Answer:
The correct answer is (-5,-5)
Step-by-step explanation:
1. Both of the equations are in standard form, so first you set them equal to each other.
2. Solve for x as a normal algebraic equation.
3. Back substitute your answer for x into one of the original equations. (back substitution is just putting the x back into the equation and solving for y.)
4. Now you have your x and y coordinates, and the point of intersection of the two lines.
Any number in fraction form is over 1, so for a negative number like -29 it would be 29 over negative 1, like this: 29/-1
Step-by-step explanation:
when having an exponent of an exponent, the exponents are simply multiplied.
so, here we have 3/4 × 2/3 = (3×2)/(4×3) = 6/12 = 1/2
so, simplified, we have 5^(1/2).
now, a fraction as exponent indicates a root to be taken. which root is identified by the denominator of the fraction.
here this is 2 (of 1/2). so we need to take the square root.
therefore
is the right answer.
Answer:
110 degrees
Step-by-step explanation:
Because these angles are vertical, 5x+15=8x-42. thus, 15=3x-42, 3x=57, and x=19. 5x+15=5(19) +15=110. So, m<CDE=110 degrees.
Answer:
6 ounces
Step-by-step explanation:
Let x = the number of ounces of the 15% alcohol solution needed to be mixed with the 4 ounces of 20% alcohol solution to obtain the 17% alcohol solution.
After converting the percentages to their decimal equivalents, set up the necessary equation as follows:
0.15x+0.20(4) = (x+4)(0.17) Simplify and solve for x.
0.15x+0.8 = 0.17x+0.68 Subtract 0.15x from both sides.
0.8 = 0.02x+0.68 Now subtract 0.68 from both sides.
0.12 = 0.02x Finally, divide both sides by 0.02
x = 6
You need to mix 6 ounces of 15% alcohol solution with 4 ounces of 20% alcohol solution to obtain 10 (x+4)ounces of 17% alcohol solution.
