The required zeros of the polynomial f(x) are 2, -2, and ±√-4.
What are zeros of the polynomial?
All the possible values of x that will make the polynomial zero are called the zeros of the polynomial, p(x). Zeros of a polynomial can either be negative or positive.
Solving for the zeros of a polynomial
f(x)=x⁴ - 16
Let, f(x) = 0
x⁴-- 16 = 0
(x²)² - 4² = 0
(x² + 4) (x² - 4) = 0
(x² + 4)(x - 2)(x + 2) = 0
i.e. x² + 4 = 0, x - 2 = 0, x + 2 = 0
x = 2, -2, ±√-4
Hence, the required zeros of the polynomial f(x) are 2, -2, and ±√-4.
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Given f(x)=2x² evaluate f(-6)
A. 72
B. 78
C. -72
D. 441
E. -441
The value of f(-6) is 72, that is, option A.
In mathematics, a function from a given set X to a given set Y allots to each element of X one and only one element of Y. The set Y is called the range of the function and the set X is called the domain of the function.
Here, we are given a function f(x) = 2x²
f(-6) means that x = -6
Substituting x = -6 in the function, we get-
f(-6) = 2(-6)²
= 2 × -6 × -6
= 2 × 36
= 72
Thus, the value of f(-6) is 72.
From the given options, hence, option A becomes the correct answer.
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29. What is the width of the rectangle written
as an exponential expression?
2-1 m
Area = 2-4 m²
? m
The width of the rectangle as an exponential factor whose length is 2^(-1) m and Area is 2^(-4) m^2 is 2^(-3) meter.
As per the question statement, we are given a triangle whose length is 2^(-1) m and Area is 2^(-4) m^2 is 2^(-3) meter. We are supposed to find out the width of the rectangle as an exponential factor.
Before solving the question, we should know the formula for calculating the area of the rectangle
Area = Length * Width
Given Area = 2^(-4) m^2
Given Length = 2^(-1) m
Let Width = "x" m
2^(-4) = 2^(-1) * x
2^(-4)/2^(-1) = x
2^(-4+1) = x
2^(-3) = x
Hence width of the given rectangle as an exponential factor is
x = 2^(-3) meter
Exponential factor: An exponential function is defined by the formula f(x) = a^x, where the input variable x occurs as an exponent.Area: The space occupied by any figure, object or body whether 2D or 3D.To learn more about exponential factor, click on the link given below:
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What is the probability that client F, the 53-year-old you’re considering for a 20-year policy, lives to be 73 years old? Remember that client F is a Hispanic female.
Step-by-step explanation:
In this question , the 20 year policy is just for fun the probability is 53 / 73
15+4a=7a
what is the value of a?
[tex]{\huge\color{green}{\boxed{\fcolorbox{white}{black}{꧁ANSWER꧂}}}}[/tex]
15+4a=7a
15=3a
3a=15
a=15/3=5
The solution of the linear equation with single variable 7a = 15 + 4a will be 3.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The equation is given below.
15 + 4a = 7a
Simplify the equation, then we have
7a = 15 + 4a
7a - 4a = 15
3a = 15
a = 15 / 3
a = 3
The solution of the linear equation with single variable 7a = 15 + 4a will be 3.
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What does 4.3 round to
Answer:
4
Step-by-step explanation:
Solve each equation. ln (x-7)=2
After the solving equation ln (x-7)=2, the value of x is equal to [tex]e^{2}[/tex] + 7
We have been asked to find x in ln (x-7)=2
⇒ ln (x-7)=2
⇒ x - 7 = [tex]e^{2}[/tex]
⇒ x = [tex]e^{2}[/tex] + 7
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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Simplify each expression. Rationalize all denominators. 4√7xz+2 √7xz
All denominators are =[tex]6\sqrt{7xz}[/tex].
The phrase simplifies manner to make something simpler to do or recognize. So, by decreasing or simplifying the fractions method we make the fraction as simple as feasible. We do this by dividing the numerator and the denominator with the aid of the most important range that could divide into both numbers precisely.
The only form is likewise known as the decreased form of a fraction. for instance, ¾ is the most effective shape of a fraction that has a not unusual thing equal to 1. but 2/4 is not the most effective form, because 2/four can in addition be simplified and written as ½.
Step one is to perceive a common issue between the denominator and numerator. The denominator and numerator are each divided by the commonplace thing. The department operation is repeated until there are not any extra elements. The fraction is said to be simplified if no greater factors go out.
[tex]4\sqrt{7xz} +2 \sqrt{7xz}[/tex]
Add similar elements :
[tex]4\sqrt{7xz} + 2\sqrt{7xz}[/tex]
[tex]= 6\sqrt{7xz}[/tex]
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Which is the best estimate for the value of r in the scatter plot? NEED HELP ASAP
A 0.7
B 0
C -0.5
D 1
Answer:
The anwser is A
Step-by-step explanation:
A is the best anwser choice given
painting worth $3000 in 2016 $4652 in 2021
if x=years since 2015 y=$ value
write an equation in point slope,
predict value in 2030
The equation for the value of the painting of the years is y = 3000 + 330.4(x).
The estimated worth of the painting in 2030 is $7956.
In 2016, the worth of the painting is $3000.
In 2021, the worth of the painting is $4652.
The increase in worth in 5 years from 2016 to 2021 is:
= $4652 - $3000 = $1652
Hence, the increase in painting worth per year will be:
= $1652 / 5 = $330.4
Now, if x is in years and y is the worth of the painting in $.
Then, the equation for the worth of a painting is:
y = 3000 + 330.4(x)
From 2015 to 2030 the span is 15 years.
Then, the value of the painting in 2030.
So,
y = 3000 + 330.4(x)
y = 3000 + 330.4 × 15
y = 3000 + 4956
y = $7956
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Add. Write your answer in scientific notation.
(1.568×10^5)+(4.79×10^5)
The sum in scientific notation is 6.358 * 10^5
How to evaluate the sum in scientific notation?The summation expression is given as
(1.568 × 10^5) + (4.79 × 10^5)
Factor out 10^5 in the above expression
So, we have
10^5 * (1.568 + 4.79)
Evaluate the sum
10^5 * 6.358
Rewrite the expression as
6.358 * 10^5
Hence, the sum in scientific notation is 6.358 * 10^5
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PLS ANSWERR i’ll mark you the BRAINLIEST!!!!
when referring to the sequence: 1,4,9,16,25,… identify the possible pairs obtained when rewriting the position and sequence values as a coordinate points.
The possible pairs when rewriting the position and sequence values are (d) (1, 1), (2, 4), (3, 9), (4, 16), (5, 25)...
How to determine all possible pairs when rewriting the position and sequence values?The sequence is given as
1, 4, 9, 16, 25...
The position and sequence values of the above sequence are
1, 2, 3, 4, 5...
1, 4, 9, 16, 25...
When represented as an ordered pair, we have
(1, 1), (2, 4), (3, 9), (4, 16), (5, 25)....
Hence, the possible pairs when rewriting the position and sequence values are (d) (1, 1), (2, 4), (3, 9), (4, 16), (5, 25)....
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The stadium's seating options will include premium seats (boxes closest to the action), medium-priced seats, and budget-friendly bleachers. Your design calls for 4,500 upper-deck premium seats and 7,500 lower-deck premium seats. The team's policy is to have a 3:2 ratio of premium seats to bleacher seats. How many bleacher seats will the stadium include?
The number of bleacher seats that the stadium will include will be 8000 seats.
How to calculate the ratio?In this situation, the The team's policy is to have a 3:2 ratio of premium seats to bleacher seats.
Therefore, the total number of premium seats are:
= 4500 + 7500
= 12000
The number of bleachers will be:
= 2/3 ×12000
= 8000
Therefore, the number of bleacher seats that the stadium will include will be 8000 seats.
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9 over 10 plus - four over five
Answer: 1 and 7 over 10
Step-by-step explanation:
Answer:
[tex]\frac{1}{10}[/tex]
Step-by-step explanation:
[tex]\frac{9}{10} + ( -\frac{4}{5} )[/tex]
change the fraction [tex]( -\frac{4}{5} )[/tex] to[tex]( -\frac{8}{10} )[/tex]
I multiplied both the denominator and numerator by 2
[tex]\frac{9}{10} + ( -\frac{8}{10} )[/tex]
simplify the negative
[tex]\frac{9}{10} -\frac{8}{10}[/tex]
subtract the numerator not the denominator
[tex]\frac{1}{10}[/tex]
what is the greatest common factor for 28 and 32
Answer:
4.
Step-by-step explanation:
28 = 2*2*7
32 = 2*2*2*2*2
Picking out the common factors:
GCF = 2 * 2 = 4.
Answer:28
Step-by-step explanation:
ask random person the explanation, sorry, I don't know how to explain
State which property or properties need to be used to write each expression as a single logarithm.
a. log₄5+log₄5
Product rule of logarithms is used in the single logarithm.
A single logarithm can be expanded into many logarithms or compressed into many logarithms by using the features of log. Just another approach to write exponents is with a logarithm. As a result, the characteristics of exponents are used to infer the characteristics of logarithms.
There are 7 properties of logarithms: Product Rule, Quotient Rule, Power Rule, Zero Rule, Identity Rule, Inverse Property of Logarithm, Inverse Property of Exponent, Change of base formula.
In the equation here, only the product rule is applied.
Product rule of logarithms states that the log of a product is equal to the sum of the logs of its factors. Example: logₐ (xy) = logₐ x + logₐ y
Therefore, in this question,log₄5 + log₄5 = log₄ 25
Therefore, in the equation log₄5 + log₄5, the property of the product rule of logarithms is used.
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A bicycle costs $175. salvadore has $55 and plans to save $18 each month. describe the number of months he needs to save to buy the bicycle. 1. choose the correct inequality to represent this situation. 2. choose the correct solution set.
Answer:
Step-by-step explanation:
55+18x=175
-55+18x=-55
18x= 120
Divide by 18
X=6,666666
So it will take 7 months
Which expression is equivalent to quantity y raised to the negative third power times z raised to the fifth power end quantity over quantity z raised to the negative fourth power times y raised to the sixth power end quantity all raised to the negative second power?
whoever gets it right gets marked branliest!!
pls pls help!!
The equivalent expression of the statement is as follows:
[tex](\frac{y^{-3} X z^{5} }{z^{-4} X y^{6} }) ^{2}[/tex]
How to find which expression is equivalent to the given expression?The expression is as follows:
Quantity y raised to the negative third power times z raised to the fifth power end quantity over quantity z raised to the negative fourth power times y raised to the sixth power end quantity all raised to the negative second power
The equivalent expression of the statement is as follows:
[tex](\frac{y^{-3} X z^{5} }{z^{-4} X y^{6} }) ^{2}[/tex]
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Write the function that models each variation. Find z when x=4 and y=9 . z varies directly with x and inversely with y . When x=6 and y=2, z=15 .
The function that models each variation is : [tex]z = \frac{5 x}{y}[/tex]
value of z = 20/9
What is inversely and directly variation ?The inverse variation property states that , whenever the product of values of two quantities is a constant value then there is opposite variation between them . Or we can also say that if the productive nature of two corresponding values is constant, then one quantity is inversely varies with second quantity. whereas, The direct variation state that the both values will show same pattern i.e. if one value will increase then another will also increase with the same amount or if one decrease another will also decrease.
In the question given,
First of all find the value of K in the model by putting in the values of x, y, and z so that to find the function model.
z = k (x) / (y)
put value of x=6, y=2 and z=15
15 = k (6) /2
k= 5
Thus we can write the equation as,
z=5x / y
put x=4, y=9
z = 20 / 9
Thus, z = 20/9
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Which system of linear inequalities is graphed?
S x < -2
ly≤-x+2
O
J x ≤-2
y≤-x-3
S. x < -2
y≤ x 2
-
{
√ x < −3
С
According to the question, to graph the linear inequality expressions then the given expressions should be equal to the respective number.
In the first equation that is: x<-2 or x = -2
The given expression can be drawn in the second quadrant when the value of the x-axis is negative and it is a straight line which tends to infinity.
In the second equation that is: y ≤ x+2 or y = x+2
The given expression can be drawn in the first as well as in the second quadrant when the value of the x-axis is negative as well as positive and it is a straight line which tends to infinity.
Similarly, in the third equation that is: y ≤ x-3 or y = x-3
The given expression can be drawn in the first as well as in the second quadrant when the value of the x-axis is negative as well as positive and it is a straight line which tends to infinity.
What is linear inequality?
Linear inequalities are those expressions in which comparison between the variables is performed. And the comparison can be done between two values or between the two expressions. It uses the symbols of the inequality like greater than, equal to, etc.
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hello, i am doing an assesment and i was wondering if i could have some help
Answer:
The absolute value of -5 is 5, it's positive opposite.
Have a fantabulous day <3
Answer:
5
Step-by-step explanation:
the only real math to absolute value is if it negative make it not.
If the sum of squares of the roots of the equation x² - 3ax + a² = 0 is equal to 4, find the value of a.
The value of a is 2/√7.
The given quadratic equation is x² ₋ 3ax ₊ a² = 0
sum of the roots of the equation = 4
here, A = 1
B = 3a
C = a²
Let α and β be the roots of the equation.
α ₊ β = ₋B/A
= ₋3a/1
= ₋3a
⇒ α×β = C/A
= a²/1
= a²
⇒α² ₊ β² = (α ₊ β )² ₋ 2αβ
= (₋3a)² ₋ 2(a²)
= 9a² ₋ 2a²
therefore, 7a² = 4
a² = 4/7
a = √4/7
a = 2/√7
Hence we found the value of a as 2/√7.
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Isabel drove 335 miles in 5 hours.
At the same rate, how long would it take her to drive 536 miles?
Answer:
8
Step-by-step explanation:
distance/time=speed
335/5=67
536/t=67
t=8
please help
4. What is 7/4 as a mixed number? A. 3/4 B. 114 C. 174 D. 134
Answer:
1 3/4
Step-by-step explanation:
Answer: Option D
Step-by-step explanation: Explanation:
7/4 is an improper fraction. Let's take the numerator and divide it by the denominator.
Divide 7 by 4. The quotient digit is 1.
Multiply the quotient digit 1 by the divisor 4.
Subtract 4 from 7.
The result of 7 divided by 4 is 1 with a remainder of 3.
Thus, 7/4 as a mixed number can be written as 1 3/4.
1. If h(x)=x² + 3x - 1, what is h(-4)?
(1) 27
(3) -5
(2) 3
(4)
−1
What is the coordinate of G' if triangle E'F'G' is created by dilating EFG with a factor of 4 about the origin?
The coordinate of G' if triangle E'F'G' is created by dilating EFG with a scale factor of 4 about the origin is (8, -8).
The types of transformation.In Mathematics, there are different types of transformation and these include the following:
ReflectionRotationTranslationDilationWhat is dilation?Dilation can be defined as a type of transformation which changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.
Since the dilatation was centered around the origin, then we would multiply the coordinate of G by a scale factor of 4 as follows:
G = (2, -2) → G'[(4 × 2), (4 × -2)]
G = (2, -2) → G'(8, -8)
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The lunch bill for Eugene and Maggie totaled $20.20. Tax
on the meal was 5% and they wanted to leave a 15% tip.
How much was the meal including tax and tip?
O $24.39
O $21.21
O $22.20
O $3.03
Correct answer is A. The cost of meal in the caffeteria is 24.39.
What percentage is it?A percentage is a figure or ratio that represents a portion of 100. In addition to the percent symbol "%," the abbreviations "pct," "pct," and occasionally "pc" are also used to denote it. A% does not have any dimensions or a corresponding unit of measurement.
Your $20.20 bill is made up of the full amount (100%) plus the 15% tip, for a total of 115%. Decimal equivalent is 1.15.
Simply divide the entire charge by 1.15 to determine the price before the tip.
20.20/1.15 = 17.56
Consequently, the final amount due before the 15% tip was $17,56.
The total cost after tax and tip = 24.39
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A Man rode His personal transporter 3/10 mi to the library, then 3/4 mi to class, and then 7/2 mi to his part-time job. How far did he ride his personal transporter?
If a man rode his personal transporter 3/10 mi to the library, then 3/4 mi to class, and then 7/2 mi to his part-time job, then he rode his personal transporter for 4.55 miles.
To determine how far the man rode his personal transporter we use addition.
total miles the man rode = miles to the library + miles to the class + miles to the part-time job
total miles = 3/10 + 3/4 + 7/2
As these fractions have an unlike denominator, we find a common denominator by determining the least common multiple.
As the least common multiple is equal to 20
Therefore,
total miles = 3(2)/10(2) + 3(5)/4(5) +7(10)/2(10)
total miles = 6/20 + 15/20 +70/20
total miles = 6+15+70/20
total miles = 91/20
total miles = 4.55
Hence, the man rode his personal transporter for 4.55 miles.
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Write each expression as a single logarithm.
log 7 +log 2
The expression log 7 +log 2 can be written as log 14 in a single logarithm form.
Given that the expression is log 7 +log 2.
We are required to write the expression is a single logarithm.
The Power Property basically states that if an exponent is being raised to another exponent, we can multiply the exponents.
The expression is log 7 +log 2.
We know that log mn= log m +log n.So,
log 7 +log 2=log (7*2)
=log 14
Hence the expression log 7 +log 2 can be written as log 14 in a single logarithm form.
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Ryan is working two summer jobs, babysitting and walking dogs. He must work at least 9 hours altogether between both jobs in a given week. Write an inequality that would represent the possible values for the number of hours babysitting, bb, and the number of hours walking dogs, dd, that Ryan can work in a given week.
The inequality that would represent the possible values for the number of hours babysitting, bb, and the number of hours walking dogs, dd, that Ryan can work in a given week is b + d >= 9.
How to illustrate the information?From the information, Ryan is working two summer jobs, babysitting and walking dogs. He must work at least 9 hours altogether between both jobs in a given week.
Therefore, the inequality that would represent the possible values for the number of hours babysitting, b, and the number of hours walking dogs, d, that Ryan can work in a given week will be:
Babysitting + Walking dogs >= 9
b + d >= 9
Therefore, the inequality is b + d >= 9.
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)The following are the ages (years) of 5
people in a room:
23, 20, 15, 12, 17
A person enters the room.
The mean age of the 6 people is now
19.
What is the age of the person
who
entered the room?
Answer:
The age of the person who entered the room is 27
Step-by-step explanation:
If there are 6 people and the mean is 19 you would need to multiply 19 by 6. You will get 114 and now you just subtract the age of the others. 114-23-20-15-12-17=27.