Answer:
a) ∠ABC = 54°
a) ∠ABC = 43°
Step-by-step explanation:
Trigonometric ratios
\(\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}\)
where:
\(\theta\) is the angleO is the side opposite the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)Part (a)
Use the cos trig ratio to find an expression for the measure of BD:
\(\implies \sf \cos (38^{\circ})=\dfrac{BD}{24.3}\)
\(\implies \sf BD=24.3\cos (38^{\circ})\)
Use the cos trig ratio and the found length of BD to find angle ABD:
\(\sf \implies \cos(ABD)=\dfrac{BD}{19.9}\)
\(\sf \implies \angle ABD=\cos^{-1}\left(\dfrac{24.3\cos (38^{\circ})}{19.9}\right)\)
\(\sf \implies \angle ABD=15.79446612...^{\circ}\)
Therefore:
\(\sf \implies \angle ABC=\angle ADB + 38^{\circ}\)
\(\sf \implies \angle ABC=15.79446612...^{\circ}+ 38^{\circ}\)
\(\sf \implies \angle ABC=54^{\circ}\:\:(nearest\:degree)\)
Part (b)
Use the tan trig ratio to find angle CAD:
\(\implies \sf \tan(CAD)=\dfrac{4.9}{7.4}\)
\(\implies \sf \angle CAD=\tan^{-1} \left(\dfrac{4.9}{7.4}\right)\)
\(\implies \sf \angle CAD=33.5110188...^{\circ}\)
Therefore:
\(\sf \implies \angle BAD=13^{\circ}+33.5110188...^{\circ}\)
\(\sf \implies \angle BAD=46.5110188...^{\circ}\)
∠ABC = ∠ABD
Interior angles of a triangle sum to 180°
\(\sf \implies \angle ABD + \angle BAD + \angle BDA=180^{\circ}\)
\(\sf \implies \angle ABC + 46.5110188...^{\circ} + 90^{\circ}=180^{\circ}\)
\(\sf \implies \angle ABC=43^{\circ}\:\:(nearest\:degree)\)
What is the radius of a circle whose circumference is 1611?
Answer:
256.4
Step-by-step explanation:
This is Rylan from yesterday
Help me please !!!!
7,8,9
Find the value of x
(9x-38)+(4x+23)=180
Answer:
x=15
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
9x−38+4x+23=180
9x+−38+4x+23=180
(9x+4x)+(−38+23)=180(Combine Like Terms)
13x+−15=180
13x−15=180
Step 2: Add 15 to both sides.
13x−15+15=180+15
13x=195
Step 3: Divide both sides by 13.
13x/13=195/13
Answer:
15
Step-by-step explanation:
9x-38+4+23=180
13x-15=180
13x=195
x=15
Underwater pressure consists of atmospheric pressure, which is
101
101101 kilopascals
(
kPa
)
(kPa)left parenthesis, start text, k, P, a, end text, right parenthesis, plus
101
kPa
101kPa101, start text, k, P, a, end text of hydrostatic pressure for every
10
1010 meters
(
m
)
(m)left parenthesis, start text, m, end text, right parenthesis of depth under water. Which inequality best represents the depth,
d
dd, in meters, that is permitted for a scuba diver who is advised not to exceed
220
kPa
220kPa220, start text, k, P, a, end text of underwater pressure?
The inequality representing the maximum depth permitted for a scuba diver is:
d < 11 meters
To find the inequality representing the maximum depth permitted for a scuba diver, we need to set up an inequality with underwater pressure (consisting of atmospheric pressure and hydrostatic pressure).
Underwater pressure is given by the equation:
Underwater Pressure = Atmospheric Pressure + Hydrostatic Pressure
where:
Atmospheric Pressure = 101 kPa
Hydrostatic Pressure = 101 kPa for every 10 meters of depth (101 kPa/10 m = 10.1 kPa/m)
Depth = d meters
Now, we know the maximum underwater pressure for the scuba diver is 220 kPa.
So, we set up the inequality:
220 kPa > 101 kPa + 10.1 kPa/m * d
Now, we need to solve for d:
220 kPa - 101 kPa > 10.1 kPa/m * d
119 kPa > 10.1 kPa/m * d
Now, divide both sides by 10.1 kPa/m:
119 kPa / 10.1 kPa/m > d
11.7821782... > d
Since we are finding the depth, we can round down to the nearest whole number:
11 > d
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Question: Underwater pressure consists of atmospheric pressure, which is 101 kilopascals (kPa), plus 101 kPa of hydrostatic pressure for every 10 meters (m) of depth under water. Which inequality best represents the depth, d, in meters, that is permitted for a scuba diver who is advised not to exceed 220 kPa of underwater pressure?
101+ 101d≤ 220
101+10.1d ≤ 220
101+10.1d> 220
4
101+101d> 220
Solve for x and show your steps. Is the solution extraneous? Check your work to show how you determined if the solution is extraneous or not.
sqrt 2x minus 7 equal 1
The solution for the given equation √2x - 7 = 1 is extraneous .
Mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Solve for x , √2x - 7 = 1
1x − 2+1x + 2=4(x − 2)(x + 2) .
1x − 2+1x + 2=4(x − 2)(x + 2)
(x − 2)(x + 2)(x − 2)+(x − 2)(x + 2)(x + 2)=4(x − 2)(x + 2)(x − 2)(x + 2)
(x−2)+(x+2)=4
2x=4
x=2
However, since division by zero is prohibited, the number 2 is not included in the range of the original equation because it would reduce one of the fractions' denominators to zero.
As a result, it can't be one of the roots of the initial equation.
2 is therefore an erroneous solution. As a result, the equation has no answers.
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Mason invests money in an account paying simple interest. He invests $70 and no money is added or removed from the investment. After one year, he has $73.50. What is the simple percent interest per year?
answer: 5%
explanation: subtract the principal from the total amount, then divide the difference by the principal
>> 73.50 - 70 = 3.50
3.50 / 70 = 0.05
0.05 x 100 = 5%
Calculate the total surface area of a hexagonal pyramid with apothem as base 20 length 18 and slant height 15
The total surface area of the hexagonal pyramid is approximately 1640.20 square units.
To calculate the total surface area of a hexagonal pyramid, you need to consider the base and the lateral faces.
First, let's find the area of the base. A hexagonal pyramid has a regular hexagon as its base. Applying the following formula to calculate the area of a regular hexagon
Area of hexagon = (3√3 × s²) / 2
Where s denotes the length of a side of the shape. In this case, the apothem is given as 20, so the side length (s) can be found using the formula:
s = 2 × apothem / √3
Substituting the given apothem value, we get:
s = 2 × 20 / √3 ≈ 23.094
Area of base = (3√3 × s²) / 2
= (3√3 × 23.094²) / 2
≈ 598.47
Next, let's find the area of the lateral faces by applying the formula for area of triangle, such that, each lateral face of a pyramid is in shape of a triangle.
Area of triangle = (base × height) / 2
In this case, the base of each triangle is the side length of the hexagon (s) and the height is the slant height (15). The hexagonal pyramid has 6 lateral faces, so the total area of the lateral faces can be found by multiplying the area of one triangle by 6:
Area of lateral faces = 6 × ((s × 15) / 2)
= 6 × (23.094 × 15) / 2
≈ 1041.73
Finally, to find the total surface area, we add the area of the base to the area of the lateral faces:
Total surface area = Area of base + Area of lateral faces
= 598.47 + 1041.73
≈ 1640.20
Therefore, the total surface area of the hexagonal pyramid is approximately 1640.20 square units.
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3 ratios equivalent to 6/18
Answer:
Step-by-step explanation:
divide them both by 2
which is 3/ 9
divide them both by 3
whic is 2/6
and finally divide them both by 6
which is 1/3
you can multiply them both by an number as well
take care
Which number line shows all the values of that make the inequality -3 +1 < 7 true?
Answer:
Number line D is true
Step-by-step explanation:
Given
\(-3x + 1 < 7\)
See attachment for number lines
Required
Which number line makes the inequality true
First, we solve for x in \(-3x + 1 < 7\)
\(-3x < 7 - 1\)
\(-3x < 6\)
Divide through by -3
\(\frac{-3x}{-3} < \frac{6}{-3}\)
\(x > -2\)
The inequality means x is greater than -2.
This means that, the line must point to the right of -2 and the "greater than" means that the circle must be opened
Number line D is true
Someone please help me! Which one is independent and dependent
Answer:
The top is independent
The bottom is dependent
Step-by-step explanation:
The top is independent because it does not rely on another variable. It is the "affector" and not dependent on it.
The bottom is dependent because it does rely on another variable. It is dependent on this other variable because it will be affected by any changes in that other variable.
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.
- Heather
The table shows the cost in dollars, y, for shipping x number of chargers and electronic tablets.
Which function shows the combined cost in dollars, y, for three shipments with x number of chargers and tablets?
y = 2.00x + 4.00
y = 6.00x + 12.00
y = 3.50x + 2.50
y = 10.50x + 7.50
Select all that are equivalent to sin ZGFH.
Answer:
<fgh <gfh
Step-by-step explanation:
solve for x ?
3(x - 2) = 18
Answer:
X=8
Step-by-step explanation:
3x-6=18
3x=18+6
3x=24
X=24÷3
X=8
Answer:
x=2
Step-by-step explanation:
,...................
GEOMETRY, pls help!!!
Factor the expression.
20g3 + 24g2 – 15g – 18
(4g2 + 6)(5g – 3)
(4g2 – 6)(5g + 3)
(4g2 – 3)(5g + 6)
(4g2 + 3)(5g – 6)
Answer:
C
Step-by-step explanation:
hope this helps I'm sorry if you need work I will do it if so
Answer:
0.03 3.00 4.00 516388383
At a sale , dresses were sold for 35% of their original price. If the dresses originally cost 40$ each how much did a dress cost on sale
Answer:
$14
Step-by-step explanation:
35% is the same as multiplying by .35
40 * .35 = 14
The most recent era of I/O psychology witnessed the creation of which of the following business titles?
a. Chief Executive Officer (CEO)
b. Chief Financial Officer (CFO)
c. Chief Operating Officer (COO)
d. Chief Information Officer (CIO)
The business titles that the most recent era of I/O psychology has created are as follows:
Chief Executive Officer (CEO)
Chief Financial Officer (CFO)
Chief Operating Officer (COO)
Chief Information Officer (CIO)
How all of the four options are correct?
I/O psychology refers to the science of understanding individuals and how they interact with their work. It is a branch of psychology that deals with the study of workplace environments, human behavior, and organizational behavior. It's a field of psychology that works to make the workplace more pleasant and comfortable for employees .I/O psychology has seen the development of several business titles.
These are the most recent titles that have been created, and their main tasks are mentioned below:
Chief Executive Officer (CEO): The CEO is responsible for the overall management of the company, and he or she is in charge of all of its operations. The CEO's main responsibility is to ensure that the company achieves its objectives.
Chief Financial Officer (CFO): The CFO is in charge of the company's finances, and he or she is responsible for managing its cash flow, analyzing the company's financial statements, and reporting on the company's financial performance. The CFO's main task is to ensure that the company has sufficient funds to operate smoothly.
Chief Operating Officer (COO): The COO is in charge of the company's operations, and he or she is responsible for ensuring that the company's processes run efficiently. The COO's main task is to ensure that the company's products or services are of the highest quality.
Chief Information Officer (CIO): The CIO is in charge of the company's information technology, and he or she is responsible for ensuring that the company's IT infrastructure runs smoothly. The CIO's primary task is to ensure that the company's technology is up to date and that it meets the company's needs.
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Find out significant number of digits below: values # of significant digits 12.03 58.2 0.002 0.0030 0.00050004 2. Convert following: a) 0.05 km to mm b) 0.15 hm to cm c) 280 dm to dam d) 500,000 mm to km e) 85 m to hm 3. Solve to the significant number of digits (a) 25.3456 +888.010 + 53.11 + 7-10 (b) (45.805*2.00)/5.0+ 0.1 4. Solve and write answer in scientific notation with significant digits: (a) 70,000,000 * 9.8540*2.00*10^8 (b) 8.888*10*14*4.00*10^-6 - 3.0*10^7 5. Using trigonometrical functions, find out missing part (? or x) in the following figures. B 14 115 A 10 C 56 35
The answers of all the parts are solved below:
1. Significant digits:
12.03: 4 significant digits
58.2: 3 significant digits
0.002: 1 significant digit
0.0030: 4 significant digits
0.00050004: 7 significant digits
2: 1 significant digit
2. Conversions:
0.05 km to mm: 0.05 km = 0.05 x 10^6 mm = 50,000 mm
0.15 hm to cm: 0.15 hm = 0.15 x 100 cm = 15 cm
280 dm to dam: 280 dm = 280 x 10 dam = 2,800 dam
500,000 mm to km: 500,000 mm = 500,000/10^6 km = 0.5 km
85 m to hm: 85 m = 85/100 hm = 0.85 hm
3. Significant digits in calculation:
(a) 25.3456 +888.010 + 53.11 + 7-10: 925.456, 4 significant digits
(b) (45.805 * 2.00) / 5.0 + 0.1: 13.52, 4 significant digits
4. Scientific notation with significant digits:
(a) 70,000,000 * 9.8540 * 2.00 * 10^8 = 1.38 x 10^18, 2 significant digits
(b) 8.888 * 10^14 * 4.00 * 10^-6 - 3.0 * 10^7 = 3.555 x 10^7, 4 significant digits
Trigonometry:
Given triangle ABC with angle B = 56, angle C = 35 and side A = 10. To find side B.
Using the law of cosines, B = sqrt(A^2 + C^2 - 2 * A * C * cos(B)) = sqrt(10^2 + 56^2 - 2 * 10 * 56 * cos(56)) = 115, 3 significant digits.
Thus, All the answers are solved above.
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A 10-foot board is reduced in a 4-foot board. What is the percent decrease in length?
Solve forj: -16 = j/2 + -19
Given:
\(-16=\frac{j}{2}+(-19)\)To solve for j :
Explanation:
Multiplying by 2 on both sides,
\(-32=j-38\)Adding 38 on both sides, we get
\(\begin{gathered} -32+38=j-38+38 \\ 6=j \end{gathered}\)Final answer:
The value of j is 6.
Mei has 2 yellow teacups and 5 brown teacups Which ratio compares the number of brown teacups to the total number of teacups
Answer: 5: 7
Step-by-step explanation:
The total number for teacups: 2 yellow teacups + 5 brown teacups = 7 teacups
the ratio compares the number of brown teacups to the total number of teacups is :
5: 7
The ratio that compares the number of brown teacups to the total number of teacups is 5: 7
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We are given that Mei has 2 yellow teacups and 5 brown teacups.
The total number for teacups is;
2 yellow teacups + 5 brown teacups = 7 teacups
Therefore, the ratio compares the number of brown teacups to the total number of teacups can be;
5: 7
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write the equation of the line that contains the following points in standard form (16,-3),(-4,12)
Answer:
y = -3/4x + 9
Step-by-step explanation:
first, find the slope by taking the difference of the y-values / difference of the x-values
(-3-12) / (16-(-4)) which equals -15/20 or -3/4
now use that value to represent the 'm' in the formula in order to find 'b'
y = mx + b
-3 = -3/4(16) + b
-3 = -12 + b
9 = b
y = -3/4x + 9
Which equation can be used to find the area of the figure below? 10 18 A = (109) +(16-8) GO A= (*)+(108) HOA = (4)+(6 8) 3. A = (6-8)+(108) 2021 Iate Ed
Answer
Second option is correct.
Option G is correct.
Area of the figure = (6.8/2) + (10.8)
Explanation
We can see that the figure is a combination of a triangle and a rectangle
Area of a rectangle = Length × Width
For the rectangular part,
Length = 10
Width = 8
Area of the rectangle = 10 × 8 = (10.8)
Area of a triangle = ½ × Base × Height
For this triangle,
Base = 16 - 10 = 6
Height = 8
Area of the triangle = ½ × Base × Height
Area of the triangle = ½ × 6 × 8 = (6.8/2)
Area of the figure = Area of the triangle + Area of the rectangle
Area of the figure = (6.8/2) + (10.8)
Hope this Helps!!!
-(3z)2 to the second power
Answer:
-12x
Step-by-step explanation:
-3x2^2
-3x4
=-12x
Shelley's kitten weights 2 1/3 times as much as she did last year. She now weighs 21 ounces. What did the kitten weight a year ago?
Answer:
weight of the kitten last year = 9 ounces
Step-by-step explanation:
Let
x = weight of the kitten last year
Weight of the kitten this year = 2 1/3 * x = 21
7/3*x = 21
7/3x = 21
x = 21 ÷ 7/3
x = 21 × 3/7
= 63/7
x = 9 ounces
weight of the kitten last year = 9 ounces
Casey currently owes $500 to his parents. He plans to pay them $60 per month until it is
paid off. Sally also owes her parents money. She borrowed $600 from them and plans to
pay them back $80 per month. Is there a time when they will both owe their parents the
same amount of money?
Answer:
They will both owe their parents $200 when Casey is paying his 5th month and Sally is paying on her 5th month.
Step-by-step explanation:
If Casey pays 60 dollars after 5 months, he will have payed $300 dollars. He still needs to pay $200.(500-300) If Sally pays 80 dollars after 5 months, she will have payed $400 dollars. She still needs to pay $200. (600-400)
min ti x₁ = x₂-u x₂ = u -144²1 (x₁, x₂) arbitrary starting point. Let (0,0) be the Check whether situation (x₁, x₂)→ (0,0) shortest time is met. the beginning of the the coordinate. generality condition of the
It appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).
Here, we have,
given that,
min t_i
x₁ = x₂-u
x₂ = u
-1 ≤ u ≤ 1, (x₁, x₂) are arbitrary starting point.
and origin (0,0) be the begging of the coordinate.
also given that, (x₁, x₂)→ (0,0)
so, min t_i at origin (0,0) = t
Therefore, the generality condition of the situation does not met.
so, we get,
The given system can be represented by the following equations:
x₁' = x₂ - u
x₂' = u
To analyze the behavior of the system, we can examine the dynamics of each variable separately.
For x₁:
x₁' = x₂ - u
The equation implies that the rate of change of x₁ is dependent on x₂ and the input u. The term (-u) acts as a control input that can affect the dynamics of x₁. If we choose an appropriate control input u, we can manipulate the rate of change of x₁ and potentially minimize the time required to reach the origin.
For x₂:
x₂' = u
The equation for x₂ indicates that the rate of change of x₂ is solely determined by the input u. The variable x₂ can be directly controlled by the input u, allowing us to influence its behavior and potentially expedite convergence.
Based on the given equations, it appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).
By carefully selecting the control input, it is possible to achieve the shortest time to reach the origin from any arbitrary starting point (x₁, x₂).
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Research indicates that there are age differences in the types of coping strategies used across the life span. For example, older adults are more likely to use (fill in the blank) than younger adults
The answer to this question is less coping strategies.
What are coping strategies?
Coping strategies are ways through which an individual gains some control over their emotions
Yes research has proved that the Younger adults use more coping strategies than Older adults because now a days so methods for coping strategies like Cigerrate, alcohol, drugs etc things are easily being available to them and they use that to overcome their emotions
where as older adults have already seen most of their life so they are less likely to use these things to overcome their emotions
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Given the number of rows and the number of columns, write nested loops to print a rectangle.
Answer:
You need to use a nested for loop. Use the range() builtin to produce an iterable sequence. The outer for loop should iterate over the number of rows.
Step-by-step explanation:
Use the range() builtin to produce an iterable sequence. The outer for loop should iterate over the number of rows overtime.
A line intersepts the point (3,-4) and has a slope of 17 . What is the slope-intersept equation for this line?
Answer:
y=17x-55
Step-by-step explanation:
y-(-4)=17(x-3)
y+4=17x-51
y=17x-55