Using Heron's formula the area of the triangle is 15.78cm²
What is Heron's FormulaHeron's formula is a formula for calculating the area of a triangle when the lengths of all three sides are known. It is named after the Greek mathematician and engineer Heron of Alexandria (c. 10–70 AD). The formula is:
Area = √s(s-a)(s-b)(s-c)
Where a, b, and c are the lengths of the sides of the triangle, and s is the semi-perimeter, or half the perimeter, of the triangle, given by:
s = (a + b + c)/2
Let's define the variables as;
a = 5.1b = 7.8c = 6.2s = (5.1 + 7.8 + 6.2) / 2
s = 9.55cm
The area can be calculated as;
A = √s(s - a)(s - b)(s - c)
A = √9.55(9.55 - 5.1)(9.55 - 7.8)(9.55 - 6.2)
A = 15.78cm²
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What is the value of x?
O 6
6V3
12
O 12
o
12V3
60°
Answer:
The answer is 12V3 60°
Hope I help you
A geologist visits 60 volcanoes in Alaska and California. What if 40% of the volcanoes were in California? How many volcanoes would the geologist have visited in California and how many in Alaska?
Answer : in California there are 24 volcanoes while in Alaska there are 36 volcanoes.
Step-by-step explanation:
Total number of volcanoes = 60.
40% of the volcanoes where in California.
i.e 100% - 40% = 60%.
60% of the volcanoes were in Alaska.
In California = 40/100 × 60 = 24 volcanoes.
In Alaska = 60/100 × 60 = 36 volcanoes.
Squares $ABCD$ and $EFGH$ are equal in area. Vertices $B$, $E$, $C$, and $H$ lie on the same line. Diagonal $AC$ is extended to $J$, the midpoint of $GH$. What is the fraction of the two squares that is shaded
The fraction of the two squares that is shaded exists 5/16 area shaded.
What is the difference between diagonal and vertices?A diagonal is a line segment connecting two opposite corners (vertexes) of a polygon, however it is not an edge (side). In other words, it connects any two non-adjacent polygonal vertices. Therefore, by connecting any two vertices in a polygon directly (i.e., without using a side), we create a diagonal.
A line segment known as a diagonal joins two polygonal vertexes (corners), although it is not an edge (side). To put it another way, it joins any two polygonal vertices that are not adjacent. Therefore, by connecting any two vertices in a polygon directly (i.e., without using a side), we create a diagonal.
The triangle on the bottom exists 1/2 × 1/2 × 1/2 of the original area of the lower square = 1/8 of the lower square
2 square = [1/2 (square) + 1/8 (square) ] / 2 square
= 5/16 area shaded
Therefore, the fraction of the two squares that is shaded exists 5/16 area shaded.
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The fraction of the two squares that is shaded exists 5/16 area shaded.
What is the difference between diagonal and vertices?A diagonal is a line segment that joins two opposed polygonal corners (vertexes), although it is not an edge (side). In other words, it joins any two polygonal vertices that are not neighbouring. As a result, we can make a diagonal by directly joining any two vertices of a polygon (i.e., without utilising a side).
Although it is not an edge, a line segment known as a diagonal connects two polygonal vertexes (corners) (side). In other words, it connects any non-adjacent pair of polygonal vertices. As a result, we can make a diagonal by directly joining any two vertices of a polygon (i.e., without utilising a side).
The triangle on the bottom exists 1/2 × 1/2 × 1/2 of the original area of the lower square = 1/8 of the lower square
2 square = [1/2 (square) + 1/8 (square) ] / 2 square
= 5/16 area shaded
Therefore, the fraction of the two squares that is shaded exists 5/16 area shaded.
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Which expression is equivalent to -3x + 5x - 2y + 5x? *
A .13x -2y
B. 7x -2y
C. 7x + 2y
An object is launched at an upward velocity of 9696 feet per second from the top of a building 160160 feet above the ground. Use the vertical motion model h=-16t^{2}+vt+c, where hh is the ending height of the object, cc is the initial height, in feet, of the object, tt is the time in seconds, and vv is the velocity of the object.
How long will it take the object to reach the maximum height and what is the maximum height? Fill in the blanks with the appropriate values.
The time that it will take for the object to reach maximum height is given as follows:
3 seconds.
The maximum height is given as follows:
304 feet.
How to model the object's height?The object's height is modeled by a quadratic function in the following format:
h = -16t² + v(0)t + h(0).
In which:
v(0) is the initial velocity.h(0) is the initial height.The parameters for this problem are given as follows:
v(0) = 96, h(0) = 160.
Hence the function is defined as follows:
h(t) = -16t² + 96t + 160.
Meaning that the coefficients of the quadratic function are given as follows:
a = -16, b = 96, c = 160.
The coefficient a is negative, meaning that this is a concave down quadratic function, thus the vertex of the quadratic function represents the maximum height.
The t-coordinate of the vertex is given as follows:
t = -b/2a = -96/-32 = 3 seconds.
Then the maximum height is of:
h(3) = -16(3)² + 96(3) + 160
h(3) = 304 feet.
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help!!!
Let f(x) represent a function.
Which descriptions match the given transformations?
Drag and drop the answers into the boxes.
f(x−5/3)
f(x)−5/3
The function f(x - 5/3) is translated 5/3 units right and the function f(x) - 5/3 is translated 5/3 units down.
What are some rules for the transformation of functions?Suppose we have a function f(x).
f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).
f(x ± c) = Horizontal left/right shift by c units (x - + c, y).
(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).
f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).
f(-x) = Reflection over the y-axis, (-x, y).
-f(x) = Reflection over x-axis, (x, -y).
Given, A function f(x) is transformed to f(x - 5/3) this results in f(x) is translated 5/3 units to the right along the x-axis.
And, The transformation f(x) - 5/3 is translated 5/3 units down along the y-axis.
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1. Combine the like like terms
14 + 8x + 2y -5x - 2
Answer: 12 +3x +2y
Step-by-step explanation:
like terms:
14 and -2
8x and -5x
2y
combine and there you go. hope this helped.
(btw. the equation can vary in different forms, like 3x+2y+12 or 2y+3x+12. They are all correct.)
Steve noticed that there were 72 lights on and 78 lights turned off.
what precent of the lights are on?
Answer:
49% of the lights are on!
Theoretically, if a fruit is chosen 300 times, how many times would you expect to pick an apple or banana?
The answer is 90 times to expect picking an apple or banana.
If the fruit is chosen 300 times, then it would be a 1:3 ratio of apple or banana to the other fruits. This means that 100 times out of the 300 times, you would expect to pick an apple or banana.
Predicting the outcome using the experiment results because 300 times is a sizable number.
8+4 is either an apple or a banana in 40 times.
Therefore, the solution would be x in 300 times.
[tex]x = \frac{300}{40}[/tex] x12
x = 90
Therefore, the probability of picking an apple or banana is 90 times.
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Can someone help me out my grades are bad
Answer:
= 2700
Step-by-step explanation:
1300+700+700
a snail traveled 3/4 mile. a radar gun clocked it at 3/10 of a mile per hour. how many hours will it take to reach 3/4 mile ?
Answer:12/30
Step-by-step explanation:
3/10 divided by 3/4 what is your answer? divide. 3/10 divided by 3/4 is 12/30. Simplify if you need to.
What is the value of x between the two triangles? *no bots or else you will be reported*
Answer:
x = 25
Step-by-step explanation:
First we need to show that these two triangles are similar. Add up the angles 68 and 38 degrees in the first triangle, and then subtract this sum from 180 degrees. This results in 74 degrees, which matches 74 degrees in the second triangle.
Next we write and solve an equation of ratios:
6 10
----- = -------
15 x
Cross multiplying returns 6x = 150, so that x = 25.
Note that 6/15 is the ratio of the shortest sides, and 10/x is the ratio of the longest sides.
A catering company is setting up tables for a big event that will host 764 people when they set up the tables they need 2 forks for each child and 5 forks for each adult the company ordered a total of 2992 forks set up a system of equations involving the number of adults,a and the number of children,c and solve to find out how many of each attended the event
Answer:
488 adults and 276 children
Step-by-step explanation:
So, we need two linear equations here to start, and we do have them.
Our first linear equation tells us how we get the number of forks:
2c + 5a = 2992
And the second tells us the number of people there:
c + a = 764
I will solve this using substitution. We start by minusing a from both sides in the second equation, giving us:
c = 764 - a
Then, we will substitute this into our first equation, giving us:
2(764 - a) + 5a = 2992
Then, we will open the parentheses, giving us:
1528 - 2a + 5a = 2992
Combining like terms and subtracting 1528 from both sides gives us:
3a = 1464
Dividing by 3:
a = 488
So there were 488 adults. Then, we take our original second equation and substitute 488 for a, giving us:
488 + c = 764
Minus 488 from both sides gives us:
c = 276
So, there were 276 children. In total, we had 488 adults and 276 children.
Hope this helped!
What is the equation of a circle with center (5, -7) and Circumference = 12
(No links)
Answer:
(x-5)2+(y+7)2=4
Step-by-step explanation:
Job 1 the base pay is 30 and the job pay 150 total for an 8 hour day job 2 y=17x+25 which one pays more
Answer:
Job 2
Step-by-step explanation:
Find how much job 1 pays for 1 hour:
(150 - 30) ÷ 8 = 15
Job 1 pays $15 per hour.
Assuming variable x stands for number of hours worked, job 2 pays $17 an hour.
Put job 1 into a similarly formatted equation:
Variable y = total pay
y = 15x + 30
Compare job 1 and 2:
Job 1: 15x + 30
Job 2: 17x + 25
Just by looking at the two expressions, there is no obvious higher paying job so let's try plugging in 8 hours for x:
15(8) + 30 = 150
17(8) + 25 = 161
$161 is more than $150 so job 2 pays more.
One side of a right triangle has a length of 12 feet. Which of the following could be lengths for the two other sides of the right triangle?
I. 5 feet and 13 feet
II. 9 feet and V63 feet
III. V2 feet and V10 feet
A. III, and III
B. I and II only
C. I only
D.II and Ill only
Answer:
B
Step-by-step explanation:
Apply the Pythagorean Theorem to determine whether or not the given triplets represent right triangles or not:
I. 5 feet and 13 feet: 5^2 + 12^2 = 13^2 is TRUE
II. 9 ft and √63 ft: 9^2, 63, 12^2: 63 + 81 do add up to 144 TRUE
III. 2, 10, 12^2: 2 + 10 do NOT add up to 144. FALSE
Answer B is correct
Jeff is three years younger than twice Michael's age, m. Which equation can be used to find Jeff's age?
Answer:
j = 2m-3
Step-by-step explanation:
Breakdown:
2m = Twice Michael's age
-3 = Three years younger
Help answer part a and b please no links!!!
Answer:
a) 64.37m^2 b) 15.71 meters
Step-by-step explanation:
Area of circle = [tex]\pi r^2[/tex]
Rectangle: quadrilateral, parallelogram, all angles are 90 degrees
a) The area of the park not covered by the wading pool is equivalent to the area of the wading pool subtracted from the total area:
because the radius of the pool is 2.5
Area of wading pool = [tex]\pi 2.5^2=6.25\pi m^2[/tex]
The total area of the park is length x width because it is a rectangle
Area of park = [tex]14*6=84m^2[/tex]
Area of the park not covered by the wading pool = [tex]84-6.25\pi[/tex] ≈ 64.37m^2
b) The meters of fence needed to surround the circular pool is the circumference of the circle
Circumference: [tex]2.5*2\pi=5\pi[/tex] ≈ [tex]15.71[/tex]
What is the probability that all the members of your mathematics class have different birthdays? What is the probability that there is a birthday coincidence in the group?
Supposing a band of 20 members, we have that the probabilities are given as follows:
All have different birthdays: 0.9466 = 94.66%.There is a birthday coincidence: 0.0534 = 5.34%.What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The parameter values for this problem are given as follows:
n = 20, as the band has 20 members.p = 1/365, as the year has 365 days, hence the probability of a person having a given day as a birthday is of 1/365.The probability that all members have different birthdays is of P(X = 0), hence:
P(X = 0) = (1 - 1/365)^20 = 0.9466.
Hence the probability that there is a birthday coincidence is of:
P(X > 0) = 1 - P(X = 0) = 1 - 0.9466 = 0.0534.
Missing InformationThis problem is incomplete, hence we suppose a band of 20 members.
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Use the FOIL Method to find (k+5)(k−1).
Answer:
(k+5)(k−1)=k2+4k−5
Step-by-step explanation
A. 109.45
B. 115.14
C. 117.85
D. 154.13
Answer: C
Step-by-step explanation: i dont know srry
1. |2x + z| + 2y
a = –2, b = –3, c = 2, x = 2.1, y = 3, and z = –4.2.
2. 4a – |3b + 2c|
Answer:
6 and -13
Step-by-step explanation:
Absolute ValueAbsolute Values are magnitudes (only positive values) of any values (be it positive or negative.)
Example: |4.5| = 4.5, |-6.7| = 6.7
Solution1. |2x + z| + 2y
= |2(2.1) + (-4.2)| + 2(3)
= |4.2 - 4.2| + 6
= 0 + 6
= 6
2. 4a - |3b + 2c|
= 4(-2) - |3(-3) + 2(2)|
= -8 - |-9 + 4|
= -8 - |-5|
= -8 - 5
= -13
what is the value of x
Answer:
the answer is 52 because all angels are equal
Step-by-step explanation:
Math joke: Tell Algebra to stop finding his X She dont want him anymore!!!!
lol hope this helps!
Answer:
128 is your answer
Step-by-step explanation:
Triangle's angles add up to 180 degrees because one exterior angle is equal to the sum of the other two angles in the triangle. In other words, the other two angles in the triangle (the ones that add up to form the exterior angle) must combine with the third angle to make a 180 angle
180-52=128
52+128=180
whats an=19-7(n-) in function form
The given expression is the explicit equation for arithmetic progression whose first term is 19 and the common difference is -7.
What is arithmetic progression?Arithmetic progression is the series of numbers that have common differences between adjacent values.
here,
Given expression,
an=19-7(n-1)
The above-given expression is an explicit formula for the arithmetic progression,
Comparing the given expression with general expression an = a + d[n-1]
From the above comparison, we
first term,a = 19 and
the common difference, d = -7
Thus, the given expression is the explicit equation for arithmetic progression whose first term is 19 and the common difference is -7.
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Marty and Ethan both wrote a function, but in different
ways.
Whose function has the larger slope?
Marty
y+3 = {(x +9)
Marty's with a slope of 2/3
Ethan's with a slope of 2/5
Marty's with a slope of 1/3
Ethan's with a slope of 1/5
Ethan
х
y
-4
9.2
-2
9.6
0
10
2
10.4
Answer:
Marty's with a slope of 1/3
Step-by-step explanation:
edge2021
Marty's function has the larger slope of 1/3.
What is meant by slope of a line ?The slope of a line is computed as the ratio of the change in the y-axis to the change in the x-axis.
Marty's equation is given as,
y + 3 = 1/3(x + 9)
The equation for point slope form is,
y - y₁ = m(x - x₁)
Where, m is the slope of the line.
So, m = 1/3
Consider a function written by Ethan,
(-4, 9.2) and (-2, 9.6)
Slope of the line,
m = (y₂ - y₁)/(x₂ - x₁)
m = (9.6 - 9.2)/(-2 - -4)
m = 0.4/2 = 0.2
Hence,
Marty's function has the larger slope of 1/3.
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help plss sjsjsjd SUUWU
Answer:
A = 18π units²
Step-by-step explanation:
The area (A) of the semicircle is calculated as
A = [tex]\frac{1}{2}[/tex] πr² ( r is the radius ) , then
A = [tex]\frac{1}{2}[/tex]π × 6² = [tex]\frac{1}{2}[/tex]π × 36 = 18π ← exact answer
To get an A in her math class, Jada needs to have at least 90% of the total number of points possible. The table shows Jada’s results before the final test in the class.
1. ) Does Jada have 90% of the total possible points before the final test? Explain how you know.
2. ) Jada thinks that if she gets at least 92 out of 100 on the final test, she will get an A in the class. Do you agree? Explain
1) Jada does not have 90% of the total possible points before the final test.
2) If Jada gets at least 92 out of 100 on the final test, she will not get an A in the class.
From the following table of Jada’s results before the final test in the class the total number of points possible:
150 + 100 + 100 + 100 = 450
And Jada’s total points before the final test:
141 + 87 + 81 + 91 = 400
To check whether Jada have 90% of the total possible points before the final test, we find the percentgae of Jada’s total points.
(400/450) × 100 = 88.89%
This means, Jada does not have 90% of the total possible points before the final test.
After final test, the total number of points possible: 450 + 100 = 550
And if she gets at least 92 out of 100 on the final test, her total points would be,
400 + 92 = 492
And the percentgae of Jada’s total points would be,
(492/550) × 100 = 89.45%
Given that Jada needs to have at least 90% of the total number of points possible.
so, she will notl get an A in the class.
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How can the surface area be calculated for the rectangular prism below?
= 5cm
w=4 cm
1 = 12 cm
A. Multiply 2 by the length, width and the height
B. Add the length, width and the height
C. Calculate the product of the length and width, height and width and height and length then
multiply by 2.
D. Multiply the length, width and the height then divide the answer by 2.
Answer:
c Calculate the product of the length and width, height and width and height and length then
multiply by 2.
Step-by-step explanation:
it will look like this 2lw+2hw+2hl
Contradiction Club holds a yearly proof competition, with special unique prizes for first, second, third, and fourth place. If 16 students enter the competition this year, how many ways can these prizes be distributed among the students
A proof competition is held annually by Contradiction Club, with special prizes awarded for first, second, third, and fourth place. If 16 students participate in the competition this year, the awards can be allocated among the students in 120 different ways.
How many ways can five different prizes be distributed among five people?120 ways, The first person has a choice from 5 prizes, the second has a choice from 4 prizes, and so on. The awards can be awarded in 5 different ways, or 5 × 4 × 3 × 2 × 1 = 120 different ways. When each student is qualified for each reward, the number of ways that 5 prizes can be distributed to 8 students is. [tex]5^(8)``8^(5)``8xx5!``5 xx 8!`[/tex] You may clear your doubts and achieve good exam results with the help of step-by-step solutions provided by specialists.For the first reward, there are 8 options. There are then 7 options for the second prize. Furthermore, there are 6 options for the third prize. As a result, there are 336 ways: 8 × 7 × 6. ∴ Total ways = 4× 3 ×2 = 24 ways = 4!To learn more about Contradiction Club refer to :
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Pls help me with this, no jokes or links please
Answer: D
Step-by-step explanation:
v=4/3*3.14*13^2