Answer:
- the only possible value of x is 5
- the dimensions are 2 × 4 × 10
Step-by-step explanation:
The cubic equation ...
(x -3)(x -1)(x +5) = 80
has one real root: x = 5. Using that value for x, the dimensions become ...
length = 5 - 3 = 2
width = 5 - 1 = 4
height = 5 + 5 = 10
The dimensions are (length, width, height) = (2, 4, 10).
_____
We cannot tell the thrust of the problem, since it has only one solution. Perhaps you're supposed to write the cubic in standard form and use the <em>Rational Root theorem</em> to find <em>possible values of x</em>. That form can be found to be ...
(x -3)(x -1)(x +5) -80 = 0
x³ +x² -17x -65 = 0
Descartes' rule of signs tells you there is one positive real root. The rational root theorem tells you possible rational roots are factors of 65:
1, 5, 13, 65
We know that x must be greater than 3 (so all dimensions are positive). Thus <em>possible values of x are 5, 13, 65</em>, and we're pretty sure that 65 is way too large.
Answer: 17.928666
Step-by-step explanation:
Answer:
(a + 4)(a + 6)
Step-by-step explanation:
f(a) = a² + 10a + 24
I think you are asking us to factor the quadratic.
1. Multiply the leading coefficient and the constant
1 × 24 = 24
2. Find two numbers that multiply to give 24 and add to give 10.
Possible pairs are 1, 24; 2, 12; 3, 8; 4, 6
Start with the numbers near the end of the list.
By trial and error, you will find that 4 and 6 work:
4 × 6 = 24 and 4 + 6 = 10
3. Rewrite 10a as 4a + 6a
a² +4a + 6a +24
4. Factor by grouping the first two and the last two terms
a(a + 4) + 6(a + 4)
5. Distribute the a + 4
(a + 4)(a + 6)
a² + 10a + 24 = (a + 4)(a + 6)
D. Multiply the top equation by 2
That way, 3y(2) - 6y = 6y - 6y = 0
hope this helps
Answer:
C
Step-by-step explanation:
The scale factor is the ratio of corresponding sides, image to original, so
scale factor =
=
=
→ C