What would be the sum of the lengths of the first and second diagonals rounded to the nearest whole number?
1 answer:
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9514 1404 393
Answer:
(x, y) = (-3, -13) or (-8, -23)
Step-by-step explanation:
The values for y can be equated and the resulting quadratic solved by factoring.
2x -7 = x^2 +13x +17
0 = x^2 +11x +24 . . . . . . subtract 2x-7
0 = (x +8)(x +3) . . . . . . . .factor*
The values of x that make these factors zero are x=-8 and x=-3. The corresponding values of y are ...
y = 2(-8) -7 = -23
y = 2(-3) -7 = -13
The solutions are ...
(x, y) = (-8, -23) and (-3, -13)
_____
* The constants in the binomial factors are factors of 24 that total 11. You know that ...
24 = 1×24 = 2×12 = 3×8 = 4×6
The sums of these factors are 25, 14, 11, 10. The factors 3 and 8 are the constants in the binomial factors of the quadratic.
"24" is the constant in the quadratic. "11" is the coefficient of the x term.
Answer:
Interest rate, R = 244%
Step-by-step explanation:
Given the following data;
Principal = $270
Simple interest = future amount - principal = 309.60 - 270 = $39.60
Time = 22/360 = 0.06 years
To find the interest rate?
Mathematically, simple interest is calculated using this formula;
Where;
- S.I is simple interest.
- P is the principal.
- R is the interest rate.
- T is the time.
Substituting into the equation, we have;
Cross-multiplying, we have;
<em>Interest rate, R = 244.44 ≈ 244%</em>
<em>Therefore, the pawnbroker charged Elisa a simple interest rate of 244%.</em>
For this case, what we must do is find the scale factor.
We have then that the scale factor is given by:
Where,
L1: side length of polygon ABCD
L2: side length of polygon PQRS
Note: both sides belong to the same side of each polygon
Substituting the values we have:
Rewriting we have:
Answer:
The scale factor of dilation is given by:
We have then that the scale factor is given by:
Where,
L1: side length of polygon ABCD
L2: side length of polygon PQRS
Note: both sides belong to the same side of each polygon
Substituting the values we have:
Rewriting we have:
Answer:
The scale factor of dilation is given by: