Solve the equation 506x - 92y + 90 = 498 - 4x + 6y

Answer:

3 solutions:

[tex]\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}} [/tex]

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is [tex]tan(\frac{\theta}{2})[/tex] so let's focus on that part of the equation first.

We know that:

[tex]tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}[/tex]

therefore:

[tex]cos(\frac{\theta}{2})\neq0[/tex]

so we need to find the angles that will make the cos function equal to zero. So we get:

[tex]cos(\frac{\theta}{2})=0[/tex]

[tex]\frac{\theta}{2}=cos^{-1}(0)[/tex]

[tex]\frac{\theta}{2}=\frac{\pi}{2}+\pi n[/tex]

or

[tex] \theta=\pi+2\pi n[/tex]

we can now start plugging values in for n:

[tex] \theta=\pi+2\pi (0)=\pi[/tex]

if we plugged any value greater than 0, we would end up with an angle that is greater than [tex]2\pi[/tex] so,  that's the only angle we cannot include in our answer set, so:

[tex]\theta\neq \pi[/tex]

having said this, we can now start solving the equation:

[tex]tan(\frac{\theta}{2})=sin(\theta)[/tex]

we can start solving this equation by using the half angle formula, such a formula tells us the following:

[tex]tan(\frac{\theta}{2})=\frac{1-cos(\theta)}{sin(\theta)}[/tex]

so we can substitute it into our equation:

[tex]\frac{1-cos(\theta)}{sin(\theta)}=sin(\theta)[/tex]

we can now multiply both sides of the equation by [tex]sin(\theta)[/tex]

so we get:

[tex]1-cos(\theta)=sin^{2}(\theta)[/tex]

we can use the pythagorean identity to rewrite [tex]sin^{2}(\theta)[/tex] in terms of cos:

[tex]sin^{2}(\theta)=1-cos^{2}(\theta)[/tex]

so we get:

[tex]1-cos(\theta)=1-cos^{2}(\theta)[/tex]

we can subtract a 1 from both sides of the equation so we end up with:

[tex]-cos(\theta)=-cos^{2}(\theta)[/tex]

and we can now add [tex]cos^{2}(\theta)[/tex]

to both sides of the equation so we get:

[tex]cos^{2}(\theta)-cos(\theta)=0[/tex]

and we can solve this equation by factoring. We can factor [tex]cos(\theta)[/tex] to get:

[tex]cos(\theta)(cos(\theta)-1)=0[/tex]

and we can use the zero product property to solve this, so we get two equations:

Equation 1:

[tex]cos(\theta)=0[/tex]

[tex]\theta=cos^{-1}(0)[/tex]

[tex]\theta={\frac{\pi}{2}, \frac{3\pi}{2}}[/tex]

Equation 2:

[tex]cos(\theta)-1=0[/tex]

we add a 1 to both sides of the equation so we get:

[tex]cos(\theta)=1[/tex]

[tex]\theta=cos^{-1}(1)[/tex]

[tex]\theta=0[/tex]

so we end up with three answers to this equation:

[tex]\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}} [/tex]

Answer:

its D. 3

Step-by-step explanation:

for speed runners

Answer:

102 pounds

Step-by-step explanation:

Volume of Right rectangular prism = 12 * 8.5 * 4  = 408 cubic feet

Density = Mass / Volume

=>  0.25  = Weight of contents in container / Volume of container

=> 0.25 = Weight of contents in container / 408

=> Weight of contents in container  = 0.25 * 408

=> Weight of contents in container  = 102 pounds

Answer:

683lb

Step-by-step explanation:

Answer:

The correct solution is "n = 16".

Step-by-step explanation:

The given equation is:

⇒  [tex]\frac{1}{2} n-3=5[/tex]

On adding "3" both sides, we get

⇒  [tex]\frac{1}{2} n-3+3=5+3[/tex]

⇒  [tex]\frac{1}{2}n=8[/tex]

On applying cross multiplication, we get

⇒  [tex]n=8\times 2[/tex]

⇒  [tex]n=16[/tex]

Answer: 14.5 feet

Step-by-step explanation: that’s he correct answer delta math gave me AFTER I got it wrong

Answer:

14.5

Step-by-step explanation:

Answer: Quinn is a contestant on a quiz show. Quinn's score changes by -15 points for 4 questions in a row. ) What is the total change in Quinn's score?

hope this help :}

Answer:

it will be x < 2

Step-by-step explanation:

Because the circle means greater than or less than. And if the circle isn't fillied up it means it is greater than or equal to or less thanor equal to.

Answer:

the answer would be 3.4 + 4 = 7.4 .

Answer:

the answer would be 3.4 + 4 = 7.4 .

Step-by-step explanation:

Answer:

D: Approximately Normal

Step-by-step explanation:

I got it right on edg.

Answer:

The correct answer is B.

Step-by-step explanation:

Because you know two of the angles in a triangle are 90° and 52°, you can infer that the third angle is 38°. There is a trigonometry rule that states the sine of an angle is equivalent to the cosine of 90° minus that angle, which you can apply to here. Since [tex]Sin(52[/tex]°[tex])[/tex] = [tex]\frac{17}{c}[/tex], you know that [tex]Cos(90[/tex]°[tex]-52[/tex]°[tex])[/tex] or [tex]Cos(38[/tex]°[tex])[/tex]also equals [tex]\frac{17}{c}[/tex], so choice B is the correct answer.

Answer:

8. 12 in

9. 30 ft

10. 87.92 in

Step-by-step explanation:

Answer:

12in, 30ft, 87.92in

Step-by-step explanation:

question 8: 24/2 = 12in

question 9: 15(2) = 30ft

question 10:

C = 2πr

C =2(3.14)(14)

C= 87.92in

Answer:

D. 16

Step-by-step explanation:

You first need to find the total percentage who liked vanilla, then subtract it from the total percentage of chocolate.

To find the total of those who liked vanilla you would have to add the given percentages and then subtract that from 100.

Chocolate: 42%

Strawberry: 18%

Coffee: 14%

Vanilla: x

42 + 18 = 60 + 14 = 74%

100 - 74 = x

Vanilla = x = 26%

To find how many more like chocolate than vanilla, you would subtract the two percentages.

Chocolate: 42%

Vanilla: 26%

42 - 26 = 16

Answer: 4.25 miles

Step-by-step explanation:

The distance he biked on Thursday and Friday combined is:

= 3.5 + 4.25

= 7.75 miles

On Saturday he biked 12 miles. The number of miles he biked over Thursday and Friday is:

= 12 - 7.75

= 4.25 miles

Answer:

Yes

Step-by-step explanation:

You will get $279,841.74 in that 50 years.

Answer:

y = [tex]\frac{1}{2}[/tex] x + 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (2, 5) ← 2 points on the line

m = [tex]\frac{5-3}{2+2}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex] , then

y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (2, 5 ) , then

5 = 1 + c ⇒ c = 5 - 1 = 4

y = [tex]\frac{1}{2}[/tex] x + 4 ← equation of line

Answer:

8 cm

Step-by-step explanation:

:)

Answer:

I know. It's a pain. I just put tons of points on and that seems to attract people.

Step-by-step explanation:

Answer:

It’s b

Step-by-step explanation:

Just think

Answer:

to get to 2/3 from 1/12, add 7/12 to 1/12.

Step-by-step explanation:

8/12 is equivalent to 2/3

The error interval for x would be (3.65, 3.75), indicating that the true value of x lies within this range.

Given that a number x is rounded to 1 decimal place and its 3.7.

We need to find the error of the interval for x,

To determine the error interval for the rounded number 3.7, we need to consider the possible range of values that could have been rounded to 3.7 when rounded to 1 decimal place.

When rounding to 1 decimal place, we look at the digit immediately to the right of the decimal point. If this digit is 5 or greater, we round up. If it is less than 5, we round down.

In this case, 3.7 is the rounded value, which means the original number could have been rounded up from a value greater than or equal to 3.65 or rounded down from a value less than 3.75.

Therefore, the error interval for x would be (3.65, 3.75).

Learn more about error interval click;

https://brainly.com/question/30473763

#SPJ4

Answer:

2x + t - 1 =14

Step-by-step explanation:

give me brainliest plz and hope this helps also i am very good at math so that is a reassurance that this is correct

Answer:

a. $250

b. 50x + 200

Step-by-step explanation:

a. For the first month, you have to account for the cost to start which is $200, and the adition of the $50 for each month.

b. the 200 is only a one time fee so you add it on to months(x)

Answer:

a. 250$

b. 200+50x

Step-by-step explanation:

#1 What is the total cost to use the cell phone plan for one month?

GIVEN:

Startup price=$200

Charge per month=50$

SOLVE:

The total cost for one month will be the startup price+ charging price for one month.

200+50=250$

#2 What is the total cost for x months?

The total cost for x months will be the startup price+charging price for x months.

200+50x

Hope this helps!! :)

Please let me know if you have any questions

Answer:

which part bro I need to know at least

Answer:

cos(θ - φ) is -240/289

Step-by-step explanation:

The given parameters are;

The location of θ = Quadrant III

The location of φ = Quadrant I

cos(θ) = -8/17

cos(φ) = 15/17

By trigonometric identities, we have;

cos(θ - φ) = cos(θ)·cos(φ) - sin(θ)·sin(φ)

Given that 'θ' is in quadrant III, we have;

sin(θ) is negative

By Pythagoras' theorem, we have;

∴ sin(θ) = -√(17²- 8²)/17 = -15/17

Whereby 'φ' is in quadrant I, by Pythagoras' theorem, we have;

sin(φ) = √(17² - 15²)/17 = 8/17

∴ cos(θ - φ) = (-8/17) × (15/17) + (-15/17) × (8/17) = -240/289 = -0.83044982699

Answer:

x=146 degrees

Step-by-step explanation:

A supplementary angle is the conrisponding angle that adds to the other angle so it is 180. So 180-34= 146

Given:

Focus of a parabola = [tex]\left(1,\dfrac{1}{2}\right)[/tex]

Directrix: [tex]y=3[/tex]

To find:

The equation of the parabola.

Solution:

The equation of a vertical parabola is:

[tex]y-k=\dfrac{1}{4a}(x-h)^2[/tex]            ...(A)

Where, [tex](h,k)[/tex] is center, [tex](h,k+a)[/tex] is focus and [tex]y=k-a[/tex] is the directrix.

On comparing the focus, we get

[tex](h,k+a)=\left(1,\dfrac{1}{2}\right)[/tex]

[tex]h=1[/tex]

[tex]k+a=\dfrac{1}{2}[/tex]           ...(i)

On comparing the directrix, we get

[tex]k-a=3[/tex]              ...(ii)

Adding (i) and (ii), we get

[tex]2k=\dfrac{7}{2}[/tex]

[tex]k=\dfrac{7}{4}[/tex]

Putting [tex]k=\dfrac{7}{4}[/tex] is (i), we get

[tex]\dfrac{7}{4}+a=\dfrac{1}{2}[/tex]

[tex]a=\dfrac{1}{2}-\dfrac{7}{4}[/tex]

[tex]a=\dfrac{-5}{4}[/tex]

Putting [tex]a=\dfrac{-5}{4},h=1,k=\dfrac{7}{4}[/tex] in (A), we get

[tex]y-\dfrac{7}{4}=\dfrac{1}{4\times \dfrac{-5}{4}}(x-1)^2[/tex]

[tex]y-\dfrac{7}{4}=\dfrac{-1}{5}(x^2-2x+1)[/tex]

[tex]y-\dfrac{7}{4}=-\dfrac{1}{5}(x^2)-\dfrac{1}{5}(-2x)-\dfrac{1}{5}(1)[/tex]

[tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x-\dfrac{1}{5}+\dfrac{7}{4}[/tex]

On further simplification, we get

[tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x+\dfrac{35-4}{20}[/tex]

[tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x+\dfrac{31}{20}[/tex]

Therefore, the equation of the parabola is [tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x+\dfrac{31}{20}[/tex].

Note: Option C is correct but the leading coefficient should be negative.