4. Find the diameter of the circle for BC = 10 and DC = 23. Round to the nearest tenth. The diagram is not drawn to scale. (1 point) 62.9 52.9 7.7 42.9
Answers
Use Pythagorean theorem:
[tex]r^2+23^2=(r+10)^2\\\\use\ (a+b)^2=a^2+2ab+b^2\\\\r^2+529=r^2+2\cdot r\cdot10+10^2\\\\r^2+529=r^2+20r+100\ \ \ |subtract\ r^2\ from\ both\ sides\\\\529=20r+100\ \ \ \ |subtract\ 100\ from\ both\ sides\\\\20r=429\ \ \ |divide\ both\ sides\ by\ 20\\\\r=21.45[/tex]
The diameter d = 2r, therefore
[tex]d=2\cdot21.45=42.9[/tex]
Related Questions
A plane is flying at an altitude of 32,000 feet. The distance between the plane and a radio tower on the ground is 50,000 feet. What is the angle of depression between the plane and radio tower (round to 1 decimal place)?
Answers
Find the first derivative?
Answers
y = 1/(x - 2) - 3
y' = d(x - 2)^-1 / dx The three is a constant and will disappear.
y' = d(x - 2)^-1 -1 d(x - 2)/dx
y' = -1*(x - 2)^-2 * 1
The minus comes from bringing down the original power down and reducing the power by one of the question. The 1 at the end comes from differentiating what is inside the brackets. It is called the chain rule
d(x - 2) / dx = d(x) / dx which is 1. The two, being a constant, disappears. The final answer is
y' = - (x - 2)^-2
Answer:
[tex]\displaystyle y' = \frac{-1}{(x - 2)^2}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \frac{1}{x - 2} - 2[/tex]
Step 2: Differentiate
Derivative Rule [Quotient Rule]: [tex]\displaystyle y' = \frac{1'(x - 2) - 1(x - 2)'}{(x - 2)^2}[/tex]Basic Power Rule [Derivative Property - Addition/Subtraction]: [tex]\displaystyle y' = \frac{-1(1)}{(x - 2)^2}[/tex]Simplify: [tex]\displaystyle y' = \frac{-1}{(x - 2)^2}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
what’s a transversal angle
Answers
A transversal is two parallel lines intersected by a third line at an angle. The third line is referred to as thetransversal line. When this line happens, severalangles are created. You can use these angles to find the measurements of other angles.
tom has twice as much as peter. peter has half as much as Mary. together they all have a total of $15.00. how much money did each have?
Answers
Tom=$6
Mary=$6
Peter=$3
Using 125 words or more, write a short paragraph discussing the reasons why someone should make a wil
Answers
A will tells everyone what will happen to your money, possessions, and property when you die. There are many reasons to make a will. First, it will be easier for your family and friends to sort everything out. Without a will, it can be very stressful and time consuming to figure out how to allocate everything. Plus, if you don't have a will the law will decide how to allocate it and this might not be the way you want it. It can be especially important to write a will if you have children or other family that depend on you financially. This way, you can leave them the most possible to help them even when you are no longer alive. By writing a will, you can decrease the amount of inheritance tax that might need to be paid on any property and money that you will leave behind. Ultimately, by writing a will you will be able to decide who you leave your money, possessions, and property to when you die which can be very important to some individuals.
Joy started with 2.75 gallons of milk. She used 1.5 pints to make mashed potatoes and another cup to make cookies. How much milk does joy have left?
Answers
1 cup=0.0625 gallons
1 pint=0.125 gallons
amount used to make mashed potatoes:
1.5×0.125=0.1875 gallons
amount used to make cookies=0.0625 gallons
total amount of milk used:
0.0625+0.1875=0.25
Remaining amount
=2.75-0.25=2.5 gallons
A class's test scores are normally distributed. If the average score is 60 and the standard deviation is 7, choose the spots where the students scoring below 46 and above 74 lie.
Answers
Answer with Step-by-step explanation:
We are given that a class's test scores are normally distributed with the average score 60.
We know that the curve of a normal distribution is symmetric about its mean.
60-14=46
60+14=74
Hence, the point 46 lies to the left of the mean and 74 lies to the right of mean and the two points have the same function value
(since the graph is symmetric to the left and right of mean i.e. points which are equidistant from the mean have same values)
Answer:
One of the answers I got that was correct was the box on the furthest left.
Step-by-step explanation:
Below is the graph of y=b^x. Find b.
Answers
when x = 1
y = b^1
y = b
Therefore, the value of b is the same as the value of y when x =1
From the graph,
When x = 1, y = 0.5
Therefore, b = 0.5
To confirm this
From the graph,
When x = -1, y = 2
Since y = b^x
2 = b^-1
2 = 1/b
2b = 1
b = 0.5
When x = -2, y = 4
Since y = b^x
4 = b^-2
4 = 1/(b^2)
b^2 = 1/4
b = √(1/4)
b = 1/2
b = 0.5
Therefore, it is conformed that b = 0.5
Functions can be represented as equations, and equations can be represented as functions.
The value of b is 1/2
The graph is given as:
[tex]\mathbf{y = b^x}[/tex]
From the graph, we have the following point:
(x,y) = (-1,2)
Substitute these values in the function
[tex]\mathbf{2 = b^{-1}}[/tex]
Rewrite as:
[tex]\mathbf{2 = \frac{1}{b}}[/tex]
Multiply both sides by b
[tex]\mathbf{2b = 1}[/tex]
Divide both sides by 2
[tex]\mathbf{b = \frac{1}2}[/tex]
Hence, the value of b is 1/2
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Amy owns a graphic design store. She purchases a new printer to use in her store.
The printer depreciates by a fixed rate of 14% per year. The function
V = 2,400(1 – 0.14)t can be used to model the value of the printer in dollars after
t years.
Question:
Part A: Explain what the parameter 2,400 represents in the equation of the function.
Part B: What is the factor by which the printer depreciates each year?
Part C: Amy also considered purchasing a printer that costs $4,000 and depreciates by 25% each year. Which printer will have more value in 5 years? Justify your answer by showing/explaining your work.
Answers
y=a(b)^x
where:
V=y
a=2400
b=1-0.14
x=t
thus:
Part A: Explain what the parameter 2,400 represents in the equation of the function.
The parameter 2400 represents the initial value of the printer at time t=0. This is the original value.
Part B: What is the factor by which the printer depreciates each year?
The factor of depreciation is 14% percent. This is the rate at which the printer depreciates and it accounts for the value of the printer at the end of every year.
Part C: Amy also considered purchasing a printer that costs $4,000 and depreciates by 25% each year. Which printer will have more value in 5 years?
Value after 5 years of the $2400 printer that depreciates at 14% per year will be:
V(t)=2400(1-0.14)^5=$1,129.025
Value after 5 years of the $4000 printer that depreciates at 25% per year will be:
F(t)=4000(1-0.25)^t
F(5)=4000(1-0.25)^5=$949.22
The printer that costs $2400 will be more valuable compared to the printer that cost $4000
When a parabola represented by the equation y - 2x 2 = 8 x + 5 is translated 3 units to the left and 2 units up, the new parabola has its vertex at
Answers
y = 2x 2 + 8 x + 5
Complete square and determine vertex.
y = 2(x 2 + 4x + 4) - 8 + 5
= 2(x + 2) 2 - 3
vertex at (- 2 , - 3)
If parabola is translated 3 units to the left and 2 units up its vertex is also translated 3 units to the right and 2 units up .
vertex after translations is at: (-2 - 3 , - 3 + 2) = (-5 , -1)
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Suppose you want to organize a community watch, one from each street. you have 5 volunteers from maple street and 3 volunteers from elm street. how many permutations do you get?
Answers
One one side there are 5 volunteers and on the other side there are 3 volunteers. You just have to multiply 5 by 3 and you get 15 different options.
Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of g(x) if g(x) = f(x) + 3?
A.
It is the graph of f(x) translated 3 units up.
B.
It is the graph of f(x) translated 3 units to the right.
C.
It is the graph of f(x) where the slope is decreased by 3.
D.
It is the graph of f(x) translated 3 units down.
Answers
The statement correctly describes the graph of g(x) if g(x) = f(x) + 3, it is the graph of f(x) translated 3 units down. The correct option is D.
What is transformation of graph?When an existing graph is modified to produce a new variation of the existing graph.
Let y = f(x) then f(x)-3 means y-3. Subtracting 3 from the y coordinate of each point will move the entire curve down 3 units.
Thus, the correct option is D.
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An electrician can wire a house in 20 hours. if she works with an apprentice, the same job can be completed in 12 hours. how long would it take the apprentice, working alone, to wire the house?
Answers
It would take the apprentice 30 hours to wire the house alone.
Explanation:Let's assume that the work done by the electrician alone in 1 hour is represented by E, and the work done by the apprentice alone in 1 hour is represented by A. According to the given information, the electrician can wire the house in 20 hours, so E = 1/20. When the electrician and the apprentice work together, they can wire the house in 12 hours, so their combined work in 1 hour is represented by (E + A) = 1/12.
To find out how long it would take the apprentice to wire the house alone, we can subtract the work done by the electrician in 1 hour (E) from the combined work done by both the electrician and the apprentice in 1 hour (E + A), which gives us A = (E + A) - E. Substitute the values:
A = (1/12) - (1/20) = (20 - 12) / (12 x 20) = 8 / 240 = 1/30.
So, the apprentice can wire the house alone in 30 hours.
At a carnival, Brian bought 9 packs of 16 tickets each. He uses 39 tickets so far . how many tickets does he have left
Answers
The number of tickets left after using 39 tickets is 105.
What is multiplication?Multiplication is the process of adding a number up to a given number
Given that, there are 9 packs and there are 16 tickets in each pack.
Therefore, the total number of tickets is:
16 × 9
= 144
Now, the number of available tickets after using 39 tickets:
144 - 39
= 105
Hence, the number of tickets left after using 39 tickets is 105.
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1)
At 1 pm the shadow of a tree is 14 feet long. At the same time the shadow of a 18 foot telephone pole is 21 feet long. What is the height of the tree?
A) 9 feet
B) 12 feet
C) 18 feet
D) 22 feet
Answers
telephone pole = 18ft high / 21ft shadow
tree = x ft high / 14 ft shadow
18/21 = x/14
cross multiply 18 x 14 = 252
21 x x = 21x
x = 252 / 21
x = 12
the tree is 12 feet tall
Answer is B
If 6 is 30% of a value,
a.what is 70% of that value? b8 is omlwhat is 10%of the value?
Answers
[tex].3x = 6 \\ x = \frac{6}{.3} \\ x = 6 \times \frac{10}{3} = 20[/tex]
so our value is 20 and as 10% of 20 is 2 we see 30% of 20 is 2×3=6
now we want to find 70% of 20 and 10% of 20. we already know 10% of 20 is 20 because to find 10% we take the value 20.0 and move the decimal 1 place to the left which gives us 2.0. To find 70% we can multiply 20 by .7 or since we know 10% just multiply that by 7 because 10% ×7 =70% so 2×7=14 so 14 is 70% of 20. solving the other way we get
[tex]20 \times .7 = 20 \times \frac{7}{10} = \frac{20}{10} \times 7 = 2 \times 7 \\ = 14[/tex]
so we can see we are correct!
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A ball is thrown into the air with an upward velocity of 32 ft/s. Its height (h) in feet after t seconds is given by the function h= -16t^2 + 32t + 6. How long does it take the ball to reach its maximum height? What is the ball’s maximum height? Roun
Answers
h = -16t ^ 2 + 32t + 6
Deriving we have:
h '= -32t + 32
We equal zero and clear t:
-32t + 32 = 0
32t = 32
t = 32/32
t = 1 s
Then, the maximum height is given by:
h (1) = -16 * (1) ^ 2 + 32 * (1) + 6
h (1) = 22 feet
Answer:
It takes the ball to reach its maximum height about:
t = 1 s
The ball's maximum height is:
h (1) = 22 feet
Find the absolute maximum value of the function
Answers
f'(x) = {2, -2 < x < 0
{ -2x, x>0
The critical number is x = 0. We can also see that f(x) is decreasing on x>0.
We check the end points and critical numbers for the absolute maximum. One end point at
f(-2) = 2(-2) + 1 = -3
The critical number checked gives
f(0) = -0^2 + 1 = 1
The absolute maximum value is 1.
5 plus 5 divided by 2 times 300032 plus 6
Answers
5/2=2.5
2.5x300,032
750,080+11
750,091
STEPS:
DIVIDE AND MULTIPLY:
5 + 5/2 (300032) + 6
= 5 + 750080 + 6
ADD:
= 750085 + 6
= 750091
FINAL ANSWER: 750091
The lenght of a rectangle is twice its width. The area of the rectangle is 18 square centimeters. Find the perimeter of the rectangle?
Answers
2x = length as given in the description
Area of a rectangle is length * width so we do:
2x(x) = 18
2x² = 18
Divide by 2 to isolate our variable:
x² = 9
√x² = √9
x = 3
Length = 6, width = 3
Perimeter = (Length * 2) + (Width * 2)
We plug in our new information to find the perimeter.
P = (6*2) + (3*2)
= 12 + 6
= 18
The perimeter of the rectangle is 18 centimeters. Ironically, matching its area.
∞∞∞∞∞∞∞∞∞
Explanation:
∞∞∞∞∞∞∞∞∞
Width = W
Length = 2W
Area = 18 cm²
Area = Length x Width
18 = 2W x W
18 = 2W²
W² = 18 ÷ 2 = 9
W = √9
W = 3
Perimeter = 2(Length + Width) = 2(3 + 2(3)) = 2(9) = 18 cm
A 4-foot tall person standing with her back to the sun casts an 6-foot long shadow. To the nearest degree, what angle does the sun make with the ground?
Answers
tan θ=opposite/adjacent
opposite=4 ft
adjacent= 6ft
thus
tan θ=4/6
θ=arctan 4/6=33.69°
width = (b - a)/n = (8 - 0)/4 = 2
2(f(0) + f(2) + f(4) + f(6))
2(-1 - 2.5 - 1.5 - 0.5)
2(-5.5)
-11
Is my answer C, -11? The question says four subintervals, so I used f(0), f(2), f(4), and f(6). I want to make sure that I am NOT supposed to be using f(8), because f(8) would give me a final answer of D. -13.5
Answers
Since it's asking for the left-endpoint Riemann Sum, you will only be using the top left point as the height for each of your four boxes, making -1, -2.5, -1.5, and -0.5 your heights. The bases are all the same length of 2. You don't include f(8) because you're not using right-endpoints, and that would also add another 5th box that isn't included in the 0 to 8 range.
How do you find the lateral area of the prism
Answers
The lateral area is the area of the figures connecting the bases. We have rectangles here. We'll need to find the area of each figure and add them together to find the lateral area.
WORK:
(2.8 x 12) + (8.1 x 12) + 2(4 x 12)
33.6 + 97.2 + 96
LA = 226.8 units^2
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A newly hatched channel catfish typically weighs 0.3 grams. During the first 6 weeks of life, its growth is approximately exponential, increasing by about 10% each day. Find the weight at the end of four weeks. (Hint: Be sure to change the number of weeks to days before plugging into the formula!) Formula: A=C(1+r)t
0.53g
4.33g
16.43g
1.14g
Answers
Explanation:
1) The formula is given: A = C(1+r)ˣ ↔ (I used x instead of t just do to limitations of the math editor. Keep in mind that here x is time in days.
2) r is the rate of increasing given: 10% = 10/100 = 0.1
3) C is the initial weight and A is the final weight after x (or t) days.
4) The equation leads to:
A = 0.3 (1 + 0.1)ˣ = 0.3(1.1)ˣ
x = number of days = 7 × number of weeks = 7 × 4 = 28 days
4) Compute:
A = (0.3g)(1.1)²⁸
A = 4.33g ← answer
The weight of a newly hatched channel catfish after four weeks of exponential growth is approximately 1.14 grams.
Explanation:To find the weight at the end of four weeks, we need to convert the number of weeks to days since the growth rate is given in terms of daily percentage increase. The formula to calculate exponential growth is A = C(1 + r)^t, where A is the final weight, C is the initial weight, r is the growth rate, and t is the number of periods. In this case, C = 0.3 grams, r = 0.10 (10% daily increase), and t = 4 weeks x 7 days/week = 28 days. Plugging in these values, we get A = 0.3(1 + 0.10)^28. Evaluating the expression, the weight at the end of four weeks is approximately 1.14 grams.
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Nearly 90 percent of the people of indonesia are _______.
Answers
Answer: Muslims
Total Muslims in Indonesia is approximately 207.2 million or 87.2 (90%) of the total population. Other religions recognized by the Indonesian government aside from Islam are Protestant, Catholic, Hindu, Buddhism, and Confucian which accounts for 6.9,2.9,1.7,.7 and .05% of the total population, respectively.
Religion is a mandatory personal data to the Indonesians.
Answer:
MUSLIMS
Step-by-step explanation:
AB is dilated by a scale factor of 3 to form A'B' . Point O, which lies on AB , is the center of dilation. The slope of AB is 3. The slope of A'B' is . through point O.
Answers
The slope will remain the same, So the slope of [tex]A'B'[/tex] will be [tex]3[/tex].
Step-by-step explanation:
Given: [tex]AB[/tex] is dilated by a scale factor of [tex]3[/tex] to form [tex]A'B'[/tex] . Point [tex]O[/tex], which lies on [tex]AB[/tex], is the center of dilation. The slope of [tex]AB[/tex] is [tex]3[/tex].
As mentioned in question:
Given that [tex]AB[/tex] has been dilated by scale factor [tex]3[/tex] to form [tex]A'B'[/tex].
So using laws of dilation, the image is congruent to the pre image.
This implies that the image will not change in any way whatsoever apart from the size.
Hence, the slope will remain the same, So the slope of [tex]A'B'[/tex] will be [tex]3[/tex].
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helppp how do u do 12
Answers
[tex] \frac{x}{100} = \frac{53}{106} \\ x = \frac{53 \times 100}{106} = \frac{5300}{106} = 50[/tex]
good luck
HELP IM GIVING 20 POINTS AND BRAINLY
What is the correlation coefficient r for the data set?
Enter your answer to the nearest hundredth in the box.
r =
x y
25 240
26 242
27 230
28 229
28 220
28 219
29 200
30 202
31 184
32 180
Answers
using a excel tool
see the attached table
the correlation coefficient r for the data set is
r=-0.96
the answer is
-0.96
we know that
using a excel tool
see the attached table
the correlation coefficient r for the data set is
r=-0.96
the answer is
-0.96
Mark placed a pool in his backyard which is enclosed by a triangular fence the radius of the pool is 20.5 feet. How backyard is not covered by the pool
Answers
Jill recorded the average number of gallons of water that she used on her garden each day during different months. The chart below displays her records.
Month
Gallons Per Day
March
35
April
37
May
42
June
55
July
65
August
34
September
24
When does Jill’s chart show the greatest increase in the gallons used per day?
A.
May to June
B.
June to July
C.
July to August
D.
March to April
Answers
In the month of May, Jill used an average of 42 gallons of water while in the month of June, he used an average of 55 gallons of water. This shows that there was an increase of 13 gallons of water used in June compared to May.
The month of July to August shows the highest decrease in the number of gallons of water used per day.