Sum is an aggregation of the numbers, quantities etc. It is write as 4 + 4 = 8 ( plus symbol (+ ) represent the sum). Similarly, ∑ (sigma) also represents the sum of numbers.
Addition is an important topic in Mathematics. When we add two or more numbers, the result is defined as the SUM. The added numbers are called addends. The sum of two or more numbers make a new number say total. A plus symbol (+) is used when we add the numbers. Summation (or) sum formula is the sum of consecutive terms of a sequence. To write the sum of more terms, say n terms, of a sequence {an} , we use the summation notation instead of writing the whole sum manually. That is summation symbol which represent the sum is ∑ (sigma). For example, Sum of two numbers say 6 and 7 is equals to 6 + 7 = 13. But in case of "n" numbers the sum is determined as following way. Consider the first n even numbers, i.e., 2,4,6,....,n and we have to calculate the sum of it. As we see the above sequence is in AP with first term, a = 2 and common difference, d= 2. Then the sum formula in AP is S = n/2[ 2a + (n -1)d ]
=> S = n/2 [ 4 + (n-1)2 ]
=> S = n/2 [ 4 + 2n - 2 ]
=> S = n(n+1) or ∑n( n+1,) ; n = 1,2,.......
Hence, the sum of first n even numbers can be written as ∑n( n+1,) ; n = 1,2,.......
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HELP THIS WAS DUE YESTERDAY!!!!!!!!!!!!
The possible outcomes for rolling one six-sided die are shown below.
Molly rolled a six-sided die 20 times. The numbers she rolled are shown below.
What is the probability that Molly will roll a four on her next roll?
A.1/6
B.1/5
C.1/3
D. 1/4
Sol divided the following polynomial and made a mistake (x³ + 8x - 16) + (x-2)
There are an equal number of roots as long as there are x powers. As a result of the four xs, the polynomial in this situation has four roots.
How can the roots of a polynomial be found given its factored form?Finding the roots of the polynomial will allow you to solve it. P(x) = 0 is obtained by setting each factor to 0 and then calculating x. The polynomial equation can be solved by factoring. For every factor, a value of 0 should be used. 2x4 = 0; (x - 6) = 0; (x + 1) = 0 the answer to x, please.
It's important to note this even if there are only two genuine roots. The final two roots of this equation, which contain the integer I, are not real because I appears in both of them.
There are an equal number of roots as long as there are x powers. As a result of the four xs, the polynomial in this situation has four roots.
The complete question is,
Calculate the overall number of roots for each polynomial function using the factored form. f (x) = (x + 2)(x - 1) (x - 1) (x - 1) [x - (4 + 3i)] [x - (4 - 3i)].
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What is the meaning of AxB?.
AxB represents the cross product (also known as the vector product) between two vectors A and B.
AxB is the symbol for the cross product (also known as the vector product) between two vectors A and B. A new vector is produced by a cross-product. The symbol for the mathematical definition of the vector product of two vectors is axb, and it is as follows. Where is the angle between a and b, axb = |a| |b| Sin.
The vector components are joined to create a vector in a vector product of vectors. A vector that is perpendicular to both of the given vectors is the result of adding two vectors together.
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Can someone please help me with this math homework, I've been struggling?
I can't use words. Only infinity symbols, numbers, etc... THANKS!
Answer:
Steps in attached photo.
Step-by-step explanation:
SolutionSolution is in attached photo, to find f(x), we have to make y as the subject in terms of x, which means putting y on the left hand side of the equation.
Question 6.
Liana needs to purchase AT LEAST 50 party decorations. The Party Palace charges $0.50 per decorative streamer and $0.25 per balloon, including tax. Which combination of streamers and balloons can Liana purchase with $15.00 at the Party Palace?
A. 8 streamers and 43 balloons
B. 10 streamers and 41
balloons
C. 11 stregmers and 38 balloons
D. 26 streamers and 24 balloons
The combination of streamers and balloons can Liana purchase with $15.00 at the Party Palace is 8 and 43.
What is Linear equation ?
Linear equation can be defined as the equation having highest degree is one.
Given ,
Liana needs to purchase AT LEAST 50 party decorations. The Party Palace charges $0.50 per decorative streamer and $0.25 per balloon, including tax.
Let number of decorative streamer be x .
and number of balloons be y .
So, As per the question
The linear equation could be
0.50 x + 0.25 y = 15
Here its equals to the $15 as given that amount.
So,
The equation , 0.50 x + 0.25 y = 15
So, in the options it is given that,
8 and 43
So lets substitute x = 8 and y = 43 in the equation ,
we get,
LHS = 0.50 * 8 + 43 * 0.25
= 4 + 10.75
14.75
< RHS
So, As LHS is less than RHS , liana can easily purchase with given $15.00 at the party place.
Hence, The combination of streamers and balloons can Liana purchase with $15.00 at the Party Palace is 8 and 43.
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Use the table to write a linear function that relates y to x
The linear function that relates y to x is given as y = 2x
What is an equation?An equation consists of numbers and variables linked together by mathematical operations to form an expression.
A linear equation is in the form:
y = mx + b
Where m is the rate of change and b is the initial value
From the table, using the points (0, 0) and (1, 2):
y - 0 = [(2 - 0)/(1 - 0)](x - 0)
y = 2x
The linear function that relates y to x is given as y = 2x
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Is Y =- 5x 3 linear or nonlinear?.
The equation y = -5x + 3 is a linear equation.
We know that a linear equation in two variables is nothing but an equation that can be written in the form Ax + By = C, where A and B are real numbers and A ≠ 0, B ≠ 0.
The above form of equation is called the standard form of a linear equation in two variables.
Here we have been given an equation y = -5x + 3
y = -5x + 3
y + 5x = -5x + 3 + 5x ........(Add 5x to each side)
y + 5x = (-5x + 5x) + 3 .......(Associative property of addition)
y + 5x = 0 + 3
5x + y = 3 ........(Commutative property of addition)
Since we can write it in the standard form, Ax + By = C, then we have a linear equation.
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Lucas bought a tablet that was on sale at a 15% discount your supra case for $24.99 which is been a total of $237.49 written equation to find the original cost of the tablet
The original cost of the tablet is $70.89 in the given algebraic equation.
What is algebraic equation?A mathematical claim containing two equated algebraic expressions is known as an algebraic equation. When P and Q are polynomials, an algebraic equation has the general form P = 0 or P = Q. The term "multivariate equation" refers to an algebraic equation that has more than one variable.
Univariate equations are algebraic equations that only have one variable. Equations in algebra are balanced by definition. Due to this, the right and left sides of the equation will be equal.
Let the original cost be x
then
15/100 = 24.99.x
x = 166.6
237.49 - 166.6
= $70.89
Thus, the original cost of the tablet is $70.89 in the given algebraic equations.
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Full question?
Lucas bought a tablet that was on sale at a 15% discount on your supra case for $24.99 which is been a total of $237.49. Write an equation to find the original cost of the tablet?
In unit 1 you learned that you could take 20% of $400 by multiplying (400) (0.2) or In unit 1 you learned that you could take 20% of $400 by multiplying (400) (0.2) or (400) (0.20). Using your ability to set up proportion what is another strategy you could use to find 20%
Another strategy that one could use to find 20% of the given number is to multiply the number by 1/5.
How to calculate the percentage?A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
In this case, another strategy that one could use to find 20% of the given number is to multiply the number by 1/5. This will be:
= 20% × $400
= 1/5 × $400
= 80
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Please help this question is on my test and if u help me and it’s right I will memorize the answer u gave me. Btw 20 points
The expression for the width is x (b) The perimeter of the rectangle in terms of x is x +8
What is perimeter?You should understand that the perimeter of a rectangle is the distance round the rectangle
The given parameters that will help us to understand and solve the question are
Length = 4 inwidth = xArea = 2x+24Area = length * width
This implies that 2x +24 =4x
Collecting like terms =4 = 4x-2x
2x = 24
Therefore x = 24/2 = 12
b) The perimeter is = L+W+L+W
Perimeter = 2L+w
Where W =x
Perimeter = 2(2x+24) +2(x)
The perimeter = 4x+48 +2x
Therefore the perimeter = 6x+48 or x+8
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What is a polynomial sum?.
Two polynomials simply mean to sum the coefficients of the same powers, if these situations occur. the result of adding two polynomials will always be another polynomial.
A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).
In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.
Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.
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A city planner wants to build a road perpendicular to D Street. What should be the slope of the new road?
The slope of the new road is zero.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Take points from the Graph (5, 0) and (5, 4).
Slope of a line = m = tanθ
where θ is the angle made by the line with the x−axis.
For a line parallel to y−axis ,θ= π/2.
∴m = tan π/2 = undefined
The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.
An horizontal line now has zero slope.
The new road has a zero slope as a result.
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Simplify the expression
using only positive exponents.
The expression is simplified to y⁹/12x². Option A
What are index forms?The index form of a number can be described as that number written as an exponential expression.
It is also seen as a single number that is raised to another number.
Other names for index forms are standard forms and scientific notation.
From the information given, we have that;
3x^⁻⁴y⁵/(2x³y⁻⁷)⁻²
expand the exponential bracket of the denominator by mutiplying the values
3x^⁻⁴y⁵/2x⁶y⁻¹⁴
Now, divide the expression into parts, we have;
3/-4 (x^⁻⁴y⁵/2x⁶y⁻¹⁴)
Since we are finding the quotient, subtract the exponents of the denominator from the numerators, we get;
3× -4(x⁻⁴⁺⁶y⁵⁻¹⁴)
Now, add or subtract the exponential values, we get;
-12(x⁻²y⁻⁹)
y⁹/12x²
Hence, the correct option is y⁹/12x²
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2s=34 please help me I'm dying
Answer:
s=17
Step-by-step explanation:
just divide 34 by 2
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{2s = 34}[/tex]
[tex]\textbf{DIVIDE 2 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{2s}{2} = \dfrac{34}{2}}[/tex]
[tex]\textbf{SIMPLIFY it}[/tex]
[tex]\mathsf{s = \dfrac{34}{2}}[/tex]
[tex]\mathsf{s = 17}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x = 17}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
the first term of arithmetic prog is 12 and sum of first 9 terms is 135 find the common difference
Hope it helps.
If you have any query, feel free to ask.
The population of North Dakota in 2012 i 0. 3 million people. North Dakota ha a yearly population growth of 0. 017 million people. The population of South Dakota in 2012 i 0. 9 million people. South Dakota ha a yearly population growth of 0. 013 million people. Enter the minimun number of year it will take the population of North Dakota to equal the population of South Dakota given the curren rate of growth. Round your anwwer to the nearet tenth of a year
150 years is time required to when the population of north Dakota is equals to the population of South Dakota .
let t is time in years after which the population of both city are equals
so the population of north dakota after t years is given by :
0.3 + 0.017 t ----(i)
Population of South dakota after t years is given by:
0.9 + 0.013 t ----(ii)
for the population to be equal to each other equation (i) must be equal to equation (ii)
so , 0.3 + 0.017 t = 0.9 + 0.013 t
=> 0. 004 t = 0.6
=> 0.6/0.004
=> 150
so 150 years is the time required to make population of both city equals.
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Follow this link to view Juan’s work. Critique Juan’s work by justifying correct solutions and by explaining any errors he made. For any errors made, provide and explain a correct response. Be sure to explain each key aspect of the graph.
Juan's observations are correct, but his incorrect observation is asymptote: x = 0
What is an exponential function?An exponential function is a mathematical function of the following form: f(x) = aˣ. where x is a variable, and a is a constant called the base of the function.
Given is a graph of an exponential function.
Juan's observations are :-
Initial value: –3
Base: 3
Asymptote: x = 0
Domain: {x | x > 0}
Range: {y | all real numbers}
Studying the graph, we can say his observations are correct but his comment on Asymptote: x = 0 is wrong because, the equation of the horizontal asymptote of the graph of is y = 0, which is the x-axis.
Other than, Asymptote: x = 0, all his comments are true.
Hence, the incorrect observation is asymptote: x = 0
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In △ABC, m∠A = 75° and m∠C = 20°, What is m∠B?
What is inverse of Tangent called?.
Arctan or tan-1 are used to denote the inverse of Tangent.
The ratio of the perpendicular of the triangle and the base of the triangle with respect to the required angle is know as the tangent of the angle. Specifically, tan = (opposite side) / (adjacent side). The inverse tan formula is thus = tan-1[(opposite side) / (adjacent side)] according to the definition of inverse tan.
The reciprocal of the tangent is the cotangent. It is basically just the reciprocal of the tangent, it means that it can be written as the ratio of the base to the perpendicular.
Arccosine is another name for inverse cosine. It is the cos function's opposite. Also known as "arccos," occasionally. When two sides of a right triangle's length are known, it is used to measure the unknown angle.
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how would i solve this
Note that the expression when simplified translates to x = -6 (Option 1)
What is a math expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms.
√(x + 14) - √2x + 5) = 1
To solve this, we must square all elements on both sides of the equation. That is:
√(x + 14)² - √(2x + 5)² = 1²
⇒ x + 14 + 2x + 5 = 1
Collect like terms to arrive at:
3x = -18
x = -18/3
x = -6
Thus the answer to the above expression is x= -6
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How do you find the x-intercept and point of a quadratic equation?.
Answer:
Step-by-step explanation:
plug in a 0 for y and simplify the equation
because 0*(constant of y)=0, so
x*(constant of x)=something, so
something/(constant of x)=x
ans is (x, 0)
an isosceles triangle of sides 100cm, 60cm, and 60 cm has a base angle f, find f
Answer:
33.56°
Step-by-step explanation:
Base angles of an isosceles triangle are equal.
Base is bisected by a line from top (vertex) of the triangle straight down to form a right angle. Base, 100 cm, has 2 equal segments, 50 cm each.
Find h, height of the triangle:
h² = 60² - 50²
h = √1100 = 33.17
sin(f) = 33.17/60 = 0.553
m∠f = sin⁻¹(0.553) = 33.56°
Please help me ASAP...
The equation that has one solution will be 4m + 5 = 25. Then the correct option is B.
The equation that has infinitely many solutions will be 2x + 7 - 2x = 7. 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.
If the variable and constant get eliminated then the equation has infinitely many solutions. If the variable gets eliminated then the equation has no solution.
7. Let's check option B, then we have
4m + 5 = 25
4m = 20
m = 5
8. Let's check option C, then we have
2x + 7 - 2x = 7
2x - 2x = 7 - 7
The equation that has one solution will be 4m + 5 = 25. Then the correct option is B.
The equation that has infinitely many solutions will be 2x + 7 - 2x = 7. Then the correct option is C.
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What is the formula of sum of all terms?.
The formula for the sum of all terms is [tex]S_n[/tex]= n(n+1)/2.
Sum most commonly means the whole of two or greater numbers delivered collectively; see addition. A summation additionally known as a sum is the result of arithmetically adding numbers or portions. A summation constantly includes a whole range of terms. There can be as few as two terms, or as many as one hundred, a thousand, or one million. some summations include infinitely many terms.
In arithmetic, the summation is the addition of a chain of any form of numbers, called addends or summands; the result is their sum or general. the combination of two or extra numbers, magnitudes, portions, or details as decided via or as if via the mathematical technique of addition: The sum of 6 and 8 is 14. a selected combination or overall, specifically with regards to money: The fees came to a giant sum.
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Adrian bought a shoe for $125 and sold it for $175. The percentage profit was
Answer:
40% profit
Step-by-step explanation:
$50 increase, and $50 is 40% of $125
Answer:
40%
Step-by-step explanation:
Sold price =SP = $ 175
Cost price = CP =$ 125
Profit = Sp - CP = 175 - 125 = $ 50
Profit = 40 %
Une étude révèle que les jeunes âgés de 11 à 14 ans passent en moyenne 12,5% d'une journée de 24 heures devant un écran.
70% de ce temps est passé devant la télévision et le reste est passé devant un ordinateur.
Combien d'heures et de minutes les jeunes de 11 à 14 ans passent-ils en moyenne chaque jour devant :
(a) un écran ? (b) la télévision ? (c) un ordinateur ?
Answer:
Step-by-step explanation:
A study reveals that young people aged 11 to 14 spend an average of 12.5% of a 24-hour day in front of a screen.
70% of that time is spent in front of the television and the rest is spent in front of a computer.
How many hours and minutes do young people aged 11 to 14 spend on average each day in front of:
(a) a screen? (b) television? (c) a computer?
a screen
The vertices of a triangle are A (6, 2), B(0, -6), and C(0, 2). Draw
the image after a dilation with a scale factor of 11/12.
CORRECT ANSWER GETS BRIANLIST
Evaluate.
−3+(9+6)÷(−3)
Responses
4
−2
negative 2
−4
negative 4
−8
negative 8
Answer: -8
Explanation: Arithmetic operations have some precedence according to each other.
Firstly, begin with the operation inside of the parenthesis:
[tex]9 + 6 = 15[/tex]
The operation becomes:
-3 + (15) ÷ (-3)
Then, you should do the division part because the division has a precedence according to addition:
[tex]15 / (-3) = -5[/tex]
Finally, it becomes:
-3 + (-5) = -8
"-8" is the answer.
Is 2x 3y 7 a linear equation?.
Yes, 2x -3y =7 is a Linear equation as the highest power of the variable is linear which is one. Although it has two variables both have one power.
Linear equations are those which have the highest power of variable as one. But it can have n number of different variables. This given equation is called a linear equation with two variables.
Moreover, any expression is called an equation when the expression is equated to some value means the equation is equal to("=") to some other expression, Number, or Zero. And here 2x+3y is being equated to 7 which is a number, So the given expression is an equation.
However if the variables x and y both came together then it will not be linear as x*y will make the power two as one of x and one of y, Which w=makes the highest power of expression two.
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How do you solve x2 5x 14 using quadratic formula?.
On solving the quadratic equation x² + 5x - 14 = 0 by using the quadratic formula , the solution is written as x = 2 , x = -7 .
The formula that is used to find the roots of the quadratic equation is called as quadratic formula and is written as ,
the general quadratic equation is ⇒ ax² + bx + c = 0, the the quadratic formula will be:
⇒ x = [-b ± √(b² - 4(a)(c))]/2a ;
the given equation is ⇒ x² + 5x - 14 = 0 ,
On comparing ,
we get that ; a = 1 , b = 5 and c = -14 ;
substituting values in quadratic formula ,
we get ;
⇒ x = [-5 ± √(5² - 4(1)(-14))]/2(1) ;
solving further ,
we get ;
⇒ x = (-5 ± √(25+56))/2(1);
⇒ x = (-5 ± √81)/2;
⇒ x = (-5±9)/2 ;
On simplifying the equations separately ,
we have ;
⇒ 2x = -5 + 9 or 2x = -5 - 9 ;
⇒ we get , "x" as 2 or "x" as -7 . ;
Therefore , the roots of equations are "x ⇒ 2" or "x ⇒ -7" .
The given question is incomplete , the complete question is
How do you solve x² + 5x - 14 = 0 using the quadratic formula ?
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