AC is a diameter of OE, the area of the
circle is 289 units², and AB = 16 units.
Find BC and mBC.
B
A
C
E
PLS HELP PLSSSS before i cry
Answers
BC is 30 units and mBC is approximately 61.93 degrees.
Given that AC is a diameter of the circle OE, we can deduce that triangle ABC is a right triangle, with AC being the hypotenuse.
We are given that the area of the circle is 289π square units, which implies that the radius of the circle is 17 units (since the formula for the area of a circle is A = πr^2).
Since AC is the diameter, its length is twice the radius, which means AC = 2 * 17 = 34 units.
We are also given that AB = 16 units.
Using the Pythagorean theorem, we can find BC and the measure of angle BC.
In the right triangle ABC, we have:
AB^2 + BC^2 = AC^2
Substituting the given values, we get:
16^2 + BC^2 = 34^2
256 + BC^2 = 1156
BC^2 = 1156 - 256
BC^2 = 900
Taking the square root of both sides, we find:
BC = √900
BC = 30 units
Therefore, BC is 30 units.
To find the measure of angle BC, we can use trigonometry. Since we know the lengths of the sides, we can use the inverse tangent function (tan^(-1)) to find the angle.
mBC = tan^(-1)(opposite/adjacent) = tan^(-1)(BC/AB) = tan^(-1)(30/16)
Using a calculator, we find that mBC ≈ 61.93 degrees.
Therefore, BC is 30 units and mBC is approximately 61.93 degrees.
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Related Questions
Leslie is saving for a new $500 iPad. She currently has $125. If she saves $15 per week, how long must she wait to save at least $600 to cover tax and extras? Let x represent the number of weeks
Answers
Answer:
x=31.66
Step-by-step explanation:
1st i did 600-125=475
so now i have to do 475 divided by 15
that is 31.66
so she has to wait 31.66 weeks to get the $475 dollars she needs
To prove that the triangles are similar by the sss similarity theorem, which other sides or angles should be used? mn and sr mn and qr ∠s ≅ ∠n ∠s ≅ ∠o
Answers
To prove that the triangles are similar by the SSS (Side-Side-Side) similarity theorem, the corresponding sides of the triangles MN and SR must be proportional to each other.
In the SSS similarity theorem, for two triangles to be similar, all three pairs of corresponding sides must be proportional. In the given scenario, we have triangles MN and SR. To establish similarity using the SSS theorem, we need to compare the lengths of the corresponding sides of these triangles.
We are given that MN is proportional to SR, and based on the information provided, we can conclude that QR is proportional to NO.
However, we don't have information about the third pair of sides, which is MN and QR, to establish similarity using the SSS theorem. Therefore, we cannot prove the similarity of these triangles solely based on the given information.
To prove the similarity of triangles MN and SR using the SSS similarity theorem, we also need to compare the lengths of the remaining pair of corresponding sides, MN and QR. Without that information, we cannot establish similarity solely based on the provided sides and angles.
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which is the best estimate of 11 1/5÷ 2 3/4?
Answers
Answer:
11/3
Step-by-step explanation:
Were there choices?
Round off 11 1/5 to 11 and round off 2 3/4 to 3. Then we get the estimate 11/3.
A company expects that the number N(x) of a product sold during a week is related to the amount spent on advertising by the function N(x)=-6x3+180x²+2250x + 13,000, where x (with 0 ≤x≤25) is the amount spent on advertising in thousands of dollars. What is the point of diminishing returns?
The point of diminishing returns is
(Simplify your answer. Type an ordered pair. Do not use commas in the individual coordinates.)
Answers
The point of diminishing returns is (20.98, 21247.3).
The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.
Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.
The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:
0 = -18x² + 360x + 2250
Dividing by -18 simplifies the equation:
0 = x² - 20x - 125
Using the quadratic formula, we find the solutions to the equation:
x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)
x₁,₂ = 10 ± 5√5
Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.
To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:
N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8
N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8
From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.
To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).
Hence, the point of diminishing returns is approximately (20.98, 21247.3).
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How can I solve this problem?
Answers
a) 108°
Answer:
b) 54°
Step-by-step explanation:
a) By arc sum property of a circle.
\( m\widehat {AEB} + m\widehat {AB} = 360°\\
252° + m\widehat {AB} = 360°\\
m\widehat {AB} = 360°- 252°\\
\huge \red {\boxed {m\widehat {AB} = 108°}} \\\)
b) In the given figure, DC is tangent to the circle with O at point A and AB is chord or secant. Therefore, by tangent secant theorem:
\( m\angle BAC = \frac{1}{2} \times m\widehat {AB}\\\\
\therefore m\angle BAC = \frac{1}{2} \times 108°\\\\
\huge \purple {\boxed {m\angle BAC = 54°}} \)
A swimsuit is on "Sale " for 98 usd If the "Sale" price had been discounted by 10% from the
original price, what was the original price?
Answers
Answer:
108.9 usd
Step-by-step explanation:
Let x be the original price of the swimsuit.
x(1-10%) = "sale" price
0.9x = 98 usd
x ≈ 108.9 usd
A GIRL WANTS TO BUY A DRESS THAT COST 125$ ANDSHE HAS A DISCOUNT OF 15% OFF OF A 5% COUPAWN HOW MUCH DID SHE PAY
Answers
The difference in cost between a large bag of chips and a small bag of chips was 90 cents.
Alicia bought 5 large bags and 3 small bags of chips for her party and spent $17.22.
What was the cost for a small bag of chips?
Answers
Answer:
From my understanding, 3.05 with tax for the 3 small bags of chips
if you can buy four Bunches of purple grapes for $10 then how many can you buy with $25 select their proportion that correctly represents the situation
Answers
If $10 can purchase 4 bunches of purple grapes, then how much can 25 purchase
Mathematically,
$10 is equivalent to 4 bunches
$25 is equivalent to x bunches since we don't know the number of bunches $25 can buy
10 dollars = 4 bunches
25 dollars = x bunches
The proportion is given below by introducing cross multiplication to the above expression
\(\frac{4\text{ bunches}}{10\text{ dollars}}\text{ = }\frac{x\text{ bunches}}{25\text{ dollars}}\)Describe some common or unique formulas that you use in your life.
Answers
Quadratic Fοrmula: This fοrmula is used tο find the rοοts οf a quadratic equatiοn. It is calculated as:
\($ \rm x = \frac{(-b \pm \sqrt{(b^2 - 4ac)}}{ 2a}\)
What is quadratic equatiοn?it's a secοnd-degree quadratic equatiοn which is an algebraic equatiοn in x. Ax² + bx + c = 0, where a and b are the cοefficients, x is the variable, and c is the cοnstant term, is the quadratic equatiοn in its standard fοrm.
1. Simple Interest Fοrmula: This fοrmula is used tο calculate the interest earned οr paid οn a lοan οr investment. It is calculated as:
\(\rm I = P \times r \times t\)
Where I is the interest earned οr paid, P is the principal amοunt, r is the interest rate, and t is the time periοd.
2. Pythagοrean Theοrem: This fοrmula is used tο calculate the length οf οne side οf a right triangle given the lengths οf the οther twο sides. It is calculated as:
\(\rm a^2 + b^2 = c^2\)
Where a and b are the lengths οf the twο legs οf the right triangle, and c is the length οf the hypοtenuse.
3. Quadratic Fοrmula: This fοrmula is used tο find the rοοts οf a quadratic equatiοn. It is calculated as:
\($ \rm x = \frac{(-b \pm \sqrt{(b^2 - 4ac)}}{ 2a}\)
Where a, b, and c are cοefficients οf the quadratic equatiοn ax² + bx + c = 0, and x is the sοlutiοn.
4. Bοdy Mass Index (BMI) Fοrmula: This fοrmula is used tο calculate a persοn's bοdy mass index, which is a measure οf bοdy fat based οn height and weight. It is calculated as:
BMI = (weight in kilοgrams) / (height in meters)²
A BMI οf 18.5 tο 24.9 is cοnsidered healthy, while a BMI οf 25 tο 29.9 is cοnsidered οverweight, and a BMI οf 30 οr higher is cοnsidered οbese.
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Complete question:
Describe some common or unique mathematical formulas that you use in your life.
Simplify -7 + [5 + (-12) / 3]
![Simplify -7 + [5 + (-12) / 3]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/o23F4zzWdWkaaybndvZ9iKfRK1gYQTLQ.png)
Answers
Step-by-Step:
-7 + [5 + (-12) / 3]
=−7+5+−4
=−7+1
=−6
please give thanks! and brainliest<3
what is the slope of the line?
Answers
The slope of the graph of the line is 40.
What is slope?The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases. The slope is constant (the same) anywhere on the line.
Taking any to points on the line point (5, 200) and (10, 400)
Slope = change in y-coordinates / change in x-coordinates
change in y-coordinate = 400 - 200 which is 200
change in x-coordinate = 10 - 5 = 5
slope = 200/5 which is 40
In conclusion the slope of the straight line graph is 40
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Got a math quiz happening, please help give a detailed explanation and I will give brainliest!
Answers
Answer:
-1.1
Step-by-step explanation:
3.1 - 1.3 = t + 2.9
t = 3.1 - 1.3 - 2.9
t = -1.1
Answer:
t = -1.1
Step-by-step explanation:
\(3.1 - 1.3 = t + 2.9 \\ 1.8 = t + 2.9 \\ 1.8 - 2.9 = t \\ - 1.1 = t \)
Sajid wants to bake cupcakes and muffins. He wants to bake a total of at least 16 cupcakes and muffins
(condition A), and he has 9000 grams of sugar (condition B).
The graph represents the constraints on the number of cupcakes C and muffins M Sajid bakes.
Sajid bakes 3 cupcakes. How many muffins can he bake to meet both his constraints?
Answers
Answer:
At least 13 muffins and at most 16 muffins
Step-by-step explanation:
Determine whether enough information is given to prove that the triangles are congruent
1. Yes
2. No
Answers
In ΔEFG, the measure of ∠G=90°, GE = 1.9 feet, and EF = 9.4 feet. Find the measure of ∠E to the nearest tenth of a degree.
Answers
Answer:
E=78.3386= 78.3 degrees
Step-by-step explanation:
fractions equivalent to - 9/16
Answers
Answer:
Equivalent Fractions for 9/16: There are infinity equivalent fractions to 916. See some examples: 916, 1832, 2748, 3664, 4580, 5496, 63112, 72128, 81144, 90160, 99176, 108192, 117208, 126224, 135240, 144256, 153272, 162288, 171304
Step-by-step explanation:
NOT my answer, got it from g0ogle..
A company makes muesli which contains nuts and sultanas.
They counted the number of nuts in 50 individual serving packets.
They drew this table.
Number of nuts
Number of
Midpoint (x)
packets (0)
fx
4-6
5
3
15
7-9
8
9
72
10 - 12
11
12
132
13 - 15
14
17
238
16 - 18
17
9
153
50
610
a) Complete the table.
b) Calculate an estimate for the mean.
Answers
A company makes muesli which contains nuts and sultanas.
They counted the number of nuts in 50 individual serving packets.
They drew a table.
Number Midpoint Number of
of nuts (x) packets (f) f.x
4 - 6 5 3 15
7-9 8 9
10 - 12 11 12
13 - 15 14 17
16 - 18 17 9
50
To Find :
complete the table
calculate and estimate for the mean
The estimate for the mean number of nuts in a serving packet of muesli is approximately 12.2 nuts.
a) To complete the table, we need to find the values of "fx" (frequency multiplied by the midpoint) for each class interval. Here's the updated table:
Number of Nuts Number of Packets Midpoint (x) fx
4-6 5 5 5 * 3 = 15
7-9 8 8 8 * 9 = 72
10 - 12 11 11 11 * 12 = 132
13 - 15 14 14 14 * 17 = 238
16 - 18 17 17 17 * 9 = 153
Total 50 610
b) To calculate an estimate for the mean, we use the formula:
Mean = Sum of (fx) / Total Number of Packets
Mean = 610 / 50
Mean ≈ 12.2
Therefore, the estimate for the mean number of nuts in a serving packet of muesli is approximately 12.2 nuts.
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can someone explain how to calculate a unit rate
Answers
Answer:
It's like 60 miles per (1) hour or 20 mL per (1) second. Independent value has to equal 1.
Someone pls help! if you only know the correct answer! thanks!!
Answers
Setting the smoothing constant (alpha) to zero makes the exponential smoothing forecasting method equivalent to the naive method. True False
Answers
It is false that setting the smoothing constant (alpha) to zero makes the exponential smoothing forecasting method equivalent to the naive method.
Setting the smoothing constant (alpha) to zero does not make the exponential smoothing forecasting method equivalent to the naive method. The naive method simply uses the most recent observation as the forecast for the future period, without any smoothing or adjustment.
In contrast, exponential smoothing uses a weighted average of past observations to generate forecasts, and the smoothing constant (alpha) determines the weight given to the most recent observation. When alpha is set to zero, exponential smoothing effectively disregards all past observations and only relies on the initial level or a single starting value, which is not the same as the naive method.
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On a trip, you had to change your money from dollars to euros.
You got 450
euros for 600
dollars.
What is a unit rate that describes the exchange?
Answers
Answer: 0.75 euros = 1 dollar
Step-by-step explanation:
Unit rate
450 euros ----> 600 dollars
450/600 = 0.75
0.75 euros = 1 dollar
Uni rate for the exchange of dollars to euros is 0.75 euros/dollars.
Explanation :\(\implies\) To find the unit rate of exchange from dollars to euros, divide the amount of euros Monica received by the amount of dollars she paid:
\(\largearrow{\sf{\boxd{\boxed{Unit \ change = \dfrac{Number \ of \ euros \ you \got}{Number \ of \ dollars \ you \ have} }}}}\)
\(\implies{\sf{Unit \ change = \dfrac{\cancel{450}}{\cancel{600}} }}\)
\(\implies{\sf{Unit \ change = 0.75 }}\)
As a result, the unit rate for the exchange of dollars to euros is 0.75 euros/dollar.
What is the solution of the equation m - 8 = -14?
Answers
\(\large\bf\blue{ \diamond} \rm \: \: m \: - \: 8 \: = \: - 14 \\ \\ \large\bf\blue{ \diamond} \rm \: \: m \: = \: - 14 \: + \: 8 \\ \\ \large\bf\blue{ \diamond} \rm \: \: m \: = \: - 6\)
(You need to get rid of the -8 because you want the letter on its own, so to get rid of it you add 8 to both sides)
m= -14 + 8
m = -6
Answer: m=-6
A 25-foot ladder is leaning against the side of a house so that the bottom of the ladder is 15 feet from the base of the house. Will the ladder reach a window that is 21.5 feet above the ground?
Answers
The ladder will not reach a window that is 21.5 feet above the ground if the length of the ladder is 25 feet.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
From the data:
The right angle triangle can be drawn:
From the diagram:
Applying Pythagoras' theorem:
BC² = AB² + AC²
25² = 15² + AC²
After solving
AC = 20 feet
AC < 21.5 feet
Thus, the ladder will not reach a window that is 21.5 feet above the ground if the length of the ladder is 25 feet.
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Answer:
No, because the ladder will only reach 20 feet high
Step-by-step explanation:
I go it right on my quiz :]
How would logx (49) = x look like in exponential form
Answers
I'm assuming the given log equation is \(\log_{\text{x}}(49) = \text{x}\)
If so, then the exponential form is \(\text{x}^{\text{x}} = 49\)
This is because the general form \(\log_{\text{b}}(\text{x}) = \text{y}\) transforms into \(\text{y} = \text{b}^{\text{x}}\)
For both equations, the 'b' is the base.
two cards are drawn without replacement from a standard deck of 52 playing cards. what is the probability of choosing a face card for the second card drawn, if the first card, drawn without replacement, was a jack? express your answer as a fraction or a decimal number rounded to four decimal places.
Answers
Probability of choosing a face card for the second card drawn, if the first card, drawn without replacement, was a jack is 11/51
What do you mean by conditional probability?
The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood of the subsequent, or conditional, occurrence to determine the conditional probability.
Total number of face cards = 12
4 kings , 4 queens and 4 jacks
If first card drawn was Jack then remaining cards = 51
Remaimng face cards = 21 - 1 = 11
P( choosing a face card for the second card drawn, if the first card, drawn without replacement, was a jack ) = 11/51
Therefore, Probability of choosing a face card for the second card drawn, if the first card, drawn without replacement, was a jack is 11/51
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-8÷+12×9-4×6÷56÷7×2
Answers
Answer:
\( \frac{ - 300}{49} \)
or -6.122
Step-by-step explanation:
In answering this kind of questions, you must take note of BODMAS. that is;
B - Bracket
O - Of (multiplication)
D - Division
M - Multiplication
A - Addition
S - Subtraction
and you have to answer by the order above to get the correct answer. thank you
hope it helps .
Answer:
-6 176/189
Step-by-step explanation:
-8÷+12×9-4×6÷56÷7×2=
-8÷108- 24÷56÷14=
-2/27-24×14÷56=
-2/27- 48/7=
-7 + 1/7- 2/27=
-7 + (27-14)/27*7=
-7+ 13/189=
-6 176/189
Find X, Y, Z,
(I believe X is 12?)
Answers
Answer:
x = 12 y = 24 z = 12\(\sqrt{3}\)
Step-by-step explanation:
you are correct. x = 12
The dotted line has a length of 12 also
The dotted line is the shorter leg of the 30-60-90 triangle.
So, z = 12\(\sqrt{3}\) and y = 24
The airline industry defines an on-time flight as one that arrives within 15 minutes of its scheduled time. The recent arrival data for a small airport shows that 700 out of 1000 flight were on-time. There are three airlines operates from the airport, Airline A had 320 flights, Airline B had 440 flights and the remainder was operated by Airline C. Suppose that 75% of Airline A's flights are on-time, and 65% of Airline B's flights are on-time.
a. If four flights are selected at random, list the sample space indicating the possible arrival status lon-time "O" Late "L").
b. What is the probability that a randomly selected flight was from Airline A and was on time?
c. What is the probability that a randomly selected flight was from Airline C or was on time?
d. Given that the flight was late, what is the probability that it was from Airline B?
e. Given that the flight was from Airline A, what is the probability that it was late?
Answers
a) The sample space for four flights selected at random, with arrival status "O" for on-time and "L" for late, is given as {OOOO, OOOL, OOLO, OOLL, OLOO, OLOL, OLLO, OLLL, LOOO, LOOL, LLOO, LLOL, LLLO, LLLL}.
b) The probability that a randomly selected flight is from Airline A and on-time, denoted as P(A), is calculated by multiplying the probability of being on-time for Airline A (75/100) with the proportion of flights operated by Airline A out of the total (320/1000), resulting in P(A) = 24/100.
c) The probability that a randomly selected flight is either from Airline C or on-time, denoted as P(C), is obtained by dividing the sum of flights on-time (700) and flights operated by Airline C (240) by the total number of flights (1000), giving P(C) = 94/100.
d) The probability that a flight is from Airline B given that it is late, denoted as P(B | L), is computed by multiplying the proportion of late flights (300/1000) with the probability of being from Airline B (35/100), resulting in P(B | L) = 77/300.
e) The probability that a flight is late given that it is from Airline A, denoted as P(L | A), is calculated by multiplying the proportion of flights on-time for Airline A (25/100) with the proportion of flights operated by Airline A (320/1000), resulting in P(L and A) = 8/100. Therefore, P(L | A) = 1 - P(A | L) = 11/15.
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A bakery sells cakes for $23 And a dozen cupcakes for $18. In one day they sold 72 items and made a total of $1446. Which system is an appropriate model for the problem?
Answers
Answer:
23c+18x=1446
Step-by-step explanation: