A, B and C are the vertices of a triangle.
A has coordinates (1,4)
B has coordinates (3, 0)
C has coordinates (-3,-2)
D is the midpoint of AB.
E is the midpoint of AC.
Prove that DE is parallel to BC.
You must show each stage of your working.
PLEASE HELP ASAP THANK YOU
Answer:
see below
Step-by-step explanation:
To find the coordinates of the midpoints, add the x's and divide by 2 and add the y's and divide by 2.
The coordinates of D, the midpoint of AB, (1+3)/2 will be the x-coordinate and (4+0)/2 will be the y-coordinate.
D (2,2)
You could also see this on a graph, see image.
E, the midpoint of AC has the x-coordinate (1+-3)/2, which is -1 and y-coordinate (4+-2)/2 which is 1.
E is (-1,1)
Then we are able to calculate the slope of DE and BC.
To calculate slope, subtract the y's and put that on top of a fraction and subtract x's and put that on the bottom of a fraction. If the slopes are the same the segment are parallel.
Slope of DE:
(2-1)/(2--1)
= 1/3
Slope of BC:
(0--2)/(3--3)
=2/6
=1/3
The slopes of BC and DE are equal, so the segments are parallel.
(Alternatively, you could show that Triangle ABC and Triangle ADE are similar. Then find the segments parallel because corresponding angles are congruent.)
The average monthly temperature of a city can be modeled by a
cosine graph. Melissa has been living in Phoenix, Arizona, where the
average annual temperature is 75°F. She would like to move, and live
in a location where the average annual temperature is 62°F. When
examining the graphs of the average monthly temperatures for
various locations, Melissa should focus on the
The average monthly temperature of a city can be modeled by a cosine graph, Melissa should focus on the Midline. This is further explained below.
What is Melissa's focus on the Midline.?Generally, The average temperature would be indicated somewhere along the curve, most likely near the middle.
In conclusion, Melissa should concentrate on the Midline, which can be used to model the average monthly temperature of a city.
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Jamaal knows that it is certain that he will win the election because he is the only person who is running for class treasurer. which value represents the probability that he will win the election? 0 one-fourth three-fourths 1
The correct answer is option D which is the probability is 1.
The complete question is given below:-
Jamaal knows that it is certain that he will win the election because he is the only person who is running for class treasurer. Which value represents the probability that he will win the election?
0
1/4
3/4
1
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
The probability of Event E is given by,
P = favourable outcomes / Total outcomes
Jamaal is the only candidate running in the class treasurer election.
There for Total No. of outcomes = 1
Here Event E is Jamaal winning the Election.
So, No. of favorable outcome = 1
P(E) = 1 / 1
P(E) = 1
This type of event is called a SURE EVENT Because the probability of a sure event is always 1.
The Probability of Jamaal winning the election is 1. So, Option D is correct.
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The probability that he will win the election will be 1. Then the correct option is D.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
The value of the probability of an event will be varying from zero to one.
Jamaal knows that it is certain that he will win the election because he is the only person who is running for class treasurer.
Then the probability that he will win the election will be
If the event will certainly happen, then the probability will be one.
P = 1
Then the correct option is D.
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Edgar runs 8/9 of a mile each day. what is the total distance that edgar runs in a 5-day week?
The distance that edgar runs in a 5-day week will be 4.45 miles.
What is the distance?Distance is defined as the length between the two points it can be represented in mm,cm, meters,km, and miles.
Given that:-
Edgar runs 8/9 of a mile each day. what is the total distance that Edgar runs in a 5-day week?
The total distance will be calculated as:-
D = [tex]\dfrac{8}{9}[/tex] x 5
D = 4.45 miles
Therefore the distance that edgar runs in a 5-day week will be 4.45 miles.
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helppp will give brainliest
Write and graph the inverse variation in which y = 8 when x = –4.
Answer:
Inverse variation here gives out a function [tex]xy=(-32)[/tex].
Step-by-step explanation:
Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value. It states if the value of one quantity increases, then the value of the other quantity decreases. While direct variation describes a linear relationship between two variables, inverse variation describes another kind of relationship.
An inverse variation can be represented by the equation
[tex]xy=k \\or \\y=kx[/tex]. That is, y varies inversely as x if there is some nonzero constant k.
Here, the product is given by
[tex]xy=(-4)[/tex]×[tex]8[/tex]
[tex]xy=(-32)[/tex]
We will be plotting the graph of the function [tex]xy=(-32)[/tex]
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In which direction must the graph of f(x) = x be shifted to produce the graph of g(x) = x − 6?
Answer:
f(x) must be shifted 6 units down in order to produce the graph of g(x).
What is the slope of the line segment?
1 over 4
Negative 1 over 4
4
−4
Two linear equations are shown.
C
654321₁
4
66
y=1/3x+2
y=4/3x-5
What is the solution to the system of equations?
O (7.4)
0 (7.33)
O
0 (8)
O
O (9.7)
Answer: Option (2)
Step-by-step explanation:
Setting the equations equal to each other,
[tex]\frac{1}{3}x+2=\frac{4}{3}x-5\\\\7=x[/tex]
If x=7, then [tex]y=\frac{7}{3}+2=\frac{13}{3}[/tex]
Problem
Solve for xxx.
5x^2 + 60x + 180 = 05x
2
+60x+180=0
Answer:
x = -6
Step-by-step explanation:
5x² + 60x + 180 = 0
5 x 180 = 900
you need 2 numbers that multiplies into 900 and adds into 60. these numbers are 30 and 30. now we can rewrite it
5x² + 30x + 30x + 180 = 0.
split it in half and factorise
5x(x + 6) + 30(x + 6) = 0
this means the brackets are:
(5x + 30)(x + 6) = 0
5x + 30 = 0
5x = -30
x = -6
x + 6 = 0
x = -6
therefore, x = -6.
If f(x) = 4x² + 1 and g(x)=x2-5, find (f- g)(x).
Answer:
3x² +6
Step-by-step explanation:
(f-g)(x) = f(x) -g(x) = (4x²+1) -(x²-5) . . . . . substitute the function definitions
... = 4x² +1 -x² +5 . . . . . . . . . . . eliminate parentheses
... = (4-1)x² +(1+5) . . . . . . . . . . . collect like terms
... = 3x² +6
the length of a rectangle is five times its width. If the perimeter of the rectangle is 84 in, find its length and width
Answer:
width=14 &Length = 70( can add unit behind the answer e.g.cm or mm etc..)
Step-by-step explanation:
we know that in a rectangle not all side are same compare to a square..
therefore:
1) write the formula for perimeter down
perimeter = the sum of all side
perimeter = 2x(width) + 2x(length)
P=2(w)+2(L)
2) substitute into the equation
P =2(w)+2(L)
84=2(w)+2(5*w)
3) perform opposite operation to make w become the subject of the formula inorder to find width
48=2(w)+2(5*w)
48=2w+10w
48=12w
48/12=12w/12( the twelves cancels out)
7=w or the width is 7
4) rewrite the formula and solve
P=2(w)+2(L)
P =2(7) + 2(5*7)
P = 14 + 70
P = 48
Assume that when adults with smartphones are randomly selected, % use them in meetings or classes. If adult smartphone users are randomly selected, find the probability that exactly of them use their smartphones in meetings or classes.
The probability that exactly 6 of 8 adult use their smartphones in meetings or classes is 0.147 or 14.7% .
The complete question is
Assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an LG Smartphone survey). If 8 adult smartphone users are randomly selected, find the probability that exactly 6 of them use their smartphones in meetings or classes.
What is Probability ?Probability is the measure of likeliness of an event to happen.
The probability given is
p = 54% = 0.54
n =8
r = 6
The binomial Probability is given by
[tex]\rm P(x) = ^n C_r p^r q^{n-r}[/tex]
The probability that exactly 6 people use smartphones in a class of 8 student is given by
[tex]P(x) = \dfrac{n!}{r! (n-r)!} p^r q^{n-r}[/tex]
Here q represents the complement
q = 1 -p
q = 1-0.54 = 0.46
[tex]P(6) = \dfrac{8!}{6! (2)!} 0.54^6 0.46^{2}\\\\\P(6) = \dfrac{8 * 7}{ 2} 0.54^6 0.46^{2}\\\P(6) = 0.147[/tex]
Therefore The probability that exactly 6 of 8 adult use their smartphones in meetings or classes is 0.147 or 14.7% .
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If m∠B = 46°, and m∠D = 67°, what is m∠BEA?
67°
46°
88°
134°
A 2-column table with 5 rows. Column 1 is labeled Number of Apples with entries 0, 1, 2, 3, 4. Column 2 is labeled Number of Slices with entries 0, 6, 12, 18, 24.
Use the table to find the constant of proportionality and the equation that represents the relationship.
Let x = number of apples and y = number of slices.
The constant of proportionality is
.
The equation for this relationship is
Answer:
The constant of proportionality is 6. This makes the relation y = 6x.
Step-by-step explanation:
Concept: As the number of apples are increasing, the number of slices are also increasing. Given that x is the number of apples and y is the number of slices. This means that y is directly proportional to x.
y ∝ x
Let the constant of proportionality be k.
y = kx
For x = 1, y = 6. So, k = 6.
For x = 2, y = 12. So, k = 6.
This follows for all the values.
Clearly, the constant of proportionality is 6.
The relationship will become y = 6x.
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A software company wants to get an idea of their customers' level of satisfaction with their software. To do so, they included a phone number on the packaging of their most recent software release, with the message, "If you have any concerns with the product, please call this number." Based on the overwhelmingly negative response they received from these calls, the company decided to stop selling the product.
What could be wrong with their decision?
A.
The phone system screened out certain positive comments because of a malfunction.
B.
The release of the software coincided with the spread of a virus which affected the performance of the program.
C.
The note on the package only told customers to call in the event that they had a concern, which could bias the results negatively.
D.
The customers were misinformed about the purpose of the program.
Answer:
C. The note on the package only told customers to call in the event that they had a concern, which could bias the results negatively.
Explanation:
Since customers were only told to call if they had concerns, all of the calls were about concerns or problems that they were having - meaning all of the calls were negative. However, they were never informed to call if they were happy or content with the product, meaning they were never informed of the people who had positive comments, only negative.
The perimeter of a rectangle is 32 inches. The length is 1 foot, what is the width of the rectangle in inches?
Answer:
15
Step-by-step explanation:
divide the perimeter by two and minus 1
Answer: 15ft
Step-by-step explanation:
Start off by drawing a rectangle with the given information. Since it is a rectangle we know that the opposite side is also 1. So subtract 2 from 32 to get 30. Divide this by 2 and you will get your width of your rectangle. Hope this helps!
Mrs. Cooper hosts an annual art contest for kids. She has records of the number of entries for the last 9 years. She received 30 entries in the first year. Over the next 3 years, the number of entries increased by 10 kids per year. In the next 2 years after that, there were 60 entries each year, and in the last 3 years, the number of entries increased by 15 kids per year. Which graph models the piecewise function for the given situation, where x represents time after the first year and y represents the number of entries in that year?
To graph this situation we must take into account the data and the organization of each of them on the X axis and Y axis.
How to graph this situation?To graph this situation we must take into account the data we have:
YearsTicketsBased on these data, we assign the horizontal axis to count years and the vertical axis to count tickets per year. We must continue the pattern of increased attendance over the years.
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Im kinda stuck i no like this type of math help please
Answer:
EAD
Step-by-step explanation:
white shapes and black shapes are used in a game. some shapes are circles. all the other shapes are squares. the ratio of white shapes to the number of black shapes is 7:3 the ratio of white circles to white squares is 2:7 the ratio of black circles to the number of black squares is 1:2 work out what fraction fo all shapes are circles give your answer as a fraction in its simplest form
[tex]\mathbf{\frac{23}{90}}[/tex] fraction of all shapes are circles.
Given that the ratio of the number of white shapes to black shapes is 7:3
Let the number of white shapes be [tex]7n[/tex]
Then the number of black shapes be [tex]3n[/tex]
So total number of shapes [tex]=7n+3n=10n[/tex]
Now ratio of white circles to white squares is 2:7
So the fraction of circles to all white shapes [tex]=\frac{2}{2+7}=\frac{2}{9}[/tex]
Hence the number of white circles [tex]=\frac{2}{9}\times7n=\frac{14n}{9}[/tex]
Again given that the ratio of black circles to the number of black sqaures is 1:2
So the fraction of circles in all black shapes [tex]=\frac{1}{1+2}=\frac{1}{3}[/tex]
The number of black circles [tex]=\frac{1}{3}\times3n=n[/tex]
Total number of circles [tex]=\frac{14n}{9}+n=\frac{14n+9n}{9}=\frac{23n}{9}[/tex]
The fraction of all shapes are circle is [tex]=\frac{\frac{23n}{9}}{10n}=\frac{23n}{90n}=\frac{23}{90}[/tex]
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Which graph represents the following system of inequalities?
y<-2x+4
yx<3
A graph which represents the given system of inequalities is Graph C.
What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following:
Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).Based on the graph for the given system of inequalities (see attachment), we can infer and logically conclude that Graph C best represents them.
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Multiply 3.4x and 1.2x.
Answer:
telmhtkhknrkh
Step-by-step explanation:
eg
Answer:
4.08x^2
Step-by-step explanation:
Find the value of x. Then find the measure of each labeled angle.
Answer:
X=20; the labeled angles are 80 and 100
Step-by-step explanation:
These angles are "consecutive interior angles" so they will add up to be 180.
180 = 5x + 4x
180 = 9x
180/9 = 9/x
20=x
A climber is on a hike. After an hour he is at an altitude of 150 feet. After 2 hours, he is at an altitude of 275 feet. After 4 hours, he is at an altitude of 525 feet and after 6 hours, he is at an altitude of 700 feet. Which table could be used to model his climb?
The table that could be used to model his climb will consist of 125 ft/h for the first two hours and 87.5 ft/h for the next 4 hours.
Equation of motion of the climberThe equation that can be used to model the motion of the climber is calculated as follows;
(1, 150)
(2, 275)
(4, 525)
(6, 700)
Slope for the first two hoursm = (275 - 150)/(2 - 1) = 125 ft per hour
Slope for the next 4 hoursm = (700 - 525)/(4 - 2) = 87.5 ft/hr
Thus, the table that could be used to model his climb will consist of 125 ft/h for the first two hours and 87.5 ft/h for the next 4 hours.
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Which quadratic equation is equivalent to (x-4)2-(x-4) - 6 = 0?
Answer:
x=4
Step-by-step explanation:
2x-8-x+4-6=0
or,2x-x-8+4=0
or,x-4=0
or,x=0+4
•°•x=4
ans
Answer:
x = 2 or 7
Step-by-step explanation:
(x-4)² - (x-4) - 6 = 0
x²-8x+16-x+4 -6 = 0
x²-9x+14 = 0
(x-2)(x-7) = 0
∴x = 2 or 7
Find the inequality represented by the graph:
The equation of linear system in the form of inequality will be x + y ≥ 2 or y ≥ 2 – x.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The graph is given below.
The graph is a linear equation.
Then the equation of linear system in the form of inequality will be
The two point are given as (0, 2) and (1, 1). Then the equation of linear system will be
y – 2 ≥ [(2 – 1) / (0 – 1)] (x – 0)
y – 2 ≥ – x
x + y ≥ 2
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In the equation above. K is a constant. If x=9, what value is k? A) 1 B) 7 C) 16 D) 79
Answer: 79
Step-by-step explanation:
[tex]\sqrt{k+2}-9=0\\\\\sqrt{k+2}=9\\\\k+2=81\\\\k=\boxed{79}[/tex]
Answer:
D) k = 79
Step-by-step explanation:
Given equation: [tex]\sf\sqrt{k+2}-x=0[/tex]
Steps:
1. Substitute 9 as the value of x in the equation:
[tex]\sf\sqrt{k+2}-9=0[/tex]
2. Add 9 to both sides:
[tex]\sf\sqrt{k+2}-9+9=0+9\\\\\Rightarrow \sqrt{k+2}=9[/tex]
3. Square both sides of the equation:
[tex]\sf\left(\sqrt{k+2}\right)^2=9^2\\\\\Rightarrow k+2=81[/tex]
4. Subtract 2 from both sides:
[tex]\sf k+2-2=81-2\\\\\Rightarrow k = 79[/tex]
5. Check your work:
[tex]\sf\sqrt{k+2}-x=0\ \textsf{[ substitute 79 for k, and 9 for x ]}\\\\\sqrt{79+2}-9=0\ \textsf{[ add ]}\\\\\sqrt{81}-9=0\ \textsf{[ take the square root ]}\\\\9-9=0\ \textsf{[ subtract ]}\\\\0=0\ \checkmark[/tex]
Which statement is needed to complete this syllogism?
If the angles of a triangle are all equal, then the sides of a triangle are all equal.
If the sides of a triangle are all equal, then the triangle is equilateral.
Therefore, if the angles of a triangle are all equal, then ________________________.
Group of answer choices
the sides of a triangle are all equal
the triangle is equiangular
the angles of a triangle are all equal
the triangle is equilateral
If the angles of a triangle are all equal, then the sides of a triangle are all equal. The correct answer is option A.
What is an equilateral triangle?A triangle having all the three sides equal and all the angles equal is called the equilateral triangle.
As we can see that if the triangle is having all the angles equal then all three sides of the triangle must be equal. The triangle is termed the equilateral triangle.
Therefore the angles of a triangle are all equal, then the sides of a triangle are all equal. The correct answer is option A.
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What are the coordThe general form of the equation of a circle is 7x2 + 7y2 − 28x + 42y − 35 = 0.
The equation of this circle in standard form is
. The center of the circle is at the point
, and its radius is
units.inates for the center of the circle and the length of the radius?
The equation of this circle in standard form is (x-2)² + (y+3)² = 18
The center of the circle is at the point (2,-3), and its radius is 4.2426 units
What is circle?Circle is the 2D geometry which is round in shape with radius R.
Given is the general form of the equation of a circle is
7x² + 7y² − 28x + 42y − 35 = 0.
Dividing by 7, we get
x² -4x + y² + 6x = 5
Completing the squares, we have
x² -4x + 4 + y² +6x + 9 = 5 +4 + 9
(x-2)² + (y+3)² = 18 = (3 √2)²
Circle's center is (2,-3) and radius = 3 √2 = 4.2426 units
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Answer:
(x-2)^2 + (y+3)^2 = 18,
2,-3
3(2^(1/2)) units
Step-by-step explanation:
Below
the inverse of f(x)=2x-10
The inverse of the function f(x) = 2x - 10 is f-1(x) would be x/2 + 5.
Lets try to solve it,
We will be using the inverse function to solve this.
f(x) =[tex]2x - 10[/tex]
Replace f(x) with y.
[tex]y = 2x - 10[/tex]
Interchange x and y
[tex]x = 2y - 10[/tex]
Solve for y
[tex]y = (x + 10) / 2[/tex]
Replace y with f-1(x).
[tex]f-1(x) = x/2 + 5[/tex]
Thus, the inverse of the function f(x) = 2x - 10 is f-1(x) = x/2 + 5
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Which equation is the inverse of y = 9x² - 4?
Answer:
y = ± [ √(x+4) ] / 3
Step-by-step explanation:
1) To find the inverse of the function y = 9x2 – 4, exchange the variables x and y, and then solve for the new y.
2) Exchange of the variables: y = 9x^2 – 4 → x = 9y^2 – 4
3) Solve for y:
=> 9y^2 = x + 4
=> y^2=> y = ± [ √(x + 4) ] / 9
= > y = ± [ √(x + 4) ] / 3
