Answer:
B' = 105°
C = 27°
A = 48°
Step-by-step explanation:
Given
B = 105°
C = (2x - 3)°
C' = (5x - 48)°
Rotation = 90°
Before solving the requirements of this question, it should be noted that rotation do not change the angle of shapes.
i.e. an angle retain its measurements pre and after rotation.
Solving (a): The measurement of B'
Using the analysis above.
B' = B
Recall that
B = 105°
So:
B' = 105°
Solving (b): A and C
First, I'll solve for C.
Using the same analysis above.
C = C'
Substitute values for C and C'
5x - 48 = 2x - 3
Collect like terms
5x - 2x = 48 - 3
3x = 45
Multiply both sides by ⅓
⅓*3x = ⅓*45
x = 15
Substitute 15 for x in
C = (2x - 3)°
C = 2 * 15 - 3
C = 30 - 3
C = 27°
Solving for A
The sum of angles (A, B and C) is represented as:
A + B + C = 180
Substitute values for B and C
A + 105° + 27° = 180°
A + 132° = 180°
Collect like terms
A = 180° - 132°
A = 48°
Answer:
x = -6, y = 12
Step-by-step explanation:
Equations:
y = 2x + 24
y = -2x
Bring the the equation together and add like terms together:
-2x = 2x + 24
-4x = 24
Divide both sides by -4 to isolate x:
![\frac{-4x}{-4} = \frac{24}{-4} \\\\x = -6](https://tex.z-dn.net/?f=%5Cfrac%7B-4x%7D%7B-4%7D%20%20%3D%20%5Cfrac%7B24%7D%7B-4%7D%20%5C%5C%5C%5Cx%20%3D%20-6)
Find y:
y = -2(-6)
y = 12
Verify:
12 =2(-6) + 12
______________
Don't forget to ask if you have any questions :D
The answer is <span>The liquid must be in the cooler fewer than 10 minutes.
</span>
Let:
m - the number of minutes the liquid is in the cooler.
a - the starting temperature
The function is:
f(m) = a - 3 * m (Since the temperature decreases by 3°F each minute m, it has a negative sign)
Let:
m - <span>the number of minutes the liquid is in the cooler.
a - the starting temperature
</span>a = 90<span>°F
</span>
<span>The temperature of a liquid must stay above 60°F:
f(m) > 60
Thus:
</span>f(m) = a - 3 * m
f(m) > 60
a - 3 * m > 60
90 - 3m > 60
90 - 60 > 3m
30 > 3 m
30/3 > m
10 > m
Or m < 10. So the correct answer is The liquid must be in the cooler fewer than 10 minutes.
Answer:
4(-5z+2)+(-6)=2(-10z+1) = True
Step-by-step explanation:
Answer:
Analyzed and Sketched.
Step-by-step explanation:
We are given ![y=\frac{\ln\left(5x)}{x^2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B%5Cln%5Cleft%285x%29%7D%7Bx%5E2%7D)
To sketch the graph we need to find 2 components.
1) First derivative of y with respect to x to determine the interval where function increases and decreases.
2) Second derivative of y with respect to x to determine the interval where function is concave up and concave down.
![y'=\frac{1-2\ln\left(5x)}{x^3}=0](https://tex.z-dn.net/?f=y%27%3D%5Cfrac%7B1-2%5Cln%5Cleft%285x%29%7D%7Bx%5E3%7D%3D0)
is absolute maximum
![y''=\frac{6\ln\left(5x)-5}{x^4}=0](https://tex.z-dn.net/?f=y%27%27%3D%5Cfrac%7B6%5Cln%5Cleft%285x%29-5%7D%7Bx%5E4%7D%3D0)
is the point concavity changes from down to up.
Here, x = 0 is vertical asymptote and y = 0 is horizontal asymptote.
The graph is given in the attachment.