Pls someone help quick

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

Assume that the terminal side of thetaθ passes through the point (negative 12 comma 5 )(−12,5) and find the values of trigonomet

zmey [24]

Answer:

$\sin \theta = \dfrac{5}{13}$ and $\sec \theta = -\dfrac{13}{12}$

Step-by-step explanation:

Assume that the terminal side of thetaθ passes through the point (−12,5).

In ordered pair (-12,5), x-intercept is negative and y-intercept is positive. It means the point lies in 2nd quadrant.

Using Pythagoras theorem:

$hypotenuse^2=perpendicular^2+base^2$

$hypotenuse^2=(5)^2+(12)^2$

$hypotenuse^2=25+144$

$hypotenuse^2=169$

Taking square root on both sides.

$hypotenuse=13$

In a right angled triangle

$\sin \theta = \dfrac{opposite}{hypotenuse}$

$\sin \theta = \dfrac{5}{13}$

$\sec \theta = \dfrac{hypotenuse}{adjacent}$

$\sec \theta = \dfrac{13}{12}$

In second quadrant only sine and cosecant are positive.

$\sin \theta = \dfrac{5}{13}$ and $\sec \theta = -\dfrac{13}{12}$

6 0

3 years ago

4x + 5y = 3 2x + 3y = 1Solve by elimination

Lesechka [4]

Answer:

The solution to the system of equations is:

x = 2, and y = -1

Explanation:

Given the pair of equations:

4x + 5y = 3 ..........................................................................(1)

2x + 3y = 1............................................................................(2)

To solve this by elimination:

Multiply equation (2) by 2, to eliminate x

Equation (2) becomes

4x + 6y = 2 .........................................................................(3)

Subtract equation (1) from (3)

4x - 4x + 6y - 5y = 2 - 3

y = -1 ....................................................................................(4)

Multiply equation (1) by 3 and equation (2) by 5 to eliminate y

Equation (1) becomes

12x + 15y = 9 .......................................................................(5)

Equation (2) becomes

10x + 15y = 5 ........................................................................(6)

Subtract equation (6) from (5)

12x - 10x + 15y - 15y = 9 - 5

2x = 4

Divide both sides by 2

x = 4/2 = 2 ............................................................................(7)

From equations (7) and (4)

x = 2, and y = -1

7 0

1 year ago

The cost to produce a product is modeled by the function f(x) = 5x2 − 70x 258, where x is the number of products produced. compl

ad-work [718]

The minimum cost to produce the product is $7.

What are functions?

A function from a set X to a set Y allocates exactly one element of Y to each element of X.

To determine the minimum cost:

We have to determine the minimum cost of producing this product.

Since $f(x) = 5x^{2} -70x+258$ .

Now, consider the equation $5x^{2} -70x+258= 0$ .

Dividing the above equation by 5, we get

$x^{2} -70x/5+258/5=0\\x^{2} -14x+258/5=0$

Now, considering the coefficient of 'x', dividing it by '2' and then adding and subtracting the square of the number which we got after dividing.

Since the coefficient of 'x' is 14, and half of 14 is '7'.

So, adding and subtracting from the above equation.

$x^{2} -14x+(7)^{2} -(7)^{2}+258/5=0\\x^{2} -14x+49 -49+258/5=0\\(x-7)^{2} -49+258/5=0\\(x-7)^{2} +258-245/5=0\\(x-7)^{2} +13/5=0\\5(x-7)^{2} +13=0$

Now, we have to determine the minimum cost to produce the product.

Since $f(x) = 5x^{2} -70x+258$ .

$f'(x) = 10x-70$

Now, let f'(x)=0

$10x-70=0\\10x=70$

Therefore, x=7

Now, consider which is greater than 0.

Therefore, x= 7 is the minimum cost.

Know more about functions here:

brainly.com/question/25638609

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5 0

1 year ago

What is the estimate of 137,638 plus 52,091

polet [3.4K]

The answer is 189,729
If to be rounded answer would be 190,000 I would say best estimate would be 180,000

3 0

3 years ago

Read 2 more answers