Given: KLMN is a trapezoid, KF =10 MF ║ LK AKLMF = AFMN Find: KN
Answers
We know:
LK // MF
KF = 10
A(KLMF) = A(FMN)
Since LM // KF (because they are bases of the trapezoid) and LK // MF because is given in the hypothesis, KLMF is a parallelogram.
The area of a parallelogram is given by the base times the height.
A(KLMF) = b × h
= 10 × h
The area of a triangle is given by the formula:
A(FMN) = (b × h) / 2
= (FN × h) / 2
We know that the two areas are congruent, therefore:
A(KLMF) = A(FMN)
10 × h = FN × h / 2
The two "h" cancel out because they are the same and we can solve for FN:
10 = FN / 2
FN = 20
Now we can calculate:
KN = KF + FN = 10 + 20 = 30
Hence, KN is 30 units long.
In a trapezoid with parallel sides, if a pair of opposite sides are equal, then the other pair of opposite sides are also equal. Therefore, in the given trapezoid KLMN, KN is equal to AN + 10.
Explanation:In the given trapezoid KLMN, the sides KF and LM are parallel. We are given that KF = 10 and AFMN = AKLMF. We need to find KN.
Since KF and LM are parallel, KF = LM. Therefore, LM = 10.
Since AFMN = AKLMF, we can say that AN = KL. So, AN + LM = KL + KF. Substituting the given values, we get AN + 10 = KL + 10. Therefore, AN = KL.
Hence, KN = KL + LM = AN + LM = AN + 10.
Therefore, KN = AN + 10.
Related Questions
The data set below shows the weights of some puppies, in pounds, at a kennel: 10, 11, 11, 12, 13, 13, 13, 14, 15 Which histogram represents the data set?
Answers
Group the data into 5 bins according to the table shown below.
Bin Count----- --------- 10 3 11 1 12 2 13 0 14 2 15 1
A plot of the histogram n shown in the figure.The data is skewed toward a value of 10, which has the largest frequency of 3.The average is 12, and the median is 12.
Answer:
I think it is C
Step-by-step explanation:
Find the area of the circle r= 7
Answers
Which number produces an irrational number when added to 2/5? A) 0.555... B) -0.4 C) -/`5 D) 2/7
Answers
Answer to this question is pie of 5
The number that produces an irrational number when added to 2/5 is 0.55....
What is a rational number?A rational number is one that can be stated mathematically as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively.
To produce an irrational number when added to 2/5, the number must be irrational itself.
Therefore, options B, C, and D are eliminated since they are all rational numbers.
Option A, 0.555..., is a repeating decimal and can be expressed as a fraction of 5/9. When added to 2/5, we get:
2/5 + 5/9 = (18/45) + (25/45) = 43/45
Since 43/45 is not a rational number, the answer is A) 0.555...
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what is the value of y /2/4/16/20
Answers
A lifeboat can carry up to 24 people. Write an inequality to represent this situation
Answers
hoped it helped
brainlist plz
Marcus has a pool that can hold a maximum of 4500 gallons of water. The pool already contains 1500 gallons of water. Marcus begins to add more water at a rate of 30 gallons per minute. Write an inequality that shows the number of minutes, m, Marcus can continue to add water to the pool without exceeding the maximum number of gallons.
Answers
4500 - 1500 = 3000
Because we need to represent an inequality:
30m = 3000
Divide both by 30:
m = 100
It will take 100 minutes
Answer:
Inequality is m ≤ 1000
Step-by-step explanation:
Capacity of the pool to hold the maximum water is = 4500 gallons of water.
Pool is already having 1500 gallons of water so remaining volume of the pool that can be filled is = 4500 - 1500 = 3000 gallons
Marcus begins to add 30 gallons water per minute and it takes "m" minutes to fill the remaining volume.
So amount of water required = 30m gallons
There is a condition that Marcus continues to add water without exceeding the maximum amount of water.
This means remaining amount "3m gallons" will be never cross the limit of "3000 gallons" of remaining volume of water.
Now we can form the inequality as 3m ≤ 3000
or m ≤ 1000
Therefore, answer is m ≤ 1000
Show that the sum, over the set of people at a party, of the number of people a person has shaken hands with, is even. assume that no one shake his or her own hand.
Answers
If we assume the total no. of people to be odd then the no. of handshakes
each person will have will be an even number.
What are sets and subsets?A set is a collection of well-defined objects.
A subset contains all the elements or a few elements of the given set.
The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.
Assuming the no. of total people to be 'n' and 'n' is an odd no.
Now if each person shakes hands with each other except their own hands each person will have (n - 1) no. of handshakes and (n - 1) or odd - 1 will always be an even no.
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The sum of handshakes is always even at a party as each handshake involves two people.
To show that the sum of handshakes is even:
Consider that each handshake involves two people, adding two handshakes to the total.
Since each person shakes hands with an odd number of people, the total sum of handshakes will be even.
Hence, the sum of the number of people a person has shaken hands with will always be even.
Analyze the diagram below and complete the instructions that follow.
Solve for y.
Answers
What is the scale factor of figure ABCD?
a. 1/3
b. 4/3
c. 3
d. the figure isn't dilated properly
Answers
measure ABCD=scale factor*[measure A1B1C1D1]
in the axis of the y coordinate
we have
scale factor=measure ABCD/measure A1B1C1D1
scale factor=3/1----->3
in the axis of the x coordinate
we have
scale factor=measure ABCD/measure A1B1C1D1
scale factor=8/6----->4/3
therefore
the answer is the option
d. the figure isn't dilated properly
Find the final amount of $1000 investment after 9 years at 8% interest compound quarterly
Answers
1000 + 0.08(1000)
But because it is 9 years:
1000 + 9(0.08(1000))
1000 + 0.72(1000)
We can make it simpler:
1.72(1000)
Multiply:
1720
You will have $1720
Hey can you please help me posted picture of question
Answers
1) Multiplication by -1.
This implies F(x) is flipped over x-axis
2) Multiplication by 1/3
This implies F(x) is compressed vertically
3) Addition of 4 to x.
This implies F(x) is shifted by 4 units to left.
Thus, G(x) is obtained from F(x) by flipping it across x-axes, compressing it vertically and shifting it towards left.
Thus, option C is the correct answer
Josefina spent 20 + 3b dollars on a pair of earrings and three blouses that cost b dollars each how much did she spend in all if each blouse cost 15 $
Answers
Step by Step-
She spent $15 on 3 blouses, so you would multiply and get that she spent $45 on blouses.
You would then add that to the $20 she spent before, and get $65.
Therefore, she spent $65.
Hope this helps!!
Josefina spent $65 in total, with $20 on earrings and $45 on three blouses at the cost of $15 each.
Calculating Total Cost
Josefina spent a certain amount of money on a pair of earrings and three blouses. The cost of the pair of earrings is separate from the blouses and is a fixed amount of $20. Each blouse costs $15, and she bought three blouses. Therefore, the total cost for the blouses is 3 times $15, which equals $45. To find the total amount Josefina spent, we need to add the cost of the earrings to the cost of the blouses.
Total spent on blouses = 3 * $15 = $45
Cost of the earrings = $20
Total amount spent = Cost of the earrings + Total spent on blouses
Total = $20 + $45 = $65
Therefore, Josefina spent a total of $65 on her purchase.
Which of these is equal to sin(70°)? A) cos(110°) B) cos(160°) C) cos(20°) D) cos(70°)
Answers
sin (70⁰)= cos (90-70⁰)=cos (20⁰)
sin (70⁰)=cos (20⁰)
Answer:
[tex]sin (70^{\circ})=cos (20^{\circ})[/tex]
Option C is correct.
Step-by-step explanation:
we have to choose the option for which the value is equals to sin(70°)
As in the first quadrant sine and cosine both are positive
[tex]\sin \theta = \cos (90-\theta)\\\\\sin (70^{\circ})= \cos (90-70)=\cos (20^{\circ})\\\\sin (70^{\circ})=cos (20^{\circ})[/tex]
hence, option C is correct.
Which properties are necessary to claim that the two prisms are congruent? Check all that apply. The lengths of corresponding edges are in a 1:1 ratio. The volumes are equal. Corresponding angles have different measures. Corresponding faces are not congruent. The base areas are equal. The prisms have the same height.
ANSWER IS:
The base areas are equal.The prisms have the same height.
The lengths of corresponding edges are in a 1:1 ratio.The volumes are equal.
Answers
The two prisms are congruent means that they have the same measures of bases, height, faces and angles.
Angles are congruent when they are the same size (in degrees or radians). Sides are congruent when they are the same length.So, for congruent prisms, the corresponding angles are expected to be of the same sizes and the corresponding sides are expected to be of the same length.
Therefore the correct statements are:
The base areas are equal.
The prisms have the same height.
The lengths of corresponding edges are in a 1:1 ratio.
The volumes are equal.
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hey can you please help me posted picture of question
Answers
Now, we need to find how many solutions the nonlinear system of equations graphed has
The points where these given graphs intersect will be the number of solutions.
We can see on the equations graphed that 3 points are where they intersect
[tex]\boxed {Therefore \ your \ answer \ will \ be \ option \ A }[/tex]
Multiple 3/4 times 16/9
Answers
Remark
Before doing the multiplication, you should do a cancellation. You can cancel fractions by dividing any numerator by the same thing that will go into any denominator or vica versa.
3 goes into 9 = 3
4 goes into 16 four times.
So the fraction cancellation looks like this.
[tex] \frac{ \frac{16}{4} }{ \frac{9}{3} } = \frac{ \frac{4}{1} }{ \frac{3}{1} } = \frac{4}{3} [/tex]
A 10-ounce container of chocolate chips can be used to make 3 desserts. Each dessert has the same amount of chocolate chips. Which equation shows how to find the number of ounces in each dessert? 10÷3=310 ounce 10÷3=103 ounces 3÷10=310 ounce 3÷10=103 ounces
Answers
Answer:
10 divided by 4 =10 over 4 is the correct answer guys if your doing think through math
Step-by-step explanation:
Leon deposited $30000 in a bank which paid 2% interest per year. After 1 year, Leon withdrew all his money including the interest. how much money did Leon withdraw?
Answers
A=P(1+r)^n
where:
P=principle
r=rate
n=time
But from the information given:
P=$30,000, r=2%, n=1 year
thus
A=30000(1+2/100)^1
A=30000(1.02)^1
A=$30600
Thus amount after 1 year was $30600
Two trucks started traveling from the same place at 9:00 a.m. One truck traveled North going 45 mph and the other traveled South going 50 mph. What time will it be when the trucks are 380 miles apart?
Answers
Givens
South bound truck's rate = 50 mph
North bound truck's rate = 45 mph
Distance apart = 380 after time t
The time that passes = t
Equations
d = r * t
d1 + d2 = 380
d1 = r_south * t
d2 = r_north * t
Substitute and solve.
r_south * t + r_north * t = 380
50*t + 45*t = 380 Combine like terms.
95t = 380 Divide by 95
t = 380 / 95
t = 4 hours
Answer
t = 9:00 + 4 hours = 1300 hours = 1:00 PM <<<< answer
Answer: 1:00 PM
Step-by-step explanation:
6.
Valdez Construction signed a note with a payment of $5,200 per quarter for 5 years.
Find the amount they must set aside today to satisfy this capital requirement in an account earning 8% compounded quarterly.
$30,506.32
$126,346.32
$51,054.38
$85,027.44
Answers
Where, PV = Present vale, C = Quarterly payments =$52,000, r = Annual interest rate = 8% = 0.08, n = Number of payments per year = 4, t= time of payment in years = 5
Substituting,
[tex]PV = 52000* \frac{1- (1+0.08/4)^{-4*5} }{0.08/4} = $85,027.53[/tex]
The closest answer is $85,027.44
12% of 250 is what answer
Answers
Hope this helped :)
alisa202
Calculate the total budget and then fill in the missing percentages. You will use some of the answers given more than once. Total budget = Household Budget Item Percent % Amount $ Donations 1,620 Taxes 1,620 Food 3,510 Clothing 2,700 Housing 1,350 Transportation 675 Insurance 675 Savings 675 Recreation and miscellaneous 675
Answers
Donations = 12%
Taxes = 12%
Food = 26%
Clothing = 20%
Housing = 10%
and the rest are 5 %
Answer:
Step-by-step explanation:
To calculate the percentage of each expenses we use this formula :
[tex]\frac{amountofbudgetitem}{Totalbudget}[/tex] × 100
Household Budget Items Amount ($) Percentage
Donations 1,620 12%
Taxes 1,620 12%
Food 3,510 26%
Clothing 2,700 20%
Housing 1,350 10%
Transportation 675 5%
Insurance 675 5%
Savings 675 5%
Recreation and
miscellaneous 675 5%
Total Budget 13,500 100%
please help........there are 3 problems
Answers
if
[tex]x^2+10x+21[/tex]
then
[tex]=x^2+7x+3x+21=x(x+7)+3(x+7)=(x+7)(x+3)[/tex]
Booker own 85 video games. He has 3 shelves to put the games on. Each shelf can hold 40 video games. How many more video games do he have room for
Answers
How many milliliters equal 1052 cm3? A. 1052 B. 1.052 C. 105.2 D. 10.52 30 points
Answers
Short answer: A. 1052 ml
Why?
1 cm = 1 ml, so what would that be? 1052 cm = 1052 ml.
Hope this helped you! ♥
Hello!
I believe the answer is A) 1052.
I hope it helps!
250 tickets are sold at a church fundraiser. if sara buys 15 tickets the probability the probability that she will win the prize quilt is
Answers
= 15/250
= 0.06
= 6%
Which answer is the best estimate of the correlation coefficient for the variables in the scatter plot?
Answers
[tex] \frac{1 - 8}{8 - 1} = \frac{-7}{7} = -1[/tex]
The answer is -0.99, as this is the closest answer to the estimate we found.
Correlation coefficient measures the relationship between two variables in a scatterplot. Its value ranges from -1.0 to 1.0. You can estimate it by observing the direction and the closeness of the data points to a line of best fit.
Explanation:The correlation coefficient is a statistical measure that calculates the strength of the relationship between the relative movements of two variables. The values range between -1.0 and 1.0. A calculated number greater than 1.0 or less than -1.0 means that there was an error in the correlation measurement. A correlation of -1.0 shows a perfect negative correlation, while a correlation of 1.0 shows a perfect positive correlation. A correlation of 0.0 shows no linear relationship between the movement of the two variables.
To estimate the correlation coefficient from a scatterplot, observe the tightness of the points around a line of best fit and whether the points are mainly increasing or decreasing. For tight points increasing, it's close to 1. For tight points decreasing, it's close to -1. If there's no pattern, it's close to 0.
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What percent of data is in quartile 1
Answers
25% of data is in quartile 1
how many lines of symmetry does the figure have??
Answers
Answer: The given figure does not have any line of symmetry.
Explanation:
Since, Given figure seems a parallelogram.
And, a line of a symmetry is an imaginary line through which we get two same figure or unchanged figure. Or, we can say that Line of symmetry makes a reflection of a figure in which the size or shape of the figure does not change.
In the case of parallelogram diagonals must be the line of symmetry. But any diagonal in parallelogram does not make symmetry. Therefore, there is no line of symmetry in parallelogram.
hello can you please help me out on this question posted picture
Answers
So, the tree will start with 3 leaves, and each leaf will further be divided into 3 leaves. Thus the total number of leaves in the tree diagram will be 3 x 3 = 9 leaves.
Option A correctly represent this situation.