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4 years ago

If the ratio of two complementary angles is 4 to 5, explain how you would set up an equation to solve for the angle measures.

1 answer:

5 0

"A ratio of 4 to 5" means that dividing the two angles (whatever they may be) simplifies to 4/5. One example is 40 degrees and 50 degrees so 40/50 = 4/5. Another example is the pair of angles 20 and 25, so 20/25 = 4/5

For now, we don't know the angles. Let's call them x and y. Based on the info above, we can say

x/y = 4/5

also we know that x and y add to 90 degrees because the angles are complementary. So x+y = 90 which solves to y = 90-x if you isolate y.

Let's cross multiply on the first equation to get...

x/y = 4/5

5*x = 4*y

Now replace y with 90-x. Solve for x

5x = 4(90-x)

5x = 360 - 4x

5x+4x = 360

9x = 360

x = 360/9

x = 40

Use this to find y

y = 90 - x = 90 - 40 = 50

So the two angles are 40 degrees and 50 degrees.

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Ganezh [65]

Answer:

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Step-by-step explanation:

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7 0

3 years ago

I need help in an hour or less pls The number N of bacteria in a refrigerated food is given by N(T ) = 20T 2 – 80T + 500, 2 ≤ T

weqwewe [10]

Answer:

The number N of bacteria in a refrigerated food is given by N(T) = 10T^2 - 20T + 600, 2 ≤ T ≤ 20 where T is the temperature of the food in degrees Celsius. When the food is removed from refrigeration, the temperature of the food is given by T(t) = 3t + 2, 0 ≤ t ≤ 6 where t is the time in hours.

Step-by-step explanation:

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4 years ago

In Exercises 1 and 2, find the equilibrium solutions of the differential equation specified.1) dy/dt = (y + 3)/(1 - y)2) dy/dt =

Aleks [24]

Answer:

1. Equilibrium solution: y= -3

2. Equilibrium solution y= ±1.414

Step-by-step explanation:

Thinking process:

The equilibrium solution can only be derived when $\frac{dy}{dt} = 0$

1. Let's look at the first equation:

$\frac{dy}{dt} = \frac{(y+3)}{(1-y)}$

equating $\frac{dy}{dt} = 0$ to the expression $\frac{(y+3)}{(1-y)}$ gives

y + 3 = 0

y = -3

Therefore, the equilibrium solution occurs at y = -3

2. Let's look at the second solution:

$\frac{dy}{dy} = \frac{(t^{2}- 1) (y^{2}-2) }{y^{2}-4 }$

dividing each side by (t²-1) gives

1/(t²-1) $\frac{dy}{dt}$ = (y²-2)/ (y²-4)

factorizing the right hand side gives:

at equilibrium: $\frac{dy}{dt} = 0$ , then

y² - 2 = 0

solving for y gives y = ±√2

= ±1.414

5 0

4 years ago

a goat is kept in a rectangular field 14.5 metre by 22 m. it is tied to a pole at the centre of the field with the chain that is

jolli1 [7]

Area of the rectangle: 14.5 x 22 = 319 square meters.

Area the goat can reach ( area of a circle): 3.14 x 2.5^2 = 19.625 square meters.

Now subtract the area of the circle from the area of the rectangle:

319 - 19.625 = 299.375 square meters. (Round the answer as needed.)

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3 years ago

2.3y +7 =-11 hehebbn

Andre45 [30]

Answer:

y=-6

Step-by-step explanation:

3y+7=-11

3y=-11-7

3y=-18

y=-18/3

y=-6

4 0

3 years ago