Answer:
14n^2.
Step-by-step explanation:
This is Arithmetic with first term a = 14 and common difference d = 28.
Sum of n terms = n/2[2a + (n-1)d]
= n/2(28 +( n -1)28]
= n/2(28 + 28n - 28)
= 14n^2
Answer:
14n²
Step-by-step explanation:
14 = 14 *1
42 = 14 *3
70 = 14 *5
28n -14 = 14*2n - 14 = 14*(2n -1)
14 + 42 + 70 + ........+(28n -14) = 14*1 + 14*3 + 14*5 + ....... + 14*(2n - 1)
= 14 * (1 + 3 + 5 + ......+ (2n-1) )
= 14 * n²
= 14n²
1 + 3 + 5 + .... +(2n -1) -> sum of first 'n' odd numbers.
Formula for finding sum of first 'n' odd numbers = n²
What is example of factoring a polynomial?
A polynomial is factored when it is broken down into the sum of two or more other polynomials. For instance, f (x) = x 2 + 5 x + 6 can be broken down into f(x) = (x+3)(x+2) and f(x) = x2 + 5 x + 6.
what are polynomials?A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.
A polynomial is factored when it is broken down into the sum of two or more other polynomials. For instance, f (x) = x 2 + 5 x + 6 can be broken down into f(x) = (x+3)(x+2) and f(x) = x2 + 5 x + 6.
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Is X² always positive?
Yes, the square of any number like X² is always positive.
Define the term positive numbers?Positive numbers are those above zero or to the right of zero on the number line. Be aware that positive numbers can be either integers or fractions, irrational numbers, or both. For instance, the square root of 2 has an infinite number of non-repeating digits.A number can be multiplied by itself to find its square.Example:
The result of two negative numbers is always positive, as explained.When two negative numbers are added together, the result is always positive.If we calculate the square of a negative number, let's say -x, where x > 0, then (-x) (-x) = x².
Here, x² > 0.
Hence, the square of any number like X² is always positive.
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Answer this question Please I need the answer know
Answer:
[tex]y= \frac{x}{2x−1}[/tex]
Step-by-step explanation:
To find the inverse function, swap x and y, and solve the resulting equation for x.
If the initial function is not one-to-one, then there will be more than one inverse.
So, swap the variables: y=x/2x−1 becomes x=y/2y−1.
Now, solve the equation x=y/2y−1 for y.
y=x/2x−1
I need helppp quickkkk
The triangles QRS and TUV are similar. They are similar as ΔTUV = 3ΔQRS.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
There are two similar looking triangles, ΔQRS and ΔTUV.
In ΔQRS, the measure of line segment QR = 9 units
In ΔQRS, the measure of line segment RS = 10 units
In ΔQRS, the measure of line segment QS = 11 units
In ΔTUV, the measure of line segment TU = 27 units
In ΔTUV, the measure of line segment UV = 30 units
In ΔTUV, the measure of line segment TV = 33 units
The pattern here can be seen that -
For the line segment TU -
3 (QR) = TU
3 (9) = 27
Similarly, for the line segment UV -
3 (RS) = UV
3 (10) = 30
Similarly, for the line segment TV -
3 (QS) = TV
3 (11) = 33
Therefore, the triangle TUV is three times scaled version of triangle QRS.
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This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form? Graph shows upward parabola plotted on a coordinate plane. The parabola has vertex at (2, minus 8) with the left slope at (0, 0) and the right slope at (4, 0). f(x) = x(x − ) f(x) = (x − )2 +
The quadratic equation written in the vertex form is:
f(x) = 2*(x - 2)^2 - 8
How to find the equation of the parabola?We know that for any parabola whose vertex is (h, k) and the leading coefficient is a, can be written in the vertex-form as:
f(x) = a*(x - h)^2 + k
In this particular case, we know that the vertex of the parabola is the point (2, -8), replacing that in the quadratic equation above we will get:
f(x) = a*(x - 2)^2 - 8
Now we also know that our parabola passes through the point (0, 0), then if we replace these values in the equation we will get:
f(0) = 0 = a*(0 - 2)^2 - 8
0 = a*4 - 8
8 = a*4
8/4 = a
2 = a
Then the quadratic equation in the vertex form is:
f(x) = 2*(x - 2)^2 - 8
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Gas mileage is the number of miles you can drive on a a gallon of gasoline. A test of a new car results in 460 miles on 20 gallons of gas. How far could you drive on 50 gallons of gas? What is the car's gas mileage?
Answer:
1,400
Step-by-step explanation:
y=mx+b
plug in 460 for b
y=mx+460
plug 20 for m
y=20x+460
and when graphed on a graph you would see the answer
What are 2 ordered pairs?
An ordered pair is a pair of numbers that are usually represented in the form of (x, y) and it is used to indicate the position of a point in a coordinate system or a Cartesian plane.
Another example is an ordered pair (-2, 1) representing a point in the coordinate system located 2 units to the left of the y-axis and 1 unit above the x-axis.
In this way, any point in a coordinate system can be represented by an ordered pair.
In summary, the ordered pair is a way to represent a point in a coordinate system and it is made up of two numbers (x, y), where x represents the horizontal position and y represents the vertical position of the point in the coordinate system.
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i need help who knows rhis
Find the measures of x and y.
X=
Y=
Answer:
x = 92
y = 92
Step-by-step explanation:
164 + 102 + 90 + x + x = 540
2x + 356 = 540
2x = 184
x = 92
What is the pattern of 1 1 2 3 5 8 13?
The pattern of the sequence 1 1 2 3 5 8 13 is that each term is obtained by adding the previous term and the term before that.
The sequence 1 1 2 3 5 8 13 is also a famous example of the Fibonacci sequence. The Fibonacci sequence is a sequence of numbers in which each term is the sum of the two preceding terms. In this case, the first two terms of the sequence are 1 and 1, and the rest of the terms are obtained by adding the previous two terms.
It's also possible to express the pattern of the Fibonacci sequence by using the formula, F(n) = F(n-1) + F(n-2) where F(n) is the nth term of the sequence.
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Which of the following is a constant polynomial?a.4x+1b. 3c. 2x2d. 6x+3
A constant polynomial is a polynomial with a degree of 0, meaning it has no variable terms. The only possible constant polynomial is the term with a coefficient of 3, which is 3.
This can be seen by looking at the formula for a polynomial, which is:
P(x) = a0 + a1x + a2x2 + ... + anxn,
where a0 is the constant term, a1 is the linear term, a2 is the quadratic term, and so on. Since this polynomial has no variable terms (x = 0), the only possible constant polynomial is the term with a coefficient of 3.
To calculate the value of a constant polynomial, you simply substitute 0 for x in the equation above. For example, in the polynomial 3, the value would be 3 when x = 0.
P(0) = 3
Therefore, the answer is option b, 3.
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Determine if the following system of
equations has no solutions, infinitely
many solutions or exactly one solution.
2x + 5y = 4
-4x - 13y
=
-9
One solution exists for the given equation.A linear equation with one variable has only ever one solution.
What is an unique solution?A linear equation with one variable has only ever one solution. The unique solution of a linear equation is the location at which LHS and RHS are identical when substituted.
The solution must be an ordered pair when there are two linear equations operating simultaneously (x, y). In this case, the ordered pair will fulfill the set of equations.
Given:
2x + 5y = 4
-4x - 13y = 9
Now,
a 1 = 2, b1 = 5 , = -4
a2 = -4 , b2 = -13, = 9
Now, = 2 / -4
= 5 / -13
As, a1/ a2 = 2/-4
b1 / b2 = 5 /-13
Thus, the relationship mentioned above reflects intersecting lines.
So, there is only one solution to the given problem.
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Find x in the equation. 4 times x plus one third equals one third times x plus 4
The value of x for the given expression is,
⇒ x = 5/44
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The algebraic expression is,
'' 4 times x plus one third equals one third times x plus 4''.
Now, The mathematical expression is,
⇒ 4x + 1/3 = 1/3 (x + 4)
Solve for x as;
⇒ 4x + 1/3 = 1/3x + 3/4
⇒ 4x - 1/3x = 3/4 - 1/3
⇒ 11/3x = 5/12
⇒ x = 5 × 3 / 12×11
⇒ x = 15/ 132
⇒ x = 5/44
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Evaluate the expression
Answer:
5.6 or 28/5
Step-by-step explanation:
We know that A = 8 and B = 4
The expression is A/5 + B
8/5 + 4
The answer in decimal is 5.6
The answer in fraction is 28/5
Liam and hi children went into a retaurant where they ell drink for two dollar each in taco for $3. 50 each. Liam i $30 to pend in ma by at leat nine drink and taco all together. If Liam decided to buy five taco, determine the maximum number of drink that he could buy
The maximum number of drinks Liam can buy is 4 without over exceeding his price.
Unitary method:
The unit method is a method of obtaining a single-unit value from a multiple-unit value and obtaining a multiple-unit value from a single-unit value. This is the method used for most calculations in mathematics. This method is useful when solving problems involving proportions and proportions, algebra, geometry, and more.
The unit method allows us to find missing values. For example, if a pack of juice costs $5. Then you can easily see that the cost is 5 packages, or $25.
According to the Question:
If Liam has $30 to spend and he must buy at least 9 drinks and tacos altogether, it means that,
$3.50 for 5 tacos
⇒ 3.50 x 5 = $17.50
Now,
9 - 5 tacos = 4 drinks
Cost of 4 drinks x $2 = $8
The total price :
$17.50 + $8 = $25.50 out of $30 price limit
Thus, the number of drinks that she could buy is 4.
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What polygon has 7 points 7 lines 7 angles?
A polygon having seven sides and seven angles is called a heptagon. Seven straight sides and seven corners, or vertices, make up a heptagon. It's also referred to as a "septagon" at times.
A seven-sided polygon is called a heptagon. A closed figure with seven vertices, it is. Another name for a heptagon is a septagon.
There are various sorts of hexagons, depending on the angles and diagonals.
Regular and Irregular Heptagons
Concave and Convex Heptagon
The following are some heptagon's characteristics:
(1) The inner angles of a heptagon add up to 900 degrees.
(2) A heptagon's outside angles add up to 360 degrees.
(3) The internal angle of a normal heptagon measures approximately 128.57 degrees.
(4) The size of a typical heptagon's central angle is roughly 51.43 degrees.
(5) There are fourteen diagonals in a heptagon.
(6) Convex heptagons are another name for regular heptagons.
(7) A heptagon has a total of five triangles.
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Identify the initial amount a and the rate of decay r (as a percent) of the exponential function f (t)=475(0.5)^t . Evaluate the function when t=3 . Round the answer to the nearest tenth
When t = 3, the exponential function has a value of 59.375.
What is exponential function?The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise indicated, the word refers to a positive-valued function of a real variable, however it can be extended to complex numbers or applied to other mathematical objects such as matrices or Lie algebras. A mathematical function of the following type is an exponential function: f (x) = an x, where x is a variable and an is a constant known as the function's basis. The transcendental number e, which is about 2.71828, is the most often encountered exponential-function base.
Here,
Given the exponential function h (t) = 475(0.5)^t
When t = 3
h(3) = 475(0.5)^3
h(3) =59.375
h(3) = 59.375
The exponential function when the value of t is 3 is 59.375.
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if you can write all of the numbers from 30 and 65 including 30 and 65
Answer:
The total number count we are looking at from the numbers 30 to 65 is 36. So that is a total of 72 digits making up this numbers from 30 to 65. Also, we can see that the whole range of numbers 0 to 9 is being used for this range
The school that Kyla goes to is selling tickets to a fall musical. On the first day of ticket sales the school sold 4 adult tickets and 10 student tickets for a total of $106. The school took in $99 on the second day by selling 4 adult tickets and 9 student tickets. Find the price of an adult ticket. a. $6 b. $9 $7 d $8
The price of the adult ticket is $9
How to determine the price of adult tickets?
Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
Set up equations to represent the problem.
Let the A and S represent the prices of adult and student ticket respectively. So we can write:
4A + 10S = 106 --- (1)
4A + 9S = 99 --- (2)
Subtracting (2) from (1) will give:
S = 7
Put S = 7 into (1):
4A + 10S = 106
4A + 10(7) = 106
4A + 70 = 106
4A = 106 - 70
4A = 36
A = 36/4
A = 9
Thus, the price of the adult ticket is $9
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12x -3y = 7 solve for X
Answer:
x = 0.25y + 7/12
Step-by-step explanation:
12x - 3y = 7
12x = 3y + 7
x = 0.25y + 7/12
What type of transformation can be defined as moving a figure to a new location with no change to the size or shape of the figure?
Translation type of transformation can be defined as moving a figure to a new location with no change to the size or shape of the figure.
Now, According to the question:
Type of Transformation:
There are four types of transformation in geometry, namely translation, reflection, rotation, and dilation. In translation, it slides the figure in any direction while in reflection, it flips the figure over a point or a line. Also, in rotation the figure turns, while in dilation the figure is either enlarged or reduced.
The type of transformation can be defined as moving a figure to a new location, without any change in the figure's size or shape being called translation. In translation, the figure merely slides or moves in the same direction and distance.
Therefore, the answer is Translation.
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What is the first step in inequality?
The first step in solving an inequality is to isolate the variable on one side of the inequality sign. This is also known as "clearing the inequality" of the variable. This can be done by using inverse operations such as addition, subtraction, multiplication, and division.
For example, if the inequality is 3x + 2 > 7, the first step is to isolate the variable x by subtracting 2 from both sides:
3x + 2 > 7
3x > 5
Then, divide both sides by 3 to get x > 5/3
This is the first step in solving an inequality, as now the variable x is isolated on one side of the inequality sign, and it's clear what the inequality is asking for.
It's important to note that when solving inequalities, it's crucial to keep the direction of the inequality sign the same, meaning if you multiply or divide by a negative number, you need to switch the direction of the inequality sign as well.
Also, it's important to check if the inequality is not valid, if the operation you are doing creates a division by zero, it will be an invalid inequality.
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PLASE, I NEED HELP
Write and solve an inequality.
Kelvin and Marsha are going to dinner and a movie this evening. Kelvin wants to have at least $70 cash in his wallet. He currently has $10. How much money, x, does Kelvin need to withdraw from the bank?
A. x + 10 > 70; x > $60
B. x + 10 ≥ 70; x ≥ $60
C. x + 10 < 70; x < $60
D. x + 10 ≤ 70; x ≤ $60
Answer:
B. x + 10 ≥ 70; x ≥ $60
Step-by-step explanation:
Given:
x = money (in dollars) Kelvin needs to withdraw from the bank.$10 = money Kelvin currently has.$70 = the least amount of cash Kelvin wants to have in his wallet.The equation that models the given parameters is:
[tex]x + 10 \geq 70[/tex]To solve for x, subtract 10 from both sides of the equation:
[tex]\implies x+10-10 \geq 70-10[/tex]
[tex]\implies x \geq 60[/tex]
Therefore, Kelvin needs to withdraw at least $60 from the bank.
I really need help . 28.25 x 9.60
Answer:
271.2
Step-by-step explanation:
Write it down and remove the decimals and do long multiplication. After that, count the decimal points and add them back ro the answer
Answer:
271.2
Step-by-step explanation:
move the decimal point 2 places to the right in the two numbers and multiple
[tex]2825 \times 960 = 2712000 [/tex]
and then move you decimal point 4 places to the left so your finally answer should be 271.2
what is the vale of the expression 3devided by 3/4
Answer:
Step-by-step explanation:
0.25
You have 2.88 meters of copper wire and 5.85 meters of aluminum wire. You need 0.24 meter of copper wire to make one bracelet and 0.65 meter of aluminum wire to make one necklace. Can you make more bracelets or more necklaces? Explain.
Answer: You can make more bracelets than necklaces. ✅
Step-by-step explanation:
You have 2.88 meters of copper wire and 5.85 meters of aluminum wire.
With 2.88 meters of copper wire, you can make 12 bracelets because each bracelet needs 0.24 meters of copper wire.
With 5.85 meters of aluminum wire, you can make 9 necklaces because each necklace needs 0.65 meters of aluminum wire.
So you can make 12 bracelets and 9 necklaces.
Therefore you can make more bracelets than necklaces.
Several students measure a 25 mm long nail and wrote the measurements show in the table below who is measurement hurt the greatest percent error? Round to the nearest percent.
The student whose measurement had the greatest percentage error is Tenicia with a measurement of 23mm.
What is percentage error?Percentage error refers to the difference between the estimated value and the actual value which is then expressed as a percentage. In the question given, the students and their values are; Layne, 26 mm, Tenicia, 23 mm, and Juan 25 mm.
Juan was the only student who had no error in the value obtained because she got the exact figure of 25 mm. Tenicia recorded the greatest value because the difference between the actual and estimated value was apart with so much difference. Her error was an 8% error.
25 -23/25 × 100
= 8%
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which form can beused to determine the slope of this equation 3f-s=24
The slope of the equation of the line 3f - s = 24 is 3.
How to find the slope of an equation?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slope of the lineb = y-interceptTherefore, let's model the equation of the line y = mx + b to 3f - s = 24. Then, we can locate the slope in the equation.
Hence,
3f - s = 24.
add s to both sides of the equation
3f - s + s = 24 + s
3f = 24 + s
subtract 24 from both sides of the equation
3f = 24 + s
3f - 24 = 24 - 24 + s
s = 3f - 24
Therefore, the slope is 3.
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What is the order of ordered pairs?
The Order of the ordered pair is defined as the specific way in which the ordered pair is written having a composition of the x coordinate and the y coordinate .
What is Ordered Pair ?
The Ordered Pair is defined as the pair of numbers in a specific order.
For Example : (x,y) , here for the given ordered pair , the element x is called as the abscissa and the element y is called as the ordinate .
The Order of the Ordered Pair (x,y) is the first element always represents the abscissa that means the x coordinate and the second element should always represent ordinate that means the y coordinate .
For Example : for the ordered pair (2,4) , the x coordinate of the point is 2 and the y coordinate of the point is 4 .
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PLS PLS PLS HELP NEED DONE ASAP
The answer is the point (5, -27) and no other solution.
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here: The equation y=-6x+23
Checking for (5, -27) we get -27=-6×5+23
=-27
Hence, The answer is the point (5, -27)
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