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2 years ago

Write an equation of a line with the given slope and y-intercept (8,1)m=-1/2

1 answer:

5 0

Slope intercept form is y=mx+b
first plug in m
y=-1/2X + b
now plug in the point (8,1) for the x and the y
1=-1/2(8) + b

now you need to solve for b
simplify
1=-4+ b
add 4
5=b

now that you know b
you can plug it into the equation along with the m

so the answer is
y=-1/2X + 5

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Now there is a square city of unknown size with a gate at the center of each side. There is a tree 20 b from the north gate. Tha

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Answer:

The length of each side of the city is 250b

Step-by-step explanation:

Given

$a = 20$ --- tree distance from north gate

$b =14$ --- movement from south gate

$c = 1775$ --- movement in west direction from (b)

See attachment for illustration

Required

Find x

To do this, we have:

$\triangle ADE \sim \triangle ACB$ --- similar triangles

So, we have the following equivalent ratios

$AE:DE = AB:CB$

Where:

$AE = 20\\ DE = x/2 \\ AB = 20 + x + 14 \\ CB = 1775$

Substitute these in the above equation

$20:x/2 = 20 + x + 14: 1775$

$20:x/2 = x + 34: 1775$

Express as fraction

$\frac{20}{x/2} = \frac{x + 34}{1775}$

$\frac{40}{x} = \frac{x + 34}{1775}$

Cross multiply

$x *(x + 34) = 1775 * 40$

Open bracket

$x^2 + 34x = 71000$

Rewrite as:

$x^2 + 34x - 71000 = 0$

Expand

$x^2 + 284x -250x - 71000 = 0$

Factorize

$x(x + 284) -250(x + 284)= 0$

Factor out x + 284

$(x - 250)(x + 284)= 0$

Split

$x - 250 = 0 \ or\ x + 284= 0$

Solve for x

$x = 250 \ or\ x =- 284$

x can't be negative;

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$x = 250$

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2 years ago

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