Answer:
Step-by-step explanation:
If the arithmetic sequence is f(x) = 3x-7, x stands for the position of the number in the sequence. In other words, we are looking to solve for x when f(x) = 8:
8 = 3x - 7 and
15 = 3x so
x = 5. The position of the number 8 is the 5th position.
What does this problem ask for:
--> position of '8' in the sequence
Since our general formula: f(x) = 3x - 7
--> 'x' represents the position of the term in the sequence
--> f(x) is the term in the sequence
--> therefore, if we plug '8' into f(x)
--> we can find 'x' which is the position of 8 in the sequence
Thus:
[tex]8=3x-7\\3x=8+7\\3x=15\\x=5[/tex]
8 is the 5th term
Answer: 5th term
What is log 10 called?
Common logarithmic functions are defined as logarithms with base 10 and natural logarithmic functions as those with base e. The common log function is primarily utilized.
The log's value can be expressed in either base 10 or base e. While the value of [tex]log_e 10[/tex] or ln(10) is 2.302585, the value of [tex]log_{10} 10[/tex] is 1. In general, there are two types of logarithmic functions, namely:
1. Frequently Used Logarithmic Function
2. Natural Logarithmic Function
If [tex]log_{a}b[/tex] = x, then axe = b is the definition of the logarithmic function.
Where x is a number's logarithm, "b," and "a" is the base of the log function, which might be either the value "e" or "10." Any positive number, other than 1, should be used as the variable "a," which should not be equal to 1.
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i-Ready
Dilations in the Coordinate Plane-Quiz - Level H
AJKL is dilated by a scale factor of with the center of dilation at the origin.
What are the coordinates of point J'?
7
4
1
C
...
8 9
5 6
3
(-)
2
?
X
+
+
X
1043
8
2
0
0
2
4
6
K
L
8
10
The coordinates of point J' are J'(-12,8)
How to determine the coordinates of point J'A dilation is a transformation that changes the size of a figure but not its shape.
In a dilation with respect to the origin, a point (x, y) is transformed to a point (kx, ky) where k is a scale factor.
In this case, the point J (-3, 2) is transformed under a dilation of 4 with respect to the origin.
So the image point J' is (kx, ky) = (-3*4, 2*4) = (-12, 8)
So the image point of J(-3,2) under a dilation of 4 with respect to the origin is J'(-12,8)
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Complete question
The triangle JKL is dilated by a scale factor of 4 with the center of dilation at the origin.
What are the coordinates of point J' if J = (-3, 2)?
show all work.
Emani subscribes to a Blind Box program that sends her random gifts from Japan every
month. The subscription has a one-time fee of $30 plus $9 per month and will continue
until she cancels.
a.
Emani plans to spend $210 or less from her summer job on this subscription. Write an
inequality to solve for the number of months she will be able to purchase this
subscription.
The inequality equation that represents this scenario is given as 9x + 30 ≤ 210
What is an equation?An equation shows the relationship between numbers and variables in an expression.
Let y represent the total amount of money paid for x months of subscription. If m is the constant rate and b is the initial amount of oil in the tank, hence:
y = mx + b
The subscription has a one-time fee of $30 plus $9 per month, hence:
b = 30, m = 9
y = 9x + 30
Emani plans to spend $210 or less from her summer job on this subscription. Therefore:
9x + 30 ≤ 210
The equation is given as 9x + 30 ≤ 210
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If two lines intersect and one of the angles formed has a measure of
67°, which of the following statements is true? Explain!! your answers.*
*More than one answer may be correct; select all correct answers.
A:Vertical angles are congruent; therefore another angle must equal 67°.
B:The lines form linear pairs.
C:The lines form complementary angles.
D:One of the angles formed measures 23°
E:Two of the angles formed measure 113°
F:Two of the angles formed will have a sum of 180°
G:None of the above.
Following are some true statements, A other angle must be 67 degrees because vertical angles are equivalent. The total of two of the produced angles will be 180°.
When two lines cross, what happens?The sum of the two angles on a straight line at an intersection is 180°, and the vertical angles of two lines are always the same.Whenever two angles are vertically opposed, they are equal. Additionally, a vertical angle and the angle to it are supplementary angles because they add up to 180 degrees. For instance, if two lines cross and form an angle with a given value (X=45°), then the opposing angle also has a value of 45°.Whenever two angles are vertically opposed, they are equal. Additionally, a vertical angle and the angle to it are supplementary angles because they add up to 180 degrees.To learn more about intersecting lines refer to:
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suppose we have a system of 5 equations with 3 variables. how many pivot columns can the corresponding matrix problem have? for any number of pivot columns that you claim is possible, give an example of a linear system where this happens. for any number of pivot columns that you claim is not possible, explain why this is the case.
Suppose we have a linear system that consists of 5 equations with 3 variables, then the maximum number of pivot columns is 3. In this case, the solution exists and unique.
A pivot is defined as the position of the leading entry in a matrix. For example in the matrix below:
1 0 *
0 1 *
0 0 0
The pivot positions are the ones with bold entries.
If we have a system of 5 equations with 3 variables, then the maximum pivot columns is 3.
If we have a system of 5 equations with 3 variables and the number of pivot columns is 3, then the system consists of 3 linearly independent equations. Moreover, the system is consistent. Hence, the solution exists and unique.If we have a system of 5 equations with 3 variables and the number of pivot columns is less 3, and there is a pivot position in the corresponding augmented column, then the system is inconsistent. Hence, the solution does not exist. Example:0 1 * | *
0 0 0 | 1
0 0 0 | 0
0 0 0 |0
The last column is an augmented column
If we have a system of 5 equations with 3 variables and the number of pivot columns is less 3, and there is no a pivot position in the corresponding augmented column, then the system is consistent but has less than 3 linear independent equations. Hence, the solution exists but not unique. It has many solutions.Learn more about linear system here:
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Consider this equation
COS (θ)= -3/ -10
if θ is an angle in quadrant II, what is the value of tan(θ)?
A. -√91/10
B. √91/10
C. √91/3
D. -√91/3
Answer:
Option D
Step-by-step explanation:
As per your question, cos θ = 3/10
tanθ = √(sec²θ - 1) = √((1/cos²θ) - 1)
Put the value of cos θ, √(1/(9/100) - 1 = √(100/9 - 1) = ±√91/9 = -√91/3 (tan θ is negative in the third quadrant.)
So, option D is the correct answer.
In a polynomial equation, the sum of the multiplicities of the roots always add up to.
The sum of the multiplicities of the roots in a polynomial equation is equal to the degree of the polynomial (the highest power of the variable in the equation).
This is known as the Fundamental Theorem of Algebra. The multiplicity of a root is the number of times a root appears in a polynomial equation, and it can be a whole number, a fraction, or even an irrational number.
For example, if the polynomial equation is x³ + 2x² + 4x - 8 = 0, then the degree of the polynomial is 3 and the multiplicities of the roots are 1, 2, and 1, respectively.
Therefore, the sum of the multiplicities of the roots in this equation is 3. This is true for any polynomial equation: the sum of the multiplicities of the roots will always be equal to the degree of the polynomial.
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Write the equation of the line represented by y=-2/3x+4 in standard form.
the line's equation, written in standard form as 2x + 3y = 4, is y=-2/3x+4.
What is a Linear equation?A linear equation is an algebraic equation of the form ax + by = c, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given a linear equation y= -2/3x + 4
from the general formula of standard form
The standard form for linear equations in two variables is Ax+By=C.
From equation 1
y = -2/3x + 4
multiply by 3 on both sides
3y = -2x +4
Taking variable terms on one side
2x + 3y = 4
therefore, the equation of the line represented by y=-2/3x+4 in standard form as 2x + 3y = 4.
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what number should be removed from the list {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} so that the average of the remaining numbers is 6.1?
The number that should be removed from the list {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} so that the average of the remaining numbers is 6.1 is 5.
An average is a single number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group.
The number in the list are {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
The average of them total is 66 so there average is ,
using the formula,
Average = addition of total number/Total number
= (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11)/11
= 66/11
=6
To get average as 6.1 we need to remove 5 to make total addition of 61 so
66 - 5 = 61
Therefore, 61/10 = 6.1
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Answer:6.1
Step-by-step explanation:
The value of a car is $21,000. It loses 11. 8% of its value every year. Find the approximate monthly decrease in value. Round your answer to the nearest tenth
If the value of a car is $21000 and it loses 8% of its value every year , then the approximate monthly decrease in value is $140 .
The value of the car is given as = $21000 ;
the percent decrease in the value of car is = 8% every year ;
So , in 1 year the value of car decreased is = [tex]0.08\times 21000[/tex]
= [tex]1680[/tex] .
So , in 1 year value of car decreased by $1680 ;
to find the monthly decrease , we divide the value by 12 ;
the monthly decrease is = [tex]\frac{1680}{12}[/tex] = $140 .
Therefore , The Approximate monthly decrease in the value of car is $140 .
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What is the answer to this equation 3(4+s)=15?
Answer: S=1
Step-by-step explanation:
9x
13x
20x+12
Solve for X
Helpppp
[tex]\it 13x+9x=20x+12 \Rightarrow 22x=20x+12\bigg|_{-20x} \Rightarrow \ 2x=12 \Rightarrow x=6[/tex]
a data analyst notices that two variables in their data seem to rise and fall at the same time. they recognize that these variables are related somehow. what is this an example of?
This is an example of correlation. Correlation is a statistical measure that describes the relationship between two variables.
A correlation coefficient (r) ranges from -1 to 1, indicating the strength and direction of the relationship.
A coefficient of 1 indicates a perfect positive correlation, meaning that the variables move in the same direction together.
A coefficient of -1 indicates a perfect negative correlation, meaning that the variables move in opposite directions.
A coefficient of 0 indicates no correlation, meaning that the variables are not related.
The variables that the data analyst is observing, that seem to rise and fall at the same time, are positively correlated. This means they are moving in the same direction and as one variable increases, the other variable is also likely to increase.
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The perimeter of a rectangle is 52 centimeters. Find the length and width if the length is an odd integer and the width is 3 times the next consecutive odd integer.
Let length of the rectangle be l
Let witdth of the rectangle be b.
Perimeter = 2*(l+b)
Given
2*(l+b) = 52. ------------(1)
Now length is an odd integer. Let it be represented as
l = 2k+1 , where k is a positive integer
Given width of the rectangle is the 3 times next consecutive odd integer( next in reference to l = 2k+1)
So b = 3*(2k+3), where k is a positive , integer
From (1) we get
2[2k+1 + 3*(2k+3)] = 52
2[2k+1 + 6k +9] = 52
2[8k +10] = 52
4[4k +5] = 52
4k + 5 = 13
4k = 8
k = 2
so length (l) = 2k +1 = 2*2 + 1 =5 cm
width b = 3(2k +3) = 3(2*2+3) = 21 cm
when a fair six-sided die is tossed on a table top, the bottom face cannot be seen. what is the probability that the product of the numbers on the five faces that can be seen is divisible by $6$?
The probability will be 1.
What is probability?
Probability denotes the likelihood of something happening. It is a mathematical discipline that deals with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of occurrences occurring. Probability is defined as the degree to which something is likely to occur. This is the fundamental probability theory, which is also utilised in probability distribution. To determine the likelihood of a particular event occurring, we must first determine the total number of possibilities.
Now,
It is absolute certain! That is, the probability is 1.
As,
Either 6 is on the bottom or it isn't.
1. If 6 is not on the bottom, then 6 can be seen, and so the product
will certainly be a multiple of 6, because 6 is included in the multiplying.
2. If 6 is on the bottom, then both 2 and 3 can be seen, and since
their product is 6, the product of all faces that can be seen will certainly
be a multiple of 6, since 2 and 3 will both be included in the multiplying.
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50 psychology students took a standardized test. the scores are summarized in the gfdt below. scores frequency 180 - 199 11 200 - 219 6 220 - 239 8 240 - 259 11 260 - 279 14 you would like to build a relative frequency distribution for this data set to easily compare it to another class of students. what is the relative fequency for the fourth class, 240 - 259? enter answer as a percent (but do not include the percent symbol).
The relative frequency for the fourth class, 240 - 259 is 22.
The number of times a specific value for a variable (data item) has been seen to occur in relation to the overall number of values for that variable is referred to as the relative frequency. By dividing the absolute frequency by all possible values of the variable, the relative frequency is derived.
To calculate the relative frequency,
Divide the frequency by the total number of data values to obtain the relative frequency. Add all of the earlier relative frequencies to the relative frequency for the current row to obtain the cumulative relative frequency.
Below you can see a distribution table to compare the relative frequencies of other class of students to better understand it.
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What is the product 7x?
7x is equal to 7 times x, so the answer is 7 times whatever x is. if x is equal to 6, then 7x would be equal to 7 multiplied by 6, which is 42. Therefore, the product of 7x is 7 times whatever x is.
7x is an expression that is asking for the product of 7 and x. The product is the result of multiplying two or more numbers together. Therefore, 7x is equal to 7 times whatever x is.
7x is an expression used to calculate the product of 7 and x. The product is the result of multiplying two or more numbers together, so 7x is equal to 7 multiplied by whatever x is. It is important to remember that the product of two or more numbers is the answer you get after multiplying them together. For example, if x is equal to 6, then 7x would be equal to 7 multiplied by 6, which is 42. Therefore, the product of 7x is 7 times whatever x is.
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How do you prove the conditions for similarity of triangles using SSS similarity theorem?
The SSS (Side-Side-Side) similarity theorem states that if three sides of one triangle are equal to the three corresponding sides of another triangle, then the triangles are similar.
To prove this theorem, one would have to use the Triangle Proportionality Theorem. This theorem states that the ratio of any two sides of a triangle is equal to the ratio of the corresponding sides of a similar triangle. Therefore, if the ratio of the corresponding sides of the two triangles is equal, then the triangles must be similar. To prove the SSS theorem, one would have to show that the ratio of the corresponding sides of the two triangles is equal.
The SSS (Side-Side-Side) similarity theorem states that if three sides of one triangle are equal to the three corresponding sides of another triangle, then the triangles are similar.
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If EG and HJ are parallel lines and mEFI = 115°, what is mJIF?
[tex]{ \qquad\qquad\huge\dag\underline{{\sf Answer}}\dag} [/tex]
As the two lines EG and HJ are parallel, we can apply angle pair properties/relations here.
[tex]\qquad \sf \dashrightarrow \: \angle EFI = \angle JIF[/tex]
[ As they form alternate interior angle pair ]
so, by this relation ~
[tex]\qquad \sf \dashrightarrow \: \angle JIF = 115 \degree[/tex]
A circle with a diameter of 32 inches is shown.
circle with diameter of 32 inches
What is the area of the circle using π = 3.14?
3,215.36 in2
803.84 in2
200.96 in2
100.48 in2
Answer:
Option B) 803.84in²
Step-by-step explanation:
We know the formula to find the area of a circle is listed as,
[tex]A = \pi r^{2}[/tex]
But over here the diameter is only given
that means we have to find the radius which is,
[tex]r = \frac{32}{2}[/tex]
[tex]r = 16in[/tex]
Now we can find the area of a circle which is,
[tex]A = 3.14X(16)^{2}[/tex]
[tex]A = 803.84in^{2}[/tex]
Hence , Option B) is the correct answer
What is the scale factor from AXYZ to AUVW?
60
/56⁰
X
83
90
75
41
O A. 1/
OB. 5
1
O C. //
OD. 4
Z
12
56°
U
-83⁰
15
18 /W
41°
The triangles are similar triangles. and the scale factor of triangle UVW to triangle XYZ is 7
What is triangle ?
triangle can be defined in which it contains three sides , three angles and the sum of three angles is always is 180 degrees.
How to determine the scale factor
From the given figure, we have the following corresponding side lengths:
UW = 2
XZ= 14
The scale factor of UVW to XYZ is then calculated using:
Scale factor = XZ/UW
Substitute known values
Scale factor = 14/2
Divide
Scale factor = 7
Hence, the scale factor of triangle UVW to triangle XYZ is 7
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In 12 years I will be five times as old as it was 32 years ago. Write an equation and define your variable.
The expression for the word problem can be written as x + 12 = 5 ( x - 32).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that in 12 years I will be five times as old as I was 32 years ago. The expression in the mathematical form will be calculated as:-
x + 12 = 5 ( x - 32 )
Here, x will be the present age.
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The ratio Tim spends on math homework to science homework is 5 to 4. If he spends 40 minutes on math homework, how many minutes does he spend on science homework?
A.20 minutes
B.32 minutes
C.60 minutes
D.90 minutes
Please explain how you got your answer.Thank you.
According to the ratio presented, he spends 32 minutes on his science homework.
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, The ratio Tim spends on math homework to science homework is 5 to 4.
thus,
(time on math)/ (time on Science) = 5/4
Since he spends 40 minutes on math homework,
From equation 1
Time spent on science = 4/5 * (time on math)
Time spent on science = 4/5 * 40
Time spent on science = 32
therefore, 32 minutes he spends on science homework as per the given ratio.
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What are 4 types of slopes on the graph?
Negative, positive, zero, and undefined are the 4 types of slopes on the graph.
the 4 types of slopes, include:
Negative slope occurs when m 0 and the line slopes downward to the right as x rises.Positive slope occurs when m > 0 and the line slopes uphill to the right as x rises. A horizontal line has a zero slope, or m = 0. The y values for any two points will be the same real number. Y = some number will be the equation. Ex:y=5Undefined Slope: The slope, m, of a vertical line is undefined. The x values for any two points will be the same real number. x = a certain number will be the formula. Ex=6To know more about types of slopes:
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Simplify the expression.
-2³
Answer:
-8
Step-by-step explanation:
What is the factored form of 27x³ 64?
After taking the common, the factored form of [tex]27x^3-64[/tex] is [tex](3x-4)(9x^2+12x+16)[/tex].
In the given question, we have to find the factored form of [tex]27x^3-64[/tex].
The following is how we factor the GCF out of a polynomial:
(1) Determine the polynomial's GCF for each term.
(2) Present each term as the GCF and another factor's product.
(3) To factor out the GCF, use the distributive property.
To solve this question we use the formula [tex](a^3-b^3) = (a-b)(a^2+ab+b^2)[/tex]
We can write [tex]27x^3-64[/tex] as
[tex]27x^3-64[/tex] = [tex](3x)^3-(4)^3[/tex]
[tex]27x^3-64[/tex] = [tex](3x-4)((3x)^2+3x\cdot4+(4)^2)[/tex]
[tex]27x^3-64[/tex] = [tex](3x-4)(9x^2+12x+16)[/tex]
Hence, the factor form of [tex]27x^3-64[/tex] is [tex](3x-4)(9x^2+12x+16)[/tex].
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The complete question is:
What is the factored form of [tex]27x^3-64[/tex]?
Degree 5. Double zero at x=2; zeros at x=3, x=1 and x= -5. Passes trough (0, -30)
So in problem number 7, we want a degree for polynomial. We wanted to have a 0 at x, equals 01 at x, equals negative 3 and double 0 at x. Equals 2 point so that polynomials going to look like x times, x, plus 3 times x, minus 2 quantity squared, but we wanted to pass through the .1 2 point.
What is polynomial?Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable. An example of a polynomial with one variable is x2+x-12. In this example, there are three terms: x2, x and -12. The word polynomial is derived from the Greek words ‘poly’ means ‘many‘ and ‘nominal’ means ‘terms‘, so altogether it is said as “many terms”. A polynomial can have any number of terms but not infinite. In mathematics, a polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example of a polynomial of a single indeterminate x is x² − 4x + 7.To learn more about exponents refer to:
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a tomato has a mass of 100 grams the mass of the ant is 4.0x10x^{3} gram the of the tomato is how much greater than the mass of the ant
Note that if a tomato has a mass of 100 grams and the mass of the ant is 4.0x10⁻³gram, then the mass of the tomato is 25,000 times greater than the mass of the ant.
What is the justification for the above result?The expression for finding the extent to which the Mass of the tomato is greater than that of the ant is given as follows:
100/4.0x10⁻³
= [100 x 10³] / 4.0x10⁻³ x 10³
= 100,000/4
= 25,000
Therefore, the tomato is 25,000 times the mass of the ant.
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Answer:yes 2.5* 10-2
Step-by-step explanation:
What is 9/4= what is the answer
Answer: 9/4 would be 2.25
Answer: 2.25 heeehee
Step-by-step explanation:
is cereal a soup? Cheers that’s all for now darling
bill can finish a report in 2 hours. maria can finish the same report in 4 hours. how long will it take them to finish the report if they work together?
Working together, Bill and Maria can finish the same report in 4/3 or 1 1/3 hours.
Work rate:
The job: 1
Bill: 1/2
Maria: 1/4
Working together: 1/x
Equation:
1/2 + 1/4 = 1/x
2/4 + 1/4 = 1/x
3/4 = 1/x
3x = (4)(1)
3x/3 = 4/3
x = 4/3 hours
Working together, Bill and Maria can finish the same report in 4/3 or 1 1/3 hours.
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