How do you describe the graph of the solution set of a quadratic inequality?
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 x2 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".
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Related Questions
The Santos family owns 30 acres of land. Of the 30 acres, only 20 acres can be farmed. What percent of the land is available for farming?(1 point)
Answers
Answer:66.67% to the nearest whole number is 67%
Step-by-step explanation:
The total number of acres available are 30
and only 20 acres of land can be farmed
20 acres out of 30 acres is available for farming
20/30 x 100%
To do with the calculator
20 ÷30 x 100=66.67% then add the percent sign
How do you find the vertical and horizontal asymptotes of a function using limits?
Answers
Consider the behavior of the function when x approaches the value of the vertical asymptote from the left and from the right in order to locate the vertical asymptotes of a function using limits. Consider the behavior of the function when x grows very big in order to determine the horizontal asymptotes of a function using limits (in either the positive or negative direction).Similary, To find the horizontal asymptotes of a function using limits, consider the behavior of the function as x becomes very large (in either the positive or negative direction). If the y-values of the function approach a fixed value as x becomes very large, then that value is the horizontal asymptote of the function.
what is an Asymptote?An asymtote is a line being approached by a curve but never touching the curve at any finite distance.It is a line that the graph approaches as either x or y in positive or negative infinity.
What is vertical asymptote?A vertical line that directs the function's graph but is not actually a part of it is called a vertical asymptote. Because it appears at an x-value outside of the function's scope, the graph can never cross it. There may be several vertical asymptotes for a given function.
Consider the behavior of the function when x approaches the value of the vertical asymptote from the left and from the right in order to identify the vertical asymptotes of a function using limits. The vertical asymptote is at that value of x if the function approaches positive infinity as x approaches the asymptote from the left and negative infinity as x approaches the asymptote from the right. Consider the function f(x) = 1/x as an illustration. We may take into account how the function behaves as x approaches 0 from the left and from the right in order to determine the vertical asymptotes of this function using limits.The y-values of the function become closer to negative infinity as x moves toward 0 from the left (negative x-values). The y-values of the function get closer to positive infinity as x gets closer to 0 from the right (positive x-values). As a result, we may infer that the function's vertical asymptote lies at x = 0.
Similary, Consider the behavior of the function when x grows very big in order to determine the horizontal asymptotes of a function using limits (in either the positive or negative direction). The horizontal asymptote of the function is the point at which the y-values of the function begin to approach a fixed value when x increases significantly.
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How do you work out 13X13?
Answers
Therefore , the solution of the given problem of squaring comes out to be square of the 13 is 169.
What does it mean to square a number?A resultant is referred to as a "Square Number" when a number or integer (not a fraction) is multiplied by itself. For instance, 3 x 3 is 32 when multiplied by itself three times. In essence, the exponential form of multiplying an integer or number by itself is referred to as a square number.
Here,
Try to add up the four stages here.
Multiplication of two-digit numbers using a math shortcut trick
shortcuts: 13 times 13 equals
13X13 = 169 is the answer when a two-digit number is multiplied.
Therefore , the solution of the given problem of squaring comes out to be square of the 13 is 169.
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Yoezer bought 25 shares that had a face value of Nu 100 but were selling at a discount of 5%. A 15% dividend rate was paid at the end of one year. He then sold the stock at a 5% premium.
i. Find the amount of his investment.
ii.Calculate his total profit.
Answers
2375 is the amount of his investment and 625 is his total profit
The discount on the shares is 5%, so the price of each share is 100 - (5/100)100 = 95.
The total price Yoezer paid for the shares is 2595 = 2375.
To calculate Yoezer's total profit, we need to find the total dividend he received and the price he sold the shares for.
The dividend rate is 15%, so Yoezer received a dividend of (15/100)100 = 15 on each share.
The total dividend he received is 1525 = 375.
The price Yoezer sold the shares for was increased by a premium of 5%, so the selling price was 100 + (5/100)100 = 105.
The total selling price for the shares is 10525 = 2625.
Yoezer's total profit is the selling price minus the price he paid for the shares plus the dividends he received. This is 2625 - 2375 + 375 = 625.
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What is the quotient?
Help :D
1065 ÷ 33
Enter your answer as a mixed number in simplest form in the box.
Answers
Answer:
32 3/11
Step-by-step explanation:
Happy Holidays!
A circle has center (0,4) and radius 5. Which of the following is an equation of the circle
Answers
Answer:
Given that a circle has a center (0,4) and the radius 5. 5. So the standard equation of the given circle is x2+(y−4)2=25.
Step-by-step explanation:
A direct variation includes the points (5,10) and (1,n). Find n.
Write and solve a direct variation equation to find the answer.
Answers
1 = k * 1
10 / 1 = k * 5 / (k * 1)
10 = 5k
k = 2
y = kx
n = 2 * 1
n = 2
Please give a step by step explanation
Answers
The evaluation of the composite figure comprising of a square and an equilateral triangle is as follows;
9 (a) ∠ABD = 90°
(b) ∠BCD = 60°
(c) ∠ADC = 105°
What is a composite figure?A composite figure is a figure comprising of two or more regular geometric figures.
9. The shape of the quadrilateral ABDE = A square
The kind of triangle specified for the triangle ΔBCD = Equilateral triangle
The sides of the square ABDE are congruent by the definition of a square
Therefore; AB = BD = DE = AE by the definition of congruency
(a) Angle ∠ABD is a corner of the square ABDE, therefore;
The size of angle ∠ABD = 90° (properties of the interior angle of a square)
∠ABD = 90°(b) The size of angle ∠BCD = 60° (Interior angle of an equilateral triangle)
∠BCD = 60°(c) The size of angle ∠ADC is found as follows;
Triangles ΔAED and triangle ΔABD formed by the diagonal AD are congruent by Side-Side-Side, SSS congruency postulate
∠DAB ≅ ∠ADB (base angles of isosceles triangle ΔABD)
∠DAB = ∠ADB (Definition of isosceles triangles)
∠ABD + ∠DAB + ∠ADB = 180° (Angle sum properties of a triangle)
90° + 2 × ∠ADB = 180° (substitution property)
∠ADB = (180° - 90°) ÷ 2 = 45°
∠BDC = 60° (Interior angle of an equilateral triangle)
∠ADC = ∠ADB + ∠BDC (Angle addition postulate)
Therefore, ∠ADC = 45° + 60° = 105°
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n is a poisson random variable that represents the number of telephone calls processed in telecommunications switch in 10sec. if the call arrival rate is .5 per second. a) what is the probability that there will be no call processed in 10seconds? b) what is the probability that at least 2 calss will be processed in 2 seconds
Answers
a)The chance that no call will be handled in 10 seconds is 0.0067
b) 0.2642 percent of classes will be processed in two seconds at least.
what is percentage?A figure or ratio that reflects a fraction of 100 is known as a percentage in mathematics. In addition to ratios, fractions, and decimals, it is one of the ways to depict a dimensionless connection between two numbers. Frequently, the symbol "%" is used after the number to indicate percentages.
given,
The number of phone calls handled by the communications switch in a 10-second period is represented by the Poisson random variable n.
a)the chance that no call will be handled in 10 seconds is
for 10 sec= λ= 10*0.5 = 5 calls per sec
P(X=0) [tex]e^{-5}[/tex](5)° / 0!
P(X=0)= 0.0067
b) percent of classes will be processed in two seconds at least is
for 2 sec =λ = 0.5 *2 = 1
P(X≥2) = 1- P(X<2)
= 1-[P(X=2) + P(X=1)]
=0.2642
a)The chance that no call will be handled in 10 seconds is 0.0067
b) 0.2642 percent of classes will be processed in two seconds at least.
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Is Cos 2x continuous?
Answers
How many solutions can 2 linear equations have?
Answers
The number of solutions that a system of 2 linear equations in 2 variables can have is explained below.
In the question ,
it is given that ,
the system of 2 linear equations in 2 variables .
we know that the linear equations represent a line .
(i) the two linear equations will have No Solution / Zero Solution if the two lines are parallel .
(ii) the two linear equations will have One Solution/Unique Solution if the two line intersect at a point .
(iii) the two linear equations will have infinitely many solution if the lines overlap on each other .
Therefore , the number of solutions of linear equation is explained above .
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What is 4 1/2÷(−2 2/3)?
Write the answer as a mixed number in simplest form.
help plssss
Answers
Answer:
Step-by-step explanation:
you cant divide fractions so you multiply the reciprocal so your answer would be
1 11/16
What will be the nature of the roots of 2x2 4x 7?
Answers
Answer: Roots of given quadratic equation are real and distinct.
If a quadratic equation is given by ,then nature of its roots can be find by it's discriminate (D).
Roots are real and distinct, if D>0
Roots are real and equal, if D=0
Roots are imaginary (no real root exists), if D<0
Step 1:
Write coefficients of x², x and constant term.
Compare the given equation with standard quadratic equation.
Thus,
Roots of given quadratic equation are real and distinct.
Learn more:
1) Find the nature of roots of quadratic equation 2x sq. + 3x - 7=0
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2) Find the nature of the roots of the following quadratic equations. If real roots exist, find them:
(i) 2x² – 3x + 5 = 0 ...
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Step-by-step explanation:
What has 4 sides and 2 sets of parallel lines?
Answers
Answer:
A parallelogram
Step-by-step explanation:
A parallelogram is a shape with four sides and two sets of parallel lines. A common example of a parallelogram is a square.
How do you identify congruent in SAS?
Answers
define the derivative of a funnction y = f(x) at the point a
Answers
Answer:
Step-by-step explanation:
The derivative of a function y = f(x) at the point a is a measure of the rate of change of the function at that point. It is represented by the symbol f'(a) or df/dx.
The derivative can be thought of as the slope of the tangent line to the curve of the function at the point a. It is calculated using the limit definition of the derivative, which states that the derivative of a function at a point is the limit of the difference quotient as the difference between x and a approaches zero.
In other words, the derivative of a function y = f(x) at the point a is the slope of the line that is tangent to the function at that point, and it is calculated using the following formula:
f'(a) = lim(h -> 0) [(f(a+h) - f(a)) / h]
This formula can be used to calculate the derivative of any function at any point. I hope this helps! Let me know if you have any questions.
A one-pound pack of wall putty costs $3. A 10-pound pack costs $24. What is the percent savings If you buy the 10-pound pack? 2096 24% 25% 60%
Answers
Answer:
20%
Step-by-step explanation:
let x = percent savings
$3/lb (cost per lb of a 1 lb pack)
$24/10lb = $2.40/lb (cost per lb for a 10 lb pack)
$3 - $3x = $2.40
-3x = -0.60
x = -0.60/3 = 0.20
0.20 x 100 = 20%
Need help as quick as possible due tmrw
Answers
The height of the tree is 61.92 feet.
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.
Given that,
Distance of Tamara from tree = 30 feet.
Angle of elevation = 62°.
And the height of Tamara from the ground = 5.5 feet.
To find the height of the tree,
Use trigonometric formula,
tan θ = height / distance
tan 62 = x / 30
1.88 = x / 30
x = 56.42 feet
The total height of tree = x + 5.5 = 56.42 + 5.5 = 61.92 feet
The height of the tree is 61.92 feet.
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Does the triangle inequality theorem apply to all equilateral triangles?
Answers
Yes, triangle inequality theorem apply to all equilateral triangles.
Describe Triangle inequality theorem:The triangle inequality theorem explains the relation between a triangle's three sides. This theorem states that for any triangle, the sum of the lengths of the first two sides is always greater than the length of the third side. In other terms, this theorem states that a straight line is always the shortest distance between any two places.
So Triangle inequality theorem is not only valid for all equilateral traingles but it is valid for all traingles.
A Triangle is only formed is if follows Triangle inequality theorem so every equilateral triangle needs to follow this theorem.
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If you cut away a triangle with an area of 59 cm from a certain square, the area
of the remaining shape will be 85 cm². Find the length of the side of the square.
Answers
The length of the side of the square is 12 cm.
Given that, a triangle with an area of 59 cm from a certain square, the area of the remaining shape will be 85 cm².
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
We know that, the area of a square is a².
Here, total area = Area of a square + The area of the remaining shape
= 59+85
= 144 cm²
So, a²= 144 cm²
⇒ a =12 cm
Therefore, the length of the side of the square is 12 cm.
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Marcia and Becky shared some money
in the ratio 1:4
Marcia gets £18 less than Becky. How
much does Marcia receive?
Answers
The money received by Marcia = £ 6
According to the given information
The money is shared between Marcia and Becky in the ratio = 1 : 4
Let the money got by Becky = £ x
Marcia got £ 18 less than Beck = x - 18
So
Taking the ratio
[tex]\frac{1}{4}=\frac{x-18}{x}[/tex]
Cross multiply both the fractions
x = 4(x - 18)
x = 4x - 72
-3x = -72
x = 24
Money got by Beck = £ 24
Money received by Marcia = 24 - 18
= £ 6
Hence
The money received by Marcia = £ 6
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-15+23r+9r^2-16r+10
A 9r^-10-7r
B 16r^2-5
C 9r^2-7r^-5
D 9r^2+tr-5
Answers
Answer:
9r^2+7r-5
Step-by-step explanation:
-15+23r+9r^2-16r+10
=-15 + 9r^2 + 7r +10
= 9r^2 + 7r - 5
Answer:
[tex]9r^2+tr-5[/tex]
The given expression is a polynomial in the variable r. The correct answer among the options provided is D, which has the same terms as the given expression, in the same order, but with an additional term (tr) at the end. The other options do not match the given expression.
7. Explain in your own words why √-4 is not possible.
Answers
Answer:
There is no real square root of -4 because it is impossible to square any real number and get a negative answer.
You might think -2 could work. However, a negative times a negative is positive → -2(-2) = +4, so the problem would have to be written as [tex]\sqrt4[/tex] instead of [tex]\sqrt{-4}[/tex]. Hence, there is no real square root of -4.
Note the word real, as it is possible to find a non-real answer to [tex]\sqrt{-4}[/tex] using the imaginary number [tex]i[/tex], which represents [tex]\sqrt{-1}[/tex].
A(n) ____ is a numerical summary of a sample.
Answers
A statistic is a numerical summary of a sample.
A sample statistic is explained as any number computed from a sample of data.
Examples include the sample average, median, sample standard deviation, and percentiles. A statistic is a random variable because it is based on data obtained by sampling technique in which each sample has an equal probability of being chosen.
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The probability of an unfavorable outcome plus the probability of a favorable outcome equals 1.
O True
O False
Answers
Your answer is False
What is linear equation answer?
Answers
Linear equations are one-degree equations. It is a straight-line equation. A linear equation with parameters a and b equal to zero has the conventional form ax + by + c = 0.
How do one express the standard form of a linear equation?A linear equation has the following standard form: ax + by + c = 0.
Here, variables x and y and constants a, b, and c are used.
Also, a ≠ 0, and b ≠ 0.
For linear equations, the slope-intercept formula is: y=mx+b
Where m stands for the line's slope and b represents the y-intercept.
The three types of linear equations are point-slope, slope-intercept, and standard form.
When an algebraic equation is graphed, it always produces a straight line since each term has an exponent of 1 or 0. This is known as linear equations.
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Find the first 5 terms of the sequence.
Answers
The first five terms of the expression are -7,-3,1,5, and 9.
What is arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that , F(1) = -3 and F(n) = F(n-1) + 4. Calculate the first term of the sequence,
F(1) = F(1-1) + 4
-3 = F(0) + 4
F(0) = -7
The common difference is calculated as,
d = -3 - 7
d = 4
The third term will be, -3 + 4 = 1
The fourth term will be, 1 + 4 = 5
The fifth term will be, 5 + 4 = 9
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How many terms does 3xy have?
Answers
3xy has two terms, 3 and xy. The term 3 is a constant and the term xy is a product of two variables.
3xy is a multiplication of three individual components. It consists of three distinct parts, namely 3, x, and y. Each of these components is considered a distinct term, so 3xy has three terms in total. The 3 represents a numerical value, while the x and y are variables that can be assigned any numerical value. When multiplied together, the three terms form a single expression, 3xy, which can then be evaluated for a resulting value.
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What is the smallest number divisible by 3?
Answers
The smallest number that is divisible by 3 is 3 itself. Every integer that is divisible by 3 is called a multiple of 3.
For example, some of the multiples of 3 are 6, 9, 12, 15, 18, 21, etc. All of these numbers can be obtained by multiplying 3 by an integer.
What does "divisible" mean in math?If a number evenly divides (leaves no residue) into another number, it can be divided. For instance, 34 may be divided by 2 equally, making it a divisible number. However, because doing so would result in a leftover, 34 cannot be divided by 3.
How are three divided?According to the law of three's divisibility, a number is completely divisible by three if the sum of its digits is also divisible by three. Take 308 as an example. To determine whether or not 308 is divisible by 3, add the digits together and find the sum (3+0+8=11).
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What is the median of 1 2 3 4 5 6 7 8?
Answers
5.5 is is the median of the set of numbers .
What are the mean, median, and example?
The most frequent number, or the one that happens the most frequently, is known as the mode.
Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.
Since the number of observations is even, the median is the average of
= (n/2) th and (n/2 +1)th observation.
The average of 5th and 6th observations = (5+6)/2 = 11/2 = 5.5.
Hence, the median of the given set of numbers is 5.5.
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