Answers
Check the picture below.
so from the picture below we can say that parallel sides or bases of the trapezoid are AB and DC, that means our midsegment is found halfway of BC and halfway of AD, let's get the midpoints for those and then get their length.
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad D(\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 2 +0}{2}~~~ ,~~~ \cfrac{ 0 +3}{2} \right) \implies \left(\cfrac{ 2 }{2}~~~ ,~~~ \cfrac{ 3 }{2} \right)\implies (1~~,~~\frac{3}{2}) \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ B(\stackrel{x_1}{2}~,~\stackrel{y_1}{5})\qquad C(\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 6 +2}{2}~~~ ,~~~ \cfrac{ 4 +5}{2} \right) \implies \left(\cfrac{ 8 }{2}~~~ ,~~~ \cfrac{ 9 }{2} \right)\implies (4~~,~~\frac{9}{2})[/tex]
let's get their distance
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{\frac{3}{2}})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{\frac{9}{2}})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(4-1)^2 + (\frac{9}{2}-\frac{3}{2})^2}\implies d=\sqrt{3^2 + 3^2}\implies {\Large \begin{array}{llll} \stackrel{midsegment}{ d=\sqrt{18}} \end{array}}[/tex]
Related Questions
Simplify 7+5(7+5n)
42+25n
2n+19
8n+6
8n+10
Answers
Answer:
42+25n
Step-by-step explanation:
[tex]7+5(7+5n)\\=7+35+25n\\=42+25n[/tex]
i need help please i have been stuck on this problem for 2 months too
Answers
Answer:
280 cubic m
Step-by-step explanation:
SA of rectangular prism = 2lh + 2lw + 2hw
w = width
l = length
h = height
SA = 2(5)(6) + 2(5)(10) + 2(6)(10)
SA = 2(30) + 2(50) + 2(60)
SA = 60 + 100 + 120
SA = 280
(4×3)÷3[-15-5{6-8+2}]
Answers
Answer:
20
Step-by-step explanation:
=12÷3[-15-5{6-8+2}]
=12÷3[-15-5{6-10}]
=12÷3[-15-5-4]
=12÷3[20-4]
=12÷3+16
=4+16
=20
What is the solution to the system of equations shown in the graph?
Responses
A (0, 5)(0, 5)
B (1, -2)(1, -2)
C no solution
D (0, -1)(0, -1)
E (-2, 1)(-2, 1)
Answers
Answer: B is the answer
Step-by-step explanation:
Have a Great day :)
please help i dont know how to do this
(will give 25 points) .
Answers
The values of x in the one-step equation are presented as follows;
x = 4x = 4x = 22x = 65x = 17x = 44x = 2.[tex]\overline{6}[/tex]x = 5x = 12x = -21x = -6.6x = -1/2The calories in the whole cake is 1,680 caloriesPedro made 54 ounces of coffeeWhat is a one-step equation?A one-step equation is one in which the solution can be found with a single step operation.
The solution of the one-step equation found using inverse operations can be presented as follows;
1. 4·x = 16
4·x/4 = 16/4 = 4
4·x/4 = x = 4
x = 4
2. x + 9 = 13
x + 9 - 9 = 13 - 9
x = 4
3. x - 8 = 14
x - 8 + 8 = 14 + 8
x = 22
4. x/5 = 13
(x/5) × 5 = 13 × 5
(x/5) × 5 = x = 13 × 5 = 65
x = 65
5. x - 6 = 11
x - 6 + 6 = 11 + 6
x = 17
6. 2·x = 88
2·x/2 = 88/2 = 44
2·x/2 = x = 44
x = 44
7. 6·x = 16
6·x/6 = 16/6
6·x/6 = x = 16/6 = 2.[tex]\overline{6}[/tex]
x = 2.[tex]\overline{6}[/tex]
8. x + 2.5 = 7.5
x + 2.5 - 2.5 = x = 7.5 - 2.5 = 5
x = 5
9. (2/3)·x = 8
(2/3)·x/(2/3) = 8/(2/3) = 8 × (3/2) = 12
(2/3)·x/(2/3) = x = 12
x = 12
10. x/3 = -7
x/3 × 3 = -7 × 3 = -21
x = -21
11. x - 1.6 = -8.2
x - 1.6 + 1.6 = -8.2 + 1.6 = -6.6
x = -6.6
12. 4·x = -2
4·x/4 = -2/4 = -1/2
4·x/4 = x = -1/2
x = -1/2
13. The number of slices into which the cake is divided = 6 Slices
The amount of calories per each slice of the cake = 280 calories
The amount of calories in the whole cake is therefore;
The sum of the calories in the cake = 6 × 280 calories = 1,680 calories
14. Amount of coffee Pedro served to his friends = 34 ounces
Amount of coffee left over = 20 ounces
The total amount of coffee Pedro made = 20 + 34 = 54
The amount of coffee Pedro makes = 54 ounces
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if one addend of x is c, what is the other addend?
Answers
If one addend of x is c, the other addend is x-c.
How to find the other addend?An addend is a term that is added to another term to form a sum. In the equation x = c + (x-c) , c and (x-c) are the two addends that make up the sum x.
The reason why x-c is the other addend is that the sum of the two addends (c and x-c) must equal x.
In other words x = c + (x-c) can be simplified to x = c + x - c which is x = x
Therefore, If one addend of x is c, the other addend is x-c.
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6.
Stem
1
2
3
Leaf
556
1 1 1
5 6
16 means 1.6
Match the stem and leaf plot to the correct set of data.
Answers
The correct set of data matched to the stem and leaf plot is given as follows:
1.5, 1.5, 1.6, 2.1, 2.1, 2.1, 3.5, 3.6.
What is a stem-and-leaf plot?The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:
1|6 = 1.6.
(in the context of this problem).
Following the key format, the measures listed in the answer represent the correct data-set from the stem-and-leaf plot.
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A company manufactures and sells shirts the daily profit. The company makes depends on how many shirts they sell the profit in dollars when the company sells X shirts can be found using the function F buy X)equals 6X -90 find the interpret the given function values and determine inappropriate domain for the function f(-9)
profit of
of the problem.
=
f(27)
profit of
of the problem.
=
f(17.5) =
profit of
of the problem.
meaning if the company sells |
dollars. This interpretation
meaning if the company sells
dollars. This interpretation
, meaning if the company sells
dollars. This interpretation
shirts, they would make a
in the context
shirts, they would make a
in the context
shirts, they would make a
in the context
Answers
Answer:
The derivative of the profit function P(x) is called marginal profit with notation: P ... Example 2: Given the average cost in dollar per unit C = 357x + 1800 , find: ... (1) the selling price to maximize the revenue is 31 − 3 = 28 dollars per unit ... Example 6: A company has established that the revenue function in dollars is R(x)=2x.
Step-by-step explanation:
27 is 7.5% of what number
Answers
Answer:
27 is 7.5% of the number 360
A team of three is chosen randomly from an office with 2 men and 4 women. Let X be the number of women on the team. (a) Identify the probability distribution of X by name. (b) Give the probability mass function of X
Answers
The probability distribution of X by name is X/6 and the the probability mass function of X is X/6 - 4
The term probability mass function is defined as a function over the sample space of a discrete random variable X which gives the probability that X is equal to a certain value.
Here we know that team of three is chosen randomly from an office with 2 men and 4 women.
And let us consider that X be the number of women on the team.
Total number of members in the term is calculated as,
=> 4 + 2 = 6
Then the the probability distribution of X by name is,
=> X/6
And the the probability mass function of X is written as,
=> x/6 - 4
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Shane bought a package of 12 bagels. He gave b of them to his friends. Write an expression that shows the number of bagels Shane has left.
Answers
The expression that shows the number of bagels Shane has left is 12-b.
What is an expression?Expression in math is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given;
Shane bought a package of 12 bagels
He gave b of them to his friends
Now;
Shane bought 12 bagels
Expression= 12
Shane gave b
Expression=12-b
Therefore, the expression will be 12-b.
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6(9−6)−23+4= I dont konw this
Answers
Answer:
-1Step-by-step explanation:
[tex]\sf 6(9-6)-23+4[/tex]
[tex]\sf (6)(3)-23+4[/tex]
[tex]\sf 18-23+4[/tex]
[tex]\sf -5+4[/tex]
[tex]\sf -1[/tex]
Answer:
First you are to do what is in the parenthesis first:
9 - 6 = 3
The equation is now:
6 * 3 - 23 + 4
Then you do the multiplcation:
6 * 3 = 18
18 - 23 + 4
23 + 4 = 27
27 - 18 = 9
Step-by-step explanation:
Hope it helps! =D
what is the answer? thanks
Answers
The solution for the expression given above would be = 31/40. That is option B.
What is a fraction?A fraction is defined as the part of a whole value which is written in the form of a numerator and a denominator.
The given fractions from the question;
2/5 + 3/8
Find the lowest common multiple of the figures below ( denominator) = 40
= 16 + 15/40
= 31/40
Therefore the correct fraction for the given expression = 31/40.
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Can someeeeeoneee helppp meeee please
Answers
Answer: Yes it's 7
Step-by-step explanation:
10/100 x 70 = 7
Answer:The correct answer would be 7
Step-by-step explanation:
Thannklkkkk you sooo much for the helppp
Answers
Answer:
33
Step-by-step explanation:
55/100×60
= 33pink blocks
Write an exponential function to model the situation. Tell what each variable represents. A price of $130 increases 5% each year.
Answers
The exponential function to model the situation is f(x) = 130(1.05)ˣ⁺¹⁶
How to find the exponential function?First of all, note that each variable represents number of years the price increases in each year
We are given,
The initial number of population = 130
Rate of growth = 5% = 0.05
Number of years = 16.
Thus, we get that the growth in population for 16 years is given by,
f(x) = 130(1.05)¹⁶
⇒f(x) = 130(1.05)¹⁶i
This gives us that the population after 16 years will be given by,
f(x) = 130(1.05)ˣ⁺¹⁶
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if jenna saves $2500 per year with an intrest of 10% compounded annually how much would she have in 30 years
Answers
Answer: Jenna would have $37,175 in 30 years if she saves $2500 per year with an interest rate of 10% compounded annually.
Step-by-step explanation:
To calculate the total amount Jenna would have after 30 years of saving $2500 per year with an interest rate of 10% compounded annually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (principal + interest)
P = the initial principal (the amount Jenna saves each year, $2500 in this case)
r = the interest rate (10% in this case, so 0.10)
n = the number of times interest is compounded per year (annually in this case, so 1)
t = the number of years (30 in this case)
Plugging in the values:
A = $2500(1 + 0.10/1)^(1*30) = $2500(1.10)^30 = $2500(14.87) = $37,175
So, Jenna would have $37,175 in 30 years if she saves $2500 per year with an interest rate of 10% compounded annually.
Answer:
$411,235.06
Step-by-step explanation:
the probability that a student is taking a math class is 60%. the probability that a student in a math class is also taking a science class is 80%. what is the probability that a student is taking both math and science?
Answers
Answer:
48%
Step-by-step explanation:
0.6*0.8 = 0.48 = 48%
INTEGRALS EXERCISES PLEASE HELPPPPP, I’LL GIVE U A CROWN
Answers
Answer:
2. sec x + c
1.1 view attached pic
1.2 view attached pic
Step-by-step explanation:
severe difficulty in making mathematical calculations as a result of a brain disorder
Answers
Dyscalculia is a learning disorder that affects a person’s ability to do the math.
A learning problem called dyscalculia diminishes a person's capacity for math. Similar to how dyslexia impairs reading-related brain regions, dyscalculia interferes with the knowledge and skills connected to math and numbers. Although dyscalculia often first manifests in childhood, it can even affect adults who are unaware of it.
The signs of this condition typically emerge in childhood, particularly as kids start to master the fundamentals of math. However, many adults who suffer from dyscalculia are unaware of it. When forced to do the math, people with dyscalculia frequently experience mental health problems like anxiety, depression, and other distressing emotions.
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Express the following as a rate.
a) 20 litres of Petrol for R180
Answers
The rate of petrol in this case is R9 per liter.
What is rate?
In mathematics, rate is a measure of how one quantity changes in relation to another quantity. It is often expressed as a ratio or fraction, where the numerator represents the amount of change in the first quantity and the denominator represents the amount of change in the second quantity.
The rate of petrol can be expressed as the cost per liter. To find the cost per liter of petrol in this case, we can divide the total cost by the total amount of petrol:
Cost per liter = Total cost / Total amount
For the given scenario, we have 20 litres of petrol for R180. So the rate can be calculated as:
Rate = Total cost / Total amount = R180 / 20 litres
Simplifying the expression, we get:
Rate = R9 per litre
Therefore, the rate of petrol in this case is R9 per liter.
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PLEASEE HELPPP
A line has a slope of –1/3 and a y-intercept of 5/3. Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
Answer:
The answer in intercept form will be
-1/3=5/3x+c
Can someone please help me with problem 6 of this assignment? I included the measurements of the triangle so that you are able to solve it accurately.
Geometry Topic: 6.1 - 6.4 Constructing Parts and Centers
Problem 6 Directions: Remember! Triangle centers may be outside the triangle. Locate the orthocenter of each triangle by finding the intersection of the altitudes.
Answers
Answer:
let say the 3 points that make the triangle is A-B-C, you draw a line from A to the line opposite to A, make it perpendicular. If it's not inside of the triangle, you just extend the line to make it work. Then repeat for B and C. Then you extend the perpendicular lines (altitude) and make them intersect. The intersect point is the orthocenter.
Step-by-step explanation:
Then you extend the perpendicular lines (altitude) and make them intersect. The intersect point is the orthocenter.
Answer:
see attached
Step-by-step explanation:
You want to construct the orthocenter of the given triangle.
OrthocenterThe orthocenter of a triangle is the point of intersection of the altitudes. The construction of it requires construction of at least two altitudes of the triangle. This is accomplished using the "perpendicular through an external point" construction.
Perpendicular through an external pointA perpendicular to a line through a point not on the line is constructed in a few simple steps:
Using the external point as a center, draw an arc that intersects the line in 2 places.Using each of those points as a center, draw intersecting arcs with the same radiusThe line through that point of intersection and the original point is perpendicular to the lineThe attachment shows arc FG using C as a center, and arc HI using A as a center. Arcs using those points as center are drawn so they intersect at points V and W.
Lines CV and AW are altitude lines that intersect at the orthocenter: point Z.
__
Additional comment
The vertices of the original triangle have been labeled A, B, C counterclockwise from upper left.
It may appear that point Z is a reflection of point C in line AB, but it is not.
How do you solve this type of problem?
Answers
It's a fact that the sum of the angles of a triangle add up to 180º.
So, 55º + 85º + (3x+4)º = 180º.
That's the equation you need to solve:
55 + 85 + 3x+4 = 180 (combine like terms)
144 + 3x = 180 (subtract 144 from both sides)
3x = 36 (divide both sides by 3)
x = 12 (you've got x)
A men's health magazine would like to conduct a survey using a simple random sample of 900 men who practice yoga. One of the goals of the survey is to create a confidence interval to estimate the proportion of all men practicing yoga who report low stress levels. Since the intended survey method requires face-to-face interaction, some of the magazine executives are concerned about the cost of the survey and suggest sampling a smaller group of 100 men instead of 900 men. Assuming the sample proportion doesn't change, which of the following best describes the anticipated effect on the width of the confidence interval if the magazine were to survey a random sample of 100 men who practice yoga, rather than 900 men? A) The width of the interval based on 100 men would be about nine times the width of the interval based on 900 men.
B) The width of the interval based on 100 men would be about three times the width of the interval based on 900 men. C) The width of the interval based on 100 men would be about the same width as the interval based on 900 men. D) The width of the interval based on 100 men would be about one-third the width of the interval based on 900 men. E)
The width of the interval based on 100 men would be about one-ninth the width of the interval based on 900 men.
Answers
The width of the interval based on 100 men would be about three times the width of the interval based on 900 men.
What is the width of the interval?
The width of a confidence interval for a proportion is proportional to the standard error of the sample proportion, which is proportional to the square root of the sample size.
The standard error is defined as the standard deviation of the sampling distribution of the sample proportion, which is estimated by the standard deviation of the Bernoulli distribution (square root of the sample proportion times (1 - sample proportion) divided by the sample size).
So, if the sample size is reduced by a factor of 9 (from 900 to 100), the standard error (and hence the width of the confidence interval) would increase by a factor of 3 (square root of 9).
Therefore, The width of the interval based on 100 men would be about three times the width of the interval based on 900 men.
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Write a system of equations.. Taxi company charges a fee of $10 plus $2.50 per mile, taxi company #2 charges $4.00 per mile with no fee
PLEASE HELP, DUE TOMORROW
Answers
The equation for the situation described in your problem would be y is $10x + $2.50 .
How do a set of equations work with answers?To utilize substitution to resolve an equational system:
Divide one of the two variables in one of the equations.
Substitute the expression that the isolated variable's equivalent from Step 1 into the other equation.
Solve the linear equation for the last variable.
system of equations, simultaneous equations Algebraic equations involving two or more must be solved cooperatively (i.e., the solution must satisfy all the equations in the system). For a system to have a single solution, the number of equations must equal the number of unknowns. Even then, a solution is not guaranteed.
The following equation would apply to the scenario in your problem:
y =$10x + $2.50
y = $2x + $4.00
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How many possible centers of rotation will produce an image of a left-pouting arrow?
Answers
The number of center of rotations to produce the image is (d) infinite
How to determine the number of centers?An arrow pointing to the left is symmetric around its central axis.
This means that any point along the central axis of the arrow can serve as a center of rotation to produce an image of a left-pointing arrow.
The central axis is a straight line that runs through the middle of the arrow from the tip to the base, and also extend through the arrow's depth.
Hence, the number of possible centers of rotation that will produce an image of a left-pointing arrow is infinite.
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factor the expression 15x - 10xy
Answers
Answer: 5x(3-2y)
Step-by-step explanation:
Step 1:
Find the greatest common factor (GCF):
Both values have 5x as the GCF.
Step 2:
Take out the GCF:
15x/5x=3
-10xy/5x=-2y
Step 3:
Write it out:
5x(3-2y)
Check:
Apply Distributive Property:
5x*3=15x
5x*-2y=-10xy
15x-10xy=15x-10xy
The amount of sand left in a 600 mL vase can be modeled by the equation s = – 1 5 t + 600, where s is the amount of sand left in the vase and t is time in minutes since the sand started leaking out. The vase is full of sand. Sand leaks out of the vase until the vase is empty. Determine the domain and range of this scenario
Answers
As per the given equation, the domain is [0, 3000] and the range is [0, 600].
In the term domain is defined as the set of values that we are allowed to plug into our function where as the range of a function is the set of values that the function assumes.
Here we know that the amount of sand left in a 600 mL vase can be modeled by the equation that is written as,
=> s = – 1/5 t + 600
here s refers the amount of sand left in the vase and t refers time in minutes since the sand started leaking out
Here we also know that the vase is full of sand and sand leaks out of the vase until the vase is empty.
Then in order to find the domain we have to put the value of s as 0, then we get the domain as,
=> 0 = -1/5t + 600
=>1/5t = 600
=> t = 3000
Then the domain is [0, 3000].
Similarly, in order to find the value of range we have to put the value of t as zero, then we get
=> s = -1/5(0) + 600
=> s = 600
Then the range is [0, 600]
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a) Complete the table of values for x + y = 6
b) On the grid draw the graph of x + y = 6
for values of x between -2 and 3.
Answers
By resolving the following equation for y, you can make the work a little simpler: x + y = 6
How to find the calculation?The link between data pieces is displayed in tables of values. In science lesson, you might utilize a values table. Data is recorded in tables of values by scientists and researchers, who then examine the data to look for patterns. As a result, they can use this pattern to anticipate future events.
y = 6 - x, which means to take 6 out of both sides.
Now you can simply fill in the x-values and determine y. For instance,
y = 6 -(-2) = 8 . . . for x = -2
y = 6 - 3 = 3 . . . . for x = 3
The table and graph that are attached both display these values.
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