MATHEMATICS HIGH SCHOOL

Could you please solve me this exercice: :3x^2-5x+√(x^2-5x+7)=5

Thank you a lot! :3 :3 :3

Answers

Answer 1
Answer: Domain:x^2-5x+7\geq0\n\na=1;\ b=-5;\ c=7\n\n\Delta=b^2-4ac\to\Delta=(-5)^2-4\cdot1\cdot7=25-28=-3 < 0\n\ntherefore\ D:x\in\mathbb{R}


Find\ minimum\ value\ of\ x^2-5x+7\n\ny_(min)=(-\Delta)/(4a)\to y_(min)=(-(-3))/(4\cdot1)=\boxed{(3)/(4)}\n-----------------------------\nx^2-5x+√(x^2-5x+7)=5\ \ \ \ \ |add\ 7\ to\ both\ sides\n\nx^2-5x+7+√(x^2-5x+7)=12\n\nsubtitute\ t=x^2-5x+7\ (t\geq(3)/(4))\n\nt+√(t)=12\ \ \ \ |subtract\ t\ from\ both\ sides\n\n√(t)=12-t\ \ \ \ \ \ |square\ both\ sides

t=(12-t)^2\n\nt=12^2-2\cdot12\cdot t+t^2\n\nt=144-24t+t^2\n\nt^2-24t+144=t\ \ \ \ \ |subtract\ t\ from\ both\ sides\n\nt^2-25t+144=0\n\nt^2-9t-16t+144=0\n\nt(t-9)-16(t-9)=0\n\n(t-9)(t-16)=0\iff t-9=0\ or\ t-16=0\n\nt=9\ or\ t=16

t+√(t)=12\ therefore\ t=16\ is\ not\ a\ solution.


t=9\to x^2-5x+7=9\ \ \ \ |subtract\ 9\ from\ both\ sides\n\nx^2-5x-2=0\n\na=1;\ b=-5;\ c=-2\n\n\Delta=(-5)^2-4\cdot1\cdot(-2)=25+8=33\n\nx=(-b\pm\sqrt\Delta)/(2a)\to x=(5\pm√(33))/(2)

Answer:\n\boxed{x=(5-√(33))/(2)\ or\ x=(5+√(33))/(2)}
Answer 2
Answer:  if xy=0 then x or/and y must be 0 so we try to get it to zero later

so first we get the square root on one side by itself
so subtract x^2-5 from both sides (-x^2+5 to both sides)

√(x^2-5x+7)=-x^2+5x+5
square both sides (or both sides to the ^2 power)
gets rid of the √
x^2-5x+7=(-x^2+5x+5)^2=x^4-10x^3+15x^2+50x+25
so subtract x^2 from both sides
-5x+7=x^4-10x^3+14x^2+50x+25
add 5x to both sides
7=x^4-10x^3+14x^2+55x+25
subtract 7 from both sides
0=x^4-10x^3+14x^2+55x+18
factor
(x^2-5x-9)(x^2-5x-2)=0
(x^2-5x-9)=0
(x^2-5x-2)=0
I'm not sure how to proceed but if you can find the factors of (x^2-5x-2) and (x^2-5x-9) and set them to zero, you can get the answers

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F(x) = 2/x, g(x) = |x| -1 What is the domain of (fog) (x)?

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Answers

Answer:

x≠-1,1

Step-by-step explanation:

f(g(x)) is a composition where g(x) is is substituted for x in f(x).

Recall, f(x) is 2/x. So we write 2/|x|-1. This places x in the denominator and 0 cannot be in the denominator x. Any value of x that makes the denominator 0 will not be in the domain.

|x|-1=0

|x|=1

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Pablo folds a straw into a triangle with side lengths of 4x2 – 3 inches, 4x2 – 2 inches, and 4x2 – 1 inches. The perimeter of the triangle is 12x2 – 6 inches. If x = 1.5, what was the length of the straw before it was folded?

Answers

The perimeter is the sum of the lengths of the traingle. So,
P = 12x2 - 6
Plugging in the given value of x,
P = 12 (1.5)^2 - 6
P = 21 inches

Assuming that the ends of the straw are not overlapping in forming the triangle, the perimeter is just equal to the original length of the straw.

Graph the linear equation 3x=10

Answers

3x = 10
3x = 10
 3      3
  x = 3¹/₃

How to show your work to solve  3r^2-16r-7=5

Answers

OK so   3r^2-16r-7=5
Subtract five from both sides
3r^2-16r-7-5=0
Add like terms
3r^2-16r-12=0
Factorise it, this means putting it into brackets
(3r + 2)(r - 6)
Find out what multiplies to make negative twelve but adds to make negative sixteen
However none of the terms do this so we put negatives next to the "r"s
(-3r + 2)(-1r - 6)
The answer is r=6

Answer:

Step 1: Subtract 5 from both sides.

3r2−16r−7−5=5−5

3r2−16r−12=0

Step 2: Factor left side of equation.

(3r+2)(r−6)=0

Step 3: Set factors equal to 0.

3r+2=0 or r−6=0

r=−2/3

or r=6

Answer:

r=−2/3

or r=6

Step-by-step explanation:

the world's narrowest electric vehicle is about 35 inches wide .how wide is the vehicle to the nearest foot

Answers

Well the conversion factor between inches and feet is that

12 inches = 1 foot
35 inches = ? Feet

? Feet = 35 X 1 / 12
? Feet = 35/12
? Feet = 2.91666 feet about.

The vehicle is about 3 feet in terms of width.

Find the volume of the attached figure...Help please!!! I'll give brainliest if you explain your answer!!!

Answers

Answer:

  • 82.5 cubic inches

Step-by-step explanation:

Given pentagonal prism.

The base is a regular pentagon with side of 4 in and the distance from the center to side 2.75 in.

By connecting the center to each vertex we get 5 equal triangles with side of 4 in and height of 2.75 in.

Find the base area:

  • B = 5*1/2*4*2.75 = 27.5

Find the volume:

  • V = Bh
  • V = 27.5*3 = 82.5

The volume is 82.5 cubic inches
First find the area of the pentagon. The equation for this is Area = pa/2, with p being the perimeter and a being the apothem (2.75in). The perimeter is 4*5, since there are five sides and one of them is four inches. This means the perimeter is 20 inches. Back to the equation, 20*2.75 = 55. 55/2 = 27.5in^2.

Next, multiply by the height. This shape’s height is 3 inches. 27.5*3 = 82.5.

The volume is 82.5 in^3
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