Given: triangle ABC,
Angle B=120°,
AB= 6, BC = 10
Find: The area of triangle ABC
Answers
The area of triangle ABC when Angle B=120°, AB= 6, BC = 10 is 25.980 square unit.
As per the question statement, we are supposed to find out the area of triangle ABC in which angle B=120°, AB= 6, BC = 10.
Lets find out AC for which we should know about Cosine formula
i.e., [tex]AC^{2} =AB^{2} +BC^{2} -2(AB)(BC)cos(B)\\AC^{2} =6^{2} +10^{2} -2*6*10cos120\\AC^{2}= 36+100-120*(-0.5)\\AC^{2}=196\\AC=\sqrt{196} =14[/tex]
Hence We have measures of all three sides of the triangle ABC.
Now we use the Heron's formula for calculating the area of triangle ABC.
We need semi perimeter i.e., [tex]s=\frac{AB+BC+AC}{2}[/tex]
[tex]s=\frac{30}{2} =15[/tex]
Now Area is given by,
[tex]area=\sqrt{s(s-AB)(s-BC)(s-AC)} \\area=\sqrt{15(15-6)(15-10)(15-14)} \\area=\sqrt{15*9*5*1} \\area=\sqrt{675} \\area = 25.980 unit^{2}[/tex]
Area: The space occupied by an object or a shape in square units.Cosine Formula: Uses the cosine of an angle to determine the remaining sides of the triangle.Heron's Formula: Uses the measure of the all sides of triangle to calculate the area of the triangle.To learn more about Heron's questions, click on the link given below:
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Related Questions
The figure is made up of two semicircles. Find the perimeter of the shaded region using 3 . 143.14 for \mathrm{\pi }π.
Answers
Answer:
69.66 cm
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4.3 cm}\underline{Circumference of a circle}\\\\ $C=\pi d$\\\\where $d$ is the diameter\end{minipage}}[/tex]
From inspection of the given diagram:
Diameter of the larger circle = 5 + 14 + 4 = 24 cmDiameter of the smaller circle = 14 cmThe perimeter of a two-dimensional shape is the distance all the way around the outside.
Therefore, the perimeter of the given shaded region is the sum of half the circumference of the larger circle, half the circumference of the smaller circle, and the two 5 cm ends.
[tex]\begin{aligned}\sf \implies Perimeter & = \sf \dfrac{1}{2} \pi (24) + \dfrac{1}{2} \pi (14) + 5 + 5\\& = \sf \dfrac{1}{2}(3.14)(24) + \dfrac{1}{2}(3.14)(14) +10\\& =\sf 37.68+ 21.98+10\\& =\sf 69.66\:\:cm\end{aligned}[/tex]
Therefore, the perimeter is 69.66 cm.
The perimeter of the shaded region is 12.56 times the radius of one of the semicircles.
To find the perimeter of the shaded region, we need to find the total length of all the boundaries.
The shaded region consists of two semicircles, so we can start by finding the circumference of each semicircle.
The formula for the circumference of a circle is C = 2πr.
Since we have two semicircles, we need to find the radius for each and then add the two circumferences together to get the total perimeter.
Let's say the radius of each semicircle is r.
Using the given value of π as 3.14,
the circumference of one semicircle is 2 * 3.14 * r = 6.28r.
Therefore, the total perimeter is 6.28r + 6.28r = 12.56r.
So, the perimeter of the shaded region is 12.56 times the radius of one of the semicircles.
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Does anyone know this answer??
Answers
Answer:
Whole numbers
Step-by-step explanation:
Integers and whole numbers are similar, but integers contain negatives and whole numbers do not. Since a city cannot have a negative population count, we'd prefer whole numbers.
Rational numbers allow for non-whole numbers, but again, a city can't havea population of something and a half person. We again prefer whole numbers.
Answer:
Whole Numbers
Step-by-step explanation:
So cities Have complete number the represent it so integers are negative numbers and fractions and rational numbers are fractions so whole number is the only number that are complete and is not a fraction so therefore the only answer it could be is whole numbers
English only and correct answers only thank you
Find the product of 4.5 x 1012 and 5.12 x 109. Write the final answer in scientific notation.
23.04 x 1021
23.04 x 1022
2.304 x 1021
2.304 x 1022
Answers
Answer: 23.04*10²¹.
Step-by-step explanation:
4.5x10¹²*5.12x10⁹=(4,5*5.12)*(10¹²*10⁹)=23.04*10¹²⁺⁹=23.04*10²¹.
Brianna is keeping track of how much money she saves.
She has $60 saved and saves another $15 each week.
How long will it take Brianna to save enough to buy a pair
of $180 sneakers? Show or explain your thinking.
Answers
15x + 60 = 180
We can subtract 60 from both sides to isolate the variable term:
15x + (60 - 60) = 180 - 60
15x = 120
120 / 15 gives us 8.
It will take Brianna 8 weeks to save enough to buy a pair of $180 sneakers.
What is the area of ABC?
I need help asap!
Answers
Step by step:
5x2x7 = 70
70 divided by 2 = 35
formula: Length•Width•Height divided by 2
. assume that the box contains 5 balls: 3 green, 1 white, and 1 red. balls are drawn in succession without replacement, and their colors are noted until a green ball is drawn.
Answers
(a)white, green, green, green, blue or green, white, green, green, blue, green, green, white, green, blue, or a green, green, green, white
(b)14 outcomes.
What is sample space?There are many situations where we cannot forecast the results with certainty, but we can always state all the possible outcomes, such as when we toss a coin or roll a die. We refer to these occurrences as random phenomena or random experiments. These kinds of random events or experiments typically include probability theory. What, though, is a sample space? A sample space for the experiment is a collection of all such potential outcomes. In other terms, the sample space, which is typically represented by the letter S, is the collection or set of potential outcomes in a random experiment. When doing a random experiment, the sample space is represented.
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3. BUSINESS Katherine spends $700.50 each month for rent and supplies to run her hair salon. If she charges $15 for a haircut, how many haircuts must Katherine do to cover her monthly expenses? Find the decimal answer then, round to the nearest whole number.
Answers
Answer: about 47 haircuts
the sides of a triangle are of lengths 13, 14, and 15. the altitudes of the triangle meet at point h
Answers
The ratio HD:HA is 5/11 when the sides of a triangle are of lengths 13, 14, and 15.
What do you mean by heron's formula?When the lengths of all three sides are known, the geometry formula Heron's formula, which bears Hero of Alexandria's name, determines the area of a triangle. There is no need to first determine the angles or other distances in the triangle, unlike other triangle area formulas. Heron of Alexandria is credited with developing the Heron's formula, which determines the area of a triangle in terms of the lengths of its sides. If the side lengths are represented by the symbols a, b, and c: Area is equal to the square root of (a + b + c)/2, where s is half the perimeter.
By Heron's Formula, the area of this triangle is 84 Thus the height perpendicular to AB has a length of 11.2, and by the Pythagorean Theorem, AE and EB have lengths 6.6 and 8.4, respectively. These lengths tell us that C is at.
The slope of BC is (0-11.2)/(15-6.6)=-4/3, and the slope of AD is 3/4 by taking the negative reciprocal of -4/3. Therefore, the equation of line AD can best be represented by y=(3/4) x.
We next find the intersection of CE and AD . We automatically know the x -value; it is just 6.6 because CE is a straight line hitting (6.6,0). Therefore, the y -value is at (3/4)* 6.6=4.95. Therefore, the intersection between CE and AD is at (6.6,4.95) .
We also need to find the intersection between BC and AD . To do that, we know that the line of AD is represented as y=3/4x, and the slope of line BC is -4/3. We just need to find line BC 's y-intercept. So far, we have y=-4/3x+b, where b is a real y-intercept. We know that B is located at (15,0), so we plug that into the equation and yield b=20. Therefore, the intersection between the two lines is
(3/4)x=-(4/3)x+20
⇒9x=-16x+240
⇒25x=240
⇒x=9.6
Now y=(3/4)*x=(3/4)*9.6=7.2
⇒y=7.2
After that, we use the distance formula: HA has a length of
√(6.6-0)²+(4.95-0)²=√(1089/25)+(9801/400)
=√(1089*16+9801)/400
=√27225/400=√1089/16=33/4=8.25
and HD has a length of
√(9.6-6.6)²+(7.2-4.95)²=√(3)²+(36/5-99/20)²
=√(9)+(81/16)
=√225/16=15/4=3.75
So the ratio os HD:HA is
⇒3.75/8.25=15/33=5/11
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Select one of the factors of x2y3 − 11x2y + 6y2 − 66.
(x2y + 6)
(x2y − 6)
(y2 + 11)
(y − 3)
Answers
Step-by-step explanation:
The factors of the equation x2y3 - 11x2y + 6y2 - 66 can be found by taking out the common terms.
x2y3 - 11x2y + 6y2 - 66
Let us take out the common from the first two terms.
⇒ x2y(y2 - 11)------>(1)
Take out common from the last two terms.
⇒ + 6 (y2 - 11)------>(2)
By combining these two, we get
x2y(y2 - 11) + 6(y2 - 11)
⇒ (x2y + 6)(y2 - 11)
Answer:
(x^2y + 6)
Step-by-step explanation:
I got it right on the test.
Compare the digits in the hundredths place of 4.241 and 4.25.
Answers
4 is less than 5, so 4.241 is less than 4.25.
Given the numbers are 4.241 and 4.25.
Because 4.241 and 4.25 have the same units and tenth digit (4.2 = 4.2)
so we need to compare the hundredths place that is, 0.041 with 0.05.
A decimal's distance from one whole increases as it increases in size. A decimal is further away from one whole the smaller it is. The amount of digits in each decimal should be your primary point of focus. Each of them contains two digits, allowing for immediate comparison.
The number following the decimal point is called the hundredths place. Round up the number of hundredths if the third number after the decimal is 5 or above. Keep the hundredths number constant if the number in the third position after the decimal point is 4 or less.
0.041 < 0.05
hence we get 4.241 < 4.25
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A school's K-Pop club is learning a new dance to a Korean pop song. They pay the dance
teacher from their bank account, which showed three changes this week.
First, a $60 withdrawal was represented using the number - 60.
• The second change was the opposite of the first.
• The third change was the opposite of the second.
What number represents the third change made to the account?
●
Type the number in the box.
Answers
The number which represents the third change made to the account according to.tge task content is; -60.
What number represents the third change made to the account?According to the task content, the second change was the opposite of the first, -60.
Hence, the second change is; +60 which is the additive inverse.
Ultimately, since the third change was the opposite of the second, it follows that the third change is; -60.
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When the following quadratic equation is written in general form, what is the value of "c"?
-3/4 x^2 + 2 = 0
-8
-2
-6
Unlimited
Answers
Answer:
the answer is
Step-by-step explanation:
c= -6
hope this help
6 divied by 6.48 how to slove it
Answers
Answer:
0.93
Step-by-step explanation:
6/6.48 = 0.92592592592592592592592592592593
Answer:0.92
Step-by-step explanation:
Calculator
If:
JL = 26,
KL=3x + 7, and
JK = 8x + 8,
Find KL.
J
K
L
Answers
Answer:
KL = 10
Step-by-step explanation:
Given:
[tex]JL=26[/tex]
[tex]KL=3x+7[/tex]
[tex]JK=8x+8[/tex]
From inspection of the given diagram:
[tex]JK+KL=JL[/tex]
Substitute the given values into the found equation and solve for x:
[tex]\implies 8x+8+3x+7=26[/tex]
[tex]\implies 11x+15=26[/tex]
[tex]\implies 11x+15-15=26-15[/tex]
[tex]\implies 11x=11[/tex]
[tex]\implies \dfrac{11x}{11}=\dfrac{11}{11}[/tex]
[tex]\implies x=1[/tex]
Substitute the found value of x into the expression for KL:
[tex]\implies KL=3(1)+7[/tex]
[tex]\implies KL=3+7[/tex]
[tex]\implies KL=10[/tex]
Formula we use,
→ JK + KL = JL
Now the value of x will be,
→ (8x + 8) + (3x + 7) = 26
→ 11x + 15 = 26
→ 11x = 26 - 15
→ x = 11/11
→ [ x = 1 ]
Then the value of KL will be,
→ 3x + 7
→ (3 × 1) + 7
→ 3 + 7 = 10
Hence, the value of KL is 10.
please answer all of them with show work! the questions are together.
Answers
Answer:
20: Pattern 8.
21: n * n = 64
Step-by-step explanation:
8*8=64, so assuming that n is the missing variable, if we use 8 in place of n, we have 64, the "equals (=)" value will always change depending on n's value. So assuming n is equal to 8, 8*8=64
what is 2 + 2
a.0
b.69
c.80085
d.106
e.200000000/100000000
Answers
Answer:
e
Step-by-step explanation:
just use a calculator for these questions
A and B agree to share the cost of a $29 pizza based on how much each ate. If B ate the amount that A ate, how much should each pay?
Answers
Answer:
The answer is $14.5 dollars
Step-by-step explanation:
So since B ate the amount A ate, this means they each ate half of the $29 pizza.
Steps:
29 / 2 = 14.5
The answer is $14.5 dollars
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!
Answer:
29/2 = 14.5
Because they both ate half, so paid for the half
Step-by-step explanation:
brainiest, please
$274+$400=___________
Answers
Answer:
$674
Step-by-step explanation: hope you have a good day
Answer:674
Step-by-step explanation: 400+200=600 70+00= 70 4+0=4
Combine like terms to find the perimeter of the figure.
Answers
Answer:
(29x +4) cm
Step-by-step explanation:
The perimeter of a figure is the sum of the lengths of all its sides.
Perimeter of figure
= 5x +5 +x +8x -3 +7x +2 +8x (sum up the lengths)
= 5x +x +8x +7x +8x +5 -3 +2 (group like terms together)
= (5 +1 +8 +7 +8)x +4
= (29x +4) cm
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Find the sum of 1/3+1/8
Answers
Answer:
11/24
Step-by-step explanation:
1/3 + 1/8
find the common denominator
that would be 24
now cross multiply
8/24+ 3/24= 11/24
Answer:11/24
Step-by-step explanation:
When adding fractions, you need to find the lcm of the denominator.
In this case, the lcm for 3 and 8 is 24 so you would do:
1*8
3*8
and
1*3
8*3
so you would get
8/24+3/24
which equals 11/24
Answer this please!!! Im struggling
Answers
Answer: 0.35
Step-by-step explanation:
there are (36)2⋅ 30 candies in a store. what is the total number of candies in the store? (5 points) group of answer choices 312 33 38 34 next
Answers
The total number of candies in the store is 312. It is obtained by using the concept of exponent and power on the given problem.
What is an Exponent?
The number of times a quantity is multiplied by itself is referred to as an exponent or power of the given quantity. For eg: 25, where 5 is an exponent or power of 2 and 2 is called the base of exponent 5. Any quantity raised to the power 0 always returns 1 as result.
Calculation of the total number of candies in the store
(36)2 * 30
Using the properties of an exponent, we have
A number with an exponent of 0 always gives 1
(36)2 * 1
(3)6×2 * 1
312 * 1
312
Thus, the total number of candies in the store is 312.
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Can someone help me please.
Answers
Answer:
1 is 6.45
Step-by-step explanation:
3.25+1.55+1.65=6.45
the points $(1,-2)$ and $(-4,10)$ are adjacent vertices of a square. what is the perimeter of the square?
Answers
The perimeter of the square is 52 units.
In this question,
the points (1, -2) and (-4, 10) are adjacent vertices of a square.
We need to find the perimeter of the square
The side length of a square is the distance between given two points.
Let a be the side length of the square.
[tex]a=\sqrt{(-4-1)^2+(10-(-2)^2)}\\\\ a=\sqrt{25+144}\\\\ a=\sqrt{169}\\\\ a=13[/tex]
The side length of the square is 13 units.
so, the perimeter of a square would be,
P = 4a
P = 4 × 13
P = 52 units
Therefore, the perimeter of the square is 52 units.
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two ships leave a harbor at the same time. the first ship heads north at 20 miles per hour, and the second ship heads west at 15 miles per hour. write an expression that gives the distance d between the ships after t hours.
Answers
According to the statement 25t is the distance between the ships after t hrs.
What is Pythagorean theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental relationship in Euclidean geometry between the three sides of a right triangle. It states that perhaps the area of something like the square on which side would be the hypotenuse is equivalent to the sum of something like the areas of the squares on each of the other two sides.
What Is the Pythagorean Theorem Formula Good For?The Pythagorean theorem is only valid for right-angled triangles. When any two numbers are known, we can use Pythagoras' theorem to compute the unknown sides of something like the triangle. Other real-world applications of Pythagoras' theorem include engineering and architecture.
According to the given information:The first ship travels north at 20 kilometers an hour, while the second travels west at 15 miles per hour.
equation for the given distance between boats after t hours:
Using Pythagoras formula:C² = a² + b²
C = √(a² + b²)
a = dist. traveled in t hrs. of the 1st ship.
b = dist. traveled in t hrs. by 2nd ship.
c = dist. between the two ships after t hrs. (d)
Using formula Distance = speed * time (t)
d = √((20t)²+(15t)²)
d = √(625t²)
d = 25t is the distance between the ships after t hrs.
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there are 30 cars in my building's parking lot. all of the cars are red or white, and a car can have either 2 doors or 4 doors. $\frac{1}{3}$ of them are red, $50\%$ of them are 4-door, and 8 of them are 2-door and white. how many of the cars are 4-door and red?
Answers
There are 10 cars with 4 doors and red color.
What is the Trial and error method?A fundamental method of solving problems is trial and error. It is distinguished by repeated, varied attempts that are continued until success or the agent gives up. The problem keeps repeating itself until the correct answer is found. This method of problem-solving is known as the trial and error method.Given:
Cars = 30All of the cars are red or white, and a car can have either 2 doors or 4 doors.1/3 of them are red and 50% of them are 4-door.8 of them are 2-door and white.Cars with four doors and red =?So,
1/3 of 30 is 10.Red cars = 10 ...(1)As given that 50% of the cars are 4-door.S, 50% of 30 is 15.We can conclude that 15 cars have 4 doors. ...(2)Taking both conclusions (1) and (2) we can say that there are 10 cars with 4 doors of red color.Therefore, there are 10 cars with 4 doors and red color.
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Find the range of each function for the given domain
F(x) = 6x - 1; D = [0, 2, 4} R={
Answers
Answer:
d. 61²-1-2 f. 6x² -17x+10. (6x-5Xx-2) i. 20x³ +8x²y-5xy² - 2y³. 4x² (5x+2y) - y² (5x+2y) ... r=0 r=4 r= {0,4} d. 3x³ +2x²-27x-18=0 x²(3x+2)-9 (3x+2) = 0.
9 pages
Step-by-step explanation:
If you were to roll the dice one time what is the probability it will not land on a 1
Answers
Answer:
5/6
Step-by-step explanation:
Answer: 5/6
Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
It will land on 1, Prob (land on 1) = 1/6
It will not land on 1, the probability will be given as:
Prob (not land on a 1) = 1 - 1/6
Prob (not land on a 1) = 5/6
Hence the probability that it will not land on a 1 is 5/6
what is the solution of 3z > 6
Answers
Answer:
Step-by-step explanation:
divide both sides by 3
3z>6
3z/3>6/3
z>2
Martha was so hungry that she devoured 7/24 of the pizza,
while Susie, also super-hungry gobbled up 1/4 of the pizza.
Debbie ate her pizza slowly, but ended up consuming 1/6 of the pizza. Which girl ate the least amount of pizza?
Answers
Answer:
Debbie
Step-by-step explanation:
1/4 = 0.25
7/24 = 0.291666..
1/6 = 0.1666..
1/6th is the least