In Euclidean geometry, parallel lines (lines that never intersect) are equidistant in the sense that the distance of any point on one line from the nearest point on the other line is the same for all points.
In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet. They can be both horizontal and vertical. We can see parallel lines examples in our daily life like a zebra crossing, the lines of notebooks, and on railway tracks around us.
There are 3 main rules:
Corresponding angles are equal. A line cutting across two parallel lines creates four pairs of equal corresponding angles, as in the diagram below.
Alternate angles are equalCo-interior angles add to 180°Vertically opposite angles are equalAngles on a line add to 180°Learn more about parallel lines to visit this link
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how many permutations of abcde are there in which the first character is abc and the last character is cde
Total number of permutations of abcde in which the first character is a, b, or c and the last character is c, d, or e is 48 permutations.
Case 1 : First letter is "a", last letter is any of {c, d, e}. Hence there are 3! ways of arranging the remaining three letters
3! * 3 = 18 combinations.
Case 2 : First letter is "b", last letter is any of {c, d, e}. Hence there are 3! ways of arranging the remaining three letters
3! * 3 = 18 combinations.
Case 3 : First letter is "c", last letter is any of {d, e}. Hence there are 3! ways of arranging the remaining two letters
3! * 2 = 12 combinations.
Hence, total number of combinations = 18 +18 + 12 = 48 permutations.
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What is the y-intercept of 5x 4y =- 12?
The y-intercept of the equation 5x-4y = -12 is 3.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
We have the equation:
5x-4y = -12
To find the y-intercept:
First, we have to simplify the equation as subject to y.
5x-4y = -12
4y = 5x+ 12
y = (5/4)x+12/4
y = (5/4)x + 3
Now, we know the slope-intercept form:
y = mx+b,
where m is the slope and b is the y-intercept.
Comparing, both the equation,
b = 3
3 is the y-intercept.
Therefore, y-intercept is 3.
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Renting a roller rink for your birthday costs $250 plus $10 per person. The total charge
for your party was $400. Translate this information into an equation using a to
represent the number of guests at your party.
Using your equation, determine how many people attended your party.
Answer:
15 people attended the party
The parent function of the function g(x)=(x-h)² + kis f(x)=2. The vertex of the function g(x) is located at (9.-
8). What are the values of h and k?
g(x)=(x-____)^2+______
Answer:
h = 9
k = -8
Step-by-step explanation:
⭐ [tex]g(x) = (x-h)^2 + k[/tex] is already written in vertex form.
⭐ Vertex form: [tex]f(x) = a(x-h)^2 +k[/tex], where the vertex is (-(-h), k)
We are already given the vertex (9,-8), so we have to substitute these numbers into g(x).
[tex]g(x) = (x-9)^2 -8[/tex]
The equation of parabola is solved and the values of h and k are 9 and -8 respectively
What is a Parabola?A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
The equation of the parabola is given by
( x - h )² = 4p ( y - k )
y = a ( x - h )² + k
where ( h , k ) is the vertex and ( h , k + p ) is the focus
y is the directrix and y = k – p
The equation of the parabola is also given by the equation
y = ax² + bx + c
where a , b , and c are the three coefficients and the parabola is uniquely identified
Given data ,
The vertex form of a parabola function is given by:
g(x) = a(x - h)² + k
where (h, k) is the vertex.
In this case, we are given that:
g(x) = (x - h)² + k
And the vertex is located at (9, -8)
So we have:
h = 9
k = -8
Therefore, the function g(x) can be written as:
g ( x ) = ( x - 9 )² - 8
Hence , the equation of parabola is g ( x ) = ( x - 9 )² - 8
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A baketball player attemptd 15 baket in a game he make 9 which ratio decribe the number of baket the player made to the number of baket the playerd attempted
The ratio that describes the number of baskets the player made to the number of baskets the player attempted is 9:15. This can be simplified to 3:5.
The ratio of the number of baskets made by the player to the number of baskets attempted is 9/15. This ratio can be simplified to 3/5, which means that for every 5 baskets attempted, the player made 3 baskets. This ratio can also be expressed as a percentage by dividing the number of baskets made by the number of baskets attempted and multiplying the result by 100%. In this case, the percentage of baskets made by the player is 60% (9 baskets made / 15 baskets attempted * 100% = 60%). This means that out of every 100 baskets attempted by the player, he made 60 baskets.
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-X+4=67
-4Z-9=67
-7Y-10=67
Answer:
the answer is 20
Step-by-step explanation:
20+0=20
what is a polynomial function in standard form with zeros 1,2,-2 and -3
The standard form of the polynomial function with zeroes 1, 2, -2, and -3 is
[tex]x^4[/tex] + 2x³ - 7x² - 8x + 12 = 0.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
The zeroes of a polynomial:
x = 1, 2, -2, and -3.
This can be written as,
(x - 1)(x - 2)(x + 2)(x + 3) = 0
Simplify to get the equation.
(x² - 2x - x + 2)(x² + 3x + 2x + 6) = 0
(x² - 3x + 2)(x² + 5x + 6) = 0
[tex]x^4[/tex] + 5x³ + 6x² - 3x³ - 15x² - 18x + 2x² + 10x + 12 = 0
[tex]x^4[/tex] + 2x³ - 7x² - 8x + 12 = 0
Thus,
The equation of the polynomial is [tex]x^4[/tex] + 2x³ - 7x² - 8x + 12 = 0.
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What does a standard deviation of 35 mean?
As the standard deviation 35 is high so the values are far from the mean.
What is standard deviation?In the statistics, standard deviation is an estimation that implies how far each available data apart from mean value. In a word, it is a measure of variances of data in relation to the mean. A low standard deviation indicates that values are closer to mean value and high standard deviation indicates the values are distributed widely.
What does a standard deviation of 35 mean?Standard deviation of a given data set 35 means that all data set are 35 unit far from the mean value. As the value is high so all the values are dispersed widely relative to the mean value.
In the other hand, this high standard deviation implies there are enough variances in the given data in relation to the mean.
Standard deviation is one of the measures of risk assessment. Imagine an organization published a number of statistical observation data. If we find a high standard deviation, then it will be high risk of collapse of the business.
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if quadrilateral abcd is rotated 90° clockwise about point a and then reflected across the y-axis to create quadrilateral a’b’c’d’, what will be the coordinate of d’?
According to the 90° clockwise rotation, the new coordinate of the quadrilateral D' is (3, -2)
Quadrilateral
Quadrilateral refers a closed shape and a type of polygon that has four sides, four vertices and four angles.
Given,
If quadrilateral ABCD is rotated 90° clockwise about point A and then reflected across the y-axis to create quadrilateral A’B’C’D’.
Here we need to find the coordinate of D'.
In order to find the new coordinates, first we have to identify the current coordinates of the quadrilateral.
While we looking into the graph, we have identify the point of
A (0,0), B(-4, 3), C(1,5) and D(2,3)
Now, we have to use the rule of clockwise 90° rotation, states that to rotate the figure 90 degrees clockwise about a point, every point(x , y) will rotate to (y, -x).
According to this rule, the new coordinates are written as,
A(0,0) = A'(0,0)
B'(-4,3) = B'(-3,-4)
C(1,5) = C'(5, -1)
D(2,3) = D' (3, -2)
Therefore, the new coordinate of D' is (3, -2).
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can anyone help me.
Answer:
Solution:
Given,
Ratio of photo to to the photo frame=2:3
Length of photo frame=36cm
= 36÷3
=13
then,
Length of photo = 13 ×2
= 26cm
Step-by-step explanation:
Therefore,the length of the photo is 26cm
x and y are integers.
y>_2
x+y≤4
y≤ 2x + 2
Mark on the grid all the points
that fulfill all three inequalities.
The common region for all the inequalities y ≥ 2, y ≤ 2x + 2and x + y ≤ 4 is represented by ΔABC (the last graph).
What is an inequality?
"It is a statement which consists of an order relationship (greater than, greater than or equal to, less than, or less than or equal to) between two mathematical expressions."
For given question,
We have been given three inequalities
y ≥ 2 ,
x + y ≤ 4 ,
y ≤ 2x + 2
If we draw the graph of these three inequalities then the common region represents the all the points that fulfill all three inequalities.
An inequality y ≥ 2 represents all the points on and above the line y = 2
An inequality x + y ≤ 4 represents all the points on and below the line x + y = 4
An inequality y ≤ 2x + 2 represents all the points on and below the line y = 2x + 2
Consider the following graphs.
The first graph represents the points which fulfill the inequality y ≥ 2
The graph for an inequality x + y ≤ 4 is represented by the shaded blue region.
The graph for an inequality y ≤ 2x + 2 is represented by the shaded green region.
The common region for all the inequalities is represented by ΔABC
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Is 9 by 16 equal to 5 by 9 yes or no?
Answer:
No
Step-by-step explanation:
9/16 and 5/9 have a common factor is 144
So, we have
81/144 and 80/144
So, 9/16 > 5/9
Answer:
Step-by-step explanation:
no they are not equal, NO
what is the smallest sample in the list below that will satisfy the conditions for the use of a normal model to represent the sampling distribution? a. 30 b. 15 c. 25 d. 20
The smallest sample size that will satisfy the conditions for the use of a normal model to represent the sampling distribution is 30, as stated in option (a).
The smallest sample size that will satisfy the conditions for the use of a normal model to represent the sampling distribution is determined by the Central Limit Theorem, which states that if the sample size is greater than or equal to 30, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.
According to this theorem, if the sample size is greater than or equal to 30, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution. Therefore, the smallest sample size that will satisfy the conditions for the use of a normal model is 30. The answer is therefore option (a).
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Are Mean and median same?
Mean and Median are not the same.
Mean is the average value of a given dataset. Mean is calculated by adding all the values in the dataset and divided by the number of values.
Median is defined as the number in the middle of the dataset. Median is calculated by arranging the values in ascending order and finding out the middle most term. If there are two middle terms, then we calculate the average of both.
Mean is the arithmetic average, while median is the positional average. There may be various external factors that contribute in defining the mean. So for uneven data, median is the more robust value. Mean defines the central value of data, but median defines the midpoint of data and classify the data points to two sets, higher value or lower value.
So mean is the average of the given dataset and Median is the mid value of the dataset when arranged in ascending order.
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Most graduate schools of business require applicants for admission to take the Graduate Management Admission Council’s GMAT examination. Scores on the GMAT are roughly normally distributed with a mean of 527 and a standard deviation of 112. What is the probability of an individual scoring above 500 on the GMAT?HOW HIGH MUST AN INDIVIDUAL SCORE ON THE G-MAT IN ORDER TO BE THE HIGHEST 5%
The probability of an individual scoring above 500 on the GMAT is 0.5984.
What is Normal Distribution?An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the centre of the range.
Given:
[tex]\mu[/tex] = 527
[tex]\sigma[/tex] = 112
Now, z= (500-527)/112
z= -27/112
z= -0.2410
and, P( X>500)= P(z> -0.2401)
= 1- 0.4052
= 0.5984
Hence, the probability of an individual scoring above 500 on the GMAT is 0.5984.
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Solve the system of equations.
−5y+3x=3
−8y+9x=−12
Answer:
The solution to the system of equations is x = 9/12 and y = 27/60.
Step-by-step explanation:
To solve a system of equations, we can use elimination or substitution. In this case, we can use elimination by adding the equations together. When we add the two equations, the y-terms will cancel out, leaving us with an equation in terms of x only.
First, let's add the equations:
-5y + 3x = 3
-8y + 9x = -12
-----------
-13y + 12x = -9
Then, we can divide both sides of the equation by -13 to get the value of x:
(-13y + 12x) / -13 = (-9) / -13
12x = 9
x = 9/12
Since we know the value of x, we can substitute it back into either of the original equations to find the value of y:
-5y + 3(9/12) = 3
-5y + 27/12 = 3
-5y = -27/12
y = 27/60
Therefore, the solution to the system of equations is x = 9/12 and y = 27/60.
Why we need to clean the measuring instrument before and after use?
Conscientiously cleaning your devices is crucial, as any residue that remains on your device may impact the accuracy of your measurements. The material your device is made of plays a significant role in the cleaning method you should use.
A tool used to measure a physical amount is called a measuring instrument. Measurement is the process of gathering and comparing physical quantities of actual things and events in the physical sciences, quality control, and engineering.
The process of measuring yields a number associating the subject under study and the referenced unit of measurement, and established standard objects and occurrences are employed as units. These numerical relations are acquired using measuring devices and rigorous test procedures that specify the instrument's use.
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Which formula can be used to find the nth term of the geometric sequence 1/6,1,6,36?
Answer:
[tex]a_n = \frac{1}{6}(6)^{n-1}[/tex]
Step-by-step explanation:
⭐What is the formula of a geometric sequence/progression?
[tex]a_n = a_1+1(d)^{n-1}[/tex][tex]a_1[/tex] is the first term of the geometric sequence[tex]d[/tex] is the common ratio (the number each consecutive term gets multiplied by) of the geometric sequence[tex]n[/tex] is the number term you want to findWe are given the geometric sequence.
Thus, we need to find the first term and the common ratio, and substitute those values into the geometric sequence formula.
The first term is [tex]\frac{1}{6}[/tex]
⭐How do we find the common ratio?
divide one term by another termmake sure both terms are consecutive of each otherI am choosing term 1 and term 2, but you can choose any other 2 terms that are consecutive.
term 1 = [tex]\frac{1}{6}[/tex]
term 2 = [tex]1[/tex]
[tex]\frac{term2}{term1} = \frac{1}{\frac{1}{6}}[/tex]
[tex]\frac{term2}{term1} = 6[/tex]
∴ The common ratio of this sequence is 6.
Now, substitute these values (common ratio & first term) into the geometric sequence equation.
[tex]a_n = \frac{1}{6}(6)^{n-1}[/tex]
What is mode 2 2 3 3 4 4 5 5 6 6 is?
The given data (2, 2, 3, 3, 4, 4, 5, 5, 6, 6) has no mode.
A mode is defined as the value that has the highest frequency in a given set of values. It is the value that appears the most number of times.
In statistics, the value that consistently appears in a particular collection is referred to as the mode. The mode or modal value in a data collection is sometimes referred to as the value or number that occurs most frequently in the data set. In addition, to mean and median, it is one of the three measures of central tendency.
The mode is the value that occurs the most often in a given set of data.
Given data: 2, 2, 3, 3, 4, 4, 5, 5, 6, 6.
In the given observations, data is repeated an equal number of times.
So, the given data has no mode.
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A new bank customer with $4,500 wants to open a money market account. The bank is offering a simple interest rate of 1.5%.
Answer:
a. 1350
b. 6500
Step-by-step explanation:
1.5%×4500=5850
1350+4500=5850
Step-by-step explanation:
39 slices from 3 cakes = blank
slices per cake
Answer:
13
Step-by-step explanation:
39/3
How many days does SSS approved disbursement account?
According to the SSS disbursement account, it takes 2 business days for approval.
The term disbursement refers to the payment of federal student aid funds to the student by the school.
Here we have to find the number of days taken for SSS disbursement account approval.
In order to find the solution, we must know the process of SSS disbursement policy, that takes the payment data and transforms it into a disbursement instrument.
Here we have given that, as per the SSS disbursement policy, it takes member-borrower shall receive the full short-term loan proceeds in their account within two banking days from the loan date provided the payment instruction of SSS was sent before the cut-off time.
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What is value of expression example?
An example of value of expression is 5 × 2a.
In the field of mathematics, a value of an expression can be described as such an expression that includes two or more two mathematical numbers. Apart from the numbers, one or more than one mathematical operation is also a part of the value of the expression.
In the example, 5×2a, 5 and 2 are the two mathematical numbers and multiplication (×) is the mathematical operation. Hence, the expression 5×2a serves as an appropriate example of the value of expression in the field of mathematics.
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This problem has a fraction bar. What
operation is the same as a fraction bar?
Division
Addition
Subtraction
Multiplication.
Answer:
Division
Step-by-step explanation:
Simple, the fraction bar basically represents the operation of division in math!
Which exponential function has a growth factor of 5?
So, an exponential function with a growth factor of 5 is of the form y = a * 5^x, where a is a constant coefficient.
An exponential function of the form y = a * b^x has a growth factor of b. Therefore, an exponential function with a growth factor of 5 is of the form y = a * 5^x, where a is a constant coefficient.
For example, if a = 2, then the function y = 2 * 5^x has a growth factor of 5.
Here is a table showing the values of y for some values of x:
x y
0 2
1 10
2 50
3 250
4 1250
As x increases, the values of y increase exponentially at a rate determined by the growth factor of 5.
Therefore, an exponential function with a growth factor of 5 is of the form y = a * 5^x, where a is a constant coefficient.
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For example, if a = 2, then the function y = 2 * 5^x has a growth factor of 5.
Here is a table showing the values of y for some values of x:
x y
0 2
1 10
2 50
3 250
4 1250
As x increases, the values of y increase exponentially at a rate determined by the growth factor of 5.
Therefore, an exponential function with a growth factor of 5 is of the form y = a * 5^x, where a is a constant coefficient.
What are the 2 types of roots and their functions?
Real roots and distinct roots are the two types of roots of quadratic function.
Given,
Real roots;-
We are aware that anytime we resolve a linear or quadratic equation, we obtain the equation's value variable, or in other words, we identify the equation's solution. We refer to this "solution" as the real roots. For instance, when we solve the equation x27x+12=0, the real roots come out to be 3 and 4.
Distinct roots;-
Whenever the answers to a quadratic equation have two distinct values that may be represented by real numbers on a number line. It is known as distinct roots.
Here,
How do you tell which roots are distinct and real?
The discriminant is the expression b² - 4ac for the quadratic equation ax² + bx + c = 0. The discriminant's value reveals how many roots f(x) has: - The quadratic function has two unique real roots if b² - 4ac > 0, otherwise it does not. The quadratic function has one repeating real root if b² - 4ac = 0.
That is,
The quadratic function has real roots and distinct roots.
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How many zeros can the polynomial 2x² 3x 4 have?
There are two zeros of the polynomial 2x²-3x+4.
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
The given polynomial is 2x²-3x+4.
Two times of x square minus three times of x plus four.
2x²-3x+4=0
We find the roots by using quadratic equation formula.
x=-b±√b²-4ac/2a
a=2, b=-3, c=4
x=3±√9-4(8)/4
x=3±i√23/4
So the roots are x=3+i√23/4 and x=3-i√23/4.
A polynomial of degree 2 can have 2 real zeros, 1 real zero, or no real zeros
Hence, there are two zeros of the polynomial 2x²-3x+4.
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How do you solve a mean table?
Mean from a frequency table is when we find the mean average from a data set which has been organised into a frequency table.
To calculate the mean we find the total of the values and divide the total by the number of values. The number of values is the total frequency. This can be abbreviated to nn.
[tex]Mean = \frac{total}{number of values} =\frac{total}{n}[/tex]
We can use an extra column to help.
Mean is a measure of central tendency, it is a value that can be used to represent a set of data.
E.g. The frequency table shows the number of people living in 1616 flats.
There are 55 flats with 11 person living there, so we work out 1\times5=51×5=5
There are 66 flats with 22 people living there, so we work out 2\times6=122×6=12
There are 33 flats with 33 people living there, so we work out 3\times3=93×3=9
There are 22 flats with 44 people living there, so we work out 2\times4=82×4=8
The number of values (n)(n) is the total frequency, here n=16n=16
mean = total/n
=34/16
= 2.125
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Can yall please help me with this I really need help
Answer:
i believe it is G
[tex] \frac{7}{3} [/tex]
if a rectangle is twice as long as it is wide and has a perimeter of 54 meters, what is the area of the rectangle?
Answer:
l = 2w (length is twice the width)
P = 2l + 2w
54 = 2l + 2w (but we know l equals 2w so we can replace l with 2w)
54 =2(2w) + 2w
54 = 6w
w = 9
l =2(9) (l = 2w
l=18
A = lw