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posledela
2 years ago
15

Find the equation of a line perpendicular to x=6+6y that passes through the point (-8,6)

Mathematics
1 answer:
alexgriva [62]2 years ago
8 0

Answer:

y = -6x - 42

Step-by-step explanation:

First solve for y in x = 6 + 6y.

6y + 6 = x

6y = x - 6

6/6y = x/6 - 6/6

y = 1/6x - 1    the slope is 1/6.  

Perpendicular lines slopes are negative reciprocals of each other.

So the new equation will have the slope of -6 ( the negative reciprocal of 1/6)

Next solve for "b" by  using y = mx + b and the new slope of -6 and the point (-8,6)

y = mx + b

6 = -6(-8) + b

6 = 48 + b

-42 = b

The equation of the line is y = -6x - 42

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Two cities are building bicycle paths. Charles City has built 5km of bicycle paths by the end of the first month, and the total
sergey [27]

Answer:

Month 4

Step-by-step explanation:

To solve this problem we must propose an equation that models the number of kilometers of bicycle trails made monthly in Charles City and in Tinsel Town

<em>For Charles City </em>we know that the number of kilometers built in the first month is 5, and it doubles every month. Then we have an exponential equation, in base 2, whose initial value is 5.

This equation has the following form:

y = C_1 (2^{x-1})

Where:

C_1 is the number of kilometers built in month 1

x is the number of months: {1, 2, 3, 4, 5 ... x}

x = 1 represents month 1.

So:

Charles\ City\ (km) = 5(2^{x-1})

<em>For Tinsel Town</em> we know that the number of kilometers built in the first month is 21 and increases at a fixed rate of 5 kilometers per month. This can be modeled by a linear equation.

Tinsel\ Town\ (km) = 21 + 5(x-1)

Where x is the number of months. x: {1, 2, 3, 4, 5 ...}

We want to know at the end of what month the total length of the cycle lanes in Charles City first exceeds the length in Tinsel Town

Then we equal both equations and clear x.

5 (2^{x-1}) = 21 + 5(x-1)\\\\5 (2^{x-1}) - (21 + 5(x-1)) = 0

Clearing x from this equation is very difficult, so to find x, we iterate until we get the value of x that causes the equation to approach 0.

For x = 3

5(2^{3-1}) - (21 +5(3-1)) = 0\\\\20- 31= -11

For x = 4

5(2^{4-1}) - (21 +5(4-1)) = 0\\\\40 - 36 = 4

<em>The value must be between x = 3 and x = 4</em>

For x = 3.8

5 (2^{3.8-1}) - (21 +5(3.8-1)) = 0\\\\34.82 - 35 = 0.18

Then x ≈ 3.8 months.

Finally we have that By the end of the fourth month the total length of the cycle lanes in Charles City exceeds the length in Tinsel Town

6 0
3 years ago
Simplify the expression using long division. (10x2 – 85x – 10) ÷ (x – 8) Question 7 options: quotient 10x – 5 and remainder –50
Anna [14]

Answer:

The quotient is (10x - 5) and the reminder is -50 ⇒ 1st answer

Step-by-step explanation:

* Lets solve the long division by easiest way

∵ (10x² - 85x - 10)/(x - 8)

∵ (10x² - 85x - 10) is the dividend

∵ (x - 8) is the divisor

- Divide the first term of the dividend by the first term of the divisor

∴ 10x² ÷ x = 10x ⇒ first term of the quotient

- Multiply 10x by the the divisor

∴ 10x(x - 8) = 10x² - 80x

- Subtract the answer from the dividend

∴ (10x² - 85x - 10) - (10x² - 80x) =

# 10x² - 10x² = 0

# -85x - -80x = -85x + 80x = -5x

# -10

∴ (10x² - 85x - 10)/(x - 8) = 10x + (-5x - 10)/(x - 8)

* Repeat the same steps again with the new dividend -5x - 10

- Divide the first term of the dividend by the first term of the divisor

∴ -5x ÷ x = -5 ⇒ second term of the quotient

- Multiply -5 by the divisor

∴ -5(x - 8) = -5x + 40

- Subtract the answer from the dividend

∴ (-5x - 10) - (-5x + 40) =

# -5x - -5x = -5x + 5x = 0

# -10 - 40 = -50

∴ (-5x - 10)/(x - 8) = -5 + -50/(x - 8)

∴ (10x² - 85x - 10)/(x - 8) = 10x - 5 + -50/(x - 8)

- The quotient is the answer of the division

∴ The quotient is (10x - 5) and the reminder is -50

7 0
2 years ago
Read 2 more answers
Hi guys! I need the answer quick for 10 points! Thx!
svlad2 [7]

D . A cube that is 1 inch long , 1inch wide and 1 inch high .

\red{ \bold{What \: is \: unit \: cube \: }}

Answer

its a cube whose side is 1 unit long .

And total surface area should be 6 square units .

as we can see

3 0
3 years ago
What is the volume of the composite object below?
castortr0y [4]

Answer:

216 cubic inches

Step-by-step explanation:

(9)(3)(3)=81

(3)(3)(9)=81

(3)(3)(6)=54

81+81+54=216

So, it's 216 cubic inches in volume.

6 0
2 years ago
The population of a certain geographic region is approximately 103 million and grows continuously at a relative growth rate of 1
aev [14]

The population increases by a factor 1.0167 every year so the require figure is:
103 * 1 . 0167^5 =   112 million
3 0
3 years ago
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