was created by repeatedly reflecting triangle NMP.
A figure is created by continuously reflecting triangle N M P. The length of side N M is 6 inches, the length of side M P is 4 inches, and the length of side N P is 8 inches.
The scale factor of the dilation of segment HG is One-sixth.
Point P is the center of dilation. Line segment H G is dilated to form shorter line segment H prime G prime. The length of P G prime is 0.5
If PG' equals 0.5 units, what is PG?
2.5 units
3 units
4.5 units
6 units
The length of PG if PG' is 0.5 units is; 3 units.
What is dilation?The act or action of enlarging, expanding, or widening : the state of being dilated: such as. : the act or process of expanding (such as in extent or volume)
Here, given that,
Dilation is simply defined as the shrinking or enlarging of an object by a scale factor.
Now, we are told that Line HG is dilated to form a shorter line H'G'.
We are told that the scale factor is 1/6.
Point P is the center of dilation and if PG' is 0.5 units, then we can write the relation as follows;
Length of PG'/Length of PG = 1/6
Thus;
0.5/length of PG = 1/6
Length of PG = 0.5/(1/6)
Length of PG = 4 units
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help pls! Given m||n, find the value of x.
(4x-6)
(8x-6)
Answer:
To find the value of x that makes the expression (4x-6) equal to (8x-6). To do this, you can set the two expressions equal to each other and solve for x:
4x - 6 = 8x - 6
4x = 8x
4x - 8x = 0
-4x = 0
x = 0
So, the value of x that makes (4x-6) equal to (8x-6) is x=0.
Answer:
-4x = -12 Divide each side by '-4'.
25PTS 25PTS don’t have to explain
Answer:
y = 3x - 2
Step-by-step explanation:
8. A quarter is what percent of a dollar?
A 5%
B 20%
C 25%
Answer:
25%
a half is 50%
a quarter is 25%
Answer: It's option C
Step-by-step explanation:
Well 1 quarter is 25
2 quarters is 50
3 quarters is 75
4 quarters is a dollar
David drives from his home to the airport to catch a flight. He drives 35 miles in the first hour,
but realizes that he will be 1 hour late if he continues at this speed. He increases his speed by 15
miles per hour for the rest of the way to the airport and arrives 30 minutes early. How many miles
is the airport from his home?
(A) 140 (B) 175 (C) 210 (D) 245 (E) 280
If David drives from his home to the airport to catch a flight. He drives 35 miles in the first hour, but realizes that he will be 1 hour late if he continues at this speed. The number of miles that is the airport from his home is 210.
How to find the distance?Let d represent the distance that is needed to travel 1 hour
1 hour late decreased to 0.5 hours early = 1.5
Hence,
d/50 + 1.5 = d/35
Simplify
7d + 525 =10d
Collect like terms
525 = 10d - 7d
525 = 3d
Divide both side by 3d
d = 525/3
d = 175
Total number of miles :
Total number of miles = 175 + 35
Total number of miles = 210
Therefore we can conclude that the correct option is C.
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please i really need help! anything will help at the moment
Answer:
-2 i think hope this helps
Step-by-step explanation:
Express the length a, b, c, and d in the figure in terms of the trigonometric ratios of θ.
a = b = c = d =
The lengths of a,b,c, and d have been derived and expressed in terms of trigonometric ratios below.
As we can see from the figure itself, the value of a = sin θ
This can be written as such because = sin θ = Perpendicular / Hypotenuse
Here, the perpendicular = a and hypotenuse = radius = 1
= sin θ = a
The value of b = tan θ
This is because tan θ = perpendicular/base
Here, the base = radius = 1
= tan θ = b
The value of c = sec θ
This is because sec θ = Hypotenuse / Base
= sec θ = c
The value of d = cos θ
This is because cos θ = Base / Hypotenuse
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How do you solve basic equations in algebra 1
PLEASE HELP ASAP
Combine like terms
8x + 3 - 5x + 9
Answer: B
Step-by-step explanation: [tex]8x-5x=3x\\3+9=12\\[/tex]
Hope this helps any
Answer:
B. 3x+12
Step-by-step explanation:
8x+3-5x+9
First combine the x. So, 8x-5x=3x
Next combine the 3 and the 9. So, 3+9=12
After you combined like terms your equation now looks like: 3x+12
Hope it helped you.
What are the solutions of the quadratic equation 2x^2 5x 12 0?
The solutions of the given quadratic equation are 4 and -3/2. Solved using the factoring method to solve a quadratic equation.
what is a quadratic equation?
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation's general form is ax^2 + b*x + c = 0.
where a, b, and c are constant terms and x is the unknown variable.
Here I am using the factoring method to solve a quadratic equation.
Given quadratic equation is
[tex]2x^2 - 5x -12 = 0.[/tex]
By comparing the General form of the quadratic equation we will get
a = 2, b = -5 and c = -12.
2x^2 - (8-3)x - 12 = 0.
2x^2 - 8x + 3x -12 = 0.
2x(x-4) + 3(x-4) = 0
(x - 4) (2x + 3) = 0.
x - 4 = 0 or 2x + 3 = 0
x = 4 or x = -3/2
Given Question is incomplete complete question here:
What are the solutions of the quadratic equation 2x^2-5x-12 = 0?
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A band wants to enter a contest that requires traveling expenses. They need at least $1,150 to cover all of the expenses. They have already saved $700. They are selling shirts with a profit of $7. 00 per shirt to earn the remaining money Part Which inequality represents the minimum number of shirts, n, the band must sell to earn the remaining money 1, 150
the number of shirts has to be an integer (you can not sell "part" of a shirt) n >= 65
They need at least $1,150
They have already saved $700
They are selling shirts with a profit of $7.00 per shirt
If they sell n number of shirts, they will earn n times $7.00
Since they have already 700, they will earn a total of 700 + 7n
If this quantity has to be equal or greater to 1,150, we can write:
1150 <= 700 + 7n
if we solve this inequality for n:
1150 <= 700 + 7n
1150 - 700 <= 7n
450 <= 7n
450/7 <= n
64.28 <= n
Since the number of shirts has to be an integer (you can not sell "part" of a shirt)
n >= 65
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How many times smaller is 2.7 x 10^3 than 5.481 x 10^5?
Function: This means that 2.7 x 10^3 is about 201.593 times smaller than 5.481 x 10^5. This can also be expressed as 0.049 or 4.9%.
What is function?A function is a mathematical relation between two sets of values, usually between an input and an output. It can be thought of as a machine that takes a certain input and produces a certain output.
2.7 x 10^3 is about 0.049 times smaller than 5.481 x 10^5.
To determine this, we can divide the two numbers. 5.481 x 10^5 divided by 2.7 x 10^3 equals about 201.593.
This means that 2.7 x 10^3 is about 201.593 times smaller than 5.481 x 10^5. This can also be expressed as 0.049 or 4.9%.
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can somebody please help me solve this question:
you are going to climb the roof of your two-story house using a 15-foot ladder. If the safety directions say that you can put the ladder only 2 feet from the house, how far up will you be able to reach on your house?
thanks
Using Pythagoras theorem to solve the right angle triangle, the height of the building is 14.87 feet
What is Pythagoras TheoremPythagoras Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as an equation:
x² = y² + z²
where x is the hypothenuse and y, z are the legs of the right angle triangle.
To determine the height of the building in which the ladder will reach, we have to use Pythagoras theorem for that.
x² = y² + z²
15² = 2² + z²
z² = 15² - 2²
z² = 221
z = √221
z = 14.87 feet
The height is 14.87 feet
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Jamila deposits $800 in an account that earns yearly simple interest at a rate of 2.65%. How much money is in the account after 3 years and 9 months?
Answer:
$821.2
Step-by-step explanation:
cause 2.65 percentage of 800 dollars is 800/100=8*2.65=21.2dollars.+800 =$821.2
How to graph 4x-6y=36
What’s the x intercept
What’s the y intercept
Therefore . the solution of the given problem of equation comes out to be x-intercept(s): (9,0) and y-intercept(s): (0,−6).
Clarify the equationA depiction of two equal variables, one on either side of a "equals" sign, is what constitutes an equation in mathematics. To solve common issues, one can use equations. We frequently look for help with pre algebra to overcome obstacles in real life. Basic mathematical concepts are covered in pre-algebra lessons.
Here,
the x-intercepts,
In order to determine the x-intercept(s), put in for y and calculate 4x6y=36.
Make the equation work.
x=9 point form x-intercepts.
x-intercept(s): \s(9,0) (9,0)
the y-intercepts, please.
In order to determine the y-intercept(s), replace with and solve for y=.4(0-)6y=36.
Make the equation work.
To continue, tap.
Point shape y=6 y-intercept(s).
The y-intercept is (0, 6).
Write down the junctions.
x-intercept(s): (9,0)
The y-intercept is (0, 6).
Therefore . the solution of the given problem of equation comes out to be x-intercept(s): (9,0) and y-intercept(s): (0,−6).
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Identify the applications that involve percentages. SELECT ALL THAT APPLY.
Commission
Original Sale Price
Retirement
Sales Tax
Loans
Income
Income Tax
here in equation function, John makes $8.00 per hour waiting tables, and after 40 hours he makes $530.50, including 210.50 in tips.
How do equations function?To create an equation, multiplying and dividing are used to separate constants and variables. In an equation, terms in various forms on each side of the equality sign are equal. John makes $8.00 per hour waiting tables, and after 40 hours he makes $530.50, including 210.50 in tips.To create an equation, multiplying and dividing are used to separate constants and variables.
so we have,
John had paid $8.00 an hour and waits tables
Therefore,
In 29 hours, he earns -
[tex]= 40 X 8\\= 320 $[/tex]
Via tups, he earned 210.50$
So, in total he earns
[tex]= 320 + 210.50\\= 530.50 $[/tex]
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GIVING BRAINLIEST AND 50 POINTS
Answer:
2x + 2
Step-by-step explanation:
Combine all the like terms:
-5x + 7x -12 + 14 = 2x + 2
Answer:
2x + 2
Step-by-step explanation:
(- 5x - 12) + (14 + 7x) ← remove parenthesis
= - 5x - 12 + 14 + 7x ← collect like terms
= (- 5x + 7x) + (- 12 + 14)
= 2x + 2
How to do 5 choose 3 on calculator?
To do 5 choose 3 on calculator, there are many methods including typing the input the mathematical expansion or in scientific calculators according to the model, there is way to represent 5C3.
The notation 5 choose 3 (also known as "5C3" or "5 comb 3") represents the number of ways to choose 3 items from a set of 5 items, also known as the binomial coefficient. It is equivalent to the formula:
5C3 = (5!) / (3! × (5-3)!)
Where "!" denotes factorial, which is the product of all positive integers up to that number.
To calculate 5C3 on a calculator, you can use the above formula and input it as follows:
5!/(3!×(5-3)!)
Most calculators have a button for factorial (symbolized by "!" or "n!"), so you can use that to calculate the factorials in the formula.
For example, on a basic calculator, you can input the following:
5!/(3!×2!)
and then press enter or the "=" button to get the result which is 10.
On some scientific or graphing calculators the notation is different, it could be represented as "comb(5,3)" or "5C3" and you just need to enter it as such.
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Select the correct answer.
What is the slope of the line that goes through the points (-1,4) and (14,-2)?
A. -15/6
B. -6/13
C. -5/2
D. -6/15
Slope = (-2 - 4)/(14 - (-1)) = -6/15
The function f is defined by f(x) = sqrt 25 - x2 for -5\leq x\leq 5. a) Determine the average rate of change of f over the interval --4\leq x\leq 3 b) Find f (prime) (x). c) Write an equation for the line tangent to the graph of f at x= -3. d) Let g be the function defined by g(x) = f(x) for -5\leq x\leq -3 and x+7 for-3\leq x\leq 5. Is g continuous at x= -3? Use the defintion of continuity to explain your answer.
a) The average rate of change of a function over an interval is the change in the function's output (f(b) - f(a)) divided by the change in the function's input (b - a). So, to find the average rate of change of f over the interval -4 <= x <= 3, we can use the formula:
(f(3) - f(-4)) / (3 - (-4)) = (sqrt(25 - 9) - sqrt(25 - 16)) / (3 - (-4)) = (-2sqrt(7) + 4sqrt(3)) / 7
b) To find the derivative of f(x), we need to use the power rule and the chain rule. The power rule states that the derivative of x^n is nx^(n-1), and the chain rule states that the derivative of f(g(x)) is f'(g(x)) * g'(x).
So, the derivative of f(x) = sqrt 25 - x^2 is:
-2x
c) To find the equation of the line tangent to the graph of f at x = -3, we need to use the point-slope form of a line, which is:
y - y1 = m(x - x1)
where m is the slope of the line (which is f'(-3) = -6), (x1, y1) is the point on the graph where the line touches (which is (-3, f(-3)) = (-3, sqrt(25 - 9) = 2sqrt(7))
so we have: y - 2sqrt(7) = -6(x + 3)
d) To check if g(x) is continuous at x = -3, we need to check if the limit of g(x) as x approaches -3 exists and is equal to g(-3).
Since g(x) = f(x) for -5 <= x <= -3 and g(x) = x + 7 for -3 <= x <= 5, we have:
g(-3) = f(-3) = sqrt(25 - 9) = 2sqrt(7)
and the limit of g(x) as x approaches -3 is:
lim x->-3 g(x) = lim x->-3 (x + 7) = -3 + 7 = 4
Since g(-3) = 2sqrt(7) and lim x->-3 g(x) = 4, g(x) is not continuous at x = -3.
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in exercise 15, find the expectation if a person buys two tickets. assume that the players ticket is replaced after each draw and that the same tiket can win more than one prize answer
The expectation is -$9.6
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Given that, a lottery offers one $1000 prize, two $700 prizes, three $300 prizes, and four $200 prizes.
Expected winning per ticket :
Σ(X × p(X)) = [(1000 × 1/1000) + (600 × 2/1000) + (300 × 2/1000) + (200 × 5/1000) - price per ticket
= 1 + 1.2 + 0.6 + 1 - 7
= 3.8-7
= -$3.2
Expected winning if 3 tickets are purchased :
3 × (-3.2) = -$9.6
Hence, the expectation is -$9.6
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Write a polynomial function in standard form
-6,0,0,2
How many one-cup servings of milk are in a two-liter bottle? Round your answer to the nearest tenth.
____________one-cup servings
Answer: 10.56 cups.
Step-by-step explanation:
1 liter = 4.22 cups; 1.5 liters = 6.34 cups; 2 liters = 8.45 cups; 2.5 liters = 10.56 cups.
Shaheen ha many triangular piece, each of area 1 q. Unit and many rectangular piece, each of area 2 q. Unit
If Shaheen has many triangular piece, each of area 1 sq. Unit and many rectangular piece, each of area 2 sq. Unit she arranges these to form the given shape then the area of shape is 14 Square Units .
The Area of one triangular piece is given as = 1 Sq . Unit ;
The Area of one rectangular piece is = 2 Sq. Unit ;
From the shape given below ,
we can see that the shape has 4 triangular pieces and 5 rectangular pieces .
So , total area of given shape is ⇒[tex]4\times Area Of Triangle + 5\times Area Of Rectangle ;\\[/tex]
Substituting the values of Area ,
we get ;
[tex]Total Area = 4\times 1 +5\times 2[/tex]
= [tex]4+10[/tex]
= 14 Sq . Units .
Therefore , the area of the given shape is 14 Sq. Units .
The given question is incomplete , the complete question is
Shaheen has many triangular piece, each of area 1 sq. Unit and many rectangular piece, each of area 2 sq. Unit .
If she arranges these to form a shape as shown below, what would be the area of this shape ?
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Is Avogadro's number equal to one mole?
One mole consists of 6.02214076×10²³ units which is Avogadro's number. Thus one mole is known as Avogadro's number.
What is one mole?
A mole is 6.02214076×10²³ of any chemical unit, including atoms, molecules, ions, and others. Due to the large number of atoms, molecules, or other components that make up any substance, the mole is a useful measure to utilize. The mole was initially defined as the quantity of atoms contained in 12 grammes of carbon-12, but the General Conference on Weights and Measures declared in 2018 that the mole will only contain 6.02214076×10²³ of some chemical unit as of May 20, 2019.
In chemistry, a mole, sometimes spelled mol, is a common scientific measurement unit for significant amounts of very small objects like atoms, molecules, or other predetermined particles.
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