154 cm3 = 0,154 dm3 = 0,154 l = 154 ml
Prove that cos⁻¹ (12/13) + sin⁻¹ (3/5) = sin⁻¹ (56/65)
Answer:
See below ↓
Step-by-step explanation:
We need to prove :
⇒ cos⁻¹ [tex]\frac{12}{13}[/tex] + sin⁻¹ [tex]\frac{3}{5}[/tex] = tan⁻¹ [tex]\frac{56}{65}[/tex]
Let's simplify the LHS.
cos⁻¹ [tex]\frac{12}{13}[/tex] + sin⁻¹ [tex]\frac{3}{5}[/tex]Convert the inverse cos and sin functions into inverse tan functions
tan⁻¹ [tex]\frac{5}{12}[/tex] + tan⁻¹ [tex]\frac{3}{4}[/tex][∴This can be found taking a right triangle and labeling the sides, and then using Pythagorean Theorem, we can find the missing side and take the ratio of tan]Identity
tan⁻¹ x + tan⁻¹ y = tan⁻¹ [tex]\frac{x+y}{1-xy}[/tex]Using this identity, we can simplify our earlier equation!
⇒ tan⁻¹ [(5/12 + 3/4)/(1 - (5/12 x 3/4))]
⇒ tan⁻¹ [(20 + 36) / (48 - 15)
⇒ tan⁻¹ (56/65)
⇒ RHS
⇒ Proved ∴√
[tex]\text{L.H.S}\\\\=\cos^{-1} \dfrac{12}{13} + \sin^{-1} \dfrac 35\\\\=\sin^{-1} \dfrac 5{13} + \sin^{-1} \dfrac 35\\\\[/tex]
[tex]=\sin^{-1}\left[\dfrac 5{13}\sqrt{1- \left(\dfrac 35 \right)^2} + \dfrac 35\sqrt{1-\left(\dfrac 5{13} \right)^2} \right]\\\\=\sin^{-1} \left(\dfrac 5{13} \sqrt{1-\dfrac 9{25} }+\dfrac 35 \sqrt{1-\dfrac{25}{169}} \right)\\\\=\sin^{-1} \left(\dfrac 5{13} \sqrt{\dfrac{16}{25}}+\dfrac 35 \sqrt{\dfrac{144}{169}} \right)\\\\=\sin^{-1} \left(\dfrac{5}{13} \cdot \dfrac 45 + \dfrac 35 \cdot \dfrac{12}{13} \right)\\[/tex]
[tex]=\sin^{-1} \left(\dfrac 4{13} +\dfrac{36}{65}\right)\\\\=\sin^{-1} \left(\dfrac{20}{65} + \dfrac{36}{65} \right)\\\\=\sin^{-1} \left(\dfrac{20+36}{65} \right)\\\\=\sin^{-1} \left(\dfrac{56}{65} \right)\\\\=\text{R.H.S}[/tex]
what is the 100th term in the sequence a¹= 222 and d= -5
The 100th term of the sequence is -273
Arithmetic sequenceArithmetic sequence is one derived from addition/subtraction of a constant term to find the next term. the constant term is usually called the common difference
first term a = 222
common difference, d = -5
nth term of an Arithmetic sequence. Tn = a + ( n - 1 ) d
T100 = a + ( 100 - 1 ) d
T100 = 222 + 99 * -5
T100 = -273
Read more on Arithmetic sequence here:
https://brainly.com/question/7882626
Find the diameter of the circle with the given circumference. Use 3.14 . C=16 cm
Answer:
5.1 cm
Step-by-step explanation:
The equation for the circumference of a circle is 2πr or πd.
So, we can plug in 16 and 3.14 to get 16 = 3.14×diameter.
Divide both sides by 3.14 to get approximately 5.1 cm.
Hope that helps! :)
What is the volume of this figure?
6004 in³
6624 in³
9936 in³
10,488 in³
The volume of the figure is the amount of space in the figure
The volume of the figure is 10488 cubic inches
How to determine the volume?The figure is a composite figure, and it contains:
A rectangular prism A triangular prismThe volume (V1) of the rectangular prism is:
V1 = Length * Width * Height
V1 = 18 in * 23 in * 16 in
V1 = 6624 cubic inches
The volume (V2) of the triangular prism is:
V2 = 0.5 * Base * Width * Height
V2 = 0.5 * 23 in * 16 in * 21 in
V2 = 3864 cubic inches
Add the volumes of both figures
V = V1 + V2
V = 6624 cubic inches + 3864 cubic inches
V = 10488 cubic inches
Hence, the volume of the figure is 10488 cubic inches
Read more about volumes at:
https://brainly.com/question/1972490
Answer:
The answer is D: 10488
Step-by-step explanation:
Carmen received a gift of $5,000 from her grandmother and decided to invest it. the expression 5000(1.0005)^12t represents the amount of the money carmen is earning on her investment. carmen wants to write an equivalent expression so that she can better understand how her money is being invested. choose an equivalent expression in each drop down.
The equivalent expression for the expression that represents the amount Carmen would earn is 5000(1.0005^12)^t.
What is the equivalent expression?Based on the expression given, Carmen's investment is compounded monthly.
The formula for calculating future value:
FV = P (1 + r)^nm
FV = Future value P = Present value R = interest rate m = number of compoundingN = number of years5000(1.0005)^12t
= 5000(1.0005^12)^t
50002.5^12t
Please find attached the complete question.To learn more about future value, please check: https://brainly.com/question/18760477
6x + 4 - 8x + 9(4 - x)
-
Answer:
6x - 8x + 4 + 36 - 9x
= 40 - 11x
explain how you know whether or not the point (0.75, 0.25) is on the unit circle.
Answer:
The point (0.75, 0.25) is not on the unit circle.
Step-by-step explanation:
The unit circle has radius 1, so:
[tex] {.75}^{2} + {.25}^{2} = .5625 + .0625 = .625 [/tex]
Angel and Jaden were at track practice. The track is 2/5 kilometers around.
Angel ran 1 lap in 2 minutes.
Jayden ran 3 laps in 5 minutes
How many minutes does it take Jayden to run 1 kilometer?
Answer:
See below ↓
Step-by-step explanation:
Information we need
Jayden runs 3 laps in 5 minutesSolving
Time taken by Jayden to run 2/5 kilometers (1 lap) = 5/3 minutesTime taken to run 1 km = Time taken to run 2/5 km x 5/2 Time taken to run 1 km = 5/3 x 5/2 ⇒ 25/6 minutes (improper fraction form)⇒ 4 1/6 minutes (mixed number form)⇒ 4.17 minutes (decimal form)a. In the library there are 2,345 science books, 1,469 history books, 270 chairs, and 628 ma zines. How many readable items in all are in the library?
Answer:
4442
Step-by-step explanation:
We Cant Read A Chair So We Exclude Chairs.
Therefore, 2345+1469+628
Which is equals to 4442
WILL GIVE BRAINLIEST ANSWER.
A soda can holds 235.5 in^3 of liquid. If the can is 5 inches tall, what is the distance across the top of the soda can?
Answer:
7.744
Step-by-step explanation:
For this problem you have to work backwards
The equation for the volume is V = (area of circle) x height
So here, to solve the area of the circle, you need to divide the 235.5 by 5
So:
235.5 = (area of circle) x 5
Area of circle is 47.1
Then, you need to find the radius of the circle by using this equation for the area of a circle
[tex]A = \pi \cdot r^{2}[/tex]
So:
47.1 = π * [tex]r^{2}[/tex]
r = 3.872
This question is asking for the diameter, which is double the radius,
2 x 3.872 = 7.744
Complete the table
I WILL MARK BRAINLIEST AND GIVE THANKS
Answer:
Step-by-step explanation:
hours Cost
0 $15
1 $15 + 2.50 = $17.50
2 $15 + 2.50(2) = $15 + 5 = $20
3 $15 + 2.50(3)= $15 + 7.50 = $22.50
4. $15 + 2.50(4)= $15 + 10 = $25
48 ounce bag of granola each month how many pounds if granola does she eat each year
Answer:
12 months = 1 year48 ounce bag of granola per month.
T = 48x
Where 'x' represents the months.
Replace x with 12, because we want to know how many ounces she eats each year.
T = 48x
T = 48(12)
T = 576 ounces, she eats each year.
maths grade 8 solution
Answer:
hope it helps
also try to find out what 5power 10 is because I have no calculator with me
Andrew has $550 in a savings account that earns 5% annually how much will she earn in interest in 4 years
Answer:
110
Step-by-step explanation:
formula= P×T×R ÷ 100
550×4×5÷100
55×4×5÷10
1100÷10
$110
Pick the biggest number.
A0.193 B0.26 C0.6 D0.308
Answer:
Hello fellow Human! ^ω^
The answer is option D. 0.308
Step-by-step explanation:
We are going to Compare the digits starting with the greatest place value.
The Number 0.193 Is not the biggest number. However, 0.193 is bigger than 0.26 and 0.60.The number 0.193 is smaller than the number 0.308.
Therefore, the answer is Option D. 0.308
Hope this helps!
Have an Awesome Friday!
A rectangular prism has a length of 14in, a height of 9in, and a width of 5in. What is its volume, in cubic in?
Answer:
630 inches³
Step-by-step explanation:
According to the question ,
length:- 14 inchwidth :- 5 inchheight :- 9 inchwe have to find the volume of rectangular prism
Volume of rectangular prism :- l × b × h
Putting the value ,
14 × 5 × 9 cubic inches
= 630 cubic inches
[tex]\rightarrow[/tex] Length(l) of prism = 14in.
[tex]\rightarrow[/tex] Width(w) of prism = 5in.
[tex]\rightarrow[/tex] Height(h) of prism = 9in.
To Find:-[tex]\rightarrow[/tex] Volume of prism.
Formula Used:-[tex]\rightarrow[/tex] Volume of rectangular prism = [tex]\sf{l×w×h}[/tex]
Solution:-[tex]\rightarrow[/tex]Volume of prism = [tex]\sf{l×w×h}[/tex](putting the value of l, w and h from the above given)
[tex]\rightarrow[/tex] [tex]\sf{=\:14×5×9}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{= \: 630 in^3}[/tex]
Therefore, volume of the given prism [tex]\sf{= \: 630 in^3.}[/tex]
________________________________
Hope it helps you:)
Here's Francesca's description of the scatterplot:
There is a strong nonlinear association between group size and time. There don't seem to be any outliers.
What, if anything, is missing from this description?
Choose 1 answer:
A:Form
B: Direction
C: Strength
D: Outliers
E: Nothing is missing: this is a complete description.
HELP!:
x^2 + 6x + 9 = ?
This is a factorizing question!! I need help, quickly!
Answer:
nasa pic yung answer
Step-by-step explanation:
hope its help
correct me if im wrong
Answer:
x=-3 x=-3
Step-by-step explanation:
You have the equation x^2+6x+9=0. So we are tying to find two terms that add to 6 but multiply to 9. Those numbers are 3 and 3. So now we have x^2+3x+3x+9=0. Then factor it to get (x+3) and (x+3) then to isolate x do x+3=0, x=-3 (move 3 to the other side to get x=-3).
Mr. Jacobsen is an electrical engineer. He earns 150,000 (GROSS) a year. He pays 20% income tax. How much income tax does he pay?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 15000}}{\left( \cfrac{20}{100} \right)15000}\implies 30000[/tex]
The Sum of the measures of angle X & Y is 90 degrees
The measure of angle X is 6x
The measure of angle Y is 24
what is the value of X?
Step-by-step explanation:
X + Y = 90
Y = 24
X = 6x
X + 24 = 90
X = 66
x = X/6 = 66/6 = 11
Type SSS, SAS, ASA, AAS, or HL to
justify why the TWO LARGER triangles are congruent.
m
BE = BC
Answer: AAS
Step-by-step explanation:
Maria has 32 tickets to sell.She sold 4/6 of them.How many did she sell?
Answer:
22 tickets
Step-by-step explanation:
4/6 is 2/3
2/3 of 32 is 21 .3
Can't sell 0.3 of a ticket, so round up.
22 tickets
Put the equation below into vertex form.
y=(x+9)(x+25)
Find the perimeter.
Write your answer as a fraction or as a whole or mixed numbe
5 1 cm
10
5 cm
10
Bloc
5
cm
10
5 cm
10
Answer:
20 2/5 cm
Step-by-step explanation:
4 ( 5 1/10)
4 × 51/10
2×51/5
0.4x51
=20 2/5
A 10 inch candle burns at a rate of 1.2 inches an hour. How many hours mess the candle burn until it is less than 1 inch tall
A bag contains 30 cookies: 9 vanilla, 9 chocolate, and 12 oatmeal. What is the probability that a chocolate is randomly selected
Answer:
30% for chocolate
Step-by-step explanation:
9÷30= 30% 0.3 vanilla
9÷30=30% 0.3 chocolate
12÷30=40% 0.4 oatmeal
The probability of choosing chocolate is 0.30.
What is the probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
Number of total cookies = 30
Number of vanilla = 9
Number of chocolate = 9
Number of oatmeal = 12
The probability that chocolate is randomly selected is;
Probability of choosing a chocolate = Number of chocolate / Number of total cookies
Probability of chosen a chocolate = 9 / 30
Probability of chosen a chocolate = 3 / 10
Probability of chosen a chocolate = 0.30
Hence, the probability of choosing chocolate is 0.30.
To know more about probability click the link given below.
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Bonjour !
Please solve My maths problem.
If X = 2y +6, then find the value of x³ - 8y³ - 36xy -216.
Hint - answer is 0
Kindly Show steps
I desperately need help with this question.
Correct person will be appreciated and brainlist will be awarded
Irellevant answer won't be tolerated and will be reported immediately.
Thank you in. advance !
y = 1
Step-by-step explanation:
X = 2y + 6
X³ - 8y³ - 36xy - 216 = 0
(subsitute)
(2y + 6)³ - 8y³ - 36(2y + 6)y -216 = 0
(concentrate on first part)
(2y + 6)(2y + 6)(2y + 6)
(4y² + 12y + 12y + 36)(2y + 6)
(4y² + 24y + 36)(2y + 6)
8y³ + 24y² + 48y² + 144y + 72y + 216
(back to full equation)
8y³ + 72y² + 216y + 216 - 8y³ - 36(2y + 6)y - 216 = 0
(factor the last part)
-36(2y + 6)y
y(-72y - 216)
-72y² - 216y
(back to main equation)
8y³ + 72y² + 216y + 216 - 8y³ - 72y² - 216y - 216 = 0
(start to cancel out)
8y³ and -8y³ cancel
72y² + 216y + 216 - 72y² - 216y - 216 = 0
72y² and -72y² cancel
216y + 216 - 216y - 216 = 0
216y and -216y cancel
216 - 216 = 0
those cancel
0y = 0
add 1 to both sides
y = 1.
(I hope this helped)
solve this system of equations using substitution, show your work (ANSWER QUICK PLEASE)
Answer:
[tex]\boxed{\sf{y=-50 \quad x=3}}[/tex]
Step-by-step explanation:
Isolate the term of x and y from one side of the equation.
y=-15x-5 and 11x+y=-17First, you have to substitute.
[tex]\sf{y=-15x-5=11x-15x-5=-17}[/tex]
Then, you solve.
[tex]\sf{-4x-5=-17}[/tex]
Add by 5 from both sides.
-4x-5+5=-17+5
Solve.
-17+5=-12
-4x=-12
Divide by -4 from both sides.
-4x/-4=-12/-4
Solve.
-12/-4=3
x=3
y=-15*3-5
Solve.
PEMDAS stands for:
ParenthesisExponentsMultiplyDivideAddSubtract15*3=45
Rewrite the problem down.
y=-45-5
Solve.
y=-50
Therefore, the correct answer is y=-50 and x=3.
I hope this helps you! Let me know if my answer is wrong or not.
-
Use inverse operations to write the inverse of f(x) = x +
3/2
Answer:
I believe the correct answer is f^-1 (x) = x - 3/2
A new club sent out 180 coupons to boost sales for next year's memberships. They provided 4 times as many to potential members than to existing members. How many coupons did they send to existing members?
They sent 36 coupons to the existing members