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3 years ago

Are two pairs of congruent angles enough information to conclude that two triangles are similar explain

1 answer:

4 0

Yes, because if two angles of a triangle are equal, then the third angle must also be equal, because angles of a triangle always add to make 180°.

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y=3x−5 y=x−1 Is ( 2 , 1 )a solution of the system?

kotegsom [21]

Answer: Yes, (2,1) is a solution.

Point for : (2,1)

Equation form : x=2 , y=1

Step-by-step explanation: Solve for the first variable in one of the equations, then substitute the result into the other equation.

Hope this helps you out! ☺

6 0

3 years ago

Read 2 more answers

In an area of the Midwest, records were kept on the relationship between the rainfall (in inches) and the yield of wheat (bushel

Liula [17]

Answer:

Option A is correct.

y = 35.4 bushels per acre when rainfall = 7.1 inches

Step-by-step explanation:

An image of the steps to obtain the equation that relates x to y is attached to this answer.

n = number of variables = 9

μₓ = mean of variable x (rainfall in inches)

μᵧ = mean of variable y (yield in bushels per acre)

σₓ = standard deviation of variable x (rainfall in inches)

σᵧ = standard deviation of variable y (yield in bushels per acre)

y = 4.379x + 4.268

when x = 7.1

y = 4.379(7.1) + 4.268 = 35.3589 = 35.4 bushels per acre.

7 0

2 years ago

write an equation in y=mx+b for a line that passes through (3,-4) & has a slope of -3. you can write it in point-slope and c

dedylja [7]

Y = -3x + b
Plug in point
-4 = -3(3) + b
-4 = -9 + b, b = 5
Solution: y = -3x + 5

5 0

3 years ago

A cold drink is poured out at 52°F. After 2 minutes of sitting in a 72°F room, its temperature has risen to 55°F. Find an equati

I am Lyosha [343]

Answer:

The model for the temperature of the drink can be written as

$T=72-20e^{-0.08t}$

Step-by-step explanation:

For a cold drink in a hotter room, we can say that the rate of change of temperature of the drink is proportional to the difference of temperature between the drink and the room.

We can model that in this way

$\frac{dT}{dt}=k*(T_r-T)$

If we rearrange and integrate

$\int\frac{dT}{(T-Tr)} =-k*\int dt\\\\ln(T-T_r)=-kt+C1\\\\T-T_r=Ce^{-kt}\\\\T=T_r+Ce^{-kt}$

We know that at time 0, the temperature of the drink was 52°F. Then we have:

$T=T_r+Ce^{-kt}\\\\52=72+Ce^0=72+C\\\\C=-20$

We also know that at t=2, T=55°F

$T=T_r+Ce^{-kt}\\\\55=72-20e^{-k*2}\\\\e^{-k*2}=(72-55)/20=0.85\\\\-2k=ln(0.85)=-0.1625\\\\k=0.08$

The model for the temperature of the drink can be written as

$T=72-20e^{-0.08t}$

7 0

3 years ago

What is the slope intercept form of 2x+y=8

sweet [91]

The slope-intercept form of 2x+y=8 is y=2x-8

7 0

3 years ago

Read 2 more answers