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cricket20 [7]
3 years ago
8

7. Calculate the volume of the triangular prism on the right.

Mathematics
1 answer:
lakkis [162]3 years ago
8 0

Answer:

A

Step-by-step explanation:

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A=L times W
Dovator [93]
A= 30ft, because you only have to multiply LxW= A that is equal to 2x15=30ft
8 0
3 years ago
Apply The Remainder Theorem, Fundamental Theorem, Rational Root Theorem, Descartes Rule, and Factor Theorem to find the remainde
Over [174]

9514 1404 393

Answer:

  possible rational roots: ±{1/3, 2/3, 1, 4/3, 2, 3, 4, 6, 12}

  actual roots: -1, (2 ±4i√2)/3

  no turning points; no local extrema

  end behavior is same-sign as x-value end-behavior

Step-by-step explanation:

The Fundamental Theorem tells us this 3rd-degree polynomial will have 3 roots.

The Rational Root Theorem tells us any rational roots will be of the form ...

  ±{factor of 12}/{factor of 3} = ±{1, 2, 3, 4, 6, 12}/{1, 3}

  = ±{1/3, 2/3, 1, 4/3, 2, 3, 4, 6, 12} . . . possible rational roots

Descartes' Rule of Signs tells us the two sign changes mean there will be 0 or 2 positive real roots. Changing signs on the odd-degree terms makes the sign-change count go to 1, so we know there is one negative real root.

The y-intercept is 12. The sum of all coefficients is 22, so f(1) > f(0) and there are no positive real roots in the interval [0, 1]. Synthetic division by x-1 shows the remainder is 22 (which we knew) and all the quotient coefficients are all positive. This means x=0 is an upper bound on the real roots.

The sum of odd-degree coefficients is 3+8=11, equal to the sum of even-degree coefficients, -1+12=11. This means that -1 is a real root. Synthetic division by x+1 shows the remainder is zero (which we knew) and the quotient coefficients alternate signs. This means x=-1 is a lower bound on real roots. The quotient of 3x^2 -4x +12 is a quadratic factor of f(x):

  f(x) = (x +1)(3x^2 -4x +12)

The complex roots of the quadratic can be found using the quadratic formula:

  x = (-(-4) ±√((-4)^2 -4(3)(12)))/(2(3)) = (4 ± √-128)/6

  x = (2 ± 4i√2)/3 . . . . complex roots

__

The graph in the third attachment (red) shows there are no turning points, hence no relative extrema. The end behavior, as for any odd-degree polynomial with a positive leading coefficient, is down to the left and up to the right.

4 0
2 years ago
Refer to the accompanying data display that results from a sample of airport data speeds in Mbps. The results in the screen disp
e-lub [12.9K]

Answer:

D. is the correct answer, hope this helps!


4 0
2 years ago
Read 2 more answers
Put brackets in the following to make it correct5-2x2+2x7-5
gayaneshka [121]
2.2=4 2.7=14 5-4+14-5=1+14-5=15-5=10 Good Luck!
5 0
2 years ago
Help me with this please<br>simplify​
anyanavicka [17]

Answer:

3^{12}

Step-by-step explanation:

\dfrac{(3^5)^2}{3^{-2}} =

= \dfrac{3^{10}}{3^{-2}}

= 3^{10-(-2)}

= 3^{10 + 2}

= 3^{12}

4 0
2 years ago
Read 2 more answers
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