C
250
4.9 cm
80°
A
3.8 cm
D
B
ABC is a triangle.
D is a point on AB.
Work out the area of triangle BCD.
Give your answer correct to 3 significant figures.
Answers
Answer:
[tex]10.4\: \sf cm^2\:(3\:sf)[/tex]
Step-by-step explanation:
[tex]\Large\boxed{\sf Formulae}[/tex]
Sine Rule
[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
Cosine rule
[tex]c^2=a^2+b^2-2ab\cos C[/tex]
Area of a triangle
[tex]\textsf{Area of a triangle}=\dfrac12ab\sin C[/tex]
where:
C is the anglec is the side opposite the anglea and b are the sides adjacent the angle[tex]\Large\boxed{\sf Calculation}[/tex]
To find the area of ΔBCD, find:
length of CDangle CDBlength of BDThen use the sine rule for area of a triangle
Calculate length CD using cosine rule:
[tex]\implies CD^2=4.9^2+3.8^2-2(4.9)(3.8)\cos 80^{\circ}[/tex]
[tex]\implies CD^2=31.98334186...[/tex]
[tex]\implies CD=5.655381673...\:\sf cm[/tex]
Calculate ∠ADC using sine rule:
[tex]\implies \dfrac{\sin 80}{CD}=\dfrac{\sin ADC}{4.9}[/tex]
[tex]\implies ADC=\sin^{-1}\left(\dfrac{4.9 \sin 80}{CD}\right)=58.568949^{\circ}[/tex]
Therefore, ∠CDB = 180° - 58.568949° = 121.431051°
Use sine rule to calculate DB:
[tex]\implies \dfrac{DB}{\sin 25}=\dfrac{CD}{\sin CBD}[/tex]
[tex]\implies DB=\dfrac{5.655381673\sin25}{\sin 33.568949}=4.322471258..\: \sf cm[/tex]
[tex]\Large\boxed{\sf Solution}[/tex]
Use the sine rule for area of a triangle to find area of ΔBCD:
[tex]\implies A=\dfrac12(CD)(DB)\sin CDB[/tex]
[tex]\implies A=\dfrac12(5.655381673)(4.322471258)\sin (121.431051)[/tex]
[tex]\implies A=10.4\: \sf cm^2\:(3\:sf)[/tex]
Related Questions
pls help on math pla
Answers
Answer:
Slope: -1/2
y-intercept: 7
Step-by-step explanation:
The slope is the interger/number in front of x in a linear equation.
y-intercept is the constant after the slope, 7, which is the value of y when x is 0.
Answer:
equation: y=mx+b
b=y intercept
the y intercept is 7
the slope is -1/2
what two numbers multiply to get -8 and add to get 4?
Answers
Answer:
-2-2√3, -2+2√3
Step-by-step explanation:
Let x and y be two numbers.
Let x represent one of the numbers. Then the other number is -4-x. We want the product to be -8:
x(-4-x) = -8
-4x -x^2 = -8 . . . . . eliminate parentheses
x^2 +4x = 8 . . . . . . multiply by -1
x^2 +4x +4 = 12 . . . add 4 to complete the square
(x +2)^2 = 12
x +2 = ±√12 = ±2√3
x = -2±2√3
I need to find the answer to...
20% of $80 = ???
Answers
Answer:
16
Step-by-step explanation:
0.20 x 80 = 16
We can double check this by dividing :)
16/80 = 0.20 = 20%
Have an amazing day!!
Please rate and mark brainliest!!
Can someone help me please?
Answers
Answer:
[tex]\bold{ \sf \theta = \dfrac{\pi }{9} , \ \ \dfrac{2}{9} \pi , \ \dfrac{7 \pi }{9}, \ \ \dfrac{8\pi }{9}, \ \dfrac{13\pi }{9}, \ \dfrac{14\pi }{9}}[/tex]
Explanation:
[tex]\dashrightarrow \ \ \sf 2sin(3\theta) = \sqrt{3}[/tex]
[tex]\dashrightarrow \ \ \sf sin(3\theta) = \dfrac{ \sqrt{3}}{2}[/tex]
[tex]\dashrightarrow \ \ \sf 3\theta = sin^{-1}(\dfrac{ \sqrt{3}}{2})[/tex]
[ your calc should be in radian mode [R] ]
[tex]\dashrightarrow \ \ \sf 3\theta = \dfrac{\pi }{3} , \ \ \dfrac{2}{3} \pi , \ \ \dfrac{7 \pi }{3}, \ \ \dfrac{8\pi }{3}, \ \dfrac{13\pi }{3}, \ \dfrac{14\pi }{3}[/tex]
[tex]\dashrightarrow \ \ \sf \theta = \dfrac{\pi }{9} , \ \ \dfrac{2}{9} \pi , \ \ \dfrac{7 \pi }{9}, \ \ \dfrac{8\pi }{9}, \ \dfrac{13\pi }{9}, \ \dfrac{14\pi }{9}[/tex]
Select three ratios that are equivalent to 7:6,
Answers
Answer: 12:14 21:18 42:36
What is the volume of this container? (image below)
Answers
Answer:
480 in³
Explanation:
Volume of Rectangular Prism = Length * Height * Width
Front Volume:
4 * 4 * 580 in³Behind Volume:
5 * 8 * 10400 in³Total volume:
400 in³ + 80 in³480 in³Both are cuboids
#1
L=8B=10C=5Volume:-
LBH8(10)(5)400in³#2
L=4B=4H=5Volume:-
4(4)(5)80in³Total:-
400+80=480in³
E 18 - 3x D F 150° B с 3.1.1 Show that: BE = AB cos 0 sin (a - 6) - 3.x2 3.1.2 Show that the area of A BCE = x 2 4
Answers
Answer:
find the ratio of 15 min and 1hiyr
you are traveling for work. You fly out of las vegas at 4:45 Am. you arrive in miami 6 hours later. what time is it when you arrive ? explain how you got your answer.
Answers
Answer:
The time wil be 1:45
Step-by-step explanation:
4:45 + 6 hours is 10:45
But since Miami is 3 hours ahead (different time zone), you
will add 3 hours. So that makes it 1:45 when you land!
Hope this helps!!
Which statements are true about fractions and ratios? Select all that apply. All ratios are fractions. Some ratios are not fractions. All fractions are ratios. All ratios compare wholes and parts.
Answers
Answer: the person above is wrong
Step-by-step explanation: Some ratios are not fractions.
and All fractions are ratios
yah..... help please bro
Answers
Answer:
I think D but I'm not too sure.
Change them all into decimals:
The square root of 2 = 1.41421356
3/2 = 1.5
15% = 0.15
Arrange them:
3/2, square root of 2, 1.3333..., 1.3, 15%
So, B is the correct answer.
Using the equation below, what is the
value of p when v = 7?
p = 6v + 21
Answers
Answer:
p = 63
Step-by-step explanation:
It is given that the variable v is equal to 7:
v = 7
Plug in 7 for v, and then solve the given equation:
p = 6v + 21
p = 6(7) + 21
Simplify. Remember to follow PEMDAS.
PEMDAS is the order of operation, and stands for:
Parenthesis, Exponents (& Roots), Multiplications, Divisions, Additions, Subtraction.
First, multiply 6 with 7:
p = (6 * 7) + 21
p = 42 + 21
Next, add:
p = 42 + 21
p = 63
63 is your answer for p.
~
Answer:
p = 63
Step-by-step explanation:
p = 6(v) = 21
add in 7 in place of v
p = 6(7) + 21
do 6(7)
p = 42 + 21
add those together
p = 63
Here you go! :)
CAN SOMEONE HELP ME PLEASE ASAP!?
Answers
Answer:
D
Step-by-step explanation:
the answer Is obviously D
1/200
Explanation:
1+999=200
-Therefore, there are 200 chances all together
-the ratio is 1:199 meaning there is 1 chance of winning a bicycle out of the total 200.
I hope this helped :)
Can someone help me understand this?? I ended up getting 594 and that’s not even an option!
Answers
Answer:
Option D
Step-by-step explanation:
I am taking a guess here, but since the volume of the rectangle part is 594, and it is sort of a similar size as the top part, then I assume it is D.
Let me know how it goes.
34. Find the surface area for the following rectangular prism
Answers
[tex] \huge\fbox\green{ANSWER} [/tex]
Surface Area = 2×(8.25×1.5 + 8.25×3 + 1.5×3) = 83.25 centimeters^2
[tex] \mathsf \blue{83.25 {cm}^{2} }[/tex]
PLEASE HELP ASAP 20 POINTS!!!
Answers
Answer:
D, I think…
Step-by-step explanation:
I used PEMDAS to go through and simplify and see which values match.
An adult human body contains 10 pints of blood.How much fluid ounces is equivalent to 10 pints? (Please answers!)
Answers
Answer:
160 fluid ounces
Step-by-step explanation:
There are 16 ounces in one pint, therefore multiply the number of pints by 16 to get your answer.
16 * 10 = 160
Hope this helped ! <3 Brainliest please :)
GIVING BRAINLIEST+20 POINTS TO BEST ANSWER FOR THESE 2 QUESTIONS!
1.Which story represents the equation six sevenths times one fourth?
1. Victoria drinks six sevenths of a cup of milk. She drinks one fourth of a cup more of milk. How much milk did she drink in all?
2. Mike walked one fourth mile and then he took the bus for six sevenths mile to school. How many miles did he travel in total?
3.Victoria has six sevenths of a pizza. She ate one fourth of it for dinner. How much pizza did Victoria eat for dinner?
4.Mike has six sevenths of a pie. He gives one fourth to his brother. How much pie does he have left
Answers
Answer:
3.
Step-by-step explanation:
Hey there!
This scenario shows that Victoria ate 6/7 of a pizza and ate 1/4 of that pizza the same day for dinner showing that she at one fourth of the six-sevenths pieces
Answer:
It is the third one.
Step-by-step explanation:
Let's take a look at each story. We need to find out which story is [tex]\frac{6}{7}[/tex]×[tex]\frac{1}{4}[/tex].
1. Victoria drinks six-sevenths of a cup of milk. She drinks one-fourth of a cup more of milk. How much milk did she drink in all?
This story is adding the fractions together since it wants to know how much did she drink in ALL. So this is not it.
(Here are some keywords to tell you if you need to add, altogether, all, in all, together, total, total number, add, increase, increased by, more than.)
2. Mike walked one-fourth mile and then he took the bus for six-sevenths mile to school. How many miles did he travel in total?
Once again this story is adding. It uses the word total. So this is not it.
3.Victoria has six-sevenths of a pizza. She ate one-fourth of it for dinner. How much pizza did Victoria eat for dinner?
This is correct since it wants to know how much she ate for dinner. She ate [tex]\frac{1}{4}[/tex] of [tex]\frac{6}{7}[/tex] of the pizza.
4.Mike has six-sevenths of a pie. He gives one-fourth to his brother. How much pie does he have left
This story is subtracting. So it is not it. (Subtracting words, minus, greater than, take away, fewer than, less than, subtract, decreased by.)
how do you graph y=2x-3
Answers
Answer:
so on the graph you can
Step-by-step explanation:
first the y axis number comes first so you look at that the you do the x axis it should look like 2,3 or 2,-3 hope this works
Answer: 2x3=y. 2x3=6
Step-by-step explanation:
one: figure out what the question is asking you. Two: do 2x3 and then get the answer. Last: switch it around to find your answer.
if a1 = 5 and an = an-1 +2 then find the value of a4
Answers
Answer:
Step-by-step explanation:
an = (an-1)2 + 5. a1 = 4. Then: a1 = 4. a2 = (4)2 + 5 = 16 + 5 = 21. a3 = (21)2 + 5 = 441 + 5 = 446. a4 = (446)2 + 5 = 198916
June’s portfolio includes 177 shares of parchar special effects, 213 shares of giaco household goods, and 152 shares of raxin accounting. if parchar special effects pays a yearly dividend of $8.21 per share, giaco household goods pays $6.97 per share, and raxin accounting pays $11.44 per share, how much does june earn in dividends per year? a. $4,449.82 b. $4,676.66 c. $3,777.74 d. $6,200.48
Answers
June's earning in dividends per year will be $4676.66
What will be junes earning?Earnings are the profit that a company produces in a specific period, usually defined as a quarter or a year. After the end of each quarter
It is given in the question that:
No. of shares of Parchar Special Effects = 177
If Parchar Special Effects pays a yearly dividend of $8.21 per share
So, It pays a yearly dividend for 177 shares
= [tex]177\times 8.21=1453.17[/tex]
No. of shares of Giaco Household Goods = 213
Giaco Household Goods pays $6.97 per share
So, It pays a yearly dividend for 213 shares
= [tex]213\times6.97=1484.61[/tex]
No. of shares of of Raxin Accounting= 152
Raxin Accounting pays $11.44 per share
So, It pays a yearly dividend for 152shares
= [tex]152\times 1.44=1738.88[/tex]
So,June earn in dividends per year
=[tex]1453.17+1453.17+1738.88=4676.66[/tex]
Hence June earn $4676.66 dividends per year
To know more about earnings follow
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Answer:
B
Step-by-step explanation:
$4,676.66
2 +√9= whats the answer number system class 9
Answers
Answer:
5
Step-by-step explanation:
2 + root 9 can be written as 2 + 3 which is answer as 5
Answer:
•SEE ABOVE ATTACHMENT•HOPE IT HELPS!
MARK AS BRAINLIAST.
HOW DO U DO THIS I LITERALLY TRIED EVERYTHING pls explain
Answers
Answer:
you just convert them into simple fractions the first one become -1159/9 and second one -790/3.
the difference in thier height is 1211/9.
Suppose a city with population 100,000 has been growing at a rate of 5% per year. If this rate continues, find the population of this city in 21 years.
Answers
Answer:
205,000
Step-by-step explanation:
(100,000*0.05) *21 +100,000
Given the speeds of each runner below, determine who runs the fastest.
\text{Frank runs 9 feet per second.}
Frank runs 9 feet per second.
\text{Tony runs 299 feet in 34 seconds.}
Tony runs 299 feet in 34 seconds.
\text{Zach runs 1 mile in 396 seconds.}
Zach runs 1 mile in 396 seconds.
\text{Will runs 675 feet in 1 minute.}
Will runs 675 feet in 1 minute.
Answers
Tony 8.79feet per second
Zach 13.34feet per second
Will 11.25feet per second
Tony runs fastest
Zach runs with 14.31 feet per second speed and faster than other runners.
What is Speed?Speed is measured as the ratio of distance to the time in which the distance was covered
Given that Frank runs 9 feet per second.
Speed=Distance /time
=9 feet/ 1 second
=9 feet per second.
Tony runs 299 feet in 34 seconds
Speed=299/34
=8.794 feet per second.
Zach runs 1 mile in 396 seconds.
We know that 1 mile =5280 feet
Speed=5280/369
=14.31 feet per second.
Will runs 675 feet in 1 minute
1 minute is 60 seconds
Speed=675/60
=11.25 feet per second.
Hence, Zach runs with 14.31 feet per second speed and faster than other runners.
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The radius of a circle is 14 meters. What is the circle's area?
r=14 m
Use 3.14 for .
Answers
Answer:
The formula for the area of a circle:
[tex]A = \pi r^{2}[/tex]
You have said:
[tex]r = 14m[/tex]
So substitute the values of pi and r into the formula:
[tex]A = \pi r^{2} \\A = (3.14)(14m)^{2} \\A = (3.14)(196m^{2} )\\A = 615.44m^{2}[/tex]
So in this case: (3.14) * (14)^2 = 615.44
What is the area of the shape?
Answers
Answer:12 units^2
Step-by-step explanation:
2*2=4
2*2*1/2=2
2*6*1/2=6
4+2+6=12
12 units^2
A baseball traveled 330 feet in 5 seconds. Which rate is equivalent to the rate at which the baseball traveled?
A.
55 feet per second
B.
66 feet per second
C.
55 seconds per foot
D.
66 seconds per foot
(just the answer pls)
Answers
Answer:
I think it's B.
Step-by-step explanation:
I need help, please and thank you
Answers
Answer:
See below ↓
Step-by-step explanation:
Problem
[tex]\frac{5x}{x+7} + \frac{7}{x}[/tex]Work
[tex]\frac{5x(x)+7(x+7)}{x(x+7)}[/tex][tex]\frac{5x^{2} +7x+49}{x(x+7)}[/tex]The student's mistake was that instead of taking x(x + 7) as the LCM (Least Common Multiple), he took x + 7, which is not possible in this caseSolution
[tex]\frac{5x^{2} +7x+49}{x(x+7)}[/tex]Do number 2 please. Please bots don’t answer! I just trying to get help :(
Answers
Answer:
no 2. cube a' will be smaller because it was multiplied by a fraction
no 3. c
The first six steps of the derivation of the Quadratic Formula are listed below.
b
x
lo
=
a
a
+
1. ax2 + bx +c=0
2. Cx2 + x + =
3. x2 + x+8 = 0
b
4. x2 +
X=
a
b2
5. x2 + x +
4a2
6. (x + )2
4a2
a
+
a
b2
4a2
b2-4ac
2a
Answers
The ninth step in the derivation is to find the lowest common multiple (LCM) to give [tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]
The derivation of quadratic formula.In Mathematics, the standard form of a quadratic equation is given by;
ax² + bx + c = 0
Mathematically, the quadratic formula is given by this equation:
[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]
The sixth step in the derivation is:
[tex](x + \frac{b}{2a} )^2 = \frac{b^2 - 4ac}{2a}[/tex]
The seventh step in the derivation is:
We would take the square of both sides to have;
[tex]x + \frac{b}{2a} = \frac{\sqrt{b^2 - 4ac}}{2a}[/tex]
The eigth step in the derivation is:
We would substract b/2a from both sides to have;
[tex]x = -\frac{b}{2a} \pm \frac{\sqrt{b^2 - 4ac}}{2a}[/tex]
The ninth step in the derivation is:
We would find the lowest common multiple (LCM) to have;
[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]
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