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julia-pushkina [17]
1 year ago
15

If (ax+2)(bx+7)=15x2+cx+14 for all values of x, and a+b=8, what are the 2 possible values fo c

Mathematics
1 answer:
dolphi86 [110]1 year ago
8 0

Given:

(ax+2)(bx+7)=15x^2+cx+14

And

a+b=8

Required:

To find the two possible values of c.

Explanation:

Consider

\begin{gathered} (ax+2)(bx+7)=15x^2+cx+14 \\ abx^2+7ax+2bx+14=15x^2+cx+14 \end{gathered}

So

\begin{gathered} ab=15-----(1) \\ 7a+2b=c \end{gathered}

And also given

a+b=8---(2)

Now from (1) and (2), we get

\begin{gathered} a+\frac{15}{a}=8 \\  \\ a^2+15=8a \\  \\ a^2-8a+15=0 \end{gathered}a=3,5

Now put a in (1) we get

\begin{gathered} (3)b=15 \\ b=\frac{15}{3} \\ b=5 \\ OR \\ b=\frac{15}{5} \\ b=3 \end{gathered}

We can interpret that either of a or b are equal to 3 or 5.

When a=3 and b=5, we have

\begin{gathered} c=7(3)+2(5) \\ =21+10 \\ =31 \end{gathered}

When a=5 and b=3, we have

\begin{gathered} c=7(5)+2(3) \\ =35+6 \\ =41 \end{gathered}

Final Answer:

The option D is correct.

31 and 41

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A=1 b=8 c=8
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h = [-8 +-sq root(32)] / 2
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h1 = <span> <span> <span> -1.1715728753 </span> </span> </span>
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3 years ago
2) Tara is trying to find the nth term of the arithmetic sequence 5,8,11, and 14…. Which expression can Tara use to find the nth
juin [17]

Answer:

Below in bold.

Step-by-step explanation:

Nth term an = a1 + d(n - 1)   where a1 = term 1 and d = common difference.

Here a1 = 5 and d = 8-5 = 3.

So an = 5 + 3(n - 1)

15th term a15

=  5 + 3(15 - 1)

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2 years ago
If r = 8 units and h = 10 units, what is the volume of the cylinder shown above? use 3.14 for pi,
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I hope this helps you



Volume =pi.r^2.h


Volume =3,14.8^2.10

Volume =31,4.64

Volume =200,96
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3 years ago
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Lunna [17]

Answer:

x = 15

Step-by-step explanation:

There are 2 triangles. The small triangle CDE has sides that are 8 and 20.

The big triangle CAB has sides 6+8 and 20 + x. Add the 6 and 8 which is 14. Create a proportion and cross multiply, divide, then solve for x.

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2 years ago
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