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Stella [2.4K]
4 years ago
8

Please help 56 points or more good answer gets branliest

Mathematics
1 answer:
Natali5045456 [20]4 years ago
5 0

The distance between the cities is 280 miles. The rule is y = 40x, where x is the distance in inches on the map and y is the distance in miles.

Step-by-step explanation:

Step 1:

The map's key shows that 5 inches on the map equal 200 miles of actual distance.

5 inches on the map = 200 miles of actual distance,

if we divide both sides by 5, we get;

1 inch on the map = 40 miles of actual distance.

Step 2:

If x is the distance on the map in inches and y is the actual distance in miles,

y = 40x.

If the map distance 7 inches, x = 7.

Substituting, x =7 in the equation,  y = 40(7) = 280.

So the actual distance between the cities is 280 miles.

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Find all solutions to the equation (x² + 5x + 6)(x² − 3x − 4) = 0.
Soloha48 [4]

Answer:

The solutions are:

x=-2,\:x=-3,\:x=-1,\:x=4

Step-by-step explanation:

To find the solutions to the equation \left(x^2+5x+6\right)\left(x^2-3x-4\right)=0 you need to:

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Break the expression into groups

x^2+5x+6=\left(x^2+2x\right)+\left(3x+6\right)

Factor out x from (x^2+2x)

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Factor out 3 from 3x+6

3x+6=3\left(x+2\right)

x^2+5x+6=x\left(x+2\right)+3\left(x+2\right)\\\\\mathrm{Factor\:out\:common\:term\:}x+2\\\\x^2+5x+6=\left(x+2\right)\left(x+3\right)

  • Factor \left(x^2-3x-4\right)

x^2-3x-4=\left(x^2+x\right)+\left(-4x-4\right)\\\\x^2-3x-4=x\left(x+1\right)-4\left(x+1\right)\\\\x^2-3x-4=\left(x+1\right)\left(x-4\right)

Therefore

\left(x^2+5x+6\right)\left(x^2-3x-4\right)=\left(x+2\right)\left(x+3\right)\left(x+1\right)\left(x-4\right)=0

Using the Zero Factor Theorem:

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