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Kirstie is testing values that would make triangle klm a right triangle when ln is an altitude, and km = 16, as shown below. which lengths would make triangle klm a right triangle? 1) lm = 13 and kn = 6 2) lm = 12 and nm = 9 3) kl = 11 and kn = 7 4) ln = 8 and nm = 10
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Answer: Option (2) is correct.
Step-by-step explanation:
Since we have given that
KLM is a right triangle, in which KM = 15, and ln is an altitude.
As we know that for right angled triangle, there are 3 conditions :
[tex]KL^2=KN.KM-----(1)\\\\ML^2=MN.KM-------(20\\\\LN^2=KN.MN------(3)[/tex]
So, According to the options ,
Put LM = 12, NM = 9,
[tex]\text{Using eq. (3), we have}\\\\LN^2=KM.MN\\\\12^2=9\TIMES 16\\\\144=144[/tex]
Since, it satisfies that KLM is a right triangle.
Hence, Option (2) is correct.
Using Pythagorean theorem, Option D: [tex]\( LM = 8 \)[/tex] and [tex]\( NM = 10 \)[/tex], satisfies [tex]\( KM^2 = LM^2 + NM^2 \)[/tex].
[tex]\( LM = 12 \) and \( NM = 9 \).[/tex]To determine which lengths would make triangle [tex]\(KLM\)[/tex] a right triangle when [tex]\(\overline{LN}\)[/tex] is an altitude and [tex]\(KM = 16\)[/tex], we can use the Pythagorean theorem to check each given set of values. We know that [tex]\(\overline{LN}\)[/tex] divides [tex]\(KLM\)[/tex] into two right triangles, [tex]\( \triangle KNL \)[/tex] and [tex]\(\triangle LNM\)[/tex].
We will check each given option to see if the Pythagorean theorem holds.
Option A: [tex]\( LM = 13 \)[/tex] and [tex]\( KN = 6 \)[/tex]
Here, [tex]\( LN \)[/tex] is the altitude. Let [tex]\( NM = x \)[/tex], then [tex]\( KM = KN + NM \)[/tex], so:
[tex]\[ x = 16 - 6 = 10 \][/tex]
For [tex]\( \triangle LNM \)[/tex]:
[tex]\[ LM^2 = LN^2 + NM^2 \][/tex]
[tex]\[ 13^2 = LN^2 + 10^2 \][/tex]
[tex]\[ 169 = LN^2 + 100 \][/tex]
[tex]\[ LN^2 = 69 \][/tex]
[tex]\[ LN = \sqrt{69} \approx 8.3 \][/tex]
For [tex]\( \triangle KNL \)[/tex]:
[tex]\[ KL^2 = KN^2 + LN^2 \][/tex]
[tex]\[ KL^2 = 6^2 + 69 \][/tex]
[tex]\[ KL^2 = 36 + 69 \][/tex]
[tex]\[ KL^2 = 105 \][/tex]
[tex]\[ KL \approx 10.2 \][/tex]
These calculations do not match the given [tex]\(KL\)[/tex] value.
Option B: [tex]\( LM = 12 \) and \( NM = 9 \)[/tex]
Here, [tex]\( LN \)[/tex] is the altitude. Let [tex]\( KN = x \)[/tex], then:
[tex]\[ x = 16 - 9 = 7 \][/tex]
For [tex]\( \triangle LNM \)[/tex]:
[tex]\[ LM^2 = LN^2 + NM^2 \][/tex]
[tex]\[ 12^2 = LN^2 + 9^2 \][/tex]
[tex]\[ 144 = LN^2 + 81 \][/tex]
[tex]\[ LN^2 = 63 \][/tex]
[tex]\[ LN = \sqrt{63} \approx 7.9 \][/tex]
For [tex]\( \triangle KNL \):[/tex]
[tex]\[ KL^2 = KN^2 + LN^2 \][/tex]
[tex]\[ KL^2 = 7^2 + 63 \][/tex]
[tex]\[ KL^2 = 49 + 63 \][/tex]
[tex]\[ KL^2 = 112 \][/tex]
[tex]\[ KL \approx 10.6 \][/tex]
These calculations do not match the given [tex]\(KL\)[/tex] value.
Option C: [tex]\( KL = 11 \)[/tex] and [tex]\( KN = 7 \)[/tex]
Here, [tex]\( LN \)[/tex] is the altitude. Let [tex]\( NM = x \)[/tex], then:
[tex]\[ x = 16 - 7 = 9 \][/tex]
For [tex]\( \triangle KNL \)[/tex]:
[tex]\[ KL^2 = KN^2 + LN^2 \][/tex]
[tex]\[ 11^2 = 7^2 + LN^2 \][/tex]
[tex]\[ 121 = 49 + LN^2 \][/tex]
[tex]\[ LN^2 = 72 \][/tex]
[tex]\[ LN = \sqrt{72} \approx 8.5 \][/tex]
For [tex]\( \triangle LNM \)[/tex]:
[tex]\[ LM^2 = LN^2 + NM^2 \][/tex]
[tex]\[ LM^2 = 72 + 9^2 \][/tex]
[tex]\[ LM^2 = 72 + 81 \][/tex]
[tex]\[ LM^2 = 153 \][/tex]
[tex]\[ LM \approx 12.4 \][/tex]
These calculations do not match the given [tex]\(LM\)[/tex] value.
Option D: [tex]\( LN = 8 \) and \( NM = 10 \)[/tex]
Here, [tex]\( LN \)[/tex] is the altitude. Let [tex]\( KN = x \)[/tex], then:
[tex]\[ x = 16 - 10 = 6 \][/tex]
For [tex]\( \triangle LNM \)[/tex]:
[tex]\[ LM^2 = LN^2 + NM^2 \][/tex]
[tex]\[ LM^2 = 8^2 + 10^2 \][/tex]
[tex]\[ LM^2 = 64 + 100 \][/tex]
[tex]\[ LM^2 = 164 \][/tex]
[tex]\[ LM \approx 12.8 \][/tex]
For [tex]\( \triangle KNL \)[/tex]:
[tex]\[ KL^2 = KN^2 + LN^2 \][/tex]
[tex]\[ KL^2 = 6^2 + 8^2 \][/tex]
[tex]\[ KL^2 = 36 + 64 \][/tex]
[tex]\[ KL^2 = 100 \][/tex]
[tex]\[ KL = 10 \][/tex]
These calculations match the given lengths.
Thus, the correct answer is:
D. [tex]\( L N = 8 \) and \( N M = 10 \)[/tex]
The correct question is given below:
Classify each polynomial (monomial, binomial, trinomial) based on number of terms it contains.
-2x^2-x+3.5
10xyz^3
-x^2y^2+2y
8x^2+0.25
x^3y^4+2x^2y-3z
Answers
Answer:
it is 10xyz^3 for monomial. 8x^2+0.25 and -x^2y^2+2y for binomial. And -2x^2-x+3.5 and x^3y^4+2x^2y-3z for trinomial.
Step-by-step explanation:
[tex]10xyz^3[/tex] for monomial. [tex]8x^2+0.25[/tex] and [tex]-x^2y^2+2y[/tex] for binomial. And [tex]-2x^2-x+3.5[/tex] and [tex]x^3y^4+2x^2y-3z[/tex] for trinomial.
What is a polynomial?They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
We need to find each polynomial (monomial, binomial, trinomial) based on number of terms it contains.
Therefore,
If there is one term, the polynomial will be called monomial thus;
[tex]10xyz^3[/tex]
If there are two terms, the polynomial will be called binomial thus;
[tex]8x^2+0.25[/tex] and [tex]-x^2y^2+2y[/tex]
If there are three terms, the polynomial will be called trinomial thus;
[tex]-2x^2-x+3.5[/tex] and [tex]x^3y^4+2x^2y-3z[/tex]
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Ali must choose a number between 61 and 107 that is a multiple of , 2, 4 and 5 . Write all the numbers that he could choose.
Answers
(2x40) (4x20) (5x16)
100 is also a multiple of all three
(2x50) (4x25) (5x20)
The numbers between 61 and 100 are given as 80 and 100.
How to find the LCM of two numbers?The LCM or least common multiple of two numbers is such a small number that is divisible by both. It can be obtained by taking the prime factors of both the numbers and then taking the product of them having highest power.
The required numbers between 61 and 107 are given as follows,
The LCM of 2,4 and 5 is 20.
Thus, the numbers divisible by 2, 4 and 5 are multiples of 20.
Now, the multiples of 20 are 20, 40, 60, 80 and 100.
80 and 100 lies between 61 and 107.
Hence, the numbers that Ali can choose are given as 80 and 100.
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WXYZ is an isosceles trapezoid with legs WX and YZ and a base XY. If the length of WX is 6x+5, the length of XY is 10x+4 and the length of YZ is 8x-3, find the value of x.
Answers
Since it is an isosceles trapezoid, the legs are congruent; that means
6x + 5 = 8x - 3
When solving this equation, we do not want a variable on both sides. We will cancel the 6x to avoid negatives:
6x + 5 - 6x = 8x - 3 - 6x
5 = 8x - 3 - 6x
Combine like terms:
5 = 2x - 3
Cancel the 3 by adding:
5 + 3 = 2x - 3 + 3
8 = 2x
Cancel the 2 by dividing:
8/2 = 2x/2
4 = x
See answer in attachment.
Hope it helps you.
The length of a rectangular park is 20 feet longer than the width of the park. If the length of the park is 36 feet, what is the width of the park? 4 feet 16 feet 42 feet 56 feet
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The sum of the first and second of three consecutive even integers is 158. find the three even integers.
Answers
evaluate -x+4y when -x=-4/5 and y= 1/3 write your anwser as a fraction or mixed number
Answers
= -4/5 + 4(1/3)
= -4/5 + 4/3
= -12/15 + 20/15
= 8/15
answer
8/15
The value of expression with the given x and y value is 8/15.
The given expression is -x+4y, -x=-4/5 and y=1/3.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Now, put x=4/5 and y=1/3 in the given expression and simplify
That is, -4/5 + 4(1/3)
=-4/5 + 4/3
Take LCM of denominators 5 and 3 is 15
Now, -12/15 + 20/15
=(-12+20)/15
=8/15
Therefore, the value of expression with the given x and y value is 8/15.
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When cyclist squeezes her brake lever, she can stop with an acceleration of -3.0 m/s^2 how far will her bike travel while coming to a complete stop if her initial speed was 11 m/s
Answers
v² = u² + 2as
where
v = final speed. v = 0 because the cyclist comes to a complete stop.
u = initial speed. u = 11 m/s, given
a = acceleration. a = -3.0 m/s², given
s = distance traveled, m.
Therefore
0 = 11² + 2(-3.0)*s
0 = 121 - 6s
That is,
6s = 121
s = 121/6 = 20.167 m
Answer: 20.2 m (nearest tenth)
Final answer:
The cyclist will travel approximately 20.17 meters before coming to a complete stop when decelerating with an acceleration of [tex]-3.0 m/s^2[/tex] from an initial speed of 11 m/s.
Explanation:
To calculate the distance the cyclist's bike will travel while coming to a complete stop with an initial speed of 11 m/s and an acceleration of [tex]-3.0 m/s^2[/tex], we can use one of the equations of motion. Specifically, we need to use the equation [tex]v^2 = u2 + 2as[/tex], where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance.
In this case, the final velocity v = 0 m/s (because the bike comes to a stop), the initial velocity u = 11 m/s, and the acceleration a = [tex]-3 m/s^2[/tex] (the negative sign indicates that it is a deceleration).
Plugging these values into the equation, we get:
0 = 112 + 2(-3)s
0 = 121 - 6s
6s = 121
s = 121/6
s = 20.17 meters
Thus, the cyclist will travel approximately 20.17 meters before coming to a complete stop.
Jen picked 3/4 of a gallon of strawberries in half an hour. If she keeps picking strawberries at the same rate, how many gallons will she have picked in 2 hours.
Answers
3/4 = 0.75 as a decimal
We know that Jen picks 0.75 of a gallon of strawberries in half an hour, and now we want to find out how many gallons she'll pick in 2 hours.
Half an hour = 0.5 2 ÷ 0.5 = 4 There are four half hours in 2 hours.
0.75 × 4 = 3
ANSWER:
Jen will have picked 3 gallons of strawberries in 2 hours.
Why is circle 1 similar to circle 2?
Circle 1: center (0, 9) and radius 14
Circle 2: center (0, 9) and radius 7
.
A) Circle 1 is a dilation of circle 2 with a scale factor of 2.
.
B) Circle 1 is a dilation of circle 2 with a scale factor of 7.
.
C) Circle 1 is a translation of circle 2.
.
D) Circle 1 and circle 2 have the same center.
Answers
1/2 = r1/r2 = 14/7 = 2 --> dilation scale factor
We have a golden rule about similarity of figures. It is "All circle are always similar to each other".
In other words, Every circle is dilated version of another circle. To find the value of dilation, we can find the ratio of its redii.
The ratio of radii of two circles is called the scale factor of dilation between them.
Given are two circles with following information :-
Circle 1: center (0, 9) and radius 14
Circle 2: center (0, 9) and radius 7
Finding the ratio of their radii :-
[tex] \frac{Circle\; 1\; radius}{Circle\; 2\; radius} =\frac{14}{7} = 2 [/tex]
So, scale factor is 2. It means circle 1 is a dilation of circle 2 with a scale factor of 2.
Hence, option A is correct i.e. Circle 1 is a dilation of circle 2 with a scale factor of 2.
Phil received a prize of x dollars from a poker tournament. The tournament cost him 100 dollars to enter. What were Phil's net winnings from the tournament? Write your answer as an expression.
Answers
Phil gets x dollars, but before he gets x dollars, he needs to pay 100 dollars to enter the tournament. Therefore the net winning is not x dollars but you should substract 100 dollars from x.
So, the expression of the net winning will be x-100
Answer: [tex]x-100[/tex]
Step-by-step explanation:
Given : Phil received a prize of x dollars from a poker tournament.
The tournament cost him 100 dollars to enter.
To find Phil's net winnings from the tournament, we need to subtract the tournament cost from the prize amount he had won.
Thus, the expression to show Phil's net winnings from the tournament :-
[tex]x-100[/tex]
.help me solve please and thank you✨
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Luiza delivers newspapers in her neighborhood. If you plot the points (−1, 1), (4, 1), (4, −2) and (−1, −2), you will create a representation of the route she takes, in miles. How many miles does her route cover?
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We have then that the resulting figure is a rectangle.
We must find the perimeter of the rectangle that is given by:
P = 2L + 2W
Where,
L: long
W: width
Restoring the values:
P = 2 * (5) + 2 * (3)
P = 16
Answer:
her route cover 16 miles.
Answer: 16 i just did this
Step-by-step explanation:
The diameter of the base of a cylindrical can is 4 in. The height of the can is 6.5 in. Find the can’s surface area to the nearest tenth.
Answers
diameter of the base of a cylindrical can= 4 in----------> r=2 in
h=6.5 in
[surface area]=2*[pi*r²]+[2*pi*r*h]
then
[surface area]=2*[pi*2²]+[2*pi*2*6.5]=[ 25.13 ]+[ 81.68 ]=106.81 in²
the answer is 106.8 in²
Answer:
106.8 in2
Step-by-step explanation:
Which of the following is a solution of y - x > -3?
(6, 2)
(2, 6)
(2, -1)
Answers
y - x > -3
(6, 2) → x = 6, y = 2
substitute
2 - 6 = - 4 < -3 NOT
(2, 6) → x = 2, y = 6
substitute
6 - 2 = 4 > -3 CORRECT
(2, -1) → x = 2, y = -1
substitute
-1 - 2 = -3 NOT
Answer: (2, 6)
Write a sentence representing the equation x+56/7=11
Answers
x+56/7=11
A number plus fifty-six sevenths is equal to eleven.
I hope this helps!
~kaikers
simplfy 5(9)
will give brainlest
Answers
Hope this helps!
What is the midpoint of the segment whose endpoints are (-6,5) and (4,-7)?
Answers
(-6+4)/2=x
(-2)/2=x
-1=x
(5+-7)/2=y
(-2)/2=y
-1=y
To start, the formula to find the midpoint coordinate pair of two given coordinates is as follows:
([tex] \frac{x1+x2}{2} [/tex], [tex] \frac{y1+y2}{2} [/tex])
Knowing this, plug in your given values (the two x values are -6 and 4; the two y values are 5 and -7) and simplify:
([tex] \frac{-6+4}{2} [/tex], [tex] \frac{5+-7}{2} [/tex])
=([tex] \frac{-2}{2} [/tex], [tex] \frac{-2}{2} [/tex])
=(-1,-1)
Therefore, the midpoint of the coordinates (-6,5) and (4,-7) would be (-1,-1).
Hope this helps and have a marvelous day! :)
If F(x)=x-5 and G(x)=x^2, what is F(F(x))?
Answers
G(F(x)) = (x -5)² . . . . . . . matches selection A.
Answer:
(A)[tex]G(F(x))=(x-5)^2[/tex]
Step-by-step explanation:
Given: It is given that [tex]F(x)=x-5[/tex] and [tex]G(x)=x^2[/tex].
To find: [tex]G(F(x))[/tex]
Solution:
It is given that [tex]F(x)=x-5[/tex] and [tex]G(x)=x^2[/tex], then [tex]G(F(x))[/tex] is written as:
[tex]G(F(x))=G(x-5)[/tex]
⇒[tex]G(F(x))=(x-5)^2[/tex]
Thus, it matches with the option A of the given options.
What is a Banknote? Does a banknote have to come from the government?
Answers
helpppppppppppppppppppppppppppppppppppppppp
Answers
What we must do in this case is to use the properties of the exponents:
We have then:
((x ^ (1/4)) * (y ^ 16)) ^ (1/2)
((x ^ (1/8)) * (y ^ 8))
answer:
((x ^ (1/8)) * (y ^ 8))
option number 2
A speech pathologist had a gross income of 62,650 last year. if 18.9% of her income got withheld for federal income tax how much of the pay got withheld for federal income tax last year
Answers
Answer:
$11,840.85
Step-by-step explanation:
Danes puppy weighed 8 ounces when it was born.Now the puppy weighs 18 times as much as it did when it was born. How many pounds does Danes puppy weigh now.
Answers
The length of a rectangle is three more than twice the width. determine the dimensions that will give a total area of 27m^2
Answers
.. A = W*L
.. 27 = x*(3 +2x)
.. 2x^2 +3x -27 = 0
.. (2x +9)(x -3) = 0
.. x = {-4.5, 3} . . . . . . . . . . width, only the positive answer is of interest
.. 3 +2x = 3 +2*3 = 9 . . . . .this is the length
The rectangle is 3 m by 9 m.
Which describes how to calculate the range of this data set?
4, 5, 6, 8, 11, 12
A. Subtract 11- 5
B. Subtract 12- 4
C. Add 11+ 5
D. Add 12+ 4
Answers
B. 12 - 4 = 8.
This is the Range.
The range of this data set will be 8. The range of the data set is simply the difference between the maximum and the minimum value.
What is a data set?A data set is a set of information that corresponds to one or more database tables in the case of tabular data,
The maximum value is 12
The minimum value is 4
The range of the data set will be;
R = M-m
R=12-4
R=8
Hence the range of this data set will be 8.
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helpppppppppppppppppppppppppp
Answers
The fourth function is just a constant (with exponent 0), so it is an even function.
1. f(x) = (x-1)^2 = x^2 - 2x + 1
f(-x) = (-x-1)^2 = x^2 + 2x + 1
These two don't match, not an even function
2. f(x) = 8x
f(-x) = -8x
These two don't match, not an even function
3. f(x) = x^2 - x
f(-x) = (-x)^2 - (-x) = x^2 + x
These two don't match, not an even function
4. f(x) = 7
f(-x) = 7
Match, is an even function
The area of a rectangle is 300 square centimeters. If the sides of the rectangle are given as 5 centimeters and [tex] \sqrt{x+2600} [/tex] centimeters, then find the value of x and the other side of the rectangle.
Answers
Area is found by multiplying length by width. Using the sides we know we have
[tex]300=5(\sqrt{x+2600})[/tex]
We divide both sides by 5:
[tex]\frac{300}{5}=\frac{5\sqrt{x+2600}}{5} \\ \\60=\sqrt{x+2600}[/tex]
To "undo" a square root, we square both sides:
[tex]60^2=(\sqrt{x+2600})^2 \\ \\3600=x+2600[/tex]
Subtract 2600 from both sides:
3600-2600=x+2600-2600
1000=x
Now we substitute this into the side with x:
[tex]\sqrt{x+2600}=\sqrt{1000+2600}=\sqrt{3600}=60[/tex]
For the following figure, complete the statement about the points. If U lies on the same line as R and N, what terms describe the relationship the three points must have?
Answers
Collinear because any points that is "on" the same line is considered collinear.
It can be Coplanar when any 3 points lie in the same plane, but this problem does not say that. It only asks if point U can be anywhere on the line including R and N.
Hope this helps! :) thanks to: Chaya1Cc for the most brainliest answer
The term that describes the relationship the three points must have is known as: collinear.
What are collinear points?Collinear points are points positioned on a shared straight line, forming a linear arrangement.
In the figure referred to above, we see that point U is on the same straight line as point R and point N. This makes than have a linear arrangement, hence, we can use the term known as collinear to describe the relationship between the three points.
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Classify the following expression by degree and term: (2 points)
x2y − 7xy + xyz + x
Answers
xyz - 5xy + x
Remember to always arrange terms in your polynomial in descending order according to the degree.
Now for degree, just get the sum of the exponents to determine the highest degree. The first term in the new equation has 3 variables, x,y, and z. Each of them, even when the power is not expressed are each raised to the power of 1. There are three variables so it will be:
1+1+1 = 3
The first term is classified as 3rd degree, which is the highest. So now you can conclude that this expression is a 3rd degree trinomial.
The given expression is a third-degree polynomial and consists of four terms: x^2y, -7xy, xyz, and x. Each term has a degree based on the sum of the exponents of the variables within it.
The expression in question is x2y − 7xy + xyz + x. To classify this expression by degree and by term, we need to look at the exponents of the variables in each term. The term 'degree' of a term in a polynomial is the sum of the exponents of the variables in that term.
x2y: The degree is 3 (2 from x2 and 1 from y).−7xy: The degree is 2 (1 from x and 1 from y).xyz: The degree is also 3 (1 from x, 1 from y, and 1 from z).x: The degree is 1, as there is only one occurrence of x.So the expression is a polynomial of third degree with four terms.
Assume that triangle GHI is congruent to LMN. Which of the following congruence statement are correct? check all that apply
Answers
Therefore, if GHI is congruent to LMN, then GH =LM, HI=MN and GI=LN, and also angle G=angle L, Angle H=angle M, while angle I = angle N, therefore the correct answers is a) ∠M= ∠H, c) ∠L=∠G. and e)IH=NM.
The congruence statements that are correct for the given scenario are △GHI ≅ △LMN, △IHG ≅ △NML, and △GIH ≅ △NML.
Explanation:The correct congruence statements for the given scenario are:
△GHI ≅ △LMN (by definition of congruence)△IHG ≅ △NML (by symmetry of congruence)△GIH ≅ △NML (by transitive property of congruence)These congruence statements indicate that the corresponding sides and angles of the triangles are equal, leading to overall congruence.
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