What is the definition of a parent function?

Explain why x and 4x - 10 are factors of the expression x(4x - 10)3 rather than terms of the expression. What are the terms of t

andriy [413]

Solution :- Let p(x) be the polynomial such that

$p(x) = x(4x-10)^3\\\text{and let f(x) be another polynomial such that }\\f(x)=4x-10\\\text{To find , Put } f(x)=0\\\Rightarrow4x-10=0\\\Rightarrow4x=10\\\Rightarrow x=5/2\\\text{Now substituting value of x in p(x),we get}\\p(x)=\frac{5}{2} .(4(5/2)-10)^3\\\Rightarrow\frac{5}{2}.(10-10)^3=0\\\text{Similarly let g(x)=x ,we get x=0 by putting g(x)=0}\\\text{now f(x)=0 for x=0}\\\text{So by Factor theorem f(x) and g(x) are the factors of polynomial p(x)}\\$

$\text{Now} p(x) = x(4x-10)^3\\=64x^4-480x^3+1200x^2-1000x\\\text{so the terms of terms of } p(x) \text{are} 64x^4,-480x^3,1200x^2,-1000x\\\text{here, by using Factor theorem x is a factor of all the terms but 4x-10 is not. }$

$\text{And the terms of the factor 4x-10 are 4x and -10}$

3 0

3 years ago

21g = 84 A. g = 3 B. g = 4 C. g = 5

natta225 [31]

21g=84
g=84/21
g=4

The answer is B

6 0

3 years ago

Read 2 more answers

You roll two fair dice, one green and one red. (a) Are the outcomes on the dice independent? Yes No (b) Find P(1 on green die an

ASHA 777 [7]

Answer:

a

Yes

b

$P(1 \& 5) = \frac{1}{36}$

c

$P(5 \& 1) = \frac{1}{36}$

d

$P(5 \& 1 | 1\& 5 ) = \frac{1}{18}$

Step-by-step explanation:

From the question we are told that

Two fair dice, one green and one red were rolled

Generally the outcomes on the dice independent because the outcome on the first dice is not affected by the second die

Generally the probability of getting a 1 on a dice rolled is $P(1) = \frac{1}{6}$

the probability of getting a 5 on a dice rolled is $P(5) = \frac{1}{6}$

Generally the probability of P(1 on green die and 5 on red die) is mathematically represented as

$P(1 \& 5) = \frac{1}{6} *\frac{1}{6}$

$P(1 \& 5) = \frac{1}{36}$

Generally the probability of P(5 on green die and 1 on red die) is mathematically represented as

$P(5 \& 1) = \frac{1}{6} *\frac{1}{6}$

$P(5 \& 1) = \frac{1}{36}$

Generally the probability of P((1 on green die and 5 on red die) or (5 on green die and 1 on red die)) is mathematically represented as

$P(5 \& 1 | 1\& 5 ) = \frac{1}{36} + \frac{1}{36}$

$P(5 \& 1 | 1\& 5 ) = \frac{1}{18}$

8 0

3 years ago

What is the solution to the system of equations?

alukav5142 [94]

Answer:

(x, y) = (-4, 15)

Step-by-step explanation:

The two equations have the same coefficient for y, so you can eliminate y by subtracting one equation from the other. Here the x coefficient is largest for the first equation, so it will work best to subtract the second equation.

(3x +y) -(2x +y) = (3) -(7)

x = -4 . . . . . . . . simplify

Now, we can find y by substituting this value for x.

2(-4) +y = 7

y = 7 +8 = 15 . . . . . add 8 to both sides of the equation

The solution is (x, y) = (-4, 15).

6 0

3 years ago

Answer if you know

Arlecino [84]

I've attached a plot of one such cross-section (orange) over the region in the x-y plane (blue), including the bounding curves (red). (I've set $y=1.25$ for this example.)

The length of each cross section (the side lying in the base) has length determined by the horizontal distance $x$ between the y-axis $x=0$ and the curve $y=\sqrt x$ . In terms of $y$ , this distance is $x=y^2$ . The height of each cross section is twice the value of $y$ , so the area of each rectangular cross section should be $2y^3$ .

This means the volume would be given by the integral

$\displaystyle\int_0^22y^3\,\mathrm dy$

8 0

3 years ago