The missing 2nd term of the given arithmetic sequence 25, _, 53,...(a₂ = 39).
What is the AP arithmetic progression sequence?The difference between the two different numerical orders is a fixed number in Arithmetic Progression (AP). Another name for it is Arithmetic Sequence.
We'd come along through a few specific words in AP that were labeled as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)The AP can also be understood in terms of common differences, as shown below.
The operation for reviewing an AP's n-th term is as follows: an = a + (n − 1) × dThe following is the arithmetic progression sum: Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, for the given AP; 25, _, 53....
Let the initial term be 'a₁' = 25
Let the second term be 'a₂' = ?
Let the third term be 'a₃' = 53.
The AP must have the same common difference. So,
d = a₂ - a₁ or d = a₃ - a₂
Equating the common difference to find the 2nd missing term.
a₃ - a₂ = a₂ - a₁
Substitute the given values;
53 - a₂ = a₂ - 25
Bring the variable part on one side.
2a₂ = 53 + 25
a₂ = 78/2
a₂ = 39
Therefore, the 2nd missing value of an AP is found to be 39.
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If mA = 29° and m/B= 29°, then mZA = m/B represents the property of what?
The statement, m∠A ≅ m∠B, represents the congruence property.
What is the Congruency Property of Equality?The congruency property of equality states that if two angles have measures that are equal to each other, then both angles are said to be congruent to each other.
Given that:
The measure of angle A = 29 degrees
The measure of angle B = 29 degrees.
Since both angles have the same measure, then both angles are congruent to each other.
Therefore, the statement, m∠A ≅ m∠B, represents the congruence property.
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Evaluate each finite series for the specified number of terms. 80-40+20- . . . ; n=8
Answer:
The value of the given series is 49.75
Step-by-step explanation:
This is a problem from geometric progression ,
As we know the formula for geometric progression is aₙ = a₁ r ⁿ⁻¹
Where , a₁ is the first term and r is the ratio , and n is the number of terms.
Ratio is , 40/80 = 1/2
Here , a₄ = 80 . (1/2)⁴ ⁻ ¹ = 80 / 8 = 10
a₅ = 80 . (1/2)⁵ ⁻ ¹ = 80 / 16 = 0.5
a₆ = 80 . (1/2)⁶ ⁻ ¹ = 0.25
a₇ = 80 . (1/2)⁷ - ¹ = 0.125
a₈ = 80 . (1/2) ⁸ ⁻ ¹ = 0.625
Now the series can be written as .
80-40+20- 10 + 0.5 - 0.25 + 0.125 - .625 = 49.75
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Help please need it for rn
Check the picture below.
what number is the square root of 78 in between of
Answer:
the square root rounded up is around 8
Step-by-step explanation:
because if the 5 is not beside the number it rounds down and the number was 3 so its 8
Define the variable?
Write the constraints ?
What is the Objective Equation?
Variable - These are the unknown quantities that expected to estimate it as an output.
Example:- In an optimization model for labor scheduling, the number of nurses to employ during the morning shift in an emergency room may be a Decision variable.
Constraints - the restrictions on the variable open linear programming problem are called constraints.
The conditions x ≥ 0, y ≥ 0 called non negative restrictions.
Objective equation - the objective equation should be specified in a quantitative way.
It is of the form Z = ax + by
where x and y are decision variable.
Z is to be maximized or minimized to find the solution.
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Suppose B is the midpoint of -AC . Use the given information to find the missing measure. A B=6 y-14, B C=10-2 y, A C= ?
If AB = 6y - 14, BC = 10 - 2y then the value of AC = 8.
What is meant by midpoint?
In geometry, the midpoint is the point in the middle of a line segment. It is equidistant from both endpoints and serves as the segment and endpoint centroid. It cuts the segment in half.
Given: AB = 6y - 14, BC = 10 - 2y
Since B is the midpoint of AC, AB = BC then
6y - 14 = 10 - 2y
Add 14 on both sides of the equation, and we get
6y - 14 + 14 = 10 - 2y + 14
6y = - 2y + 24
Add 2y on both sides of the equation
6y + 2y = - 2y + 24 + 2y
simplifying the above equation, we get
8y = 24
y = 24/8
y = 3
Substitute the value of y in AC then we get
AC = 2(6(3) - 14)
= 2(4)
AC = 8
Therefore, the value of AC = 8.
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NEED THIS NOW DONE CORRECTLY
The figure shows three quadrilaterals on a coordinate grid:
B and C are similar and also congruent.
A and B are similar but not congruent.
A and B are similar and also congruent.
A and C are similar but not congruent.
Step-by-step explanation:
A and B are similar but not congruent
similar=same shape
congruent=same shape and same size
Write the equation of each line in standard form.
slope =0 ;(0,2)
The standard equation for the given slope is y - 2 = 0
These are two methods for finding the equation of a line given a point and slope. Create the equation y = mx + b.
We just solved using the m given in the problem and the b. Point-slope form = y-y1 = m (x-x1), where (x1, y1) is the specified point and m is the specified slope. "x" and "y" remain as variables.
Putting (0,2) for (x1, y1) and m=0, we get
y-2=0(x-0)
(y-2) =
y-2=
+y-2=0
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Complete the square. x² -5 x+ ____
The full quadratic expression is expressed as follows:
x² - 5x + 6.25
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 - 5x + ?
x² = a²5x = 2abb = ?5x = 2xb
2b =5
b = 5/2
Let's complete the square
x² - 5x + (5/2)²
x² - 5x + 25/4
x² - 5x + 6.25
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Find the first five terms of each sequence. an =5 n-3
The first five terms of the sequence an =5 n-3 are 2, 7, 12, 17 and 22.
According to the question.
We have a formula or a rule for finding the terms of a sequence i.e.
an = 5n -3.
The first term of the sequnence an = 5n - 3 is given by
a(1) = 5(1) -3 = 5 -3 = 2
The second term of the sequence an = 5n - 3 is given by
a(2) = 5(2) - 3 = 10 - 3 = 7
The third term of the sequence an = 5n -3 is given by
a(3) = 5(3) - 3 = 15 - 3 = 12
The fourth term of the sequence an = 5n - 3 is given by
a(4) = 5(4) - 3 = 20 - 3 = 17
The fifth term of the sequence an = 5n - 3 is given by
a(5) = 5(5) - 3 = 25 - 3 = 22
Hence, the first five terms of the sequence an =5 n-3 are 2, 7, 12, 17 and 22.
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Lisa wants to buy some new shirts are her favorite store. Each shirt costs $15 and she wants to buy a pair of shoes that are $35. Lisa only has $137 to
spend
Let S represent the number of shirts that Lisa buys
Which inequality describes this scenario?
O 137 < 158 +35
O 137 > 158 +35
O 137 >_ 158 +35
O 137 <_158 +35
The inequality that shows the number of shirts that Lisa buys is given as 15x + 35 ≤ 137
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let s represent the number of shirts that Lisa buys. Lisa only has $137 to spend, therefore:
15x + 35 ≤ 137
The inequality that shows the number of shirts that Lisa buys is given as 15x + 35 ≤ 137
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Evaluate 6(x-5) at x=8
Answer:
18
Step-by-step explanation:
Substitute x with 8 :
6(8-5) =
8-5 = 3
6(3) = 6 × 3 = 18
Therefore 18 is our final answer
Hope this helped and have a good day
Hey there!
6(x - 5)
= 6(8 - 5)
= 6(8) + 6(-5)
= 48 - 30
= 18
OR EVEN:
6(x - 5)
= 6(8 - 5)
= 6(3)
= 18
18 = 18
Therefore, your answer should be:
18
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
A. Solves each equation by extracting square root.
1.) x² = 16
2.) x² = 49
3.) x² = 128
4.) x² = 108
5.) x² = 121
6.) x²-169 = 0
7.) x²-80=0
8.) x²-63=0
9.) 5x2 – 125 = 0
10.) 3x²-132-0
1,2,5 square root both sides
47simplify into 8 root 2simplify into 6 root 311add 169 to both sides and square root to get 13add 80 to both sides and simplify into 4 root 5add 63 to both sides and simplify into 3 root 7add 125 to both sides, divide both sides by 5, x^2=25, square root, x=5add 132 to both sides, divide by 3, x^2=44, square root simplified is 2 root 11I need help with both question pls
Answer:
0.03x+0.05=1.50
Hopely this can help you
Step-by-step explanation:
Find the coordinates of point P on →AB that partitions the segment into the given ratio AP to PB .
a. A(0,0), B(0,6), 2 to 1
The point P which partitions the line segment AB have coordinates as P(0,3)
Line Segment is a line which joins together two points to form a straight line. It can be extended in either side.
It is given that,
A line segment AB having coordinates such as A(0,0) and B(0,6) respectively
The line segment AB is partitioned by a given point P in two minor line segments AP and PB
We need to find, the coordinates of the partitioning point i.e. P
The given formula will be used,
The coordinates of the point P = ([tex]\frac{x1+x2}{2}[/tex], [tex]\frac{y1 + y2}{2}[/tex])
Now, x1 = 0, x2 = 0, y1 = 0, y2 = 6
Putting values in the formula, we get
([tex]\frac{0+0}{2}[/tex], [tex]\frac{0+6}{2}[/tex])
(0,3)
Hence, the point P which partitions the line segment AB have coordinates as P(0,3)
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What is the sum of the solutions of |3|y-4| = 9 and |y-4|=3 ?
The sum of the solutions are 32/3.
The modulo (or "modulus" or "mod") is the remainder after dividing one number by another.
Example: 100 mod 9 equals 1
Because 100/9 = 11 with a remainder of 1
Another example: 14 mod 12 equals 2
Because 14/12 = 1 with a remainder of 2
12-hour time uses modulo 12 (14 o'clock becomes 2 o'clock)
It is where we end up, not how many times around.
|3y-4|=9
3y-4=9 or 3y-4=-9
3y=13 or 3y=-5
y=13/3 or y-5/3
|y-4|=3
y-4=3 or y-4=-3
y=7 or y=1
The solutions are y=13/3, y=-5/3, y=7, y=1
Hence the sum of the solutions are 32/3.
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Determine whether the graph represents a function. Explain
In a rectangle, the width is 1 feet shorter than the length. The area of the rectangle is 30 square feet. Find the length of the rectangle.
(ANSWER ASAP EXTRA POINTS)
Two stores are having sales on the same shirt. the sale at store 1 is "2 shirts for $22" and the sale at store 2 is "each $12.99 shirt is 10% off". explain how much will you save by buying at store 1.
Answer:
22 divided by 2 equals 11, so each shirt at store one, you are getting for $11. Store 2 is having a sale of 10% off 12.99 is 11.69, so each shirt is $11.69. So, Store 1 is a better deal.
Step-by-step explanation:
Answer:
1.38$
Step-by-step explanation:
QUESTION
Two stores are having sales on the same shirt. the sale at store 1 is "2 shirts for $22" and the sale at store 2 is "each $12.99 shirt is 10% off". explain how much will you save by buying at store 1.
EXPLANATION
store one 2 shirts 22$
store 2 1 shirt 12.99/10=1.30 so 12.99-1.30=11.69x2=23.38
23.38-22=1.38
y-2=¼(x+5) into slope-intercept form?
The slope intercept form is y = 1/4x + 13/4
The general expression for slope intercept form is given as follows
y = mx + c
where, m = slope of the line
c = intercept
We have been given the equation that is,
y – 2 = 1/4(x+ 5)
We will solve this step by step to convert it into the general form that is,
y – 2 = 1/4(x+ 5)
y – 2 = 1/4x + 5/4
y = 1/4x + 5/4 + 2
y = 1/4x +13/4
which is in the general form of y= mx + c where m = 1/4 and c = 13/4
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in exercises 1-4, find m 1 and m 2. Tell which theorem you use in each case.
Answer:
m1 = 122°
m2= 58°
Step-by-step explanation:
M1 is an alternate interior angle, of 122°, which means that that angle is also 122°.
The line with m1 and m2 added together equal 180°, so we can subtract 122 from 180 to find m2.
180-122= 58
if the lenght and breadth of the rectangular sheet of paper is 49 1/2 cm and 23 1/2 cm repsectivly . Find its perimeter
Answer: 146 cm
Step-by-step explanation:
A simple way to find the perimeter of a rectangle is to double both sides and add them.
(49.5 * 2) + (23.5)
= 99 + 47
= 146
Select the correct answer. Which equation has no solution? A. 24x + 32 − 2.1x = 20.9x + 30 + x + 2 B. 24x + 32 − 2.1x = 20.9x + 30 + x − 2 C. 24x + 32 − 2x = 20.9x + 30 + x − 2 D. 24x + 32 = 20.9x + 30
The equation that has no solution is 24x+32-2.1x = 20.9x+30+x-2
Part A
24x+32-2.1x = 20.9x+30+x+2
Add like terms
24x-2.1x-20.9x-x = 30+2-32
0x = 0
Infinitely many solutions
Part B
24x+32-2.1x = 20.9x+30+x-2
Add like terms
24x-2.1x-20.9x-x = 30-2-32
0x = -4
There is no solution
Part C
24x+32-2x = 20.9x+30+x-2
Add like terms
24x-2x-20.9x-x = 30-2-32
0.1x = -4
x = (-4)/0.1
x = -40
It has only one solution
Part D
24x+32 = 20.9x+30
Add like terms
24x-20.9x = 30-32
3.1x = -2
x= (-2)/3.1
x = -0.64
It has only one solution
Hence, the equation that has no solution is 24x+32-2.1x = 20.9x+30+x-2
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What are the solutions of the quadratic equation x²-20=8 x ?
F. 2,10
G. 20,1
H. -1,20
J. -2,10
The solutions of the quadratic equation [tex]x^{2}[/tex]-20=8 x are -2 and 10.
The given quadratic equation is [tex]x^{2}[/tex] - 20 = 8 x . To get the solutions of the given quadratic equation we need to simplify the quadratic equation. The step wise simplification of the given quadratic equation is,
[tex]x^{2}[/tex] - 20 = 8 x
[tex]x^{2}[/tex] - 8x -20 =0
on breaking -8x in two parts as -10x + 2x , we will get
[tex]x^{2}[/tex] -10x + 2x -20 = 0
x (x - 10) + 2 (x - 10) = 0
On taking (x-10) as common, we get
(x-10) (x+2) = 0
x = -2 , 10
The solutions of the quadratic equation [tex]x^{2}[/tex]-20=8 x are -2 and 10.
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−
6
x
−
4
≤
2
(
x
−
10
)
Answer:
x > 2
Step-by-step explanation:
because , you have to use inverse operation to check your answer .
-6x-4< 2x-20
-6x-4+4<2x-20=4
-6x<2x-16
-6x-2x<2x-16-2x
-8x<-16
(-8x)(-1)>(-16)(-1)
8x>16
8x/8 > 16/8
x>2
Simplify each expression.
-35 / (-5)
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
The simplified expression of -35 / (-5) is 7.
What is an expression?A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms.In order to help establish the order of operations and other elements of logical syntax, mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.An expression can be used in algebra to represent a value, and that value may rely on the values given to the variables that appear in the expression.Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
Let the given expression be -35 / (-5) then
-35 / (-5) = -35/-5
simplifying the above equation, we get
= 35/5
= 7
Therefore, the value of -35 / (-5) is 7.
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Evaluate each expression for the given value of the variable. 5c³ - 6c√-2 c ; c=-5
The value of the expression [tex]5c^{3} -6c\sqrt{-2c}[/tex] at c = -5 is [tex]5(-125 +6\sqrt{10})[/tex] .
An algebraic expression is an expression having constant and variable joined with algebraic operation(+,-,×,÷).
For Example , 2c+5x+6 is an algebraic expression.
In the given expression
[tex]=5c^{3} -6c\sqrt{-2c}[/tex]
Substituting the value of c = -5 .
We get ;
[tex]=5(-5)^{3} -6(-5)\sqrt{-2(-5)}[/tex]
[tex]=5(-125) +30\sqrt{-2(-5)}\\ \\ =-625 +30\sqrt{10}[/tex]
taking 5 common from both the terms
[tex]=5(-125 +6\sqrt{10})[/tex]
Therefore , the value of the expression [tex]5c^{3} -6c\sqrt{-2c}[/tex] is [tex]5(-125 +6\sqrt{10})[/tex].
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Use this activity to explain how the AA criterion for triangle similarity follows from the definition of similarity in terms of dilations. (Hint: Use parallel lines)
The AA criterion for triangle similarity states that if two triangles have two pairs of congruent angles, then the triangles are similar.
What is a triangle similarity criterion?
According to the Angle-Angle (AA) criterion, two triangles are considered comparable if "two angles of one triangle are respectively equivalent to two angles of another triangle."
What distinguishes AA similarity from AAA similarity?
The total number of angles in a triangle is 180. Therefore, the third angle of a triangle will automatically become equal if two of its angles are equal. Triangles are related because of the AA resemblance. Three angles should equal the other triangle in AAA.Learn more about Angle-Angle-Side (AAS)
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Here is a distribution of quiz scores for a statistics course: 87, 91, 74, 73, 80, 84, 68, 75 what is the standard deviation?
The standard deviation is 7.35.
What is standard deviation?Standard deviation is used to determine how the values in a group differs from the mean of the values in the group
In order to determine the standard deviation, take the following steps:
Determine the mean of the observation: (87 + 91 + 74 + 73 + 80 + 84 + 68 + 75) / 8 =79
Determine the difference between each value and the mean and then square the result:
(87 - 79)² + ( 91 - 79) ² + (74 - 79)² + (73 - 79)² + (80 - 79)² + (84- 79)² + (68 - 79)² +( 75- 79) ²
64 + 144 + 25 + 36 + 1 + 25 + 121 + 16 = 432
Determine the mean of the sum of the squared differences and then find the square root of the mean:
√432 / 8 = 7.35
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What is the equation of the line that is perpendicular to the line y=3/5x+10 and passes through the point (15,-5)?
y=3/5x-20
y=-3/5x+20
y=5/3x-20
y=-5/3x+20
Answer: Option (4)
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals of each other, so the slope of the line we want to find is -5/3.
Of the options, the only one that satisfies this is choice 4.
