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3 years ago

what is the slope of the line that passes through the points (-3,1) and( 7,-14)? write your answer in simplest from.

Mathematics

1 answer:

Harrizon [31]3 years ago

3 0

Answer:

slope = m = (0--3)/(14--4) = 3/18 = 1/6

y=mx + b

y =(1/6)x + b

0= (1/6)14 + b

b = - 14/6 = - 7/3

y = (1/6)x - 7/3

6y-x = -14

Step-by-step explanation:

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Given the net of the rectangular prism, what is its surface area?

Llana [10]

Answer:

Step-by-step explanation:

Look at the picture.

We have :

4 rectangles 3m × 4m → A₁ = 3 · 4 = 12 m²

2 rectangles 3m × 3m → A₂ = 3 · 3 = 9 m²

Therefore the Surface Area of the rectangular prism is:

S.A. = 4A₁ + 2A₂

Substitute:

S.A. = 4(12) + 2(9) = 48 + 18 = 66

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3 years ago

Round 95.588 to the nearest whole number.

pishuonlain [190]

Answer:

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2 years ago

What is the value of x in the solution to this system of equations?<br> x + 2y = -2<br> x = 4y - 8

Pepsi [2]

Answer:

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8 0

3 years ago

If dy dx equals cosine squared of the quantity pi times y over 4 and y = 1 when x = 0, then find the value of x when y = 3.

Afina-wow [57]

Answer: $x = -\frac{8}{\pi}$

Explanation: Note that

$\frac{dy}{dx} = \cos^2 \left ( \frac{\pi y}{4} \right )
\\
\\ \frac{dy}{\cos^2 \left ( \frac{\pi y}{4} \right )} = dx
\\
\\ \int{\frac{dy}{\cos^2 \left ( \frac{\pi y}{4} \right )}} = \int dx
\\
\\ \boxed{x = \int{\sec^2 \left ( \frac{\pi y}{4} \right )dy}}$

To evaluate the integral in the boxed equation, let $u = \frac{\pi y}{4}$ . Then,

$du = \frac{\pi}{4} dy 
\\ \Rightarrow \boxed{dy = \frac{4}{\pi}du}$

So,

$x = \int{\sec^2 \left ( \frac{\pi y}{4} \right )dy}
\\
\\ = \int{\sec^2 u \left ( \frac{4}{\pi}du \right )}
\\
\\ = \frac{4}{\pi}\int{\sec^2 u du}
\\
\\ = \frac{4}{\pi} \tan u + C
\\
\\ \boxed{x = \frac{4}{\pi} \tan \left ( \frac{\pi y}{4} \right ) + C}\text{ (1)}$

Since y = 1 when x =0, equation (1) becomes

$0 = \frac{4}{\pi} \tan \left ( \frac{\pi (1)}{4} \right ) + C 
\\ 
\\ 0 = \frac{4}{\pi} (1) + C 
\\
\\ \frac{4}{\pi} + C = 0
\\
\\ \boxed{C = -\frac{4}{\pi}}$

With the value of C, equation (1) becomes

$\boxed{x = \frac{4}{\pi} \tan \left ( \frac{\pi y}{4} \right ) -\frac{4}{\pi} }$

Hence, if y = 3,

$x = \frac{4}{\pi} \tan \left ( \frac{\pi y}{4} \right ) -\frac{4}{\pi} 
\\
\\ x = \frac{4}{\pi} \tan \left ( \frac{\pi (3)}{4} \right ) -\frac{4}{\pi} 
\\
\\ x = \frac{4}{\pi} (-1) -\frac{4}{\pi} 
\\
\\ \boxed{x = -\frac{8}{\pi}}$

6 0

3 years ago

The base of a triangle is 21 inches and the height is 12 inches which of these expressions correctly shows how to calculate the

I am Lyosha [343]

½ x 21 x 12=126

So the answer is a

5 0

3 years ago