The quadratic form of (x² - 1)² + (x² - 1) - 12 = 0 is (x² + 3)(x² - 4) = 0 and the roots are x = ± i√3 Or x = ± 2.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, (x² - 1)² + (x² - 1) - 12 = 0.
∴ x⁴ - 2x² + 1 + x² - 1 - 12 = 0.
x⁴ - x² - 12 = 0.
x⁴ + 3x² - 4x² - 12 = 0.
x²(x² + 3) - 4(x² + 3) = 0.
(x² + 3)(x² - 4) = 0.
Now (x² + 3) = 0 Or (x² - 4) = 0.
x² = - 3 Or x² = 4.
x = ± √-3 Or x = ± 2.
x = ± i√3 Or x = ± 2.
We can also solve this equation by assuming x² = t and substitute we will get the roots in terms of t and then we'll replace x² again in t.
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what is the smallest positive integer a such that the intermediate value theorem guarantees a zero exists between 0 and a?
The smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.
What is the intermediate value theorem?
Intermediate value theorem is theorem about all possible y-value in between two known y-value.
x-intercepts
-x^2 + x + 2 = 0
x^2 - x - 2 = 0
(x + 1)(x - 2) = 0
x = -1, x = 2
y intercepts
f(0) = -x^2 + x + 2
f(0) = -0^2 + 0 + 2
f(0) = 2
(Graph attached)
From the graph we know the smallest positive integer value that the intermediate value theorem guarantees a zero exists between 0 and a is 3
For proof, the zero exists when x = 2 and f(3) = -4 < 0 and f(0) = 2 > 0.
Your question is not complete, but most probably your full questions was
Given the polynomial f(x)=− x 2 +x+2 , what is the smallest positive integer a such that the Intermediate Value Theorem guarantees a zero exists between 0 and a ?
Thus, the smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.
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What is the coefficient of this number written in scientific notation?
(3.6 x 10^5)
Enter the coefficient only. Don't change to standard form!
The coefficient would be 3.6
Does anyone know how to solve this?
(2x^2)-6x+9 can be written in the form (a(x-b)^2)+c where a b c can be written as integers or fractions in their simplest form.
a) work out the values of a b c
b) using your answer to part a), solve (2x^2)-6x+9=12.5. give any fractions or surds in your answers in their simplest forms.
Answer:
it needs to be written step by step
solve for y and then graph the solution: -25 < 4y + 3 < 19
So, for this question, there are two answers possible that you could put in.
-25 < 4y + 3 < 19 in inequality form: -7<y<4
-25 < 4y + 3 < 19 in interval notation form: (-7,4)
The graph that goes alongside it should be attached to this answer as well.
Hope this helps! :)
Choose Yes or No to tell whether the expression represents a 20% discount off the price of an item that originally cost d dollars. 0.8d Choose... d – 0.2 Choose... d – 0.2d Choose... 1 – 0.2d Choose...
The expression that represents a 20% discount off the price of an item that originally cost d dollars include:
0.8d
d - 0.2d
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this case, the cost of the item is d. Since there's a 20% discount, the new cost will be:
= d - (20% × d)
= d - 0.2d
= 0.8d
The cost is 0.8d.
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(3+6n³ + 3n) - (3n+3n³-2n¹)
Answer:
3n³ + 2n + 3
Step-by-step explanation:
(3+6n³ + 3n) - (3n+3n³-2n¹)
3 + 6n³ + 3n - 3n - 3n³ + 2n
3n³ + 2n + 3
Would 8.1^4 x 8.1^8 be equal to 8.1^12? If so, would 8.1^12 = 8.1^6?
8.1^4 x 8.1^8 will be equal to 8.1^12. But, 8.1^12 will not be equal to 8.1^6.
Some laws of exponents are:
(a²) · (a³) = a²⁺³ = a⁵(a²)³ = a²ˣ³ = a⁶(a²) ÷ (a³) = a²⁻³ = a⁻¹We are given:
8.1^4 x 8.1^8
We need to check if 8.1^4 x 8.1^8 be equal to 8.1^12 and if 8.1^12 be equal to 8.1^6.
We will use laws of exponents to solve the given expression:
8.1^4 x 8.1^8 = 8.1^(4 + 8) = 8.1^12
So, 8.1^4 x 8.1^8 = 8.1^12
Also,
8.1^12 = 8.1^(2 * 6) = (8.1^2)^6
So, 8.1^12 ≠ 8.1^6.
Thus, 8.1^4 x 8.1^8 will be equal to 8.1^12. But, 8.1^12 will not be equal to 8.1^6.
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find the following percentiles for the standard normal distribution. interpolate where appropriate. (round your answers to two decimal places.)
The interpolations;
(a) 81st
= NORM.INV(0.81;0;1)
0.878
(b) 19th
=NORM.INV(0.19;0;1)
-0.878
(c) 76th
=NORM.INV(0.76;0;1)
0.706
(d) 24th
=NORM.INV(0.24;0;1)
-0.706
(e) 11th
=NORM.INV(0.11;0;1)
-1.227
Given,
Data near the mean are more likely to occur than data distant from the mean, according to the normal distribution, which is a probability distribution that is symmetric around the mean.
"A numerical measurement used in statistics of a value's relationship to the mean (average) of a set of values, assessed in terms of standard deviations from the mean," according to Wikipedia, is the Z-score.
For this case we can find the percentiles with the Norm.inv function in Excel and we got:
(a) 81st
= NORM.INV(0.81;0;1)
0.878
(b) 19th
=NORM.INV(0.19;0;1)
-0.878
(c) 76th
=NORM.INV(0.76;0;1)
0.706
(d) 24th
=NORM.INV(0.24;0;1)
-0.706
(e) 11th
=NORM.INV(0.11;0;1)
-1.227
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the point p p is on the unit circle. if the x-coordinate of p p is 3 4 34 , and p p is in quadrant iv , then what is the value of y? evaluate by using the one of the pythagorean identities.
The value of y coordinate of the unit circle is given by [tex]\sqrt{7}/4[/tex]
Given that,
x - coordinate of p =-3/4 . Let the co-ordinate of point P = (-3/4 , y).
To find : The y coordinate in Quadrant IV
By using the formula for unit circle,
Unit circle means a circle whose radius is one or 1
x²+ y² = 1
y²+ (-3/4)² = 1
y²+ (9/16) = 1
y² = 1 -9/16
y² = 7/16
y= [tex]\sqrt{7/16}[/tex]
y = ± [tex]\sqrt{7}/4[/tex]
It is given that point P is in quadrant IV so in IV quadrant y is positive.
Therefore, y = [tex]\sqrt{7}/4[/tex]
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The temperature today in Chicago is 50°E
Instead of using the standard conversion
formula °C = x(°F - 32), Tommaso uses his
9
grandmother's rule, which is easier but gives
an approximate value: "Subtract 32 from the
value in °F and multiply the result by 0.5."
Error = (10-9)°C & Error percentage = 10%.
Given that temperature today in Chicago is 50°F
Standard conversion formula
°C = [tex]\frac{5}{9} *(T^{0}F-32)[/tex] - 1
Given T = 50°F
Put the value in equation 1
[tex]^{0}C = \frac{5}{9} *(50-32) \\\\= \frac{5}{9}*18\\ \\= \frac{90}{9}[/tex]
= 10°C
Tommasa's grandmothers rule is to subtract 32 from the value in °F and multiply the result by 0.5
i.e. [tex]^{0}C = 0.5(T^{0} F-32)[/tex] - 2
Given temperature is T = 50°F
Put the value of T in equation 2
[tex]^{0}C = 0.5*(50-32)[/tex]
= 0.5 * 18
= 1/2 * 18
= 9°C
Temperature obtained by standard conversion Formula is 10°C and the temperature obtained by Tammaso's grandmother rule is 9°C.
So error = (10-9)°C
= 1°C
Error percentage = [tex]\frac{1}{10}*100[/tex]
= 10%
Hence the answer is Error = (10-9)°C & Error percentage = 10%.
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In triangle EFG, m∠E = 84.3° and m∠F = 36.4°. Determine the measure of the exterior angle to ∠G.
47.9°
59.3°
121.1°
120.7°
By applying the exterior angle property, the measure of the exterior angle to ∠G in triangle EFG is 120.7°
What is the exterior angle property?In Mathematics, the exterior angle property can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle.
To determine the value of ∠G in triangle EFG (ΔEFG), we would have to apply exterior angle property.
Then, the exterior angle property can be used to model triangle EFG (ΔEFG) is given by:
∠G = m∠E +m∠F
Now Substituting the given parameters into the formula, we have
∠G = 84.3° + 36.4°.
∠G = 120.7°.
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mating eagle pairs typically have two baby eagles (called eaglets). when there are two eaglets, the parents always feed the older eaglet until it has had its fill, and then they feed the younger eaglet. this results in an unequal chance of survival for the two eaglets. suppose that the older eaglet has a 50 percent chance of survival. if the older eaglet survives, the younger eaglet has a 10 percent chance of survival. if the older eaglet does not survive, the younger eaglet has a 30 percent chance of survival. let x be the number of eaglets that survive. which of the following tables shows the probability distribution of x ?
The set of probabilities for the number of eaglets is the
probabilities for how many eaglets will survive.
The table that shows the probability distribution is the option C;
X 0 1 2
p(x) 0.35 0.60 0.05
P(O) = 0.5 is the likelihood that the elder eaglet will live.
Therefore;
P(O') = 1 - 0.5 = 0.5 is the probability that the older eaglet won't survive.
The likelihood that the younger eaglet will survive if the older eaglet does not P(Y|O) = 10%
Therefore;
The likelihood that the elder eaglet will live while the younger eaglet does not survive is P(Y'|O) = 1 - 10% = 90%.
When the older eaglet does not survive, the younger eaglet has a 30% survival chance (P(Y|O')).
Therefore;
The likelihood that the younger eaglet will not survive, compared to the elder eaglet, is P(Y'|O') = 1 - 30% = 70%
The collection of potential probabilities for the number of eaglets that survive is expressed as the probability distribution, or P(X)
The range of potential results includes:
Never survives:
The likelihood that no eaglets survive is equal to P(O') × P(Y'|O') = 0.5 × 0.7 = 0.35.
The only survivor is:
The likelihood that only one eaglet survives is determined by P(O) = P(Y'|O) × P(O') = P(Y|O'), which results in P = 0.5 × 0.9 + 0.5 × 0.3 = 0.6 Both survive:
The odds of both eaglets surviving are P(O) ×P(Y|O) = 0.5 × 0.1 = 0.05.
The table of the probability distribution is therefore;
X 0 1 2
p(x) 0.35 0.60 0.05
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What does the transformation f(x)—>f(1/3x) do to the graph of f(x)?
The transformation f(x)—>f(1/3x) due to the graph of f(x), will be dilation horizontally and vertically.
What is Transformation of Function?
Transformation of functions refers to the graph's curve moving to the left, right, up, or down, expanding, contracting, or reflecting. Just dilation, out of these three transformations, alters the size of the original shape; the other two only adjust the position.
A translation happens when each point on a graph (which represents a function) travels in the same direction and by the same amount. There are two kinds of function translations.
Stretching or compressing is a dilation. The x-values on a graph are all scaled up by the same amount when a dilation that is parallel to the x-axis occurs. The y-values are all increased by the same scale factor if it is dilated parallel to the y-axis.
f(x) to become f(1/3x), Then it will go dilation "vertically and horizontally".
Referring to the graph mentioned below we can conclude the same.
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Suppose the math club is going on a field trip. Members will be riding in vans that will hold 7 people each including the
driver. More than 28 people will be going on the field trip. Do not put spaces in your answers.
Write an inequality to model this situation using V as the variable.
Solve the inequality.
What is the least number of vans needed to make the trip?
Since more than 4 vans will be required in total, at least 4 vans should be reserved.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another. In mathematics, inequalities specify the relationship between two non-equal values. Equal does not imply inequality. The "not equal symbol ()" is typically used to indicate that two values are not equal. The expression 5x 4 > 2x + 3 resembles an equation, but the equals sign has been replaced by an arrowhead. It is an illustration of inequality. This shows that the left part, 5x 4, is bigger than the right part, 2x + 3.
Here,
Since the total number of people is at least 28, then the total number of people must be 28 or more, so
7v≥28
v≥4
The total number of vans needed will be more than 4 that is at least 4 vans should be booked.
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Determine the largest integer value of a in the solution of the following inequality.
4x+6 -13
The largest integer value of x in the solution of the following inequality is 7/4.
We have given equation is 4x+6 ≥13
In the question we have to determine the largest integer value of a in the solution of the following inequality.
So first we have to solve this inequality equation:
4x+6 ≥13
4x≥13-6
4x≥7
x≥7/4
So the largest value of x is 7/4
Hence, the largest integer value of a in the solution of the following inequality is 7/4.
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The right answer is
Determine the largest integer value of x in the solution of the following inequality.
4x+6≥13
whats eleven decreased by k ?
Answer:
11-k
Step-by-step explanation:
if you are asking what is as a equation its 11-7 because decreased means minus
The required mathematical expression for the given statement is 11-k.
What are expressions?A mathematical statement containing variables, numbers and related by at least one mathematical operator is considered as an expression.
Given that, a statement, what's eleven decreased by k,
Converting it into a mathematical expression,
Here, a value k is being extracted or subtracted by 11, that mean, the expression should be like k is being subtracted by 11.
That is = 11-k
Hence, the required mathematical expression for the given statement is 11-k.
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A farmer grows 128 red tomatoe plants and 102 yellow tomato plants each plants about 32 tomatoes the farmer plants to sell each tomatoes for $2 explain how to find a reasonable as the meal for the total of money is the farmers market
The total amount of money that farmer will make to sell the tomatoes for $2 per tomato will be $14720.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
Multiplication = to multiply any two or more numbers or variables called multiplication.
The number of red tomato = 128 × 32
The number of yellow tomato = 102 × 32
The total cost will be,
2(128 × 32) + 2(102 × 32)
⇒ 2(4096) + 2(3264)
⇒8192 + 6528
⇒$14720
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Wich rule best represents the dilation that was applied to the quadrilateral ABCD to create quadrilateral A'B'C'D'?
Answer:
Step-by-step explanation:
It A (x,y) (0.4x,0.4y)
based on the information given above is it possible to compute the probability that a randomly selected cookie has a weight less than 14 g?
0.1367 percent of randomly chosen cookies will weigh less than 14 grams.
Given data;
Is it possible to calculate the likelihood that a randomly selected cookie weighs less than 14g using the information provided above?
Let,
X = Average cookie weight in a pack of 30
E (X) = μ = 15
Var (X) = σ²/n
= 1²/30 = 0.0333
⇒ Standard Deviation (X) = √0.0333 = 0.1826
P(X ≤ 14.8) = (X-15 / 0.1826 < 14.815/0.1826)
= P(14.815 - 0.1826)
= P(Z-1.1)
= 0.1367
Hence, the probability that a randomly selected cookie has a weight less than 14g is 0.1367
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the international air transport association surveys business travelers to develop quality ratings for transatlantic gateway airports. the maximum possible rating is . suppose a simple random sample of business travelers is selected and each traveler is asked to provide a rating for the miami international airport. the file miami contains the ratings obtained from the sample of business travelers. develop a confidence interval estimate of the population mean rating for miami. round your answers to two decimal places.
The confidence interval estimate is (6.41, 7.11) of the population mean rating for Miami
The question includes a sample of the data.
The sample size, n = 50
The sample mean:
x= ∑X /n
= 6.76
The sample standard deviation;
s= √∑(X-x)²/(n-1)
=2.55
The confidence level =0.95
The significance level , α = 0.05
The sample mean, X
= 6.76
The sample standard deviation, s = 2.55
The sample size , n= 50
Degree of freedoms :
Df = n-1
=49
Using the t-distribution table, the critical value of t is:
t critical = t α/2, df
= t 0.025,49
= 0.098
95% confidence interval :
μ = X ± t.s/√n
t.s /
= 6.76 2.01 2.55 / √50
= 6.76 0.7249
Therefore, The confidence interval is ( 6.41, 7.11)
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Jared had two numbers to multiply. They were written as 64⋅3.He thought that it would be easier to multiply them as 3⋅64.What property would he be using?
Answer:
He is using the commutative property of multiplication.
Which expression represents the product of 3 and 7? 7 ÷ 3 7 + 7 + 7 37 3 × 7
Answer:
3x7
Step-by-step explanation:
product is multiplication so 3x7 is only correct answer
Hopes this helps please mark brainliest
help please i will give you a snack
Answer:
26
Step-by-step explanation:
you are given 45° and 90° so you know the third angle will also be 45° because the sum of all angles always is 180°
with all 3 angles you apply the sine law
a / sin( α ) = b / sin( β ) = c / sin( γ )
then you'll see that a = 26
. If he is paid $15 per hour and $200 for each car that he sells, how many hours did he work if he sold 2 cars and made $520?
Answer:
8 hours
Step-by-step explanation:
2 cars will be $400 since 2x200=400
500-400=120
He made $120 from hours alone so now we divide by 15
120/15=8
He worked 8 hours
Hopes this helps please mark brainliest
What is the value sinθ?
question options:
A. 5/13
B. 13/5
C. 12/13
D.5/12
The value of sin θ of the given right angle triangle using trigonometric ratios is; A: 5/13
How to solve Trigonometric ratios?The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). They are based on the angles formed from the ratio of sides of a right angle triangle. Thus;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
From the given image, we see that;
Hypotenuse = 13
Adjacent = 12
Opposite = 5
Thus;
tan θ = 5/12
θ = tan⁻¹(5/12)
sin θ = 5/13
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PLEASE HELP!!!!!!! i dont know how to solve this problem
Answer:
Step-by-step explanation:
3 because at the bottem it is 3 away and top three away.
A local farmer had a mouse problem in his barn. He estimated there were about 800 mice to start with. He adopted some cats and noticed that the number of mice was decreasing by 8%/wk. The graph models the number of mice x weeks after the farmer adopted the cats.
Identify and interpret the key features of the exponential function modeled in terms of this situation.
Select each correct answer.
Question 3 options:
The asymptote indicates that as the number of weeks the farmer has had the cats increases, the population of mice approaches 0.
The y-intercept represents the number of mice the farmer had in the barn at the time he adopted the cats.
The line x = 0 is an asymptote of the graph.
The point (0,30) contains the x-intercept.
The line y = 0 is an asymptote of the graph.
The y-intercept is 800.
The asymptote indicates that there were never more than 800 mice in existence.
The asymptote tells us the number of mice will approach zero as cats increased y-intercept shows the number of mice with zero cats and the asymptote is y = 0 thus option (A),(B), and (E) is correct.
What is a graph?The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.
For example plot of y = x³ ,y = sinx.
The given graph of the number of mice in the number of weeks the cat adopted.
The asymptote of the graph is y = 0.
The asymptote tells that the number of the mouse will become zero when the number of cats becomes infinite.
Hence "The asymptote tells us the number of mice will approach zero as cats increased y-intercept shows the number of mice with zero cats and the asymptote is y = 0".
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A cell phone company charges a flat rate of $3. 99 per month, with an additional charge of $0. 05 per minute. How many minutes did casey talk on her cell phone if her monthly bill was $38. 44?.
Answer:Total time minute Casey can talk= 689 Minute
Step-by-step explanation:Total charges of flat rate per month= $3. 99
Total Additional charge per minute = $0.05
Total monthly bill = $38. 44
Total additional charge=Total monthly bill - Total charge of flat rate
=$38.44-$3.99
=$34.45
Total time minute Casey cann talk=Total additional charge÷Total additional charge per minute
=$34.45÷$0.05
=689 Minute
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689 minutes long If Casey's monthly bill was $38.44, she would talk on her cell phone.
Given;
A cell phone provider charges a set monthly fee of $3. 99 plus an extra $0.05 per minute.
If Casey's monthly phone bill was $38.44, how many minutes did she use?
The total charges of the flat rate per month = $3.99
The total additional charge per minute = $0.05
Total monthly bill = $38.44
Total additional charge = Total monthly bill - Total charge of flat rate
= $38.44 - $3.99
= $34.45
Total time per minute Casey can talk = Total additional charge/Total additional charge per minute
= $34.45 / $0.05
= 689 Minutes
Therefore, for 689 minutes Casey talk on her cell phone if her monthly bill was $38.44
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As a fraction in simplest terms, what would you multiply the first number by to get
the second?
First number: 79
Second number: 65
First number 79 about friction is correct statement with initial velocity .
What is friction?
Friction is a force that opposes motion between any surfaces that are touching. Friction can work for us yet against of us .
It is the action of one surface or object rubbing against another .
According to the given question in this case force of friction has a tendency to rotate the cube in anticlock wise direction. So normal reaction will shift in forword direction to balance the force due to torque of friction.
Thus, During motion the normal reaction shift towards posetive x- axis from the centre of mass is correct.
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In the next several games, the pitcher threw a total of 384 pitches and used a fastball 240 times. What decimal should Juanita use to update her report?
Juanita should use the decimal to update her report.
The decimal that Juanita can use to update her report is 1.6.
What is a decimal?A decimal is a number with a whole and a fractional part. Decimal numbers are between integers and represent numerical value for whole plus some fraction of a whole.
The decimal numeral system is the most widely used system for representing both integer and non-integer numbers. It is the Hindu-Arabic numeral system's extension to non-integer numbers. Decimal notation refers to the method of representing numbers in the decimal system.
In this case, the the pitcher threw a total of 384 pitches and used a fastball 240 times. The decimal will be:
= Number of throws / Fastball
= 384 / 240
= 1.6
The decimal is 1.6.
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