solving quadratic inequalities

Solving Quadratic Inequalities

Answers

Answer 1

Answer:

[tex]\boxed{\sf x < -3\quad \mathrm{or}\quad \:x > -1}[/tex]

Step-by-step explanation:

[tex]\sf x^2+4x+3 > \:0[/tex]

In order to solve inequality, we need to factor the left hand side. we can use the transformation [tex]ax^2+bx+c=a(x-x_1)(x-x_2)[/tex] to factor quadratic polynomials. where  x(1) & x(2)  are the solutions of the quadratic equation  ax²+bx+c=0 .

[tex]\sf x^2+4x+3=0[/tex]

Quadratic formula:-

[tex]\boxed{\sf x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}}[/tex]

[tex]\sf a=1\\b=4\\c=3[/tex]

[tex]\sf \cfrac{-4\pm \sqrt{4^2-4\times \:1\times \:3}}{2\times \:1}[/tex] ← Calculate

[tex]\sf \sqrt{4^2-4\times \:1\times \:3}=\boxed{2}[/tex]

[tex]\sf \cfrac{-4\pm \:2}{2\times \:1}[/tex]

Now, let's Separate the solutions,

[tex]\sf x_1=\cfrac{-4+2}{2\times \:1},\:x_2=\cfrac{-4-2}{2\times \:1}[/tex]

Do the calculations,

[tex]\sf x_1=\cfrac{-4+2}{2\times \:1}=\boxed{-1}[/tex]

[tex]\sf x_2=\cfrac{-4-2}{2\times \:1}=\boxed{-3}[/tex]

[tex]\boxed{\sf x < -1\quad \mathrm{or}\quad \:x > -3}[/tex]


Related Questions

Triangle EFG has an area of 70 m².

EF: FG= 1:2 and angle EFG = 40°.

(a) Calculate EF.

Answers

The measure of length EF is the triangle EFG has an area of 70 m² is 7.38m

How to calculate the area of a triangle?

A triangle is a 2-dimensional shape with 3 sides and angles. The formula for calculating the area of a triangle is expressed as:

A = (EF)(FG) sin theta

If the ratio of EF to FG is 1:2, then FG = 2EF
A = (EF)(2EF) sin theta
70 = 2EF²sin40
70 = 1.2856EF²
EF² = 54.474
EF = 7.38m

Hence the measure of length EF is the triangle EFG has an area of 70 m² is 7.38m

Learn more on area of triangle here: https://brainly.com/question/17335144

Find the perimeter of the isosceles triangle with points A (0,0); B (3,3); and C (6,0)

Answers

Answer:

3+3+6=12

Step-by-step explanation:

the sides are both3 and bottomed is 6

Charles bought 11 bottles of juice for $22.33. What is the unit rate?

Answers

$2.03. The unit rate is the price of one bottle of juice. To solve this simply divide $22.33 by 11.

The function h(x) = x2 +3 and g(x) = x2 – 6. If g(x) = h(x) + k, what is the value of k?

Answers

Answer:

g(x) = x² - 6

h(x) = x² + 3

   g(x) = h(x) + k

 x² - 6 = (x² + 3) + k

 x² - 6 = x² + 3 + k

- x²       - x²

     -6 = 3 + k

    - 3  - 3

     -9 = k

The value of k is -9.

Step-by-step explanation:

MathPapa.com

How many possible outcomes exist when two fair coins are flipped and a three-section spinner is spun? a penny.a penny. a spinner with 3 equal sections labeled 1 through 3. 3 6 7 12

Answers

Answer:

12

Step-by-step explanation:

What other situations can you think of where you gain or lose an amount that you could use negative
numbers to talk about? What would positive and negative changes mean in those situations?

Answers

Answer:

it would mean that the anwser is positive

Step-by-step explanation:

which is a proportional relationship

Answers

Answer:

Proportional relationships are relationships between two variables where their ratios are equivalent.

So if one of your answers have equivalent ratios, that is your answer

Find the equation of the line shown

Answers

y=x+1.
Explanation: The equation for any straight line graph is y=mx+c where m is the gradient and c is the y-intercept. To find the gradient you have to do the change in y divided by the change in x. So it’s 1. The y-intercept is where the line crosses the y axis so in this graph it’s 1.

if i got paid 10 dollars an hours and wrk for 7 hours a day how much would i make a week including mon-fri. but got in a car crash and died how much would my bill be to pay.

Answers

Hii.

So first, lets caculate how much you get in one day

-------------------------------------------------------------------------------------------

In one day..

10x7= 70$

So, in one day you make 70$.

-------------------------------------------------------------------------------------------

Since we make 70$ in one day, we need to find out if we worked all week.

70x7 = 490$

So in one week,we make $490.

~NatLikesAnime~

x is directly proportional to the square of y.
.
y is directly proportional to the cube of z.
z= 2 when x = 32
Find a formula for r in terms of z.

Answers

The direct variation of x to y implies that x and y increases at the same time, and the formula of x in terms of z is [tex]x = 4z^3[/tex]

How to determine the formula for x?

The direct proportion of x to y is represented as:

[tex]x\ \alpha\ y^2[/tex]

As an equation, we have:

[tex]x\ =\ ky^2[/tex]

The direct proportion of y to z is represented as:

[tex]y\ \alpha\ z^3[/tex]

As an equation, we have:

[tex]y\ =\ kz^3[/tex]

Square both sides

[tex]y^2 = k^2z^3[/tex]

Substitute [tex]y^2 = k^2z^3[/tex] in [tex]x\ =\ ky^2[/tex]

[tex]x =k^3z^3[/tex]

When z = 2, x = 32.

So, we have:

[tex]32 =k^3 * 2^3[/tex]

Evaluate

[tex]32 =k^3 * 8[/tex]

Divide both sides by 8

[tex]k^3 =4[/tex]

Substitute [tex]k^3 =4[/tex] in [tex]x =k^3z^3[/tex]

[tex]x = 4z^3[/tex]

Hence, the formula of x in terms of z is [tex]x = 4z^3[/tex]

Read more about direct variation at:

https://brainly.com/question/6499629

If 1 - cosA= 1/2 show that tan²A + 4sin²A = 6​

Answers

[tex]\text{Given that,}\\\\1-\cos A = \dfrac 12\implies \cos A = 1-\dfrac 12 = \dfrac 12\\\\\text{L.H.S}\\\\=\tan^2 A + 4 \sin^2 A\\\\=\dfrac{\sin^2 A}{\cos^2 A}+4(1-\cos^2 A)\\\\\\=\dfrac{1-\cos^2 A}{\cos^2 A} +4-4\cos^2 A\\\\\\=\dfrac{1-\left( \dfrac 12 \right)^2 }{\left(\dfrac 12 \right)^2 } +4 -4 \left( \dfrac 12 \right)^2\\\\\\=\dfrac{1- \dfrac 14}{\dfrac 14}+4-4\cdot \dfrac 14\\\\\\=\dfrac{\tfrac 34}{\tfrac 14}+4-1\\\\\\=\dfrac 34 \cdot 4 +3\\\\=3+3\\\\=6\\\\=\text{R.H.S}[/tex]

please help i need help

Answers

Answer:  

[tex]\mathrm{Slope = \dfrac{1}{2}}[/tex]

Step-by-step explanation:

To find the slope of a graph, we use the formula below:

[tex]\mathrm{m =\dfrac{y\x_{2}-y\x_{1}}{x\y_{2}-x\y_{1}}}[/tex]

m = slope

(x1, y1) = coordinates of first point in the line

(x2, y2) = coordinates of second point in the line

Step 1: Find any two points on the line

Lets choose: (0, 3) and (2, 4)

Step 2: Put these points into the slope formula

[tex]\mathrm{m =\dfrac{y\x_{2}-y\x_{1}}{x\y_{2}-x\y_{1}}}[/tex]

Step 3: Substitute points into formula

[tex]\mathrm{m =\dfrac{4-3}{2-0}}[/tex]

Step 4: Subtract 3 from 4 and 0 from 2

[tex]\mathrm{m =\dfrac{1}{2}}[/tex]

----------------------------------------------------------------------------------------------------------

Another way you could easily do this is:

Step 1:  Find two ponts on the line

For this problem, let's use (0, 3) and (2, 4)

Step 2: Then from the first point, how much do you need to go up and to the left or right to get to the second point

For this problem, we start on the on the point (0, 4) and go up by 1 and then to the right by 2

Step 3: Then you do rise over run to get the slope

The slope is rise over run:

Rise = 1

Run = 2

So, the slope is 1/2

________________________________________________________[tex]\mathrm{Answer:\dfrac{1}{2}}[/tex]                                                                                                                     ----------------------------------------------------------------------------------------------------------    

3x^2=4x+3 Solve using quadratic formula

Answers

Answer:

x = 2-√13/3

Step-by-step explanation:

Mary made $144 for 8 hours of work.
At the same rate, how much would she make for 12 hours of work?

Answers

Answer:

$216

Step-by-step explanation:

Find how much Mary made per hour by dividing 144 by 8 to get 18. Then, multiply that number by 12 which $216

Answer:

$216

Step-by-step explanation:

First, find out what Mary makes every hour. To find this, we divide 144 by 8.

144/8 = $18

This means that Mary makes $18 per hour.

Now, we find out how much Mary would make if she worked for 12 hours:

x = # of hours worked

18n

18(12)

$216

Therefore, Mary would make $216 in 12 hours.

Hope this helps!

Please help me with this math problem!! Will give brainliest! :)

Answers

Answer:

I believe it is 6 but I'm not sure

Step-by-step explanation:

Sorry I am unsure

Step-by-step explanation:

the function for x≥—1 is x²—3

so f(3) = 3²—3=9—3=6

A cylinder has a height of $10$ and a radius of $3.$ Determine the total surface area, including the two ends, of the cylinder.

Answers

Check the picture below.

[tex]\textit{surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=10 \end{cases}\implies \begin{array}{llll} SA=2\pi (3)(10+3) \\\\\\ SA=6\pi (13)\implies SA=78\pi \\\\\\ SA\approx 245.04 \end{array}[/tex]

Answer:

[tex]78\, \pi[/tex].

Step-by-step explanation:

A cylinder of height [tex]h[/tex] and radius [tex]r[/tex] could be unrolled into:

two identical circles, one for the top and one for the bottom, andone rectangle, for the side.

The radius of each circle is the same as the radius of the cylinder, [tex]r[/tex].

The height of the rectangle is the same as the height of the cylinder, [tex]h[/tex].

The width of this rectangle would be [tex](2\, \pi\, r)[/tex], same as the circumferences of the two circles. The reason is that when this rectangle is rolled to build the cylinder, the top and bottom edges of the rectangle would wrap around the circumference of the two circles.

The area of each circle would be [tex]\pi\, r^{2}[/tex]. Note that there are two such circles, one at the top of the cylinder and one at the bottom.

With a height of [tex]h[/tex] and a width of [tex](2\, \pi\, r)[/tex], the area of the rectangle on the side would be [tex](2\, \pi\, r)\, h[/tex]. Add these areas up to find the total surface area of this cylinder:

[tex]\begin{aligned}& \text{(Surface Area of the Cylinder)} \\ =\; & (\text{Surface area of circle on the top}) \\ & + (\text{Surface area of circle at the bottom}) \\ & + (\text{Surface area of rectangle on the side}) \\ =\; & \pi\, r^{2} + \pi\, r^{2} + (2\, \pi\, r)\, h \\ =\; & 2\, \pi\, r^{2} + (2\, \pi\, r)\, h \end{aligned}[/tex].

For the cylinder in this question, [tex]h = 10[/tex] whereas [tex]r = 3[/tex]. The surface area of this cylinder would be:

[tex]\begin{aligned}& 2\, \pi\, r^{2} + (2\, \pi\, r) \, h \\ =\; & 2 \,\pi \times 3^{2} + (2\, \pi\times 3) \times 10 \\ =\; & 78\, \pi\end{aligned}[/tex].

Which expression represents the volume of the prism? x(x – 2) cubic units x(x 1) cubic units x2(x – 2) cubic units x2(x 1) cubic units

Answers

The expression that represents the volume of the prism is x²(x-2).

Given side of the base =[tex]x[/tex]

So, the area of the base =[tex]x^{2}[/tex]

Given the height of the prism = [tex]x-2[/tex]

What is the volume of the prism?

The volume of the prism with base area A and height h is Ah.

So, the volume of the given prism with the base area [tex]x^{2}[/tex] and height [tex](x-2)[/tex] will be:

V= [tex]x^{2} *(x-2)[/tex]

V= [tex]x^{2} (x-2)[/tex]

Hence, the expression that represents the volume of the prism is x²(x-2).

To get more about prisms visit:

https://brainly.com/question/23963432

Answer:

its C trust me

Step-by-step explanation:

Nevaeh has 840 pictures saved on her laptop. Of these
pictures, 20% are nature, 45% are fashion, and the rest
are food. How many pictures in Nevaeh’s computer
are food?

Answers

Answer:

40%

Step-by-step explanation:

20+45=60

100-60=40

10x -3 = -33

please help lol

Answers

Answer:

-3

Step-by-step explanation:

10x=-33+3 isolate the variable

10x=-30 divide by 10

X=-3

Answer:

x=-3

Solution:First, add 3 to both sides:10x-3=-3310x=-33+310x=-30Now, divide both sides by 10:x=-3The value of x=-3

Hope it helps.

Do comment if you have any query.

Please help me with this one to (PLEASE NO LINKS)

Yvette spins the following spinner 35 times.

A spinner with 5 equal sections labeled 1 through 5.

How many times should she expect it to land on 4?
Enter your answer as a number, like this: 42

Answers

Answer:
7

Step-by-step explanation:

because if you spinned it , it has a 1/5 chance, if we divide 35 by 5 we can see its 7 meaning she could exect a average of 7 spins.

Katrina's ski boots cost 8% more than
her skis. Her ski boots cost $162. Which
equation can be used to find the cost, c,
of Katrina's skis?
I need pls!!

Answers

I am not sure about my answer.But I guess it may be correct.Hope the picture will help you..

Miguel cabrera has had 369 at bats, and he has 127 hits and 21 home runs. (note: the home runs are included in the hits data.) if he is challenged to a batting battle, what is the expected score of each at bat if he earns 1 point for each hit that is not a home run and 5 points for each home run?

Answers

The expected score of each at bat if he earns 1 point for each hit that is not a home run and 5 points for each home run is 0.57

What is probability?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.

Number of bats = 369

Number of hits = 127

Number of home runs = 21

The probability of a hit:

[tex]=\frac{127}{369}[/tex]   (includes home run)

The probability of home run:

[tex]=\frac{21}{369}[/tex]

The probability of hit run(without home run)

[tex]=\frac{127}{369}-\frac{21}{369}[/tex]

[tex]=\frac{106}{369}[/tex]

The probability of no hit:

[tex]=\frac{369-127}{369}[/tex]

[tex]=\frac{242}{369}[/tex]

For home run, the score will be 5 points.

If not, a home run score will be 1 points.

If Miguel does not get hit, score will be zero point.

Expected value of Miguel hit at each bat is (without home run):

For 5 hit:

[tex]=\frac{106}{369}[/tex]

For 21 home runs, the points will be 21×5 = 105  (5 points for each home run)

The expected value for this:

[tex]\frac{105}{369}[/tex]

Adding both expected hits, we get:

[tex]=\frac{106}{369}+\frac{105}{369}[/tex]

[tex]=\frac{211}{369}[/tex]

= 0.571 ≈ 0.57

Thus, the expected score of each at bat if he earns 1 point for each hit that is not a home run and 5 points for each home run is 0.57

Learn more about the probability here:

brainly.com/question/11234923

Answer:

0.57

Step-by-step explanation:

Section 1
Variability
Which of the following survey question yields data with
Variability? Write Y for yes or N for no.
1) How many bananas did Joe eat yesterday?
2) What is the population of Austin, Texas?
3) What kind of sandwiches does your class like?
4) What is the name of your teacher?
5) How much do televisions cost?
Unlock section 1 by finding the code.
Instructions: Write the answers in order for #1-5. Write Y for yes and
N for no. Use all capitals and no spaces. For example: YYYNN
TA

Answers

Answer:

1) Y

2) Y

3) N

4) N

5) N

steps

1) How many bananas did Joe eat yesterday?

The word "many" tells you that its talking about variability.

2) What is the population of Austin, Texas?

The phrase "What is the population..." tells you that its talking about variability.

3) What kind of sandwiches does your class like?

Doesn't talk about variability.

4) What is the name of your teacher?

Doesn't talk about variability.

5) How much do televisions cost?

Doesn't talk about variability.

(YYNNN)

A town's yearly snowfall in inches over a 10-year period is recorded in this table.

What is the mean of the snowfall amounts?

Answers

18.8
hope this helps :)

Answer:

18.9

Step-by-step explanation:

what’s the slope of those? please help

Answers

Answer:

8 is 5/2, 9 is an undefined slope

Step-by-step explanation:

8 rise 5 and runs 2 and 9 is a vertical line so there is no slope meaning its undefined.

X-
On a piece of paper, graph y+4<3x – 1/2x - 2. Then determine which answer
choice matches the graph you drew.
A
B
C
D


6
-10
5
(4.-4)
(4.-4)
(4.-4)
(4.-4)
(0.-6)
(0.-6)
6.
(
0-6)
0.-6)
O A. Graph A
B. Graph B
C. Graph
D. Graph D

Answers

Answer:

c

[tex]6.46 \geqslant \frac{ { {x \sqrt[ |)x \frac{ {?}^{?} }{?} | ]{?} }^{?} }^{2} }{?} [/tex]

d

The graph of the inequality is attached to the solution.

What is graph?

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Given is an inequality, y+4 < 3x - 1/2x - 2, we need to graph it,

This graph represents inequality y+4 < 3x - 1/2x - 2,

Learn more about graph,

brainly.com/question/16608196

#SPJ7

What is the domain of the function h(x) = 4 log2 (x - 6) +1?​

Answers

The domain of the function h(x) = 4·㏒₂(x - 6) + 1, using interval notation is (6, ∞)

What is the domain of a function?

The domain of a function is the set of the possible input values of the function, which is denoted as dom(f).

The domain of the function f: X → Y, is defined as the values of X

The given function is; h(x) = 4·㏒₂(x - 6) + 1

The domain of a function is the set of the possible input (x-values) of the function.

The values which the function ㏒₂(x - 6) can have as input, which is the domain of the function, ㏒₂(x - 6) is; 0 < x - 6 < ∞

Which gives: 6 < x < ∞

The domain of the function, h(x) = 4·㏒₂(x - 6) + 1 is 6 < x < ∞, which using interval notation is (6, ∞)

Learn more about the domain and range of a function here:

https://brainly.com/question/10197594

#SPJ1

nina ran 6 miles in 49.2 minutes. if she keeps the same pace, how long will it take her to run 13 miles?

Answers

Answer:

106.6 minutes

Step-by-step explanation:

49.2/6 = 8.2

8.2x13 = 106.6

I WILL GIVE BRAINLEIST!!!
Jocelyn participates in three track events: the 200-meter sprint, the 400-meter hurdles, and the 800-meter run. She calculated the mean absolute deviation of her race times throughout the season in each event.

200-meter sprint: mean absolute deviation of 2.05

400-meter hurdles: mean absolute deviation of 2.82

800-meter run: mean absolute deviation of 1.9

In which event were her times the most spread out?


A. 200 meter sprint

B. 800 meter run

C. 400 meter hurdles

Answers

Answer:

ill say C too

Step-by-step explanation:

Answer:The answer is 400

I hope this helps have a great day!

Step-by-step explanation:

PLEASE HELP!!!! HURRY​

Answers

Slope = (y2-y1) / (x2-x1)

So,
(2- (-3)) / (7 - 1)

5/6

Answer:

the sum of 6 and a number g

Other Questions
What sort of case would be held first at a state court?Select one:a. Video game piratingb. Child custody argumentc. Treasond. Bankruptcy declaration Describe the two alternatives for specifying structural constraints on relationship types. what are the advantages and disadvantages of each? The value of -9 is not -3 because _____. A. (-9)^2 -3 B. 9^2 -3 C. 3^2 -9 D. (-3)^2 -9 What year was Nixon up for reelection? A squirrel burled four holes in five minutes how many holes could this world borrow in 15 minutes How does carbon dioxide increase the earths temperature?Answer If material, separate categories of property and equipment should be disclosed in the notes to the financial statements. What category of Dollar Generals property and equipment is the largest at the end of fiscal year 2020 (ending 1/29/2021)? The origin of setting off firecrackers in Chinese New Year Which foods would be classified as fats? (Select all that apply.) no links-vegetables-fruit-dairy-fish-water-nuts how did the Cold War impact American adults and theirdaily lives Please help this is my last time asking these 2 questions I need the correct answers no more fake links pls I need help, I'll give Brainest What is the missing number in the following series?12, 144, 16, ?, 20, 324 How can Microsoft PowerPoint help me in my studies? Which equation accurately represents this statement? Select three options.Negative 3 less than 4.9 times a number, x, is the same as 12.8.Negative 3 minus 4.9 x = 12.84.9 x minus (negative 3) = 12.83 + 4.9 x = 12.8(4.9 minus 3) x = 12.812.8 = 4.9 x + 3 Which of the following reversed the Supreme Court ruling in Dred Scott v Sandford?Question 18 options:The Dawes ActThe Fourteenth AmendmentThe Compromise of 1877The Kansas-Nebraska Act Guys please help questions 7-8-9-10 are also on my page please!! An individual who comes from a violent family or lives in a culture that condones intimate partner violence experiences ________ on violence. Each equation represent a proportional relationship. Choose the equation for which the constant of proportionality is 4/5 The Liquid TransmitterIt was March 10, 1876. Alexander Graham Bell stared down at this latest device. It was called the liquid transmitter. The 29-year-old inventorhoped it would not be called a failure, but the odds weren't good. He had been working on his device for few years now, but he had notsucceeded yet. In the meantime, Samuel Morse's telegraph was extremely popular. What if the idea of sending voices was impossible?Nevertheless, Bell went ahead with the plan. He stared at his liquid transmitter and said into it, "Mr. Watson, come here-I want you."From down the hall, 22-year-old Thomas Watson stood wide-eyed over the device. He could not believe it! Was it possible? Had he imaginedit? Watson had heard every word-crisp and clear-come out of the liquid transmitter in front of him. This was one of the most amazing momentsof Watson's young life. He and Bell had actually invented a device that could send the human voice across distances! The impossible had becomepossible in an instant, and that meant that the possibilities were endless.Which statement best describes how the author introduces Watson to the reader? 1. The author defines the relationship between Watson and Bell. 2. The author emphasizes Watson's role in a successful outcome. 3. The author focuses on Watson's reaction to the events that take place.O 4. The author creates a contrast between the personalities of Watson and Bell.