How do you plot or graph a quadratic inequality in a number line?
Answers
A quadratic inequality of the form
y>a[tex]x^{2}[/tex]+bx+c
(or substitute <,≥ or ≤ for > ) represents a region of the plane bounded by a parabola
A quadratic inequality of the form
y>a[tex]x^{2}[/tex]+bx+c
(or substitute <,≥ or ≤ for > ) represents a region of the plane bounded by a parabola .
To graph a quadratic inequality, start by graphing the parabola. Then fill in the region either above or below it, depending on the inequality.
If the inequality symbol is ≤ or ≥ , then the region includes the parabola, so it should be graphed with a solid line.
Otherwise, if the inequality symbol is < or > , the parabola should be drawn with a dotted line to indicate that the region does not include its boundary.
Example:
Graph the quadratic inequality.
y≤[tex]x^{2}[/tex]−x−12
The related equation is:
y=[tex]x^{2}[/tex]−x−12
First we notice that a , the coefficient of the [tex]x^{2}[/tex] term, is equal to 1 . Since a is positive, the parabola points upward.
The right side can be factored as:
y=(x+3)(x−4)
So the parabola has x -intercepts at −3 and 4 . The vertex must lie midway between these, so the x -coordinate of the vertex is 0.5 .
Plugging in this x -value, we get:
y=(0.5+3)(0.5−4)
y=(3.5)(−3.5)
y=−12.25
So, the vertex is at (0.5,−12.25) .
We now have enough information to graph the parabola. Remember to graph it with a solid line, since the inequality is "less than or equal to".
To learn more about quadratic inequality:
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Related Questions
5-3x=2
What is x equals to?
Explain too please.
Answers
x=1
Explanation:
-3x+5=2 subtract 5 on both sides to get -3x=-3 divide -3 from -3 to get 1
the polynomial 3x+5 is divided by x+2 what is the quotient, pls be quick im taking a algebra progress check due in 25 min
Answers
Answer:
The quotient of the rational function is [tex]3 -\frac{1}{x+2}[/tex].
Step-by-step explanation:
We proceed to solve the expression by solely algebraic means below:
1) [tex]\frac{3\cdot x + 5}{x+2}[/tex] Given
2) [tex]\frac{(3\cdot x + 5) + 0}{x + 2}[/tex] Modulative property
3) [tex]\frac{(3\cdot x +5) + [1+(-1)]}{x+2}[/tex] Existence of additive inverse/Associative property
4) [tex]\frac{(3\cdot x + 6)+(-1)}{x+2}[/tex] Definition of addition/Commutative and associative properties
5) [tex]\frac{3\cdot (x+2)}{x+2} + \left(-\frac{1}{x+2} \right)[/tex] [tex]\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}[/tex]/ [tex]\frac{-a}{b} = \frac{a}{-b} = -\frac{a}{b}[/tex]/Distributive property
6) [tex]3 -\frac{1}{x+2}[/tex] Definition of division/Existence of multiplicative inverse/Modulative property/Definition of subtraction/Result
The quotient of the rational function is [tex]3 -\frac{1}{x+2}[/tex].
At Lake Clay, marine biologists catch,
tag, and release 50 smallmouth bass.
Over the next few days, they catch 175
smallmouth bass, of which 7 have the
original tags. What is the estimated
population of smallmouth bass in Lake
Clay?
Answers
Step-by-step explanation:
Answer from: Quest
the answer is thin because within context, the stanza concludes the and frail tone the people have toward each other, and the fact that it would be thin, makes the most sense compared to "pliable" or "not hard or firm to the touch". hope this , good luck.
step-by-step explanation:
can i have brainliest
Plz help me out it would be a life time
Answers
Answer:
a= 3 w- 1
Step-by-step explanation:
Answer:
A=12[tex]u^{2}[/tex]
Step-by-step explanation:
A=bh/2
A=(4)(6)/2
i really need help asap!!
Answers
Given:
A figure of a parallelogram.
The vertex angles are [tex](12b+8)^\circ,(5b+2)^\circ,2a^\circ[/tex].
To find:
The values of a and b.
Solution:
We know that the pairs of consecutive angles of a parallelogram are supplementary angles. It mean their sum is 180 degrees.
[tex](12b+8)^\circ+(5b+2)^\circ=180^\circ[/tex] (Supplementary angles)
[tex](17b+10)^\circ=180^\circ[/tex]
[tex]17b+10=180[/tex]
Subtract 10 from both sides.
[tex]17b=180-10[/tex]
[tex]17b=170[/tex]
Divide both sides by 17.
[tex]b=\dfrac{170}{17}[/tex]
[tex]b=10[/tex]
Now,
[tex](5b+2)^\circ=(5(10)+2)^\circ[/tex]
[tex](5b+2)^\circ=(50+2)^\circ[/tex]
[tex](5b+2)^\circ=52^\circ[/tex]
And,
[tex](5b+2)^\circ+2a^\circ=180^\circ[/tex] (Supplementary angles)
[tex]52^\circ+2a^\circ=180^\circ[/tex]
[tex]2a^\circ=180^\circ-52^\circ[/tex]
[tex]2a^\circ=128^\circ[/tex]
Divide both sides by 2.
[tex]a^\circ=\dfrac{128^\circ}{2}[/tex]
[tex]a^\circ=64^\circ[/tex]
[tex]a=64[/tex]
Therefore, the value of a is 64 and the value of b is 10.
Item 5
How many meters are in 8 kilometers?
80 meters
800 meters
8,000 meters
80,000 meters
Answers
yesh plesse help me eith this im dyinggg
Answers
I NEED HELP ASAP!!!
**Ignore the theorem portion above. Answer the angle measure questions, rounding all answers to the nearest tenth***
Answers
Answer:
SVU = 90
TUV = 65
Step-by-step explanation:
Answer:
sorry if it's messy, I tried my best even though I'm not sure for ST.
what is equivalent to 5,710,900 in scientific notation
Answers
(C) A bakery sells 9 types of sandwiches. Here are their calorie amounts: 562.568. 590. 599. 611.621. 623. 641, 938. Which measure should be used to summarize the data? A-Mean B-Median C-Mode
Answers
Answer:
611
Step-by-step explanation:
The mean is 632.9 which is a lot higher than 611, and is actually higher than the penultimate value 632, and if presented as a general single value, it may mislead customers into thinking that the sandwiches have a high calorific value. We don’t know how many sandwiches of different types there are, and there may only be a few with high values. So I would use the median 611 as a typical value for the number of calories.
25a9 ÷5a
??????????????????????????
Answers
Answer:
[tex]5a^8[/tex]
Step-by-step explanation:
[tex]\frac{25a^9}{5a}[/tex]
[tex]=5a^8[/tex]
PLEASE HELP I WILL GIVE BRAINLIEST
Suppose that z varies jointly with x and y. When x = 2, y =2 and z = 7
3) Write the equation that models the relationship
4) Find 7 when x - 4 and y 8
Answers
what is 5+21 and 54+1
Answers
Answer:
26 and 55
Step-by-step explanation:
Answer: 5+21 = 26 and 54+1=55
Step-by-step explanation: You add 21 + 5, to get 26. same for the other.
Help needed!
The photo attached is the question :)
Answers
Answer:
x = 90°
Step-by-step explanation:
This is very simple. Any triangle embedded in a circle with it's long side as the diameter is a right triangle. Thus, x = 90°.
use long division to rewrite the following expression. write your answer in the format of q(x) + r(x) / b(x)
/|\
|
(that's a fraction)
Answers
Hello!
Here we are given a long division question.
The first thing I would do is see how many times the term of the highest degree in the divisor could go into the term of the highest degree in the dividend, which would be 3.
Then, we could already see that the divisor's degree would be higher than that of the dividend, so the rest would go in the remainder over the divisor.
[tex]\frac{18x^2+5x+5}{6x^2-4x+1}[/tex]
[tex]3+\frac{17x+2}{6x^2-4x+1}[/tex]
Hope this helps!
Answer:
This is it trust me
Step-by-step explanation:
I just took it and got a 100
please help, i will give brainliest
Answers
Answer:
13. (E) all of the above 14. (E) the diagonals bisect the angles at the vertices
Step-by-step explanation:
Due soon helppp no links pls
Answers
Answer:
A = 28.26
C = 18.84
Step-by-step explanation:
A = [tex]\pi r^{2}[/tex]
C = 2[tex]\pi r[/tex]
A = 3.14 x 3 x 3 = 28.26
C = 2 x 3.14 x 3 = 18.84
Let me know if this helps!
............... help me please i don’t understand this
Answers
Answer:
x = 11
Step-by-step explanation:
Tracy rode her mountain bike 2 ⅘ miles on Monday. She rode
2 7/10 miles on Tuesday. On which day did she ride a longer distance?
Answers
Answer:
Monday
Step-by-step explanation:
please mark me brainliest
An IceBerg has 1/9 of its volume above the water. If an IceBerg has 360 cubic meters below the water, how many cubic meters are above the water.
Answers
hello
i think so...
hope it helps
have a nice day
write an equation for the number 40 is 5 times as many as 8 please hurry
Answers
Answer:
5x8=40
Step-by-step explanation:
The profits of two different manufacturing plants can be modeled as shown. Where x is the number of units produced at each plant.
Plant 1 : P1 (x) = -0.03x^2 + 25x - 1500
Plant 2 : P2 (x) = -0.02x^2 + 21x - 1700
Find polynomials representing the difference in profits between the companies. Find P1(x) - P2 (x) and P1 (x). Compare the two differences and draw conclusions. Show work and make a equation
Answers
P1(x) - P2(x) = -0.01x² + 4x + 200
This shows that P1(x) profit is less than P2(x).
P2(x) - P1x = 0.01x² - 4x - 200
This shows that P2(x) profit is more than P1(x).
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
Plant 1:
P1 (x) = -0.03x² + 25x - 1500
Plant 2:
P2 (x) = -0.02x² + 21x - 1700
P1(x) - P2(x):
= -0.03x² + 25x - 1500 - (-0.02x² + 21x - 1700)
= -0.03x² + 25x - 1500 + 0.02x² - 21x + 1700
= -0.01x² + 4x + 200
For any x value, we will get a negative value.
This means,
P1(x) profit is less than P2(x).
P2(x) - P1x:
= -0.02x² + 21x - 1700 - (-0.03x² + 25x - 1500)
= -0.02x² + 21x - 1700 + 0.03x² - 25x + 1500
= 0.01x² - 4x - 200
For any x value, we will get a positive value.
This means,
P2(x) profit is more than P1(x).
Thus,
P1(x) - P2(x) shows that P1(x) profit is less than P2(x).
P2(x) - P1x shows that P2(x) profit is more than P1(x).
Learn more about polynomials here:
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A biologist is comparing the growth of a population of flies per week to the number of flies a lizard will consume per week. She has devised an equation to solve for which day (x) the lizard would be able to eat the entire population. The equation is 7x = 3x + 4.
Explain to the biologist how she can solve this on a graph using a system of equations.
Answers
Answer:
(-1.307, 0.079), (1, 7)Step-by-step explanation:
Given equation:
7ˣ = 3x + 4To solve this, express each side of the equation as different function and find the intersection of graphs of those functions:
y = 7ˣy = 3x + 4As per graph, the solution is:
(-1.307, 0.079), (1, 7)Break into two parts
y=3x+4y=7^xNow graph and find the solution
Helpp! Pls. I am desperate i will mark brainliest
Answers
It’s the only choice that is absolute, the others are only possible but not be true.
Please help, i will give each 10 points if it’s correct :)
Answers
Answer:
1080
Step-by-step explanation:
Answer:
90 Cubic Inches
Step-by-step explanation:
I believe that the answer is 90 because Volume is calculated by doing Length x Width x Height (X is Multiplication) so if you multiply 10 x 6 x 1.5 which would end up with the end result of 90. If you find any fault in my answer please let me know. Thanks. Have a good day!
Which of these four sets of side lengths will form a right triangle?
Answers
Can someone please help my son on his work he broke both of his arms in a car crash please
Answers
Answer:
https://brainly.com/question/23106827?answeringSource=feedPublic%2FhomePage%2F4
Step-by-step explanation:
Please help me out :D
Answers
Answer:
384 cubic inches
Step-by-step explanation:
For this problem, we simply need to apply the volume formula for a box. The volume is length times width times height.
We are given length = 12 inches
We are given width = 8 inches
We are given tall(height) = 4 inches
So let's Calculate the volume.
Volume = Length * Width * Height
Volume = 12 inches * 8 inches * 4 inches
Volume = 384 cubic inches
Hence, the volume of the box is 384 cubic inches.
Cheers.
Use 3. 14 as an approximation for pie.
Which is the circumference of a plate with a radius of 5 cm?
Answers
Answer:
D
Step-by-step explanation:
Express the following ratio as a fraction in simplest form.
$32 for 10 tickets
Answers
Answer:
$16/5tickets
Step-by-step explanation:
it be in simplest form mate.