The 2nd and 3rd term of an AP is found to be (a₂ = 95) and (a₃ = 110).
What is the sequence of AP arithmetic progression?In Arithmetic Progression, the difference between the two numerical orders is a fixed number (AP). Arithmetic Sequence is another name for it.
We'd come across a few key concepts in AP that had been labeled as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)As shown below, the AP can also be referred to in terms of common differences.
The following is the procedure for evaluating an AP's n-th term: an = a + (n − 1) × dThe arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, the given sequence is; 80, _, _, 125.
The series comprises of four given terms.
Let the first term be 'a₁' = 180.
The second term be 'a₂'.
The third term be 'a₃'.
And, the fourth term is 'a₄' = 125.
Use the nth term formula to find the common difference 'd'.
n-th term: an = a + (n − 1) × d
a₄ = a + (n - 1)d
125 = 80 + (4 - 1)d
45 = 3d
d = 15
Thus, the common difference is 15.
The second term is calculated as;
a₂ = a₁ + d
a₂ = 80 + 15
a₂ = 95.
The third term is estimated as;
a₃ = a₂ + d
a₃ = 95 = 15
a₃ = 110
Therefore, the 2nd and third term of an AP is computed as 95 and 110.
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3x+4y=10 , 2x +3y = 7
Answer: x=2, y=1
Step-by-step explanation:
Find the exact circumference of circle by using the given polygon.
b. circumscribed square with side 10 feet long
The hypotenuse of the right triangle is the diameter of the circle then the circumference of the circle is 17[tex]\pi[/tex] centimeters.
What is circumference of a circle?The midpoint is the point in the middle of a line segment in geometry. It serves as the segment and endpoint centroid because it is equidistant from both endpoints. The segment is cut in half.
The diameter of the circle is the hypotenuse of the right triangle.
Use the Pythagorean Theorem to find the diameter.
By using Pythagorean theorem we get
[tex]$$c^2 = a^2 +b^2[/tex]
substituting the values in the above equation, we get
[tex]$$c^2 = 8^2 +15^2[/tex]
simplifying the equation
[tex]$$c^2[/tex] = 289
c = 17
The diameter of the circle is 17 cm.
The circumference C of a circle is given by C = [tex]\pi[/tex] d.
Circumference of a circle = [tex]\pi[/tex]d
= [tex]\pi[/tex] (17) = (17) [tex]\pi[/tex]
Therefore, the circumference of the circle is 17[tex]\pi[/tex] centimeters.
The correct question is:
Find the exact circumference of each circle by using the given inscribed or circumscribed polygon.
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Write an equation of a parabola with its vertex at the origin and the given characteristics. directrix x=7
Answer:
ggr44tt55ttffghhtft hyy
Tell whether the difference of two positive integers is always, sometimes, or never positive.
The difference of two positive integers is sometimes positive.
How to illustrate the information?For example the difference of 3 and 5 will give a value of -2. This is negative.
On the other hand, the difference of 10 and 6 is 4. Therefore, this is positive.
Therefore, the difference of two positive integers is sometimes positive. It can also be negative.
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For an analysis of variance comparing four treatments, msbetween = 12. what is the value of ssbetween? group of answer choices
a. 3
b. 4
c. 36
d. 48
For an analysis of variance comparing four treatments, msbetween = 12. The value of ssbetween is 36.
What is variance ?A measure of variability is the variance. It is determined by averaging the squared deviations from the mean. Your data set's variability is shown by its variance. The variance is greater in respect to the mean when the data are more dispersed.
Finding the mean will allow you to compute the population's variance (the average). Squaring the result after deducting the mean from each data point in the sample. The outcomes are squared to make the adverse findings positive.
Data points' deviations from the mean are quantified by their variance. Layman defines variance as the degree to which a set of data (numbers) deviates from the mean (average) value.
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Evaluate each function for the given value of x , and write the input x and output f(x) as an ordered pair.
f(x) = -12x/5 for x=-1
f (-1) = 12/5 the output for the given input .
How can you tell whether a function is linear or not?
Looking at a function's graph will reveal if it is linear or not with the greatest ease.When a linear function is plotted on a graph, a straight line is formed. A nonlinear function is curved in some way; it does not form a straight line.f(x) = -12x/5
Put x = -1 ⇒ - 12 * -1 /5
⇒ 12/5
Therefore f (-1) = 12/5
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Simplify the expression:
2(5 + 6q) =
Answer: Evaluate
2(5+6q)
Apply the distributive property
2×5+2×6q
Multiply the terms
10+2×6q
Solution
10+12q
Step-by-step explanation:
hope this helps
Joshua purchased a game card for the arcade for a total of $18. He played two basketball hoop games for $3.25 each and four rounds of air hockey for $1.75 each. How much did he have left on the game card?
$4.50
$6.50
$13.00
$13.50
The amount left when Joshua played two basketball hoop games for $3.25 each and four rounds of air hockey for $1.75 each is A. $4.50.
How to calculate the value?From the information, Joshua purchased a game card for the arcade for a total of $18 and played two basketball hoop games for $3.25 each and four rounds of air hockey for $1.75 each.
Therefore, the amount left will be:
= Total amount with him - Amount spent
= $18 - (2 × $3.25) - (4 × $1.75)
= $18 - $6.50 - $7
= $4.50
The amount left is $4.50
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Answer:
4.50
Step-by-step explanation:
Find the 32 nd term of each sequence. 23,30,37,44, ...........
The 32nd term of the arithmetic sequence AP is calculated to be 240.
What basically is an AP arithmetic sequence?In mathematics, an arithmetic progression (AP) is a list and possibly sequence of numbers where each term is collected by adding a sequence towards the term before it.
The fixed number, without regard to arithmetic progression, is signified by the letter 'd.'Common difference => d = a2 - a1 = a3 - a2 = a4 - a3 =...... = a - an-1.nth term of AP: an = a + (n - 1) dThe sum of n terms of an AP's => Sn = n/2(2a+(n-1)d) = n/2(a + l), where l = last term of the AP.Finally, here is the answer to the question:
The following are the numbers with in displayed sequence:
23,30,37,44, ...........
The 32nd number in the series must be investigated because it contains 32 terms.
The common difference between two consecutive terms of an AP that are equal is denoted by the letter 'd.'
Let's consider the first term is'a₁' = 23.
Let's consider 'a₂' = 30 is the second term.
Let's consider the third term is 'a₃' = 37.
Substitute the values the above obtained equation; the 32nd term is-
d = a₂ - a₁
Estimate the common difference;
d = 30 - 23
d = 7
Substitute the values in the next formula; the 32nd term is
The formula given will estimate the nth term equation;
nth term of an AP: an = a + (n - 1) d
Total number of terms ; n = 32
Initial term is a = 23
Common difference d = 7
Substitute the given values in nth term formula;
a₃₂ = a + (n - 1) d
a₃₂ = 23 + (32 - 1)(7)
a₃₂ = 23 + 217
a₃₂ = 240
Thus, the 32nd term value of the given arithmetic sequence is estimated to be 240.
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Solve each equation. 5(s-12)-24 = 3(s+2)
The solution of the given linear equation in one variable 5(s -12) - 24 = 3(s + 2) is at s = 45.
According to the given question.
We have an equation.
5(s -12) - 24 = 3(s + 2)
Since, we have to solve the above linear equation in one variable.
As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Thereofre, the solution of the linear equation in one variable 5(s -12) - 24 = 3(s + 2) is given by
5(s - 12) -24 = 3(s + 2)
⇒ 5s - 60 - 24 = 3s + 6 ( by distributive rule)
⇒ 5s - 84 = 3s + 6
⇒ 5s - 3s = 84 + 6
⇒ 2s = 90
⇒ s = 90/2
⇒ s = 45
Hence, the solution of the given linear equation in one variable 5(s - 12) -24 = 3(s + 2) is at s = 45.
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Riley has been keeping an eye on an emerald ring she likes. Its original price was $4,510, but it is now on clearance, marked down by 60%. What is the price of the ring now?
$
Answer:
Step-by-step explanation:
9989898989
An art museum is putting together an exhibit using
paintings in its collection. The table shows the surface
areas of the paintings being considered. The museum
wants the displayed paintings to be of a similar size, so
it decides to display each painting with the mean surface
area with an absolute deviation of 1500 in.2. How many
paintings are displayed?
Painting Surface Areas
2200 in.²
1500 in.²
2000 in.²
850 in.²
4400 in.²
500 in.²
7800 in.²
2400 in ²
150 in.²
1200 in.²
3100 in.²
900 in.²
Answer:
17 paintings are displayed
Step-by-step explanation:
Solve using zero-factor product property. (x + 7)(2x + 4)(3x - 6) = 0
Answer:
¯＼_(ツ)_/¯
Step-by-step explanation:
x(2x+4)+7(2x+4)[3x-6]=0
(2x^2 + 4x + 14x + 28)(3x-6)=0
(2x^2 + 18x + 28)(3x-6)=0
3x(2x^2 + 18x + 28) -6(2x^2 +18x + 28)=0
6x^2 + 54x^2 + 84x - 12x^2 - 108x - 168 =0
6x^2 + 54x^2 - 12x^2 + 84x - 108x - 168 =0
48x^2 - 24x - 168 =0 {quadratic equation}
When striping the practice football field, Mr. Hawkins first painted the sidelines. Next he marked off 10-yard increments on one sideline. He then constructed lines perpendicular to the sidelines at each 10-yard mark. Why does this guarantee that the 10 -yard lines will be parallel?
This ensures that the lines will be parallel since two lines that are perpendicular to one another must also be parallel.
What is a perpendicular line?Two lines that meet or cross at right angles (90°) are known as perpendicular lines in geometry. The word "perpendicular" comes from the Latin "perpendicularis," which denotes a plumb line.
We can write two lines, AB and CD, as AB ⟂ CD if they are perpendicular to one another. The lines are denoted as being perpendicular by the ⟂ symbol.
The following list includes the two main characteristics of perpendicular lines.
These lines will always cross at right angles.Two lines will always be parallel to one another if they are perpendicular to the same line.Learn more about perpendicular
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Which is the graph of the solution set of −2x + 5y > 15?
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, 3) and (10, 7). Everything above and to the left of the line is shaded.
On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (5, 1). Everything below and to the left of the line is shaded.
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, 5) and (10, 9). Everything above and to the left of the line is shaded.
Answer:
it is the first option
Step-by-step explanation:
First step. Switch the greater than sign and turn the linear inequality to slope formula. after that graph the line. it is a dashed line due to not being greater than EQUAL to. if not equaled to then it is dotted. then you need a point as your testing point to see if it is shaded in that area. I chose to(0,0) but you could have chose any point. Once you plug in the zeros you will notice you get the false statement of 0 greater than 15. so obviously that is a no so you shade the opposite side of your testing point. phew
Answer:
A. On a coordinate plane, a dashed straight line has a positive slope and goes through (0, 3) and (10, 7). Everything above and to the left of the line is shaded.
Step-by-step explanation:
nine square root of two minus three square root of seven plus square root of eight minus square root of twenty eight
[tex]9\sqrt{2} - 3\sqrt{7} + \sqrt{8} - \sqrt{28}[/tex] =[tex]= 11\sqrt{2} - 5\sqrt{7}\\[/tex]
Given an Simplification :
[tex]9\sqrt{2} - 3\sqrt{7} + \sqrt{8} - \sqrt{28}Now, \sqrt{8} = \sqrt{2 \times 2 \times 2} = 2\sqrt{2}\sqrt{28} = \sqrt{2 \times 2 \times 7} = 2\sqrt{7}∴ 9\sqrt{2} - 3\sqrt{7} + \sqrt{8} - \sqrt{28}= 9\sqrt{2} - 3\sqrt{7} + 2\sqrt{2} - 2\sqrt{7}= 9\sqrt{2} + 2\sqrt{2} - 3\sqrt{7} - 2\sqrt{7}= 11\sqrt{2} - 5\sqrt{7}[/tex]
Simplifying rational expressions entails lowering the value of a rational expression to its simplest form. A rational expression is simplified in the same way that fractions are simplified. When the numerator and denominator of a rational number have no common factor other than 1, we consider it to be its simplified version in fractions. The same method may be used to simplify rational expressions; the only difference is that polynomials are included in the fraction.
The procedure for conducting operations on rational expressions is same to that for fractions.
Simplifying rational expressions means reducing their value to their most basic form. Rational expressions are simplified in the same manner that fractions are.
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A=5,5-(+2)+(-11,5)-(-6)
The value of the expression A will be negative 2.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The expression is given below.
A = 5.5 - 2 + (-11.5) - (-6)
Simplify the expression, then the value of the expression A will be
A = 5.5 - 2 - 11.5 + 6
A = 11.5 - 13.5
A = - 2
The value of the expression A will be negative 2.
Your question was incomplete, the question probably was ...
Find the sum of the expression A=5,5-(+2)+(-11,5)-(-6).
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what's a factor in math
Answer:
factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.
Under her cell phone plan, Ava pays a flat cost of $58 per month and $4 per gigabyte.
She wants to keep her bill at $62.40 per month. How many gigabytes of data can she
use while staying within her budget?
If w = 22, what is the value of 4w − 12?
Answer:76
Step-by-step explanation:
you replace W with 22
4(22)-12
=88-12
=72
hope this helps! :)
Answer:
76
Step-by-step explanation:
4w-12
4(22)= 88-12
88-12
76
Hope It Helps
Sorry If I'm Wrong
log6⁸+2log6³+log6¹²-log6²⁴
The solution of expression is 8log6.
What are the properties of logarithms?There are four basic properties of logarithms:
logₐ(xy) = logₐx + logₐy.
logₐ(x/y) = logₐx - logₐy.
logₐ(xⁿ) = n logₐx.
logₐx = logₓa / logₓb.
According to the problem, we will use some of the basic logarithmic properties,
We have been given that expression as
⇒ log6⁸ + 2log6³ + log6¹² - log6²⁴
[used property : logₐ(xⁿ) = nlogₐx]
⇒ 8log6 + 6×2log6³ + 12log6 - 24log6
⇒ 8log6 + 12log6³ + 12log6 - 24log6
⇒ 8log6
Hence, the solution is 8log6.
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Please help me please help me please
Answer:
the answe r is I because it does not mirror the other side
The medical examiner is called in to determine how long a person has been deceased. The rate of decay is -0.026 and the temperature outside is 55 degrees. When the medical examiner arrives the temperature of the body was 82 degrees. Assuming the person had a normal body temperature of 98.6 degrees when they passed, how long had the person been deceased? Round answer to the nearest hour.
The person had been deceased for 12 hours
According to given data,
Temperature of normal person had 98.6 degrees,
and the temperature of the person was 82 degrees
outside temperature is 55 and
rate of decay is -0.026
The temperature of body drops :
98.6 - 82 = 16.6 degrees
[tex]\frac{16.6}{55}[/tex] ≈ 0.3
[tex]\frac{0.3}{0.026}[/tex] ≈ 12 hours
therefore, 12 hours had the person been deceased
The rules for exponential decay is f(x) = a b x, where b denotes the decay factor. In the rule of exponential decay function, the decay rate as a decimal. The decay rate represent as a percentage. We change it into a decimal by simply reducing the percent and dividing it by 100.
The amount reduces by a predetermined percentage at regular periods. The exponential decay formula is used to find decrease in growth.
f(x) = a (1 – r)x is form of generic
Where,
a = The initial value
r = decay rate
x = time period
Advantage of the exponential growth and decay graph
The domain is all Real numbers.
The range is all positive real numbers (exclude zero).
Graph has a y-intercept at (0,1). we know that zero power of any number is 1.
we get When b > 1, the graph increases. and 0 < b < 1, the graph decreases.
Has an asymptote (a line that the graph is very close, but never crosses). For graph the asymptote is the x-axis (y = 0).
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Consider the following vector field. f(x, y, z) = 5xyez i yzex k (a) find the curl of the vector field.
The curl of the vector field is:
[tex]=z e^x \hat{\imath}-\left(y z e^x-7 x y e^z\right) \hat{\jmath}-7 x e^z \hat{k}[/tex]
What do we mean by multivariable calculus?Multivariable calculus (also known as multivariate calculus) is the extension of one-variable calculus to multivariable calculus: the differentiation and integration of functions involving multiple variables rather than just one.Multivariable calculus is a fundamental component of advanced calculus. Calculus on Euclidean space is an advanced calculus topic.So,
To find the curve:
[Vector Field] Set up [curl F]:
[tex]Curl F=\left|\begin{array}{ccc}\hat{1} & \hat{\jmath} & \hat{k} \\\frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\7 x y e^z & 0 & y z e^x\end{array}\right|[/tex]
Simplify [3x3 Matrix Determinant] with [curl F]:
[tex]Curl F=\left|\begin{array}{cc}\frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\0 & y z e^x\end{array}\right| \hat{i}-\left|\begin{array}{cc}\frac{\partial}{\partial x} & \frac{\partial}{\partial z} \\7 x y e^z & y z e^x\end{array}\right| \hat{j}+\left|\begin{array}{cc}\frac{\partial}{\partial x} & \frac{\partial}{\partial y} \\7 x y e^z & 0\end{array}\right| \hat{k}[/tex]
Simplify [2x2 Matrix Determinant] with [curl F]:
[tex]Curl F=\left[\frac{\partial}{\partial y} y z e^x-\frac{\partial}{\partial z} 0\right] \hat{\mathrm{i}}-\left[\frac{\partial}{\partial x} y z e^x-\frac{\partial}{\partial z} 7 x y e^z\right] \hat{\mathrm{\jmath}}+\left[\frac{\partial}{\partial x} 0-\frac{\partial}{\partial y} 7 x y e^z\right] \hat{\mathrm{k}}[/tex]
The partial derivatives can be differentiated using the basic differentiation techniques listed above under "Calculus":
[tex]\begin{aligned}&\frac{\partial}{\partial y} y z e^x=z e^x \\&\frac{\partial}{\partial z} 0=0 \\&\frac{\partial}{\partial x} y z e^x=y z e^x \\&\frac{\partial}{\partial z} 7 x y e^z=7 x y e^z \\&\frac{\partial}{\partial x} 0=0 \\&\frac{\partial}{\partial y} 7 x y e^z=7 x e^z\end{aligned}[/tex]
When we substitute our partial derivative values, we get:
[tex]\begin{aligned}Curl F&=\left(z e^x-0\right) \hat{1}-\left(y z e^x-7 x y e^z\right) \hat{\jmath}+\left(0-7 x e^z\right) \hat{k} \\&=z e^x \hat{\imath}-\left(y z e^x-7 x y e^z\right) \hat{\jmath}-7 x e^z \hat{k}\end{aligned}[/tex]
So, we've discovered the curl of the given vector field.
Therefore, the curl of the vector field is:
[tex]=z e^x \hat{\imath}-\left(y z e^x-7 x y e^z\right) \hat{\jmath}-7 x e^z \hat{k}[/tex]
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The correct question is given below:
Consider the following vector field. f(x, y, z) = 7xyezi + yzexk (a) find the curl of the vector field.
Can you list all the real numbers frim 1 through 5? Explain
There is a infinite number of real numbers from 1 through 5
How to determine the count of real numbers from 1 through 5?The range is given as
1 to 5
The set of numbers is given as
Real numbers
Real numbers are any number that are not complex or imaginary numbers
This type of number covers all types of number that are not complex or imaginary numbers and it has an infinite count
Since the numbers cannot be counted, we can conclude that there is a infinite number of real numbers from 1 through 5
Hence, there is a infinite number of real numbers from 1 through 5
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The flywheel on a steam engine rotates 60 revolutions every 15 seconds.
What is the flywheel’s rate of revolutions per second?
Identify the unit rate.
Answer:
Step-by-step explanation:
4 revolutions per second
Which of the following has NO SOLUTION?
A x +5=5+x
B 2(x+5) = 2x + 10
с 3x - 5 =-3x - 5
D
x+7>x+10
OA
Answer:
D, since 7 is less than 10.
i can figure out the answer to this question
The sum of the series of three numbers, which includes the counting number, n, the number before n, and the number after n is 3•n
What is a series?A series of a sequence of numbers is the sum of the numbers up to a specified term.
The given parameters;
n = A counting number
Counting numbers are the natural numbers which is the set of all positive integers.
Given that n is a counting number, we have that n is a positive whole number.
Which gives;
The whole number before n = n - 1
The whole number after n = n + 1
Which gives;
The sum of n, the whole number before n, and the whole number after n is part of a series and can be written mathematically as follows;
The sum = n + n - 1 + n + 1 = 3•n -1 + 1 = 3•n
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Name a pair of vertical angles.
Answer:
TWO PAIR OF VERTICAL ANGLES ARE
D,C
A,R
Complete the square. x² +8 x+ ____
The full quadratic expression is expressed as follows:
x² + 8x + 16
What are equations?An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.
Equations can be graphed, just like a function.
To solve this problem we must complete square in the expression, it is necessary to note that perfect square trinomial has the form of:
(a + b)² = a² + 2ab + b²
x² + 8x + ?
x² = a²8x = 2abb = ?8x = 2xb
2b =8
b = 4
Let's complete the square
x² + 8x + (4)²
x² + 8x + 16
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