Answer:
- 84 + 10i
Step-by-step explanation:
A complex number in standard form is a ± bi
a is the real part and bi the imaginary part
and
= i
Given
- 84
=
- 84
=
×
- 84
= 10i - 84
= - 84 + 10i ← in standard form
Answer:
15(2r^2+2r+5)
Step-by-step explanation:
I'm more of a guess and check type of person, but 15 x 2r^2 = 30r^2, 15 x 2r = 30r, and 15 x 5 = 75
General Idea:
(i) Assign variable for the unknown that we need to find
(ii) Sketch a diagram to help us visualize the problem
(iii) Write the mathematical equation representing the description given.
(iv) Solve the equation by substitution method. Solving means finding the values of the variables which will make both the equation TRUE
Applying the concept:
Given: x represents the length of the pen and y represents the area of the doghouse
<u>Statement 1: </u>"The pen is 3 feet wider than it is long"

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<u>Statement 2: "He also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base"</u>

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<u>Statement 3: "After putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen."</u>

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<u>Statement 4: "The perimeter of the pen is 3 times greater than the perimeter of the doghouse."</u>

Conclusion:
The systems of equations that can be used to determine the length and width of the pen and the area of the doghouse is given in Option B.

The answer is c. 64 divided by 4 is 16 and 8 divided by 5 is 16
You can set up an equation based off of the information given:
x represents the unknown number
3/5x - 1 = 23
add 1 to both sides to isolate the 3/5x
3/5x = 24
divide both sides by 3/5 to solve for x
x = 120/3
120/3 can be simplified into 40
Final answer: x = 40