can anyone give an explanation and answer to this question,my sister needed help on this also :) Thank you again for taking your time to answer and read this <3
what is the circumference of a circular pond with a radius of 14 meters?
Can you solve the measure of an angle is twenty-nine times the measure of a supplementary angle. what is the measure of each angle
find the measures of two angles one positive and negative that are coterminal with pi/2
Answer: The required measures of two angles one positive and negative that are co-terminal with [tex]\dfrac{\pi}{2}[/tex] are [tex]-\dfrac{3\pi}{2}[/tex] and [tex]\dfrac{5\pi}{2}.[/tex]
Step-by-step explanation: We are given to find measures of two angles one positive and negative that are co-terminal with [tex]\dfrac{\pi}{2}.[/tex]
Let x and y represents the positive and negative co-terminal angles respectively.
We know that
the measures of any two co-terminal angles differ from each other by a multiple of [tex]2\pi.[/tex]
So, the values of x and y can be found as follows :
[tex]x=\dfrac{\pi}{2}-2\pi=-\dfrac{3\pi}{4},\\\\\\y=\dfrac{\pi}{2}+2\pi=\dfrac{5\pi}{2}.[/tex]
Thus, the required measures of two angles one positive and negative that are co-terminal with [tex]\dfrac{\pi}{2}[/tex] are [tex]-\dfrac{3\pi}{2}[/tex] and [tex]\dfrac{5\pi}{2}.[/tex]
Final answer:
The positive coterminal angle with π/2 is 5π/2, and the negative coterminal angle is -3π/2; both angles are found by adding and subtracting 2π radians from the original angle.
Explanation:
To find the measures of two angles, one positive and one negative, that are coterminal with π/2, we need to add and subtract 2π (360 degrees) to the original angle since the angles are coterminal when they share the same initial and terminal sides and differ by a full circle (360 degrees) or a multiple thereof. The angle π/2 radians is equivalent to 90 degrees, so adding 2π radians (360 degrees) gives us a positive coterminal angle, and subtracting 2π radians (360 degrees) gives us a negative coterminal angle.
Positive coterminal angle: π/2 + 2π = 5π/2.
Negative coterminal angle: π/2 - 2π = -3π/2.
According to the Fundamental Theorem of Algebra, which polynomial function has exactly 11 roots?
A ) f(x) = (x - 1)(x + 1)^11
B ) f(x) = (x + 2)^3(x^2 -7x +3)^4
C ) f(x) = (x^5 + 7x + 14)^6
D ) f(x) = 11x^5 + 5x + 25
I originally chose A, but that was incorrect on my quiz.
Answer:
The correct answer is B
Step-by-step explanation:
What is the x-coordinate for the minimum point in the function f(x) = 4 cos(2x − π) from x = 0 to x = 2π?
Sara left home and drove East 12 miles to Bakersville for her friends birthday cake then she drove 10 miles south to a friends house how far apart is Sarah's friends house and Sarah's house
How can one 1/4x − 3 = 1/2x + 8 be set up as a system of equations?
a. 4y + 4x = −12
2y + 2x = 16
b.4y − x = −12
2y − x = 16
c.4y + x = −12
2y + x = 16
d.4y − 4x = −12
2y − 2x = 16
highest value on the domain of the function is called what.
What is the measure of AC ? Enter your answer in the box. ° Circle with inscribed angle A B C. Angle A B C is 3 x minus 1.5 degrees. The intercepted arc A C is 3 x plus 9 degrees.
Use the Inscribed Angle theorem to get the measure of AC. The intercepted arc AC is [tex]21^{\circ}[/tex].
Given,
The inscribed angle [tex]\angle ABC[/tex] is [tex]3x-1.5[/tex].
And the Intercepted arc AC is [tex]3x+9[/tex].
What is the Inscribed Angle theorem?We know that, Inscribed Angle Theorem stated that the measure of an inscribed angle is half the measure of the intercepted arc.
So,
[tex]3x-1.5=\frac{1}{2} (3x+9)[/tex]
[tex]2 (3x-1.5)=3x+9[/tex]
[tex]6x-3.0=3x+9[/tex]
[tex]6x-3x=9+3[/tex]
[tex]3x=12\\x=4[/tex]
Since the intercepted arc AC is [tex]3x+9[/tex], putting the value of [tex]x=4[/tex] we get,
intercepted arc AC is [tex]21^{\circ}[/tex].
Hence the intercepted arc AC is [tex]21^{\circ}[/tex].
For more details on the Inscribed Angle theorem follow the link:
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Rylie's gross paycheck amount is $1305.60. She has 4% deducted from her paychecks for her 401(k). Her employer matches her deduction, up to 4%.
How mach is deducted from her paycheck for retirement plan?
A) $26.11
B) $52.22
C) $104.44
D) $522.24
The deduction from her paycheck is 52 dollars and 22 cents. Then the correct option is B.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
Rylie's gross paycheck amount is $1305.60. She has 4% deducted from her paychecks for her 401(k). Her employer matches her deduction, up to 4%.
So the deduction will be given as
[tex]\rm Deduction = \dfrac{4}{100} *1305.6\\\\Deduction = 0.04 * 1305.6\\\\Deduction = 52.224 \approx 52.22[/tex]
The deduction from her paycheck is 52 dollars and 22 cents. Then the correct option is B.
More about the percentage link is given below.
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a taxi company charges passengers $2.00 for a ride, no matter how long the ride is, and an additional $0.20 for each mile traveled. the rule c=0.20m + 2.00 describe the relationship between the number of miles m and the total cost of the ride c.
picking a multiple of 5 from the integers between 1 and 40
Are the two expressions equivalent when x = 20?
8(12x + 4)
96x + 32
The solution of the two expressions for x = 20 will be equivalent.
What is an expression?The mathematical expression combines 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 denote the logical syntax's operation order and other properties.
Given that the two expressions are 8(12x + 4) and 96x + 32. The expressions will be solved as,
8(12x + 4) = 8[12(20) + 4 ] = 1952
96x + 32 = 96 (20) + 32 = 1952
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Tara and julia run a race. Julia takes 42 seconds to run the race. She is 7 seconds faster than Tara. How many seconds does Tara take?
(HURRY!!! GET 24 PTS) The residential colony has a population of 5400 requires 60 liters of water is per person per day. For the effective utilization of rain water, a group of people decided for WATER HARVESTING. They constructed a water reservoir measuring 49mx27mx25m to collect the rain water. It this water reservoirs is full of water then for how many days it will last for the colony?
what he said hope it helped
Step-by-step explanation:
10 POINTS AND BRAINLIEST FOR CORRECT ANSWER!
A rectangle is inscribed in a square so that each vertex of the rectangle is located on one side of the square, and the sides of the rectangle are parallel to the diagonals of the square. Suppose that one side of the rectangle is twice the length of the other and that the diagonal of the square is 12 meters long. Find the sides of the rectangle.
9514 1404 393
Answer:
The sides of the rectangle are 4 and 8 meters long.
Explanation:
Please consider the attached figure. Both the rectangle and the square are symmetrical about the x- and y-axes, so we only need to consider the corner of the rectangle in one quadrant.
If the rectangle is twice as long as wide, then the distance of the corner to one axis (we chose y) will be twice the distance to the other axis. The locus of points for which that is true is the line with slope 1/2. The corner of the rectangle will be on that line.
If the corner of the rectangle is also on the square, then it will be located at the point of intersection of the line with slope 1/2 and the line representing the edge of the square. That point of intersection is the point (4, 2) on this graph. That is, half the length of the rectangle is 4 m, and half the width is 2 m. This indicates the sides of the rectangle are 8 m and 4 m in length.
__
The diagonals of the square are 12 m long, so orienting the square the way we have makes the x- and y-intercepts 6 units from the origin in each quadrant.
Answer:
Step-by-step explanation:
four and eight, use soh cah toa
Please help! The question is attached. And also I know the numbers on the triangle are blurry. The number on the long bottom of the triangle is 24, the one in the corner of the bottom of the triangle is 90 degrees, the side length is 18, and the diagonal angle is 26.
Which of the following is not a classification of the number given below? -3
What is a simpler form of the radical expression square root of 36g^6?
Hannah has $1000 in her savings account. During 1 month , she withdraws $25. Each successive month, she withdraws $10 more than the previous month . How much remains in her savings account after 10 months ?
Answer: A-$300 is correct
glacier is moving at a rate of 0.3 inches every hour. The table below represents this relationship.Glacial Movement
Distance Moved (inches)
Time
(hours)
0.3
1
0.6
2
0.9
3
x
4
What value of x completes the table?
1.2
1.5
3.6
13.3
Answer:
The correct option is 1.
Step-by-step explanation:
It is given that the glacier is moving at a rate of 0.3 inches every hour. It means the average rate of change is 0.3.
Let d is the total moved distance of glacier and t is number of hours. Then the total moved distance of glacier after t hours is defined as
[tex]d=0.3t[/tex]
At t=1,
[tex]d=0.3(1)=0.3[/tex]
At t=2,
[tex]d=0.3(2)=0.6[/tex]
At t=3,
[tex]d=0.3(3)=0.9[/tex]
At t=4,
[tex]d=0.3(4)=1.2[/tex]
Total moved distance of glacier after 4 hours is 1.2 inches.
The value of x is 1.2. Therefore the correct option is 1.
Find the value of x and the value
A: x=20,y=45
B:x=45,y=20
C:x=60,y=120
D:x=90,y=60
What is the area of a sector with a central angle of 4pi/3 radians and a radius of 11cm
Use 3.14 for pi and round to the nearest hundredth
675,360.41 in expanded notation
The expanded notation of 675,360.41 is 6 * 100000 + 7* 10000 + 5 * 1000 + 3 * 100 + 6 * 10 + 0 * 1 + 4 * 0.1 + 1 * 0.01
How to rewrite the number?The number is given as:
Number = 675,360.41
Express the numbers using their place values
Number = 6 * 100000 + 7* 10000 + 5 * 1000 + 3 * 100 + 6 * 10 + 0 * 1 + 4 * 0.1 + 1 * 0.01
The above expression represents the expanded notation
Hence, the expanded notation of 675,360.41 is 6 * 100000 + 7* 10000 + 5 * 1000 + 3 * 100 + 6 * 10 + 0 * 1 + 4 * 0.1 + 1 * 0.01
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how many triangles have the following measurements? A=38, a=432, b=382
Using the Law of Sines, we determined that it is possible to form one triangle with the given measurements A=38°, a=432, and b=382. The calculation includes finding angle B and angle C, ensuring all triangle conditions are met.
To determine how many triangles can have the given measurements (A=38°, a=432, b=382), we need to check if these values satisfy the triangle inequalities and if they can form a possible triangle using the Law of Sines.
First, let's use the Law of Sines which states that:
sin(A)/a = sin(B)/b = sin(C)/c
Given:
A = 38° (angle)a = 432 (side opposite to angle A)b = 382 (side opposite to angle B)We can calculate angle B using:
sin(B) = (b × sin(A)) / a
sin(B) = (382 × sin(38°)) / 432 ≈ 0.556
Finding the arc sine of 0.556, we get:
B ≈ 33.8°
Now, we find angle C:
C = 180° - A - B ≈ 180° - 38° - 33.8° = 108.2°
Using the Law of Sines again to find side c:
c = (a × sin(C)) / sin(A)
c = (432 × sin(108.2°)) / sin(38°) ≈ 676.85
Thus, it's possible to form one such triangle with the given conditions.
What's the difference between residential heating and cooling systems and commercial/industrial heating, cooling, or refrigerating facilities? A. The amount of energy the building or facility uses B. The location of the system—in a home or a business C. The number of people that occupy the building or facility D. The size of the building or facility
What is the value of x in the quadrilateral shown below?
A. 80°
B. 70°
C. 60°
The two figures are similar. What is the value of the marked angle?
A. 108
B. 72
C. 90
D. 162
I think its b
Hope this helps
If the radius of a circle is 18 yd, then the diameter of the circle is 9 yd
TRUE OR FALSE
Answer:
Step-by-step explanation: False.
What is the solution of the system?
{ 2x+y=15
{x−y=3
Enter your answer in the boxes.
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