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2 years ago

What is the equation, in slope-intercept form, for the line through the point

Mathematics

1 answer:

goblinko [34]2 years ago

3 0

Answer:

A perpendicular line has an opposite-reciprocal slope.

The slope given is m = 5. So the perpendicular slope is m = $-\frac{1}{5}$ .

Now subsitute your (x, y) values to find the y-intercept, b.

$y = -\frac{1}{5} x + b$

$-1 = -\frac{1}{5}( 3) + b$

$-1 = -\frac{3}{5}+ b$

$-1 + \frac{3}{5} = b$

$-\frac{5}{5} + \frac{3}{5} = b = -\frac{2}{5}$

Answer: $y = -\frac{1}{5} x - \frac{2}{5}$

Step-by-step explanation:

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A rectangle has an area of x square units. The rectangle is dilated to create a new rectangle with an area of 9x square units. D

Alika [10]

The reactangle has an area of x.

So that means two numbers multiplied to each other equal to x. We can just think of itwo numbers that when multiplied equal to x as a and b.

So that means the side lengths are a and b. And ab = x (will be using this right next).

And it was multiplied by some scale factor that made the new area 9x. So if the scale factor is y, then:

$(y\times a)\times (y\times b)=9x$
$y^2ab=9x$
$y^2x=9x$
$y=3$

y can not equal to -3, because the length of a side of any polygon can never be negative.

So the dilation is 3.

And so if the dimension is 5 by 8.

Then the area is $5 \times 8=40$

And so then $x=40$

And then after the dilation, it would be $9x=9(40) = 360$

We could check it another way too. Since we said the scale factor is 3, then:

$( 5 \times 3) \times (8 \times 3) = 15 \times 24 = 360$

So basically 15 by 24 is the new dimensions :)

6 0

3 years ago

What is 6 to the second power divided by 2(3)+4=

Alecsey [184]

If you mean 6²
2(3)+4 that would be 36
 10 or 3.6

If you mean 6²/2(3)+4 then 36/2=18 x 3= 54 +4=58 (following order of operation)

If you meant the first example I did, I would have rewritten it as
6² ÷ (2x3+4)= for clarity. That would force me to do what is in parentheses first.

3 0

3 years ago

Read 2 more answers

Helpppppppppppppppppppp

Naddika [18.5K]

The answer is the first one

7 0

3 years ago

If Santiago wanted to turn his $279.89 into as many nickels as possible, how many would he have?

Elina [12.6K]

Answer:

5,597 nickels and 4 pennies

Step-by-step explanation:

First, we can take away 4 cents since we know 4 isn't divisible by 5.

Our new number would be 279.80

Then, we divide 279.80 by 0.05 since 0.05 is what a nickel equals>

279.85/0.05 = 5597

Therefore, he would have 5,597 nickels and 4 pennies.

6 0

3 years ago

I don’t know how to solve this

sleet_krkn [62]

9514 1404 393

Answer:

x ∈ (-∞, 9) U (-1, ∞)

Step-by-step explanation:

Get the absolute value by itself. Do that by multiplying by 4.

|3x +15| > 12

This resolves to two cases:

3x +15 > 12

x +5 > 4 . . . . divide by 3

x > -1 . . . . . . .subtract 5

-(3x +15) > 12

x +5 < -4 . . . . divide by -3

x < -9 . . . . . . . subtract 5

Then the solution in interval notation is ...

x ∈ (-∞, 9) U (-1, ∞)

6 0

3 years ago