=
15. Given a rectangle ABCD with AD 12. The diagonals AC and BD intersect at point O such that
mZDOC = 30°. Find the area of the rectangle.
Answers
Answer:
To find the area, we need to find the side length AB (and DC).
The easiest way to approach this is to draw a sketch with all the given information (see attached).
As point O is the center point of the rectangle, we can draw a horizontal line from point O to the center point of BC (point M on the diagram) and create a right triangle. We can then use the Sine rule to find the shortest leg of the triangle (marked as x on the diagram). This will be half of the side length AB, and so to find the side length, simply multiply it by 2.
To find the missing angles of the right triangle:
m∠COM = (180° - 30°) ÷ 2 = 75°
m∠OCM = 180° - 90° - m∠COM = 90° - 75° = 15°
Sine rule
[tex]\sf \dfrac{a}{sinA}=\dfrac{b}{sinB}=\dfrac{c}{sinB}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
[tex]\implies \dfrac{x}{\sin(15)}=\dfrac{6}{\sin(75)}[/tex]
[tex]\implies x=\sin(15)\cdot \dfrac{6}{\sin(75)}[/tex]
[tex]\implies x=12-6\sqrt{3}[/tex]
As AB = [tex]2x[/tex]
[tex]\begin{aligned} \implies AB & =2x\\ & =2(12-6\sqrt{3})\\ & =24-12\sqrt{3}\end{aligned}[/tex]
Now we have both side lengths of the rectangle, we can easily calculate the area.
Area of a rectangle = width × length
= (24 - 12√3) × 12
= 288 - 144√3
= 38.5846837...
= 38.585 units² (nearest thousandth)
Related Questions
Use the following statement to answer parts a) and b). One hundred raffle tickets are sold for $3 each. One prize of $500 is to be awarded. Winners do not have their ticket costs of $3 refunded to them. Raul purchases one ticket.
a) Determine his expected value.
b) Determine the fair price of a ticket.
Answers
Using the expected value of a discrete distribution, it is found that:
a) His expected value is of -$2.5.
b) The fair price of a ticket is of $0.5.
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
In this problem, the distribution for the net value of the ticket is:
P(X = 497) = 1/1000.P(X = -3) = 999/1000.Item a:
The expected value is given by:
[tex]E(X) = 497\frac{1}{1000} - 3\frac{999}{1000} = -2.5[/tex]
His expected value is of -$2.5.
Item b:
With an unknown ticket price, the distribution is:
P(X = 500 - x) = 1/1000.P(X = -x) = 999/1000.The game is fair if E(X) = 0, hence:
[tex]\frac{500 - x}{1000} - \frac{999x}{1000} = 0[/tex]
0.5 - x = 0
x = 0.
The fair price of a ticket is of $0.5.
More can be learned about the expected value of a discrete distribution at https://brainly.com/question/24855677
In a certain state, speeding fines are determined by the
formula F = 5 (X-60 + 40, where F is the cost in dollars of the
fine if a person is caught driving x miles per hour. How fast a person was speeding if the fine comes to $115?
Answers
Step-by-step explanation:
If u casually solve the given equation by putting 115 instead of 'F' u will get the value of 'X' which is 43 and i guess it's the answer
2. Bart sold 5 more than 3 times as many refrigerators last month than the number of
refrigerators sold by Bill. If together they sold 125 refrigerators last month, how many did
each person sell?
Answers
Answer:
Bart 95 bill 30
Step-by-step explanation:
Bill=b
Bart = (3b+5)
b+ (3b+5) = 125
4b=120
b=30 Bill sold 30 refrigerators
3(30)+5 = 95 (Bart sold 95 refrigerators)
95+30=125
Select ALL of the expressions that are equivalent to 4√5.
A. 2√20
B. 6^1/2-5^1/2
c. 3*5^1/2+5^1/2
D.4*5^1/2
E.2√10
F.3*5^1/2
Answers
Answer:
A, C, D
All 3 of those simplfiy to 4√5
PLEASE HELPPPPPPPPPPPPPPPPPPPPPPPPPPP
Consider this dilation.
(a) Is the image of the dilation a reduction or an enlargement of the original figure? Explain.
(b) What is the scale factor? Explain and show your work.
ANSWER BOTH PARTS YOU MAY GET EXTRA POINTS!
Answers
Step-by-step explanation:
1) if the initial figure ABCD, then the figure A'B'C'D' is reduction of the initial one.
2) the scale factor is 0.5: the ratio of all the corresponded coordinates is 2:1 [D(8;4) - D'(4;2); C(4;0)-C'(2;0); B(0;-2)-B'(0;-1) and A(-4;4)-A'(-2;2)].
Mark the quadrilaterals ABcD and A'B'C'D'
The image is reduced in size hence it's reduction
Take 2 sides two calculate scale factor
AD=12unitsA'D'=6unitsScale factor:-
6/121/2Write 8.6 × 10–3 as a basic numeral.
Answers
Answer:
[tex]8.6\times 10^{-3}=0.0086[/tex]
Step-by-step explanation:
can someone help me with this and i have more of these i need help on
Answers
Answer:
Square
Step-by-step explanation:
Hope this helps!
Answers:
Choice A) SquareChoice B) PentagonChoice D) TrapezoidChoice E) HexagonChoice F) RectangleChoice G) TriangleIn other words, it's nearly everything except choice C (octagon).
==========================================================
Explanation:
Search out "Cross sections of a cube" and you'll see visual examples of what is possible.
Here are the list of possible cross sections
SquarePentagonTrapezoidHexagonRectangleTriangleA parallelogram is also possible, but that isn't one of the listed choices so we can ignore it. The triangle can either be equilateral or won't be, depending how the cross section plane is oriented.
Nearly every box is checked except for the octagon, because we simply don't have enough faces to get 8 sides needed for the cross section.
Find the magnitude and direction (in degrees) of the vector. (Assume 0° ≤ < 360°.)
= 6i + 2sqrt3j
Answers
[tex]6i~~ + ~~2\sqrt{3}j\implies < \stackrel{a}{6}~~,~~\stackrel{b}{2\sqrt{3}} > \\\\[-0.35em] ~\dotfill\\\\ \stackrel{magnitude}{\sqrt{a^2+b^2}}\implies \sqrt{6^2+(2\sqrt{3})^2}\implies \sqrt{36+(2^2\cdot 3)}\implies \sqrt{36+12}\implies \sqrt{48} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{direction}{tan^{-1}\left( \cfrac{b}{a}\right)}\implies tan^{-1}\left( \cfrac{2\sqrt{3}}{6} \right)\implies tan^{-1}\left( \cfrac{\sqrt{3}}{3} \right) \\\\\\ tan^{-1}\left( \cfrac{1}{\sqrt{3}} \right)\implies 30^o[/tex]
Rachel made $176 for 11 hours of work.
At the same rate, how many hours would she have to work to make $128?
Answers
Answer:
8 hours
Step-by-step explanation:
11 hours = $176
⇒ 1 hour = $176 ÷ 11 = $16
To determine how many hours she would have to work to make $128, divide $128 by $16:
⇒ number of hours = $128 ÷ $16
= 8 hours
___________________________________________________
Calculate[tex]\frac{128\times11}{176}[/tex]
___________________________________________________
Cross out the common factor[tex]\frac{8\times11}{11}\\ 8[/tex]
I hope this helps you
:)
can someone help with this pls:)!!!!
Answers
Answer:
-8.5
Step-by-step explanation:
no step involved just trace 2 out from y-axis
A researcher collected the heights of male seniors at a high school. The data collected are normally distributed with a mean of 70.21 inches and a standard deviation of 1.35.
What is the z-score of a high school senior who is 68 inches tall?
Enter your answer rounded to the nearest hundredth, like this: 4.23
Answers
Z = z-value
x = observed value
sd = standard deviation
Z = (68-70.21)/1.35
Z = -1.64 (this is below mean average)
HELPPPPPP PLEASEEE PLEASEEEEEEEEEEEEEEEEEE
Answers
Answer:
31.63495408
Step-by-step explanation:
Find area of trinagles and semicurucles and then add up
Answer:
31.625 ft²Step-by-step explanation:
It is assumed we need to find the area of shaded figure.The figure comprises of two semicircles and a triangle.
The two semicircles add to one full circle with the diameter of 5 ft.
Area of circle
A = πr² = 3.14*(5/2)² = 19.625 ft²Area of triangle
A = 1/2bh = 1/2(6)(4) = 12 ft²Total area
19.625 + 12 = 31.625 ft²30
According to a survey at a local mall, 32% of the shoppers jog at least 3 days per week. Sam
asked 15 people at the mall whether they jog at least 3 days per week, and 8 people said yes.
Based on the survey, how many people should Sam have expected to say yes?
A
3
B 5
С
7
D 10
to know the most imnortant reason that neonle choose their brand of
Answers
Using the binomial distribution, it is found that Sam should have expected 5 people to say yes.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The expected value is given by:
E(X) = np.
In this problem:
15 people were sampled, hence n = 15.32% of the shoppers jog at least 3 days per week, hence p = 0.32.Hence, the expected value for the number of people that say yes is given by:
E(X) = np = 15 x 0.32 = 5.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
If you owned 2,000 shares of Exxon Mobile stock, how much dividend did you receive? Use the stock table below to find
your answer.
Name
Exxon Mobil
Symbol
XOM
Close
$82.80
Day Range
$82.47-$83.23
52-Week Range $80.30-$95.55
Volume
7,513,630
P/E
34.50
Dividend
$3.08
Dividend Yield
3.7%
EPS
$2.40
Answers
Answer:
$6,160
Step-by-step explanation:
The total amount of dividend received is the product of the number of shares and the dividend per share:
(2000 shares) × ($3.08/share) = $6,160.00 . . . dividend received
I NEED HELP ASAP
QUESTION BELOW
Answers
Answer:
Circumference ≈ 50.27
Area ≈ 201.06
Step-by-step explanation:
The circumference of a circle is [tex]2\pi r[/tex] while the area of the circle [tex]\pi r^{2}[/tex]
Since the diameter is the radius multiplied by 2, the radius of the circle is 8. So substituting 8 for r, the circumference is 2 × [tex]\pi[/tex] × 8, which is approximately 50.27 (rounded to the nearest hundredth) and the area of the circle would be [tex]\pi[/tex] × 8². 8² is 64 so 64 times pi is approximately 201.06 (rounded to the nearest hundredth)
Which decimal is greater: 0.347 or 0.437?
Answers
Answer:
0.437
Step-by-step explanation:
Decimals are read the same as whole numbers, starting with the first digit, which is the largest, to the right. So, to find the larger decimal you need to look at the first digit. If this digit is the same then continue to the right until there is a difference in the number. In this case, the first digit is different. Therefore, whichever has the larger first digit must be the greater one. Since 4 > 3, 0.437 must be greater than 0.347.
Felix buys five vests for $22 each, three pairs of shoes for $50 each, and six hats for
$17 each.
What is the mean amount that he spent?
$34.62
$32.81
$25.86
$22
Answers
Answer:
25.86
Step-by-step explanation:
22 * 5 = 110
50 * 3 = 150
17 * 6 = 102
110 + 150 + 102 = 362
362 / 14 = 25.86
please help! (math)
Which expression is equivalent to the one below?
-1/2(10+1/4)
Answers
Answer:
B
Step-by-step explanation:
-½(10+¼)
-½*10 + -½*¼
-5 + -⅛
-5-⅛
Don't forget a positive and negative makes a negative
Write the standard equation of the circle with the center (-14,-5) that passes through the point (-7,5).
Answers
equation: (x + 14)² + (y + 5)² = 149
Given:
centre : (-14,-5)point (-7,5)=============
Formula's:
(x-h)² + (y-k)² = r²centre : (h, k)radius : rdistance between points : [tex]\sf \sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]Find the radius:
[tex]\rightarrow \sf \sqrt{(-7-(-14))^2 + (5-(-5))^2}[/tex]
[tex]\sf \rightarrow \sqrt{\left(-7+14\right)^2+\left(5+5\right)^2}[/tex]
[tex]\sf \rightarrow \sqrt{149}[/tex]
Equation of circle:
(x-h)² + (y-k)² = r²(x-(-14))² + (y-(-5))² = (√149)²(x + 14)² + (y + 5)² = 149Graph for clarification:
Answer:
[tex]\sf (x+14)^2+(y+5)^2=149[/tex]
Step-by-step explanation:
Standard equation of a circle: [tex]\sf (x-a)^2+(y-b)^2=r^2[/tex]
(where (a, b) is the center and r is the radius of the circle)
Substitute the given center (-14, -5) into the equation:
[tex]\sf \implies (x-(-14))^2+(y-(-5))^2=r^2[/tex]
[tex]\sf \implies (x+14)^2+(y+5)^2=r^2[/tex]
Now substitute the point (-7, 5) into the equation to find r²:
[tex]\sf \implies ((-7)+14)^2+(5+5)^2=r^2[/tex]
[tex]\sf \implies (7)^2+(10)^2=r^2[/tex]
[tex]\sf \implies 149=r^2[/tex]
Final equation:
[tex]\sf (x+14)^2+(y+5)^2=149[/tex]
I sold 853 raffle tickets at 5 for $20. How much money did I make?
Answers
Answer:
17,060$
Step-by-step explanation:
#CarryOnLearning Free to ask
What is the value of h?
21 + h = 345
Answers
Answer:
324
Step-by-step explanation:
21 + h = 345
group like terms
h = 345 - 21
h = 324
Answer:
h=324
Step-by-step explanation:
21+h = 345
(Substituting the equation)
h=345 - 21
h= 324
!!PLEASE PLEASE PLEASE MARK ME THE BRAINLIEST!
1.Measurement of segment QR is 2Measurement of segment TS is 3.Measurement if segment QT is
4 The vallue of x is 5 the value of y is
Answers
In a parallelogram, opposite sides are of equal measure.
QR = TS
find x
5(x) - 1 = 2(x) + 55(x) - 2(x) = 5 + 13(x) = 6x = 21)
QR:5(x) - 15(2) - 110 - 192)
QR = TS = 9Find value of y:
QT = RSy + 8 = 3(y) - 2y - 3(y) = -2 - 8-2(y) = -10y = 53)
QT:
y + 85 + 8134)
if x = 5
means the diagram is enlarged.
scale factor = 5/2 = 2.5then y will be:
2.5 * 5 = 12.5We need x and y
Opposite sides of a parallelogram are equal
QR=TS5x-1=2x+53x=6x=2And
RS=QT3y-2=y+82y=10y=5Hence
QR=TS=5x-1=5(2)-1=9RS=QT=y+8=5+8=13#3
Segment QT is 4
so
y+8=4y=4+8y=12Another way
x is 5old x is 2So
scale factor:-
k=5/2=2.5Find y
y=5ky=5(2.5)y=12.5Helpp. Mee\\\..........
Answers
Answer:
may not be exact
1- surveying every fifth student who walks in
2-randomly selected people of both genders
3-asking 8 random students from each second period
4-asking 4 girls and 4 boys from each~~
5-randomly choosing a page and counting the words
Step-by-step explanation:
1-explanation; the first one is skewed two 7th graders, the third one is skewed to volleyball players, the fourth one is skewed to eight graders
PLEASE HELP
find the area
Answers
Answer:
372
Step-by-step explanation:
This is because the formula is a+b/2 x h and 7 is a 24 is b and the other 24 is h so 7 + 24 = 31/2 x 24 is 312
PLEASE HELP 100 POINTS AND BRAINLY
Answers
Answer:
Step-by-step explanation:
Answer:
(2 , 2) is the solution
Step-by-step explanation:
7x - 4y = 6
-6x + 7y = 2
49x - 28y = 42
-24x + 28y = 8
25x = 50
therefore
x = 2
7x - 4y = 6
7×2 - 4y = 6
14 - 4y = 6
14 - 6 = 4y
8 = 4y
8 ÷ 4 = 4y ÷ 4
2 = y
therefore
x = 2
y = 2
hope this will helpful to you....
Please help me with Part C of this question
Answers
Answer:
14-18 minutes
Step-by-step explanation:
Part a is 32 inches per minute
part b is 252 inches per minute
The question asks the change in elevation fastest, in part b 252 is greater than 32 so 14-18 minutes is the answer.
Answer:
14-18 minutes
Step-by-step explanation:
Part a is 32 inches per minute and part b is 252 inches per minute
this question asks the change in elevation fastest, in part b 252 is greater than 32 so 14-18 minutes is the answer.
Find the value of y.
Answers
Answer:
this is your answer hope u like it
Determine the correct answer to the following
system of equations:
=
3x – y = 2
-2x + 4y = -8
Answers
Answer:
(0,-2)
Step-by-step explanation:
one way to solve...
3x - y = 2 --> *4
-2x + 4y = -8
multiply the first equation by 4
12x - 4y = 8
-2x + 4y = -8
-----------------
10x = 0
x = 0
y = -2
this method is called elimination
another way to solve...
3x - y = 2 simplify for y to get y = 3x - 2
-2x + 4y = -8 substitute y into this equation to solve for x
-2x + 4(3x - 2) = -8
-2x + 12x - 8 = -8
10x = 0
x = 0
y = -2
substitution
alsoo if there are options, just plug in the numbers to the correct variables
Answer:
3xy=2 2x4y=8
3x2=6x8=48x8
16. An online magazine charges $45,000 for a 3-month contract for a banner ad
displayed above its weekly feature article. The magazine has 120,000
subscribers and gets 195,000 hits per day. What is the banner's cost per
subscriber if a banner ad was taken for a year?
Answers
Answer:
$1.50
Step-by-step explanation:
There are 4 3-month periods in a year.
$45,000 per 3 months period × 4 = $180,000 cost
$180,000 ÷ 120,000 subscribers = $1.50
The banner ad costs about $1.50 per subscriber
Which of the following q values satisfies: 6-3q≤1
Q=0
Q=1
=
Q=2
Answers
Answer:
Q = 2
Step-by-step explanation:
6-3(2) = 0
0 ≤ 1