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OlgaM077 [116]
4 years ago
13

The graph shows the distances traveled by two trains over several hours.

Mathematics
1 answer:
jeka944 years ago
4 0

Train A is moving at a faster rate because the line is steeper.

Hope this helps :)

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According to the Rational Root Theorem, which number is a potential root of f(x) = 9x8 + 9x6 – 12x + 7?
notsponge [240]

<u>Answer-</u>

\boxed{\boxed{\frac{7}{3}}}

<u>Solution-</u>

Rational Root Theorem-

f(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+.......+a_1x+a_0\ \ \ and\ a_n\neq 0

All the potential rational roots are,

=\pm (\dfrac{\text{factors of}\ a_0}{\text{factors of}\ a_n})

The given polynomial is,

f(x) = 9x^8 + 9x^6-12x + 7

Here,

a_n=9,\ a_0=7\\\\\text{factors of}\ 9=1,3,9\\\\\text{factors of}\ 7=1,7

The potential rational roots are,

=\pm \frac{1}{1},\pm \frac{1}{3}, \pm \frac{1}{9}, \pm \frac{7}{1}, \pm \frac{7}{3}, \pm \frac{7}{9}

=\pm 1,\pm \frac{1}{3}, \pm \frac{1}{9}, \pm 7, \pm \frac{7}{3}, \pm \frac{7}{9}

From, the given options only \frac{7}{3} satisfies.

6 0
3 years ago
Read 2 more answers
Solve the equation: k^2+5k+13=0
mr_godi [17]

Step-by-step explanation:

k² + 5k + 13 = 0

Using the quadratic formula which is

x =  \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}  \\

From the question

a = 1 , b = 5 , c = 13

So we have

k =  \frac{ - 5 \pm \sqrt{ {5}^{2} - 4(1)(13) } }{2(1)}  \\  =  \frac{ - 5 \pm \sqrt{25 - 52} }{2}  \\  =  \frac{ - 5 \pm \sqrt{ - 27} }{2}  \:  \:  \:  \:  \:  \:  \\  =  \frac{ - 5  \pm3 \sqrt{3}  \: i}{2}  \:  \:  \:  \:  \:  \:

<u>Separate the solutions</u>

k_1 =  \frac{ - 5 + 3 \sqrt{3} \: i }{2}  \:  \:  \:  \: or \\ k_2 =  \frac{ - 5 - 3 \sqrt{3}  \: i}{2}

The equation has complex roots

<u>Separate the real and imaginary parts</u>

We have the final answer as

k_1 =  -  \frac{5}{2}  +  \frac{3 \sqrt{3} }{2}  \: i \:  \:  \:  \: or \\ k_2 =  -  \frac{5}{2}  -  \frac{3 \sqrt{3} }{2}  \: i

Hope this helps you

8 0
3 years ago
F(x) = 11x³ - 6x² + x + 3
anzhelika [568]

Answer:

3

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
What is 2p6−19=−9 I need help pls I don't understand this at all
Aleonysh [2.5K]

Answer:

5/6. Is this what u are looking for?

Step-by-step explanation:

Step 1 Simplify:2x(6)-19=-9 to 12x+-19=-9

Step 2 Add 19 to both sides: 12x-19+19=-9+19. You should get 12x=20

Step 3 Divide 12 on both sides: 12x/12=10/12

x=10/12. Simplified= x=5/6

7 0
3 years ago
When the expression $-2x^2-20x-53$ is written in the form $a(x+d)^2+e$, where $a$, $d$, and $e$ are constants, then what is the
Sladkaya [172]
We start with 2 x^{2} -20x-53 and wish to write it as a(x+d) ^{2} +e

First, pull 2 out from the first two terms: 2( x^{2} -10x)-53

Let’s look at what is in parenthesis. In the final form this needs to be a perfect square. Right now we have x^{2} -10x and we can obtain -10x by adding -5x and -5x. That is, we can build the following perfect square: x^{2} -10x+25=(x-5) ^{2}

The “problem” with what we just did is that we added to what was given. Let’s put the expression together. We have 2( x-5) ^{2}-53 and when we multiply that out it does not give us what we started with. It gives us 2 x^{2} -20x+50-53=2 x^{2} -20x-3

So you see our expression is not right. It should have a -53 but instead has a -3. So to correct it we need to subtract another 50.

We do this as follows: 2(x-5) ^{2}-53-50 which gives us the final expression we seek:

2(x-5) ^{2}-103

If you multiply this out you will get the exact expression we were given. This means that:
a = 2
d = -5
e =  -103

We are asked for the sum of a, d and e which is 2 + (-5) + (-103) = -106


7 0
3 years ago
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