solve 2x^2+5x-3>0 quadratic inequalities
Answers
The solution set of the inequality 2 · x² + 5 · x - 3 > 0 is (- ∞, - 3) ∪ (1 / 2, + ∞).
How to solve a quadratic inequality
Herein we find a quadratic inequality, whose solution set can be found by factoring the expression and determine the interval where the expression is greater than zero. Initially, we use the quadratic formula to determine the roots of the quadratic function:
2 · x² + 5 · x - 3 = 0
x₁₂ = [- 5 ± √[5² - 4 · 2 · (- 3)]] / (2 · 2)
x₁₂ = (- 5 ± 7) / 4
x₁ = 1 / 2, x₂ = - 3
Then, the factored form of the inequality is:
(x - 1 / 2) · (x + 3) > 0
In accordance with the law of signs, we must look for that intervals such that: (i) (x - 1 / 2) > 0, (ii) (x + 3) > 0, (ii) (x - 1 / 2) < 0, (x + 3) < 0. Then, the solution set of the quadratic inequality is:
Inequality form - x > 1 / 2 ∨ x < - 3
Interval form - (- ∞, - 3) ∪ (1 / 2, + ∞)
The solution set of the inequality is (- ∞, - 3) ∪ (1 / 2, + ∞).
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Related Questions
The fraction models below represent two fractions of the same whole: How much of the8음을16
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So 4/5 times 5/8 is 1/2.
A toy rocket is shot vertically into the air from a launching pad 5 feet above the ground with an initial velocity of 32 feet
per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function
h(t)=1612 +32t+5. How long will it take the rocket to reach its maximum height? What is the maximum height?
Answers
Find X of the vertex by using -b/2a
Then take X and plug back into equation for y.
X= time
Y= height
Equation makes a parabola that opens down.
22The value of the hypotenuse in the right triangle shown isinches.14 in48 inFigure not drawn to scale
Answers
SOL
Step 1 :
In this question, we are meant to find the value of
the hypotenuse in the right angle below:
Before, we proceed, we still need to remind ourselves of Pythagoras' theorem,
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
Step 2 :
From the above theorem, we can see that that the two adjacent sides are :
14 inches and 48 inches.
From the principle of Pythagoras' Theorem,
[tex]\begin{gathered} c^2=a^2+b^2 \\ \text{where a = 14 inches} \\ b\text{ = 48 inches} \\ c^2=14^2+48^2 \\ c^2\text{ = ( 14 x 14 ) + ( 48 x 48 )} \\ c^2\text{ = 196 + 2304} \\ c^2\text{ = 2500} \\ \text{square root both sides, we have that :} \\ c\text{ = 50 inches} \end{gathered}[/tex]
CONCLUSION :
The value of the hypotenuse in the Right angle, c = 50 inches.
Given ΔABC with m∠B = 62°, a = 14, and c = 16, what is the measure of A?
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1) Let's sketch this out to better grasp it
2) We can see that there are two legs and two angles (one of them is missing) so let's solve it using the Law of Sines:
[tex]undefined[/tex]Send me Answers for Questions A, B, and C
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Answer: A) 4 B) 30 C) 6
Step-by-step explanation:
For question A, you subtract the highest number and the lowest number (10-6)
For question B, you add all the frequency numbers together
For question C, you use your answer on B and divide it by 5
What is a stem and leaf plot? How is it used and how exactly do i solve one? (an example would be great)
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A stem and leaf plot is a table where each of the data is divided into two parts. The stem, that is the first digit and the leaf is the last digits. Let's say that we have the following set of data.
[tex]10,\text{ 12, 25, 28, 29, 35, 38, 40, 44}[/tex]If we want to make a stem and leaf plot of that data, we first write a column where we place the first digit of each number without repetition, like this:
[tex]\begin{gathered} 1 \\ 2 \\ 3 \\ 4 \end{gathered}[/tex]These are the stems. Now the leaves are the last digit of each number put in order next to the corresponding first digit, like this:
[tex]\begin{gathered} 1\parallel\text{ 0 2} \\ 2\parallel\text{ 5 8 9} \\ 3\text{ }\parallel\text{5 8} \\ 4\text{ }\parallel\text{0 4} \end{gathered}[/tex]Which values are solutions to the inequality below?Check all that apply.√x ≤ 5A. 1B. 18C. -5D. 25E. 24F. 625
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Given the inequality:
[tex]\sqrt[]{x}<5[/tex]We need to solve the inequality to get a range of values for x.
This we can do by finding the square of both sides:
[tex]\begin{gathered} (\sqrt[]{x})^2<5^2 \\ x<25 \end{gathered}[/tex]On checking the options given, we will pick the numbers that are strictly less than 25.
Therefore, the correct options are:
OPTION A
OPTION B
OPTION C
OPTION F
8. Anna withdrew $50 from her checking account. She spent $28 on a pair of shoes. What fraction of her money does Anna have left?
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Explanation:
If she spent $28 of the $50 she withdrew, she now has:
[tex]50-28=22[/tex]$22
The fraction is:
[tex]\frac{22}{50}=\frac{11}{25}[/tex]Answer:
Anna has 11/25 of her money left.
I am struggling with this question. could you help me please??
Answers
Problem
Solution
Let x = age, W= weight the two variables of interest
We have the following probabilities given:
P(x<37) =0.142
P(W< 2500) = 0.051
P(x <37 AND W<2500)= 0.031
And we want the following probability and we can use the total probability rule:
P(x < 37 OR W< 2500) = P(x<37) +P(W< 2500) -P(x<37 AND W<2500)
If we replace we got:
P(x < 37 OR W< 2500)= 0.142+ 0.051- 0.031= 0.162
what property is used to solve this?
4x-3
x=2
4(2)-3
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Hello! I need a little bit of help with this question please. (This information is not from an open test, it is a book as I'm studying for the ASVAB I am going to take later on.)
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Given:
[tex]\sqrt{100}-\sqrt{64}[/tex]To find:
We need to solve this sum and find the final answer
Step-by-step solution:
To solve this problem, we need to know the square root of 100 and 64.
√100 = 10
√64 = 8
[tex]\begin{gathered} =\sqrt{100}-\sqrt{64} \\ \\ =10\text{ - 8} \\ \\ =2 \end{gathered}[/tex]Final answer:
Thus 2 (Option A) is the correct answer.
In an arithmetic sequence with a1=-5 and d=-3, which term is -24?The term -24 is the ___th term of the sequence
Answers
Given:
[tex]\begin{gathered} a_1=-15 \\ d=-3 \\ a_n=-24 \end{gathered}[/tex]To find:
The value of n.
Explanation:
The nth term formula for the arithmetic sequence is,
[tex]a_n=a_1+(n-1)d[/tex]Substituting the given values we get,
[tex]\begin{gathered} -24=-15+(n-1)(-3) \\ -24=-15-3n+3 \\ -24=-3n-12 \\ -3n=-24+12 \\ -3n=-12 \\ n=4 \end{gathered}[/tex]Thus, -24 is the 4th term of the sequence.
Final answer:
The term -24 is the 4th term of the sequence.
compare and contrast the graphs y=2x+1 with the domain {1,2,3,4} and y=2x+1 with the domain of all real numbers
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Comparison of both the graphs y=2x+1 with domain {1,2,3,4} and set of all real numbers is :
Slope =2 , y-intercept =1 and x-intercept = -1/2 is same.
Contrast is range is different:
Range = { 3, 5, 7, 9} for domain {1,2,3,4}
Range = set of all real numbers for domain all real numbers.
As given in the question,
Given function for the graphs are:
y =2x+1
Different domains
Domain ={1,2,3,4}
Domain =All real numbers
Compare with y=mx +c
Slope m =2
For y-intercept put x=0
y=2(0) +1
=1
For x-intercept put y=0
0 =2x+1
⇒x=-1/2
Contrast:
For domain ={1,2,3,4}
Range is :
y = 2(1)+1
=3
y=2(2)+1
=5
y=2(3) +1
=7
y=2(4)+1
=9
Range ={ 3, 5, 7,9}
For domain= all real numbers
Range = set of all real numbers
Therefore, comparison of both the graphs y=2x+1 with domain {1,2,3,4} and set of all real numbers is :
Slope =2 , y-intercept =1 and x-intercept = -1/2 is same.
Contrast is range is different:
Range = { 3, 5, 7, 9} for domain {1,2,3,4}
Range = set of all real numbers for domain all real numbers.
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Please help me with the question below(also please answer the question in a maximum of 5-10 minutes).
Answers
Given that Tom's yard is in the shape of a trapezoid, you know that the formula for calculating the area of a trapezoid is:
[tex]A=\frac{(b_1+b_2)}{2}\cdot h[/tex]Where "h" is the height of the trapezoid and these are the bases:
[tex]\begin{gathered} b_1 \\ b_2 \end{gathered}[/tex]In this case, you can identify that:
[tex]\begin{gathered} b_1=65\text{ }ft \\ b_2=50\text{ }ft \\ h=30\text{ }ft \end{gathered}[/tex]Then, you can substitute values into the formula and evaluate:
[tex]A=\frac{(65\text{ }ft+50\text{ }ft)}{2}\cdot30\text{ }ft[/tex][tex]A=\frac{115\text{ }ft}{2}\cdot30\text{ }ft[/tex][tex]A=\frac{3450\text{ }ft^2}{2}[/tex][tex]A=\frac{3450\text{ }ft^2}{2}[/tex][tex]A=1725\text{ }ft^2[/tex]Hence, the answer is:
[tex]1725\text{ }ft^2[/tex]I need help with this question... it's about special triangles and I need to find y and z.. it should also not be a decimal.
Answers
To find z, consider the right-angled triangle at the botton in the diagram showm
[tex]\begin{gathered} \sin 45\text{ = }\frac{z}{20} \\ z\text{ = 20 }\sin 45 \\ z\text{ = }20\text{ }\times\frac{1}{\sqrt[]{2}} \\ z\text{ = }\frac{20}{\sqrt[]{2}} \\ z\text{ = }\frac{20}{\sqrt[]{2}}\times\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ z\text{ = }\frac{20\sqrt[]{2}}{2} \\ z\text{ = 10}\sqrt[]{2} \end{gathered}[/tex]Let the common base of both triangles be m
[tex]\begin{gathered} \cos 45\text{ = }\frac{m}{20} \\ m\text{ = 20 }\cos 45 \\ m\text{ = }\frac{20}{\sqrt[]{2}} \\ m\text{ = }\frac{20}{\sqrt[]{2}}\times\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ m\text{ = 10}\sqrt[]{2} \end{gathered}[/tex]To find y:
[tex]\begin{gathered} \tan 30\text{ = }\frac{y}{m} \\ \tan 30\text{ = }\frac{y}{10\sqrt[]{2}} \\ \frac{1}{\sqrt[]{3}}=\text{ }\frac{y}{10\sqrt[]{2}} \\ y\text{ = }\frac{10\sqrt[]{2}}{\sqrt[]{3}} \\ y\text{ = }\frac{10\sqrt[]{6}}{3} \end{gathered}[/tex]To find x:
[tex]\begin{gathered} \sin 30=\frac{y}{x} \\ \frac{1}{2}=\frac{10\sqrt[]{6}}{3}\div x \\ \frac{1}{2}=\frac{10\sqrt[]{6}}{3}\times\frac{1}{x} \\ x\text{ = }\frac{20\sqrt[]{6}}{3} \end{gathered}[/tex]On a particular day, the amount of untreated water coming into the plant can be modeled by f(t) = 100 + 30cos(t/6) where t is in hours since midnight and f(t) represents thousands of gallons of water. The amount of treated water at any given time, t, can be modeled by g(t) = 30e^cos(t/2)a) Define a new function, a′(t), that would represent the amount of untreated water inside the plant, at any given time, t.b) Find a′ (t).c) Determine the critical values of this function over the interval [0, 24).
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a)The amount of untreated water inside the plant will be the difference between the difference f(t) - g(t), then, a(t) can be defined as follows:
[tex]a(t)=100+30cos(\frac{t}{6})-30e^{cos(\frac{t}{2})}[/tex]b) the derivative of a(t) is the following:
[tex]a^{\prime}(t)=-5sin(\frac{t}{6})+15sin(\frac{t}{2})e^{cos(\frac{t}{2})}[/tex]c) the critical values of a(t) over the interval [0, 24) are:
[tex]\begin{gathered} t=0 \\ t=6\pi \end{gathered}[/tex]J(-6-2)3-*NWMark this and return2--9-8-7-6-5-4-3-2-3₁ 1 2 3 4 5 61-5737-2-cd-6--7--8-2 do-9--10--11--12--13-8 9 10 11 xK(8,-9)What is the x-coordinate of the point that divides thedirected line segment from J to K into a ratio of 2:5?X == (m²²7 m )(x₂ − ×₁) + X₁m+n0 000-22Save and ExitNextSubmit
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Use the given formula:
[tex]x=(\frac{m}{m+n})(x_2-x_1)+x_1[/tex]Being m: 2 and n: 5
x1: -6
x2: 8
[tex]\begin{gathered} x=(\frac{2}{2+5})(8-(-6))+(-6) \\ \\ x=\frac{2}{7}*(14)-6 \\ \\ x=4-6 \\ \\ x=-2 \end{gathered}[/tex]Then, the x-coordinate of th point that divides the directed line segment from J to K into a ratio 2:5 is -2Answer: -2write an equation of each parabola in vertex form. Vertex (3,-2) Point (2,3)
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The equation of Parabola in the vertex form with vertex (3,-2) and point(2,3) is y = 5(x-3)² - 2 .
The equation of parabola with vertex (h,k) is denoted by the equation
y = a(x-h)² + k
In the question ,
it is given that
the vertex of the Parabola is (3,-2) and the point is (2,3)
So, the equation of the parabola with vertex (3,-2) will be
y = a(x-3)² - 2
Since the point (2,3) lies on the parabola ,
So, 3 = a(2-3)² - 2
3 + 2 = a*(-1)²
5 = a
Substituting a in the equation y = a(x-3)² - 2 ,
we get
y = 5(x-3)² - 2
Therefore , The equation of Parabola in the vertex form with vertex (3,-2) and point(2,3) is y = 5(x-3)² - 2 .
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Use the graph to answer the question.Which statement matches the vector operation shown on the coordinate grid?
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We have the correct statement about the vectors in the graph.
We can already see that it is a sum of vectors like:
[tex]v+w=u[/tex]As v has starting point at (-1,0) and ending point at (3,3), we can describe the vector as:
[tex]v=(3-(-1))\hat{i}+(3-0)\hat{j}=4\hat{i}+3\hat{j}[/tex]As w starts at (3, 3) and ends on (5, 2), we can describe it as:w
[tex]w=(5-3)\hat{i}+(2-3)\hat{j}=2\hat{i}-1\hat{j}[/tex]Finally, u starts at (-1,0) and ends at (5,2), so it can be described as:
[tex]u=(5-(-1))\hat{i}+(2-0)\hat{j}=6\hat{i}+2\hat{j}[/tex]Answer: v + w = u for v = 4i + 3j, u = 2i - j and u = 6i + 2j [Option C].
Hello, I really need help on this assignment I don't understand what to do.
Answers
Answer:
-2 and -10
Explanation:
There are two numbers at a distance of 4 units from -6, the number that is 4 units to the right and the number that is 4 units to the left.
So, the number that is 4 units to the right is equal to
-6 + 4 = -2
And the number that is 4 units to the left is equal to
-6 - 4 = -10
Therefore, the numbers are -2 and -10 and they are represented as
An envelope is 15 centimeters wide, and it measures 17 centimeters along the diagonal. The envelope is __ centimeters tall.
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An envelope is rectangular in shape.
Given the width = 15cm, and diagonal = 17cm
Let h represent the tall length of the envelope
Applying Pythagoras theorem, we have
[tex]\begin{gathered} 17^2=15^2+h^2 \\ 289=225+h^2 \\ h^2=289-225 \\ h^2=64 \\ h=\sqrt[]{64} \\ h=8\operatorname{cm} \end{gathered}[/tex]The envelope is 8cm tall
Compare the triangles and determjne whether they can be proven congruent, if possible by SSS, SAS, ASA, AAS or HL
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Since the triangles has a pair of congruent (equal) angles , and an equal side between the angles. It is congruent by ASA ( angle -side -angle)
what is the y intercept of y = 250 + 15x
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The y-intercept of y = 250 + 15x is (0,250)
What is y-intercept?A line's y-intercept is the distance in y coordinates from the line's intersection with the y-axis at its origin. A location on the graph where x is 0 is known as the y-intercept. The y-intercept of a line that is perpendicular to the x-axis is undefined.
This is an illustration of a y-intercept. Think about the line y = x + 3. The point where this graph crosses the y-axis is (0,3). Therefore, the y-intercept of the line y = x+ 3 is (0,3).
Here to determine the y-intercept put x=0,
Given, y = 250 + 15x
Replacing x by 0 in the above equation we get,
y = 250 + 15×0
y=250 +0
y=250
Therefore, the y-intercept of y = 250 + 15x is (0,250)
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Polynomial Functions:Find P(-1) and p(2) for each function.“P(x) = 4-3x”
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P(-1):
[tex]\begin{gathered} P(-1)=4-3(-1) \\ P(-1)=4+3 \\ P(x)=7 \end{gathered}[/tex]P(2):
[tex]\begin{gathered} P(2)=4-3(2) \\ P(2)=4-6 \\ P(2)=-2 \end{gathered}[/tex]work out sues total pay
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Sue's total pay for the year given the salary, bonus and share of profit is £38,110.
What is the total pay?Sue's total pay for the year is a function of the salary, the share of the profit that she earns and the bonus.
Salary for the year = monthly salary x number of months in a year
£1410 x 12 = £16,920
The next step is to determine the profit last year
Profit = total revenue - total cost
£549,000 - £473,500 = £75,500
Now determine the share of profit that Sue would earn.
Share of profit = 26% x £75,500
0.26 x £75,500 = £19,630
Now determine the total bonus she would earn : 4 x £390 = £1560
Total salary = £1560 + £19,630 + £16,920 = £38,110
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SOMEONE PLEASE HELP ME QUICKLY WITH THIS,ITS AN EMERGENCY!!!!! pls explain how you get the solution as well, sorry!
Thank you <3
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The statement that reflects the running rates is Pepe ran 9/8 mile in 1/2 hour and Paul ran 19/24 mile in 1/3 of an hour.
What is the speed?Speed is the total distance run per time. It can be determined by dividing the total distance travelled by the total time.
Speed = distance / time
Speed if Paul ran 1/5 mile in 4/15 hour
Speed = 1/5 ÷ 4/15
1/5 x 15/4 = 3/4 miles per hour
Speed if Pepe ran 8/10 mile in 1/4 of an hour
Speed = 8/10 ÷ 1/4
8/10 x 4 = 16/5 = 3 1/5 mile per hour
Difference in speeds =
[tex]3\frac{1}{5}[/tex] - [tex]\frac{3}{4}[/tex]
[tex]3\frac{4 - 15}{20}[/tex] = [tex]2\frac{9}{20}[/tex]
Speed if Paul ran 4/15 mile in 1/5 hour
Speed = 4/15 ÷ 1/5
4/15 x 5 = 4/3 = 1 1/3 miles per hour
Speed if Pepe ran 1/4 mile in of 8/10 an hour
Speed = 1/4 ÷ 8/10
1/4 x 10/8 = 5 / 16
Difference in speeds = [tex]1\frac{1}{3} - \frac{5}{16}[/tex] = [tex]1\frac{1}{48}[/tex]
Speed if Paul ran 1/3 mile in 19/24 hour
Speed = 1/3 ÷ 19 / 24
1/3 x 24/19 = 8/19 miles per hour
Speed if Pepe ran 1/2 mile in of 9/8 an hour
Speed = 1/2 ÷ 9/8
1/2 x 8/9 = 4/9 mile per hour
Difference = 4/9 - 8/19 = 4/171
Speed if Pepe ran 9/8 mile in 1/2 hour
Speed = 9/8 ÷ 1/2
9/8 x 2 = 2 1/4 miles per hour
Speed if Paul ran 19 / 24 mile in of 1/3 an hour
Speed = 19 / 24 ÷ 1/3
19 / 24 x 3 = 2 3/8 miles per hour
Difference =
[tex]2\frac{3}{8} - 2\frac{1}{4}[/tex]
[tex]\frac{3 - 2}{8}[/tex] = [tex]\frac{1}{8}[/tex] miles per hour
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Which expression demonstrates how the Distributive Property could be used to find the product of 5 and 48?
A. 50 − 5 (2)
B. 5 (50) − 2
C. 5 (50) + 5 (2)
D. 5 (50 − 2) + 5 (2)
E. None of these
Answers
Answer:
Step-by-step explanation:
C
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.Solve the inequality and describe the solution set.y-6 > 1232, Math symbolsRelations► Geometry► Groups► Trgonometry3 of 3 AnsweredType here to searcho66F Mosty clou
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The problem gives the inequality:
[tex]y-6\ge12[/tex]solving for y we get:
[tex]\begin{gathered} y\ge12+6 \\ y\ge18 \end{gathered}[/tex]The solution set is all real numbers equal or greater than 18, i.e.,
[tex]\lbrack18,+\infty)[/tex]Four points are labeled on the number line. M K L zo 0.5 1 Which point best represents 3? F. Point K G. H. Point 2 Point M Point N J.
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The point that best represents 1/3 is point M .
The number line ranges from 0 to 0.5 with 10 divi
Please help! I have 3 questions that I'm not sure what to do about :( if you could answer them that would be great
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The resultant matrix for the given expressions are as follows -
[A] → 2B - C = [tex]\begin{pmatrix}7.5&2.4\\ -16.4&-8.8\end{pmatrix}[/tex]
[B] → C + 2A = [tex]\begin{pmatrix}18.5&-8.4\\ 16.4&6.8\end{pmatrix}[/tex]
[C] → 2B - 10C + A = [tex]\begin{pmatrix}12&-36\\ -31&25\end{pmatrix}[/tex]
What is a Matrix?Matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. A matrix has [n] rows and [m] columns. The order of a matrix is given by - [m] x [n].
Given are the three different matrices as -
A = [tex]\left[\begin{array}{ccc}9&-6\\7&5\\\end{array}\right][/tex]
B = [tex]\left[\begin{array}{ccc}4&3\\-7&-6\\\end{array}\right][/tex]
C = [tex]\left[\begin{array}{ccc}0.5&3.6\\2.4&-3.2\\\end{array}\right][/tex]
We can solve the given expressions as follows.
[A] → 2B - C = [tex]\begin{pmatrix}7.5&2.4\\ -16.4&-8.8\end{pmatrix}[/tex]
[B] → C + 2A = [tex]\begin{pmatrix}18.5&-8.4\\ 16.4&6.8\end{pmatrix}[/tex]
[C] → 2B - 10C + A = [tex]\begin{pmatrix}12&-36\\ -31&25\end{pmatrix}[/tex]
Therefore, the resultant matrix for the given expressions are as follows -
[A] → 2B - C = [tex]\begin{pmatrix}7.5&2.4\\ -16.4&-8.8\end{pmatrix}[/tex]
[B] → C + 2A = [tex]\begin{pmatrix}18.5&-8.4\\ 16.4&6.8\end{pmatrix}[/tex]
[C] → 2B - 10C + A = [tex]\begin{pmatrix}12&-36\\ -31&25\end{pmatrix}[/tex]
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