A can of soda is placed inside a cooler. As the soda cools, it’s temperature T in degrees Celsius is given by the function, T(x)=-22+42exponent^-0.05x
Where x is the number of minutes since the van was placed in the cooler
Find the initial temperature of the soda and it’s temperature after 15minutes
To find the initial temperature of the soda, we need to substitute x = 0 into the temperature function.
T(0) = -22 + 42e^(-0.05*0)
T(0) = -22 + 42e^0
T(0) = -22 + 42(1)
T(0) = -22 + 42
T(0) = 20
Therefore, the initial temperature of the soda is 20 degrees Celsius.
To find the temperature of the soda after 15 minutes, we need to substitute x = 15 into the temperature function.
T(15) = -22 + 42e^(-0.05*15)
T(15) = -22 + 42e^(-0.75)
T(15) ≈ -22 + 42(0.472367)
T(15) ≈ -22 + 19.833014
T(15) ≈ -2.166986
Therefore, the temperature of the soda after 15 minutes is approximately -2.17 degrees Celsius.
A figure displays two nonadjacent angles with measures 3° and (4x+1)˚. If the angles are complementary, what is the simplified equation corresponding to the measures of the angles? (1 point)
O (1x+1)= 90°
O (7x+1)= 90°
O (1x+1)= 180°
O (7x+1)= 180°
If two angles are complementary, their measures add up to 90 degrees.
So the equation corresponding to the measures of the angles is:
3° + (4x + 1)° = 90°
Simplifying this equation, we get:
4x + 4 = 87
Subtracting 4 from both sides:
4x = 83
Dividing both sides by 4:
x = 83/4
Therefore, none of the given options (1x+1)=90°, (7x+1)=90°, (1x+1)=180°, (7x+1)=180° correspond to the simplified equation for the measures of the angles.
A figure displays two nonadjacent angles with measures 3x° and (4x+1)˚. If the angles are complementary, what is the simplified equation corresponding to the measures of the angles? (1 point)
O (1x+1)= 90°
O (7x+1)= 90°
O (1x+1)= 180°
O (7x+1)= 180°
If two angles are complementary, their measures add up to 90 degrees.
So the equation corresponding to the measures of the angles is:
3x° + (4x + 1)° = 90°
Simplifying this equation, we get:
7x + 1 = 90
Subtracting 1 from both sides:
7x = 89
Dividing both sides by 7:
x = 89/7
So the correct equation corresponding to the measures of the angles is: (7x + 1) = 90°.
Therefore, the option is O (7x+1) = 90°.
there is a complementary angle split in two one side has the value of 5x-22° the other is 2x. What is the simplified equation corresponding to the measures of the angles?
(1 point)
(3x-22) = 90°
O (3x22) 180° =
O (7x22) 90° =
O (7x-22) 180° =
If two angles are complementary, their measures add up to 90 degrees.
So, we can set up the equation:
(5x - 22)° + 2x° = 90°
Simplifying this equation, we get:
7x - 22 + 2x = 90
Combining like terms, we have:
9x - 22 = 90
Adding 22 to both sides:
9x = 112
Dividing both sides by 9:
x = 112/9
Therefore, the simplified equation corresponding to the measures of the angles is (7x - 22)° = 90°.
The correct option is O (7x - 22) = 90°.
Three angles have measures that add to 180°. They have the following angle measures: m angle ABC = (x − 6)˚, m angle CBD = (4x-14)˚, and m angle DBE = 52°. What is the equation to solve for x? (1 point)
10x° - 20° = 180°
10x °+ 20° = 180°
9x° - 20° = 180°
x° - 20° = 180°
The sum of the angle measures in a triangle is always 180 degrees.
So we can set up the equation:
(x - 6)° + (4x - 14)° + 52° = 180°
Simplifying this equation, we get:
5x - 20 + 52 = 180
Combining like terms, we have:
5x + 32 = 180
Subtracting 32 from both sides:
5x = 148
Dividing both sides by 5:
x = 148/5
Therefore, none of the given options (10x - 20 = 180), (10x + 20 = 180), (9x - 20 = 180), or (x - 20 = 180) correspond to the equation to solve for x.
Three angles have measures that add to 180°. They have the following angle measures: m angle ABC = (x − 6)˚, m angle CBD = (4x-14)˚, and m angle DBE = 5x°. What is the equation to solve for x? (1 point)
10x° - 20° = 180°
10x °+ 20° = 180°
9x° - 20° = 180°
x° - 20° = 180°
The sum of the angle measures in a triangle is always 180 degrees.
So we can set up the equation:
(x - 6)° + (4x - 14)° + 5x° = 180°
Simplifying this equation, we get:
x - 6 + 4x - 14 + 5x = 180
Combining like terms, we have:
10x - 20 = 180
Adding 20 to both sides:
10x = 200
Dividing both sides by 10:
x = 20
Therefore, the equation to solve for x is x° - 20° = 180°.
The correct option is x° - 20° = 180°.
Two supplementary angles have the following measures: m angle ABC = 135° and
m angle CBD = 9x°. What is the equation to solve for x? (1 point)
9x° + 135° = 90°
9x° = 180°
9x° - 135° = 180°
9x° + 135° = 180°
Two angles are supplementary if their measures add up to 180 degrees.
So we can set up the equation:
135° + 9x° = 180°
Simplifying this equation, we get:
9x° = 180° - 135°
Combining like terms, we have:
9x° = 45°
Therefore, the correct equation to solve for x is 9x° = 45°.
The correct option is 9x° = 45°.
There is a pair of vertical angles whose measures are m angle 1 = 106˚ and m angle 2=(3x-75)°. What equation can you write to solve for x? (1 point)
3x° - 75° = 106°
3x° - 75° + 106° = 90° -
3x° - 75° -106° = 180°
3x° - 75° + 106° = 180°
Vertical angles are congruent, meaning they have the same measure.
So, we can set up the equation:
106° = (3x - 75)°
Simplifying this equation, we have:
3x - 75 = 106
Adding 75 to both sides:
3x = 181
Dividing both sides by 3:
x = 181/3
Therefore, the equation to solve for x is 3x° - 75° = 106°.
The correct option is 3x° - 75° = 106°.
Two intersecting lines create four angles; angle 1 and angle 3 are a vertical pair. Their sum of their measures is equal to 68°. What equation solves for the value of each angle? (1 point)
2x° = 68°
x° = 68°
2x° + 68° = 180°
68x° = 2°
Vertical angles are congruent, meaning they have the same measure.
So, we can set up the equation:
angle 1 + angle 3 = 68°
Since angle 1 and angle 3 are a vertical pair, they have the same measure. Let's call this measure x.
So, the equation becomes:
x + x = 68°
Simplifying this equation, we have:
2x = 68°
Dividing both sides by 2:
x = 34°
Therefore, the equation that solves for the value of each angle is 2x° = 68°.
The correct option is 2x° = 68°.
For two vertical angles with measures m angle 2 = (5x +23) ˚ and m angle 4 = (3x + 35) °, о what is the measure of each angle? (1 point)
53°
29°
15.3°
6°
Vertical angles are congruent, meaning they have the same measure.
So, we can set up the equation:
(5x + 23)° = (3x + 35)°
Simplifying this equation, we get:
5x + 23 = 3x + 35
Subtracting 3x from both sides:
2x + 23 = 35
Subtracting 23 from both sides:
2x = 12
Dividing both sides by 2:
x = 6
Now that we have the value of x, we can substitute it back into either angle to find its measure.
Let's use angle 4:
m angle 4 = (3x + 35)°
m angle 4 = (3*6 + 35)°
m angle 4 = 18 + 35
m angle 4 = 53°
Therefore, the measure of each angle is 53°.
The correct option is 53°.
There are two complementary angles, angle 5 and angle 6. If m angle 5 = 39°, what equation can you write to solve for m angle 6? (1 point)
m angle 6 = 180° - 39°
m angle 6 = 39°
m angle 6+39° = 180°
m angle 6+39° = 90°
Complementary angles are two angles that add up to 90 degrees.
So, if m angle 5 = 39°, we can set up the equation:
m angle 5 + m angle 6 = 90°
Substituting the given value, we have:
39° + m angle 6 = 90°
To solve for m angle 6, we subtract 39° from both sides:
m angle 6 = 90° - 39°
Simplifying this equation, we have:
m angle 6 = 51°
Therefore, the equation to solve for m angle 6 is m angle 6 = 51°.
The correct option is m angle 6 = 51°.