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3 years ago

What is the supplementary angle of 30 degrees?

Mathematics

1 answer:

Vedmedyk [2.9K]3 years ago

4 0

Answer:

The answer is 150 degree.

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The table below represents a function. Which of the following equations could be its function rule?

worty [1.4K]

Answer:

$y=2x-2$ is the required equation.

Therefore, the second option is true.

Step-by-step explanation:

We know that the slope-intercept form of the line equation of a linear function is given by

$y=mx+b$

where m is the slope and b is the y-intercept

Taking two points (0, -2) and (1, 0) from the table to determine the slope using the formula

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(0,\:-2\right),\:\left(x_2,\:y_2\right)=\left(1,\:0\right)$

$m=\frac{0-\left(-2\right)}{1-0}$

$m=2$

substituting the point (0, -2) and the slope m=2 in the slope-intercept form to determine the y-intercept i.e. 'b'.

$y=mx+b$

$-2 = 2(0)+b$

$-2=0+b$

$b=-2$

Now, substituting the values of m=2 and b=-2 in the slope-intercept form to determine the equation of a linear function

$y=mx+b$

$y=2x+(-2)$

$y=2x-2$

Thus, $y=2x-2$ is the required equation.

Therefore, the second option is true.

3 0

3 years ago

A’s DJ service charges a $200 setup fee and $75 an hour after that.

Bogdan [553]

The total cost includes the setup cost + per hour cost.

Let, x represents the time and y represents the total cost.

$y=200+75x$ .... (1)

Let Y represent the cost for B's DJ service.

$y=125x$ .... (2)

a. Graphing both the equations give the intersection point (solution) as (4,500)

It means for 4 hours, the total cost of both the DJ's is same at $500.

b. Substitution Method.

Plug y = 125x in equation (1)

$125x= 200+75x$

$125x-75x=200$

$50x=200$

$x=4$

$y=125\times 4 =500$

Hence, the total cost for 4 hours in both the service is $500.

c. Addition method.

Multiply equation (2) by -1

$-y = -125x$ .... Equation (3).

Add euation (1) and equation (3)

$y+(-y) = 200+75x-125x$

$0=200-50x$

$50x=200, x=4$

$y=500$

Solution: For x = 4, y = 500 ( same as the previous two methods)

For x = 2, equation (1)

$y=200+(75\times 2) = 350$

For x = 2, equation (2)

$y= 125\times 2 =250$

Hence, for 2 hours, DJ B would be a better choice since it would charge $250.

For x = 6 hours, equation (1)

$y=200+(75\times 6) =650$

For x= 6, equation (2)

$y=125\times 6=750$

For 6 hours, DJ A would be better option since it charges $650 for 6 hours.

8 0

3 years ago

Y is directly proportional to x,and y=216 when x=2. Find y when x=7.

makkiz [27]

$\bf \qquad \qquad \textit{direct proportional variation}\\\\
\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------\\\\
\textit{we also know that }
\begin{cases}
y=216\\
x=2
\end{cases}\implies 216=k2\implies \cfrac{216}{2}=k
\\\\\\
108=k\qquad therefore\qquad \boxed{y=108x}
\\\\\\
\textit{when x = 7, what is \underline{y}?}\qquad y=108(7)$

6 0

3 years ago

Consider the implicit differential equation <img src="https://tex.z-dn.net/?f=%2849%20y%5E%7B3%7D%20%2B%2045%20xy%29%20dx%20%2B%

BaLLatris [955]

We're looking for an integrating factor $\mu(x,y)=x^py^q$ such that

$\mu\underbrace{(49y^3+45xy)}_M\,\mathrm dx+\mu\underbrace{(98xy^2+50x^2)}_N\,\mathrm dy=0$

is exact, which would require that

$(\mu M)_y=(\mu N)_x$
$(49x^py^{q+3}+45x^{p+1}y^{q+1})_y=(98x^{p+1}y^{q+2}+50x^{p+2}y^q)_x$
$49(q+3)x^py^{q+2}+45(q+1)x^{p+1}y^q=98(p+1)x^py^{q+2}+50(p+2)x^{p+1}y^q$
$\implies\begin{cases}49(q+3)=98(p+1)\\45(q+1)=50(p+2)\end{cases}\implies p=\dfrac52,q=4$

You can verify that $(\mu M)_y=(\mu N)_x$ if you'd like. With the ODE now exact, we have a solution $F(x,y)=C$ such that

$F_x=\mu M$
$F=\displaystyle\int(49y^3+45xy)x^{5/2}y^4\,\mathrm dx$
$F=10x^{9/2}y^5+14x^{7/2}y^7+f(y)$

$F_y=\mu N$
$50x^{9/2}y^4+98x^{7/2}y^6+f'(y)=98x^{7/2}y^2+50x^{9/2}y^4$
$f'(y)=0$
$\implies f(y)=C$

and so the general solution is

$F(x,y)=10x^{9/2}y^5+14x^{7/2}y^7=C$

8 0

3 years ago

How do I show my work for this and get the answer? Thanksss

adoni [48]

Answer:

the answer for this problem is 135

6 0

3 years ago