Geometry question finding radius and area
Thank You!!
Answer:
The radius of Circle D is 8 cm.
The perimeter of ΔABC is (24 + 6√7) cm.
Step-by-step explanation:
First, let the intersection point below D be K and let the intersection point between A and B be J.
Since segment BK, which passes through the center of the circle, is perpendicular to chord AC, BK also bisects AC. Hence, AK = CK.
Connect points A and D to create radius AD. Note that BD is also a radius. Hence, AD = BD.
For ΔABK, by the Pythagorean Theorem:
[tex]AB^2=(BD+1)^2+AK^2[/tex]
Since AB = 12:
[tex]144=(BD+1)^2+AK^2[/tex]
For ΔADK, by the Pythagorean Theorem:
[tex]AD^2=1^2+AK^2[/tex]
Since AD = BD:
[tex]BD^2=1+AK^2[/tex]
Subtract the second equation into the first:
[tex]144-(BD^2)=(BD+1)^2+AK^2-(1+AK^2)[/tex]
Simplify:
[tex]144-BD^2=BD^2+2BD+1-1[/tex]
Hence:
[tex]2BD^2+2BD-144=0[/tex]
Simplify:
[tex]BD^2+BD-72=0[/tex]
Factor:
[tex](BD+9)(BD-8)=0[/tex]
By the Zero Product Property:
[tex]BD=-9\text{ or } BD=8[/tex]
Since the radius must be positive, the radius is 8 cm.
Since we already know AB and BC, we need to find AC to find the perimeter.
Note that AC = AK + CK = 2AK.
From the second equation:
[tex]BD^2=1+AK^2[/tex]
Thus:
[tex]AK=\sqrt{BD^2-1}=\sqrt{(8)^2-1}=\sqrt{63}=3\sqrt{7}[/tex]
Hence:
[tex]AC=2(AK)=2(3\sqrt7)=6\sqrt7[/tex]
Therefore, the perimeter of ΔABC is:
[tex]P=(12)+(12)+(6\sqrt7)=24+6\sqrt7\text{ cm}[/tex]
A national survey of 1516 respondents reached on land lines and cell phones found that the percentage of adults who favor legalized abortion has dropped from 55% a year ago to 45%. The study claimed that the error
atributable to sampling is 4 percentage points. Would you claim that a majority of people are not in favor of legalized abortion?
Answer:
The upper bound of the interval is below 0.5, which means that it can be claimed that a majority of people are not in favor of legalized abortion
Step-by-step explanation:
Confidence interval:
Sample proportion plus/minus margin of error.
In this question:
Sample proportion of 0.45, margin of error of 0.04. So
0.45 - 0.04 = 0.41
0.45 + 0.04 = 0.49
The confidence interval is of (0.41,0.49). The upper bound of the interval is below 0.5, which means that it can be claimed that a majority of people are not in favor of legalized abortion
singh works at a restaurant where he is paid by the hour plus time and a half for his hours over 40. last week he worked four hours overtime and his gross pay was $391.00. What is his hourly wage
Answer:
$8.5 per hour
Step-by-step explanation:
Number of overtime hours = 4 hours
Since overtime starts after 40 hours, then the number of hours worked = 40 + 4 = 44 hours
Total amount earned = $391
Let Hourly pay = x
Overtime pay = 1 1/2x = 3/2x
Therefore ;
40x + (4*3/2x) = 391
40x + 6x = 391
46x = 391
x = 391 / 46
x = 8.5
Hourly pay = $8.5 per hour
I need help with #3. Please help. I have to show all work so please explain
Answer:
a = 2
Step-by-step explanation:
Use Pythagorean Theorem:
[tex]a^2+b^2=c^2\\a^2+2.1^2=2.9^2\\a^2+4.41=8.41\\a^2=4\\\sqrt{a^2}=\sqrt{4}\\a=2[/tex]
Therefore, a is 2 meters.
Madison and Aidan roll two number cubes. Which of the following rules will make the game fair?
Madison wins if a total of 5 is rolled. Aidan wins if a total of 10 is rolled.
Madison wins if a total of 8 is rolled. Aidan wins if a total of 6 is rolled.
Madison wins if a total of 9 is rolled. Aidan wins if a total of 7 is rolled.
Madison wins if a total of 2 is rolled. Aidan wins if a total of 11 is rolled.
Answer:
If I understand this right I think it would be 8 and 6?
Step-by-step explanation:
Sorry if this is wrong I'm really bad at math, please tell me if this is right.
PLSSSSSS HELP ASAP !!!
Answer:
m4+m5=180
answer is second option
Which equation is correct?
cos x° = adjacent ÷ hypotenuse
tan x° = hypotenuse ÷ adjacent
cos x° = hypotenuse ÷ adjacent
tan x° = adjacent ÷ hypotenuse
Answer:
cos x° = adjacent ÷ hypotenuse
Step-by-step explanation:
Option (A) cos x° = adjacent ÷ hypotenuse is correct because cos is the ratio of the side adjacent to the angle to the hypotenuse option (A) is correct.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have given trigonometric ratios in the options.
As we know the trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
In the 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)
cos is the ratio of the side adjacent to the angle to the hypotenuse
cos x° = adjacent ÷ hypotenuse
tan is the ratio of the side opposite to the angle to the side adjacent to the angle.
tan x° = opposite ÷ adjacent
Thus, option (A) cos x° = adjacent ÷ hypotenuse is correct because cos is the ratio of the side adjacent to the angle to the hypotenuse option (A) is correct.
Learn more about trigonometry here:
brainly.com/question/26719838
#SPJ5
football team consists of 20 each freshman and sophomores, 15 juniors, and 10 seniors. Four players are selected at random to serve as captains. Find the probability that.
a. All 4 are seniors.
b. There is 1 each: freshman, sophomore, junior, and senior.
c. There are 2 sophomores and 2 freshmen.
d. At least 1 of the students is a senior.
Answer:c
Step-by-step explanation:
c
It took Fred 12 hours to travel over pack ice from one town to another town 360 miles away. During the return journey it took him 15 minutes
Step-by-step explanation:
what is your question please
A man invests K8 000 for 5 years at 10%p.a. compound interest.
Calculate the investment value at the end of 5 years.
Answer:
Step-by-step explanation:
Compoud interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. the formula is:
[tex]c_n=c_o(1+i)^n\\\\c_o->initial~invesment\\i->interest\\n->number~of~ intervals[/tex]
[tex]c_5=8000(1+\frac{10}{100})^5\\c_5=12848.88[/tex]
Tom has a steel box that has a capacity of 5 gallons. What is the maximum amount of fluid, in quarts, that this box can hold?
A. 10 qt.
B. 15 qt.
C. 18 qt.
D. 20 qt.
Answer:
d. 20 qt.
Step-by-step explanation:
4 quarts to a gallon so 4x5= 20
Find the value of y
A) 9.850
B) 18.610
C) 65.825
D) 125.365
Answer:
B) 18.610
Step-by-step explanation:
Using SOHCAHTOA (trig ratios), the tangent of 28° is the ratio of its opposite length to its adjacent.
in this scenario, the side opposite to 28°, and the side adjacent to it is 35°
tan 28° = y/35
Using inverse operations, multiply both sides by 35
y = 35 * tan 28
Solve your answer using your calculator.
I attached a picture that can help you later to recognize what function to use depending on the sides given.
A label printer prints 9 pages of labels in 2.0 seconds. How long will it take to print 396 pages of labels?
Answer:
88 or 1 minute and 28 seconds
Step-by-step explanation:
396/9= 44 times the two seconds it takes to print is 88
Answer:
1782
Step-by-step explanation:
9 divided by 2.0
=4.5
4.5×396
=1782
A rancher has 600600 feet of fencing to put around a rectangular field and then subdivide the field into 33 identical smaller rectangular plots by placing two fences parallel to one of the field's shorter sides. Find the dimensions that maximize the enclosed area. Write your answers as fractions reduced to lowest terms.
Answer:
x = 150 ft
y = y = 150 / 17 ft
Step-by-step explanation:
Area of the field is A = x*y
Let´s assume x is the larger side of the rectangle, and that we will get 33 identical smaller rectangular plots dividing x into 33 rectangles ( using 34 sides of length y ) then the quantity of fence is:
p = 2*x + 34*y ⇒ 600 = 2*x + 34*y y = ( 600 - 2*x)/34
A = x*y
A (x) = x* ( 600 - 2*x)/34
A (x) = ( 600*x - 2*x²)/34
Taking derivatives on both sides of the equation:
A´(x) = (1/34)* ( 600 - 4*x )
A´(x) = 0 (1/34)* ( 600 - 4*x ) = 0 600 - 4*x = 0
x = 600/4
x = 150 feet
And y = (1/34)( 600 - 2*150)
y = 300/34 y = 150 / 17 ft
y = 8.82 ft
How do we know that is a maximum area, we find the second derivative of A
A´´(x) = - 4/34 then A´´(x) < 0
We get a maximum of function A for the value x = 150
Which score is better in terms of percentages: 12 out of 15 or 23 out of 26?
Answer:
23/26 is a greater percentage, it equals around 88% while 12/15 equals 80%
Step-by-step explanation:
cuadrado de binomio
(x-2)(-2+x)
Answer:
x^2-4x+4
Step-by-step explanation:
See image below:)
If the diameter of a circle is 50 yds, the radius is
Answer:
r = 25 yds
Step-by-step explanation:
The radius is 1/2 of the diameter
r =1/2d
r =1/2( 50 yds)
r = 25 yds
Help plz so close to being done
Answer:
20 is the answer I got
Please help and explain
9514 1404 393
Answer:
d. f(2) < g(2)
Step-by-step explanation:
The attached table and graph shows how the functions relate for the various x-values of interest. The true statement is ...
f(2) < g(2)
-3 < 0
solve the equation
x + -18 = 3x + 54
Answer:
-36
Step-by-step explanation:
See image below:)
Answer:
x = -36
Step-by-step explanation:
subtract 'x' from each side to get:
-18 = 2x + 54
subtract 54 from each side to get:
-72 = 2x
x = -72/2
x = -36
Calculate the value of 3x³ -2x²- 9x+2 if x= -2
Answer: -12
Step-by-step explanation:
3(-2)^3 - 2(-2)^2 - 9(-2) + 2 = N
3(-8) - 2(4) - 9(-2) + 2 = N
-24 - 8 + 18 + 2 = N
-12 = N
abb
9. Hãy đặt các phán đoán đơn và biểu thị thành phán đoán hợp câu
sau đây: "Nếu bị đau đầu hoặc sốt thì có thể uống thuốc Panadol,
Nếu bị cảm cúm hoặc đau đầu thì có thể uống thuốc Tiffy. Thơm
bị cảm cúm và đau đầu. Do đó Thơm có thể uống thuốc Panadol
hoặc thuốc Tiffy". Hãy xác định giá trị của phán đoán hợp trên.
Answer:i took the test
Step-by-step explanation: 76879686
Soda is often sold in 20 ounce bottles. A pack of sugar (the kind they have at restaurants for your coffee or tea) typically contains 4 grams of sugar. If an 8 ounce bottle of cream soda has 30 grams of sugar, then drinking a 20 ounce bottle of cream soda would be equivalent to eating how many packets of sugar?
Answer:
18.75 packs of sugar
Step-by-step explanation:
20/8 = 2.5 (how many 8 ounce bottles in 20 oz)
2.5 * 30 = 75 (to find how many grams of sugar in the 20 oz bottle)
75/4 = 18.75 (how many packs of sugar it's equal to)
you can also use a ratio to solve:
8/30 = 20/x; cross multiply
600 = 8x; divide 8 on both sides
x = 75
75/4 = 18.74 (how many packs of sugar it's equal to)
need help asap! The graphs below have the same shape. what is the equation of the red graph?
no links
Answer:
B. [tex]g(x) = x^{3} - 5[/tex]
Step-by-step explanation:
The graph of f(x) is the graph of g(x) translated 5 units downwards.
Draw and label the solution to each
solve the following equation algebraically please
Answer: A
Step-by-step explanation:
Determine if the triangles are congruent. If they are, state how you know. NO LINKS!!!!
Part 1c. Show your work please.
Answers:
Each pair of triangles are congruent. The congruence reasoning is shown below.
ASASSSHA======================================
Further Explanation:
ASA is where we have the marked side between two marked angles. This is slightly different from AAS or SAA. The order is important. The diagram shows how the angles pair up (eg: the double arc angles are the same measure). Using ASA is enough to prove the triangles congruent.SSS is used here because we have three pairs of congruent sides. The unmarked sides overlap perfectly, so we consider this a shared side. They are congruent to each other (because of the reflexive property). So we have enough info to show that the triangles are congruent.HA stands for hypotenuse angle. It's probably not that often used. It only applies to right triangles. The two overlapped segments are the hypotenuse of each right triangle, so that takes care of the "H" of "HA". The A part refers to the congruent acute angles (not the right angles). Therefore, the triangles are congruent by the HA theorem.Abbreviations:
ASA = angle side angle
SSS = side side side
HA = hypotenuse angle
Under the translation (X +3, y - 1) the point (3,4) will become (0.5)
True or False
9514 1404 393
Answer:
False
Step-by-step explanation:
Point (3, 4) will become (3+3, 4-1) = (6, 3), not (0, 5). The statement is False.
_____
Additional comment
The point (0, 5) would be translated to (3, 4). That is not what the question is asking.
Complete the remainder of the
table for the given function rule
Answer:
y = 3
y = 2
y = 1
y = 0
Step-by-step explanation:
Given expression;
y = (-x/3) + 2
Find:
Value of y, if x = -3Value of y, if x = 0Value of y, if x = 3Value of y, if x = 6Computation:
Value of y, if x = -3
y = (-x/3) + 2
y = (3/3) + 2
y = 3
Value of y, if x = 0
y = (-x/3) + 2
y = (-0/3) + 2
y = 2
Value of y, if x = 3
y = (-x/3) + 2
y = (-3/3) + 2
y = 1
Value of y, if x = 6
y = (-x/3) + 2
y = (-6/3) + 2
y = 0
A coin is flipped 60 times and lands on heads 36 times. Based on the experimental probability, how many heads would you predict for 200 flips of the coin?
Answer:
108
Step-by-step explanation:
200 divided by 60 equals 3 then 36 times 3 equals 108
Answer:
120 heads
Step-by-step explanation:
The Experimental probability for heads is 36/60. now we have to find the experimental probability for 200 flips. so 36/60 = ?/200. We have to find a number that 60 multiplies by to get 200. That number is 200/60 = 20/6 = 3 1/3. So multiply 36 by 3 1/3: 36 * 3 = 108. 36 * 1/3 = 12. 108 + 12 = 120. So it is 120 heads
