Answer:
correct
Step-by-step explanation:
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.
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Kate wants to run at least 8 miles north she plans to run 1/3 mile each day how many days will it take kate to run
Answer:
24 days
Step-by-step explanation:
8 divided by 1/3 is 24
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.
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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
pls help me plsssssssssss
Answer:
Step-by-step explanation:
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.
Solve the equation sin^2x= 3 cos^2x.
The value of x that satisfies the equation if x lies in the second quadrant is what degrees?
The value of x that satisfies the equation if x lies in the third quadrant is what degrees?
Step-by-step explanation:
sin^2(x)= 3 cos^2(x)
Subtract sin^2(x) on both sides
0=3cos^2(x)-sin^2(x)
By Pythagorean Identity sin^2(x)+cos^2(x)=1, we can replace cos^2(x) with 1-sin^2(x)
0=3(1-sin^2(x))-sin^2(x)
Distribute
0=3-3sin^2(x)-sin^2(x)
Combine like terms
0=3-4sin^2(x)
Add 4sin^2(x) on both sides
4sin^2(x)=3
Divide both sides by 4
sin^2(x)=3/4
Take the square root of both sides
sin(x)=+ or - sqrt(3/4)
sin(x)=+ or - sqrt(3)/sqrt(4)
sin(x)=+ or - sqrt(3)/2
This happens on the unit circle at
60 degrees
120 degrees
240 degrees
300 degrees
If we go around and around again forwards or backwards, we get the infinitely many other solutions including the one's already stated in the following solution sets
(60 +360n) degrees
(120 +360n)degrees
(240 +360n)degrees
(300 +360n)degrees
where n is an integer
x is 120 degrees or (120+360n) degrees in the second quadrant. I didn't know if you were just looking for solutions in the first nonnegative cycle of the unit circle or not.
240 degree one or the (240+360n) degrees terminates in the third.
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
3 daily attendance at the water park: 346, 250, 433, 369, 422,298
Find the median, Q1, Q3,and IQR
Answer:
Median --> 357.5
Q1 --> 298
Q3 --> 422
IQR > 124
Step-by-step explanation:
3 daily attendance at the water park: 346, 250, 433, 369, 422,298
Find the median, Q1, Q3,and IQR
Step 1
We rearrange the given data set
250, 298, 346, 369, 422, 433
a) The Median
The formula to find the Median
= 1/2( n + 1)th term
Where n = Number of terms = 6
Median = 1/2(6 + 1)th
= 1/2(7)th term
= 3.5th term
The 3.5th term = The number between the 3rd and 4th term
3rd term = 346
4th term = 369
Hence,Median = 346 + 369/2
= 357.5
2) Q1 = First Quartile
= 1/4(n + 1)the
= 1/4( n + 1)th term
Where n = Number of terms = 6
Median = 1/4(6 + 1)th
= 1/4(7)th term
= 1.75th term
The 1.75th term = 2nd term
= 298
Q1 = 298
3) 3/4( n + 1)th term
Where n = Number of terms = 6
Median = 3/4(6 + 1)th
= 3/4(7)th term = 21/4th term
= 5.25th term
The 5.25th term = 6th term
Q3 = 422
4) Interquartile Range = Q3 - Q1
= 422 - 398
= 124
Nicholas spent $10, including tax, on 2.5 centimeters of metal cable. what is the cost, in dollars, per centimeter of cable
Answer:
for each centimeter its $4
Step-by-step explanation:
10 divided by 2.5 is 4
1 = 4
2 = 8
2.5 equals 4 divided by 2 so 8 + 2 = 10
Task 4 Task 다. Given: m
Answer:
where the choices?
Step-by-step explanation:
What is the domain of the graph?
Answer:
B
Step-by-step explanation:
x is greater than or equal to 2 and x is less than or equal to 5
7/20X5/5 equals? Any help
?
Determine if the 2 triangles are congruent.
A) AAS
B) Not enough information
C) SAS
D) HL
pls help meeeeeeeeeeeeee
Answer:
the right answer is:
(A) [tex]2+\frac{1}{2}a[/tex]Step-by-step explanation:
You take the equations that the exercise give you:
x + y = 4x - y = aNow you clear the "y" variable in any equation you want, in this case, I'm gonna use the second equation:
x - y = a-y = a - x3. y = x - a
And now, you'll replace this third equation in the equation you didn't take (the first in this case).
x + y = 4x + (x - a) = 4x + x - a = 4Add the x variables:
2x - a = 42x = 4 + ax = (4 + a) / 2That's the answer of the exercise, but you can represent this in this form:
x = (4 + a) / 2 ↔ [tex]x = \frac{4}{2} + \frac{1}{2} a[/tex]x = (4 + a) / 2 ↔ [tex]x = 2+ \frac{1}{2} a[/tex]By this reason, the right answer is [tex]x = 2+ \frac{1}{2} a[/tex].
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
Explain the differences and similarities between 8 + (−5) and 8 − 5.
Answer:
The use different equations but both equal 3
Step-by-step explanation:
factorise fully the following
3 x + 6
Answer:
[tex]3x + 6 = 0 \\ 3x = 0 - 6 \\ 3x = - 6 \\ x = \frac{ - 6}{3} \\ x = - 2[/tex]
Answer: 3(x+2)
Step-by-step explanation:
ask yourself what numbers can I take out of 3 and 6, you can divide by 3 :)
3x / 3
1x
x
6 / 3
2
3(x+2)
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 + 9help im doing a test in 6th grade- I LITERALLY FORGOT WHAT THE MEDIAN IS
Answer:
iit's the middle of numbers to find the median place the number in value order
Answer:
15
Step-by-step explanation:
You add up all the numbers then divide it by how ever many numbers there are for example 15+5+5 is 25 divided by 3 is 8.333333
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.
simplify the expression below (3³-3²)+2³=
Answer:
1^1+2^3 I believe
Step-by-step explanation:
=3³-²+2³
=3¹ + 2³
= 3+ 8
=11
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.
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 ꒱ ‧₊˚
find the volume of an construction cone if it has a radius of 9 in and a height of 18 in
Answer:
1526.04 cubic inches
Step-by-step explanation:
V=π r 2 h
3
= pi x r(r) x (height/3)
= 3.14 x 9(9) x (18/3)
= 3.14 x 81 x 6 = 1526.04 cubic inches
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:
What are the missing numbers in the data set? Assume the numbers are in order
24, 28, 32, 39___ Range=18
Answer:
This answer is 42
Step-by-step explanation:
42 - 24 = 18
For what values of x is the trinomial 2x2−x+55 equal to the square of binomial x+5?
The value of x for which the trinomial 2x^2−x+55 equal to the square of binomial x+5 is 5 and 6
Given the equation 2x^2−x+55, if the expression is equal to the square of binomial x + 5, then;
2x^2−x+55 = (x+5)^2
2x^2−x+55 = x^2 + 10x + 25
Collect the like terms;
2x^2-x^2-x-10x+55-25 = 0
x^2 - 11x + 30 = 0
Factorize the result
x^2 - 6x - 5x + 30 =0
x(x-6)-5(x-6) = 0
x-5 = 0 and x - 6 = 0
x = 5 and 6
Hence the value of x for which the trinomial 2x^2−x+55 equal to the square of binomial x+5 is 5 and 6
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helppppppppppppppppppppp
Answer:
C. 2, 1
Step-by-step explanation:
Where is the mistake in the following problem?
1) 3/12
2)9/12
3)3/4
4)1/3