Resolver las siguientes inecuaciones cuadráticas y presentar el conjunto solución en forma de intervalo y gráficamente. 1) X2 < 10 – 3x 2) 2x2 + 3x ≥ 2
Answers
Respuesta:
1) (-5,2)
2) [tex](-\infty,-2]U(\frac{1}{2},\infty)[/tex]
Explicación paso a paso:
1)
[tex]x^{2}<10-3x[/tex]
Para comenzar este problema, debemos moverlo todo al lado izquierdo de la inecuación, por lo que obtenemos:
[tex]x^{2}+3x-10<0[/tex]
Ahora podemos factorizar el lado izquierdo para obtener:
[tex](x+5)(x-2)<0[/tex]
Ahora podemos cambiar el símbolo < por un = para encontrar los valores de x en los cuales la inecuación es igual a cero.
(x+5)(x-2)=0
Y luego despejamos x.
x+5=0
x=-5
y
x-2=0
x=2
Ahora construimos nuestros intervalos posibles.
[tex](-\infty,-5)[/tex]
(-5,2)
y
[tex](2,\infty)[/tex]
Y escogemos algunos valores de prueba. Estos nos ayudarán a determinar si cada intervalo hace que la inecuación sea verdadera o falsa.
[tex](-\infty,-5)[/tex]
Para este intervalo escojamos -6 y evaluemoslo en la inecuación.
(x+5)(x-2)<0
(-6+5)(-6-2)<0
(-1)(-8)<0
8<0
falso, así que este intervalo no es parte de nuestra respuesta.
(-5,2)
para este escojamos x=0 y probémoslo en la inecuación.
(x+5)(x-2)<0
(0+5)(0-2)<0
(5)(-2)<0
-10<0
verdadero, así que este intervalo es parte de nuestra respuesta.
[tex](2,\infty)[/tex]
Para este escojamos 3 y probémoslo en unestra inecuación.
(x+5)(x-2)<0
(3+5)(3-2)<0
(8)(1)<0
8<0
falso, así que este intervalo no es parte de nuestra respuesta.
así que nuestra respuesta es: (-5,2)
Vea imagen adjunta para representación gráfica.
2)
[tex]2x^{2}+3x\geq2[/tex]
Para resolver este problema, comenzamos moviéndolo todo al lado izquierdo de la inecuación.
[tex]2x^{2}+3x-2\geq0[/tex]
Ahora podemos factorizar el lado izquierdo de la inecuación para obtener:
[tex](2x-1)(x+2)\geq0[/tex]
Ahora podemos cambién el símbolo ≥ por un símbolop de = para obtener los valores de x que hacen que la inecuación sea igual a 0.
(2x-1)(x+2)=0
y ahora despejamos x.
2x-1=0
[tex]x=\frac{1}{2}[/tex]
y
x+2=0
x=-2
Ahora construimos nuestros intervalos posible.
[tex](-\infty,-2][/tex]
[tex][-2,\frac{1}{2}][/tex]
y
[tex][\frac{1}{2},\infty)[/tex]
Ahora escogemos los valores de prueba correspondientes.
[tex](-\infty,-2][/tex]
para este, escojamos -3 y probémoslo en la inecuación.
[tex](2x-1)(x+2)\geq0[/tex]
[tex](2(-3)-1)(-3+2)\geq0[/tex]
[tex](-7)(-1)\geq0[/tex]
[tex]7\geq0[/tex]
verdadero, así que este intervalo es parte de nuestra respuesta.
[tex][-2,\frac{1}{2}][/tex]
para este, utilicemos 0 como valor de prueba.
[tex](2x-1)(x+2)\geq0[/tex]
[tex](2(0)-1)(0+2)\geq0[/tex]
[tex](-1)(2)\geq0[/tex]
[tex]-2\geq0[/tex]
falso, así que este intervalo no es parte de nuestra respuesta.
[tex][\frac{1}{2},\infty)[/tex]
para este, utilicemos 1 como valor de prueba.
[tex](2x-1)(x+2)\geq0[/tex]
[tex](2(1)-1)(1+2)\geq0[/tex]
[tex](1)(3)\geq0[/tex]
[tex]3\geq0[/tex]
verdadero, así que este intervalo es parte de nuestra respuesta.
Así que nuestra respuesta es la unión entre los dos intervalos que resultaron verdadero, por lo que nuestra respuesta es:
[tex](-\infty,-2]U[\frac{1}{2},\infty)[/tex]
Vea la representación gráfica en la imagen adjunta.
Related Questions
Farmer Dan wants to build a new pen for his pigs using 200 feet of fencing. He wants the pen to be in
the shape of a rectangle with the length being four more than twice the width. What should the
width of the pen be?
Answers
Geeta saves 18% of her monthly salary. If she spends Rs.10250 per month, what is her monthly salary? Please explain by step by step procedure.
Answers
Answer:
Rs.12500
Step-by-step explanation:
18% = saved
100 - 18 = 82%(used salary)
82% = 10250
100% = ?
100 × 10250 = 1025000
1025000 ÷ 82 = Rs.12500
Hey, I need to find the vertex and show work. The equation is down below and photo:
y = x^2 + 4x - 7
The number for the question is 14
Answers
Answer:
this answer for this question
y=833
Answer:
y = x^2 + 4x - 7
y=833
Step-by-step explanation:
brainliest?
3k^2-11k-4=0 solve with quadratic formula
Answers
Evaluate the expression when a = -3. a^2 +6a +8
Answers
Explanation:
-3^2 + 6(-3) + 8
9 + (-18) + 8
-9 + 8
-1
Which is a better estimate for the volume of a shoebox? 5) 4 liters 4 milliliter
Answers
Answer:
4 liters
Step-by-step explanation:
S part of a statistic project, a math class weighed all the children who were willing to participate as shown below.
How many children weighed less than 50 pounds?
Answers
Answer:
18 children weighed less than 50 pounds.
Step-by-step explanation:
Ok, adding into the explanation what the heck this kind of a table is. The "stem" column is the tens place of each of the children's weights. The "leaf" is the ones digit of each of the children's weights. So in the row where the stem is 2, there were 2 kids weighing 23 and 25 pounds.
For your question, we have to add up how many students have a weight with a "stem" less than 5, because that's where 50 pounds starts.
8 + 2 + 5 + 3 = 18 children weighed less than 50 pounds.
I NEED HELP ASAP PLEASE What is the area of this trapezoid? Enter your answer in the box.
Answers
Answer:
A=153
Step-by-step explanation:
Small Base - a=10
Small Base - b=10+7+7=24
Height - h=9
[tex]A=\frac{a+b}{2} h=\frac{9(10+24)}{2}=153[/tex]
buyhvgyhvtyhgv gyhv tyhgvgyhv hgvbnghvghv hgv ghv ghvvhgv ghv find the diameter
Answers
Answer:
The answer is 2 thousand 900 and eight and 33cent = 2,908.33
Answer:
The answer is 2 thousand 900 and eight and 33cent = 2,908.33
Step-by-step explanation:
what integer divided by 6, less eighteen, is negative 22
Answers
Answer: -24
Step-by-step explanation:
[tex]\frac{x}{6} -18 = -22[/tex]
[tex]\frac{x}{6} = -22 + 18[/tex]
[tex]\frac{x}{6} = -4[/tex]
[tex]x= -4*6[/tex]
[tex]x= -24[/tex]
check work
[tex]\frac{(-24)}{6} -18 = -22[/tex]
[tex]-4 -18 = -22[/tex]
[tex]-22 = -22[/tex]
if 20% of a number is 386, what will be 30% of the same number
Answers
if the 20% of a number is 386, what will be 30% of the same number
Answer will be 157
If 20% of a number is 386, 30% of the same number is 579
How to determne the number?Let the number be x.
So,we have:
20% * x = 386
Express 20% as 0.20
0.20 * x = 386
Divide both sides by 0.20
x = 1930
30% of the number is represented as:
30% * 1930
Evaluate the product
30% * 1930 = 579
Hence, 30% of the same number is 579
Read more about percentage at:
https://brainly.com/question/11360390
The image shows the angles formed by a pair of scissors. When the scissors are closed, m∠1 = 0°. As the scissors are opened, the measures of all four angles change in relation to each other.
Describe how the measures change as m∠1 increases from 0° to 180°.
Answers
Angle 3 is a vertical angle of angle 1 and will always be identical to what angle 1 is.
Angle 2 and angle 4 are supplementary angles to angle 1 and will always be the difference between 180 and what angle 1 is.
For example if angle 1 was 45 degrees, angle 3 would also be 45 degrees and angle 2 and angle 4 would be 180-45 = 135 degrees.
A coin is tossed 4 times. Find the probability of getting at 4 tails in a row.
Answers
Answer:
6.25%
Step-by-step explanation:
Each time you flip a coin, there is a 50% probability of it landing on tails. Each time you flip the coin, the 50% gets multiplied by [tex]\frac{1}{2}[/tex].
[tex]\frac{1}{2}[/tex] to the power of 4 is 0.0625. 0.0625 in percentage form is of course 6.25%
A cell phone company expects that every 2 out of 25 cell phones will have some formof defect. At this rate, how many cell phones out of 500 will be expected to have a defect?
Answers
Answer: 40 phones
Step-by-step explanation:
The company expects that every 2 out of 25 phones will have some form of defect.
In percentage terms, this is:
= 2 / 25 * 100%
= 8%
If there are 500 phones therefore, the defected phones would still be the same percentage and the actual number would be:
= 8 % * 500
= 40 phones
I need help with question 18. The answer is53√3 ft^2. But how do I get there?
Answers
Answer:
Hope it helps....
Step-by-step explanation:
Answer:
52√3 ft²
Step-by-step explanation:
sin 60° = (√3) / 2 = h/8
h = 8 x (√3) / 2 = 4√3
cos 60° = 1/2 = a/8
a = 4 b = 15-4 = 11
area = left triangle + right rectangle
area = (4*4√3) / 2 + 11*4√3
= 8√3 + 44√3
= 52√3
What did the magician do when he lost his temper?
Answers
Answer:
He pulled out his hare
Step-by-step explanation:
answer the questions correctly and put them in order
help im in the 6th grade
Answers
Answer:
what do you need help with
Step-by-step explanation:
Find the point of intersection of the lines:
y = 4x + 1 and y = - 2x + 4
Answers
Answer:
(0.5, 3)
Step-by-step explanation:
i used desmos
Find the surface area of the rectangular prism
Answers
Answer:
430 cm squared
Step-by-step explanation:
SA= 2(Length x Base, Base x Height, Height x Length)
15cm x 5cm +
15cm x 7xm +
7cm x 15cm =
215cm
215cm x 2 = 430 cm squared.
(it's perimeter of a 3D object so it must be squared, then volume would be cubed)
I hope this helps <3
High Points!!!
Which of the following tables best represents the relationship between p and f in the equation p = 3.5f?
Answers
Answer:
A
Step-by-step explanation:
what is ( 17 + 21 ) - 5 x 3 + 2
Answers
Mark sold x pens for $2 each. He received less than $80 from the sale. a. Write an inequality for the number of pens sold.
Answers
Answer:
x <40
Step-by-step explanation:
The income from the pens is 2*x
He made less than 80
2x <80
Divide each side by 2
2x/2 < 80/2
x < 40
Roberto bought snacks to take to his soccer ball practice. He bought a bag of oranges that were $5.65 and a 12 pack of water bottles. The total cost was $12.13 before tax was added. Which equation could be used to find the cost of each water bottle,b?
A. 12(b+5.65)=12.13
B. 5.65(12+b)=12.13
C. 5.65b+12+12.13
D. 12b+5.65=12.13
whoever answers correctly and first will get a brainly
Answers
Answer:
d
Step-by-step explanation:
please help !! :)))
Answers
Tom earns $36 a week mowing lawns. He spends 1/6 of his earnings on lunch and 1/3 of his earnings on music. He saves the rest. How many dollars does Tom save? Tell how you found the answer.
Answers
Answer:
$18
Step-by-step explanation:
spent = 1/6 + 1/3 = 1/2
1/2 x 36 = $18
Answer :_
18$
●●●●●●●●●●●
Find a quadratic equation whose roots are -3 and 5. NO LINKS PLZ!!!!!
Answers
Answer:
Y = x^2 - 2x - 15
Step-by-step explanation:
You deposit $2500 in an account that pays 3% annual interest compounded continuously. What is the balance in your account after 4 years?
Answers
Answer:
A≈$2819
Step-by-step explanation:
In this case P=$2500, r=3%, t=4
attachment image = question
please answer
Answers
Answer:
In group A, they have at least one 90 degree angle. In Group B, they do not have any 90 degree angles.
If CosA= sqrt 3/2, what is TanA?
Answers
Answer:
√(3)/3
Step-by-step explanation:
cos(A) = adj./hyp.
adj. = √(3) or √(3)/2
hyp. = 2 or 1
use unit circle:
hyp. = 1
adj. = √(3)/2
use pythagorean theorem c² - b² = a²
1² - (√(3)/2)² = 1 - 0.75 = 0.25
a² = 0.25
a = √(0.25)
a = 0.5
tan(A) = opp./adj.
tan(A) = 0.5/(√(3)/2)
tan(A) = 1/√(3)
rationalize
tan(A) = √(3)/3
What is the area of this triangle?
h = 5 in.
b = 6 in.
Answers
Answer:
15 in.
Step-by-step explanation
AREA OF A TRIANGLE= B X H / 2
6 X 5=30
30/2=15