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 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
21 answers
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°
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.
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°
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°.
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° =
(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°.
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°
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.
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°
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°.
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°
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°.
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°
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°.
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°
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°.
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°
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°.
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°
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°.
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°.
4 answers