So the value of x in terms of the radius r is 4r cos(42).
What is tangent line?A tangent line is a straight line that touches a curve or surface at a single point and has the same slope as the curve or surface at that point. In geometry, the tangent line to a curve at a particular point is defined as the limit of the secant line through two points on the curve that approach the point as these points get closer and closer. The tangent line provides a good approximation to the curve near the point of tangency and is used in many applications such as calculus, physics, and engineering.
Here,
Let's consider a circle with center O and radius r, and let A and B be the points where the tangent lines intersect the circle. We are given that the angle between the tangent lines is 84 degrees, which means that angle AOB is also 84 degrees (because it is a central angle that intercepts the same arc as the tangent lines). Now, let's draw a line from the center O to the midpoint C of segment AB. Since OC is perpendicular to AB (by the tangent-secant theorem), we can use trigonometry to find its length. Let x be the length of the sector intercepted by arc AB, and let y be the distance from O to C. Then, we have:
sin(42) = y / r (because angle COA is 42 degrees, half of 84)
cos(42) = x / (2r) (because angle AOB is 84 degrees, so angle AOC is 42 degrees)
Solving for y and x, we get:
y = r sin(42)
x = 2r cos(42)
Finally, we can use the Pythagorean theorem to solve for the length of AB:
AB² = 4y² + x²
= 4r² sin²(42) + 4r² cos²(42)
= 4r² (sin²(42) + cos²(42))
= 4r²
Therefore, AB = 2r. Now we can use the equation x = 2r cos(42) to solve for x:
x = 2r cos(42)
= 2AB cos(42)
= 2(2r) cos(42)
= 4r cos(42)
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PLSS HELP ME ASAP!! I WILL GIVE YOU BRAINLYEST!
A tree casts a 9-foot shadow while a 5-foot
pole casts a 2h foot shadow. How tall is the
tree?
the answer tho this is that the tree is 14ft
Answer:
22.5
Step-by-step explanation:
20 ft for an 8 foot shadow but since you need 1 more foot
take half of 5 (2.5) and you get 22.5
If a certain cannon is fired from a height of 9.8 meters above the ground, at a certain angle, the height of the cannonball
above the ground, h, in meters, at time, t, in seconds, is found by the function h(t) = -4.9t² + 24.5t+9.8. Find the time it
takes for the cannonball to strike the ground.
Answer:
5.4 seconds-----------------------------------------
When the cannonball lands the height h is zero.
Set the value of the function as zero and solve for t:
-4.9t² + 24.5t + 9.8 = 0t² - 5t - 2 = 0t = (5 ± √(5² + 8))/2 t = (5 ± √33)/2t = (5 - √33)/2 or t = (5 + √33)/2 t = - 0.4 or t = 5.4 (rounded)The greater value of t represents the time we need.
Warren earns $21.75 per hour and worked 36.5 hours last week and 32 hours the
week before. What is Warren's gross pay for the two weeks? Show your work.
Answer:
$1,489.88 (nearest cent)
Step-by-step explanation:
To calculate gross pay, multiply the number of hours worked by the pay per hour.
Warren worked 36.5 hours one week and 32 hours the week before.
Therefore, the total number of hours Warren worked was:
36.5 + 32 = 68.5 hoursMultiply the total number of hours worked by Warren's rate of pay of $21.75 per hour:
68.5 × 21.75 = 1489.875Therefore, Warren's gross pay for the two weeks was $1,489.88 (nearest cent).
Answer:
$1489.875
Step-by-step explanation:
Warren's gross pay for 36.5 hours last week can be calculated as follows:
Gross pay for 36.5 hours = $21.75/hour * 36.5 hours = $793.875
Similarly, Warren's gross pay for 32 hours the week before can be calculated as follows:
Gross pay for 32 hours = $21.75/hour * 32 hours = $696
Adding the gross pay for the two weeks, we get:
Gross pay for 2 weeks = $793.875 + $696 = $1489.875
Ryan invested \$4,800$4,800 in an account in the year 1990, and the value has been growing exponentially at a constant rate. The value of the account reached \$6,300$6,300 in the year 1998. Determine the value of the account, to the nearest dollar, in the year 2007.
well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.
\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8\)
\(\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r\)
now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?
\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02\)
If b and c are the same distance from 0, describe their relationship to each other as it is represented on the number line.
Answer:
opposite numbers
equidistant
Step-by-step explanation:
example, if 'b' = 1 then 'c' is the opposite which is -1
please tell me please
The cost price is always used to compute the loss or gain percentage.
How are the prices and their percentages calculated?No. of packets purchased = 250
Cost price of 250 packets = 8 (250) = 2000
Selling price of 70% of packets = 11 per packet
Selling price of 30% of packets = 9 per packet
II) Selling price of 70% of packets
70% of 250
= 70/100×250
= 175
Selling price of 70% of packets is 11 per packet
S. P of 70% = 175 * 11
= Rs.1925
S. P of 30% = 250- 175 = 75
=75* 9
= Rs.675
Selling price of 250 packets = Rs.2600
So, option (a) is correct.
III) 30% of 250
= 30/100×250
= 75
So, option (c) is correct.
IV ) Gain = Selling price - Cost price
=2600 - 2000
= 600
So, option (d) is correct.
I) Gain % = Gain/ C.P * 100
= (600/ 2000) * 100
= 30 %
So, option (c) is correct.
V) Gain % is always calculated on Cost price
So, option (a) is correct.
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x+y=16
y=3x=4
find the solution using substitution
Answer: x=3 ; y=13
Step-by-step explanation:
1. isolate y from equation to substitute into the second equation
y= 16-x ---> (16-x) = 3x+4
2. move to one side and solve for x
4x=12 --> x=3
3. plug in x value to solve for y
3+y=16 or 3(3)+4
y=13
how to find the rate of change
Answer:
Step-by-step explanation:
rate of change is essentially slope
\(Rate Of Change = \frac{rise}{run}\) or
\(Rate Of Change = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }\) or
\(Rate Of Change = \frac{f(x_{2})- f(x_{1}) }{x_{2} -x_{1} }\)
Please help I need help please
Step-by-step explanation:
There are 84% out of 225. First find 10%. To do that divide the number by 10, so 225 ÷ 10 = 22.5 Next, do 22.5 x 8. Then you have 80%. Now, all that is need ed is the 4%. To get that, divide 225 by 100. Multiply the answer by 4 to get the 4%. Add the 80% and the 4% to get your answer. I really hope this helps. answers
Also, since I am just helping, I am un able to give you straight answers. I hope this also helps with work in the future.
Which equation represents the line that passes through points (1, –5) and (3, –17)? y = negative 6 x + 1 y = 6 x + 1 y = negative 6 x minus 1 y = 6 x minus 1
Answer:
[see below]
Step-by-step explanation:
Finding the slope of the two points:
\(m=\frac{-17+5}{3-1}=\frac{-12}{2}=\boxed{-6}\)
The slope is -6.
Using an incomplete slope-intercept form equation to find the y-intercept:
\(y=6x+b\\\\-5=6(1)+b\\\\-5=6+b\\\\-5-6=6-6+b\\\\\boxed{1=b}\)
The equation for the line passing the points is \(y=-6x+1\).
The equation in standard from would be \(6x+y=1\).
Which of the following would not be used to describe a slope?
steepness of a line.
ratio of rise to run of a line.
ratio of the horizontal change to the vertical change of a line.
Answer:
C: ratio of the horizontal change to the vertical change of a line
Step-by-step explanation:
A and B are correct.
C is incorrect.
2. 5 kg of potatoes cost £1. 40
workout the cost of 4. 25 kg of potatoes
Write down the reciprocal of 3, a quarter, and 6a
Answer:
3= 1/3
25=100/25
i dont know about 6a on what u want me to do
sorry
Step-by-step explanation:
Mandy makes beaded bracelets and sells them for $5 each. If she sells the bracelets for 250% of the cost of her materials, how much does each bracelet cost to make?
Each bracelet costs $
to make.
Answer:
Each bracelet cost $2 to make.
Step-by-step explanation:
I did the assignment.
Answer:
$2
Step-by-step explanation:
(Brainliest plz) if im right
Lena buys a brand new washing machine and a dryer for $7500
.
The washing machine costs 70%
of the price of the dryer.
What is the price of the dryer?
Answer:
$2250
Step-by-step explanation:
if the cost of the washing machine is 70% of the cost she paid. then the cost of the dryer must be:
100-70 =30%
Now, to find the cost of the dryer, you just have to find 30%of 7500
30/100x 7500 = 2250
Thus, the dryer costs $2250.
Hope this helps.
Good luck
PLEASE HELP!
Line R is represented by the following equation: x + y = 2
Which equation completes the system that is satisfied by the solution (1, 1)?
2x + y = 2
4x − 2y = 2
2x − 2y = 2
x + y = 4
Answer:
4x - 2y = 2
Step-by-step explanation:
Given that (1, 1 ) is a solution then it must satisfy the equation
Consider the equations given
2x + y = 2 → 2(1) + 1 = 2 + 1 = 3 ≠ 2 ← not True
4x - 2y = 2 → 4(1) - 2(1) = 4 - 2 = 2 ← True
2x - 2y = 2 → 2(1) - 2(1) = 2 - 2 = 0 ≠ 2 ← not True
x + y = 4 → 1 + 1 = 2 ≠ 4 ← not True
Thus
4x - 2y = 2 completes the system.
on a number line,AB=3 2/3.The position of point B is 2/5.What is the position of point A
Answer:
-49/15
Step-by-step explanation:
To determine the position of point A on the number line, we need to subtract the length of segment AB from the position of point B.
Given that the position of point B is 2/5, we can subtract the length of AB, which is 3 2/3, from 2/5.
To subtract fractions, we need to find a common denominator. The least common denominator for 3/3 and 5 is 15.
Converting 3 2/3 to an improper fraction:
3 2/3 = (3 * 3 + 2)/3 = 11/3
Subtracting the fractions:
2/5 - 11/3 = (2 * 3 - 11 * 5)/(5 * 3) = (6 - 55)/15 = -49/15
The position of point A is -49/15 on the number line.
(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)
please hurry I really need help!
13. The table shows the times of runners completing a
marathon. To qualify for the next marathon, a
runner's time must be less than 3 hours. Which
runners qualify?
Cho
Kevin
Runner
Ojas
Sydney
Time (h)
3-1/
3.2
8
30
13
360
3-
Answer:
Step-by-step explanation:
the answer is 30
As an estimation we are told 5 miles is 8 km.
Convert 84 km to miles.
Answer:
52.5 miles
Step-by-step explanation:
5 miles = 8 km
→ Find how many miles in 1 km
8 km = 5 miles
1 km = 0.625 miles
→ Multiply both sides by 84
84 km = 52.5 miles
i hope this work for you
and sory if im wrang
Determine the zeroes of the function of f(x)=
3(x2-25)(4x2+4x+1)
The zeroes of the function f(x) = 3(x²-25)(4x^2+4x+1) are x = -5, x = 5, x = -0.5 - 0.5i, and x = -0.5 + 0.5i.
To find the zeroes of the given function f(x), we set f(x) equal to zero and solve for x. The function f(x) can be factored as follows: f(x) = 3(x²-25)(4x²+4x+1).
The first factor, (x²-25), is a difference of squares and can be further factored as (x-5)(x+5). The second factor, (4x²+4x+1), is a quadratic trinomial and cannot be factored further.
Setting each factor equal to zero, we have three equations: (x-5)(x+5) = 0 and 4x²+4x+1 = 0. Solving the first equation, we find x = -5 and x = 5 as the zeroes.
To solve the second equation, we can use the quadratic formula: x = (-b ± √(b²-4ac))/(2a), where a = 4, b = 4, and c = 1. Plugging in these values, we get x = (-4 ± √(4^2-4*4*1))/(2*4). Simplifying further, we have x = (-4 ± √(16-16))/(8), which simplifies to x = (-4 ± √0)/(8). Since the discriminant is zero, the quadratic has complex conjugate zeroes. Therefore, x = -0.5 - 0.5i and x = -0.5 + 0.5i are the remaining zeroes of the function.
In summary, the zeroes of the function f(x) = 3(x²-25)(4x²+4x+1) are x = -5, x = 5, x = -0.5 - 0.5i, and x = -0.5 + 0.5i.
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1 Write down: 1.1.1 The factors of 18
Answer:
1 2 3 6 9 and 18
Step-by-step explanation:
the 111 factors of 18 is 1 2 3 6 9 ang 18
A survey item asked students to indicate their class rank in college: freshman, sophomore, junior, or senior. Which measure(s) of location would be appropriate for the data generated by that questionnaire item
For the data generated by the questionnaire item that asked students to indicate their class rank in college, the appropriate measure of location would be the mode.
The mode is the value that occurs most frequently in a dataset and represents the most common response. In this case, the mode would indicate the most common class rank among the students surveyed. It is important to note that the use of the mode as a measure of location is most appropriate when dealing with nominal or ordinal data, such as class rank, where there is no inherent numerical relationship between the categories.
Other measures of location, such as the mean or median, are more appropriate for interval or ratio data where there is a meaningful numerical relationship between the values.
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For the point P(-3,0) and Q(4,3), find the distance d(P,Q) and the coordinates ofthe midpoint M of the segment PQ.
SOLUTION
Write out the given coordinate of point P and Q
\(\begin{gathered} P=(-3,0) \\ \text{and} \\ Q=(4,3) \end{gathered}\)
The distance between two point is given by
\(\text{dist}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}^{}\)
Given point P(-3,0) and Q(4,3)
\(\begin{gathered} x_2=4,x_1=-3,y_2=3,y_1=0 \\ \text{Then } \\ \text{dist(P,Q)}=\sqrt[]{(4-(-3)^2+(3-0)^2} \end{gathered}\)Hence, by simplification, we have
\(\begin{gathered} \text{dist(P,Q)}=\sqrt[]{7^2+3^2}=\sqrt[]{49+9}=\sqrt[]{58} \\ \end{gathered}\)Hence
The distance between point P and Q is √58 unit
Then
The coordinates of the midpoint is given by
\(\begin{gathered} Let\text{ the coordinate of the midpoint m be } \\ (x_m,y_m) \\ \text{Hence } \\ (x_m,y_m)=(\frac{x_1+x_2}{2}+\frac{y_1+y_2}{2}) \end{gathered}\)
Where
\(\begin{gathered} x_2=4,x_1=-3,y_2=3,y_1=0 \\ \text{Then} \\ (x_m,y_m)=(\frac{-3+4}{2},\frac{3+0}{2}) \\ \\ (x_m,y_m)=(\frac{1}{2},\frac{3}{2}) \end{gathered}\)Therefore
The coordinates of the midpoint M of the segment PQ is (1/2,3/2)
A group of 8 people bought tickets to a show. the tickets cost $21.48 each. what was the total cost of the tickets? enter your answer in the box. $
A group of 8 people bought tickets to a show. the tickets cost $21.48 each. then we get total cost is $ 171.84.
According to the question, given that
A group of 8 persons purchased show tickets for a price of $21.48 each.
The total cost of the tickets was calculated as follows:
= 8 * 21.48
= 171.84
Therefore, we get total cost = $ 171.84
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions written on the left and the right.
Mathematicians refer to equations with a degree of 1 as linear equations. The largest exponent of terms in these equations is 1, which equals. These can also be broken down into linear equations with one variable, two variables, three variables, etc. A linear equation with the variables X and Y has the usual form an X + b Y - c = 0, where a and b are the corresponding coefficients of X and Y and c is the constant.
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6 ( x- 5 )^(2) + 1 = 19
options:
5 plus-or-minus square root of 3
5 plus-or-minus square root of 10 over 3 end root
13 over 2
Answer:
=5±3
Step-by-step explanation:
HELP
Karen bought a pizza for $11.95. She got back $3.05 in change. Write a
subtraction equation to find out how much money Karen had before she
the pizza.
with which measurement procedure is the target behavior recorded if it occurs at any point within the scoring interval?
If the target behavior is recorded whenever it occurs at any point within the scoring interval, the measurement procedure used is called continuous recording or event recording. This method involves observing and recording each instance of the behavior without considering its duration or intensity.
Continuous recording is typically used when the target behavior is discrete and occurs relatively infrequently or has a short duration. With this measurement procedure, each occurrence of the behavior is recorded as a separate event, regardless of when it starts or ends within the scoring interval. Examples of behaviors that can be measured using continuous recording include vocalizations, hand clapping, or instances of aggression.
Continuous recording provides a comprehensive account of the frequency or rate at which the behavior occurs, allowing for a detailed analysis of its occurrence patterns. This method is particularly useful when a precise count of behavior instances is needed and when the duration or intensity of the behavior is not a focus of measurement.
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Many psychologists do not use hypnosis in their
practices, it is because they know very little about it
and are wary of it as a result.
(A) practices, it is because they know very little about
it and are wary of it as a result
(B) practices because they know very little about it
and are therefore wary of it
(C) practices for the reason that they know very little
about it, with resulting wariness
(D) practices because of knowing very little about it
and therefore they are wary of it
(E) practices, their knowledge of it being very little
results in wariness of it
Many psychologists do not use hypnosis in their practices, it is because they know very little about it and are wary of it as a result.
Who are psychologists?A psychologist is a specialist in the field of psychology who investigates behavior as well as mental states, perceptual, cognitive, emotional, and social processes. They frequently experiment with, observe, and interpret how people interact with one another and their surroundings as part of their work. Someone who examines the mind and behavior is called a psychologist. When people hear the word "psychologist," they frequently picture talk therapy; however, this profession actually covers a wide range of specialization areas, including things like animal studies and organizational behavior.
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The americans with disabilities act states that ramps must have an angle less than or equal to 4.8 degree angle in a right triangle has a 1:12 ratio for the legs. Select all designs of a ramp that meet the americans with disabilities act requirements. Answers to pick from : Right triangle with legs 3 meters and 33 meters. Right triangle with legs 1 meters and 15 meters. Right triangle with legs 12 meters and 140 meters. Right triangle with legs 12 meters and 150 meters. right triangle with legs 24 meters and 240 meters.
Answers are ,Right triangle with legs 3 meters and 33 meters, Right triangle with legs 1 meter and 15 meters, Right triangle with legs 12 meters and 140 meters, Right triangle with legs 12 meters and 150
what is Right triangle ?
A right triangle is a triangle that has one angle equal to 90 degrees (a right angle). The other two angles are acute angles (less than 90 degrees). The side opposite to the right angle is called the hypotenuse, and the other two sides are called legs.
In the given question,
The ratio of the legs of the right triangle for a ramp should be 1:12, which means that for every 1 inch of rise, there should be 12 inches of ramp length. To calculate the angle of inclination, we can use the inverse tangent function, which gives us the angle whose tangent is equal to the ratio of the legs. The angle of inclination should be less than or equal to 4.8 degrees.
Let's calculate the angle of inclination for each ramp design:
Right triangle with legs 3 meters and 33 meters:
The ratio of the legs is 3:33, which simplifies to 1:11. The length of the ramp is 11 times the height of the rise. The angle of inclination is:
arctan(1/11) ≈ 4.76 degrees
The angle of inclination is less than or equal to 4.8 degrees, so this ramp design meets the requirements of the Americans with Disabilities Act.
Right triangle with legs 1 meter and 15 meters:
The ratio of the legs is 1:15. The length of the ramp is 15 times the height of the rise. The angle of inclination is:
arctan(1/15) ≈ 3.81 degrees
The angle of inclination is less than or equal to 4.8 degrees, so this ramp design also meets the requirements of the Americans with Disabilities Act.
Right triangle with legs 12 meters and 140 meters:
The ratio of the legs is 12:140, which simplifies to 3:35. The length of the ramp is 35 times the height of the rise. The angle of inclination is:
arctan(3/35) ≈ 4.56 degrees
The angle of inclination is less than or equal to 4.8 degrees, so this ramp design meets the requirements of the Americans with Disabilities Act.
Right triangle with legs 12 meters and 150 meters:
The ratio of the legs is 12:150, which simplifies to 2:25. The length of the ramp is 25 times the height of the rise. The angle of inclination is:
arctan(2/25) ≈ 4.62 degrees
The angle of inclination is less than or equal to 4.8 degrees, so this ramp design meets the requirements of the Americans with Disabilities Act.
Right triangle with legs 24 meters and 240 meters:
The ratio of the legs is 24:240, which simplifies to 1:10. The length of the ramp is 10 times the height of the rise. The angle of inclination is:
arctan(1/10) ≈ 5.71 degrees
The angle of inclination is greater than 4.8 degrees, so this ramp design does not meet the requirements of the Americans with Disabilities Act.
Therefore, the ramp designs that meet the requirements of the Americans with Disabilities Act are:
Right triangle with legs 3 meters and 33 meters.
Right triangle with legs 1 meter and 15 meters.
Right triangle with legs 12 meters and 140 meters.
Right triangle with legs 12 meters and 150 meters.
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A rectangle has a length of (10x-3) and a width of (2x+2). Find the perimeter
Answer:
24x-2
Step-by-step explanation:
Perimeter is 2(L+w)
(10x-3)+(2x+2)
Combine like terms
12x-1
2(12x-1)
24x-2
Answer:
The perimeter is 24x - 2.
Step-by-step explanation:
The perimeter of a rectangle is found using the following formula: \(2(l+w)\). The length and width added together are 10x - 3 + 2x + 2 or 12x - 1, multiply that by 2 and you'll get that the perimeter is equivalent to 24x - 2.