Answer:
Θ = (π/6) + πn
Θ = (5π/6) + πn
Step-by-step explanation:
4sin²Θ + 4 = 5
-4 -4
4sin²Θ = 1
÷4 ÷4
sin²Θ = (1/4)
√sin²Θ = √(1/4)
sinΘ = (1/2), (-1/2)
-------------------------
Θ = arcsin (1/2)
Θ = (π/6)
to find the quadrant subtract π
Θ = π - (π/6)
Θ = (5π/6)
Find the period
2π / |b|
b = 1
2π/1 = 2π
The sin Θ function is 2π, so values will repeat 2π in both directions.
Θ = (π/6) + 2πn (n is the variable)
Θ = (5π/6) + 2πn
-------------------------------------------------------------------------------------------------------
sin Θ = (-1/2)
Θ = arcsin (-1/2)
Θ = (-π/6)
To find the second function add π
Θ = 2π + (π/6) + π
Θ = (7π/6)
Find the period
2π/|b|
2π/1
2π
(-π/6) + 2π
2π 6 π
----- × ----- - -----
1 6 6
Θ = (11π/6) will repeat every 2π in both directions
-------------------------------------------------------------------------------------------------------
Θ = (π/6) + 2πn
Θ = (5π/6) + 2πn
Θ = (7π/6) + 2πn
Θ = (11π/6) + 2πn
(π/6) + π = (7π/6)
(5π/6) + π = (11π/6)
Θ = (π/6) + πn
Θ = (5π/6) + πn
----------------------------------------------------------------------------------------------------------
I hope this helps!
In a circle, a 270° sector has area 300s in? What is the radius of the circle?
.
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ A=300\pi \\ \theta =270 \end{cases}\implies 300\pi =\cfrac{(270)\pi r^2}{360}\implies 300\pi =\cfrac{3\pi r^2}{4} \\\\\\ 1200\pi =3\pi r^2\implies \cfrac{1200\pi }{3\pi }=r^2\implies 400=r^2\implies \sqrt{400}=r\implies 20=r[/tex]
Fastest answer gets brainliest (must provide an explanation and steps for proof)
Answer:
[tex]\sf g(x+5) = \dfrac{x+6}{4x+17}[/tex]
explanation:
g(x + 5) || this function refers to x = x + 5
solving steps:
[tex]\sf g(x) = \dfrac{1+x}{-3+4x}[/tex]
[tex]\rightarrow \sf g(x+5) = \dfrac{1+(x+5)}{-3+4(x+5)}[/tex]
[tex]\rightarrow \sf g(x+5) = \dfrac{6+x}{-3+4x+20}[/tex]
[tex]\rightarrow \sf g(x+5) = \dfrac{x+6}{4x+17}[/tex]
Answer:
Given function:
[tex]g(x)=\dfrac{1+x}{-3+4x}[/tex]
To find [tex]g(x+5)[/tex], substitute [tex]x+5[/tex] into the function in place of [tex]x[/tex]:
[tex]\implies g(x+5)=\dfrac{1+(x+5)}{-3+4(x+5)}[/tex]
[tex]=\dfrac{1+x+5}{-3+4x+20}[/tex]
[tex]=\dfrac{x+6}{4x+17}[/tex]
A laptop computer is purchased for $2350. After each year, the resale value decreases by 35% . What will the resale value be after 4 years?
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &2350\\ r=rate\to 35\%\to \frac{35}{100}\dotfill &0.35\\ t=years\dotfill &4\\ \end{cases} \\\\\\ A=2350(1 - 0.035)^{4}\implies A=2350(0.965)^4\implies A\approx 2037.87[/tex]
Find the area of the shaded polygons.
Answer: 372 sq. un
Step-by-step explanation:
7+24=31
Divided by 2 = 15.5
15.5x24 = 372
super easy algebra 4 x (15- ?) =48
Put the following investment options in order of least to greatest risk:
starting a business
B-rated bond
speculative stock
property
The order of investment options from least to greatest risk is:
B rated bond.Property.Speculative stock. Starting a business. How risky are some investment options?A B rated bond is considered safer than the rest because there is a high chance that the owners of the bond will redeem it. Property is not very risky but can be susceptible to market shocks.
Speculative stock is the third riskiest because its prices are prone to fluctuation. Starting a business is by far the riskiest because a lot of new businesses fail.
Find out more on risky investments at https://brainly.com/question/25219850.
Answer:
B-rated bond
property
starting a business
speculative stock
Step-by-step explanation:
Liz flips a coin 60 times. The coin lands head up 24 times and tails up 36 times. The EXPERIMENTAL probability of the coin landing headS up is ___%.
Answer:
60%
Step-by-step explanation:
36= heads
36/60= 60%
Answer:
60x24x36=51,840%
Step-by-step explanation:
The diameter of a circle is 12 ft. Find its area to the nearest whole number. Answer: A =
Answer:
113 ft²
Step-by-step explanation:
π = 3.14
r = 6
Use the formula for the area of a circle:
A = πr²
A = 3.14*6²
A = 3.14*36
A = 113.04
A = 113
Hope this helps :)
Answer:
Area = 113 ft²
Step-by-step explanation:
The formula to find the area of a circle is:
Area = π × r²
r is the radius that can be found by taking half of the diameter.
r = [tex]\frac{12}{2}[/tex] = 6
Area = π × 6²
Area = π × 36
Area = 113.09 = 113 [ to the nearest whole number ]
could someone explain to me how to multiple/divide equations in scientific notation im super confused :(
Solve for c
Can you pls help me??
Answer:
5(c+3)=85
divide both sides by 5
c+3=17
taking 3 to the other side gives us -3
c=17-3
c=14
Find the area of the 2.5 m circle using 3.14 or 2/7 four pi
Answer:
Formula for area of circle;
A = π[tex]r^{2}[/tex]
Where 'π' represents pi (22/7 or 3.14), and 'r' is the radius which is being squared.
Plug in your values:-
A = π[tex]r^{2}[/tex]
A = 3.14(2.5^2)
A = 3.14(6.25)
A = 19.625 meters is your answer.
Simplify.
1/3 ≠ 18n^2 * 2n
Answer:
n³ ≠ 108
Step-by-step explanation:
1/3 ≠ 18n² * 2n
1/3 ≠ 18 * n² * 2 * n
1/3 ≠ 18 * 2 * n² * n
1/3 ≠ 36n³
Cross multiply,
1 * n³ ≠ 3 * 36
n³ ≠ 108
Hence simplified.
PLEASE HELP!
The scatter plot shows the number of years of experience, x, and the
amount charged per hour, y, for each of 25 dog sitters in Texas.
(a) Write an approximate equation of the line of best fit for the data. It doesn't have to be the exact line of best fit.
(b) Using your equation from part (a), predict the amount charged per hour by a dog sitter with 18 years of experience.
Answer:
(a) [tex]\sf y=\dfrac{11}{20}x+7[/tex]
(b) $16.90
Step-by-step explanation:
Part (a)
Add a line of best fit (see attached).
Find two points on the line: (7, 0) and (20, 18)
Use these points to find the slope of the line:
[tex]\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{18-7}{20-0}=\dfrac{11}{20}[/tex]
Use the found slope and one of the points in the point-slope form of the linear equation to find an equation for the line of best fit:
[tex]\sf\implies y-y_1=m(x-x_1)[/tex]
[tex]\sf\implies y-7=\dfrac{11}{20}(x-0)[/tex]
[tex]\sf\implies y=\dfrac{11}{20}x+7[/tex]
Part (b)
Substitute x = 18 into the equation and solve for y:
[tex]\sf\implies y=\dfrac{11}{20}(18)+7=\$16.90[/tex]
Triangle A′B′C′ is a dilation of triangle ABC .
What is the scale factor?
Enter your answer in the box.
Answer:
1/2
Step-by-step explanation:
The scale factor is 1/2 because each side length of [tex]\triangle{A'B'C'}[/tex] is 1/2 of the length of the side lengths of [tex]\triangle{ABC}[/tex].
Hope this helps :)
Answer:
1/2
Step-by-step explanation:
took the test
Determine the type of symmetry of r =5-sin11ø from the equation, if any. Make sure to confirm graphically. Symmetric with respect to the:
A) pole
B) line /2
C) polar axis
D) none of these
well, let me not bore you to death on how we test it and test it.
[tex]\underline{\textit{testing for symmetry to the }\frac{\pi }{2}~line\qquad \qquad r=-r~~,~~\theta =-\theta } \\\\\\ r=5-sin(11\theta )\implies (-r)=5-sin[11(-\theta )]\implies -r=5-sin(-11\theta ) \\\\\\ \stackrel{symmetry~identity}{-r=5-\stackrel{\downarrow }{[-sin(11\theta )]}}\implies\implies r=-5-sin(11\theta )\impliedby \textit{no dice} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\underline{\textit{testing for symmetry to the polar axis}\qquad \qquad \theta =-\theta} \\\\\\ r=5-sin(11\theta )\implies r=5-sin[11(-\theta )]\implies r=5-sin(-11\theta ) \\\\\\ r=5-[-sin(11\theta )]\implies r=5+sin(11\theta )\impliedby \textit{no dice} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\underline{\textit{testing for symmetry to the pole}\qquad \qquad r=-r} \\\\\\ r=5-sin(11\theta )\implies -r=5-sin(11\theta )\implies r=-5+sin(11\theta )\qquad \textit{no dice}[/tex]
so the symmetry tests didn't pass, notice the picture below though, looks a bit deceiving, it looks as if it'd have π/2 symmery, but it doesn't show in the test.
A rectangle is shown with the area of 14/32 square in. Label two sides of the rectangle with appropriate fractions that would come up with the area of 14/32 square inches when multiplied together.
The dimensions of the rectangle that would have a value of 14/32 inches square are a length of 2/16 and a width of 31/2 inches.
What are the dimensions of the rectangle?
A rectangle is a 2-dimensional quadrilateral with four right angles that has a value of 360 degrees. It has two diagonals that bisect each other.
Area of a rectangle = length x width
2/16 x 7/2 = 14/32
To learn more about how to calculate the area of a rectangle, please check: https://brainly.com/question/16595449
Am I right??? Please help me
Function: y = 2x²-5
Find y-intercept:
y = 2(0)²-5
y = -5
Find x-intercept:
2x²-5 = 0
2x² = 5
x² = 2.5
x = ±√2.5
x = -1.5811 , 1.5811
Graph plotted:
Answer:
Vertex and y-intercept (0, -5)
x-intercepts (-1.58, 0) (1.58, 0)
opens upwards
other plot points: (-2, 3) (-1, -3) (1, -3) (2, 3)
Step-by-step explanation:
The graph is not quite correct - it's a little too narrow and doesn't go through the points on the graph.
The y-intercept is when x = 0:
f(0) = 2(0)² - 5
= - 5
Therefore, the y-intercept is at (0, -5)
We also know that the y-intercept is the vertex since the equation is in the form [tex]f(x)=ax^2+c[/tex]
The x-intercepts are when f(x) = 0:
[tex]\implies 2x^2 - 5 = 0[/tex]
[tex]\implies x^2 =\dfrac52[/tex]
[tex]\implies x=\pm1.58113883...[/tex]
As the leading coefficient is positive, the parabola opens upwards.
Finally, input values -2 ≤ x ≤ 2 to find plot points:
(-2, 3)
(-1, -3)
(0, -5)
(1, -3)
(2, 3)
Find the missing side length using the Pythagorean Theorem.
a²+6² = ²
The missing length is 18
Using Pythagorean rule
Hyp^2 = Opp^2 + adj^2
Opp^2 = hyp^2 - adj^2
Opp^2 = 30^2 - 24^2
Opp^2 = 900 - 576
Opp^2 = 324
Opp = sqrt ( 324 )
Opp = 18
The response to a question has three alternatives: A, B, and C. A sample of 120 responses provides 60% A, 23% B, and 37% C. Show the frequency and relative frequency distributions
Answer:
0.5,0.2,0.3
Step-by-step explanation:
divide 60,23,37 by 120
Write the number in standard form
and word form.
7 x 10 + 5 x 1 + 6 x (1/100) + 2 x
(1/1,000)
Answer:
75.062
Step-by-step explanation:
just add and multiply then remember that 1/100 or 1/1000 is just 0.001 or 0.01
The height h(t) (in feet) of the seat of a child’s swing above ground level is given by the equation
below where t is the time in seconds after the swing is set in motion.
ℎ() = −1.1 cos ((2/3) ) + 3.1
a. Find the maximum and minimum height of the swing.
b. When is the first time after t = 0 that the swing is at a height of 3 feet?
c. When is the second time after t = 0 that the swing is at a height of 3 ft?
Answer: See below
Step-by-step explanation:
The function of the seat’s height from the ground level is given as,
[tex]h(t)=-1.1 \cos \left(\frac{2 \pi}{3} t\right)+3.1[/tex]
Here, t denotes the time.
(a) The height will be maximum or minimum when the derivative of the function of height is equal to zero.
[tex]\begin{aligned}h^{\prime}(t) &=0 \\\frac{d}{d t}\left(-1.1 \cos \left(\frac{2 \pi}{3} t\right)+3.1\right) &=0 \\-1.1 \times \frac{2 \pi}{3}\left(-\sin \left(\frac{2 \pi}{3} t\right)\right) &=0 \\t &=0,1.5\end{aligned}[/tex]
The height of the seat at time t = 0 s can be determined as,
[tex]\begin{aligned}h(0) &=-1.1 \cos \left(\frac{2 \pi}{3}(0)\right)+3.1 \\&=2 \mathrm{ft}\end{aligned}[/tex]
Therefore, the maximum height of the swing is 4.2 ft and the minimum height of the swing is 2 ft.
(b) The height of the swing is given as,
[tex]\begin{aligned}h &=3 \mathrm{ft} \\-1.1 \cos \left(\frac{2 \pi}{3} t\right)+3.1 &=3 \\t &=0.7 \mathrm{~s}\end{aligned}[/tex]
Therefore, the first time after t = 0 s that the swing’s height of 3 ft is 0.7 s.
(c) The height of the swing is given as,
[tex]\begin{aligned}h &=3 \mathrm{ft} \\-1.1 \cos \left(\frac{2 \pi}{3} t\right)+3.1 &=3 \\\frac{2 \pi}{3} t &=1.47976+2 \pi \\t &=3.7 \mathrm{~s}\end{aligned}[/tex]
Therefore, the second time after t = 0 s that the swing’s height of 3 ft is 3.7 s.
the legnth of a rectangle is three times its width. if the perimeter of the rectangle is 64 in, find the length and width
Step-by-step explanation:
According to the question,
Let the width of rectangle be x and length of rectangle be 3x
Perimeter of Rectangle :- 2(L+B) = 64 in
Putting the values we get ,
2(3x+x) = 64 in
8x = 64 in
x = 8 in
Putting the value of x ,
Width :- 8 Inch
Length :- 24 inch
[tex]\rightarrow[/tex] Length(l) of the rectangle is three times it's width(w) = 3w.
[tex]\rightarrow[/tex] Width(w) of the rectangle = w.
[tex]\rightarrow[/tex] Perimeter of the rectangle = 64in.
To Find:-[tex]\rightarrow[/tex]Length and width of the rectangle.
Solution:-[tex]\rightarrow[/tex] Perimeter of rectangle = [tex]\sf{2(l+w)}[/tex] putting the value of perimeter, l and w from the above given)
[tex]\rightarrow[/tex] 64 = [tex]\sf{2(3w+w)}[/tex]
[tex]\rightarrow[/tex] 64 = [tex]\sf{2(4w)}[/tex]
[tex]\rightarrow[/tex] 64 = [tex]\sf{8w}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{\frac{64}{8}}[/tex]= [tex]\sf{w}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{8}[/tex]= [tex]\sf{w}[/tex]
Therefore, width of the rectangle = 8in.
And Length = 3(8)in. = 24in.
To check whether the answer is correct or not, we can put the value of length and width in the formula = [tex]\sf{2(l+w)}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{=\: 2(24+8)}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{=\: 2(32)}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{=\: 64in.}[/tex]
Since, the perimeter of the rectangle is same as given in the question, therefore the value of length and width are correct.
_______________________________
Hope it helps you:)
the ratio of the length of shantels pool to the length of juan's pool is 3 to 5 shantels pool is 30 meters how long is Juan’s pool
Step-by-step explanation:
the ratio of the pool lengths is 3/5.
that means for every 3 meters of length on Shantel's pool, there are 5 meters of length on Juan's pool.
it the other way around : to get to the size of Shantel's pool, every 5 meters of length on Juan's pool are converted to 3 meters.
x = length of Juan's pool
x × 3/5 = 30
3x = 150
x = 50 meters
you see the relationship ?
3/5 = 30/50 = 300/500 = ...
but it is true for any factor
3/5 = 15/25 = 24/40 = 6/10 = ...
once you see the factor for one part of the ratio, you know there is the same factor for the other part (or parts) of the ratio. otherwise the ratio would not stay the same and keep the relationship.
Write an equation in standard form of an ellipse that is 10 units high and 8 units wide. The center of the ellipse is (0, 0).
Answer:
[tex]\frac{x^2}{25} + \frac{y^2}{16} = 1[/tex]
Step-by-step explanation:
Great, so the question already tells you that you're using the standard form of an ellipse. All you gotta do is apply your knowledge of the characteristics of an ellipse graph.
The standard form of an ellipse is:
[tex]1 = \frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2}[/tex]
[tex]h[/tex] and [tex]k[/tex] are the offset, or the coordinates of the center of the ellipse. The center of the ellipse will always be on (h,k). Now because the question says the center is (0,0), we can make h and k equal to 0 in the equation giving:
[tex]1 = \frac{x^2}{a^2} + \frac{y^2}{b^2}[/tex].
Now, the height of the ellipse will always be equal to 2a. The width will be equal to 2b.
Since we are told what the height and width should be, we can find the a and b values quite easily using algebra.
So first, height:
[tex]10 = 2a\\5 = a[/tex]
Now width:
[tex]8 = 2b\\4 = b[/tex]
Subbing for a and b in the equation give you:
[tex]1 = \frac{x^2}{5^2} + \frac{y^2}{4^2}\\=\\1 = \frac{x^2}{25} + \frac{y^2}{16}[/tex]
Help help help help math math
Answer:
the answer in the question mark that was in the green box ???
Please answer this relatively quickly, I'm not in very much of a rush but would like to get this done.
Answer: 6
Step-by-step explanation:
Because you have to multiply then remove the fraction and set equal to 0 and solve for x which I’m pretty sure gives u 6
Given the function
[tex]f(x) = (x + 4){(x - 2)}^{2} [/tex]
Determine the end behavior of the graph of the function. Show all/any work
[tex]lim \: f(x) = ( \infty + 4)( \infty - 2) {}^{2} \\ x - > \infty [/tex]
[tex]lim \: f(x) = \infty \times \infty \\ x - > \infty [/tex]
[tex]lim \: f(x)= \infty \\ x - > \infty [/tex]
[tex]lim \: \frac{f(x)}{x} = \frac{x(1 - \frac{4}{x})(x - 2) {}^{2} }{x} \\ x - > \infty [/tex]
[tex]lim \: \frac{f(x)}{x} = (1)( \infty - 2) {}^{2} \\ x - > \infty [/tex]
[tex]lim \: \frac{f(x)}{x} = \infty \\ x - > \infty [/tex]
We can then say that the function f(x)=(x-4)(x-2)² admits an asymptotic direction parallel to the y-axis at +∞ and -∞ as well since we have to follow the same steps.
What percent of 1/4 is 1/5
5%
16%
24%
80%
[tex]\text{Let it be x percent}\\ \\\dfrac 14 \times x\% = \dfrac 15\\\\\\\implies\dfrac 14 \times \dfrac x{100} = \dfrac 15\\ \\\\\implies x = \dfrac{400}{5} = 80\\\\\\\text{Hence the answer is}~ 80\%[/tex]
sketch the graph of y=2x^2-3x-4
Q. If A is a square matrix such that A² = A, then write the value of 7 A −(I + A)³, where I is an identity matrix.
Since [tex]A^2=A[/tex], we have
[tex](I + A)^2 = I^2 + IA + AI + A^2 = I + A + A + A = I + 3A[/tex]
[tex](I + A)^3 = (I + A) (I + 3A) = I^2 + 3IA + AI + 3A^2 = I + 3A + A + 3A = I + 7A[/tex]
Then the target expression is
[tex]7A - (I + A)^3 = 7A - (I + 7A) = \boxed{-I}[/tex]