Answer:
x = log 7
Step-by-step explanation:
10^x=7
Take the log base 10 on each side
log10 (10^x)=log10 (7)
We dont need to write the 10, it is implied
log(10^x)=log (7)
The exponent goes out front since log a^b = b log a
x log 10 = log 7
log 10 = 1 since the base is 10 log10(10) =1
x = log 7
Answer: [C]:
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" Equation F can be written as 4n + 1 = 6n + 8. "
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Answer:
First angle: 60°
Second angle: 30°
Step-by-step explanation:
Let the two angles be signified by the variables x & y.
Let the first angle = x, and the second angle = y.
It is given that:
"The measure[ments] of the complementary angles...": x + y = 90°
"The measure of the first angle is 30 greater than the measure of the second angle": x = y + 30°
Use the system of equations. Plug in y + 30 for x in the first equation:
(y + 30) + y = 90
Combine like terms:
(y + y) + 30 = 90
2y + 30 = 90
Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. First, subtract 30 from both sides of the equation:
2y + 30 (-30) = 90 (-30)
2y = 90 - 30
2y = 60
Next, divide 2 from both sides of the equation:
(2y)/2 = (60)/2
y = 60/2
y = 30°
Plug in 30 for y in one of the equations:
x = y + 30
x = (30) + 30
x = 60°
Your answers:
First angle: 60°
Second angle: 30°
First you would find the area of the square:
230*230= 52,900
Next you would find the area of one on the triangles:
230*187=43,010 * 1/2= 21,505
Then you would multiply the area of the one triangle by four:
21,505*4= 86,020
Finally, you would add the area of the square to the combined area of the triangles:
86,020+ 52,900=138,920
Answer:
x=2, y=5
Step-by-step explanation:
PT=TR
QT=TS
get the system:
y = 2x + 1
3y = 3x + 9
3 * (2x+1) = 3x + 9
6x + 3 = 3x + 9
3x = 6
x = 2
y = 2x + 1 = 2*2 + 1 = 5
