The point after all the rotation and translation will become (17 - y, x + 12) from (x, y).
We need to first rotate the point 90° counterclockwise around the origin.
Let the point be (x, y)
When rotating a point 90° counterclockwise about the origin, the coordinate of the point (x, y) will become (-y, x). In other words, x and y will be switched and y will become negative.
Now, we need to translate the point 17 units right.
So, it means that the x - coordinate of the point will become x + 17
So, the point now becomes:
( -y , x ) = ( - y + 17 , x)
(17 - y, x)
Now we have to translate the point 12 units up.
So, we get that:
(17 - y, x + 12)
Therefore, the point after all the rotation and translation will become (17 - y, x + 12) from (x, y).
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How is 14,398 written in scientific notation?
The given number written in scientific notation is 1.4398 × 10⁴
From the question, we are to write the given number in scientific notation.
The given number is 14,398.
A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.
Thus,
To write the numbers in scientific notation, we will express the number as the multiplication of a number between 1 and 10 and a power of 10.
A number between 1 and 10 that can easily be formed from the number is 1.4398
Then, we can write that
14,398 = 1.4398 × 10⁴
Hence, the given number written in scientific notation is 1.4398 × 10⁴
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How many times do you need to divide by ten to get from 7190.77190.77190, point, 7 to 0.719070.719070, point, 71907?
The stemplot displays the selling prices of homes for ABC Realty in April. A stemplot titled Home Sale Data for A B C Realty. The stems are 0, 1, 2, 3, 4. The first column of leaves is 67, 23, 13, blank, 59. Column 2 is 85, 81, 25, blank, 82. Column 3 is 92, 81, 76, blank, blank. Column 4 is blank, 96, 77, blank, blank. Column 5 is blank, blank, 87, blank, blank. Key: 1 slash 23 = 123,000 dollars. Select the correct set of data for the stemplot. $459,000, $277,000, $67,000, $123,000, $213,000, $482,000, $85,000, $181,000, $300,000, $225,000, $92,000, $181,000, $287,000, $196,000, $276,000 $459,000, $277,000, $67,000, $123,000, $213,000, $482,000, $85,000, $225,000, $92,000, $181,000, $287,000, $196,000, $276,000 $459,000, $277,000, $67,000, $123,000, $213,000, $482,000, $85,000, $181,000, $225,000, $92,000, $181,000, $287,000, $196,000, $276,000
The data from the stemplot is $459,000, $277,000, $67,000, $123,000, $213,000, $482,000, $85,000, $181,000, $225,000, $92,000, $181,000, $287,000, $196,0900, $276,000.
What is the data from the stemplot?A stemplot is a table that has similar features with to a histogram. A stemplot divides a number into a stem and a leaf. The stem is the first digit in a number and the leaf is the rest of the numbers. For example, the number 223, 2 would be the stem and 23 would be the leaf.
Advantages of a stemplot is that it displays all of the data in the dataset. A stemplot is also easy to interpret. Stemplots also give a concise representation of a dataset. A disadvantage of a stemplot is that is can only be used for a small dataset.
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Pleasee helppppp! I will mark BRAINLIEST!!
The mass of a paperclip is 9.0 × 10−4 mg. If a box of paperclips has 6.14 × 104 paperclips, determine the total mass of the paperclips in the box. Write the final answer in scientific notation with the correct number of significant digits. 2.86 × 100 mg 5 × 101 mg 5.5 × 101 mg 5.526 × 101 mg
The total mass of the box of paperclips in scientific notation is 5.526 × 10¹ miligrams. (Correct choice: D)
What is the mass of a box of paperclips in scientific notation?
In this question we must use, interpret and manipulate numbers in scientific notation to find the total mass of the paperclips in a box. The statement indicates the mass of a paperclip and the number of paperclips in the box, then the total mass of the box of paperclips is equal to the product of mass of the paperclip and the number of paperclips. Then, the total mass in the box is:
m = (9.0 × 10⁻⁴ mg) · (6.14 × 10⁴)
m = (9.0 · 6.14) · (10⁻⁴ · 10⁴)
m = 55.26 · 10⁰
m = 55.26 mg
m = 5.526 × 10¹ mg
The total mass of the box of paperclips in scientific notation is 5.526 × 10¹ miligrams. (Correct choice: D)
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P(x)=x2+5x-3 findthe following:
b) p (2)=
Answer:
if x=2
P(2) = (2)² + 5(2) -3
= 4 + 10 - 3
= 14 - 3
= 11
help d-7 < 12; d = 19
Answer:
12 ≮ 12
False
Step-by-step explanation:
19 − 7 < 12
12 ≮ 12 (<--- line through the less than sign)
False
(I'm not 100% sure)
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{d - 7 < 12}\\\\\mathsf{\rightarrow 19 - 7 < 12}\\\\\mathsf{\rightarrow 12 < 12}\\\\\large\text{Thus, the left and right should be equivalent to each other.}\\\\\mathsf{12 \nless 12}\\\\\mathsf{12 = 12}[/tex]
[tex]\huge\text{The correct symbol should be: \boxed{\mathsf{\boxed{=}\ because\ the}}}\\\\\huge\boxed{\mathsf{numbers\ are\ equal\ to\ each\ other.}}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]A line has one endpoint of (-3,7) and a midpoint of (5,2). What is the other endpoint ?
The another endpoint of a line is (13, -3).
What is Straight line?
A line with no curve is called a straight line.
Given that;
One endpoint of a line = (-3, 7)
Midpoint of a line = (5, 2).
Now, Let the other endpoint of a line = (x, y)
Then, Other endpoint is solve by the definition of midpoint of two points as;
(x + (-3) / 2 , y + 7 / 2 ) = (5, 2)
(x - 3 / 2 , y + 7 / 2) = (5, 2)
By compare we get;
x - 3/ 2 = 5
x - 3 = 2 * 5
x - 3 = 10
x = 10 + 3
x = 13
And,
y + 7 / 2 = 2
y + 7 = 2 * 2
y + 7 = 4
y = 4 - 7
y = -3
Hence, The another endpoint of a line is (13, -3).
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02.05 MC)
The functions f(x) = −x + 3 and g(x) are shown in the graph. The function g(x) is a transformation of f(x), such that g(x) = kf(x), where k is a rational number.
Graph of linear function f of x going through negative 1 comma 4, 0 comma 3, and 1 comma 2 and linear function g of x going through negative 1 comma 8, 0 comma 6, and 1 comma 4. The functions intersect at 3 comma 0.
Which of the following statements describes the effect and value of k?
a
The graph of g(x) is a vertical stretch of the graph of f(x); the k value is positive and greater than 1.
b
The graph of g(x) is a vertical compression of the graph of f(x); the k value is positive and less than 1.
c
The graph of g(x) is a vertical stretch of the graph of f(x); the k value is positive and less than 1.
d
The graph of g(x) is a vertical compression of the graph of f(x); the k value is positive and greater than 1.
The statements that describes the effect and value of k in the functions f(x) = −x + 3 and g(x) as shown in the graph where function g(x) is a transformation of f(x), such that g(x) = kf(x) and k is a rational number, is
a. The graph of g(x) is a vertical stretch of the graph of f(x); the k value is positive and greater than 1.
What is vertical stretch?A vertical stretch refers to a movement in the upward direction. A transformation that leads to a vertical stretch is as a result of multiplying by a positive number that is above or greater than 1.
The given graphs f(x) was factored and this lead to a vertical stretch to produce g(x), and the factor that leads to vertical stretch is a positive number greater that 1. Hence we say that The graph of g(x) is a vertical stretch of the graph of f(x); the k value is positive and greater than 1.
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If 6x = 1/216 what is the value of x
Answer:
The answer is in the attached screenshot (I wanted to show properly formatted fractions)
Explanation:
The explanation is in the attached screenshot (I wanted to show a properly formatted fraction)
If f(-2)=3x+2 and g(4)=x^2-x find each value
Answer:
a) -3
b)12
Step-by-step explanation:
For f(X)= 3x+2
Where x=-2(Substitute for x in the expression)
F(-2)=3(-2)+2
= -6+2
= -3
G(4)=
[tex]x^{2} -x\\4^{2} -4\\=16-4\\=12[/tex]
I need help with this problem please and thank you
The transformation here is; the original function was moved '1' unit downwards.
What is the Transformation of the given Function?Transformations simply takes the basic function and transforms it to another function.
The rules of transformation are;
f(x) transformed to f(x) + a means that the function will be moved 'a' units upwards.f(x) transformed to f(x) - a means that the function will be moved 'a' units downwards.f(x) transformed to f(x + a) means that the function will be moved 'a' units to the left.f(x) transformed to f(x - a) means that the function will be moved 'a' units to the rightFrom the question, the original function is;
f(x) = x + 4
Now, we are told that it undergoes a transformation to;
f(x + 4) - 1
From the transformation rules above, we can say that the transformation here is; the original function was moved '1' unit downwards.
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Write each equation in logarithmic form. 5⁴=625
The logarithmic form of the given equation (5⁴=625)is = log₅(625) = 4.
logarithmic exponential form:Logarithmic functions are the inverses of exponential functions. So a log is an exponent! y=logbx if and only if by=x for every x>0 and 0b1.
Why we employ logarithms?Logarithms depict changes in terms or multiplication: in the instances above, each step is 10x larger. Each step on the natural log is "e" (2.71828...) times longer. When dealing with a sequence of multiplications, logarithms let us "count" them in the same way that addition counts on our behalf when effects are added.
According to the given data:using the property of log:
5⁴=625
Apply logarithmic definition: aⁿ = b gives logₐᵇ = n
so,
a = 5
b = 625
n = 4
equation would be as follows:
log₅(625) = 4
The logarithmic form of the given equation (5⁴=625)is = log₅(625) = 4
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Answer: [tex]log_{5} 625 = 4[/tex]
Step-by-step explanation:
1. Which fraction is greater? a. 5/2 b. 9/4 please help me
Answer: 5/2
Step-by-step explanation:
5/2 is greater because divided it’s 2.4 and 9/4 is 2.25. 2.5 > 2.25.
help i do not understand this
Answer:
74 degrees
Step-by-step explanation:
180-32=148
148÷2=7
The diagonals of parallelogram LMNO intersect at point P. If MP = 2x + 5 and OP = 3x − 7, what is MP?
29
12
1
−2
The measure of the segment MP is 29 units.
In this question we have been given a parallelogram LMNO
The diagonals of parallelogram LMNO intersect at point P.
The diagonals of parallelogram LMNO are LN and MO.
The point P divides each diagonal into exactly two equal parts.
So, MP = OP
If MP = 2x + 5 and OP = 3x − 7, we need to find MP.
As, MP = OP
2x + 5 = 3x − 7
2x - 3x = -7 - 5
-x = -12
x = 12
So, the value of the MP would be,
MP = 2x + 5
= 2(12) + 5
= 24 + 5
= 29
Therefore, the measure of the segment MP is 29 units.
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aisha has a collection of 180 coins. how many coins represent 10% of her collection?
divide/scale down to solve for the missing percent.
In percentage, the 10% of her collection is a 18 coins.
According to the statement
We have to find that the 10% of her collection.
So, For this purpose, we know that the
A percentage is a number or ratio expressed as a fraction of 100.
From the given information:
Aisha has a collection of 180 coins. how many coins represent 10% of her collection
Then
The percentage of the collections of the 180 coins = 10% of 180 coins
Then
Collection of the coins = 10% of 180
Collection of the coins = 10/100*180
Collection of the coins = 0.1*180
Collection of the coins = 18.
So, In percentage, the 10% of her collection is a 18.
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I need some help TwT
2.64 + -0.2 + -0.35 + 0.625=?
Answer: 2.715
Step-by-step explanation:
Answer:
2.715
Step-by-step explanation:
We have 2.64 - 0.2 - 0.35 + 0.625.
2.64 - 0.2 = 2.44
2.44 - 0.35 + 0.625
Next, we subtract 0.35 from 2.44
2.09 + 0.625 = 2.715
Which inequality is represented by the number line?
The inequality represented by the number line is x ≤ -6
What is straight line?A straight line of numbers is shown visually as a number line. . On a horizontal number line, the numbers grow as we walk to the right and decrease as we move to the left.
Given that,
The response must include both a less than and a negative sign.
At -6, the graph displays a closed circle.
which means that -6 is a solution to the inequality.
The darkened arrow on all values greater than -6 denotes that x -6 is the proper inequality.
The inequality represented by the number line is x ≤ -6
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Students at a middle school take an elective during the last hour of the school day. There are 11 students who take an art class. There are 3 times as many students who take a music class as students who take an art class. What is a ratio that relates the number of students who take a music class to the number of students who take an art class.
The ratio that relates the number of students who take a music class to the number of students who take an art class is 3 : 1 .
A ratio is defined as a comparison of two sets of the same unit, showing how much of one set is contained in the other. A common form to express the relationship between two quantities, such as 'a' and 'b', is a:b, read as 'a follows b'.Let the number of students taking arts class be "x"
and number of students taking music class be "y".
It is given that 11 students take an art class which can be given by
x = 11 ...(1)
There are 3 times as many students who take a music class as students who take an art class which can be given by
y = 3x = 3(11) = 33 ....(2)
On dividing equation (1) by (3) , we get
x/y = 11/33 = 1/3
This can be written as x : y = 1 : 3 but here we are asked about the ratio of music class to the art class then ratio is given by y : x = 3 : 1
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Which variable is discrete? length of jacket length of jacket weight of jacket weight of jacket number of pockets inside jacket number of pockets inside jacket size of jacket pocket in square inches size of jacket pocket in square inches
Discrete variables are Number of pockets inside the jacket .
A variable whose value is determined by counting is referred to as a discrete variable. examples: the number of students in attendance. how many red marbles are in the jar. number of heads when three coins are flipped. The number of students, kids, the shoe size, and so forth are some typical examples of discrete data. Height, weight, length, time, temperature, age, and other continuous data are typical examples. Discrete data are represented by integer and ordinal data values. Continuous Variable. "Discrete variables" are variables that have a finite number of possible values. Each and every qualitative variable is discrete. Certain quantitative variables, like performance ratings of 1, 2, 3, 4, or 5, or temperature rounded to the nearest degree, are discrete.
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Find the value of a^2+b when a=-2and b=5
Answer:
9
Step-by-step explanation:
Just substitute -2 in for a and 5 in for b
[tex]a^2 + b\\-2^2 + 5\\4 + 5\\9[/tex]
Whenever you square a negative number the result is positive
Answer:
The answer is 9 or 3squared
Step-by-step explanation:
Swap the -2 in for a and 5 in for b
When ever a negative number is squared the answer will be a postive number.
The equation y=6.72(1.014) x models the world population y , in billions of people, x years after the year 2000 . Find the year in which the world population is about 8 billion.
the population will reach 8 billion by 2012 ,as calculated by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Given:
y = 6.72 ( [tex]1.014^x[/tex]), wherey = population in billionsx = time in yearsTo find: Year when population is 8 billion, i.e., y = 8.
Finding:
8 = 6.72 ( [tex]1.014^x[/tex])
=> [tex]\frac{8}{6.72}= ( 1.014^x)[/tex]
Taking log on both sides
=> [tex]log(\frac{8}{6.72})= log( 1.014^x)[/tex]
=> log(1.19) = x (log 1.014) (as [tex]log_b(a)^m = m (log_b(a))[/tex] )
=> [tex]\frac{log(1.19)}{log (1.014)}[/tex] = x
=> x = [tex]\frac{0.0755}{0.006}[/tex]
=> x = 12.58
Hence, the population will reach 8 billion by 2012 ,as calculated by properties of logarithm.
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An arithmetic sequence has first term 4 and constant difference 20.
The fifth term of the arithmetic sequence is 84
How to determine the valueThe formula for determining the nth term of an arithmetic sequence is expressed as;
Tn = a + (n -1)d
Where;
a is the first termn is the number of termsd is the common differenceTo determine the fifth term, we have to substitute the value of nas 5, we have;
T5 = 4 + (5-1) 20
T5 = 4 + 4(20)
expand the bracket
T5 = 4 + 80
T5 = 84
Thus, the fifth term of the arithmetic sequence is 84
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The complete question;
An arithmetic sequence has first term 4 and constant difference 20. Find the fifth term of the sequence
A family plans to have 3 children. For each birth, assume that the probability of a boy is the same as the probability of a girl. What is the probability that they will have at least one boy and at least one girl?.
Answer:
0.75
Step-by-step explanation:
The outcomes are equally likely, so the easiest way to work this problem is to write out the 8 outcomes in this sample space. In two outcomes the gender of all three children is the same (GGG, BBB). The other 6 outcomes contain at least one boy and one girl.
*Please mark brainliest
Simplify each radical expression. Use absolute value symbols when needed. √9x⁴/ 36
The value of the given expression √9x⁴/ 36 in simplified form is x² / 2.
By canceling it with its common factors, we must create this expression in its most basic form.So, we have to make this expression √ 9x⁴ / 36 in its lowest form by cancelling it with its common factors.√ 9x⁴ / 36
Take 9 from this since the common factor is 9.= √ 9 x⁴ / 9*4
= √ x⁴ / 4
We must now rewrite it as follows:4 = 2*2 = ( 2 )² and x⁴ = x² * x² = ( x² )²
As a result, the square root of x⁴ is x².Moreover, 2 is the square root of 4.hence, √ x⁴ / 4 = ( x² / 2 )²
Taking positive real numbers as a given, words are extracted from the radical.√ x⁴ / 4 = x² / 2
Therefore, the value of the given expression √9x⁴/ 36 in simplified form is x² / 2
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Solve each equation.
3²x=27
After solving the equation, x = 3/2 is the value of x in [tex]3^{2x}[/tex] = 27
⇒ [tex]3^{2x}[/tex] = 27
⇒ [tex]3^{2x}[/tex] = [tex](3)^3[/tex]
⇒ 2x = 3
⇒ x = 3/2
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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find the product of 3x^4y^5 and 2x^2+y
Darren is purchasing a car that costs $12,000. He is taking out a simple interest loan at an annual rate of 3%. If he makes monthly payments over a period of 3 years, how much is his monthly payment?
$363.33
$349.12
$333.33
$296.13
Based on the cost of the car and the simple interest loan amount, the amount of Darren's monthly payment is $363.33
What is the monthly payment?First, find the simple interest on the loan:
= 12,000 x 3% x 3 years
= $1,080
The total amount to be repaid:
= 1,080 + 12,000
= $13,080
The monthly payment is:
= 13,080 / (12 x 3 years)
= $363.33
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Answer: its 363.33
Step-by-step explanation:
The equation says x - 0.8 divided by 1.2 = 6 This is a multi step with decimals find the x equation
The value of x in the equation (x – 0.8) / 1.2 = 6 is 8.
Given,
The equation = (x – 0.8) / 1.2 = 6
We have to expand this equation and find x.
That is,
(x – 0.8) / 1.2 = 6
Multiply 1.2 both sides.
(x – 0.8) x (1.2) / 1.2 = 6 x 1.2
(x – 0.8) = 6 x 1.2
(x – 0.8) = 7.2
Shift 0.8 to right hand side
Then we get,
x = 7.2 + 0.8
x = 8
Therefore, the value of x in the equation (x – 0.8) / 1.2 = 6 is 8.
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What's the distance between 3/4 and 1/8 on a number line?
Answer:
5/8
Step-by-step explanation:
3/4 = 6/8. so 6/8-1/8= 5/8. 5/8 is the answer.