please check my answers

Suppose that the temperature outside is dropping at a constant rate. At noon, the temperature is 70 F and it drops to 58 F at 5 p.m. How much did the temperature change each hour?
12/5=2.4 degrees per hour.

Evaluate the expression if a=-2, b=5,c=-4, and d=6:4b+5d-c/a


4b+5d-c/a =

4(5)+5(6)-(-4)/(-2)
4x5=20
5x6=30
-4/-2=2
answer= 20+30+2=52

Evaluate the expression if a=-2, b=5,c=-4, and d=6: 6^2-2bc+c^2

---> 5² - 2(5)(-4) + (-4)²
= 25 + 40 + 16
= 81

The simple interest I on a principle of P dollars at interest rate r for time t, in years, is given by I=Prt. Find the simple interest on a principle of $6000 at 3% for 2 years. (Hint: 3%=0.03)
Interest = 6000*.03*2

Simplify using the distributive property:7(4w-3)-25=
-21+25w+28w=
-21+3w
A triangle has sides 3x+7, 4x-9, and 5x+6. Find the expression that represents the perimeter.

=3x + 7+ 4x - 9+5x +6
=3x+4x+5x +7-9+6
=12x-3


Simplify, if possible: 6x^2y^3+9x^2y^3/3x^2y^2

The temperature one is correct. You may want to include a negative sign to indicate that the temperature is dropping.

You made a sign mistake on the first evaluation. (You dropped one of your negative signs.)

On the second evaluation, you changed "6^2" to "5^2" in your work.

For the simple interest, you should multiply what you have to get a numerical answer in dollars.

Your distributive property problem is quite wrong. The distributive property states for an expression a(b+c), the answer will be ab + ac. Try to apply that to your problem.

On the perimeter, check 7-9+6. It's not -3.

-x+2y=3

3x+2y=-1

To find the change in temperature each hour, you need to find the difference between the initial temperature and the final temperature, and then divide that difference by the number of hours.

Initial Temperature: 70°F
Final Temperature: 58°F
Number of hours: 5 - 12 = 5 hours

Temperature change per hour: (Final temperature - Initial temperature) / Number of hours

Temperature change per hour: (58°F - 70°F) / 5 hours
Temperature change per hour: -12°F / 5 hours
Temperature change per hour: -2.4°F

So, the temperature dropped 2.4°F every hour.

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To evaluate the expression 4b + 5d - c/a, substitute the given values for a, b, c, and d:

a = -2
b = 5
c = -4
d = 6

4b + 5d - c/a = 4(5) + 5(6) - (-4) / (-2)
= 20 + 30 + 4 / (-2)
= 54 - 2
= 52

Thus, the value of the expression is 52.

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To evaluate the expression 6^2 - 2bc + c^2, substitute the given values for a, b, c, and d:

a = -2
b = 5
c = -4
d = 6

6^2 - 2bc + c^2 = 36 - 2(-4)(5) + (-4)^2
= 36 + 40 + 16
= 92

Thus, the value of the expression is 92.

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To find the simple interest on a principle of $6000 at 3% for 2 years, use the formula:

Interest = Principle * Rate * Time

Principle = $6000
Rate = 3% = 0.03 (convert percentage to decimal)
Time = 2 years

Interest = 6000 * 0.03 * 2
Interest = $360

Therefore, the simple interest on a principle of $6000 at 3% for 2 years is $360.

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To simplify the expression 7(4w-3) - 25:

Apply the distributive property by multiplying 7 to each term inside the parentheses.

7(4w-3) - 25 = 7*4w - 7*3 - 25
= 28w - 21 - 25
= 28w - 46

Therefore, the simplified expression is 28w - 46.

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To find the expression that represents the perimeter of a triangle with sides 3x + 7, 4x - 9, and 5x + 6:

Perimeter = sum of all three sides

Perimeter = (3x + 7) + (4x - 9) + (5x + 6)
Perimeter = 3x + 7 + 4x - 9 + 5x + 6
Perimeter = 12x + 4

Therefore, the expression that represents the perimeter of the triangle is 12x + 4.

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To simplify the expression (6x^2y^3 + 9x^2y^3) / (3x^2y^2):

Combine like terms on the numerator.

(6x^2y^3 + 9x^2y^3) / (3x^2y^2) = 15x^2y^3 / (3x^2y^2)

Divide the coefficients and subtract the exponents of the variables.

15x^2y^3 / (3x^2y^2) = 5x^(2-2) y^(3-2)
= 5xy

Therefore, the simplified expression is 5xy.