Josh is 3 inches taller than his brother <br> translate the following to mathematical expressions

Determine wheather the graphs of y = 2x+1 and y=-3X-7 are parallel, perpendicular, coincident, or none of these

Readme [11.4K]

Answer:

The two graphs are perpendicular

Step-by-step explanation:

The slope of the first one is the reciprocal of the second. Also I graphed it.

5 0

3 years ago

What is the slope of the line that crosses through points (0,0) and (1,2). How can Find the answer to the problem?

qwelly [4]

Answer:

The correct answer is m = 2/1 because they first point it reaches is (1,2) and so you insert those numbers (x,y) into the rise and run equation (y/x) and get the answer 2/1.

Hope this helps!

(Hint: M = Slope)

5 0

3 years ago

I will give 50 points

kupik [55]

Answer:

High

Step-by-step explanation:

the only numbers that don't overlap is 53 and 59 all the others would overlap.

5 0

2 years ago

Read 2 more answers

Which is an equation in slope intercept form of the line that passes through (1, 3) and (2, 4)?

Murrr4er [49]

Answer:

y = x + 2

Step-by-step explanation:

The slope-intercept equation is:

y = mx + b

First, you should use the point-slope formula to find the slope. Plug in the "x" and "y" values given from the points:

Point 1: (1,3) Point 2: (2,4)

y₁ - y₂ = m(x₁ - x₂) <--- Point-slope formula

(3 - 4) = m(1 - 2) <--- Plug in "x" and "y" values from points

-1 = -m <--- Simplify inside parentheses

1 = m <--- Divide both sides by -1

Finally, use one of the points to solve for the y-intercept (b):

Point 1: (1,3) m = 1

y = mx + b <--- Slope-intercept formula

3 = 1(1) + b <--- Plug in values from point and slope (m)

3 = 1 + b <--- Multiply slope and "x" value

2 = b <--- Subtract 1 from both sides

Since the slope = 1, it does not need to be included in the final formula. The final answer is:

y = x + 2

7 0

2 years ago

A box designer has been charged with the task of determining the surface area of various open boxes (no lid) that can be constru

Viktor [21]

Answer:

1) $S = 2\cdot w\cdot l - 8\cdot x^{2}$ , 2) The domain of S is $0 \leq x \leq \frac{\sqrt{w\cdot l}}{2}$ . The range of S is $0 \leq S \leq 2\cdot w \cdot l$ , 3) $S = 176\,in^{2}$ , 4) $x \approx 4.528\,in$ , 5) $S = 164.830\,in^{2}$

Step-by-step explanation:

1) The function of the box is:

$S = 2\cdot (w - 2\cdot x)\cdot x + 2\cdot (l-2\cdot x)\cdot x +(w-2\cdot x)\cdot (l-2\cdot x)$

$S = 2\cdot w\cdot x - 4\cdot x^{2} + 2\cdot l\cdot x - 4\cdot x^{2} + w\cdot l -2\cdot (l + w)\cdot x + l\cdot w$

$S = 2\cdot (w+l)\cdot x - 8\cdpt x^{2} + 2\cdot w \cdot l - 2\cdot (l+w)\cdot x$

$S = 2\cdot w\cdot l - 8\cdot x^{2}$

2) The maximum cutout is:

$2\cdot w \cdot l - 8\cdot x^{2} = 0$

$w\cdot l - 4\cdot x^{2} = 0$

$4\cdot x^{2} = w\cdot l$

$x = \frac{\sqrt{w\cdot l}}{2}$

The domain of S is $0 \leq x \leq \frac{\sqrt{w\cdot l}}{2}$ . The range of S is $0 \leq S \leq 2\cdot w \cdot l$

3) The surface area when a 1'' x 1'' square is cut out is:

$S = 2\cdot (8\,in)\cdot (11.5\,in)-8\cdot (1\,in)^{2}$

$S = 176\,in^{2}$

4) The size is found by solving the following second-order polynomial:

$20\,in^{2} = 2 \cdot (8\,in)\cdot (11.5\,in)-8\cdot x^{2}$

$20\,in^{2} = 184\,in^{2} - 8\cdot x^{2}$

$8\cdot x^{2} - 164\,in^{2} = 0$

$x \approx 4.528\,in$

5) The equation of the box volume is:

$V = (w-2\cdot x)\cdot (l-2\cdot x) \cdot x$

$V = [w\cdot l -2\cdot (w+l)\cdot x + 4\cdot x^{2}]\cdot x$

$V = w\cdot l \cdot x - 2\cdot (w+l)\cdot x^{2} + 4\cdot x^{3}$

$V = (8\,in)\cdot (11.5\,in)\cdot x - 2\cdot (19.5\,in)\cdot x^{2} + 4\cdot x^{3}$

$V = (92\,in^{2})\cdot x - (39\,in)\cdot x^{2} + 4\cdot x^{3}$

The first derivative of the function is:

$V' = 92\,in^{2} - (78\,in)\cdot x + 12\cdot x^{2}$

The critical points are determined by equalizing the derivative to zero:

$12\cdot x^{2}-(78\,in)\cdot x + 92\,in^{2} = 0$

$x_{1} \approx 4.952\,in$

$x_{2}\approx 1.548\,in$

The second derivative is found afterwards:

$V'' = 24\cdot x - 78\,in$

After evaluating each critical point, it follows that $x_{1}$ is an absolute minimum and $x_{2}$ is an absolute maximum. Hence, the value of the cutoff so that volume is maximized is:

$x \approx 1.548\,in$

The surface area of the box is:

$S = 2\cdot (8\,in)\cdot (11.5\,in)-8\cdot (1.548\,in)^{2}$

$S = 164.830\,in^{2}$

4 0

3 years ago

Josh is 3 inches taller than his brother translate the following to mathematical expressions