Answer:
Step 1 The two sides we know are Opposite (300) and Adjacent (400).
Step 2 SOHCAHTOA tells us we must use Tangent.
Step 3 Calculate Opposite/Adjacent = 300/400 = 0.75.
Step 4 Find the angle from your calculator using tan-1
PLEASE HELP ME! If an arithmetic sequence has a4 = 107 and a8 = 191, what is a₁? (I need the steps too please).
Answer:
[tex]\displaystyle a_1 = 44[/tex]
Step-by-step explanation:
Recall the direct formula for an arithmetic sequence:
[tex]\displaystyle a_n = a_1 + d(n-1)[/tex]
Where d is the common difference.
Therefore, we can write the following two equations:
[tex]\displaystyle \left \{ {a_4 = 107 = a_1 + d(4-1)\atop {a_8 = 191 = a_1 + d(8-1)}} \right.[/tex]
Solve the system. Simplifying yields:
[tex]\displaystyle 107 = a_1 + 3d\text{ and } 191 = a_1 + 7d[/tex]
Subtracting the two equations into each other yields:
[tex]\displaystyle \begin{aligned} (191) - (107) & = (a_1 + 7d) - (a_1 + 3d) \\ \\ 84 & = 4d \\ \\ d & = 21 \end{aligned}[/tex]
Using either equation, solve for the initial term:
[tex]\displaystyle \begin{aligned} 107 & = a_1 + 3(21) \\ \\ a_1 & = 107-63 \\ \\ & = 44\end{aligned}[/tex]
In conclusion, the initial term is 44.
Answer:
[tex]\huge\boxed{\bf\:a_{1} = 44}[/tex]
Step-by-step explanation:
In the given arithmetic series,
[tex]a_{4} = 107[/tex][tex]a_{8} = 191[/tex][tex]a_{1} = ?[/tex]We know that,
[tex]\boxed{a_{n} = a + (n - 1)d}[/tex]
Therefore,
[tex]a_{4} = a + 3d = 107 -----(1)\\a_{8} = a + 7d = 191 -----(2)[/tex]
By solving the two equations (1) & (2)....
[tex]\:\:\:\:a + 7d = 191 \\-\underline{a + 3d = 107 }\\ \underline{\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:4d = 84\:\:\:\:\:\:\:\:}}\\\\\\\\4d = 84\\d = 84 \div 4\\\boxed{d = 21}[/tex]
Now, we have the value of the common difference (d). To find [tex]a_{1}[/tex] or a, let's substitute the value of 'd' in (1).
[tex]a + 3d =107\\a + 3(21)=107\\a + 63 = 107\\a = 107 - 63\\\boxed{\bf\:a_{1} = 44}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
The maximum grain yield for corn is achieved by planting at a density of 37,000 plants per
acre. A farmer wants to maximize the yield for the field represented on the coordinate grid.
Each unit on the coordinate grid represents one foot. How many corn plants, to the nearest
thousand, does the farmer need? (Hint: 1 acre = 43,560 ft?)
у
5001
E
F
F
х
lo
-500
500
G
-500
H
The farmer needs approximately
corn plants.
Since there are 37000 plants per hectare, the total corn plan required is 475,665.75 corn plants
How to determine the area of a trapezium?The trapezium is a 2 -dimensional shape consisting of a triangle and a square.
The formula for calculating the area of a trapezoid is expressed as:
Area = 0.5(a + b)h
Area = 0.5(500 + 900) * 800
Area = 700 * 800
Area = 560000 square feet
Since 1 acre is equivalent to 43560 square feet, hence the total acre required is expressed as:
Required acre = 560000/43560
Required acre = 12.856 acres
Also since there are 37000 plants per hectare, the total corn plan required is 475,665.75 corn plants
Learn more on area of trapezoid here: https://brainly.com/question/1463152
How many kilograms in 1 1/2 pounds?
Answer:
67.5 kgs.
Step-by-step explanation:
1 pound = 0.45 kg
1 1/2 pounds = 0.45 + 1/2 * 45
= 67.5 kgs.
Please help!! What do I do
Answer:
a(5) = 1.080
a(10) = 0.393
a(20) = 0.122
Step-by-step explanation:
Take the derivative of velocity v(t) -> acceleration a(t)
v(t) -> a(t)
Quotient Rule: [tex]\frac{u*dv-du*v}{u^2}[/tex]
[tex]120*\frac{x}{5x+13}[/tex]
Make u= 5x+13 and v=x
[tex]120*\frac{x'*(5x+13)-x*(5x+13)'}{(5x+13)^2}\\\\120*\frac{1*(5x+13)-x*(5)}{(5x+13)^2}\\\\120*\frac{(5x+13)-5x}{(5x+13)^2}\\120*\frac{13}{(5x+13)^2} \\\\a(t)=\frac{1560}{(5x+13)^2}[/tex]
Now Subsitute your a(5) , a(10) , a(20). Also, round to 3 decimal place.
a(5) = 1.08033241 = 1.080
a(10) = 0.3930461073 = 0.393
a(20) = 0.122170826 = 0.122
Answer:
(a) 1.080 ft/s²
(b) 0.393 ft/s²
(c) 0.122 ft/s²
Step-by-step explanation:
Acceleration is the derivative of velocity. You are being asked to differentiate the given function and evalutate the derivative at three different times. The function is a rational function, so the formula for the derivative of a ratio is applicable.
(u/v)' = (vu' -uv')/v²
__
For the given velocity function, the accleration is ...
v(t) = (120t)/(5t +13)
a(t) = v'(t) = ((5t +13)(120) -(120t)(5))/(5t +13)² = 1560/(5t +13)²
(a)At t=5, the acceleration is ...
a(5) = 1560/(5·5 +13)² = 1560/1444 ≈ 1.080 . . . ft/s²
(b)At t=10, the acceleration is ...
a(10) = 1560/(5·10 +13)² = 1560/3969 ≈ 0.393 . . . ft/s²
(c)At t=20, the acceleration is ...
a(20) = 1560/(5·20 +13)² = 1560/12729 ≈ 0.122 . . . ft/s²
_____
Additional comment
Many graphing calculators are capable of finding the numerical value of the derivative of a function.
What is the value of x in |-6|=x
Which of the following describes the polynomial function?
8
==
4
-2
2
09
00
8
X
1
-5
do
9
The function has a negative leading coefficient.
O The function has an even degree.
O The function has zero turning points.
The function has one x-intercept.
Answer:
the function has one x intercept is the correct answer of given statement
6) Find the approximate perimeter of the following shape. Use 3.14 for pi
Answer:
where is the shape ???????
If the following line segment is reflected across the y-axis, what are the coordinates of the new endpoints?
A. (1, 6) and (3, 2)
B. (-1, -6) and (-3, -2)
C. (6, -1) and (2, -3)
D. (-6, 1) and (-2, 3)
Answer:A
Step-by-step explanation: im right im a god at answering these kind of equations.
OLZ HELP ILL MARK AS BRAINLEST
find the slope
Answer:
-1
Step-by-step explanation:
Here are the chorus datz: {0, 10, 10, 20, 20, 20, 20,30, 30, 40) What is the mean?
Answer:
7 is 20
8 is 40
Step-by-step explanation:
Mean is the total of all the numbers divided by the amount of numbers
7. 20
8. 40
Add them all up divide by the total amount of them
Miquel runs 5 days a week. He runs 2 7/10 miles each day that he runs. What is the total number of miles Miguel runs each week?
Answer:
13.5
Step-by-step explanation:
If he runs five times a week and his route is 2 7/10 then you do 5x2 7/10
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
Step-by-step explanation:
17) Find sine and cot
Answer:
79/156
Step-by-step explanation:
we know that cosx is the adjacent side over the hypotenuse.
hence, we can find the opposite side using the pythagorean theorem.
sqrt(13^2 - 5^2)
therefore, the opposite side is 12
opposite: 12
adjacent: 5
hypotenuse: 13
not that cot is adjacent over opposite while sin is opposite over hypotenuse.
So,
12/13 - 5/12
the answer is 79/156
Which fraction make comparison 3/4
Answer:
6/8, 12/16, and so on. I wasn't sure how you wanted this question to be answered, but 3/4 is also 0.75
Step-by-step explanation:
please help!
elect the correct answer.
Which statement is true?
A.
The function is an odd function because its graph is symmetric about the y-axis.
B.
The function is an even function because .
C.
The function is an odd function because .
D.
The function is an even function because its graph is symmetric about the origin.
The true statement is The function f(x)= tan(x) is an odd function because f(-x) = -f(x).
What is odd function?When x is substituted with -x, the odd functions are those that return their negative inverse. When f(-x) = -f(x), it follows that f(x) is an odd function (x). The trigonometric sine function, tangent function, cosecant function, etc. are a few examples of odd functions.
If f(x) = f(x), then the function is odd for all x. An odd function's graph will be symmetrical in all directions around the origin. Consider how unusual f(x) = x³ is. In other words, the function on one side of the x-axis is graphically symmetric about the origin or sign inverted with respect to the other side.
As, we know for the
even function: f(-x) = f(x)
odd function: f(-x)= -f(x)
and, using Trigonometry
tan x = sin x / cos x
Then,
f(-x) = sin (-x) / cos (-x)
= -sin (x) / cos (x)
= -tan (x)
= -f(x)
Thus, tan (x) is an odd function.
Hence, the function f(x)= tan(x) is an odd function because f(-x) = -f(x).
Learn more about odd function here:
https://brainly.com/question/20049729
#SPJ1
who wan na ta lk? im bo red
Answer:
So this is what hello means :):):):):):):)
Step-by-step explanation:
Leo drew a line that is perpendicular to the line shown on the grid and passes through point (F, G). Which of the following is the equation of Leo's line?
A) y - F = -2(x - G)y
B) y + F = 2(x + G)
C) y - G = -1/2(x - F)
D) y - G = -1/2(x + F)
The equation of the perpendicular line drawn by Leo is [tex]y-G=\dfrac{-1}{2}(x-F)[/tex]. Option C is the correct answer.
The equation of the line is [tex]y-y_1=m(x-x_1)[/tex] where, [tex]m[/tex] is the slope of the line and [tex](x_1,y_1)[/tex] is the point through which it is passing.
How to determine the equation of a line?
A line is drawn perpendicular to the line shown in the image. The perpendicular line passes through the coordinate point [tex](F,G)[/tex].
The slope of the line from the graph is-
[tex]m=\dfrac{y-intercept}{x-intercept}\\=2[/tex]
Therefore, the slope of the perpendicular line is [tex]\dfrac{-1}{2}[/tex].
Also, it is being given that Leo's line is passing through the coordinate point [tex](F,G)[/tex].
So, the equation of the Leo's line is-
[tex]y-G=\dfrac{-1}{2}(x-F)[/tex]
Thus, the equation of the perpendicular line drawn by Leo is [tex]y-G=\dfrac{-1}{2}(x-F)[/tex].
Learn more about the equation of line here- https://brainly.com/question/20632687
#SPJ2
Function or not a function pls help giving brainlest
Answer:
function
Step-by-step explanation:
For every value of 'x' ....there is only ONE value of 'y'
so it IS a function
A rental car company charges $72.37 per day to rent a car and $0.06 for every mile
driven. Colton wants to rent a car, knowing that:
• He plans to drive 275 miles.
• He has at most $450 to spend.
Answer:
5.99 days.
Step-by-step explanation:
If you are asking how many days he can rent the car then this is the correct answer.
So first multiply 275 x .06 to get how much money he will spent on the mileage. Which is $16.50. Then subtract that from $450 which is $433.50 and divided by $72.37.
Based on the graph how many distinct real number solutions does the equation x^3-3x^2+4=0 have
Answer:
2 solutions
Step-by-step explanation:
In order to answer a question "based on the graph," we need to have a graph of the equation. A graph provided by a graphing calculator is attached.
The cubic intersects the x-axis at two distinct points.
There are two (2) distinct real solution to the equation. (x = -1, x = 2).
Help me pls lol
I don’t understand
[tex]J'= (-5,-6)[/tex]
[tex]K'=(-5,-1)[/tex]
[tex]L'=(-10,-2)[/tex]
See graph below.
[tex]Hope[/tex] [tex]this[/tex] [tex]helps![/tex] [tex]Have[/tex] [tex]a[/tex] [tex]good[/tex] [tex]day![/tex] [tex]:)[/tex]
Ashley makes 9 dollars for each hour of work. Write an equation to represent her total pay p after working h hours
Answer:
twin what does H mean?
Step-by-step explanation: if you mean 8 the answer is 72.
Find the area of the shaded regions
your answer would be 254 I just did it and I got it right ✨
Elise, Jake, Malik, and Xiao each solved the same inequality.
Random Reply:
Indeed, so they have.
which angle is conterminal with a 645 degree angle
a. an angle measuring 75 degrees
b. an angle measuring 265 degrees
c. an angle measuring 345 degrees
d. an angle measuring 285 degrees
Answer:
D. An angle measuring 285 degrees
Step-by-step explanation:
An angle that is coterminal is congruent to the other angle whether negative or positive or more than 360.
An angle that is 645 degrees can be broken down into 360 + 285.
Since 360 is one revolution the angle would finish with 285 degrees.
Therefore the coterminal angle to 645 is 285.
Assume that the weights of ripe watermelons grown at a particular farm are normally distributed with a mean of 30 pounds and a standard deviation of 1.9 pounds. If the farm produces 400 watermelons, how many will weigh less than 27.87 pounds?
We know that,
[tex] \rightarrow \: z = \frac{x - \mu}{\sigma} \\ [/tex]
z = standard scorex = measuring valueμ = meanσ =standard derivationinserting the given values in the formula
[tex]\rightarrow \: z = \frac{27.87 - 30}{1.9} \\\rightarrow \: z = - 1.121[/tex]
Area that's left to z = -1.121
Area that's left to -1.121 = 0.1311
= 13.11%
Hence ,
13.11% of the watermelons weigh less than 27.87 pounds
To find the number of watermelons,
We'll find 13.11% of 400
= 13.11% x 400
= 13.11/100 x 400
= 52.44
hence , approx 52 watermelons would be lesser than 27.87 pounds
Which linear inequality represents the solution set graphed?
Answer:
Your Answer is D.
Step-by-step explanation:
There isn't much to explain but look at the graph.
The slope of m = rise/run.
m = 1/2
b = -3/2
y = mx + b
please help! a point is chosen at random in the square, what percent of the time will the point be in the circle,round to the nearest tenth of a percent?
Answer:
78.5%
Step-by-step explanation:
You take the area of the circle which is pie*r^2
and divide it by the area of the square
A box contains 3 orange pencils, 9 yellow pencils, and 5 green pencils.
Two pencils are selected, one at a time, with replacement.
Find the probability that the first pencil is green and the second pencil is yellow.
Express your answer as a decimal, rounded to the nearest hundredth.
The probability that the first pencil is green and the second pencil is yellow is 0.16.
What is the probability?Probability determines the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that the first pencil is green and the second pencil is yellow = (number of green pencils / total number of pencils) x (number of yellow pencils / total number of pencils)
5/17 x 9/17 = 0.16
To learn more about probability, please check: https://brainly.com/question/13234031
#SPJ1
Find the area of the shape based on the provided measurements
Answer:
375 units²
Step-by-step explanation:
A = bh/2
A = (75)(10)/2
A = 750/2
A = 375