The area of the Triangle ABC will be 18 cm²
In the question, It is given that ∠B = 75° and ΔABC is Right angeled at ∠C = 90° and AB = 12CM.
We know that the Area of Δ is defined by : \((\frac{1}{2} *b*h)\)
In the picture below, we have base and height BC and AC respectively.
We don't have the values for AC and BC. So to find the values of Base & Height we will use Trigonometric Ratios.
We know Sin(∠) = Perpendicular/Hyoptenuse and,
Tan(∠) = Perpenciular/Base. Putting values into the respective ratios and taking ∠B = 75°, we get
=> \(Sin(B) = \frac{AC}{BC} = > Sin(75) = \frac{AC}{12}\)
=> \(AC = 0.96 * 12 = > AC = 11.59\)
Similarly, \(Tan(B) = \frac{AC}{BC} = > Tan(75) = \frac{11.59}{BC}\)
=> \(BC = \frac{11.59}{3.73} = > BC = 3.10\)
Now, we have AC = 11.59cm and BC = 3.10cm putting these values in the Area of the Triangle we get :
Area = \(\frac{1}{2} *b*h\) => Area = \(\frac{1}{2}\) * BC * AC
Area = \(\frac{1}{2}\) * 3.10 * 11.59 => Area = 18
Hence, we get the Area of Δ ABC = 18cm²
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Answer:
18
Step-by-step explanation:
let an be a bounded sequence of complex numbers. show that for each c > 0, the series l~=l ann- z converges uniformly for rez ~ 1 c. here we choose the principal branch of n- z
Whave established that the series l~=l an - z converges uniformly for Re(z) ≤ c
What is uniformly?
The keyword "uniformly" refers to the concept of uniform convergence. In the context of the given question, it is stated that the series l~=l an - z converges uniformly for Re(z) ≤ c. Uniform convergence means that the convergence of the series is independent of the value of z within a certain range (Re(z) ≤ c in this case).
To show that the series l~=l an - z converges uniformly for Re(z) ≤ c, where an is a bounded sequence of complex numbers and we choose the principal branch of n - z, we need to demonstrate that for any ε > 0, there exists an N such that for all n > N and for all z with Re(z) ≤ c, the inequality |l~=l an - z| < ε holds.
Given that an is a bounded sequence, there exists an M > 0 such that |an| ≤ M for all n.
Let's consider the series l~=l an - z. We can write it as:
l~=l an - l z.
Now, since |an| ≤ M for all n, we have:
|an - z| ≤ |an| + |z| ≤ M + c.
By choosing N such that M + c < ε, we can ensure that for all n > N and for all z with Re(z) ≤ c, the inequality |an - z| < ε holds.
Now, using the triangle inequality, we have:
|l~=l an - z| ≤ |an - z|.
Since we have shown that |an - z| < ε for n > N and Re(z) ≤ c, it follows that |l~=l an - z| < ε for n > N and Re(z) ≤ c.
Therefore, we have established that the series l~=l an - z converges uniformly for Re(z) ≤ c.
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4 +42x - 1) = 12 what are the solutions
Answer:
x = 2
Step-by-step explanation:
Simplifying
4(2x + -1) = 12
Reorder the terms:
4(-1 + 2x) = 12
(-1 * 4 + 2x * 4) = 12
(-4 + 8x) = 12
Solving
-4 + 8x = 12
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '4' to each side of the equation.
-4 + 4 + 8x = 12 + 4
Combine like terms: -4 + 4 = 0
0 + 8x = 12 + 4
8x = 12 + 4
Combine like terms: 12 + 4 = 16
8x = 16
Divide each side by '8'.
x = 2
Simplifying
x = 2
hope it helps
can someone please help PLEASE
Ms. Sublett's math class is putting three numbers (0.3, 1/4, and 20%) in order from least to greatest. What order should the numbers be from least to greatest?
Answer:
least to greatest
20% , 1/4, 0.3
20% = 1/5 = 0.2
0.3 = 3/10 = 30%
1/4 = 25% = 0.25
Find the least common multiple (LCM) of 9 and 12.
O A. 36
O B. 24
O c. 3
O D. 18
Answer:
option A is the correct answer.
HURRY!! What is the distance between points G and H?
Points G (-5,-8) and H (3,7) are plotted on a coordinate grid.
___ units
The distance between Points G (-5,-8) and H (3,7) are plotted on a coordinate grid will be 17 units.
What is distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations. The distance formula is typically employed to determine the separation between two places. The Pythagoras theorem is used to help create a triangle and to derive the formula.
It is given that the points are plotted on a coordinate grid. are, G (-5,-8) and H (3,7).
The distance between the two points is obtained for the point (x₁.y₁) and (x₂,y₂) is,
\(\rm d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)
The distance between the points G (-5,-8) and H (3,7).
\(\rm d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \\\\ GH = \sqrt{(3-(-5))^2 + (7-(-8))^2} \\\\ GH = \sqrt{289} \\\\ GH = 17 \ units\)
Thus, the distance between Points G (-5,-8) and H (3,7) plotted on a coordinate grid will be 17 units.
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If anyone can help that would be much appreciated. ^^
Answer:
21.......celcius scale is used....as the thermometer shows 100...and water boils at 100 degree Celsius.....( shown that water is boiling)...
22......liquid to gas
The poster shows how many of its games the football team has won. Express this information as a fraction a percent and decimal
Answer:
Percentage: 80%
Decimal: 0.8
I think this could be an answer
a food truck sells 1200 burgers a week on average. the truck operates 7 days a week. (we will assume no variability from day to day.) the food truck owner of wants to be sure that the ingredients are fresh and that hamburger is not kept in the refrigerator more than 2 days on average. if each burger uses .25 pounds of hamburger, what should the maximum pounds of hamburger in the food truck be?
To ensure that the hamburger is not kept in the refrigerator for more than 2 days on average, the food truck should have a maximum of approximately 42.86 pounds of hamburger.
Given that the food truck sells an average of 1200 burgers per week, and it operates 7 days a week, we can calculate the total burgers sold per day:
Burgers per day = Total burgers per week / Number of days per week
Burgers per day = 1200 burgers / 7 days
Burgers per day ≈ 171.43 burgers
Since each burger uses 0.25 pounds of hamburger, we can calculate the maximum pounds of hamburger needed per day:
Pounds of hamburger per day = Burgers per day * Hamburger per burger
Pounds of hamburger per day = 171.43 burgers * 0.25 pounds/burger
Pounds of hamburger per day ≈ 42.86 pounds
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The maximum pounds of hamburger that should be stored in the food truck to ensure freshness and avoid exceeding 2 days on average is approximately 42.86 pounds.
To ensure that the hamburger is not kept in the refrigerator for more than 2 days on average, we need to calculate the maximum pounds of hamburger that should be stored in the food truck.
Average number of burgers sold per week = 1200
Number of operating days per week = 7
Weight of hamburger per burger = 0.25 pounds
To calculate the maximum pounds of hamburger, we can use the following formula:
Maximum pounds of hamburger = Average burgers sold per day × Number of days
First, we calculate the average number of burgers sold per day:
Average burgers sold per day = Average burgers sold per week / Number of operating days per week
Average burgers sold per day = 1200 / 7
Average burgers sold per day ≈ 171.43 (rounded to two decimal places)
Now, we can calculate the maximum pounds of hamburger:
Maximum pounds of hamburger = Average burgers sold per day × Weight of hamburger per burger
Maximum pounds of hamburger = 171.43 × 0.25
Maximum pounds of hamburger ≈ 42.86 (rounded to two decimal places)
Therefore, the maximum pounds of hamburger that should be stored in the food truck is approximately 42.86 pounds.
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what is the area of the shaded region?
Answer:
The area of the shaded region is the difference between the area of the entire polygon and the area of the unshaded part inside the polygon. The area of the shaded part can occur in two ways in polygons.
Step-by-step explanation:
Observe that the area of the unshaded region is equal to the area of the shaded region subtracted from the area of the rectangle, i.e. . ar(Unshaded) = ar(ABCD) – ar(Shaded).
please give me brainlist!
what should be added to -7/4 to get -2
Answer:
\(-\frac{1}{4}\) or -0.25
Step-by-step explanation:
he way to set this up in an equation is like this:
\(- \frac{7}{4} +x= -2\)
so what we have to do is add \(-\frac{7}{4}\) to -2
\(x=-2+(-\frac{7}{4})\\x=-\frac{4}{4} +(-\frac{7}{4})\)
in result we get: \(-\frac{1}{4}\) or -0.25
Hope this helps!
Answer:
x = -1/4
Step-by-step explanation:
-7/4 + x = -2
Add 7/4 to each side
-7/4 +7/4 + x = -2+7/4
x = -2 +7/4
Get a common denominator
x = -2*4/4 + 7/4
x = -8/4 + 7/4
x = -1/4
mr. goodman sets a goal to outscore these numbers. at the end of the year he takes a random sample of his evaluations and finds 10 1's, 13 2's, 48 3's, and 52 4's. at the 0.05 level of significance, can mr. goodman claim that his evaluations are significantly different than the history department's?
No as their no difference in Mr. Goodman's evaluation and the History department
What is Statistics ?
The study of statistics is the field that deals with the gathering, structuring, analyzing, interpreting, and presenting of data. In order to apply statistics to an issue in science, business, or society, it is customary to start with a statistical population or a statistical model that will be investigated.
descriptive statistics types in mathematics The data in this type of statistics is summarized using the provided observations. Statistics that are inferential. To interpret the meaning of descriptive statistics, this kind of statistics is employed. Example of Statistics.
Seeing the data we can conclude that their no difference in Mr. Goodman's evaluation and the History department
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A plant that floats on the surface of rural bodies of water is known as duckweed. The initial mass of a population of duckweed is 500g The mass of the population triples every Ͷͷ hours and can be represented by the function m(t)= 500x3^t/45 where (t) is time in hours. Determine how many hours it would take for the duckweed to grow to a mass triple the original size.
Therefore , the solution of the given problem of function comes out to be the duckweed to grow a mass triple the original size will be 45 hours.
Explain function.The mathematics curriculum involves examining numbers, the equation the environment we live in, structures, and both actual and hypothetical locations. A function is a variable representation of the relationship between the quantities of intake and the corresponding outputs for each. Simply explained, a function is a collection of inputs that, when combined, provide unique outputs for each input.
Here,
Given :
mass of a population of duckweed is 500g
=> function m(t)= 500x³^t/45
So,
=> t = 45 hours
Since it is given that the mass of the population of the duckweed triples every 45 hours
it is clear that the time taken for the duckweed to grow a mass triple the original size will be 45 hours .
Therefore , the solution of the given problem of function comes out to be the duckweed to grow a mass triple the original size will be 45 hours.
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I need help in this one! Thank you!
Answer:
Grey dice. White dice
1 1. 52 2. 65 3. 16 4. 2Step-by-step explanation:
Flip them around, this one really got me lol
Jacob took a total of 12 quizzes over the course of 3 weeks.
How many weeks of school will Jacob have to attend this quarter before he will have taken a total of 22quizzes?
Find the surface area of the triangular prism.
12 in
15 in
20 in
9 in.
The surface area is ?
square inches.
Answer:
720 square inches.
Step-by-step explanation:
To find the surface area of a triangular prism, we need to find the area of each face and add them together.
The triangular bases have base 12 in and height 15 in, so the area of each is:
(1/2) × 12 in × 15 in = 90 in²
The rectangular faces have dimensions 20 in × 15 in and 20 in × 12 in, so their areas are:
20 in × 15 in = 300 in²
20 in × 12 in = 240 in²
Adding these up, we get:
2 × 90 in² + 300 in² + 240 in² = 720 in²
the surface area of the triangular prism is 720 square inches.
Formalize the following in terms of atomic propositions r, b, and w, first making clear how they correspond to the
English text. (a) Berries are ripe along the path, but rabbits have not been seen in the area.
(b) Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.
(c) If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.
(d) It is not safe to walk along the path, but rabbits have not been seen in the area and the berries along the path are ripe.
e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to
pave been seen in the area.
Walking is not safe on the path whenever rabbits have been seen in the area and berries are ripe along the path.
Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path. This is formalized by using the →(if-then) and ∧(logical and) operators.
Given information and corresponding atomic propositions:
We need to formalize the given statements in terms of atomic propositions r, b, and w, which are defined as follows:
r: Rabbits have been seen in the area.
b: Berries are ripe along the path.
w: Walking on the path is safe.
Now, let us formalize each of the given statements in terms of these atomic propositions:
a) Berries are ripe along the path, but rabbits have not been seen in the area.
b: Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.
c: If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.
d: It is not safe to walk along the path, but rabbits have not been seen in the area, and the berries along the path are ripe.
e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.
Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path.
The formalizations in terms of atomic propositions are:
a) b ∧ ¬r.b) ¬r ∧ w ∧
b.c) (b → w) ∧ (¬r → w).
d) ¬w ∧ ¬r ∧
b.e) (¬r ∧ ¬b) → w.b ∧
Berries are ripe along the path, but rabbits have not been seen in the area.
This is formalized by using the ∧(logical and) operator.
(¬r ∧ ¬b) → w: It means For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.
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Construct a 3x3 matrix A, with nonzero entries, and a vector b in R3 such that b is not in the set spanned by the columns of A. Choose the correct answer below 11 13 1114 3 A. B. L333J 333] 111] L9 「1 1 2 33 3 4 56 3 3 21
none of the dot products are equal to b, we can conclude that b is not in the set spanned by the columns of A. C. 13 2 13 2 13 2 L1 1 2 1 1 2 111] 33 3 4 56 3 3 2!
First we need to create a 3x3 matrix A, with nonzero entries. We can do this by choosing any non-zero entries for each of the nine elements in the matrix. For example:
A = [11 13 1114 3
13 2 13 2
111] 33 3 4]
Next, we need to create a vector b in R3 that is not in the set spanned by the columns of A. To do this, we can choose any three values that are different from the values in A. For example:
b = [9 1 2]
Now we can check if b is not in the set spanned by the columns of A. To do this, we can calculate the dot product of b and each column of A. If the dot product of any of the columns is equal to b, then b is in the set spanned by the columns of A. Since none of the dot products are equal to b, we can conclude that b is not in the set spanned by the columns of A.
The complete question is : Construct a 3x3 matrix A, with nonzero entries, and a vector b in R3 such that b is not in the set spanned by the columns of A. Choose the correct answer below 11 13 1114 3 A. B. L333J 333] 111] L9 「1 1 2 33 3 4 56 3 3 21 C. D. 13 2 13 2 13 2 L1 1 2 1 1 2 111] 33 3 4 56 3 3 2!
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pls can anybody give answers for 1 , 2 , 3 , 4 questions
Answer:
1 and 2
1 and 5
10 and 0.1
the last is unreadable
Step-by-step explanation:
Write an addition problem that has a sum of -24. Include one positive number and one negative number in the problem
-26 + 2 = -24
I hope this helps you, have a great rest of your day. :)
Answer:
-30 + 6 = -24
Step-by-step explanation:
Having -30 as the first number in the equation makes the equation negative. But by adding 6, then it will be -24, which is the answer we are trying to get to.
Hope this helped!
brainly?...
please please help its geometry
In response to the given question, we can state that we know that sum of all angles in a triangle is 180. m∠C = 4*11.67+43 = 89.68 = =90
What precisely is a triangle?A triangle is a polygon because it contains four or more parts. It features a simple rectangular shape. A triangle ABC is a rectangle with the edges A, B, and C. When the sides are not collinear, Euclidean geometry produces a single plane and cube. If a triangle contains three components and three angles, it is a polygon. The corners are the points where the three edges of a triangle meet. The sides of a triangle sum up to 180 degrees.
we know that sum of all angles in a triangle is 180.
2x - 12 + 4x + 43 + 9x - 26 = 180
15x + 5 = 180
15x = 175
x = 11.67
m∠C = 4*11.67+43 = 89.68 = =90
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Answer:
m∠C = 119°
Step-by-step explanation:
According to the Exterior Angle Theorem, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.
From inspection of the given triangle, the exterior angle is (9x - 26)° and the two non-adjacent interior angles are ∠B and ∠C.
Equate the sum of the two non-adjacent angles to the exterior angle and solve for x:
⇒ (2x - 12)° + (4x + 43)° = (9x - 26)°
⇒ 2x - 12 + 4x + 43 = 9x - 26
⇒ 6x + 31 = 9x - 26
⇒ 57 = 3x
⇒ x = 19
To calculate the measure of angle C, substitute the found value of x into the expression for the angle:
⇒ m∠C = (4x + 43)°
⇒ m∠C = (4(19) + 43)°
⇒ m∠C = (76 + 43)°
⇒ m∠C = 119°
Could anyone help me out with this?
Answer: they are abt the same its all abt percentage now- Pitcher A
Step-by-step explanation: more water lessens the strength
Help! Clear the fractions
Answer:
x = - \(\frac{27}{20}\)
Step-by-step explanation:
Given
\(\frac{5}{6}\) x + 2 = \(\frac{7}{8}\)
Multiply through by 24 ( the LCM of 6 and 8 ) to clear the fractions
20x + 48 = 21 ( subtract 48 from both sides )
20x = - 27 ( divide both sides by 20 )
x = - \(\frac{27}{20}\)
A simple random sample of 49 8th graders at a large suburban middle school indicated that 82% of them are involved with some type of after school activity. Find the 99% confidence interval that estimates the proportion of them that are involved in an after school activity.
Answer:
0.142
Step-by-step explanation:
From the question, we identify the following parameters;
n = 49
p = 82% = 82/100 = 0.82
alpha, α = 1-0.99 = 0.01
Zα/2 = Z_0.005 = 2.575
margin of error = Zα/2 * √( p(1-p)/n)
Margin of error = 2.575 * √(0.82)(1-0.82)/49
Margin of error =0.1416005 which is approximately 0.142
Find x in the parallelogram ?
Answer:
\(x=14\)
Step-by-step explanation:
The diagonals of all parallelograms bisect each other. Therefore, we have the following equation:
\(2x+10=5x-32\)
Solving for \(x\):
\(2x+10=5x-32,\\42=3x,\\x=\boxed{14}\)
The most commonly used descriptive statistics for a set of numerical scores are the mean and the ____.
Answer: Standard Deviation.
Step-by-step explanation:
DescriptionIn insights, the standard deviation is a proportion of the measure of variety or scattering of a lot of qualities. A low standard deviation demonstrates that the qualities will in general be near the mean of the set, while an elevated expectation deviation shows that the qualities are spread out over a more extensive territory.
write-2.16 as a fraction asap!!!!1m
Answer:
-2 wholes 4/25
Step-by-step explanation:
I used calculator. btw its -2 4/25
hope this helps! mark as brainliest!
Answer:
-2 4/25
Step-by-step explanation:
Can i please get some help please?
I need help with B
Answer:
it b7857575757575757575757575775757575757577575757575757575757756886868686979708
Step-by-step explanation:
uhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Plot the points on a graph
(3,6) , (-6,-3) and (-3,0)
Step-by-step explanation:
Plot the points on a graph. As stated, you will plot based on the (x , y) values of the given point. The x-value will determine where on the x-axis (left->right) the point will coincide, while the y-value will determine where on the y-axis (top->down) it will coincide:
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For organisms which need a partner for reproduction but rely on a chance encounter for meeting a mate, the birth rate is proportional to the square of the population. Thus, the population of such a type of organism satisfies a differential equation of the formdP/dt=aP2−bPwith a,b>0.Sketch a graph of dP/dt against P. Note when dP/dt is positive and negative.
The graph of dP/dt against P is a parabola, with the equation of the form \(y = ax^2 - bx\) where a and b are positive parameters.
The graph has a vertex at \((b/2a, -b^2/4a)\).
When P is less than b/2a, dP/dt will be positive, meaning the population is increasing. As P increases, dP/dt will reach a maximum at (b/2a, -b^2/4a) and then decrease, meaning the population is decreasing. When P is greater than \(b/2a, dP/dt\) will be negative.
For example, if a = 4 and b = 1, the graph of dP/dt against P is \(y = 4x^2 - x\), with the vertex at (0.5, -0.125). When P is less than 0.5, dP/dt will be positive, and when P is greater than 0.5, dP/dt will be negative.
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