Answer:
x = 42
Step-by-step explanation:
The marked angles are supplementary, so their sum is 180°.
(2x +8) +(2x +4) = 180
4x +12 = 180 . . . . . . . . . simplify
x +3 = 45 . . . . . . . divide by 4 (because we can)
x = 42 . . . . . . subtract 3
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<em>Additional comment</em>
A "two-step" linear equation like this one is usually solved by subtracting the unwanted constant, then dividing by the coefficient of the variable. Here, we have done those steps in reverse order. This makes the numbers smaller and eliminates the coefficient of the variable. Sometimes I find it easier to solve the equation this way.
Divide both numbers in one of the ratios by their highest common factor. This will give you the scale factor of the bigger triangle to the smaller triangle.
Answer:
<em>Circumference:</em> 18.84 cm
<em>Area:</em> 28.26 cm^2 (exponent 2)
Step-by-step explanation:
Circumference = 2(pi)r
The diameter is 6. Means the radius is 3 (half of 6)
pi = 3.14
2(3.14) x 3 = 18.84
Circumference is 18.84 cm.
Area of a circle = (pi)r^2
(3.14)(3)^2 = 28.26 cm^2 (exponent 2)
Question 1:
For this case, the first thing we must do is define variables.
We have then:
x: number of nickels
y: number of dimes
We write the system of equations that adapts to the problem.
We have then:
0.05x + 0.10y = 6.10
x + y = 67
Solving the system we have:
x = 12
y = 55
Answer:
there are 12 nickels
Question 2:
For this case, the first thing we must do is define variables.
We have then:
x: Allan's score
y: Dave's score
We write the system of equations that adapts to the problem.
We have then:
x + y = 375
x = 2y-60
Solving the system we have:
x = 230
y = 145
Answer:
Dave: 145 Allan: 230
