Answers
Answer: Approximately 1336.50301206033 square cm
=======================================================
Explanation:
If we know the three side lengths of a triangle, then we can use Heron's formula to get the area
Heron's formula is
[tex]A = \sqrt{S(S-a)(S-b)(S-c)[/tex]
with S being the semiperimeter, or half the perimeter, so [tex]S = \frac{a+b+c}{2}[/tex]. We add up all three sides and divide by 2.
----------------
The smaller triangle has side lengths of a = 19, b = 40, c = 41. So we get a semiperimeter of S = (a+b+c)/2 = (19+40+41)/2 = 50
Plug this along with the a,b,c values to get an area of...
[tex]A = \sqrt{S(S-a)(S-b)(S-c)}\\\\A = \sqrt{50(50-19)(50-40)(50-41)}\\\\A = \sqrt{139500}\\\\A \approx 373.496987939661\\\\[/tex]
which is approximate
-----------------
Do the same for the larger triangle as well
S = (a+b+c)/2 = (19+180+181)/2 = 190
[tex]A = \sqrt{S(S-a)(S-b)(S-c)}\\\\A = \sqrt{190(190-19)(190-180)(190-181)}\\\\A = \sqrt{2924100}\\\\A = 1710\\\\[/tex]
Interestingly enough, we get an exact area value this time as opposed to some approximation.
-----------------
The difference between the two results is the area of the shaded region
1710 - 373.496987939661 = 1336.50301206033
This is approximate since the first result was approximate.
Answer:
K = 1710 cm^2 - K = 373.497 cm^2 = 1337 cm^2
Step-by-step explanation:
Why don't you just look for the whole area and deduct the non-shaded area?
Total
Sides:
a = 180 cm
b = 181 cm
c = 19 cm
Angles:
A = 83.9744 °
B = 90 °
C = 6.02558 °
Other:
P = 380 cm
s = 190 cm
K = 1710 cm^2
r = 9 cm
R = 90.5 cm
________________________
Non shaded area:
Answer:
Sides:
a = 40 cm
b = 41 cm
c = 19 cm
Angles:
A = 73.519 °
B = 79.3849 °
C = 27.0961 °
Other:
P = 100 cm
s = 50 cm
K = 373.497 cm^2
r = 7.46994 cm
R = 20.8569 cm
where:
A = angle A
B = angle B
C = angle C
a = side a
b = side b
c = side c
P = perimeter
s = semi-perimeter
K = area
r = radius of inscribed circle
R = radius of circumscribed circle
Related Questions
Find the common difference of the arithmetic sequence. 6, 9.4, 12.8, 16.2, . . .
Answers
Answer:
The answer is 3.4Step-by-step explanation:
The sequence above is an arithmetic sequence
So in order to find the common difference subtract the previous term from the next term
So we have
Taking 9.4 and 6
That's
9.4 - 6 = 3.4
Taking 12.8 and 9.4
12.8 - 9.4 = 3.4
Taking 16.2 and 12.8
16.2 - 12.8 = 3.4
Since the common difference is the same for any of the terms taken , the common difference is 3.4
Hope this helps you
Answer:
3.4
Step-by-step explanation:
This is URGENT! Please help me solve this question with full solutions
Answers
Answer:
B
Step-by-step explanation:
Given
[tex]\frac{1}{(t-2)^2}[/tex] = 6 + [tex]\frac{1}{(t-2)}[/tex] ( multiply through by (t - 2)²
1 = 6(t - 2)² + t - 2 ← distribute parenthesis and simplify
1 = 6(t² - 4t + 4) + t - 2
1 = 6t² - 24t + 24 + t - 2
1 = 6t² - 23t + 22 ( subtract 1 from both sides )
6t² - 23t + 21 = 0 ← in standard form
(2t - 3)(3t - 7) = 0 → in factored form
Equate each factor to zero and solve for t
2t - 3 = 0 ⇒ 2t = 3 ⇒ t = [tex]\frac{3}{2}[/tex] ← p
3t - 7 = 0 ⇒ 3t = 7 ⇒ t = [tex]\frac{7}{3}[/tex] ← q
Thus
p × q = [tex]\frac{3}{2}[/tex] × [tex]\frac{7}{3}[/tex] = [tex]\frac{21}{6}[/tex] = [tex]\frac{7}{2}[/tex] → B
Which pair of fractions shows a correct comparison? A.2/3 = 5/10 B.2/3 1/9 D.1/3 = 3/10 E.1/3 > 5/6 F.1/3 < 4/12
Answers
The transitive property of equality states that _____. if a = b, then b = a if a = b, then ac = bc if a = b and b = c, then a = c if a = b and c = c, then a + b = b + c
Answers
Answer:
If a = b and b = c, then a = c
Step-by-step explanation:
The transitive property of equality tells us that if we have two things that are equal to each other and the second thing is equal to a third thing, then the first thing is also equal to the third thing.
Answer:
If a = b and b = c, then a = c
Step-by-step explanation:
i got it right on a test
5. What are the names of the segments ?
6. What are the names of the rays ?
Answers
DF
Answer:
de ef and df
Step-by-step explanation:
This equation shows how the total cost of visiting the art museum as a member is related to the number of visits. c = v + 11 The variable v represents the number of visits to the art museum, and the variable c represents the total cost of those visits. What is the maximum number of visits a member of the art museum can make for a total cost of $14?
Answers
Answer:
6
Step-by-step explanation:
C=9.2v + 21.2
76.4 = 9.2v + 21.2
76.4 - 21.2 = 9.2v
55.2 = 9.2v
v= 55.2 / 9.2 = 6
(Giving Branliest)
The length of a desk is 3.5 feet. How many centimeters is the length? (There are 2.54 cm in an inch)
A. 60
B. 117.12
C. 120.23
D. 106.68
Answers
Answer:
106.68 cm
Step-by-step explanation:
Change ft to inches
3.5 ft * 12 inches / 1 ft = 42 inches
Change inches to cm
42 inches * 2.54 cm/ inch =106.68 cm
Answer:
106.68cm
Step-by-step explanation:
divide by feet untill you get inches
square root of 87 to the nearest 10th
Answers
Answer:
9.3
Step-by-step explanation:
Step 1: Calculate. We calculate the square root of 87 to be: √87 = 9.32737905308882.
Step 2: Reduce. 9.32.
Step 3: Round. Round 9.32 so you only have one digit after the decimal point to get the answer: 9.3.
- Suppose Q is the midpoint of PR. Use the information to find the missing value. PQ = 3x + 14 and QR = 7x - 10; Find x.
Answers
Answer:
x =6
Step-by-step explanation: Q is the midpoint of PR.
Therefore PQ = QR
3 x + 14 = 7 x -10
-14 -14
3 x = 7 x-24
-7x -7x
-4x = -24 Divide both sides by -4
x = 6
The value of x for PQ = 3x + 14 and QR = 7x - 10 is 6 units.
What is midpoint of line segment?
The midpoint divides the line segment into two equal parts.
It is given that Q is the midpoint of PR which implies Q will divide PQ into two equal parts that is PQ (3x+14) equals QR (7x-10). now calculating x value :
[tex]\begin{aligned}PQ&=QR\\3x+14&=7x-10\\7x-3x&=14+10\\4x&=24\\x&=6\end{aligned}[/tex]
Therefore, the value of x for PQ = 3x + 14 and QR = 7x - 10 is 6 units.
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5. If median =137 and mean = 137.05, then find the value of mode. (2marks)
Answers
Answer:- 136.9
Step-by-step explanation:
3median=2mean+mode
3(137)=2(137.05)+mode
411=274.1+mode
411-274.1=mode
mode=136.9
At a carnival game, you randomly throw two darts at the board and break two balloons. What is the probability that both the balloons you break are purple? Write your answer as a fraction or percent rounded to the nearest tenth. there are 15
Answers
Details are missing;
A board of 15 balloons. 4 are purple, 3 red, 4 blue, 2 yellow and 2 green
Answer:
the probability that both the balloons you break are purple = 2/35
Step-by-step explanation:
Since there are 15 balloons and 4 are purple. It means that probability of the first balloon being purple is;
4/15
Now, if the first balloon is purple, it means we have 3 purple left out of the remaining 14. Thus probability of the second being purple = 3/14
Thus;
the probability that both the balloons you break are purple = 4/15 × 3/14 = 2/35
Which situation represents a propertional relationship between the hours worked and the amount earned fir matt and jane?
Answers
What is the arc length S what is shown below?
The angle in the image is a central angle în radians.
Answers
Answer:
14 cm
Step-by-step explanation:
The applicable formula is ...
s = rθ
s = (7 cm)(2) = 14 cm
Can some one help me with my advanced math homework it’s due tomorrow
Answers
Answer:
1.) 88
2.) 196
3.) 63
4.) 90
5.) 367.142857143
6.) 695. 2 repeating
7.) 109.285714286
8.) 63.5593220339
Step-by-step explanation:
Georgette created a factor tree and wrote the prime factorization of 72 shown here. A factor tree of 72. 72 branches to 8 and 9. 8 branches to 2 and 4. 4 branches to 2 and 2. 72 = 23 × 9 What is Georgette’s error? A. Georgette should have started the factor tree with 2 × 36. B. Georgette did not complete the factorization; 9 is a composite number. C. Georgette should have expressed 4 as 4 x 1, not 2 x 2. D. Georgette should have expressed 8 as 4 × 4, not 2 × 4.
Answers
Answer:
Georgette did not complete the factorization; 9 is a composite number.
Step-by-step explanation:
9 can be broken down to 3x3
So it the prime factorization of 72 should be 2x2x2x3x3
Georgette’s error is Georgette should have expressed 8 as 4 × 4, not 2 × 4.
The correct option is D.
The correct prime factorization of 72 is 2³ × 3², which means it can be expressed as the product of prime numbers raised to their respective exponents.
Analyzing the factor tree provided by Georgette, we can see that she made an error when branching from 72 to 8 and 9.
The prime factorization of 8 should be 2³, not 2 × 4, and the prime factorization of 9 should be 3², not 2 × 2.
Therefore, Georgette's error is that she have expressed 8 as 2³ × 1 or 4 × 2, not as 2 × 4.
The correct factor tree for 72 would be:
72
/ \
2 36
/ \
2 18
/ \
2 9
/ \
3 3
So, the prime factorization of 72 is 2³ × 3².
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True or False: Segment AB is congruent to segment BC. A B C -2 0 1 3 Select one: True False
Answers
Solving the equation x + 2(x – 5) = 320
will need the following steps:
1. x + 2x + 10 = 320
II. 3x + 10 = 320
III.
3x = 310
310
IV.
x =
3
Which step above is incorrect?
A Step
B Step III
C Step IV
D All steps are correct
Lo
Answers
Answer:
A. Step I
Step-by-step explanation:
Appropriate application of the distributive property would give ...
x +2x -10 = 320 . . . . . . . does not match step I
Further solution steps would be ...
3x -10 = 320
3x = 330
x = 110
101) Nicole was 16 years old twelve years ago.
How old is she now?
help asap please!!!
Answers
Hey there! I think Nicole would be 28.
Mrs. Kim spent $4.77 on her favorite imported cheese. She bought 9/10 of a pound. Find how much cheese cost per pound.
Answers
A thermometer comes with a guarantee that the stated temperature differs from the actual temperature by no more than 1.5 degrees Fahrenheit. Write an equation to represent the minimum and maximum actual temperatures when the thermometer states that the temperature is 87.4 degrees Fahrenheit.
Answers
Answer:
The equation is;
T = 87.4 ± 1.5
Maximum value of T = 88.9 °F
Minimum value of T = 85.9 °F
Step-by-step explanation:
We are given the stated temperature as 87.4 °F
Now, we are told that this stated temperature differs from the actual temperature by no more than 1.5 degrees Fahrenheit.
Thus, if the actual temperature is T, it means that T should either be 1.5 more than 87.4 or 1.5 less than 87.4.
Thus the equation is;
87.4 ± 1.5 = T
So maximum value of T = 87.4 + 1.5 = 88.9 °F
While minimum value of T = 87.4 - 1.5 = 85.9 °F
Danny and 4 friend go to the movies. Each person buys a movie ticket for $10, a snack for $2 and a drink for $3. Write an expression which shows how much Danny and his friends spent.
Answers
8000647 dollars
Step-by-step explanation:
broggxtxycycuvuh8y7rtwh4w5iwutettixgdbf
NEED HELP FAST!!! Determine the momentum: An electron (m= 9.1 x 10-31 kg) moving at 2.18 x 106 m/s (as if it were in a Bohr orbit in the H atom)
Answers
Answer:
p= (9.1 x 10^-31)(2.18 x 10^6) p = 1.9 x 10^-22kg*m/s
Step-by-step explanation:
for i said so
The momentum of electron is [tex]1.9\times 10^{26}[/tex] kg m per second.
Given, mass of electron is [tex]9.1\times 10^{-31}[/tex] kg.
And its velocity is [tex]2.18 \times 10^6[/tex] m per s.
We have to calculate its momentum.
We know that momentum is numerically equal to the product of mass and velocity of a particle and denoted by p.
So, [tex]p=mv[/tex]
[tex]p= 9.1\times10^{-31}\times2.18\times10^{6}[/tex]
[tex]p=19.838\times10^{25}[/tex]
[tex]p=1.9\times10^{26}[/tex]
Hence the momentum of electron is [tex]1.9\times 10^{26}[/tex] kg m per second.
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A bike shop rents bikes for $4.50 per hour, plus a $7.50 insurance charge. For how many hours can Peter rent a bike if he has $30?
Answers
Answer:
With $30, Peter can afford 5 hours
Step-by-step explanation:
Given
Insurance Charge = $7.5
Charges = $4.5 per hour
Required
Determine the number of hours $30 can afford
First, we need to determine the equation.
Total Charges = Charges per hour + Insurance Charge
Substitute values for Charges per hour and Insurance Charge
Total Charges = 4.5 per hour + 7.5
Let the number of hours be n;
So,
Total Charges = 4.5n + 7.5
To calculate Peter's; substitute 30 for total charges
[tex]30 = 4.5n + 7.5[/tex]
Subtract 7.5 from both sides
[tex]4.5n = 30 - 7.5[/tex]
[tex]4.5n = 22.5[/tex]
Divide both sides by 4.5
[tex]n = \frac{22.5}{4.5}[/tex]
[tex]n = 5[/tex]
Hence;
With $30, Peter can afford 5 hours
1/2a+6b/7 Verbal Expression?
Answers
Answer:
one half of a plus six times b divided by seven
Step-by-step explanation:
18 = 3(3x − 6) multi step equations show all steps pls
Answers
Answer:
x=4
Step-by-step explanation:
18 = 3(3x − 6)
Divide each side by 3
18/3 = 3( 3x-6)/3
6 = 3x-6
Add 6 to each side
6+6 = 3x-6+6
12 = 3x
Divide by 3
12/3 = 3x/3
4 =x
Answer: 4 = x
Step-by-step explanation: To solve this equation, we start by
distributing the 3 through the parenthses on the right side.
3(3x) is 9x and 3(-6) is -18.
So our equation now reads 18 = 9x - 18.
Our next step is to get the x term by itself on the right side.
So we add 18 to both sides to get 36 = 9x.
Now divide both sides by 9 to get 4 = x.
-3(-9v-4)-2(v-2)????
Answers
Solution: Distribute the -3 to the whole equation in the parenthesis. This will make the equation 27v+12-2(v-2). Do the same thing with the -2 and the other parenthesis. This will make the equation 27v+12-2v+4. Combine like terms. This will make the equation 25v+16.
Hope this helped
Solve 1. At a concert, a band sold t-shirts for $18 and hats for $12. They sold 60 t-shirts and hats combined for a total of $870. How many t-shirts did they sell? How many hats?
Answers
Answer:
25 t-shirts and 35 hats were sold
Step-by-step explanation:
Here, we want to calculate the number of hats and the number of t-shirts sold.
Let the number of hats be h and the number of t-shirts be t
The sum of both is 60;
Mathematically;
h + t = 60 •••••••••••(i)
The total revenue from selling h hats at $12 per one is 12 * h = $12h
The total revenue from selling t t-shirts at $18 per one is 18 * t = $18t
So the addition of this gives the total;
12h + 18t = 870 ••••••••(ii)
From i, h = 60-t; substitute this into ii
12(60-t) + 18t = 870
720 -12t + 18t = 870
720 + 6t = 870
6t = 870 -720
6t = 150
t = 150/6
t = 25
From the substitution;
h = 60-t
h = 60-25
h = 35
Answer:
48 hats
Step-by-step explanation:
im not sure if this is the right answer but i hope this helps
Point C is on line segment \overline{BD} BD . Given BC=x+4,BC=x+4, CD=5x,CD=5x, and BD=5x+7,BD=5x+7, determine the numerical length of \overline{CD}. CD .
Answers
Answer:
[tex]CD = 15[/tex]
Step-by-step explanation:
Given
[tex]BC = x + 4[/tex]
[tex]CD = 5x[/tex]
[tex]BD = 5x + 7[/tex]
Required
Determine CD
Since Point C is on segment BD, then we have
[tex]BD = BC + CD[/tex]
Substitute x + 4 for BC; 5x for CD and 5x + 7 for BD
[tex]5x + 7 = x + 4 + 5x[/tex]
Collect Like Terms
[tex]5x - 5x - x = 4 - 7[/tex]
[tex]- x = -3[/tex]
Multiply both sides by -1
[tex]x = 3[/tex]
Substitute 3 for x in [tex]CD = 5x[/tex]
[tex]CD = 5(3)[/tex]
[tex]CD = 15[/tex]
Hence, the length of CD is 15 units
Answer:
Step-by-step explanation:
Given
Required
Determine CD
Since Point C is on segment BD, then we have
Substitute x + 4 for BC; 5x for CD and 5x + 7 for BD
Collect Like Terms
Multiply both sides by -1
Substitute 3 for x in
Hence, the length of CD is 15 units
Step-by-step explanation:
-8 is a term. true or false
Answers
Answer:
false
Step-by-step explanation:
Write 8660 in scientific notation
Answers
Answer:
8.66 x 10^3
Step-by-step explanation:
8.66 * 1000 (10^3) = 8660
This is the answer