Answers
Answer:
KN = 11
Step-by-step explanation:
In right triangle LNM, by Pythagoras theorem:
[tex]LN=\sqrt{LM^2 -MN^2} \\ \\ \implies \: LN=\sqrt{ {(100)}^{2} -(80)^2} \\ \\ \implies \: LN=\sqrt{ 10000 -6400} \\ \\ \implies \: LN=\sqrt{ 3600} \\ \\ \implies \: LN=60[/tex]
In right triangle LNK, by Pythagoras theorem:
[tex]KN = \sqrt{LK^2-LN^2}[/tex]
[tex]\implies KN = \sqrt{(61)^2-(60)^2}[/tex]
[tex]\implies KN = \sqrt{3721-3600}[/tex]
[tex]\implies KN = \sqrt{121}[/tex]
[tex]\implies\huge{\orange{ KN =11}}[/tex]
Answer:
11[tex] \: [/tex]
Step-by-step explanation:
Before, Finding the length of KN, we must have to find the length of LN. So
[tex] \: [/tex]
Here, LNM is a right angled triangle where measure of two sides are given and we are to find the measure of the third side LN(Perpendicular).
[tex] \: [/tex]
We'll find the measure of third side with the help of the Pythagorean theorem.
[tex] \\ {\longrightarrow \pmb{\sf {\qquad (Base) {}^{2} + (Perpendicular {)}^{2} = (Hypotenuse {)}^{2} }}} \\ \\[/tex]
Here,
The base (NM) is 80The perpendicular is LNThe hypotenuse (LM) is 100.[tex] \: [/tex]
So, substituting the values in the above formula we get :
[tex]\\ {\longrightarrow \pmb{\sf {\qquad (NM) {}^{2} + (LN {)}^{2} = ( LM{)}^{2} }}} \\ \\[/tex]
[tex] {\longrightarrow \pmb{\sf {\qquad (80) {}^{2} + (LN {)}^{2} = ( 100{)}^{2} }}} \\ \\[/tex]
[tex] {\longrightarrow \pmb{\sf {\qquad (LN {)}^{2} = ( 100{)}^{2} - (80) {}^{2}}}} \\ \\[/tex]
[tex] {\longrightarrow \pmb{\sf {\qquad (LN {)}^{2} = 10000 - 6400}}} \\ \\[/tex]
[tex] {\longrightarrow \pmb{\sf {\qquad (LN {)}^{2} = 3600}}} \\ \\[/tex]
[tex] {\longrightarrow \pmb{\sf {\qquad LN = \sqrt{3600} }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad LN = \frak{60}}}} \\ \\[/tex]
Therefore,
The length of LN is 60.[tex] \\ [/tex]
As, we found the length of LN, now we can find the length of KN.
Where,
The base is KNThe perpendicular (LN) is 60.The hypotenuse (LK) is 61.So, in the right angled triangle LKN, by Pythagorean theorem we get,
[tex]\\ {\longrightarrow \pmb{\sf {\qquad (KN) {}^{2} + (LN {)}^{2} = ( LK{)}^{2} }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad (KN) {}^{2} + {60}^{2} = ( 61{)}^{2} }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad (KN) {}^{2} = ( 61{)}^{2} - {(60)}^{2}}}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad (KN) {}^{2} =3721 - 3600}}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad (KN) {}^{2} = 121}}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad KN = \sqrt{121} }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad KN = \frak{11} }}} \\ \\[/tex]
Therefore,
The length of KN is 11.Related Questions
if i gain 50 coins per 52.2 seconds how long would it take to reach 400,500 coins
Answers
Answer:
418122 seconds
Step-by-step explanation:
First divide 400,500 by 50. That is 8010.
Then multiple 8010 by 52.2 and you answer is 418122 seconds. OR
6968.7 Minutes, OR 116.145 Hours, OR 4.839375 Days
What is the best estimate of the area of the figure on the grid if each square has a side length of 1 inch?
12 square inches
O 20 square inches
25 square inches
O 33 square inches
Answers
Answer:12 i think
Step-by-step explanation:
If the diameter is 11, then what's the radius?
Answers
EXPLANATION: The radius of a circle is the distance from the center of the circle to any point on the circumference.
The easiest way to find the radius is by dividing the diameter in half
1/2 x 11 = 11/2 OR 5.5
ANSWER: the radius of the circle 11 cm in diameter would be 5.5 cm.
Michael is painting a cylindrical tank with a radius of 15 feet and a height of 60 feet. he must determine the surface area of the tank so that he knows how much paint to purchase. what is the surface area of the tank? use 3.14 for π, and round your answer to the nearest whole number. refer to your staar 8th grade math reference sheet for the appropriate formula. question 9 options: 1413 ft2 5655 ft2 6855 ft2 7069 ft2
Answers
The surface area of the cylindrical tank on which the Michael is painting is 7065 ft².
What is surface area of cylinder?Surface area of cylinder is the area of each faces by which it is enclosed. The surface area of cylinder can be calculated with the following formula;
[tex]A=2\pi rh+2\pi r^2[/tex]
Here, (h) is the height of the cylinder and (r) is the radius.
Michael is painting a cylindrical tank with a radius of 15 feet and a height of 60 feet. He must determine the surface area of the tank so that he knows how much paint to purchase.
Put the values in the above formula,
[tex]A=2(3.14) (15)(60)+2(3.14)(15)^2\\A=7065\rm\; ft^2[/tex]
Thus, the surface area of the cylindrical tank on which the Michael is painting is 7065 ft².
Learn more about the surface area of cylinder here:
https://brainly.com/question/20771646
124 7/8 drained in 25 mins how much is drained each min
Answers
Convert 124 7/8 to 999/8
In 25 minutes, 999/8 is drained -> every minute, 999/200 is drained (4.995)
I just am confused what to do on 11-16 and if able to can’t 1-9 be checked
Answers
Answer:
add all the sides that you have and subtract it from 180
Step-by-step explanation:
consider the system of linear inequalities {y<1/2x-1, y>2x+3} Which points are in the solution set?
a. (-4,-3)
b. (1,3)
c. (-5,-7)
d. (3,0)
e. (-6,-5)
f. (-7,-2)
g. (-4,-4)
h. (-3,-3)
Answers
Answer: g, e
e. (-6,-5)
g. (-4,-4)
Step-by-step explanation:
While we could plug in each value of data points to see if it solves correctly, a quicker way to solve this problem is to graph.
The points that are a solution to the set are points in the area of overlap created by the two equations graphed. Points that are on a line in the overlap, but not over, are not a solution because the equations do not include "equal to."
See attached for the graph.
The solution set of y < 1/2x - 1 and y > 2x + 3 are their true values
The solution set of the system of linear inequalities are (-6,-5) and (-4,-4)
How to determine the solution set?The system of linear inequality is given as:
y < 1/2x - 1
y > 2x + 3
Start by plotting the graph of both inequalities
Because both inequalities do not have any form of equation i.e. ≤ and ≥, then only the points in the shaded area represents the solution set of the inequality.
The points in the shaded area are (-6,-5) and (-4,-4)
Other points are either outside the shaded area or on the line of the inequalities
Hence, the solution set of the system of linear inequalities are (-6,-5) and (-4,-4)
Read more about inequalities at:
https://brainly.com/question/18881247
Write the phrase as an expression.
18 added to a number n
Answers
Answer:
n + 18
Step-by-step explanation:
n + 18
Ex: 7 added to 3 = 3 + 7 = 10
Hope this helps!
I don't get this one?
Answers
Answer:
4000
Step-by-step explanation:
V=4/3(3)(10)^3
V= 4/3 (3)(1000)
V=4/3 (3000)
V=4000
he roof of a castle tower is shaped like a cone. The base of the cone is 24 m across and the height is 16 m. The slant height of the roof, which is unknown, is the hypotenuse of the right triangle formed with the radius and the height of the cone.
What is the slant height of the roof?
Answers
==========================================================
Explanation:
The base of the cone is 24 m across. This is the diameter of the circle. Divide it in half to get 24/2 = 12 m as the radius.
We can form a right triangle inside the cone such that the horizontal piece is the radius 12 m and the vertical piece is the height 16 m. The hypotenuse of this right triangle is the slant height. This is all mentioned in the instructions of course.
We'll use the pythagorean theorem to find the hypotenuse.
[tex]a^2 + b^2 = c^2\\\\c = \sqrt{ a^2 + b^2 }\\\\c = \sqrt{ 12^2 + 16^2 }\\\\c = \sqrt{ 144 + 256 }\\\\c = \sqrt{ 400 }\\\\c = 20 \text{ meters is the slant height}\\\\[/tex]
It is the distance from the circular base to the peak of the cone, when traveling along the outside of the cone. This is a straight line distance.
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
Answers:
Mode = 6
Range = 7
====================================================
Explanation:
The mode is the most frequent value. Based on that, we simply go for the tallest stack of 'x's which in this case is 6.
Therefore, 6 is the mode. It shows up four times which is the most of any other value.
-------
The range is the difference of the min and max
range = max - min = 8 - 1 = 7
There are 8 red marbles, 2 green marbles, and 5 blue marbles in a bag. Marbles are replaced after each draw. What is the probability that the first marble drawn is red and the second marble drawn is green?
Answers
Answer:
[tex]\frac{16}{225}[/tex]
Step-by-step explanation:
When attempting probability problems we want to figure out the chances of something happening. This turns into something like:
[tex]\frac{\text{marble drawn}}{\text{total marbles}}[/tex]
In this case we have 8 red marbles, 2 green marbles, and 5 blue marbles in a bag. That brings us to a total of 15 marble.
Since we want to first draw a red marble the chance of that happening would be:
[tex]\frac{8\text{(the marble drawn)}}{15\text{(total # of marbles)}}[/tex]
Now we replace the marble as stated in the problem so we then draw the next marble, which is green.
[tex]\frac{2\text{(the marble drawn)}}{15\text{(total number of marbles)}}[/tex]
All that's left is to multipy the values we got:
[tex]\frac{8}{15} *\frac{2}{15}=\frac{16}{225}[/tex]
That's our answer.
Use the scale factor 1:8 to find the missing dimension.
Item = baby giraffe
model = height = cm
actual = height = 1.84m
Answers
Answer:
0.23 m or 23 cmStep-by-step explanation:
Accordingto the scale factor, the model is 8 times smaller than actual figure.
Its height is:
1.84 m * 1/8 = 0.23 m or 23 cmSo
Actual=1.84mModel:-
1.84/80.23mTell which value of the variable is the solution of the equation.
30 = 6w
w = 3, 5, 6, 8
Answers
Answer:
w = 5
Step-by-step explanation:
6w/6 = 30/6
= 5
WILL GIVE BRAINLIEST, THANKS, AND 5 STARS!
PLEASE HELP AND EXPLAIN!
The Cosmic Pool company is building a pool in Mary’s back yard. The pool is to be 8ft longer than it is wide and cover 240 square feet of the back yard. Determine both dimensions of the pool and the perimeter.
Group of answer choices
(A) Dimensions: width = 20ft & length = 12ft
Perimeter: 32ft
(B) Dimensions: width = 20ft & length = 12ft
Perimeter: 64ft
(C) Dimensions: width = 12ft & length = 20ft
Perimeter: 32ft
(D) Dimensions: width = 12ft & length = 20ft
Perimeter: 64ft
Answers
Answer:
(D) Dimensions: width = 12ft & length = 20ft / Perimeter: 64ftStep-by-step explanation:
Let the length be x and width be y.
We have:
x = y + 8Area = 240 ft²Set equation and solve
xy = 240y(y + 8) = 240y² + 8y = 240y² + 8y + 16 = 256(y + 4)² = 16²y + 4 = 16y = 12 ftThe length is:
x = 12 + 8 = 20 ftThe perimeter is:
P = 2(x + y) = 2(20 + 12) = 2(32) = 64 ftCorrect choice is D
Let they be l and b
l=b+8l-b=8--(1)And
lb=240So
(l+b)^2=(l-b)^2+4b=(8)^2+4(240)=64+960=1024l+b=32--(2)From both equations
2l=40l=20And.
b=20-8=12ft
Option D
AABC is equilateral.
AB = 22x-33 and AC = 7x + 57.
=
B
A
A
с
x = [?]
Answers
Answer:
Answer is 6
Step-by-step explanation:
See it is equilateral so AB=AC=BC
Now we are given values of AB and AC, but they are equal so,
22x-33 = 7x+5722x-7x = 57+3315x = 90x= 15 / 90x=6Hope it helps
BYE
A suit is on sale for $414 , which is 28% less than the regular price.
What is the regular price?
Answers
Answer:
.72x=414
Step-by-step explanation:
Max has a square piece of cloth. He cuts it in half from one corner to the opposite corner. How many sides does each of the cut pieces have?
Answers
Answer:
Step-by-step explanation:
You have a cloth:
____________
| |
| |
|___________|
and you cut it in half.
There are three sides
Answer:
Step-by-step explanation:
The cut pieces will each have three sides: two that are equal and one that is the hypotenuse.
If the original square had sides of length s, then the cut pieces would each have two of that length: s and s; the third side would have length h = √(s² + s²), or h = s√2.
pls answer its important
Answers
Answer:
i dunno'
Step-by-step explanatio i dont know how to explain diss this
a) Factorise
x2 - 422
Answers
Answer:
(x + 42)(x - 42)
Step-by-step explanation:
Keep this in mind :
a² - b² = (a + b)(a - b)In this case,
a = xb = 42So, by factorizing,
x² - 42² = (x + 42)(x - 42)★a²-b²=(a+b)(a-b)
So
x²-42²a=x ,b=42
(x+42)(x-42)Done!
Two triangles make a parallelogram ABCD. The area of triangle BCD is 15 square meters. DC is the base of the parallelogram and is 6 meters long. What is the height?
Answers
Answer:
Area of a parallelogram is a region covered by a parallelogram in a two-dimensional plane. In Geometry, a parallelogram is a two-dimensional figure with four sides. It is a special case of the quadrilateral, where opposite sides are equal and parallel. The area of a parallelogram is the space enclosed within its four sides. Area is equal to the product of length and height of the parallelogram.
Step-by-step explanation:
Area = b × h Square units
Find two numbers whose product is 3 and the sum of whose reciprocals is 76/15
Answers
Answer:
xy=3_equation I
x+y=76/15 eq 2
Step-by-step explanation:
from eq
x=3/y
now put x=3/y in eq 2
3/y+y=76/15
(3+y^2) 15=76y
45+15y^2=76y
15y^2-76y+45=0
by using quardic equation
x=76+_root under 76^2-4×15×45/2×15
y= 5776+- 53.62/2×15
taking positive sign and taking negative sign
y=194.32
y=190.745
HI can somebody outline it pls and tyy
Answers
Answer:
Step-by-step explanation:
*View the attached file*
Hope this helps!
In 1932, the average house in the united states cost $3,900. today, the average cost of a house is $350,000. what is the percent of change in the average price of a house in the united states (round to the nearest whole percentage)?
Answers
Answer:
8,874%
Step-by-step explanation:
Find percent of change by finding the differnce between the original price and new price. You can then use a proportion "change/original = percent/100"
Give me full working and explanation and I give you stars and mark you as brainliest.
Answers
700-505.75=$194.25
for the second question, all we have to do is multiply the previous answer by 3 since there are 3 times the amount of watches being sold.
194.25x3=$582.75
Please help!!! i'll give brainliest and offering 20 pts each!!!
write each trinomial in the form a(x+b)^2 or a(x-b)^2
please answer all questions correctly! please no spam :-(
5x^2 + 15x + 11.25
10x^2 +20x +10
1/4x^2 + x + 1
3x^2 + 5x + 25/12
explanation isn't necessary, but i will give brainliest to the person with an explanation/best explanation
Answers
Answer:
5(x +1.5)^210(x +1)^21/4(x +2)^23(x +5/6)^2Step-by-step explanation:
When your desired form is expanded, it becomes ...
a(x +b)^2 = a(x^2 +2bx +b^2) = ax^2 +2abx +ab^2
This tells you the overall factor (a) is the leading coefficient of the given trinomial. Factoring that out, you can find b as the root of the remaining constant.
a) 5x^2 +15x +11.25 = 5(x^2 +3x +2.25) = 5(x +1.5)^2
b) 10x^2 +20x +10 = 10(x^2 +2x +1) = 10(x +1)^2
c) 1/4x^2 +x +1 = 1/4(x^2 +4x +4) = 1/4(x +2)^2
d) 3x^2 +5x +25/12 = 3(x^2 +5/3x +25/36) = 3(x +5/6)^2
_____
Additional comment
If you know beforehand that the expressions can be factored this way, finding the two constants (a, b) is an almost trivial exercise. It gets trickier when you're trying to write a general expression in vertex form (this form with an added constant). For that, you must develop the value of b from the coefficient of the linear term inside parentheses.
I need help on this image below
Answers
Answer: 70 degrees
Step-by-step explanation:
A glass container holds 40 fluid ounces of tea. How many pints of tea does the glass container hold?
Answers
Answer:
2.5
Step-by-step explanation:
40 divided by 16 is 2.5
Larry has a bag of candy that weighs 12 pounds. He wants to divide the candy into 5 equal groups. How much will each group weigh
Answers
Answer:
2.4 pounds
Step-by-step explanation:
12/5=2.4
To get 5 equal parts of 12, you have to do 12 divided by 5.
a fence is shown on a blueprint and has sides of length 17 cm, 18 cm, 15 cm, and 19 cm. If the scale on the blueprint is 2 cm:7 m, what is the total length of the fence? show ur work pls
Answers
Answer:
241.5
Step-by-step explanation:
First add all your numbers togather
17 + 18 + 15 + 19
= 69
THEN..
Multiply by 7
= 69 × 7
= 483
After that divide it by 2..
483 ÷ 2
= 241.5