Answer: c:ray
Step-by-step explanation:
A ray is like a line, but the line takes off in one direction to infinity while the other side is like a line segment. The end of the line is called the endpoint. That's why it is a defined term.
which choices if multiplied by 0.5 would result in a rational number answer?
If the integer begins through being rational, multiplying by 0.5 would not change whether or not something is rational. It will continue with rational numbers.
What is a rational number?In mathematics, a rational number is a number that can be written as the quotient or fraction p/q of two numbers, an integrand p and a non-zero denominator q.
For instance, −3/7 is a rational number, and so is every integer.
So, in that case, any even number would be 12 * 0.5 = 6.
The solution is reasonable because 12 began as rational (6).
Any odd number also is rational:
23 * 0.5 = 11.5
23 and 11.5: Both rational
1.818181818 is reasonable hence when multiplied by 0.5 the result will be rational 3.636363636.
Therefore, if we begin with an irrational number like π:
π*0.5: Not rational
Therefore, if the integer begins through being rational, multiplying by 0.5 would not change whether or not something is rational. It will continue rational.
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Correct question:
Which number produces a rational number when multiplied by 0.5?
Solve the following system of equations graphically on the set of axes below.
y= x - 8
2x + y = −5
Answer:
Step-by-step explanation:
Hello...
y=x-8
2x+y=-5 -> y=-2x-5
subsitution
-2x-5=x-8
3x=3
x=1
y=x-8
y=1-8
y=-7
(1,-7)
The letters and represent nonzero constants. Solve ax+b=37,for x
The value of x is [tex]\frac{37 - b}{a}[/tex] by taking a and b as non-zero constant . It is solved by using simple arithmetic calculations .
What are arithmetic calculations?
Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.,
Addition : (+)
The addition is the process of taking two or more numbers and adding them together. In other words, it is the total sum of all the numbers.
Subtraction : (-)
Subtraction is the process in which we remove objects from the original group.
Multiplication : (×)
Multiplication is adding the same number to itself a certain number of times.
Division : (÷)
The division is breaking a large object or group into smaller parts or groups.
Here ,
given equation: ax + b = 37
To calculate value of x :
ax = 37 - b
As, it is given that a is non-zero constant then,
x = (37 - b)/a
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The table compares the average daily temperature and ice cream sales each day.
Temperature (°F) Ice Cream Sales
56.1 $107
60.3 $116
64.2 $120
66.4 $122
71.3 $125
73.9 $130
74.2 $132
75.2 $135
80.1 $141
84.8 $152
What is the slope of the line of best fit, where x represents the average daily temperature and y represents the total ice cream sales? (Round your answer to one decimal place.)
6.3
4.2
2.8
1.4
Therefore, the slope of the line of best fit is 1.4.
Where do I find the average formula?Average By adding a collection of numbers and then dividing by their count, the arithmetic mean—also known as the median—is determined. For instance, 30 divided by 6 equals 5, which is the https://brainly.com/question/24057012of 2, 3, 4, 5, 7, and 10.
To find the slope of the line of best fit, you will need to use the formula:
slope = (mean(x) * mean(y) - mean(x*y)) / (mean(x)^2 - mean(x^2))
where x represents the average daily temperature and y represents the total ice cream sales.
First, you will need to calculate the mean of x, the mean of y, the mean of x*y, and the mean of x^2.
The mean of x is (56.1 + 60.3 + 64.2 + 66.4 + 71.3 + 73.9 + 74.2 + 75.2 + 80.1 + 84.8) / 10 = 71.54
The mean of y is (107 + 116 + 120 + 122 + 125 + 130 + 132 + 135 + 141 + 152) / 10 = 128.6
The mean of xy is (56.1107 + 60.3116 + 64.2120 + 66.4122 + 71.3125 + 73.9130 + 74.2132 + 75.2135 + 80.1141 + 84.8*152) / 10 = 8707.7
The mean of x^2 is (56.1^2 + 60.3^2 + 64.2^2 + 66.4^2 + 71.3^2 + 73.9^2 + 74.2^2 + 75.2^2 + 80.1^2 + 84.8^2) / 10 = 6043.17
Plugging these values into the formula for the slope, we get:
slope = (71.54 * 128.6 - 8707.7) / (71.54^2 - 6043.17) = 1.4
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Point W is located at (-2, 3) on a coordinate plane. Point W is reflected over the x-axis to create
point W. Point W' is then reflected over the y-axis to create point W". What ordered pair
describes the location of point W"?
Answer Point W" C
Explain how you determined your answer.
The required coordinate pair for W" is (2,-3)
What is reflection of the point?When a point is reflected over axes, its position changes and sign of coordinates also change.
Given that, Point W is located at (-2, 3) on a coordinate plane. Point W is reflected over the x-axis to create point W'. Point W' is then reflected over the y-axis to create point W".
When a point is reflected over the x-axis, then we know,
(x, y) = (x,-y)
W(-2,3) = W (−2,−3)
And,
When a point is reflected over the y-axis, then we know,
(x, y) = (-x, y)
Therefore, W'(-2,-3) = W" (2,-3)
Hence, the coordinates of the point W" are (2,-3)
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Four gallons of water weigh 33.4 lb.
How much do 7.5 gallons of water weigh?
Answer:
62.625
Step-by-step explanation:
First, we divide 33.4 by 4 to see what ONE gallon weighs.
33.4/4=8.35
8.35*7=58.45+(8.35*(1/2))= 62.625
Therefore, your answer is 62.625
I hope you understand my explanation. I pride myself on making my answers, short, descriptive, yet easy to read.
please give brainliest! Thanks! Hope this helped.
Answer:
62.625 lb
Step-by-step explanation:
Define the variable:
Let x be the weight of 7.5 gallons of water (in pounds).Set up a ratio of weight to number of gallons:
[tex]\implies x:7.5=33.4 :4[/tex]
Solve for x:
[tex]\implies \dfrac{x}{7.5 }=\dfrac{33.4}{4}[/tex]
Cross multiply:
[tex]\implies 4x=33.4 \cdot 7.5[/tex]
[tex]\implies 4x=250.5[/tex]
Divide both sides by 4:
[tex]\implies \dfrac{4x}{4}=\dfrac{250.5}{4}[/tex]
[tex]\implies x=62.625[/tex]
Therefore, the weight of 7.5 gallons of water is 62.625 lb.
the coast guard cutter angelica travels at 30 knots from its home port of coprus christi on a course of 95 for 2 hr and then changes to a course of 185 for 2 hr. find the distance and the bearing from the corpus christi port to the boat.
The boat's distance and bearing from the port regions are as follows;
The boat is located around 157.15 kilometers from the harbor on a bearing of 150°.
In mathematics, a bearing is an angle measured clockwise from the north or y-axis direction.
The Coast Guard cutter travels at a speed of 30 kno
Angelica, a Coast Guard cutter, has a bearing of 95 degrees.
The coast guard goes for 2 hours in the first direction.
The shift in direction of the Coast Guard cutter = 185°
Travel time in the new direction = 2 hours
30 knots equals 55.56 km/hr
The distance traveled in the first direction = 55.56 km/hr = 111.12 km in 2 hours
Distance traveled in the other direction = 55.56 km/hr 2 hours = 111.12 km
According to the accompanying graphic, the figure produced by the Coast Guard cutter's course is an isosceles triangle.
The Pythagorean theorem gives the distance from the port to the position of the boat as l = √(111.122^2 + 111.122^2) ≈ 157.15.
The boat is roughly 157.15 kilometers away from the port.
An isosceles right triangle has 45° base angles.
As a result, the bearing is 95° + 45° = 150°.
The angle between the port and the boat is 150°.
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Given the function h(t) = 5 - 3(t-2)2
Which formula gives t in terms of h
To write its equation in the form y is a(xh)2+k and then determine the value of the coefficient a.
How do you solve a parabola equation?The equation of a parabola can be found using the vertex form. If we can read the coordinates (h,k) from the graph, we may use those coordinates to write its equation in the form y=a(xh)2+k and then determine the value of the coefficient a.Assuming the given function, h(t) = 5 - 3 (t -2) h = 5 - 3 is a new equation to use when rewriting the function (t - 2) 2 H - 5 = -3 is the result of deducting 5 from both sides (t - 2) 2 (h - 5) /3 = -3(t - 2)2/3 (h - 5) /3 = (t - 2)2 is obtained by dividing both sides of the equation by (-3).To learn more about Parabola refer to:
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Find the coordinates of the circumcenter of the triangle with the given vertices.
A(0, 0), B(0, 8), C(6, 0)
x =3 and y = 4 , these two perpendicular bisectors will come together. These are the triangle's circumcenter's coordinates.
What is perpendicular in triangle?
The sides of a triangle are divided into two equal portions by the perpendicular, which is parallel to the sides drawn from the opposing vertices.
The circumcenter of a triangle is the location where the three perpendicular bisectors of the triangle meet.
A(0, 0), B(0, 8), C(6, 0)
Circumcenter , P(x,y)
AP = BP = CP
AP² = BP²
(x - 0 )² + ( y - 8 )² = ( x- 0)² + ( y - 0 )²
x² + y² + 64 - 16y = x² + y²
64 - 16y = 0
16y = 64
y = 4
BP = CP
BP² = CP²
(x - 0)² + ( y- 0 )² = ( x- 6)² + ( y - 0)²
x² + y² = x² 36 - 12x + y²
36 - 12x = 0
12x = 36
x = 3
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Which of the following is true about k-means clustering Group of answer choices A tree diagram is used to illustrate the steps in the clustering analysis We choose the value for k before doing the clustering analysis It is a type of hierarchical clustering The cluster analysis will give us an optimum value for k In a cluster analysis, the distance between the clusters should be: Group of answer choices Maximized Minimized Even Zero THANK YOU :)
Prior to performing the clustering analysis, we select the value for k, the statement regarding k-means clustering is accurate and the minimum distance between the clusters should be used.
Data is divided into groups (clusters) using cluster analysis that is relevant, practical, or both. If creating meaningful groups is the goal, the clusters should reflect the data's inherent structure. However, cluster analysis can occasionally merely serve as a valuable starting point for other tasks, including data summarization. In a wide range of disciplines, including biology, statistics, pattern recognition, information retrieval, machine learning, and data mining, cluster analysis has long been crucial, whether for understanding or usefulness. Cluster analysis has been used to solve numerous practical issues.
Hartigan (1975, pp 90-91) provides the following general guideline when determining the number of clusters. When (sum(k$withinss)/sum(kplus1$withinss)-1)*(nrow(x)-k-1) is more than 10, it is justified to add the extra group if k is the result of k-means with k groups and kplus1 is the result with k+1 groups.
As a result, choice B is the appropriate response.
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if a carpenter wants to make sure that the corner of a room is square and measures 12 ft and 35 ft along the walls, how long should he make the diagonal?
On solving the provided question, we got to know that - carpenter should make the diagonals 37 ft
What are the diagonals?A diagonal is a line connecting two vertices of a solid or polygon whose vertices do not share an edge in mathematics. The vertices of a shape are connected by oblique or sloping lines, which are known as diagonals. A horizontal shape with sides/edges, corners, and is called a diagonal.
We can answer this problem using Pythagoras' Theorem since the diagonal would turn the angle into a right angle.
[tex]12^2+35^2= d^2[/tex]
[tex]d^2 = 144 + 1225\\d^2 = 1369\\d = 37\\[/tex]
So, carpenter should make the diagonals 37 ft
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Find a point on the line and the line's slope.
y-5=-2/(x-3)
Answer:
Slope: - 4/3
Point (4,1)
Step-by-step explanation:
hope this helps
a magazine publisher mailed a survey to all of its subscribers asking if the magazine is helpful in their daily lives. of those who responded, 78% replied that the magazine was helpful. the proportion that replied that the magazine is helpful is known
The percentage of respondents who said the magazine is useful is referred to as the population parameter of interest.
Is the percentage of respondents who said the publication is useful?The percentage of respondents who said the magazine is useful is referred to as the population parameter of interest.The demographic metric of interest is the percentage of respondents who indicated that the magazine is useful.A population parameter is a metric that quantifies a population numerically or a figure that conveys information about a large group or population.the average body weight of American women in their middle years. All American women in their middle years make up the population, and the parameter is.the typical size of a butterfly. This information about the total butterfly population makes it a parameter.the class X average height. This qualifies as a parameter because it provides information about class X as a whole.The demographic metric of interest is defined as the proportion of respondents who felt the magazine is useful.To learn more about population parameter refer to:
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what is the hypotenuse?
Answer:
20
Step-by-step explanation:
h=hypotenuse. s1=side 1. s2=side 2
h^2 = (s1)^2 + (s2)^2 ==> hypotenuse formula
h^2 = 12^2 + 16^2 => plug in known values
h^2 = 144 + 256
h^2 = 400 ==> simplify
[tex]\sqrt{h^2 = 400}[/tex] ==> take the square root on both sides to remove the power
[tex]\sqrt{h^2}[/tex] = [tex]\sqrt{400}[/tex]
h = 20
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find formulas for the entries of mn, where n is a positive integer.
The formula for the entries of [tex]M^{n}[/tex], where n is a positive integer is [tex]=\left[\begin{array}{cc}2 \times 9^n-7^n & 7^n-9^n \\2\left(9^n-7^n\right) & 2 \times 7^n-9^n\end{array}\right][/tex] for M = [tex]\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right][/tex] .
Let us find the formula for entries of [tex]M^{n}[/tex], where n is a positive integer.
Let M be a 2 x 2 matrix [tex]\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right][/tex]
we get the eigenvalues and their associated eigenvectors as follows-
Eigenvalue : 9λ , multiplicity : 1λ, eigenvector : [ 1, 1]
Eigenvalue : 7λ , multiplicity : 1λ, eigenvector : [ 0.5, 1]
now, we have
[tex]{\left[\begin{array}{ll}9 & 0 \\0 & 7\end{array}\right] }[/tex] = [tex]\left[\begin{array}{cc}1 & \frac{1}{2} \\1 & 1\end{array}\right]^{-1}[/tex] [tex]\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right][/tex] [tex]\left[\begin{array}{cc}1 & \frac{1}{2} \\1 & 1\end{array}\right][/tex]
= [tex]\left[\begin{array}{cc}2 & -1 \\-2 & 2\end{array}\right][/tex] [tex]\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right][/tex] [tex]\left[\begin{array}{cc}1 & \frac{1}{2} \\1 & 1\end{array}\right][/tex]
hence, [tex]\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right][/tex] = [tex]\left[\begin{array}{cc}1 & \frac{1}{2} \\1 & 1\end{array}\right][/tex] [tex]\left[\begin{array}{cc}9 & 0 \\0 & 7\end{array}\right][/tex] [tex]\left[\begin{array}{cc}2 & -1 \\-2 & 2\end{array}\right][/tex]
So,
[tex]{\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right]^n } & =\left[\begin{array}{ll}1 & \frac{1}{2} \\1 & 1\end{array}\right]\left[\begin{array}{ll}9 & 0 \\0 & 7\end{array}\right]^n\left[\begin{array}{cc}2 & -1 \\-2 & 2\end{array}\right][/tex]
[tex]= \left[\begin{array}{ll}1 & \frac{1}{2} \\1 & 1\end{array}\right]\left[\begin{array}{cc}9^n & 0 \\0 & 7^n\end{array}\right]\left[\begin{array}{cc}2 & -1 \\-2 & 2\end{array}\right][/tex]
[tex]=\left[\begin{array}{cc}2 \times 9^n-7^n & 7^n-9^n \\2\left(9^n-7^n\right) & 2 \times 7^n-9^n\end{array}\right][/tex]
Thus, the formula for the entries of [tex]M^{n}[/tex], where n is a positive integer is [tex]=\left[\begin{array}{cc}2 \times 9^n-7^n & 7^n-9^n \\2\left(9^n-7^n\right) & 2 \times 7^n-9^n\end{array}\right][/tex] for M = [tex]\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right][/tex] .
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Jose can put together a transmission in 10 hours. Luis can build the same transmission in 8 hours. How long will it take them to build the transmission together?
The total time taken to finish building the transmission if Jose and Luis worked together is 4.44 hours
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total time required to finish building the transmission if Jose and Luis works together be = A
Now , the equation will be
The time required by Jose to build a transmission = 10 hours
The time required by Luis to build a transmission = 8 hours
If it takes one person 10 hours to build a transmission and another person 8 hours to build the same transmission , working together they could build the transmission even quicker
So ,
If Jose builds the transmission is 10 hours , he builds 1/10th of the transmission in one hour
If Luis builds the transmission in 8 hours , he builds 1/8th of the transmission in one hour
And ,
Together they build the transmission in
1/A = 1/10 + 1/8
where A is the total time required to finish building the transmission if Jose and Luis works together
So , the equation is
1/A = 1/10 + 1/8
1/A = 18/80
Taking reciprocals on both sides of the equation , we get
A = 80/18
A = 40/9
On simplifying the equation , we get
A = 4.44 hours
Therefore , the value of A is 4.44 hours
Hence , The total time taken to finish building the transmission if Jose and Luis worked together is 4.44 hours
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On July 14, Gracie Paul accepted a $60,000, 6%, 160-day note from Mike Lang. On November 12, Gracie discounted the note at Lend Bank at 7%. What proceeds did Gracie receive? (Use Days in a year table) (Round your answer to the nearest cent. )
Therefore, Gracie will earn $61600 if she waits until December 21. However, she will earn bank discount $61132.87 on November 12.
A bank discount is interest that the bank deducts beforehand in the basic discount note. The maturity value less the bank discount equals the amount owed. The total of the principle and interest due at the conclusion of the time period is the maturity value.
Date of note = 14th July
Face value = $60000
Length of note = 160 days,
Interest rate = 6%
Calculating the interest and maturity value:
Interest = Principal × interest × time
= 60000 × 0.06 × 160/360
= 1600
So the maturity value MV = Face value + interest
= 60000 + 1600
= 61600
2. Calculating discount period:
Note discounted on 12th November
Time till 12th November = 315 days
Time till 14th July = 194 days
So days before note is discount = 315 - 194= 121 days
Length of note = 160 days,
So the discount period = 160 - 121 = 39 days
3 - Bank discount:
Bank discount = MV × Bank discount rate × number of days bank waits till due date
= 61600 × 0.07 × 39/360
= 467.133
4 - Proceeds from bank: Proceeds = MV - Bank discount
= 61600 - 467.133
= 61132.87
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Suppose Juan Pablo has 6.93 kilograms of seed. If it takes 6.3 kilograms of seed to plant one hectare of land, how many hectares of land can be planted
Answer:
1.1 hectares
Step-by-step explanation:
6.93/6.3 = 1.1
He can plant 1.1 hectares of land.
The table shows the proportional relationship between the number of tickets required per game at a carnival.
Games 4 10 16
Tickets 16 40 64
Determine the constant of proportionality.
4
6
12
24
Answer:
6
Step-by-step explanation:
all are divisible by 6 or can be added by six to get the next number
The required value of the contant of proportionality is given as 1/4.
What is proportionality?Proportionality is described as the relationship between two or more sets of values, and whether these values are directly proportional or inversely proportionate to one other.
Here,
Let G be the number of games and T be the number of tickets,
G ∝ T
So,
G = kT
From the table,
4 = 16k
k = 4/16
k = 1/4
Thus, the required value of the contant of proportionality is given as 1/4.
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What effect does decreasing the sample size have on a distribution of sample means? a) It will have more variation b) It will not make any difference cIt will have less variation
c) It will have less variation.
Decreasing the sample size will generally result in more variation in the distribution of sample means. This is because with a smaller sample size, there is less information available to estimate the population mean, which means that the sample mean will be less precise and will vary more from one sample to the next.
For example, if you take a sample of 10 individuals from a population and calculate the mean of their heights, the sample mean will likely be a good estimate of the population mean height. However, if you take a sample of just 2 individuals and calculate the mean of their heights, the sample mean will be less precise and will be a less reliable estimate of the population mean height. This is because the sample of 2 individuals may not be representative of the overall population, and the sample mean will be more influenced by extreme values or outliers.
In general, as the sample size decreases, the distribution of sample means will become more spread out and will have more variation. This is because with a smaller sample size, there is more uncertainty about the population mean, and the sample means will be more likely to deviate from the true population mean.
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what is the term used to denote the process that builds a regression equation one independent variable at a time, starting with the one the most highly correlated and keeping only terms with significant coefficients?
The term used to denote the process that builds a regression equation by testing one variable at a time, starting with the one which is significantly corelated and keeping only the other significant coefficients is known as stepwise regression.
What is stepwise regression?Iteratively building a regression model step by step, stepwise regression entails choosing independent variables to be included in the final model. It entails successively introducing or eliminating putative explanatory factors and assessing statistical significance after each iteration.
Stepwise regression can be accomplished in one of two ways: either by including all potential independent variables in the model and removing those that are not statistically significant, or by attempting each independent variable one at a time and including it in the regression model if it is statistically significant.
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SOMEONE PLEASE HELP I DONT UNDERSTAND
Answer:
(-41, 30)
Step-by-step explanation:
The midpoint of a segment lies on the segment.
x: (-88 + 6)/2 = -41
y: (61 + (-1)) = 30
Answer: (-41, 30)
PLEASE HELP QUICK
A system of equations is graphed on a coordinate plane.
Which coordinates are the best estimate of the solution to the system of equations?
A. (−1, 0)
B. (−1, −1)
C. (1, 0)
D. (1, −1)
Answer: The solution of this system of equations is the point of cut of these line.
Point of cut is when x is close to -1, and y is close to 0; therefore the best estimate of the solution would be:
A) (-1,0)
We can check it out our answer solving the system of equations:
-3x+y=2
-4x+7y=1
We solve this system by substitution method.
-3x+y=2 ⇒ y=2+3x
-4x+7(2+3x)=1
-4x+14+21x=1
-4x+21x=1-14
17x=-13
x=-13/17=-0.764....≈-1
y=2+3x
y=2+3(-0.764)
y=2-2.292
y=-0.292≈0
The approximate solution will be (-1,0)
A dress marked at 550 is discount at 5%. Find the discount offered and the selling price of the dress?
!!Answer fast and if u give correct answer I will mark as brainliest!! Answering for points will lead to a report!!
discount= 27.5
S.P= 522.5
Step-by-step explanation:
Marked price of dress(m.p)= 550
Discount % = 5%
Discount amount = 5% of MP
=5÷100×550
=27.5
S.P of the dress = ?
we know,
S.P = MP- discount
= 550-27.5
=522.5
what are 3 combinations of coins with the value of 30% of a dollar
The 3 combinations of coins with the value of 30% of a dollar are 2 dimes + 1 Nickel + 5 Pennies, 1 dime + 2 Nickels + 10 Pennies, 3 Nickels + 1 dime + 5 Pennies.
How many types of coins are there?
There are 4 types of coins. They are Quarter, Nickel, dime, and Penny.
1 Quarter = 25 cent
1 dime = 10 cents
1 Nickel = 5 cents
1 penny = 1 cent
Now calculate 30 percentage of a dollar.
1 dollar = 100 cents.
30% of 100 cents = (30/100) × 100 = 30 cents.
2 dimes + 1 Nickel + 5 Pennies = 20 cents + 5 cents + 5 cents = 30 cents
1 dime + 2 Nickels + 10 Pennies = 10 cents + 10 cents + 10 cents = 30 cents
3 Nickels + 1 dime + 5 Pennies = 15 cents + 10 cents + 5 cents = 30 cents
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Bisectors of two adjacent angles of angles A and B of qudrilateral ABCD intersect at a point O. Prove that 2∠= ∠+∠
From the quadrilateral proof seen below we can prove that;
∠C + ∠D = 2∠AOB
How to find bisected angles?The bisection of an angle simply means to divide an angle into two equal parts.
The sum of the interior angles of a quadrilateral is 360 degrees. Thus;
∠A + ∠B + ∠C + ∠D = 360° ------(1)
In △AOB,
∠AOB + ∠A/2 + ∠B/2 = 180°
Multiply through by 2 to get;
2∠AOB + ∠A + ∠B = 360°
Thus;
∠A + ∠B = 360° - 2∠AOB
Put 360° - 2∠AOB for ∠A + ∠B in eq 1 to get;
360° - 2∠AOB + ∠C + ∠D = 360°
This simplifies to;
∠C + ∠D = 2∠AOB
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Complete question is;
Bisectors of two adjacent angles of angles A and B of quadrilateral ABCD intersect at a point O. Prove that 2∠AOB = ∠C + ∠D
Solve 2v² + 4y = 6 by factoring.
The solutions are v =
and v=
On factorizing 2v² + 4v = 6 the obtained solutions of the quadratic equation are v = 1 and v = -3.
What is factorization by splitting middle term?
The method of Splitting the Middle Term by factorization is where you divide the middle term into two factors. We know that composite numbers can be expressed as the product of prime numbers.
Rule to factorize trinomial expression where coefficients are real numbers, is to split b (the coefficient of x) into two real numbers such that the algebraic sum of these two numbers is b and their product is c, then factorize by grouping method.
According to the given question:
Factorizing 2v² + 4v = 6 by Splitting the Middle Term method
2v² + 4v = 6
2v² + 4v - 6 = 0
2v² + 6v - 2v - 6 = 0
2v(v+3) - 2(v+3) = 0
(2v-2)(v+3) = 0
Therefore the solutions are
2v - 2 = 0 v +3 = 0
v = 1 v = -3
Hence on factorizing 2v² + 4v = 6 the obtained solutions of the quadratic equation are v = 1 and v = -3
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write an equation in point-slope form of each line that passes through the given points. (4, 1), (-2, 7)
Step-by-step explanation:
which of the following, when included, distorts the effectiveness of charting data points? a) too many series b) too many data points c) too much variance in the values of the data d) aggregates
Aggregates is distorts the effectiveness of charting data points. So the option d is correct.
In the given question, we have to select which of the following, when included, distorts the effectiveness of charting data points.
Charts are a quick and efficient way to communicate information to your audience. If the charts are properly created, that is.
A lot goes into creating the ideal visual material, and it's simple to let some components slip. Charts that are hurriedly created are frequently more detrimental than beneficial.
We've compiled a list of useful do's and don'ts to bear in mind while building your own data representations, whether they take the shape of straightforward bar charts and graphs or more intricate interactive visualizations, in order to help you prevent this.
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There are 18 pieces of chalk. The ratio of chalk that is yellow to chalk that is blue is 1:2. How many pieces of chalk are blue?
The number of pieces of blue chalk is 6.
What is an expression?Expression in mathematics is combination of variables with the use of operations and given rules. It can be in the form of equation, numbers etc.
Let x be the number of blue chalk and y be the number of yellow chalk.
Given that, the ratio of yellow chalk and blue chalk is 1:2.
And there are 18 pieces of chalk.
That means the expression x + y = 18
And according to condition,
x/y = 1/2
Using cross multiplication,
2x = y
And we have the expression ,
x + y = 18
substituting 2x = y,
x + 2x = 18
3x = 18
x = 6
Therefore the number of pieces of blue chalk is 6.
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