The zeros of polynomial 4x² - 1 are x = 1/2 and x = -1/2
Let us assume that given polynomial be p(x) = 4x² - 1
We know that from the definition of zeros , the zeros of a polynomial are nothing but the values of the variable of the polynomial that makes the polynomial value equal to 0.
To find the zeros of polynomial p(x), we need to equate p(x) to zero then solve it for x.
⇒ p(x) = 0
⇒ 4x² - 1 = 0
⇒ 4x² = 1
⇒ x² = 1/4
⇒ x = ±(1/2)
Thus x = 1/2 and x = -1/2 are zeros of given polynomial.
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The complete question is:
What are the zeros of the polynomial 4x² - 1 ?.
5. In the circle, arc AD = 79, and
A circle is a closed two-dimensional shape because every point in the plane that makes up a circle is evenly separated from the "centre."
What are the 2 standard equation of circle?The collection of all points in the plane that make up a circle are all equally spaced from a certain point known as the "centre," making the form a closed two-dimensional shape. The reflection symmetry line is created by all lines that traverse the circle. Additionally, it is symmetrical in rotation around the centre at all angles.
The two foci are located in the middle of a circle, a particular type of ellipse.
a circle's equation, represented as (xh)2+(yk)2=r2, where r is the radius and (h,k) is the centre. The equation for the circle, which has a radius of 1, is x2+y2=1. Its centre is at the origin. x2+y2+cx+dy+e=0 is the formula for the equation of a circle.
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How many real solutions are there?.
The sign of the discriminant [tex]b^{2}-4ac[/tex] of a quadratic equation determines how many real solutions there are to that quadratic equation.
The value of the expression is the discriminant of a quadratic equation in standard form : This quantity specifies how many different ways a quadratic problem can be solved.
Solutions to quadratic equations can be 0, 1, or 2. If the discriminant has a positive value, then there are two genuine solutions for x, and the graph of the solution has two different x-intercepts. There is only one actual solution for x if the discriminant's value is zero, which means that the solution's graph only has one x-intercept.
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how to find the zeros and multiplicity of a polynomial
If a polynomial function can be factored, you can factor it and set each component's value to zero to find its zeros.
What is polynomial?A polynomial is an expression in mathematics made up of variables (also known as indeterminates) and coefficients, and it only uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of the variables. The polynomial x2 4x + 7 is an illustration of one with a single indeterminate x. Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable). A polynomial function is a function in an equation, such as the quadratic equation, cubic equation, etc., that only uses non-negative integer powers or only positive integer exponents of a variable. A polynomial with an exponent of 1 is, for instance, 2x+5.If a polynomial function can be factored, you can factor it and set each component's value to zero to find its zeros. Finding the places at which the graph of a polynomial function crosses the x-axis is another method for locating its x-intercepts.To learn more about polynomial refer to:
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find the missing side lengths 65 √2 x y 45°?
Answer:
x = 65
y = 65
Step-by-step explanation:
This is a special right triangle with angle measures as follows:
90° - 45° - 45°
The side lengths are represented respectively as follows:
a√2 - a - a
The side length that sees angle measure 90°, hypotenus, is given as 65√2.
The legs are congruent because this is a isosceles triangle at the same time so each = 65.
solve for a side in right triangles
Answer:
AC ≈ 4.28
Step-by-step explanation:
using the tangent ratio in the right triangle
tan35° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{3}{AC}[/tex] ( multiply both sides by AC )
AC × tan35° = 3 ( divide both sides by tan35° )
AC = [tex]\frac{3}{tan35}[/tex] ≈ 4.28 ( to the nearest hundredth )
How do you decide whether to use substitution or elimination to solve a system?.
When deciding whether to use substitution or elimination to solve a system of linear equations, it is important to consider the size and complexity of the system.
Substitution is generally recommended for systems with two equations and two variables, as it can be a simpler and quicker approach. For larger systems with more equations and/or variables, elimination may be a better option as it can reduce the number of steps required to solve the system.
When using either method, it is important to keep track of all the steps you take and double check your work for accuracy. Additionally, both methods involve solving for one variable in terms of the others, so if you are dealing with an equation that already has only one unknown variable, then substitution could be the best approach. Ultimately, it is important to assess each situation individually and decide which method would be most effective.
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*URGENT*
i’m so confused when it comes to this, please help
The value of w has been solved to be 57.7 m.
What are trigonometric functions?Trigonometric functions are set of functions which can be applied so as to determine the unknown value of a side or angle of a right triangle. Some of the basic functions are: Sine, Cosine, Tangent etc.
In the given question, to solve for w let us applying sine function of the angle.
Sin θ = opposite/ hypotenuse
We have;
Sin θ = opposite/ hypotenuse
Sin 25 = 10/ w
w = 10/ sin 25
= 57.6877
w = 57.7 m
The value of w is 57.5 m.
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What is the conjugate of 4 3i?.
The complex conjugate of 4 − 3i is;
4 - (-3i) = 4 + 3i .
Now, According to the question:
The complex number is basically the combination of a real number and an imaginary number. The complex number is in the form of a+ib, where a = real number and ib = imaginary number. Also, a,b belongs to real numbers and i = √-1.
Hence, a complex number is a simple representation of addition of two numbers, i.e., real number and an imaginary number. One part of it is purely real and the other part is purely imaginary.
The complex conjugate of a + bi is a - bi
So, the complex conjugate of 4 − 3i is;
4 - (-3i) = 4 + 3i .
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Two angles are supplementary. If the m∠A is five times the sum of the m∠B plus 7.2°, what is m∠B?
The angle measure of m∠B = 24°.
Two angles are supplementary.
What is an angle measure?When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
Given:
Two angles are supplementary.
The m∠A is five times the sum of the m∠B plus 7.2°.
That means,
5(B + 7.2) + B = 180
6B = 180 - 36
B = 24.
Therefore, the angle measures of m∠B = 24°.
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What would determine the value of Edubucks?
The value of Edubucks would be determined by a variety of factors, including:
supply and demand, the overall economic environment, and any news or events related to the company or the education industry as a whole.Additionally, speculation and sentiment could also play a role in determining the value of Edubucks.
What is an Edubucks?Edubucks is a virtual currency created by the educational platform Edmodo. It is used to reward students for completing tasks and participating in activities on the platform.
Also, Edubucks could also be described as the virtual currency created to motivate or compensate the effort made on certain task done by students which is meant to boost their morales and aid their eagerness to doing more.
Therefore, the correct answer is as given above
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What is the formula for log A log B?.
The formula for the logarithmic function log A ± log B is given by
log A + log B = log ( AB )
log A - log B = log ( A / B )
As given in the question,
For the given logarithmic function is given by :
Addition of two logarithmic function represents the multiplication of two numbers.
log ( A × B ) = log A + log B
Example : log ( 6 )
= log ( 2 × 3 )
= log 2 + log 3
Subtraction of two logarithmic function represents the division of two numbers.
log ( A ÷ B ) = log A - log B
Example :
log ( 5 ÷ 2 ) = log 5 - log 2
Therefore, the formula of the logarithmic function log A ± log B is given by :
log A + log B = log ( AB )
log A - log B = log ( A / B )
The above question is incomplete, the complete question is:
What is the formula for logarithmic function log A ± log B?.
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Political pollsters now make sure to conduct a percentage of their telephone interviews by calling mobile phones. This policy best addresses which potential source of bias?
Some of the population may not have access to other types of phones.
The survey only reaches individuals who volunteer to be interviewed.
The policy helps individuals understanding the wording of survey questions.
Some individuals contacted may choose to not participate.
The bias that is taken care of here is that; Some of the population may not have access to other types of phones. Option A
What is a bias?When we talk about a bias in research we mean the kind of scenario that is able to cause the result of a research to become lobe sided. In other words, it is that which introduces inaccuracy to a research.
A lot of people if not everyone has access to a mobile phone and this would help more people to be able to participate in the interview. Some of these people may not have any of the other kinds of phone.
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Answer:
A
Step-by-step explanation:
took the test
Suppose that c and d vary inversely and that d=4/3 when c = 9. Write a function that models the inverse variation and find d when c = 3.
The equation for the inverse variation is:
d = 12/c
And evaluating that we can see that when c = 3, d = 4.
How to find the inverse variation equation?A genearl inverse variation equation can be written as:
y = k/x
Where k is a constant.
Here we know that there is an inverse variation between c and d, then we can write:
d = k/c
We know that d = 4/3 when c = 9, replacing that we will get:
4/3= k/9
9*(4/3) = k
12 = k
Then the equation is:
d = 12/c
Now we can evaluate this in c = 3 so we get:
d = 12/3
d = 4
When c =3, d = 4.
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What is the binomial factor of the polynomial x³ Y³?.
The binomial factor for the given expression is x = 4.
In mathematics, a binomial is an expression that is made up of two terms. The binomial factor of an expression is the part of the expression that is written in the form (x - a)^n, where a is a constant and n is a positive integer.
The binomial factor of x³ is x³. The equation x³ = 64 is not a binomial equation, as it does not have the form (x - a)^n = 0, where a is a constant and n is a positive integer. If you are trying to solve for x in the equation x³ = 64, one solution is x = 4. However, there are also three other solutions, which are the cube roots of 64 that are not real numbers (they are complex numbers).
Hence, The binomial factor for the given expression is x = 4.
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Why the range of square root function Cannot be negative?.
In the realm of real numbers, there is no solution for square root of any negative number. Therefore, there is no negative range for the function f(x) = sqrt(x). The range extends from 0 to any number that is positive.
Why is a square root's range not negative?The range is [0,]=y: y≥0}. By looking at its defining equation, f(x)=x2, we can algebraically determine its domain. We are aware that the square root of a negative number cannot be taken. As a result, the expression that lies beneath the radical has to be positive or zero, not negative.
Can a negative square root function exist?However, negative square roots are also possible. Consequently, the number -6 can be a principal square root of the number 36, but not a square root. As a result, the principal square root and the negative square root both have the same number.
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What does it mean when your solving a linear equation and you get 2=2
Answer:
When you solve a linear equation and get 2=2, this means that the equation is true and there is no solution. This is because both sides of the equation are equal, so there is no value that can satisfy both sides of the equation at the same time.
give me brainiest
Answer: It means that the equation is balanced and both sides have the same value (they are equal)
Ticket will cot $24. 00 per peron and there i one-time $12 group regitration fee. Write and expreion for the cot of the whole group if there i going to be p people going
The cost of the whole group would be: (24 * p) + 12 or 24p + 12.
The cost of a group of peopleThe expression (24 * p) + 12 represents the total cost of the group. The "24 * p" part represents the cost of the individual tickets, with "p" representing the number of people in the group. The "12" represents the one-time group registration fee. The expression calculates the total cost by multiplying the number of people in the group by the cost of an individual ticket, and then adding the group registration fee to that total.
Specifically, the operation being used is arithmetic, specifically multiplication and addition. The expression provided is used to calculate the total cost for a group by multiplying the number of people in the group by the cost of an individual ticket and then adding the group registration fee to that total. This is a basic mathematical operation that is a part of arithmetic.
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Find the difference. Show each step for full credit. Use ^ for exponents, for instance, x^2 means x
3n3+ 4n2– 9 and -2n3+ 4n – 9^323
5n³ + 4n² -4n + 720 is the difference between these two given expressions.
What are Systems of equations?Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.
Given a system of equation 3n³+ 4n²– 9 and -2n³+ 4n – 9³
We need to find the difference between These given Systems of equation
Difference = 3n³+ 4n²– 9 -( -2n³+ 4n – 9³)
Difference = 3n³+ 4n²– 9 + 2n³- 4n + 9³
Difference = 5n³ + 4n² -4n + 720
therefore, The difference between these two given equations is 5n³ + 4n² -4n + 720.
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If p(x) = x² + 2√2x + 1, find p(2√2)
Answer: p(2√2) = 17
Step-by-step explanation:
Given,
p(x) = x² + 2√2x + 1....(i)
To find p(2√2) , we need to substitute x=2√2 in the given equation
p(2√2) = (2√2)² + 2√2(2√2) + 1
= 8 + 8 + 1
= 17
So p(2√2) is 17
Answer: 17
Step-by-step explanation:
[tex]P(x) = x^{2} + 2\sqrt2x + 1[/tex]
[tex]P (2\sqrt{2}) = 2\sqrt{2})^2 + 2\sqrt{2}*2\sqrt{2} + 1[/tex]
[tex]P (2\sqrt{2}) = 8 + 8 + 1[/tex]
[tex]P (2\sqrt{2}) = 17[/tex]
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g3(7+h) using the Distributive Property
Helpppppp
The value of the equation is A = 21g + 3gh
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = g3 ( 7 + h ) be equation (1)
On simplifying the equation , we get
Applying the distributive property , we get
A = g3 ( 7 ) + g3 ( h )
A = 21g + 3gh
Therefore , the value of A is 21g + 3gh
Hence , the equation is A = 21g + 3gh
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Draw a Venn Diagram to show the following categorical data.Hint: all 30 countin be listed neatly in your Venn Diagram
a. Counting numbers 0 ≤ n ≤ 30 that have 2 as a factor.
b. Counting numbers 0 ≤ n ≤ 30 that have 3 as a factor.
The required Venn diagram for the given condition has been shown.
What is a Venn diagram?A Venn diagram is a graphical representation of the relationship between sets or groups of items. It consists of overlapping circles, each representing a different set, with the overlapping areas showing the items that belong to both sets.
Here,
U = 0 ≤ n ≤ 30
A = 2 ≤ n ≤ 30 [multiple of 2]
B = 3 ≤ n ≤ 30 multiple of 3
From above, the rectangle represents the universal set u, and the circle represents the two subsets A and B.
Thus, the required Venn diagram for the given condition has been shown.
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15 In the circle, AD = 100, & AD = 99. Find∢DCQ. (The figure is not drawn to scale.)
a. 31
b. 161
c. 62
d. 80.5
The value of m∠DCQ is 31°.
What is a measure of an angle?
An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
Here, we have
Given: mAD = 100, & m∠D = 99.
First, we find the measure of arc ABC
we know that
The inscribed angle is half that of the arc it comprises
so
m∠D = (1/2)[arc ABC]
we have
m∠D = 99°
substitute and solve for arc ABC
99° = (1/2)[arc ABC]
198° = [arc ABC]
Now, we find the measure of arc DC
we know that
arc ABC+arc AD+arc DC = 360° -----< by complete circle
substitute the given values
198°+100°+arc DC = 360°
arc DC = 360°-298°
arc DC = 62°
Now, we find the measure of angle DCQ
we know that
The inscribed angle is half that of the arc it comprises
so
m∠DCQ = (1/2)[arc DC]
we have
arc DC = 62°
substitute
m∠DCQ = (1/2)[62°] = 31°
Hence, the value of m∠DCQ is 31°.
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What is the exponential function represented by the table below?
What is the final step in solving the inequality 5 4x )< 6x 4?.
The inequality you provided is a linear inequality in one variable x. To find the solution to this inequality, we need to follow these steps:
First, we will simplify the inequality by combining like terms on the left side:
5 + 4x <= 6x + 4
4x <= x + 9
Next, we need to get x alone on one side of the inequality by subtracting x from both sides:
4x-x <= 9
3x <= 9
We will divide both sides of the inequality by 3:
x <= 3
The final step is to check our solution by plugging it back into the inequality and making sure that it satisfies the inequality: 5 + 4(3) <= 6(3) + 4
5 + 12 <= 18 + 4
17 <= 22 which is true
So the solution to the inequality 5 + 4x <= 6x + 4 is x <= 3. It's worth mentioning that this is the only solution that this inequality has since it's a linear inequality which has only one solution.
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Find each product mentally show the steps you used 9 x44
Answer:
396
Step-by-step explanation:
I found this answer by using standard multiplication but mentally.
4x9 is 36
and 4x9 is also 36, but for the sake of this way of solving we must add a zero the end of this answer making it 390
Now you have to add these two together:
36
+ 360
396
Hope this helps :)
How do u solve this?
Answer:
-f(x)
Step-by-step explanation:
Figure H is just Figure G reflected across the x-axis meaning that you just have to slap a negative symbol in front of whatever function gave you Figure H.
How do you describe the end behavior of the graph if the degree is even?.
If the degree of the function is even then the end behaviour of the graph depends upon the leading coefficients of the function .
The End Behaviour of the graph of the polynomial is defined by the degree and the leading coefficient of the polynomial .
the end behaviour for the even degree polynomial is given as ;
(i) If the degree of the polynomial is even and the lead coefficient is also positive, then both the ends of graph of polynomial will point up.
(ii) If the degree is of polynomial is even and the lead coefficient is negative, then both ends of graph of polynomial will point down.
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19. Which can be used to find the product: 398 x 5? A 400-2 X 5 B (400 x 5) - (2 x 5) C (400 x 5) + (2 X 5) D (400 x 5) -2
The product of 398×5 is equal to (400-2)×5
What Is Distributive Property?According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
Given here: The product of two numbers as 398×5
Now 398 can be rewritten as 400-2
Thus the expression 398×5 =(400-2)×5 ( Using distributive property)
1990 = 1990
Thus they are also equivalent.
Hence, The product of 398×5 is equal to (400-2)×5
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call thrown vertically in the air reaches its peak height after 3.5 seconds. If its height as a function of time is given by h=-16t^2+bt+4, then which of the following is the values of b?
(1) 56
(2) -56
(3) -112
(4) 112
A falling object's height above the ground at time t is calculated using the formula s (t) = 5t2 + v0t + s0, where s is measured in metres, t is measured in seconds, v0 is the starting velocity in metres per second, and s0 is the starting location in meters. Thus, option D is correct.
What is the height as a function of time?((0 - 24t2) - 30t) + 4 = 0 Pull out like factors: -16t2 - 30t + 4 = -2 • (8t2 + 15t - 2)
Factoring 8t2 + 15t - 2
The last term, "the constant", is -2 Multiply the coefficient of the first term by the constant 8 • -2 = -16. Rewrite the polynomial splitting the middle term using the two factors found in step 2 above1 and 16
8t2 - 1t + 16t - 2
Add up the first 2 terms, pulling out like factors:
t • (8t-1)
2 • (8t-1)
Add up the four terms of t • (8t-1)
(t+2) • (8t-1)
Therefore, 112 s the values of b.
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Select the correct answer from each drop-down menu.
A veterinarian's office recorded one particular week that they had 50 patients. The table shows the recorded number of dogs.
Monday Tuesday Wednesday Thursday Friday
7
4
5
5
2
Use the given data to complete the sample proportion and confidence intervals for this situation.
Percentage of patients that were dogs
90% confidence interval
95% confidence interval
1. The correct answer is 46 percent, 2. The correct answer is .07, 3. The correct answer is (34%,58%), 4. The correct answer is (32%,60%)
What is standard error?The term "standard error" is used to refer to the standard deviation of various sample statistics, such as the mean or median. For example, the "standard error of the mean" refers to the standard deviation of the distribution of sample means taken from a population. The smaller the standard error, the more representative the sample will be of the overall population.
The relationship between the standard error and the standard deviation is such that, for a given sample size, the standard error equals the standard deviation divided by the square root of the sample size. The standard error is also inversely proportional to the sample size; the larger the sample size, the smaller the standard error because the statistic will approach the actual value.
1. Let's calculate the percentage or proportion of patients that were dogs:
p = (7 + 4 + 5 + 5 + 2)/50 = 23/50 = 0.46
The correct answer is 46%
2. Let's estimate the standard error, using the given formula, this way:
S.e = √ (0.46 * 0.54)/50 = √0.049 = 0.07
The correct answer is .07
3. Let's calculate the confidence limits of the 90% confidence interval, this way:
Confidence limits = proportion +/- 1.645 * standard error
Confidence limits = 0.46 +/- 1.645 * 0.07
Confidence limits = 0.46 +/- 0.12
Confidence limits = 0.34, 0.58
The correct answer is (34%,58%)
4. Let's calculate the confidence limits of the 95% confidence interval, this way:
Confidence limits = proportion +/- 1.96 * standard error
Confidence limits = 0.46 +/- 1.96 * 0.07
Confidence limits = 0.46 +/- 0.14
Confidence limits = 0.32, 0.60
The correct answer is (32%,60%)
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