to solve the equation 2x=5 for x, which value would you divide ?
you would divide both sides by 2. in this case that would be 2x/2 and 5/2.
Write a recursive definition and an explicit formula for each sequence. Then find a₁₂. 10,20,40,80,160, . . . .
Geometric Progression is a type of recursive mathematical sequence in which the next term is generated by multiplying the previous term with a fixed number that is called the Common Ratio represented by 'r'.It is calculated by the ratio of two consecutive terms.
The formula to calculate the 12th term of a Geometric Progression is :
=> [tex]a_{12} = a.r^{(12-1)}[/tex]
Here a = first term, r = common ratio calculated by => r=(a2/a1), and n = [tex]n^{th}[/tex] term to find
In the given question, First term a = 10, n = 12, and calculating r,
=> r = (a2/a1) => r = (20/10) = 2
Calculating,
[tex]a_{12\\} = (10).(2^{(12-1)})[/tex] => [tex](10).(2048)[/tex]
[tex]a_{12} = 20480[/tex]
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$1 on the first friday. Each Friday after that, the payment will increase by 20% until the end of the school year or $50 every Friday
Refer to ®R .
Identify a chord that is also a diameter.
A circle chord exists a straight line segment with both endpoints on a circular arc.
SU goes through the center, R, so SU is a diameter.
What is the difference between the diameter and chord of a circle?Any straight line segment that traverses a circle's center and has ends on the circle exists said to have that circle's diameter in geometric terms. It exists even comprehended as the longest chord of the circle. Both definitions apply to the diameter of a sphere.
The line segment joining any two points on a circle's circumference exists known as the chord. A circle's diameter exists described as the lengthiest chord that passes through its center.
A circle chord exists a straight line with circular arcs at both ends. A secant line, or simply secant, is the infinite line extension of a chord. A chord exists a segment of a line that connects two points on a curve, such as an ellipse.
SU goes through the center, R, so SU is a diameter.
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Karen is planning a graduation party for the senior class. She plans to rent a meeting room at the convention center that costs 400 . There is an additional fee of 5.50 for each person who attends the party.
d. If the senior class has raised 2000 for the party, how many people can attend?
Approximately 291 people can attend the party.
Given,
The rent of the meeting room at the convention center = 400
Additional fee for each person who attends the party = 5.50
The amount raised by the senior class for the party = 2000
Now we have to find the number of people can attend the party.
That is,
Amount raised by seniors – rent of meeting room = 2000 – 400 = 1600
Now,
The number of people can attend the party = (Amount raised by seniors – rent of meeting room) / additional fee for each person
= 1600 / 5.50
= 290.91
That is, approximately 291 people can attend the party.
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2, 12, 72, 432, ... match the sequence to its equation
Answer:
This is a geometric sequence since there is a common ratio between each term.
Step-by-step explanation:
2592
read warriors
by eren hunter
Answer: the sequence by 6 gives the next term.
Step-by-step explanation: hope this helps!!!
Gas prices averaged $4.33 per gallon in january and $3.89 per gallon in february. what was the percent decrease of the average gas price from january to february? 8.98% 10.16% 11.31% 44%
The percent decrease is 10.16%
How to calculate the percent decrease ?Percent decrease can be calculated by dividing the decrease by the original value and multiplying by 100
The first step is to calculate the decrease
= 4.33 - 3.89
= 0.44
The percent decrease can be calculated as follows
= 0.44/4.33 × 100
= 0.1016 × 100
= 10.16
Hence the percent decrease is 10.16 %
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Answer:
(B) 10.16%
Step-by-step explanation:
Correct on my quiz.
Write the function rule for each function reflected in the given axis.
f(x)=2 x-6 ; y -axis
Functions can be reflected on the x-axis, the y-axis, or both axes. For example, function reflection y= f(x) can be written as y= -f(x) or y= f(-x) even y= -f(-x). There are four types of function or graph transformations: reflection, rotation, translation, and dilation. In mathematics, especially geometry, mirror or mirroring means flipping, so basically, the mirroring of a function is the mirror image of a given function or graph. Hence the reflection function is commonly known as the reflection function.
The function's reflection should be similar in size and shape to the original function.
f(x)=2x-6; y -axis
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The sum of three times x and y equal to 5
The sum of three and the product of x and y ia equal to 5
The product of three times x and y equal to 5
The product of three and the sum of x and y is equal to 5
Answer:
The sum of three and xy is equal to 5
or
The difference of xy and 3 is 5
Step-by-step explanation:
[tex]{ \tt{xy = 5 + 3}} \\ [/tex]
Pls help me math pls help I’ll make you brainless
The difference between average call time on weekdays and average call time on weekends is 2.98 minutes.
Subtraction operation
What do I know?
Short call < 5.5 minutesAverage call time on weekdays = 6.4 minutesAverage call time on weekends = 9.38 minutesWhat do I need to know?
Difference between average call time on weekdays and average call time on weekendsWhat operations, drawings, expressions or formula will I use?
Subtraction operation will be used to determine the difference between average call time on weekdays and average call time on weekendsWork:
Difference between average call time on weekdays and average call time on weekends = Average call time on weekends - Average call time on weekdays
= 9.38 - 6.4
= 2.98 minutes
Writing:
The difference between average call time on weekdays and average call time on weekends can be found by subtracting average call time on weekdays from average call time on weekends.
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A 320 meter long tightrope is suspended between two poles. Assume that the line has an equal chance of breaking anywhere along its length.
b. Determine the probability that the break will occur within 20 meters of a pole.
The probability that the break will occur within 20 meters of a pole is 12.5%.
Probability:
The term probability refers the possible occurrence of the required event.
Given,
A 320 meter long tightrope is suspended between two poles.
Here we assume that the line has an equal chance of breaking anywhere along its length.
Now, we need to determine the probability that the break will occur within 20 meters of a pole.
From the given question,
The line has an equal chance of breaking anywhere along its length.
The first and last 20meters form,
=> [ (20 + 20) / 320 ] x 100
=> [ 40 / 320 ] x 100
=> [ 1 / 8 ] x 100
=> 12.5 %.
Therefore, the probability that a break will occur within 20 meters of a pole is about 12.5%.
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Write a recursive definition and an explicit formula for each sequence. Then find a₁₂. 7,13,19,25,31, . . . .
Arithmetic Progression is a recursive mathematical sequence in which the next term is generated by adding the previous term with a fixed number that is called the Common difference represented by 'd'. This is calculated by the difference between any two terms in the given sequence.
The formula to calculate the 12th term of an Arithmetic Progression is :
=> [tex]a_{12} = a_{(12-1)} + d[/tex]
Here, a = first term, n = nth term, and d = common difference
In the given question, First term a = 7, n = 12, and calculating d,
=> [tex]d = a_{2} - a_{1}[/tex] => d = 6
But for a12 we need to find out a11, a10, a9, a8, a7, a6 using the same formula we get :
[tex]a_{6} = 37, a_{7} = 43, a_{8} = 49, a_{9} = 55, a_{10} = 61, a_{11} = 67[/tex]
Now for a12 we have a11 = 67, by using formula :
[tex]a_{12} = a_{11} +d[/tex]
[tex]a_{12} = 73[/tex]
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what is the value of digit 4 in the decimal 5.04
The value of the 4 is in the hundredth value.
which expression is equivalent to 7 3/4 subtracted by 1/2
The expression which is equivalent to 7 3/4 subtracted by 1/2 will be ( 31 / 4 ) - ( 2 / 4 ).
We are given a statement:
7 3/4 subtracted by 1/2
We need to write an expression to represent the same.
We know that:
7 3/4 can also be written as an improper fraction as:
31 / 4
And 1 / 2 can be written as an equivalent fraction to 2 / 4.
Subtracting the values, we will get the expression as:
( 31 / 4 ) - ( 2 / 4 )
Therefore, the expression which is equivalent to 7 3/4 subtracted by 1/2 will be ( 31 / 4 ) - ( 2 / 4 ).
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Find x, y, z. EXPONENTS!! please hurry.
[tex]3^{9} . 2^{12} .5^{11}[/tex]
Power :
An expression that represents repeated multiplication of the same factor is called a power.
Factor: The number 5 is called the base, and the number 2 is called the exponent. The exponent corresponds to the number of times the base is used as a factor.
the expression 5 x 5. This expression can be written in a shorter way using something called exponents.
5⋅5=5^2
An expression that represents repeated multiplication of the same factor is called a power.
The number 5 is called the base, and the number 2 is called the exponent. The exponent corresponds to the number of times the base is used as a factor.
3 to the first power 3
4^2 4 to the second power or 4 squared 4 ∙ 4
5^3 5 to the third power or 5 cubed 5 ∙ 5 ∙ 5
2^6 2 to the power of six
= [tex](3.5)^{4} (2.3)^{5} (2.5)^{7}[/tex]
= [tex]3^{4+5} .2^{5+7} .5^{4+7}[/tex]
=[tex]3^{9} . 2^{12} .5^{11}[/tex]
Ans : [tex]3^{9} . 2^{12} .5^{11}[/tex]
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b. If you know the 5th and 6th terms of an arithmetic sequence, how can you find term 7 using the arithmetic mean?
The 7th term of the Arithmetic Progression (AP) is found using the common difference formula.
What is the sequence of AP arithmetic progression?In Arithmetic Progression, the difference between the two arithmetical orders is just a constant value (AP). Arithmetic Sequence is another name for it.
We'd come across the few key phrases in AP that were denoted 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 described in terms of common differences.
The following is the formula for determining 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, according the given condition in the question.
Let the 5th term is defined by 'a₅'.
Let the 6th term is defined by 'a₆'.
Let the 7th term is defined by 'a₇'.
The common difference of the can be calculated as;
d = a₆ - a₅
Now, for the second case, it could be written as;
d = a₇ - a₆
So,
a₇ = d + a₆.
Therefor, the 7th term of an AP can be computed by adding the common difference to the 6th term of an AP.
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-10x/21+27/8>9x/10-27/23
Answer:
Answer on screen
Step-by-step explanation:
I hope everything is clear
The radius r og a sphere is increasing at a rate of 6 inches per minute. find the rate of change of the volume when r=11 inches
The rate of change of the volume is 9123 . 185 inches³/min.
What is volume of the sphere?
V = 4/3 r3 is the formula for a sphere's volume. See how the formula is applied in an example where the sphere's diameter is provided.Volume of sphere is
V = 4/3 π r³
differentiating with respect to time
[tex]\frac{dv}{dt} = \frac{4}{3} \pi . 3r^{2} . \frac{dr}{dt}[/tex]
[tex]\frac{dv}{dt} = 4\pi r^{2} . \frac{dr}{dt}[/tex]
now [tex]\frac{dr}{dt} = 6 inches/min ,[/tex] when r = 11
[tex]\frac{dv}{dt} = 4\pi (11)^{2} . 6[/tex]
= 2904 π cubic inches per minute
≅ 9123 . 185 inches³/min
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What is an integer number that is also a rational number 
Answer:
all integers are rational numbers
State the property that justifies the following statement.
If 7(x-3)=35, then 35=7(x-3).
The property that justifies the following statement, if 7(x-3)=35 then 35=7(x-3) is the symmetric property.
Symmetric property is one of the properties of equality which states that if there is an equality sign (=) between two values or numbers, then the two values will always remain equal even if you change the sides of the values. Therefore if ab = cd, then cd = ab
Hence, according to this property, the left side of the equation can be transferred to the right side and the right side of the equation can be transferred to the left side as the order of the equation can be ignored.
The symmetric property also justifies that if the values on the two sides are not equal, then they will remain unequal even if the sides are changed. That is if ab ≠ cd, then cd ≠ ab.
So, according to the symmetric property, the statement, if 7(x-3)=35 then 35=7(x-3) is valid.
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Write a recursive definition for each sequence. 1,4,7,10, . . . .
We get the following order:
1, 4, 7, 10, ....
Given that each term has a common difference, this is an arithmetic
sequence. In this instance, the next item in the series is obtained by multiplying the preceding term by 3.
The formula for arithmetic series is as follows:
an = a + (n - 1)d
Our first term is now a1 = 1.
Common variation d=3
Therefore, by entering these numbers into the given formula,
an = 1 + (n-1)3
an = 3n - 2
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Which inequality is true?
What word makes the statement "The domain and range of a(n) ___________ function is the set of all real numbers" sometimes true?
(F) polynomial
(G) logarithmic
(H) exponential
(I) quadratic
The word that makes given statement sometime true is: quadratic.
The correct answer is an option (I)
We know that, the domain of a function is the set of all possible values for which function is well defined.
And the range of a function is the set of all output values for given input.
We know that the domain of polynomial function is the set of all real numbers but the range of a polynomial function depends on the polynomial.
In case of a logarithmic function, the domain is the set of all non-negative numbers and the range is the set of all real numbers.
For exponential function, the domain of a function is the set of all real numbers and the range is all positive real numbers.
The domain as well as the range of a quadratic function is the set of all real numbers.
So the given statement would be, "The domain and range of a(n) quadratic function is the set of all real numbers."
Therefore, the word that makes given statement sometime true is: quadratic.
The correct answer is an option (I)
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Kylie swam 6 feet below sea level and Bryan swam 8 feet below sea level. Find the difference between the absolute values for each depth.
The difference between the absolute values of Kylie's and Bryan's depth is 2 feet.
Here, we are given that Kylie swam 6 feet below the sea level and Bryan swam 8 feet below sea level.
This implies,
Kylie's distance from the ground level = -6 feet
and Bryan's distance from the ground level = -8 feet
We need to find the difference between the absolute values of their depth.
Thus, we ignore the minus (-) sign and find the difference as follows-absolute difference = | 6 - 8 |
difference = 2 feet
Thus, the difference between the absolute values of their depth comes out to be 2 feet.
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What is the area of the smaller figure, in square centimeters?
04
08
O 20
O 40
Answer:
020
Step-by-step explanation:
I hope it will be helpful for u
3. For this exercise, find the distance between the cities. Assume the earth is a sphere of radius 4,000mi and the cities are on the same meridian.
Answer:
Step-by-step explanation:
Length of an arc of a circle = rC where r = radius and r is the angle in radians
So, the answer is 4000(0.54+0.55)
= 3960 miles.
Compare and contrast the parallelogram and triangle methods of adding vectors.
The laws of parallelogram and triangle methods of adding vectors is compared and the differences are stated.
Triangle Law of Vector Addition
Triangle law of vector addition states that when two vectors are represented as two sides of the triangle with the order of magnitude and direction, then the third side of the triangle represents the magnitude and direction of the resultant vector.
Parallelogram Law of Vector Addition:
The Parallelogram law states that the sum of the squares of the length of the four sides of a parallelogram is equal to the sum of the squares of the length of the two diagonals.
Given,
Here we need to compare and contrast the law of parallelogram and triangle methods of adding vectors.
While we looking at the definition of the both law,
We have identified that both are performing the sum operation, but Triangle law is for two vectors when the second vector deviates from the direction of the first vector. Note here that second vector starts after the first vector.
Where as in parallelogram law, the two vectors start from the same initial point in two different directions.
So, the laws of parallelogram and triangle methods of adding vectors is compared and the differences are stated.
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I need help now!!!!
Problem 2 Got It? Reasoning: How can you prove ∠1 ≅ ∠2 ≅ ∠3 ≅ ∠4 without using the Vertical Angles Theorem? Explain in the response field.
Answer:
use the math skills 9+9+9
Step-by-step explanation:
Determine whether each sequence is arithmetic, geometric, or neither. Then find the tenth term. 1/4, 1,4,16,. . . .
The sequence 1/4, 1, 4, 16, . . . . is a geometric sequence and its 10th term is 65,536
To determine whether the sequence is an arithmetic or geometric one, we need to check the relation between two consecutive terms.
If it is an arithmetic sequence, then:
a(n) = a(n-1) + d
where d is the common difference.
If it is a geometric sequence, then:
a(n) = a(n-1) . r
where r is the common ratio.
The given sequence is:
1/4, 1, 4, 16, . . . .
In this sequence:
a(1) = 1/4
a(2) = 1
a(3) = 4
a(4) = 16
Notice that
a(2) : a(1) = 1 : 1/4 = 4
a(3) : a(2) = 4 : 1 = 4
and so on
Since the ratio of consecutive terms are constant, then the given sequence is a geometric sequence. Furthermore, its ratio, r = 4.
To find the 10th term, use the formula:
a(n) = a(1) . rⁿ⁻¹
Substitute n = 10, r = 4, and a(1) = 1/4
a(10) = 1/4 . 4⁹
a(10) = 4⁸ = 65,536
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If f(x)=x³- x²- x , what is the value of f(-3)?
A. -39
B. -33
C. -21
D. -15
E. -12
-33 is the value of f(-3) if the equation is If f(x)=x³- x²- x .
Explain what a linear equation is.
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.f(x)=x³- x²- x
f(-3) = ( - 3)³ - ( -3)² - ( -3)
= - 27 - 9 + 3
= - 36 + 3 = -33
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