The area of triangle ABC, with sides of 8 km and 5 km and an internal angle of 150 degrees, is calculated using the formula for the area of a non-right triangle. The result is 10 km².
Explanation:The subject of this question is Mathematics, specifically Geometry dealing with calculation of area of a triangle using the properties of a non-right triangle.
The area of the triangle ABC can be calculated using the formula 0.5 * a * b * sin(C), where C is the angle between sides a and b.
Here, a is the length from A to B, which is 8 km; b is the length from B to C, which is 5 km; and the angle C (angle ABC) is 150°.
Plug these values into the formula: 0.5*8km*5km*sin(150°) which equals to 10 km².
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I need help!!
I don’t get it!!
Answer:
170
Step-by-step explanation:
what is n if 8n-(4n+7) = 13
Answer:
5
Step-by-step explanation:
Which expression has a negative value ?
A. -12 x (-8)
B. -72 divided by (-9)
C. -11 x 6
D. -14 + 24
Answer:
C. -11 x 6
Step-by-step explanation:
When you multiply a negative number with a positive, your answer will always be negative. In this case:
-11 x 6 = -66.
~
Answer:
C. -11 × 6
Step-by-step explanation:
A. -12×(-8) =96
B. -72÷(-9) =8
C. -11×6 =-66
D. -14+24=10
Only option C gives a negative answer.
30 points!!!
i’m looking at number 5 right now. i don’t know what -2x means. can someone show me an example of how you do it
-2x means -2*x or "-2 times x" where x is a placeholder for any number you want.
To graph y = -2x, you just need two points. Each point is of the form (x,y)
Let's plug in zero as it is often the easiest to work with.
If x = 0, then -2*x = -2*0 = 0. Notice how I replaced x with 0 and simplified.
Therefore, if x = 0, then y = 0. We have (x,y) = (0,0) as one point on this line. I have marked it as point A in the graph.
Point B is (1, -2) and it is found by plugging x = 1 into the equation to get...
y = -2x
y = -2*1
y = -2
You could find other points, but two points is enough to draw a straight line through them. The slope of this line is -2 = -2/1. The y intercept is 0.
What is the next number in pattern from 2,9,28,65
Answer:
126
Step-by-step explanation:
2=1³+1
9=2³+1
28=3³+1
65=4³+1
=>5³+1=126
The rule is: n³+1
Find the monthly payment needed to amortize a typical 100,000 mortgage loan over 30 years at annual interest rate of 4.7%, compounded monthly. Find the total interest paid on the loan after 30 years
Answer:
Monthly amortization paid is $1,135
Amount of interest paid is $308,469
Step-by-step explanation:
Here, we are interested in calculating the monthly payment paid and the total value of this interest.
Firstly, we calculate the amount which this loan would be at the end of the 30 years.
To calculate this amount, we make use of the compound interest amount formula
A = P(1 + r/n)^nt
where A is the amount we want to calculate
P is the amount borrowed which is $100,000
r is the interest rate which is 4.7% or simply 4.7/100 = 0.047
n is the number of times yearly which the interest is compounded which is 12 since it is compounded monthly
t is the total time taken to repay the loan which is 30 years
Plugging these values, we have
A = 100,000( 1 + 0.047/12)^(12 * 30)
A = 100,000( 1+ 0.00392)^360
A = 100,000(1 .00392)^360
A = $408,469
The monthly payment needed to amortize the loan will be the amount after 30 years divided by the number of months in 30 years
The number of months in 30 years is 30 * 12 = 360 months
The monthly payment amount is thus 408,469/360 = 1,134.6 approximately $1,135
The total interest paid will be the amount minus the principal
This is $408,469 - $100,000 = $308,469
If a car company makes a car with the option of 4 exterior colors, 3 interior colors, and 2 engines, how can the multiplication principle help us determine the total number of different variations of the car?
There are a total of 24 different combinations of exterior color, interior color, and engine that the car company can offer.
What is the multiplication principle?The multiplication principle states that if there are a number of choices for one aspect of a problem, and a number of choices for another aspect of the problem, and the choices for each aspect are mutually exclusive (i.e., they do not overlap), then the total number of choices is the product of the number of choices for each aspect.
As per the question, there are 4 choices for the exterior color of the car, 3 choices for the interior color of the car, and 2 choices for the engine of the car.
Using the multiplication principle, we can determine that the total number of different variations of the car is :
4 x 3 x 2 = 24.
This means that the car company may provide a total of 24 distinct exterior colors, interior colors, and engine combinations.
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Using the multiplication principle, by simply multiplying together the number of options for each feature (4 exterior colors, 3 interior colors, 2 engines), we find that there are 24 possible variations of the car that the company can make.
Explanation:The multiplication principle in mathematics is a tool used in combinatorics that suggests that if you have multiple groups of items, and you want to know how many different combinations there are of one item from each group, you can simply multiply the amount of items in each group. In the context of your car company question, with 4 exterior colors, 3 interior colors, and 2 types of engines, the multiplication principle suggests you can calculate the total combinations by multiplying these numbers together. So, you would have:
4 (exterior colors) * 3 (interior colors) * 2 (engine types) = 24 total variations
Therefore, according to the multiplication principle, there would be 24 different variations of the car the company could produce.
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In triangle ABC, angle A measures 50 degrees, angle B measures 30 degrees. Find the measure of angle C.
A.100 degrees
B.50 degrees
C.110 degrees
Answer:
100 degrees
Step-by-step explanation:
5. What is 60% of 45?
Answer:
27
Step-by-step explanation:
Of means multiply
60% * 45
Change to decimal form
.60* 45
27
What is the volume of the following cylinder?
43.96 in.3
12.56 in.3
21.98 in.3
87.92 in.3
Answer:
d) 87.92
Step-by-step explanation:
V = A(base)* height= πr² * h= 3.14*2²*7=87.92
Easy Question, Easy points
Topic: Volume
Answer:
(a) 55080 m³
(b) 1312 truckloads
(c) 11 days
Step-by-step explanation:
(a) We have a rectangular prism with the dimensions 12 by 85 by 54, so the volume is just the product of these numbers:
V = 12 * 85 * 54 = 55080 m³
(b) The truck can hold 42 m³ of earth, so divide 55080 by 42 to get the number of truckloads required:
55080 / 42 = 1311.4
Since we will still need a truckload to hold that little bit of earth that involves 0.4 of a truck, we round up to 1312 truckloads.
(c) In one day, 4 trucks work for 6 hours and since each truck can remove 42 m³ with 5 loads per hour, we have:
42 * 5 * 6 * 4 = 5040 m³ earth removed a day
Divide 55080 by 5040 to get the number of days:
55080 / 5040 = 10.9 ≈ 11 days
Part A:
The volume can be found by multiplying all the dimensions of the earth being evacuated.
12 * 85 * 54 = 55,080m³
Part B:
Divide the number of capacity that each truck carries of earth.
55,080 / 42 = 1,311.4285
I would assume we round up since that little bit that's left over is another load.
So, 1,311.4285 → 1,312 truckloads
Part C:
4 trucks work non-stop for a 6 hour day, each truck can transport 5 loads per hour, and each truck can carry 42m³ of earth. We can multiply all these numbers and divide by the total earth capacity.
42 * 6 * 5 * 4 = 5,040
55,080 / 5,040 = 10.9285...
Round up.
10.9285... → 11 days
Best of Luck!
#2 Find the slope given the points (6,-12) and (15,-3)*
Greetings :)
To find slope of two points we will need to use this equation: [tex]\frac{y^2-y^1}{x^2-x^1}[/tex]
[tex]x^1[/tex] [tex]x^2[/tex] [tex]y^1[/tex] [tex]y^2[/tex]
( 6 , -12 ) ( 15 , -3 )
Now let's replace the equation with the numbers. (it will be a fraction).
[tex]\frac{-3-(-12)}{15-12}[/tex] = [tex]\frac{9}{9}[/tex]
The equation equals 9 over 9, which also equals 1.
The slope of the line is 1.
What is the explicit formula for this geometric sequence -6,-18,-54,-162,…
Answer: an= -6(3)^(n-1)
(B)
Step by step explanation: a1 is -6 and a2 is -18, only B would match the sequence. The only other answer that comes close is -6(-3)^(n-1) but if you multiply -6 by -3 you get 18 instead of -18
Angles A M Y and Y M B form a line. Angles Y M B and B M X form a line. Angles X M A and A M Y form a line. Choose each angle to complete the linear pairs. ∠AMY and ∠AMX ∠BMY and ∠BMX and ∠AMX and
Answer:
AMY
BMY
BMX
Step-by-step explanation:
I took the assignment
Answer:
The answers are : B, B, A
Step-by-step explanation:
RIGHT ON EDG!
Simplify 5m - {2n + [3p - (m + 3n - 7p)]}.
//////
Find the sum of the three expressions and choose the correct answer.
2x2y2 - 7xy + 5y2
8xy - 3y2
x2y2 + 4y2
//////
Answer:
1st Problem: 6m + n - 10p
Step-by-step explanation:
5m - {2n + [3p - (m + 3n - 7p)]}
5m - {2n + [ 3p - m - 3n + 7p]}
5m - {2n + 10p - m - 3n}
5m - {-n + 10p - m}
5m + n - 10p + m
6m + n - 10p
** I don't understand what you are trying to say in the 2nd problem **
Which point has the coordinates (−1.5, −4)?
Answer:
Point D
Step-by-step explanation:
The cup was filled at a constant rate. It started empty. After 2 seconds, it held 70 cm^3 of water.
Find the percent of the cup that is filled with water after 3 seconds.
Answer:
About 90%
Step-by-step explanation:
If the cup was filled at a constant rate, then the cup fills at 70/2=35 cubic centimeters per second. The formula for the volume of a cone is [tex]\frac{1}{3} \pi r^2 h[/tex], or in this case [tex]\frac{112}{3}\pi[/tex] cubic centimeters. After 3 seconds, the cup would have 35*3=105 cubic centimeters of water inside of it, or about 89.52% which rounds to 90%. Hope this helps!
What are the roots of the function?
0 -8 and 20
O _40 and -8
O-8 and 8
O _40 and 20
Answer:
0
−
8
=
−
8
0-8=-8
20
=
−
8
20=-8
O
⋅
40
=
40
O
O⋅40=40O
−
8
=
40
O
-8=40O
O
−
8
=
40
O
O-8=40O
8
=
40
O
8=40O
O
⋅
40
=
40
O
O⋅40=40O
20
=
40
O
20=40O
Find the student’s error in solving the following inequality.
31 < –5x + 6
25 < –5x
–5 < x
A.) The student should have added 6 to both sides instead of subtracting it.
B.) The student divided 25/–5 incorrectly.
C.) The student should have switched the direction of the inequality sign to get –5> x for a final answer.
Answer:
The correct option is:
The student should have switched the direction of the inequality sign to get –5> x for a final answer
Step-by-step explanation:
The students has made a mistake in the 3rd step.
We know that when we multiply or divide any negative number on both sides of the inequality, the sign of inequality reverse its direction.
In step 3 the student divided 25 by -5 but did not switch direction of the inequality sign.
Therefore the correct option is: The student should have switched the direction of the inequality sign to get –5> x for a final answer
Answer:
C
Step-by-step explanation:
Just did it
The students in Mr. McIntyre’s class and in Mrs. Ramos’s class were asked how many pets they each have. The dot plots below show the results.
Mr. McIntyre’s Class
A dot plot titled Mister McIntyre's Class. A number line going from 0 to 5 is labeled Number of Pets. There are 5 dots above 0, 5 above 1, 4 above 2, 1 above 3, and 0 above 4 and 5.
Mrs. Ramos’s Class
A dot plot titled Misses Ramos's Class. A number line going from 0 to 5 is labeled Number of Pets. There is 1 dot above 0, 2 above 1, 2 above 2, 4 above 3, 3 above 4, 3 above 5.
Which statement correctly compares the measures of center of the data in the dot plots?
The median is greater for Mr. McIntyre’s class.
The median is the same for both classes.
The mode is greater for Mrs. Ramos’s class.
The mode is the same for both classes.
The correct statement is the mode is greater for Mrs. Ramos’s class.
What is the correct statement?Median is the number in the middle of a dataset. Mode is the number that occurs most frequently in the dataset.
Number of pets in Mr. McIntyre’s class = 0,0,0,0,0,1, 1, 1, 1, 1, 4, 4, 4, 4, 1,
Median = 1 Mode = 0 and 1Number of pets in Mrs. Ramos’s Class = 0, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 3, 3, 3
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Answer:
The answer is C) the mode is greater for Mrs. Ramos’s class.
Step-by-step explanation:
If you need any help with this question please ask me! :)
AB =
Round your answer to the nearest hundredth.
А
?
4
35°
B
С
Answer:
6.97
Step-by-step explanation:
t r u s t me
Rounding to the nearest hundredth, we get [tex]\( AB \approx 6.97 \)[/tex]. So, the correct answer is indeed [tex]\( x \approx 6.97 \).[/tex]
To find the length of side AB, we can use the sine function as follows:
[tex]\[ \sin(B) = \frac{{\text{opposite}}}{{\text{hypotenuse}}} \][/tex]
In this case, [tex]\( \sin(35^\circ) = \frac{4}{AB} \).[/tex]
We rearrange this equation to solve for AB:
[tex]\[ AB = \frac{4}{{\sin(35^\circ)}} \][/tex]
Now, we'll calculate:
[tex]\[ AB = \frac{4}{{\sin(35^\circ)}} \]\[ AB \approx \frac{4}{{0.5736}} \]\[ AB \approx 6.97 \][/tex]
Rounding to the nearest hundredth, we get [tex]\( AB \approx 6.97 \)[/tex]. So, the correct answer is indeed [tex]\( x \approx 6.97 \).[/tex]
The volume of a square pyramid is 15 cubic centimeters. If the height of the pyramid is 5 cm, what is the length of the base edge?
Answer:
The length of the base edge is 3 cm
Step-by-step explanation:
Volume of square pyramid =[tex]\frac{1}{3}BH[/tex]
Where B = area of square base
H = Height
Let the length of base edge be x
Area of base = [tex]Side^2 = x^2[/tex]
Height of pyramid = 5 cm
So,Volume of square pyramid =[tex]\frac{1}{3}BH=\frac{1}{3} \times x^2 \times 5[/tex]
We are given that The volume of a square pyramid is 15 cubic centimeters.
So,[tex]\frac{1}{3} \times x^2 \times 5=15[/tex]
[tex]x^2 = \frac{15 \times 3}{5}[/tex]
[tex]x=\sqrt[2]{\frac{15 \times 3}{5}}[/tex]
x=3
Hence the length of the base edge is 3 cm
the data is the number of text messages you send a day. find the mean, median, and mode of the data.
10, 12, 20, 8, 6, 18
please help!!!
Answer:
6, 8, 10, 12, 18, 20
Mean: 6 + 8 + 10 + 12 + 18 + 20 = 74/6 = 12.3
Median: 11
Mode: there are no mode in the following listed numbers or data set.
~hope this helps~
would highly appreciate it if you would mark me the brainliest
THow much will fencing cost to enclose a field that is 725 feet by 1,021 feet if fencing costs $13.57 per foot? $47,386.44 $23,693.22 $10,044.85 $10,044,853.25
Answer:
$47,386.44
Step-by-step explanation:
Given;
Dimension of the field = 725 feet by 1,021 feet
Length = 1021 ft
Breadth = 725 ft
Cost per foot = $13.57 per foot
Perimeter of the field = 2 × (length + breadth)
Perimeter = 2 × ( 1021 + 725) = 3492 ft
The cost of fencing the field is;
Cost per feet × perimeter
= $13.57 × 3492
= $47,386.44
Find the elapsed time between 5:25 pm and 11:11 pm
Answer:
5 hours 46 minutes
Step-by-step explanation:
P varies inversely with x. if p=7 when x=8, find the value of P when x=7
9514 1404 393
Answer:
P = 8
Step-by-step explanation:
The "varies inversely" relation can be expressed by the equation ...
P = k/x
For the given values, we can find k to be ...
k = Px = (7)(8) = 56
Then for the new value of x, we have ...
P = 56/x = 56/7
P = 8
Final answer:
P varies inversely with x and given P=7 when x=8, the constant of variation k is determined to be 56. Using this constant, the value of P when x=7 is calculated to be 8.
Explanation:
The student's question relates to the concept of inverse variation in mathematics. The relationship between two variables is described as inversely proportional if their product is constant. In the given scenario, P varies inversely with x and the student provided a specific condition where P = 7 when x = 8. Therefore, using the constant of variation k, the equation can be written as P = k/x. To find the constant of variation, we use the provided values:
7 = k/8k = 7 times 8k = 56Now with the constant k found, to calculate the value of P when x = 7, we set up the equation:
P = 56/7P = 8Therefore, the value of P when x = 7 is 8.
escribir dos ejemplos numeros decimales y conviertelos a fraccion?
Answer:
0.25
0.5
Step-by-step explanation:
[tex]\frac{1}{4}[/tex]
[tex]\frac{1}{2}[/tex]
.25 = 25/100 = 1/4
.50 = 50 /100 = 1/2
SOMEONE PLEASE HELP ME WITH THIS!!! I really need help I try doing it but I just end up getting lost, please help me, I give out brainliest!!!!
((Trigonometry))
What is the factor 5k2 - 35k3.
Answer:
the factored form is -5x^2(7x-1)
Answer:
5k^2(1 - 7k)
Step-by-step explanation:
hope this helps(:
What is the length of the missing side
Answer:
a=8
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 +b^2 = c^2 where a and b are the legs and c is the hypotenuse
a^2 +15^2 = 17^2
a^2 +225 = 289
Subtract 225 from each side
a^2 +225-225=289-225
a^2 = 64
Take the square root of each side
sqrt(a^2) = sqrt(64)
a = 8
Answer:
8
Step-by-step explanation:
Using the Pythagorean theorem, you can find that the missing side length is [tex]\sqrt{17^2-15^2}=8[/tex] units. Hope this helps!