Answer:
Step-by-step explanation:
12
For positive acute angles A and B, it is known that sin A = 8/17 and cos B = 24/25
Find the value of sin(A + B) in simplest form.
Answer:
Step-by-step explanation:
Here we use the SUM FORMULA: sin(a + b) = sin a cos b + cos a sin b
sin(A + B) = sin A*cos B + cos A*sin B. We are not given cos A or sin B and so must find them using the Pythagorean Theorem x^2 + y^2 = z^2.
Looking at sin A = 8/17, we see that the "opposite side" is 8 and the "hypotenuse" is 17. Then (adjacent side) = √(17² - 8²) = 15; that is, the side adjacent to Angle A is 15. Thus, cos A = 15/17 and sin A = 8/17.
We find sin B similarly. cos B = (side adjacent to B)/25 = 24/25. Therefore the side opposite B is √(25² - 24²) = 7. Thus, sin B = 7/25 and cos B = 24/25.
Then sin (A + B) = sin A*cos B + cos A*sin B
= (8/17)*(24/25) + (15/17)(7/25)
Here there are two products of fractions. This product (above) can be rewritten as
8(24) + 15(7) (3)(64) + (3)(5)(7)
= sin A*cos B + cos A*sin B = --------------------------- = --------------------------
17(25) 17(25)
The graph of a function is shown on the coordinate plane below.
Which statement correctly describes the function on a given interval?
Answer: D
Step-by-step explanation:
I did it
The statement that correctly describes the function is:
The function is decreasing and nonlinear from x = 4 to x = 11.
Option D is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
From the graph,
We see that,
The function is increasing and nonlinear from x = -7 to x = -4.
The function is constant and linear from x = -4 to x = 1.
The function is increasing and nonlinear from x = 1 to x = 4.
The function is decreasing and nonlinear from x = 4 to x = 11.
Thus,
The function is decreasing and nonlinear from x = 4 to x = 11.
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Evaluate the following for f(x) = 3(2)^x
1. f (2) =
2. f (-1) =
3. f (10) =
Answer:
1. f (2) = 3 x 2^x-1
2. f (-1) = -3 x 2^x
3. f (10) = 3 x 2^x/10
Step-by-step explanation:
What is the percent difference between comedy and
action?
a) 22%
b) 5%
c) 13%
d) 10%
5
Answer: 22%
Step-by-step explanation:
write an exponential formula of the form f (t)= a×b^t to represent the following situation. assume t is in years. The beginning population is 27, 000, decreasing by 3.5% annually. f(t)=__________
Answer:
[tex]f(t)= 27000 * 0.965^t[/tex]
Step-by-step explanation:
Given
[tex]a = 27000[/tex] -- initial
[tex]r = 3.5\%[/tex]
Required
The exponential equation
The exponential equation is
[tex]y =ab^t[/tex]
Where
[tex]b=1 -r[/tex]
We used minus, because the rate decreases..
So, we have:
[tex]b=1 -3.5\%[/tex]
[tex]b=1 -0.035[/tex]
[tex]b=0.965[/tex]
So:
[tex]y =ab^t[/tex]
[tex]y = 27000 * 0.965^t[/tex]
Hence:
[tex]f(t)= 27000 * 0.965^t[/tex]
Class intervals in a grouped frequency distribution are given as 4−11, 12−19, 20−27, 28−35, 36−43. Write the next two class intervals.
i) what is the each class interval?
ii) write the class boundaries of all classes?
iii) what are the class marks of each class?
Answer:
{44-55}{52- 59 } are the last two interval sStep-by-step explanation:
To get the class boundaries deduct 0.5 from the first number and add 0.5 to the second number = 4-0.5 = 3.5 = 11.5 + 0.5 = 11.5 = 3.5 -11.5 as in the fish class boundary .same for all other boundariestrue or false
1) m<1=50 degrees
2) m<2=130 degrees
3) y=26 degrees
4) x=4 degrees
5) m<1+m<3=180 degrees
Answer:
1. true
2. false
3. false
4. false
5. false
Step-by-step explanation:
4. Find PQ
N
Р
5x + 16
S
R.
9x - 32
Q
Answer on= 12
Step-by-step explanation:
The value of PQ in rhombus NPQR is 76 units.
The figure above is a rhombus.
Properties of a rhombus:All the sides are equal opposite angles are equalThe diagonal are perpendicular bisector of each other.Therefore,
PQ = NR = NP = RQ
5x + 16 = 9x - 32
5x - 9x = -32 - 16
-4x = -48
x = -48 / -4
x = 12
PQ = 5(12) + 16 = 60 + 16 = 76 units
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Determine if the representation below is an example of a function or not a function (1,3), (3,3), (4,5), (6,5), (7,7), (9,7)
Answer:
Yes.
Step-by-step explanation:
No x value is used twice.
What is the area of the square pictured here?
2 in.
2 in.
Answer:
4in
Step-by-step explanation:
To find area, you must multiply the given measurement.
2x2=4
Area= 4in
PLEASE HELP ASAP!!!! GOING TO GIVE 30 POINTS
Answer:
The second answer option
Step-by-step explanation:
Lmk if you need explanation
A box of chocolates was shared evenly between 5 people. Each person received 4 chocolates.
How many chocolates were in the box?
Answer:
20
Step-by-step explanation:
5x4=20
plz give me a thx! IF I HELPED :)
Sara uses 9.3 pints of white paint and blue paint to paint her bedroom walls.
3/5 of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use to paint her bedroom walls?
Answer:2.65
Step-by-step explanation:
The answer is 2.65
What are the next 4 multiples of 4/8 in a fraction
Answer:
8/16, 12/24, 16/32, and 20/45
Step-by-step explanation:
What does not contribute to the destruction of the rainforest in Brazil? farming and ranching cutting down trees to sell the wood constructing a highway having heavy rains
Answer:
heavy rains
Step-by-step explanation:
it makes the forest grow!!1!!1!!!!11111!1!!
What is the Area of the right angle
Answer:
141.96
Step-by-step explanation:
The area or solution for the area of a triangle is base* height divided by 2 so what I did was 31.2cm as the base and 9.1 as the height and I multiplied them together and then I divided by 2! Hope this helped!
Please Help!, Brainliest to whoever helps
how can I subtract 9 2/5 - 8 4/5
Answer:
0.6
Step-by-step explanation:
First make them into decimals so.
9.4 - 8.8 = 0.6
Step-by-step explanation:
okay so let's convert this from mixed to improper fraction
9 2/5= 47/5
8 4/5= 44/5
47/5-44/5= 3/5
which of the following is a example of a proportional relationship
*photo is down there
show proof for brainliest
Answer:
The third one
Step-by-step explanation:
You multiply x by 6 to get y. 1x6=6, 2x6=12, 3x6=18.
Pls help need help with answer b
Answer:
Field hockey has a higher variation of heights.
There is more of a difference between the different heights in field hockey.
LM is 3x, MN is 2x+2. M is the midpoint of LN. What is LM?
Answer:
1/2
Step-by-step explanation:
3x=(1/2)(2x+2)
3x=x+1
3x-x=x-x+1
2x=1
x=1/2
NEED HELP I WILL MARK BRAINLIEST PLZ HELP
Jeremiah wants to send some of his shirts to a dry cleaner. he usually takes his clothes to Spot-Less Dry cleaners, where he pays $4.50 per shirt. He sees a sign at No Mess or Stress Dry Cleaners that says it's $21.00 to have 4 shirts cleaned. Which is the better deal?
answer:spot-less
Step-by-step explanation:
21.00 divided by 4 is 5.25 so you'd be payingmore at "no mess or stress dry"
Courtney made a 5.5 foot ramp
to help her dog get in her minivan.
If the back of her van is 3 feet
from the ground, what will be the
angle of elevation from the base of
the ramp to the van?
9514 1404 393
Answer:
33°
Step-by-step explanation:
We assume the 5.5 foot measurement is the length of the ramp surface. It will be the hypotenuse of a right triangle with the 3 ft side opposite the angle of interest. The applicable relationship is ...
Sin = Opposite/Hypotenuse
sin(angle) = (3 ft)/(5.5 ft)
angle = arcsin(3/5.5) ≈ 33.0°
The angle of elevation of the ramp is about 33°.
If gas costs $2.19 per gallon, how many whole gallons of gas could you buy with $17.00? (Make sure to answer with a whole number.)
With $17.00, you can buy approximately 8 whole gallons of gas.
To calculate the number of whole gallons of gas that can be bought with $17.00, we need to divide the total amount of money by the cost per gallon.
Given that the cost of gas is $2.19 per gallon, we can set up the following equation:
Number of gallons = Total money / Cost per gallon
Substituting the values into the equation, we have:
Number of gallons = $17.00 / $2.19
Performing the division, we get:
Number of gallons ≈ 7.7625570776255707762557077626
Since we are asked to provide a whole number, we round the decimal to the nearest whole number:
Number of gallons ≈ 8
It's important to note that this calculation assumes that the cost per gallon remains constant, and any taxes or additional fees are not taken into account. Additionally, the actual number of gallons that can be purchased may vary depending on the specific pricing and location.
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SOMEONE PLEASE HELP ME
There are 72 items on Ginny's bookshelf. of the items are hardcover books, 3 Imtia of the items are softcover books. 9 • The remaining items are DVDs. How many DVDs are on Ginny's shelf?
Answer:
There are 60 dvds.
Step-by-step explanation:
72 - 3 - 9 = 60
the percent of the principal that is earned in return for loaning the bank the funds?
a. compound interest
b. simple interest
c. interest rate
d. principal
Answer:
B
Step-by-step explanation:
One bar of candy A and two bars of candy B
have 767 calories. Two bars of candy A and
one bar of candy B contain 775 calories. Find
the caloric content of each candy bar.
I'm not 100% sure, but imma have a go.
Answer:
a = 261; b = 253
Step-by-step explanation:
label candy bar A as a
label candy bar B as b
Make 2 equations.
2b + a = 767 (1)
b + 2a = 775 (2)
Solve for a in (1)
2b + a = 767 (-2b)
a = -2b + 767
Substitute for into (2)
b + 2( -2b + 767 ) = 775 (flip)
2( -2b + 767 ) + b = 775 (solve)
−4b + 1534 + b = 775 (add b)
-3b + 1534 = 775 (subtract 1534 from both sides)
−3b = −759 (divide both sides by 3)
b = 253
Substitute b into (1)
a = -2b + 767 (substitute)
a = -2 (253) + 767 (solve)
a = -506 + 767 (add)
a = 261
Find the sum of these
Step-by-step explanation:
5x² - 8x + 2 + x² - 6x +3
= 6x²- 14x + 5
Find the value of x in the triangle shown below 8 10
Answer:
x = 6
Step-by-step explanation:
pythagorean theorem
a^2 = c^2 - b^2
a^2 = 10^2 - 8^2
a^2 = 100 - 64
a^2 = 36
sqrt a^2 = sqrt 36
a = 6
CHECK:
6^2 + 8^2 = 10^2
36 + 64 = 100
yes.