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VLD [36.1K]
3 years ago
9

Multiply x^2+5•x^3+7 I’m getting x^5+5x^3+7x^2+35 But I’m not sure if I’m right

Mathematics
1 answer:
user100 [1]3 years ago
6 0

Answer:

x⁵ + 5x³ + 7x² + 35

Step-by-step explanation:

(x² + 5) (x³ + 7)

To distribute binomials (expressions with two terms), you can use the FOIL method (First, Outer, Inner, Last):

x⁵ + 7x² + 5x³ + 35

To put into standard form, rearrange from highest power to lowest power:

x⁵ + 5x³ + 7x² + 35

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Suppose that y = k * (x - 1/3) ^ 2 is a parabola in the xy -plane that passes through the point (2/3, 1) :Find k and the length
Dennis_Churaev [7]

Answer:

k = 9

length of chord = 2/3

Step-by-step explanation:

Equation of parabola:   y=k (x-\frac13)^2

<u />

<u>Part 1</u>

If the curve passes through point (\frac23 ,1), this means that when x=\dfrac23, y = 1

Substitute these values into the equation and solve for k:

\implies 1=k \left(\dfrac23-\dfrac13\right)^2

\implies 1=k \left(\dfrac13 \right)^2

Apply the exponent rule \left(\dfrac{a}{b} \right)^c=\dfrac{a^c}{b^c} :

\implies 1=k \left(\dfrac{1^2}{3^2} \right)

\implies 1=\dfrac{1}{9}k

\implies k=9

<u>Part 2</u>

  • The chord of a parabola is a line segment whose endpoints are points on the parabola.  

We are told that one end of the chord is at (\frac23 ,1) and that the chord is horizontal.  Therefore, the y-coordinate of the other end of the chord will also be 1.  Substitute y = 1  into the equation for the parabola and solve for x:

\implies 1=9 \left(x-\dfrac13 \right)^2

\implies \dfrac19 = \left(x-\dfrac13 \right)^2

\implies \sqrt{\dfrac19}  = x-\dfrac13

\implies \pm \dfrac13  = x-\dfrac13

\implies x=\dfrac23, x=0

Therefore, the endpoints of the horizontal chord are: (0, 1) and (2/3, 1)

To calculate the length of the chord, find the difference between the x-coordinates:  

\implies \dfrac23-0=\dfrac23

**Please see attached diagram for drawn graph. Chord is in red**

6 0
2 years ago
Can someone help me with this question please and thank you.
Ainat [17]
Where’s the question at?
3 0
3 years ago
For better clarification I guess
marissa [1.9K]

Answer:

1.) =\frac{\sqrt{3}}{3}

2.) 42\sqrt{30}

Step-by-step explanation:

1.) \mathrm{Multiply\:by\:the\:conjugate}\:\frac{\sqrt{3}}{\sqrt{3}}

2.) \mathrm{Apply\:radical\:rule}:\quad \sqrt{a}\sqrt{b}=\sqrt{a\cdot b}

\sqrt{6}\sqrt{5}=\sqrt{6\cdot \:5}

6 0
3 years ago
2x2x7x13<br> Write the number whose prime factorization is given
kramer

Answer:

364

Step-by-step explanation:

2x2x7x13

The prime factorization is just the factors of a number.

To find the number, multiply the numbers together

2*2 = 4

4*7 = 28

28*13 = 364

3 0
2 years ago
Read 2 more answers
F(x)=x^2 what is g(x)
AysviL [449]
Is C g(x) = -X^2 -3

This is the answer
4 0
3 years ago
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