Trigonometric equations
4sin^2(theta) + 4 = 5

Answer:

60%

Step-by-step explanation:

36= heads

36/60= 60%

Answer:

60x24x36=51,840%

Step-by-step explanation:

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

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.

[tex]\rightarrow[/tex]Length and width of the rectangle.

[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:)

Answer: 372 sq. un

Step-by-step explanation:

7+24=31

Divided by 2 = 15.5

15.5x24 = 372

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

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.

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.

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.

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 ]

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)

[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]

The order of investment options from least to greatest risk is:

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:

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]

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

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.

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]

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]

[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]

[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]

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]

Answer:

the answer in the question mark that was in the green box ???

[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.

Answer:

0.5,0.2,0.3

Step-by-step explanation:

divide 60,23,37 by 120

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

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

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.

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.

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