Find all zeros of the function and write the polynomial as a product of linear factorsf(x)=x^4+29x^2+100

Answers

Answer 1

Answer: $f(x)=x^4+29x^2+100=\left(x^2\right)^2+29x^2+100\n\nx^2=v;\ v\geq0\n\nf(v)=v^2+29v+100\n\na=1;\ b=29;\ c=100\n\n\Delta=b^2-4ac;\ v_1=(-b-\sqrt\Delta)/(2a);\ v_2=(-b+\sqrt\Delta)/(2a)\n\n\Delta=29^2-4\cdot1\cdot100=841-400=441;\ \sqrt\Delta=√(441)=21\n\nv_1=(-29-21)/(2\cdot1)=(-40)/(2)=-20 < 0;\ v_2=(-29+21)/(2\cdot1)=(-8)/(2)=-4 < 0$

$Function\ has\ no\ zeros.\n\n\nf(x)=x^4+29x^2+100=x^4+25x^2+4x^2+100\n\n=x^2(x^2+25)+4(x^2+25)=(x^2+25)(x^2+4)\n\nis\ not\ impossible\ write\ the\ polynomia\l as\ a\ product\ of\ linear\ factors.$

Answer 2

Answer: take x² = t
t²+29t+100
=(t²+25t) +(4t+100)
=t(t+25) + 4(t+25)
=(t+4)(t+25)
=(x²+4)(x²+25)

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The braking distance, D, of a car is directly proportional to the square of its speed, v. When d=5, v=10Find d when v=70

Answers

$d \propto v^2$

$\implies d=kv^2$

substitute the given values, $5=k(10)^2\implies k=\frac1{20}$

now, $d=\frac{1}{20}\times( 70)^2=\frac{70\times70}{20}=245$

A big blunder from my side, now fixed!

What is the quotient of 2,173 ÷ 53

Answers

Answer:

Step-by-step explanation:

PLEASE HELP, DUE AT MIDNIGHT >>>>>

Answers

Answer:

BELOW

Step-by-step explanation:

$\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)\n\n\left(x_1,\:y_1\right)=\left(-8,\:-11\right),\:\left(x_2,\:y_2\right)=\left(17,\:4\right)\n\nm=(4-\left(-11\right))/(17-\left(-8\right))\n\nm = (4+11)/(17+8)= (15)/(25) \n\mathrm{Refine}\n\nm=(3)/(5)$

$\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)\n\n\left(x_1,\:y_1\right)=\left(10,\:-15\right),\:\left(x_2,\:y_2\right)=\left(13,\:-17\right)\n\nm=(-17-\left(-15\right))/(13-10)\n\nm = (-17+15)/(13-10)\n \nm = (-2)/(3)\n \nSimplify\nm=-(2)/(3)$

$\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)\n\n\left(x_1,\:y_1\right)=\left(-6,\:-7\right),\:\left(x_2,\:y_2\right)=\left(5,\:-7\right)\n\nm=(-7-\left(-7\right))/(5-\left(-6\right))\n\nm = (-7+7)/(5+6)\n \nm = (0)/(11)\n \nSimplify\nm=0$

10.

$\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)\n\n\left(x_1,\:y_1\right)=\left(-4,\:-3\right),\:\left(x_2,\:y_2\right)=\left(2,\:-9\right)\n\nm=(-9-\left(-3\right))/(2-\left(-4\right))\n\nm = (-9+3)/(2+4)\n \nm = (-6)/(6) \n\nSimplify\nm =-1$

11.

$\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)\n\n\mathrm{When\:}y_1\ne \:y_2\mathrm{\:and\:}\:x_1=x_2\mathrm{\:the\:slope\:is\:}\infty \n\nm = \infty$

12.

$\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)\n\n\left(x_1,\:y_1\right)=\left(-5,\:3\right),\:\left(x_2,\:y_2\right)=\left(19,\:-6\right)\n\nm=(-6-3)/(19-\left(-5\right))\n\nm = (-6-3)/(19+5)\n \nm = (-9)/(24)\n \nSimplify\nm=-(3)/(8)$

13.

$\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)\n\n\left(x_1,\:y_1\right)=\left(-7,\:-12\right),\:\left(x_2,\:y_2\right)=\left(1,\:-16\right)\n\nm=(-16-\left(-12\right))/(1-\left(-7\right))\n\nm = (-16+12)/(1+7) \n\nm = (-4)/(8) \n\nSimplify\nm=-(1)/(2)$

14.

$\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)\n\n\left(x_1,\:y_1\right)=\left(-18,\:0\right),\:\left(x_2,\:y_2\right)=\left(-13,\:1\right)\n\nm=(1-0)/(-13-\left(-18\right))\n\nm = (1-0)/(-13+18)\n \nm = (1)/(5) \n$

15.

$\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)\n\n\left(x_1,\:y_1\right)=\left(1,\:-11\right),\:\left(x_2,\:y_2\right)=\left(-2,\:-4\right)\n\nm=(-4-\left(-11\right))/(-2-1)\n\nm = (-4+11)/(-2-1)\n \nm = (7)/(-3) \n\nSimplify\nm=-(7)/(3)$

A chord can contain at most how many diameters

Answers

A cord links any two points on a circle.

The greatest distance between two points on a circle is the length of the diameter.

Hence a chord can contain at most one diameter.

27/45=_/5?
2/6=_/3?jjjjjj

Answers

Answer:

27/45=3/5

2/6=1/3

Step-by-step explanation:

The sum of two numbers is 67. The larger number is 4 more than 2 times the smaller. What are the two numbers?a) 23 and 44
b) 21 and 46
c) 19 and 48
d) 17 and 50

Answers

x,y - two numbers (x > y)

(1) x + y = 67 ⇒ x = 67 - y
(2) x - 4 = 2y

subtitute (1) to (2)

67 - y - 4 = 2y
63 - y = 2y |add y to both sides
63 = 3y |divide both sides by 3
y = 21

subtitute the value of y to (1)

x = 67 - 21 = 46

Answer: 21 and 46.

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