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3 years ago

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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

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: $y=k (x-\frac13)^2$

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<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