For the given Trapezoid ABCD the value of BC:BN is BC:BN=8:3.
What is Trapezoid?
A trapezoid is a quadrilateral in American and Canadian English that has at least one pair of parallel sides. A trapezium is the term used in British and other varieties of English. In Euclidean geometry, a trapezoid is invariably a convex quadrilateral. The trapezoid's parallel sides are referred to as its bases.
Given:
In the trapezoid ABCD ( AB ∥ CD ) point M∈ AD , so that AM:MD=3:5.
Line l ∥ AB and going trough point M intersects diagonal AC and leg BC at points P and N respectively.
We have to find BC:BN
ABCD is a trapezoid and there is a point m which belongs to AD such that AM:MD=3:5.Line "l" parallel to AB intersects the diagonal AC at p and BD at N.
Now, we know that the parallel lines divide the transversal into the segments with equal ratio, therefore, BN:NC=AM:MD
But, BC= BN+NC
Therefore, BC:BN = (BN + NC): BN
⇒ BC:BN = (3 + 5): 3
⇒ BC:BN = 8:3
Hence, for the given Trapezoid ABCD the value of BC:BN is BC:BN=8:3.
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MATH HELP PLEASE ---->
#13 - 16 Solve for x
16.) -31 < 3x – 7 < 14
17.) xy – ab = cd ; solve for b
18.) 3(a – b) = 9mn ; solve for a
#19 – 28 Factor Each Expression (If possible)
19.) 3x2 (y – 2) – 5(y – 2)
20.) kmfd – 3jkm
21.) 49x2– 9
22.) 64x2+ y2
23.) x2+ 7x – 35
24.) 2x2+ 11x + 14
25.) x2- 2x – 63
26.) 3x2– 2x + 7
Answer:
16.) The solution to this inequality is x < -4 or x > -3.
17.) To solve for b, we need to isolate b on one side of the equation. To do this, we can subtract ab from both sides of the equation, which gives us xy = cd - ab. Then, we can divide both sides of the equation by xy, which gives us b = (cd - ab)/xy.
18.) To solve for a, we need to isolate a on one side of the equation. To do this, we can divide both sides of the equation by 3, which gives us a - b = 3mn. Then, we can add b to both sides of the equation, which gives us a = b + 3mn.
19.) To factor this expression, we first distribute the 3x2 to get 3x2y - 6x2. Then, we notice that the 3x2 and the -6x2 have a common factor of -3x2, so we can factor them out to get -3x2(y - 2) - 5(y - 2). Finally, we notice that the -3x2(y - 2) and the -5(y - 2) have a common factor of -(y - 2), so we can factor them out to get -(y - 2)(3x2 - 5).
20.) To factor this expression, we notice that the kmfd and the -3jkm have a common factor of -jkm, so we can factor them out to get -jkm(f - 3).
21.) To factor this expression, we notice that 49 is a perfect square, so we can write 49 as 72. Then, we can factor out the x from the x2 to get 7x(x - 9).
22.) To factor this expression, we notice that 64 is a perfect square, so we can write 64 as 82. Then, we can factor out the x from the x2 to get 8x(x + y).
23.) To factor this expression, we notice that the x2 and the -35 have a common factor of x - 5, so we can factor them out to get (x - 5)(x + 7).
24.) To factor this expression, we notice that the 2x2 and the 14 have a common factor of 2, so we can factor them out to get 2(x2 + 11x + 7). Then, we notice that the x2 and the 7 have a common factor of x + 1, so we can factor them out to get 2(x + 1)(x + 7).
25.) To factor this expression, we notice that the x2 and the -63 have a common factor of x + 9, so we can factor them out to get (x + 9)(x - 7).
26.) To factor this expression, we notice that the 3x2 and the 7 have a common factor of 3x + 7, so we can factor them out to get 3(x + 1)(x - 2).
14) -3x+3y=3
-5x + y = 13
Answer:
x = -3, y = 28
Step-by-step explanation:
-5x + y = 13
y = 13+5x
-3x+3(13+5x)=3 substitute
-3x + 39 + 15x = 3
12x + 39 = 3
12x = -36
x = -3
-5(-3) + y = 13 substitute into -5x+y=13
15 + y = 13
y = 28
Simplify (4 xy) (−2x)
Answer:
-x2 y
Step-by-step explanation:
The radius of circle S is half the radius of circle L. The radius of circle L is 8 millimeters.
Which measurement is closest to the area of circle S in square millimeters?
Area of the circle S be 16π square. millimeter
What is an area of circle ?
The area of a circle is the space the circle occupies in the two-dimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is A = πr2, where r is the radius of the circle. A unit area is a unit square. Examples: m2, cm2, in2, etc. Circle area = π[tex]r^{2}[/tex]in square units (Pi)π = 22/7 or 3.14. Pi (π) is the ratio of the circumference to the diameter of any circle. This is a special mathematical constant.
It is given that the radius of circle S is half the radius of circle L and the radius of circle L is 8 millimeters.
Radius of the circle S = 8/2 = 4 millimeters
Area of the circle S = π[tex]r^{2}[/tex] = π[tex](4)^{2}[/tex] = 16π square. millimeter
Therefore, area of the circle S be 16π square. millimeter
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pls help due now!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
A. 9x = 18
Step-by-step explanation:
4x - y + 5x + y = - 3 + 21
9x = 18
x = 2
PLEASE HELP! THANK YOU
Answer:
1. A repeating decimal is a fraction [tex]\frac{a}{b}[/tex] where a and/or b are fractions and b is not equal to 0.
2. A decimal that ends is a ( n ) terminating decimal
3. Two numbers that have a sum of 0 are additive inverses
What is the 3n^2 first 4 terms and the 10th term?
Answer:
a1=3 ;a2=12 ;a3=27 ;a4=48 ;a10=300
Step-by-step explanation:
an=3n^2
a1=3(1)^2
a1=3
a2=3(2)^2
a2=12
a3=3(3)^2
a3=27
a4=3(4)^2
a4=48
a10=3(10)^2
a10=300
Gavin observed 22 flowers on each block of his neighborhood. Each block has an equal number of flowers. Is this sample of the flowers in the neighborhood likely to be biased?
Yes, this sample of the flowers in the neighborhood is likely to be biased. This is because the number of flowers observed on each block is relatively small and may not be representative of the entire neighborhood.
What is neighborhood?A neighborhood is a local geographic area typically containing a cluster of families and individuals who live nearby and interact with each other. It is usually a residential area, although some neighborhoods may be mixed-use, containing both residential and commercial buildings. Neighborhoods are typically identified by geographical boundaries such as a street, a park, or a body of water. People living in a given neighborhood often share certain characteristics including socio-economic status, culture, ethnicity, and even language. Neighborhoods play an important role in the lives of individuals and families, providing a sense of belonging, safety, and identity.
Additionally, if there is any external factor that influences the number of flowers on certain blocks (such as the amount of sunlight or water) then the sample may be skewed.
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1. predict whether you think this a fair game or not. explain your response. a. play the game 5 times. b. now do you think the game if fair or not? ju
A game that has an equal probability of winning or losing is said to be fair.
What is probability ?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
The foundational elements of fair play can be observed and learned both on and off the field, and include honesty, solidarity, tolerance, care, excellence, and joy. Fair competition, respect, camaraderie, team spirit, equality, and sport without doping are also examples.
A simple game of chance is deemed fair if there is an equal chance of winning for each player. If there is an equal chance of selecting each alternative, the decision is fair. Your understanding of probability can help you evaluate the fairness of games and make just decisions.
Children love playing together more when everyone is being fair. Additionally, it plays a significant role in getting along with people.
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Can i please have help?
Analyzing the graph of the linear equation, we can see that for 1.4 grams of chemical A you will need 1.2 grams of chemical B.
How much of chemical B is needed?The amounts of chemicals A and B needed are modeled by the linear equation on the graph.
Here we want to see how much of chemical B is needed if we decide to use 1.4g of chemical A.
Chemical A is on the horizontal axis, so we need to find 1.4 on the horizontal axis, and then move upwards until we reach the linear equation, and then move to the left until we reach the vertical axis.
Doing that we can see that we will need 1.2 grams (3 little squares in the vertical axis) of chemical B.
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A student raises her grade average from a 75 to a 90. What was the percent of increase in the
student's grade average? Round your answer to the nearest tenth of a percent, if necessary,
20%
016.7%
08.3%
015%
Answer:
Step-by-step explanation:
D: 15%
These are the times for 200 people to get to work
time people
0
10
30
40
50
A 10% sample, stratified by time, is taken.
complete the table
time people
0
10
30
40
50
got to work out the number of people using the same time
please help
The entries that complete the table are 1, 2, 8, 6 and 3.
Given:
These are the times for 200 people to get to work time people. A 10% sample, stratified by time, is taken.
Complete the table :
To do this, we multiply the number of people by the proportion of sample i.e. 10%.
The product is then approximated to the nearest unit
So, we have:
7 => 7 * 10 % ≈ 1
22 => 22 * 10 % ≈ 2
77 => 77 * 10 % ≈ 8
63 => 63 * 10 % ≈ 6
31 => 31 * 10 % ≈ 3
Hence, the entries that complete the table are 1, 2, 8, 6 and 3.
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What i the meaure of an arc correponding to the ector with an area of 24π ft² if the circle ha a 12 ft. Radiu?
When the arc's area is 24 square feet and its radius is 12 feet, the arc's length is 36.56 feet.
What is arc?An arc is a section of a circle's or curve's border in mathematics. It is additionally known as an open curve. The circumference, commonly referred to as the perimeter, is the measurement around a circle that defines its edge. A sector is referred to as a component of a circle made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radii of the circle at its ends. A slice of pizza or a pie can be used as an analogy for the form of a circle's sector.
Here,
area of sector=24π ft²
radius of sector=12 ft
area=θ/360*Π*12²
24π=θ/360*Π*12²
2=θ/360*12
2*360/12=θ
θ=60°
length of arc=2r+θ/360*(2Πr)
=2*12+60/360(2*3.14*12)
=24+2*2*3.14
length of arc=36.56 ft
The measure of arc is 36.56 feet when the area of arc is 24π feet² and it has the radius of 12 feet.
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Point K i on line egment \overline{JL}
JL. Given JL=x10,JL=x10, KL=4x,KL=4x, and JK=2x,JK=2x, determine the numerical length of \overline{KL}. KL
If the value of x will be 2. Then the length of KL will be 8 units.
What does cooperation with an example mean?
Being ability to use your body properly while moving around and cooperating with other people or things is the concept of coordination.
A gymnast walking on a tightrope without falling is an illustration of coordination. Working together to arrange or coordinate a party is an example of coordination.
Point K is on line segment JL. Given JL = x + 10, KL = 4x, and JK = 2x.
Then the value of x will be
JL = JK + KL
x + 10 = 2x + 4x
5x = 10
x = 2
Then the length of KL will be
KL = 4x
KL = 4 (2)
KL = 8 units
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The complete question is-
Point K is on line segment JL. Given JL = x + 10, KL = 4x, and JK = 2x,
determine the numerical length of KL.
when adding √9 and -7 which time of number is the sum'
The 7th grade Science classes are raising money for charity. Their goal is $750.00
class has raised 50% of the total needed to meet the goal of $750.00.
class has raised one-third of the amount of their goal of $750.00
.How much more money is needed to reach their goal of $750.00?
Simplify: 5m + 3b - 9m - 4w Responses 14m + 7b 14m + 7b 14m + 3b - 4w 14m + 3b - 4w -4m + 3b - 4w -4m + 3b - 4w 21
Answer:
3b-4w-4m
Step-by-step explanation:
3b-4w+5m-9m
3b-4w-4m
Answer:
-4m+3b-4w
Step-by-step explanation:
5m+3b-9m-4w
we combine like terms but in this case only the m are like terms
5m-9m+3b-4w
-4m+3b-4w
i cant really see the options but it looks like it is the second to last or c option
hopes this helps please mark brainliest
CC wants to buy online tickets for a concert. Two options are given here.
Option 1: $85 for each ticket plus a shipping fee of $15
Option 2: $95 for each ticket and free shipping
Select the equation for Option 2.
Responses
y=15x+85y is equal to 15 x plus 85
y=85x+15y is equal to 85 x plus 15
y=95xy is equal to 95 x
y=−95xy is equal to negative 95 x
The equation for $95 for each ticket and free shipping y = 15 + 95x
How to illustrate the equation?In this situation, an equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions.
Let the number of tickets be x.
Let the total amount is y.
The equation for $95 for each ticket and free shipping will be:
y = 15 + (95 × x)
y = 15 + 95x
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Fill in the blank
The _________of a number is the distance between the number and zero on a number line
The distance on the number line between a number and 0 is its absolute value.
What is number line?The visual representation of numbers on a straight line, either horizontally or vertically, is known as a number line.
When numbers are written down on a number line, it is straightforward for humans to compare them and perform basic arithmetic operations on them.
One might assume that a number line starts at zero (0). There are only negative numbers to the left of zero and only positive numbers to the right of zero.
In other words, as we move to the right on a number line, the value of the numbers increases.
The part of the number line to the left of zero is called the negative number line. But all is in the region to the right of zero.
Hence, The distance on the number line between a number and 0 is its absolute value.
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Please help me solve!
Answer:
13.5%
Step-by-step explanation:
Given that μ = 144, σ = 27:
For x = 90: z= 90-144/27=-2
For x = 117: = 117-144/27 = -1
Therefore, From the normal distribution table: -2 gives .02275 and -1 gives .15866
So the required percentage = .02275 - .15866 = -0.13591= 13.5%
Hence, 13.5% of the population would be between 144 and 198
2x - 5y = 23 and -4x + 5y = -11 solve by elimination
Answer: x= -1 y= -5
Step-by-step explanation: Multiply by 2 to eliminate the x
4x - 10y = 46
-4x + 5y = -11
-5y = 35
y= -5
Put -5 back in the equation for the letter y, and you will get x = -1
This weekend, Jerome earned 252.50 in all. What was the dollar amount of the meals that Jerome served?
Jerome served $
worth of meals this weekend.
Using algebra, we conclude that the dollar amount of meals Jerome served this weekend is $1150.
Given: The total amount Jerome earned this weekend is $252.50.
He earned every weekend = $80.
He earned 15% of the cost of meals as tips by serving them.
To find: The cost of meals served by Jerome in this weekend.
The total amount, $252.50, is the sum of the tips amount Jerome earned from serving meals and sum of the amount Jerome earned every weekend. To solve this, we must first translate the conditions of the problem, into an algebraic expression with a variable referring to the unknown quantity. This expression is then converted to an equation to find the value of the unknown quantity.
Let x be the cost of meals that Jerome served this weekend.
The equation for the problem statement becomes
[tex]\$80 + \frac{15}{100} x = \$252.50\\\\[/tex]
Keeping only the x term on the left side of the equation and constant terms on the right side we get
[tex]\frac{15}{100} x = \$252.50 - \$80\\\\\frac{15}{100} x = \$172.50\\\\\\[/tex]
Multiply both the sides of the equation by 100
[tex]\frac{15}{100} x \times 100 = \$172.50 \times 100\\\\15x = \$17250[/tex]
Divide both sides of the equation by 15
[tex]\frac{15x}{15} = \frac{\$17250}{15}\\\\x = \$1150[/tex]
What is algebra?Algebra is a field of mathematics in which letters are substituted for numbers, and an algebraic equation depicts a scale in which what is done on one side of the scale is likewise done on the other side of the scale, with the numbers acting as constants.
What is an equation?An equation is a mathematical statement that two expressions are equal. If it is an algebraic equation, two algebraic expressions has to have the same value on either side of the equal sign.
What is an algebraic expression?A meaningful collection of numbers, variables, and signs (positive or negative) of operations that must make mathematical and logical sense is referred to as an algebraic expression.
Expressions contain any number of algebraic terms. They use signs of operation like addition, subtraction, multiplication, and division and also do not contain an equality sign (=).
Using algebra, we conclude that the dollar amount of meals Jerome served this weekend is $1150.
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A multiple-choice quiz has 5 questions. Each question has 3 possible answers. A student guesses the answer to each question. Find the probability that the student answers all 5 questions incorrectly.
Answer: 3^5=243. 1/243
Step-by-step explanation:
We calculate the amount of ways he can answer 5 questions. It's 3x3x3x3x3 because he has 3 questions at the start with each of the 3 having another 3 questions to choose from and so on.
let x and y be independent gaussian distributed random variables each with zero mean and unity variance. define the gaussian process:
As per the gaussian distributed random variables , the joint probability density function of the given variable is E [Z(t1)] = cos(2πt1)E [X] + sin(2πt1)E [Y]
Gaussian distribution:
In statistics, the Gaussian distribution refers the normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.
Given,
Here we need to find the the joint probability density function of the variables x and y be independent gaussian distributed random variables each with zero mean and unity variance.
Here we know that every weighted sum of the samples of the Gaussian process Z(t) is Gaussian, Z(t1), Z(t2) are jointly Gaussian random variables. Hence we need to find mean, variance and correlation co-efficient to evaluate the joint Gaussian PDF.
Then the equation is written as,
=> E [Z(t1)] = cos(2πt1)E [X] + sin(2πt1)E [Y]
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Which of the following constructions must you know how to do in order to construct an inscribed circle for a given triangle?
angle bisector
perpendicular bisector
duplicating a line segment
bisecting a segment
For the construction of an inscribed circle the required construction that must be known is the angle bisector. The correct option is (A).
What is an angle bisector?The angle bisector is a line that divides an angle into two equal parts. For a circle inscribed in a triangle the line joining the center to the vertex is the angular bisector of the interior angle.
The diagram for the given case can be drawn as follows,
For the circle inscribed in the circle, all the sides are tangents.
By the property of tangents to a circle ∠ODB and ∠OFB are right angles.
Now, in ΔODB and ΔOFB the relation is obtained as,
∠ODB = ∠OFB (right angles)
OB = OB (Common sides)
And, OD = OF (radius of the circle)
⇒ ΔODB ≅ ΔOFB (by RHS criteria)
This implies that ∠ODB ≅ ∠OFB.
Thus, the line joining the centre and the vertex of triangle bisects its angles.
Hence, for the given case the required construction to be known is the angle bisector of triangle.
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You have 10lbs of bananas after peeling the bananas you 3lbs. 6oz. Of banana peels. What is the yield percent
15. Find the perimeter of the triangle.
2х + 1
3x
X
Answer:
6x + 1
Step-by-step explanation:
When you are finding the perimeter of any shape, you will combine the measurements of each side together. Note any variables when combining. They must have the same amount of the same variables to be combined:
[tex]P = (2x + 1) + (3x) + (x)\\P = (2x + 3x + x) + 1[/tex]
Combine like terms. Add 3x, 2x and x together:
[tex]P = (2x + 3x + x) + 1\\P = (6x) + 1\\[/tex]
The perimeter of the triangle is 6x + 1.
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Marc mows lawns for $25 each lawn, plus $5 for every hour he spends mowing. The equation for his total earnings per lawn is y = 25 + 5h, where y represents his total earnings and h represents the number of hours he works. What does the flat pay of $25 represent in this situation?.
The $25 represent the constant for the equation y=25+5h where she lawns for $25 each lawn, plus $5 for every hour she spends mowing.
What is constant?A constant is a value or number that is consistently the same regardless of how it is expressed. For instance, in the a forementioned figure, when its face value is 36 and 82 respectively, 36 and 82 remain constant. Its worth remains constant. A constant in mathematics is a particular number or symbol that has been given a stable value. In other words, a constant is an expression-unchanging value or integer. It always has the same value.
Here,
The $25 serves as the constant in the equation y=25+5h, where she charges $25 for each lawn she mows and an additional $5 per hour.
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If the breadth of a rectangle is one-third of its length and perimeter is 32 ft, find the length and breadth of the rectangle. square
Answer:
breadth = 4 ft ; length = 12 ft
Step-by-step explanation:
p/2 = 32/2 = 16ft
l + b = 16
b = 1/3 l
l + 1/3 l = 16
(3 + 1)/3 l = 16
4/3 l = 16
l = 16 · 3/4
l = 4 · 3
l = 12 ft
b = 12 · 1/3
b = 4 ft
The sum of two numbers is 45
and their difference is 5.
What are the two numbers?
Larger number
1
Smaller number
Answer: 20 and 25
Step-by-step explanation: we know that there are 2 numbers and the sum is 45. Let's put one number as x. The other number is x+5 because the difference is 5. So our equation is- x+x+5=45. After we solve the equation by subtracting 5 from each side and simplifying x, we get x=20. The other number should be 5 more so the second number is 25. The numbers are 20 and 25. Please rate this answer!