The solution is
The distance between the point A and C is greater than the distance between the points B and C
What is the distance of a line between 2 points?The distance of a line between 2 points is always positive and given by the formula
Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )
The distance between A and B is D , and the distance D is
Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
Given data ,
Let the first point be = A
The value of A = A ( 5 , 6 )
Let the second point be = B
The value of B = B ( 5 , 3 )
Let the reference point be C = C ( -3 , 2 )
Now , the distance between the points A and C = P
The distance between the points B and C = Q
Now , the value of P is calculated from the distance formula
Distance Q = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
Substituting the values in the equation , we get
P = √ ( 5 - ( - 3 ) )² - ( 6 - 2 )²
P = √ ( 8 )² + ( 4 )²
P = √ ( 64 + 16 )
P = √80 units
Now , the value of Q is calculated from the distance formula
Substituting the values in the equation , we get
Distance Q = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
Q = √ ( 8 )² + ( 1 )²
Q = √ ( 64 + 1 )
Q = √65 units
So , the value of Q is less than value of P
Therefore , the distance of point B to C is lesser than point A to C
Hence , The point B ( 5 ,3 ) is closer to the point C ( -3 , 2 )
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what's the answer of this please say
Answer:
Below
Step-by-step explanation:
See diagram below....you are looking for 'x' in the right triangle
Use Pythagorean Theorem :
5^2 + x^2 = 13 ^2
x ^2 = 13^2 - 5^2
x ^2 = 144
x = 12 m
I need to determine whether the function is a polynomial function, and if so I have to write it in standard form and state it’s degree type and leading coefficient.
f(x) = 7-1.6x² - 5x
Answer:
It is a polynomial, the standard form is -1.6[tex]x^{2}[/tex]-5x+7, and the degree is 2.
Step-by-step explanation:
1. Polynomials can be positive, negative, a zero, a whole number, decimals, or a fraction.
2. When writing a polynomial in standard form arrange the terms from least degree to greatest degree.
3. In this instance the degree of the polynomial is 2 because the term with the highest degree only has x to the second power.
;)
Which equation represents the line that passes through point (2,3) and is perpendicular to 4x-5y=7
Answer:
Step-by-step explanation:
First, find the slope of 4x - 5y = 7
Simplify it down to a readable form:
5y = 4x - 7
y = (4x - 7)/5
y = 4/5 x - 7/5
slope = 4/5
slope perpendicular to 4/5 is its opposite reciprocal, which would be -5/4.
given the point (2,3), we can get the equation using point slope form for linear equations: y-k = m(x-h) for point (h,k).
now plug:
y-3 = (4/5)(x-2)
y-3 = (4/5)x - 8/5
fifth degree, 4 is a zero of multiplicity 2, −4 is the only other zero, leading coefficient is 2.
The equation of the polynomial equation with a fifth degree is P(x) = (x + 4)³(x - 4)²
How to determine the polynomial equation?The given parameters are
Degree of polynomial = 54 is a zero of multiplicity 2-4 is the only other zeroThe sum of multiplicities of the polynomial equation must be equal to the degree.
This means that the multiplicity of the zero -4 is 3
The equation of the polynomial is then calculated as
P(x) = (x - zero)^multiplicity
Substitute the known values in the above equation, so, we have the following representation
P(x) = (x - (-4))³ * (x - 4)²
Open the inner brackets
P(x) = (x + 4)³ * (x - 4)²
This gives
P(x) = (x + 4)³(x - 4)²
Hence, the equation is P(x) = (x + 4)³(x - 4)²
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The sum the sum of the first nine terms of an ap is 126 and the sum of the second nine terms is 369 then
The arithmetic sequence that has the given features is presented as follows:
[tex]a_n = 2 + 3(n - 1)[/tex]
What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and called common difference d.
The nth term of an arithmetic sequence is obtained by the following rule:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term of the sequence.
The sum of the first n terms is presented as follows:
[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]
The sum of the first nine terms is of 126, hence:
[tex]S_9 = 126[/tex]
[tex]\frac{9(a_1 + a_9)}{2} = 126[/tex]
[tex]4.5(a_1 + a_9) = 126[/tex]
The ninth term is written as follows:
[tex]a_9 = a_1 + 8d[/tex]
Hence:
[tex]4.5(a_1 + a_1 + 8d) = 126[/tex]
[tex]9a_1 + 36d = 126[/tex]
[tex]a_1 + 4d = 14[/tex]
The sum of the second nine terms is of 369, hence:
[tex]S_{18} = 126 + 369[/tex]
[tex]S_{18} = 495[/tex]
Then:
[tex]\frac{18(a_1 + a_{18})}{2} = 495[/tex]
[tex]a_{1} + a_{18} = 55[/tex]
The 18th term is:
[tex]a_{18} = a_1 + 17d[/tex]
Hence:
[tex]2a_1 + 17d = 55[/tex]
From the first equation, it is found that:
[tex]a_1 = 14 - 4d[/tex]
Hence the common difference is obtained as follows:
2(14 - 4d) + 17d = 55
28 - 8d + 17d = 55
9d = 27
d = 3.
Hence the first term is of:
[tex]a_1 = 14 - 4(3) = 2[/tex]
Thus the definition of the sequence is:
[tex]a_n = 2 + 3(n - 1)[/tex]
Missing InformationThe problem asks for the definition of the arithmetic sequence.
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In triangle OPQ, o=700 cm, p=840 cm and q=620. Find the meaure of ide P to the nearet degree
The measure of side P to the nearest degree is 79 degrees.
Given:
ΔOPQ ,
O = 700 cm,
P = 840cm
Q = 620cm.
To find:
The measure of angle P.
According to the Law of Cosines:
In trigonometry, the law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. The law of cosines states:
[tex]cos A = b^{2} +c^{2} - a^{2} / 2bc[/tex]
Using Law of Cosines ΔOPQ, we get,
cos P = o² +q²- p² / 2oq
⇒ cos P = (700)² + (620)² -(840)² /2×700×620
⇒ Cos P = 490000 + 384400 - 705600 / 868000
⇒ Cos P = 168800/868000
on further simplification, we get,
Cos P = 0.19447
P = Cos⁻¹ (0.19447)
P = 78.786236
P = 79.
∴ the measure of angle P is 79 degrees.
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Therefore, the measure of angle P is 79 degrees.
im so confused please help :(
Brianna and Gavin used partial quotients to show 552 divided by 23
Briannas work:
Step 1: Subtract (20×23) from 552 to get 92.
Step 2: Subtract (4×23) from 92 to get 0.
Step 3: Add partial quotients.
Gavins work:
Step 1: Subtract (10×23) from 552 to get 322.
Step 2: Subtract (10×23) from 322 to get 92.
Step 3: Subtract (2×23) from 92 to get 46.
Step 4: Subtract (2×23) from 46 to get 0.
Step 5: Add the partial quotients.
Which student(s) correctly calculated the quotient? Explain your answer
Answer:
Both are correct. Gavin just took more steps to get his answer.
Step-by-step explanation:
Briana's work:
20x23=460
522-460=92
4x23=92
92-92=0
24x23=552
Gavin's work:
10 x 23=230
552-230=322
10x23=230
322-230=92
2x23=46
92-46=46
46-46=0
24x23=552.
Hope this helps :)
Rewrite the equation so that it does not have fractions, without using decimals (please answer quickly)
Answer:
should be
38 = 9x
Step-by-step explanation
multiply both sides with the least common denominator of the denominator of the fraction (the number below the line).
of the numbers 4 and 6, the least common denominator is 12.
so multiply both sides of the equation by 12.
you will have
12 * (4 - 3/4 x) = 12 * 5/6
simplify and you will get
48 - 9 x = 10
and you can even more simplify it to 9x = 38 or 38 = 9x
Solve five-ninths minus two-sixths equals my answers are 8/36 20/54 6/3 3/1
I think it is 2/9ths? Look it up on a calculator to check
One solution each is given for four quadratic equations. Assuming that each quadratic equation has two solutions, what is the second solution for each equation?.
For the quadratic equation other solution is given by :
x = 4-5i other solution is x = 4 + 5i
x= 5 + 4i other solution is x = 5 -4i
x = -5 -4i other solution is x = -5 + 4i
x = -4 + 5i other solution is x = -4 -5i
As given in the question,
Number of quadratic equations mentioned = 4
Given one solution for each quadratic equation is given by:
x = 4-5i
x= 5 + 4i
x = -5 -4i
x = -4 + 5i
In standard form:
if the one of the solution of quadratic equation is in complex form x + iy then other solution is given by its conjugate x - iy.
Hence,
Other solution are given by :
x = 4-5i other solution is given by its conjugate x = 4 + 5i
x= 5 + 4i other solution is given by its conjugate x = 5 -4i
x = -5 -4i other solution is given by its conjugate x = -5 + 4i
x = -4 + 5i other solution is given by its conjugate x = -4 -5i
Therefore, for the quadratic equation other solution is given by :
x = 4-5i other solution is x = 4 + 5i
x= 5 + 4i other solution is x = 5 -4i
x = -5 -4i other solution is x = -5 + 4i
x = -4 + 5i other solution is x = -4 -5i
The complete question is:
One solution each is given for four quadratic equations. Assuming that each quadratic equation has two solutions, what is the second solution for each equation?.
x = 4-5i
x= 5 + 4i
x = -5 -4i
x = -4 + 5i
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Of the teacups in Cassie’s Tea Shop, 1/12 are indigo and another 5/12 are teal. What fraction of the teacups are either indigo or teal?
The fraction of the teacups that are either indigo or teal in Cassie's Tea Shop are 1/2.
How to find the fraction?The fraction of teacups in Cassie’s Tea Shop which will either be indigo or teal can be found by adding the fractions of the tea cups which are indigo, to those which are teal.
Fraction of teacups which are indigo = 1/12
Fraction of teacups which are teal = 5/12
The fraction of teacups which are indigo or teal is:
= 1 / 12 + 5 / 12
= 6 / 12
In the simplest form, this is:
= (6 / 6) / (12 / 6)
= 1 / 2
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Answer: The answer to this problem is 1/2.
Step-by-step explanation:
The first thing you do is to add 1/12 and 5/12 together.
1/2 + 5/12 = 6/12
Then you simplify 6/12 to get the answer.
6/12 = 1/2
6/6 = 1
12/6 = 2
This is how you get the answer!
The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 97% of the people who have a disease. However, it erroneously gives a positive reaction for 5% of the people who do not have the disease. Consider the null hypothesis "the individual does not have the disease". What is the probability of type i error if the new blood test is used?.
Researchers developed a blood test which is quite fair. It gives a positive reaction of 97% people who have that disease and 5% who don't have that disease.
Therefore, the Probability of Type I error if the new blood test is used is 0.025.
H₀ : "the individual does not have the disease"
(a) Probability of Type I error of rejecting when is true =
Probability of concluding the individual has the disease when in fact the individual does not have the disease = 0.025 because the blood test erroneously gives a positive reaction in 2.5% of the people who do not have the disease.
(b) Probability of Type II error = Probability of fail to reject when is true= Probability of concluding the individual does not have the disease when in fact he has the disease = 0.05 because the blood test gives a positive reaction in 97% of the people who have the disease, this implies that the test gives a negative reaction in 5% of the people who have the disease.
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Yusuf sat 8 examinations.
Here are his marks for 5 of the examinations.
68 72 75 77 80
For his results in all 8 examinations
the mode of his marks is 80
the median of his marks is 74
the range of his marks is 16
Find Yusuf’s marks for each of the other 3 examinations.
Yusuf remaining observations, considering the statistical measures, are given as follows:
64, 73, 80.
What are the statistical measures in this problem?There are four statistical measures used in this problem, which are:
Median.Mode.Range.The mode is the observation that appears the most times, hence one of the remaining observations is of 80.
The median is the middle value of the data-set, which is the value of which 50% of the measures are less than and 50% of the measures are greater than.
In this problem, the data-set has an even cardinality, hence the median is the mean of the 4th and of the 5th element, hence, considering the median of 74, the missing element is given as follows:
(x + 75)/2 = 74.
x + 75 = 148
x = 73.
The range is the difference between the largest value and the smallest value in the data-set.
Considering the range of 16 and the highest value of 80, the remaining value is given as follows:
80 - x = 16
x = 80 - 16
x = 64.
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A bell-shaped curve that results from a large group of measurements is the basic concept of?
Normal Distribution or central tendency is a bell-shaped curve that is produced by many measurements.
The graphical representation of a normal probability distribution, whose underlying standard deviations from the mean form the curved bell shape, is referred to as having a "bell curve." The variability of data dispersion, in a set of provided values around the mean, is measured using a standard deviation. The highest point on the bell curve is the mean, which is the average of all the data points in the data set or sequence.
A bell-shaped normal distribution graph is referred to as a bell curve.
At the peak of the curve, the mean, mode, and median of the collected data are shown.
The standard deviation of the bell curve reveals how pronounced the bell curve is around the mean.
Bell curves (normal distributions) are extensively used in statistics, particularly when analyzing financial and economic data.
Hence Normal Distribution is the basic concept of bell shaped curve.
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through (3,3) perp to y=-3/8x+4
NEED HELP
By using the equation of the line and the perpendicular line relationship, the equation of the perpendicular line y = (8 / 3) · x - 5
How to determine the equation of a line perpendicular to another line
Mathematically speaking, lines are represented by equations of the form:
y = m · x + b
Where:
x - Independent variabley - Dependent variablem - Slopeb - y-InterceptAnd two lines perpendicular to each other observe the following relationship:
m · m' = - 1
Where:
m - Slope of the original line.m' - Slope of the perpendicular line.First, determine the slope of the perpendicular line by perpendicular line relationship:
m = - 3 / 8
m' = - 1 / (- 3 / 8)
m' = 8 / 3
Second, calculate the intercept of perpendicular line by the equation of the line:
b = y - m · x
b = 3 - (8 / 3) · 3
b = 3 - 8
b = - 5
Third, write the equation of the perpendicular line:
y = (8 / 3) · x - 5
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A farmer wants to build a rectangular pen with 80 feet of fencing. The pen will be built against the wall of the barn, so one side of the rectangle won't need a fence. What dimensions will maximize the area of the pen? Find length and width.
Ron wins £1 1/4 million. He gives 3/5 million to his daughter and £1/3 million to his wife. How much does he have left?
Answer:
0.31
Step-by-step explanation:
1 1/4 - 1/3 - 3/5 = 19/60
≅ 0.3166667
Identity the domain and the range of each function
a) Domain={2,3,4,5,6}, Range={0,1,2,3,4}
b)Domain={-3,-1,1,3,4}, Range={1,3,-2,2,6}
What are the domain and range of a function?
The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
a) Domain is the set of x values:
x={2,3,4,5,6}
The range is the set of y values:
y={0,1,2,3,4}
b) Domain is the set of x values:
x={-3,-1,1,3,4}
The range is the set of y values:
y={1,3,-2,2,6}
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The amusement park is open from 10:00 A.M. to 6:00 P.M. How many hours could a visitor spend at the amusement park in one day?
write a equation or inequality
the park is open for 8 hours.
find the measure of each missing angle. a//b PLSS HELP
The measure of each of the missing angles is m<1 = 40°, m<2 = 61°, m<3 = 119°, m<4 = 61°, m<5 = 58°, m<6 = 122°, m<7 = 58°, m<8 = 82° and m<9 = 98°
How to determine the measure of each missing angle?
To solve this problem, we need some angle geometry knowledge:
Since the sum of angles on a straight is 180°. Thus:
m<1 + 82° + 58° = 180°
m<1 = 180° -82° - 58° = 40°
The sum of angles on a triangle is 180°:
m<2 + 58° + 61° = 180°
m<2 = 180° - 58° - 61° = 61°
m<2 + m<3 = 180° (angles on a straight )
61°+ m<3 = 180°
m<3 = 180°-61° = 119°
m<4 = m<2 = 61° (alternate angles)
m<5 + m<4 + 61 = 180° (angles on a straight )
m<5 + 61° + 61 = 180°
m<5 = 180°- 61°-61° = 58°
m<5 + m<6 = 180° (angles on a straight )
58°+ m<6 = 180°
m<6 = 180°-58° = 122°
m<7 = 58° (alternate angles)
m<1 + m<7 +m<8 = 180° (angles on a triangle )
40+58°+m<8 = 180°
m<8 = 180°-40-58° = 82°
m<8+m<9 = 180° (angles on a straight )
82+m<9 = 180°
m<9 = 180°-82° = 98°
The measure of the missing angles m<1, m<2, m<3, m<4, m<5°, m<6, m<7, m<8 and m<9 are 40°, 61°, 119°, 61°, 58°, 122°, 58°, 82° and 98° respectively
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I don't understand a word of this! Due tomorrow and I've been trying all weekend to solve...
Could somebody help me?
The mean price of one of Henry's stamp is $34.7.
The mean number of plays is 6.33.
The mean length of phone call is 11.79.
What is the mean?Mean is the average of a set of numbers.
Mean = ∑(midpoint x frequency) / frequency
Midpoint = (upper boundary + lower boundary) / 2
Stamp price Frequency Midpoint (Midpoint x frequency)
20 - 26 24 (20 + 26) / 2 = 23 552
27 - 33 39 (27 + 33) / 2 = 30 1170
34 - 40 50 (34 + 40) / 2 = 37 1850
41 - 47 37 (41 + 47) / 2 = 44 1628
Sum 150 5200
Mean = 5200 / 150 = 34.7
Number of weeks Frequency Midpoint Midpoint x Frequency
1 - 3 4 (1 + 3) / 2 = 2 8
4 - 6 27 (4 + 6) / 2 = 5 135
7 - 9 16 (7 + 9) / 2 = 8 128
10 - 12 4 (10 + 12) / 2 = 11 44
13 - 15 1 (13 + 15) / 2 = 14 14
Sum 52 329
Mean = 329 / 52 = 6.33
Length of call Frequency Midpoint Midpoint x frequency
1 - 4 3 (1 + 4) / 2 = 2.5 7.5
5 - 8 32 (5 + 8) / 2 = 6.5 208
9 - 12 30 (9 + 12) / 2 = 10.5 315
13 - 16 45 (13 + 16) / 2 = 14.5 652.50
17 - 20 17 (17 + 20) / 2 = 18.5 314.50
Sum 127 1,497.50
Mean = 1497.50 / 127 = 11.79
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ON 7 SESSION 2
Use what you learned to solve these problems.
7
Use linear pairs to find the sum of all the angles labeled in the triangle.
Then use what you know about the interior angles of a triangle to show
that the sum of the measures of the exterior angles of a triangle, one at
each vertex, is 360°.
The sum of the measures of the exterior angles of a triangle, one at each vertex, is 360° and it proved.
Exterior angle
The the angle that is formed with one side and the adjacent extended side of a triangle is known as exterior angle.
Given,
Here we use linear pairs to find the sum of all the angles labeled in the triangle.
And then use what you know about the interior angles of a triangle to show that the sum of the measures of the exterior angles of a triangle, one at each vertex, is 360°.
While we looking into the following figure, we can see that R and Y are the interior and exterior angles of the triangle respectively.
Therefore, here the angles Y and R form a linear pair.
So, we can written it as,
=> Y + R = 180°
Then the value of y is
=> Y = 180° - R
Therefore, when we calculate the value of the full triangle, then we get
=> (Y + R) + (Y + R) + (Y + R) = 180° + 180° + 180°
When we simplify this one,
=> 3Y + 3R = 540° --------- (1)
We already know that, the sum of interior angles of the triangle is as follows,
=> R + R + R = 180°
By using angle sum property of a triangle,
WE can written this like the following,
=> 3R = 180° --------- (2)
Now, substituting the value from equation(2) in equation(1) we get,
Then,
=> 3Y + 180° = 540°
=> 3Y = 540° - 180°
=> 3Y = 360°
Therefore, the sum of exterior angles = 360°
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Find the equation of a line parallel to -2y = 4 - 2x that passes through the point
(-5,9).
y=x-2
y=-x+14
2x + 2y = 8
2x - 2y = -28
(E) None of these equations of a line is parallel to the equation [-2y = 4 - 2x] and passes through the point (-5. 9).
What is the equation of a line?A straight line's general equation is y = MX + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis.
On the y-axis, this value c is referred to as the intercept.
Y = MX + c represents the equation of a straight line with gradient m and intercept c on the y-axis.
So, first plot the equation [-2y = 4 - 2x] on the graph:
Now, plot all the equations on the graph.
We can now check which equation is parallel to [-2y = 4 - 2x] and passing through the point (-5. 9).
According to the plotting, we can say that no equation is parallel to the equation [-2y = 4 - 2x] and passes through the point (-5. 9).
Therefore, (E) none of these equations of a line is parallel to the equation [-2y = 4 - 2x] and passes through the point (-5. 9).
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Complete question:
Find the equation of a line parallel to -2y = 4 - 2x that passes through the point.
(-5,9).
A. y=x-2
B. y=-x+14
C. 2x + 2y = 8
D. 2x - 2y = -28
E. None of these
Security x has expected return of 9% and standard deviation of 18%. Security y has expected return of 12% and standard deviation of 21%. If the two securities have a correlation coefficient of 0. 4, what is their covariance?.
Their covariance is -0.0151
Given;
The expected return on security x is 9%, whereas the standard deviation is 18%. The expected return on security y is 12%, and the standard deviation is 21%. If the correlation between the two securities is 0.4
Security X:
Expected return E(Rx) = 9% = 0.09
Standard deviation (σx) = 18% = 0.18
Security Y:
Expected return E(Ry) = 12% = 0.12
Standard deviation (σy) = 21% = 0.21
and
Corr(X,Y) = -0.4
We know that,
Corr(X,Y) = Cov(X,Y)/ σx*σy
Substituting the above-given values, we get;
-0.4 = Cov(X,Y)/ 0.18*0.21
-0.4 = Cov(X,Y)/ 0.0378
Cov(X,Y) = -0.4*0.0378
Cov(X,Y) = -0.0151
Therefore, the covariance is -0.0151.
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another advantage of using anova is that it ________ so the significant differences can be located and interpreted easily.
Another advantage of using Anova is that it arranges the means so the significant differences can be located and interpreted easily.
The ANOVA test is a type of statistical test used to determine whether there is a statistically significant difference between two or more categorical groups by testing mean differences using variance.
Another important part of the ANOVA is the splitting of the independent variables into two or more groups.
The assumptions for the ANOVA test are the same as those for general parametric tests.
ANOVA can only be performed if there is no relationship between subjects in each sample. Sample size for different groups/levels must be the same.ANOVA can only be performed if the dependent variable is normally distributed.the population variances of must be equal (that is, homoscedasticity). Homogeneity of variance means that the variability of results is similar across populations.Advantages of ANOVA:
The z-test can only be used to compare two population means, whereas the ANOVA test can be used to compare three or more population means.When there are two different treatments/factors affecting the dependent variable, the Two Way ANOVA test can be used to analyze the effect of each treatment.To learn more about ANOVA test , refer:
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Find the exact value of CSC(COS^-1(-5/8))
The exact value of CSC(COS^-1(-5/8)) is 8/[tex]\sqrt{39}[/tex].
Given:
= CSC(COS^-1(-5/8))
= 1/sin(cos^-1(-5/8)
we know identity sin(cos^-1(x)) = [tex]\sqrt{1-x^{2} }[/tex]
= 1/[tex]\sqrt{1-(-5/8)^{2} }[/tex]
= 1/[tex]\sqrt{64-25/64 }[/tex]
= 1/[tex]\sqrt{39}[/tex]/8
= 8/[tex]\sqrt{39}[/tex].
Therefore the value of CSC(COS^-1(-5/8)) is 8/[tex]\sqrt{39}[/tex].
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Here is a diagram of a pentagon.
Calculate the size of angle x
115°
100°
104°
x
Answer:
319 would be the sum
Step-by-step explanation:
Look at the table below what’s the value of k
Answer:
k = 5
Step-by-step explanation:
substitute the values of x into 3x + k and equate with the corresponding value, that is
x = 1
3(1) + k = 8
3 + k = 8 ( subtract 3 from both sides )
k = 5
x = 3
3(3) + k = 14
9 + k = 14 ( subtract 9 from both sides )
k = 5
x = 5
3(5) + k = 20
15 + k = 20 ( subtract 15 from both sides )
k = 5
the value of k is therefore 5
Put the steps in order for changing the repeating decimal, which is rational, to a ratio or fraction. 0.171717.... what
fraction?
1. x = 17/99
2. 99x = 17
3. x=0.171717
4. subtract (x=0.171717…..)
5. 100x=17.1717……
To write our number as a fraction, the order of the steps is:
step 3.step 5.step 4.step 2.step 1.How to write the repeating decimal as a fraction?First, we define our number:
x = 0.1717...
So we start with the step 3.
Now notice that there are two repeating decimals, so we need to multiply both sides by 100 (as many zeros as repeating decimals)
100*x = 10*0.1717... = 17.1717...
This is step 5.
Now we can subtract the original number in both sides so we remove the repeating decimals:
100*x - 0.1717... = 17.1717... - 0.1717...
99*x = 17
These are steps 4 and 2.
Finally, we divide both sides by 99 to get:
x = 17/99
Which is step 1.
And that is our number written as a fraction.
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Sports Over the course of his career in major league baseball, Willie Mays hit 58 more than double the number of home runs Roger hit. How many home runs did Mays hit?
I AM IN MIDDLE SCHOOL
thx
Runs scored by Willie Mays is given by the linear equation y = 2x+58.
What is a linear equation?A linear equation is an algebraic equation which is in the form y=mx+b, where m is said to be the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.
The variables in the preceding equation are x and y, and it is commonly referred to as a "linear equation of two variables."
Let the runs scored by Roger be x.
According to the question, Willie Mays hit 58 more than double the number of home runs Roger hit.
Runs scored by Willie Mays = 2x+58
Let the runs scored by Willie May be y.
Then, y = 2x+58.
Hence, the runs scored by Willie Mays is given by the linear equation
y = 2x+58.
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