In the data set below, what is the median
The diagram shows a square ABCD
M is the midpoint of AB
N is the midpoint of AD
The area of the shaded triangle AMN is 8cm^2
Work out the area of triangle MCN
The area of the triangle, Δ AMN is 8 cm², so the area of the triangle, ΔMCN is 24 cm².
A triangle is one of the most basic geometric figures with 3 sides, 3 angles, and 3 vertices.
The area of a triangle is half of the product of the base and height.
Given that
ABCD is square and M and N are mid-points of lines AB and AD respectively.
Area of triangle, ΔAMN = 8 cm²
[tex]\dfrac{1}{2} \times AN \times AM = 8\\AN \times AM = 8 \times 2\\AN \times AM = 16[/tex] ...(i)
Since ABCD is square, therefore AB = AD.
Also, as M and N are mid-points of lines AB and AD, so
AN = AM.
Substitute AN = AM in equation (i),
[tex]AN \times AN = 16\\AN^2 = 16\\AN = \sqrt{16}\\AN = 4\ cm[/tex]
So,
AD = 2 × AN
= 2 × 4
= 8 cm
As ABCD is square,
AB = BC = CD = AD = 8 cm.
Area of the square ABCD = 8² = 64.
Since CD = BC, ND = MB, ∠D = ∠B.
Therefore by SAS property of similarity,
ΔCDN ≅ ΔCBM
Area of the triangle, ΔCDN = Area of the triangle, ΔCBM.
[tex]= \dfrac{1}{2} \times CB \times BM\\= \dfrac{1}{2} \times 8 \times 4\\\\= 16\ cm^2[/tex]
Area of the triangle, ΔCMN = Area of ABCD - Area of ΔAMN - Area of ΔCDN - Area of ΔCBM
Area of the triangle, ΔCMN = 64 - 8 - 16 - 16
= 24 cm²
Therefore, the area of ΔCMN is 24 cm².
Learn more about Triangles here:
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Good luck Question 16 Which of the following is the graph whose equation is (x + 1)2 + (y - 6)2 = 9?
Answer:
Step-by-step explanation:
This should have choices, but I'll provide a graph. You choose which one is it like.
Center: -1,6
radius: 3
Notice that the radius is 3 when measured between y = 6 and y = 9
WILL MARK BRAINLYEST! 1567584+3121350393X59=
Answer:184161240771
Step-by-step explanation:
Calculator
Answer:
184,161,240,771
Step-by-step explanation:
have a nice day!
₊˚ ‧꒰ mei ꒱ ‧₊˚
A frustum of solid right pyramid has a square base and a square base and a square top with sides 12 cm and 8 cm respectively. The height of the frustum is 5.4 cm
Answer:
a. S = 6.72 cm
b. A = 1075.70 cm²
c. V = 1,719.1 cm³
Step-by-step explanation:
How to Find
The volume of a frustum of a regular pyramid is equal to one-third of the altitude multiplied by the sum of its bases and the geometric mean between them.
How to Solve
Volume = (1/3)πh (r12 + r22 + (r1 * r2))
Lateral Surface Area
= π(r1 + r2)s = π(r1 + r2)√((r1 - r2)2 + h2)
Top Surface Area = πr12
Base Surface Area = πr22
Total Surface Area
= π(r12 + r22 + (r1 * r2) * s)
= π[ r12 + r22 + (r1 * r2) * √((r1 - r2)2 + h2) ]
To find:
a. the height of the pyramid of which the frustum is a part.
Then, s = 6.7201190465646 cm
In the nearest tenths, the slant height is S = 6.72 cm
b. the surface area of the pyramid.
Then, L = 422.23753255872 cm²
In the nearest tenths, the Surface area of the pyramid is A = 1075.70 cm²
c. the volume of the frustum
Then, V = 1719.0795000443 cm³
Therefore, the volume is 1719.01 cm³ In the nearest tenths
Write an exponential equation for the following situation: A city's population increases each year by 2.7 percent. The current population is 280,000.
7. Marcy is taking part in a summer movie club. She will
earn 3 points for each movie she attends throughout the
summer. Which equation represents the relationship
between y, the total points, and x the number of movies?
A y=3x
B. y = 3+x
C. x= 3y
D. x=y+3
Answer:
The equation that represents the relationship between 'y' the total points, and 'x' the number of movies is option A;
A y = 3·x
Step-by-step explanation:
The information required in the question is an equation that represents the the relationship between the number of movie attended and the total number of points Marcy has given that she earns a fixed amount of points for attending each movie
The number of points she will earn for attending each movie = 3 points
The total number of points she will earn 'y' when she attends 'x' number of movies is given as follows;
y = 3 + 3 + 3 + ... + 3, 'x' number of times, and we can write
[tex]y = \sum\limits_{i =1}^x 3 = 3 \times x[/tex]
Therefore the equation that represents the relationship between 'y' the total points, and 'x' the number of movies is y = 3·x.
Determine if the 2 triangles are congruent.
A) AAS
B) Not enough information
C) SAS
D) HL
please help !! thank youuu
Answer:
No, she should have added ([tex]6^2[/tex]) and ([tex]8^2[/tex]) and compared that too ([tex]10^2[/tex]).
Step-by-step explanation:
An easy way to determine if a triangle is right is by using the Pythagorean theorem. The Pythagorean theorem states the following,
[tex]a^2 + b^2 = c^2[/tex]
Where (a) and (b) are the legs or the sides adjacent to the right angle, and (c) is the hypotenuse or the side opposite the right angle. The hypotenuse is always the largest side in a right triangle.
One can substitute in the given sides and solve to prove that the given triangle with the following side lengths (6, 8, 10) forms a right triangle.
[tex](6)^2 + (8)^2 = (10)^2\\\\36 + 64 = 100\\\\100 = 100[/tex]
Thus the given triangle is a right triangle because one can apply the Pythagorean theorem to its side lengths.
The mistake that was made in the given problem was that the person in the given situation set up the equation using the wrong sides, and thus got a wrong result. Therefore, one should select the following option as their answer,
No, she should have added ([tex]6^2[/tex]) and ([tex]8^2[/tex]) and compared that too ([tex]10^2[/tex]).
At the library, Herb spent hour looking for a book, 1 hour
reading, and į hour doing research on the computer. How many
hours did Herb spend at the library?
Answer:
3 hours obviously
Step-by-step explanation:
1 hour looking for a book, 1 hour reading it, and one hour doing research on the book = 3 hours
I didnt answer the question but if it looks like i did i did by accident but still help me
Answer:
15% because it's 15 out of 100
Help plzz need the answer and that explanation plz don't send a file I need help with question 21!!
Answer:
No, they cannot be becuase the points are too different- no same numerical values.
Humphrey needs to mail a package. He weighs it at home as 20.2 ounces. When he gets to the post office, the clerk weighs it at 18.6 ounces. What is the percent error in the weight of the package, assuming that his home weight is the correct weight?
Answer:
7.92%
Step-by-step explanation:
Given the following
Weight of package at home = 20.2 ounces.
Weight of the package at the office = 18.6ounces
Decrement = 20.2 - 18.6
percentage error = decrement/wt at home * 100
percentage error = 1.6/20.2* 100
percentage error = 160/20.2
percentage error = 7.92
HEnce the percent error in the weight of the package is 7.92%
What is the surface area?
5 mm
4 mm
5 mm
6 mm
7 mm
square millimeters
Answer:
136 square millimeters
Step-by-step explanation:
Seven buddies got together to eat chicken wings. There were total of 133 chicken wings. If each of the buddies ate the same number of chicken wings, how many did each person eat?
A 19
B. 13
C. 15
D. 17
Answer:
133÷7=19
19 is the answer
A concrete mixing tub contains 34 liters of water and 22 liters of sand. Starting at the same time, water is added to the tub at a rate of 5 liters per minute,
while sand is also added to the tub at a rate of 7 liters per minute.
Part A
In how many minutes will the tub contain equal amounts of water and sand?
2 minutes
6 minutes
12 minutes
24 minutes
Answer:
6 minutes
6
6 minutes
6 minutes
A house has a square room with an area of 125 ft2.
What is the length of the side of the square room to the nearest tenth?
Answer:
11.2 ftStep-by-step explanation:
doing map testing rn el o el
Choose the greatest-.03; .3; .291; or.34
Answer:
The greatest number would therefore be 291
Answer:
.34
Step-by-step explanation:
It's literally the biggest out of the four.
7/20X5/5 equals? Any help
?
In AGHI, the measure of ZI=90°, the measure of ZG=5°, and IG = 57 feet. Find the
length of GH to the nearest tenth of a foot.
9514 1404 393
Answer:
57.2 ft
Step-by-step explanation:
The relevant trig relation is ...
Cos = Adjacent/Hypotenuse
cos(G) = IG/GH
GH = IG/cos(G) = (57 ft)/cos(5°)
GH ≈ 57.2 ft
Please help me!!
3. Determine whether or not AB is tangent to circle O. Show your work.
Answer:
not tangent
Step-by-step explanation:
two reasons, first
Triangle AOB is not a right triangle
line AB intersects the circle O at two points.
The line AB touching the circle at point B in the considered diagram is not tangent to the circle O.
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
How are radius and tangent to a circle related?There is a theorem in mathematics that:
If there is a circle O with tangent line L intersecting the circle at point A, then the radius OA is perpendicular to the line L.
So, if AB is a tangent, then ∠ABO = 90° and therefore satisfies Pythagoras theorem.
Assuming AB is tangent, then ABO is right angled we should get:
[tex]H^2 = P^2 + B^2\\30^2 = 16^2 + 12^2\\900 = 256 + 144\\900= 500[/tex]
This statement is false, and therefore, so as our assumption is false that AB is tangent to circle O. Thus, AB is not tangent to circle O.
(so it might be that even if AB looks like touching at one point the circle O, but AB might be intersecting the circle at two points, or not touching it at all)
Thus, the line AB touching the circle at point B in the considered diagram is not tangent to the circle O.
Learn more about tangent to a circle here:
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Which is NOT a test to prove triangles congruent?
SAA SAS SSS SSA
A ball is thrown into the air from the top of a building. The height, h (t), of the ball
above the ground t seconds after it is thrown can be modeled by the function
h (t) = -16t+64t + 80. Explain the meaning of h (0) = 80 in the context of
the problem.
Answer:
See below
Step-by-step explanation:
h(0) is the height of the ball when it is thrown. h(0) = 80 ft. The top of the building is 80 ft. above ground.
What is the coefficient of the term of degree 7 in the polynomial below? 2x^6 + 2 – 4x^2 + 5x^7 – 4x A. 2 B. 4 C. 6 D. 5
Answer:
C.6
Step-by-step explanation:
I've tried to get the answer for this 13 times now (not joking), plzzz help: write a formula that represents the number of people in the nth row (pre-calc problem, I only need the formula)
I will report if sent a link
Answer:
2820 seatsaₙ = 3n + 9Step-by-step explanation:
This is an AP with:
The first term a₁ = 12Common difference d = 3Number of terms n = 40Number of the seats:
Sₙ = 1/2*n(a₁ + aₙ) = 1/2n(2a₁ + (n - 1)d)S₄₀ = 1/2*40(12*2 + 39*3) = 2820 seatsFormula of nth term:
aₙ = a₁ + (n - 1)daₙ = 12 + (n - 1)*3 = 12 + 3n - 3 = 3n + 9aₙ = 3n + 9What is the mean of 15, 16, 16, 18, 17
Answer:
16
Step-by-step explanation:
Answer:
16.4
Step-by-step explanation:
To find the mean of this set, add up the elements and divide the result by 5 (the number of elements):
15 + 16 + 16 + 18 + 17
------------------------------ = 82/5, or 16.4
5
Using the markings below, determine which of the following is the measure of angle 2
Answer:
4. 132°Step-by-step explanation:
Both the triangles on the left and right are isosceles
The top angle of the triangle on the left:
180° - 2*69° = 42°The top angle of the triangle on the right:
90° - 42° = 48°This is the same angle as supplementary with angle 2:
∠2 = 180° - 48° = 132°Correct choice is 4
1. Find the exact value of sin and cos of 195 degrees.
Answer:
Sin195* = -[tex]\frac{\sqrt{6}-\sqrt{2} }{4 }[/tex]
Cos195* = - [tex]\frac{\sqrt{6} +\sqrt{2} }{4}[/tex]
Step-by-step explanation:
What is formed when a sodium atom and chlorine atom react chemically
Answer:
Step-by-step explanation:
When sodium and chlorine atoms come together to form sodium chloride (NaCl), they transfer an electron. The sodium (Na) atom transfers one electron to the chlorine (Cl) atom, so that they both have full outer shells.
PLEASE HELP!! I WILL GIVE POINTS AND BRAINEST!
Answer:
Yes. They are similar because they have the same shape and one is just flipped and smaller.
Answer: Yes
Step-by-step explanation: For a quadrilateral to be similar, the angles must be congruent. This is true since the angle measures are the same since it flipped and dilated.