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3 years ago

Write in slope intercept form of the equation of a line passing through (-1,4) and perpendicular to y=x-5.

Mathematics

1 answer:

andrew11 [14]3 years ago

7 0

Answer:

y=-x+3

Step-by-step explanation:

The general slope-intercept equation of a line is y=mx+b where m is the slope and b represents the y intercept. y and x are simply a point the line passes through. In this case, y=x-5, meaning m=1 and b=-5.

In order to find the perpendicular slope, we should take the current slope's <u>negative reciprocal</u>. We have:

$-\frac{1}{1} =\\-1$

Therefore, our perpendicular slope is -1. We now have equation:

$y=-x+b$

We can plug in the known values of the point (-1,4) to solve for b.

$4=(-1)*(-1)+b\\4=1+b\\b=3$

If we now put what we found together, we have equation

$y=-x+3$

<em>I hope this helps! Let me know if you have any further questions :)</em>

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3 years ago

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trasher [3.6K]

The function is graphed as shown below

Part A:

We use the formula $- \frac{b}{2a}$ to find the vertex of the function. A quadratic function of the form of $a x^{2} +bx+c$ and equating this form to the given function $- x^{2} +20x-75$ , we have
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Substituting $a$ and $b$ into the vertex formula, we have
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This calculation means that the highest profit is achieved when the number of photo printed equals to ten photos

Part B:

We can find solution to this equation by factorising

$- x^{2} +20x-75=0$
$-( x^{2} -20x+75)=0$
$x^{2} -20x+75=0$
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$x=5$ and $x=15$ , as shown in the graph

The two values means that the company makes no profit when they either produce 5 or 15 photos

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4 years ago

An object with a mass of 3.0 g raises the level of water in a graduated cylinder from 25.1 mL to 33.1 mL. What is the density of

evablogger [386]

The displaced volume of the water, because of the submersion of the object, is equal to the volume of the object.

So to find the volume of the object we calculate the difference in volume of water:
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Since 1 mL of water has the volume of 1cm^3, then the volume of the object is 8 cm^3.

The density of the object is found by the formula:

density= mass/volume= (3 g) / (8 cm^3) = 3/8 (g/cm^3)= 0.375 g/cm^3

Answer: 0.375 g/cm^3

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3 years ago