Step-by-step explanation:
[tex] \tan(2x) = 1.5[/tex]
Take the arc tangent,
[tex] \tan {}^{ - 1} ( \tan(2x) ) = \tan {}^{ - 1} (1.5) [/tex]
[tex]2x = 56.3[/tex]
[tex]x = 28.15[/tex]
b.
[tex](3 \cos(x) + 1)(2 \cos(x) + 3) = - 2[/tex]
[tex]6 \cos {}^{2} (x) + 11 \cos(x) + 3 = - 2[/tex]
[tex]6 \cos {}^{2} (x) + 11 \cos(x) + 5 = 0[/tex]
[tex]6 \cos {}^{2} (x) + 6 \cos(x) + 5 \cos(x) + 5 = 0[/tex]
[tex]6 \cos(x) ( \cos(x) + 1) + 5( \cos(x) + 1) = 0[/tex]
[tex](6 \cos(x) + 5)( \cos(x) + 1) = 0[/tex]
Set each factor equal to zero.
[tex]6 \cos(x) + 5 = 0[/tex]
[tex]6 \cos(x) = - 5[/tex]
[tex] \cos(x) = - \frac{5}{6} [/tex]
[tex]x = \cos {}^{ - 1} ( \frac{5}{6} ) [/tex]
[tex]x = 146.4[/tex]
For the second factor,
[tex] \cos(x) + 1 = 0[/tex]
[tex] \cos(x) = - 1[/tex]
[tex]x = 180[/tex]
So the answer for the second one is
146.4 and 180.
Choose the polynomial written in standard form. x2 4x4 10x6 x4 4x3 10x x7 4x3 10x4 x6 4x3 10x7
The polynomial that is written in standard form out of the given options is given by: Option 2: x^4 + 4x^3 + 10x
What is standard form of a polynomial?Suppose the considered polynomial is of only one variable.
Then, the standard form of that polynomial is the one in which the terms with higher exponents are written on left side to those which have lower exponents.
What are terms in polynomials?Terms are added or subtracted to make a polynomial. They're composed of variables and constants all in multiplication.
Example:
[tex]x^3 + 3x +5[/tex]
is a polynomial consisting 3 terms as [tex]x^3, 3x \: \rm and \: 5[/tex]
Cheking all the options for them being in standard form or not:
Option 1: [tex]x^2 + 4x^4 + 10x^6[/tex]Second term has 4 as exponent, but on its left, the first term has 2 as exponent. So higher expoent holding term is not on left. Thus, this polynomial is not in standard form.
Option 2: [tex]x^4 + 4x^3 + 10x[/tex]4 > 3 > 1 (comparing the exponents), and the terms holding them are also in this order (left to right).
Thus, this polynomial is in standard form.
Option 3: [tex]x^7 + 4x^3 + 10x^4[/tex]Not in standard form because the last term has bigger power then the term on its left.
Option 4: [tex]x^6 + 4x^3 + 10x^7[/tex]Not in standard form because the last term has bigger power then the term on its left.
Thus, the polynomial that is written in standard form out of the given options is given by: Option 2: x^4 + 4x^3 + 10x
Learn more about standard form of a polynomial here:
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helpp Its for calculus
Answer:
its 18
Step-by-step explanation:
Answer:
the answer is 18
Step-by-step explanation:
round to the nearest whole number
Answer:
SA = 527.52 cm²
Step-by-step explanation:
Cone SA = πr(r + √(h² + r²))
π = 3.14r = 7h = ?Find h
Step 1. Create a right triangle with the radius (attached image)
Step 2. Pythagorean Theorem
a² + b² = c²
7² + b² = 17²
b² = 289 - 49
b = √240
b or h = 4√15
Solve for SA
SA = πr(r + √(h² + r²))
SA = 3.14 · 7 · (7 + √(4√15² + 7²))
SA = 21.98(7 + √(240 + 49))
SA = 21.98 (7 + 17)
SA = 527.52 cm²
Hope this helps!
can someone help me.
Answer:
D. 75 m²
Step-by-step explanation:
l = 15m
b = 5m
area of rectangle = l × b = 15 × 5 = 75 m²
Graph help fast!!!!!!!!!!1111
Answer:
(0,0)
(1,3)
(2,6)
(3,9)
(-1,-3)
(-2,-6)
(-3,-9)
Step-by-step explanation:
The equation of the graph is y=3x
Find the sum of the following series. Round to the nearest hundredth if
necessary
5 + 10 + 20 + ... + 163840
Sum of a finite geometric series:
ai
Sn
di — airon
1 - 1
Answer:
327675
Step-by-step explanation:
the formula of the series is:
16
∑5*2^(n-1)
n=1
the formula for the sum of a geometric series is:
Sn=a(1-r^n)/(1-r)
plug in the values from above
n=16 a=5 and r=2 (values from the geometric function) so
Sn=5(1-2^16)/(1-2)
Sn=327675
There was a blizzard. Snow was falling at a rate of 4 ½ inches per hour. If the snow kept accumulating at the same rate, how long would it take for 27 inches of snow to accumulate?
Consider the equations y = 3x and y = -12- x.
Complete the table of values for the equation y = 3x.
Х
-7
-5
-3
Answer:
x | -7 -5 -3
y | -21 -15 -9
Step-by-step explanation:
y = 3x
If x = -7 then y = 3 × (-7) = -21
x = -5 then y = 3 × (-5) = -15
x = -3 then y = 3 × (-3) = -9
Can someone help me? ill give brainlyest if u answer!!
Answer:
Kiko was right.
Step-by-step explanation:
When a positive integer is multiplied by another positive integer, the product is positive. When a negative integer is multiplied by a positive integer, then the product is negative. The power should also be considered as well, since it can affect whether the integer is positive or negative depending on if it's even or odd.
Help, please! It's all in the screenshot
Answer:
cube root of 9. the third option
Step-by-step explanation:
x^3 = 9
we take the cube root of both sides.
so x = cube root of 9
Find the missing angle.
Step-by-step explanation:
Angles in a quadrilateral add to 360 degrees. So, x = 360-88-142-106=24 degrees
5 STARS ON YOUR ACCOUNT!!! AND COMMENTS AND A THANK YOU
Answer:
OPTION B
Step-by-step explanation:
1 cm=0.75 m
I hope it helped you
The polygons are similar. Find the value of x.
PLEASE HELP
Answer:
x = 30
Step-by-step explanation:
[tex]\frac{x}{21} =\frac{20}{14}[/tex]
[tex]x=\frac{(21)(20)}{14}=\frac{420}{14} =30[/tex]
Hope this helps
What is the perimeter, rounded to the nearest tenth? 24.2 ft 28.3 ft 48.5 ft 56.8 ft
Answer:
48.5 ft
Step-by-step explanation:
What equation has the solution x=8?
Answer:
X/4 = 2
X=8
8 divided by 4 is 2 and 4x2 is 8
Evaluate the expression y-3+2 when x = 6 and y=8
Answer:
7
Step-by-step explanation:
Hey there!
In order to answer this question you need to substitute the "y-value"
As you can see, y=8 and we need to put 8 where there is y
8-3+2 is what the equation will look like
Now we can simplify
8-3 is 5 and 5+2 is 7
So your answer is 7
PLEASE ANSWER - BRAINLY IF 2 ANSWERS - THANKS ON PROFILE TOO - 5 STAR RATING!
Answer:
b
Step-by-step explanation:
What is
8 divided by 4 (3-1)
Answer:
[tex]8 \div 4(3 - 1)[/tex]
let's follow BODMAS for solving this expression ~
the BODMAS rule states the order for solving a given question and the order lies in its full form which is as follows ~
B - brackets
O - of
D - division
M - multiplication
A - addition
S - subtraction
using the order , let's move to the expression given now ~
[tex]\dashrightarrow \: 8 \div 4(3 - 1) \\ \\ as \: the \: rule \: states \: , \: we \: will \: solve \: the \: brackets \: first \\ \\\dashrightarrow 8 \div 4(2) \\ \\ brackets \: again \\ \\ \dashrightarrow \: 8 \div 8 \\ \\ and \: finally \: divison \\ \\ \dashrightarrow \: 1[/tex]
hope helpful :D
The value of expression 8 divided by 4 (3-1) would be equal to 1
How can we interpret the division?When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.
We need to find the expression of 8 divided by 4 (3-1)
A negative divided by a negative is positive, therefore,
8 / 4 (3-1)
8 / 4(2)
8/8 = 1
Therefore, The value of 8 divided by 4 (3-1) is; 1
Learn more about division here:
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#SPJ2
How many solutions can be found for the equation 5x + 3(x − 1) = 10x − 2x − 3? (4 points) None
One
Two
Infinitely many
Answer:
The answer is infinitely many.
Step-by-step explanation:
5x + 3(x − 1) = 10x − 2x − 3 is simplified to 0=0, which is infinitely many solutions.
-
4. Which shows the solution to the
inequality? 6(x-2) +21 <39
PLEASE HELP ANSWER
I will give 20 points
What is the measure of the given angle in radians
Answer:
[tex]\frac{11\pi }{6}[/tex]
Step-by-step explanation:
To convert an angle from degrees to radians, you need to multiply the degrees by [tex]\frac{\pi }{180}[/tex].
[tex]\frac{330}{1}[/tex] × [tex]\frac{\pi }{180}[/tex] = [tex]\frac{330\pi }{180}[/tex]
[tex]\frac{330\pi }{180}=\frac{11\pi }{6}[/tex]
6. A rectangular pyramid fits exactly on top of a rectangular prism. The prism has a length of 16 cm, a width of 6 cm, and a height of 8 cm. The pyramid has a height of 14 cm. Find the volume of the composite space figure.
Answer:
V = 682.66667
Step-by-step explanation:
ANSWER ASAP PLS! WILL GIVE MAX PTS Three times x is 13 less than y. The sum of x and two times y is 12. Write two equations and graph to find the value of y.
Group of answer choices
y = -2
y = 2
y = 7
y = -7
Solution For Given Question
Three times x is 13 less than y
[tex]3x = y - 13 \\ = > 3x + 13 = y[/tex]
The sum of x and two times y is 12.
[tex]x + 2y = 12[/tex]
Replacing Value of Y with 3x + 13
[tex]x + 2y = 12 \\ \\ \implies x + 2(3x + 13) = 12 \\ \\ \implies x + 6x + 26 = 12 \\ \\ \implies7x = 12 - 26 \\ \\ \implies 7x = - 14 \\ \\ \implies x = \cancel\frac{ - 14}{7} \\ \\ \implies x = - 2[/tex]
Now we need to fine Value of'y' i e.,
[tex]y = 3x + 13 \\ \\ \implies y = 3( - 2) + 13 \\ \\ \implies y = - 6 + 13 \\ \\ \implies y = 7[/tex]
[tex] \therefore \text{option c.(y = 7) is your answer}[/tex]
Hope this helpsFind the 7th term of the geometric sequence.
14, 28, 56, ...
Answer:
The 7th term is 896
Step-by-step explanation:
= ar^n-1
a = 14
r = 28/14
= 2
n = 7
= 14 X 2 ^ 7-1
= 14 X 2 ^ 6
= 14 X 64
= 896
Tommy ran 15.4 miles in 7 days. How many miles did Tommy run per day
CAN SOMEONE HELP ME 50 POINTS
What are m∠1 and m∠2?
A. ∠1 = 30°, m∠2 = 35°
B. ∠1 = 35°, m∠2 = 30°
C. ∠1 = 65°, m∠2 = 60°
D. ∠1 = 85°, m∠2 = 80°
What is the length of the parks boundary to the nearest yard
hmmm taking a peek at the triangles inside the park, hmmm let's notice both triangles have all interior angles of 60°, meaning the triangles are equilateral both, so all sides are equal, since we know one side is 50 yards, well, all sides are 50 yards, so the top and bottom straight-lines are both 50 each.
looking at the left and right sides, hmmm those are just sectors of a circle, both have a radius of 50 yards and a central angle of 120°.
[tex]\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=50\\ \theta =120 \end{cases}\qquad \implies s=\cfrac{(120)\pi (50)}{180}\implies s=\cfrac{100\pi }{3} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{straight~lines}{2(50)}~~ + ~~\stackrel{circular~lines}{2\left( \cfrac{100\pi }{3} \right)}\implies 100+2\left( \cfrac{100(3.14) }{3} \right)~~\approx~~309~yards[/tex]
50 POINTS PLEASE ANSWER!
Solve it through arithmetic sequence
First term=a=17Common difference=d=-3Rule is
a_n=a+(n-1)d=17-3(n-1)So
a_2=17-3=14a_3=17-6=11a_4=17-9=8Answer:
[tex]14 \\ 11 \\ 8[/tex]
ANSWER PLEASE LINKS , SPAM , OR WRONG ANSWER WILL BE REPORTED AND DELETED 100 POINTS TO ANSWER AND YOU WILL GET BRAINLIEST PLEASE DONT WASTE YOUR TIME AND SEND LINKS , SPAM. OR WRONG ANSWER !!!!! HAVE A BLESSED NIGHT/DAY
Answer:
Area of polygon = 42.63 mm²
Step-by-step explanation:
Given:
L = 8.7 mmW = 4.9 mmTo find the area of the polygon (rectangle), multiply the length with the width.
⇒ Area of polygon = LW
Substitute the values into the area:
⇒ Area of polygon = (8.7)(4.9) [L = 8.7 mm; W = 4.9 mm]
⇒ Area of polygon = 42.63 mm²
As it's a rectangle
Area:-
Length×Breadthlw8.7(4.9)42.6mm^2