The polynomial function, y= (x+4)(x-2)²(x+7) has three different roots
How to determine the number of roots?From the question, we have the following parameters that can be used in our computation:
y = (x+4)(x-2)^2(x+7)
Rewrite the equation properly
So, we have the following representation
y= (x+4)(x-2)²(x+7)
Set the factor to 0
So, we have
x + 4 = 0, x - 2 = 0 and x + 7 = 0
When these equations are solved, we have
x = -4 , x = 2 and x = -7
See that the counts of the values of x is 3
Hence, it has three different roots
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Find the value of $x$ so that $3^x = (-27)^{-6}$.
[tex]3^x=(-27)^{-6} \\ \\ 3^x=(-3^3)^{-6} \\ \\ 3^x=(3^3)^{-6} \\ \\ 3^x=3^{-18} \\ \\ \boxed{x=-18}[/tex]
PLEASE HELP ASAP!!! Will IMMEDIATELY give Brainliest to the correct answer!! 100 pt question!!
The function f(x)=∣x−3∣ can be used to determine how far a number x is away from the number 3 on the number line. Find and interpret the given function values and determine an appropriate domain for the function.
Answer:
The function f(x) = |x - 3| can be used to determine how far a number x is away from the number 3 on the number line. To find the function value for a given x, we first need to subtract 3 from x and then take the absolute value of the result. For example, if x = 5, then the function value would be f(5) = |5 - 3| = |2| = 2.
The domain of the function is the set of all possible values of x that we can plug into the function to get a real number result. In this case, the function will work for any real number value of x, so the domain of the function is the set of all real numbers, which can be written as:
Domain: (-∞, ∞)
In other words, the function f(x) = |x - 3| can be used to determine how far any real number x is away from the number 3 on the number line.
Music Company A charges a 15$ membership fee and 0.75$ each to download a song. Music Company B charges 0.90$ each to download a song with no membership fee.
a. For what number of songs will both companies charge the same amount? Justify your answer using mathematics.
_________ Songs
You anticipate that you will download 150 songs. Which company should you choose if you want to spend the least amount of money? Justify your answer using mathematics.
________ (Type Company A or Company B)
a. Using linear equations in one variable we get the number of songs at which both companies would charge the same amount is 100 songs.
b. Company B would be a better choice as the total charges for 150 songs would be $127.5.
Explain linear equations in one variable.
A straight line with only one variable is a linear equation. the single variable's power is 1. Simple algebraic methods are used to solve these equations, which have the form ax+b=0.
a) Assume the number of songs downloaded is 'x'.
Now according to the question,
Total charges by company A is 15+0.75x
Total charges by company B is 0.90x
For equal charges, both must be equal,
Hence equating the 2 expressions we get,
15+0.75x=0.90x
15=0.15x
x=100
Hence total number of songs to reach the charge of the same amount is 100.
b)Let us take 150 songs from company A, we get the total charge to be
15+0.75*150=$127.5
Taking for company B, we get
0.90*150=$135.
We see that for 150 songs, the charges of company A is less compared to company B. Therefore I would choose company B over company A.
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What is the solution to the division problem below? (You can use long division or synthetic division.)
(2x2 + 7x-15) - (x+ 5)
Pls answer free brainliest
The expression that is a factor of the polynomial x³ + 2x² - 9x - 18 is (x + 2).
How to find the factors of a polynomial?Factoring of a polynomial is the method of breaking the polynomial into a product of its factors.
For example x² - 4 can be broken as (x - 2) and (x + 2).
Therefore, the expression that factor the polynomial x³ + 2x² - 9x - 18 is as follows:
Therefore,
x³ + 2x² - 9x - 18 = (x - 3)(x² + 5x + 6)
Let's break (x² + 5x + 6) down
x² + 5x + 6
x² + 2x + 3x + 6
x(x + 2) + 3(x + 2)
(x + 3)(x + 2)
Therefore, the factors are (x + 3)(x + 2) and (x - 3)
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Answer:
The answer is C, (x+2).
Unless specified, all approximating rectangles are assumed to have the same width. Evaluate the upper and lower sums for f(x) = 1 + cos - SXST, with n = 3, 4, and 6. Illustrate each case with a sketch similar to the figure shown below.
The upper and lower sums for f(x) = 1 + cos - SXST, with n = 3, 4, and 6 is 10.1913798 and 10.19913798.
What is upper and lower sums?
Using rectangles that are both enscribed in and circumscribed by a curve, we may approximate the area under a curve. The total area of the rectangles that are inscribed is the lower sum, while the total area of the rectangles that are circumscribed is the higher sum.
[tex]$n=6: \quad \Delta x=\frac{2 \pi}{6}$[/tex]
[tex]\begin{aligned}& \text { Lower sum }=\frac{2 \pi}{6}\left[f(-\overline{4})+f\left(-\frac{2 \pi}{3}\right)+f\left(-\frac{\pi}{3}\right)+f(0)+f\left(\frac{\pi}{3}\right)+f\left(\frac{2 \pi}{3}\right)\right] \\& c_6=\frac{2 \pi}{6}[1+1.5+1.8660256+2+1.8660254+1.5] \\& c_6=10.1913798\end{aligned}[/tex]
upper sum:
[tex]\begin{aligned}& =\frac{2 \pi}{6}\left[f\left(-\frac{2 \pi}{3}\right)+f\left(-\frac{\pi}{3}\right)+f(0)+f\left(\frac{\pi}{3}\right)+f\left(\frac{2 \pi}{3}\right)+f(\pi)\right] \\R_6 & =\frac{2 \pi}{6}[1.5+1.8660254+2+1.8660254+1.5+1] \\R_6 & =10.1913798]\end{aligned}[/tex]
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Find a linearization at a suitably chosen integer near a at which the given function and its derivative are easy to evaluate. f(x) = x^(-1), a = 0.9
A linearization at a suitably chosen integer near a at which the given function and its derivative are easy to evaluate is L(x)=-6 -4x .
What is function ?
A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.
Nearest integer is x =-1
Centre of linearization as x =-1
f(x)=3x2 +2x -3
f(-1)=3(-1)2 +2(-1) -3
f(-1)=-2
f(x)=3x2 +2x -3
f '(x)=6x +2
f '(-1)=6(-1) +2
f '(-1)= -4
L(x)=f(-1) + f '(-1) (x-(-1))
L(x)=-2 -4(x+1)
L(x)=-2 -4x -4
L(x)=-6 -4x
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Show the optimal binary search tree for the following words, where the frequency
of occurrence is in parentheses: a (0.18), and (0.19), I (0.23), it (0.21), or (0.19).
The optimal binary search tree for the given frequency is attached below.
Binary search tree:
Binary search tree refers the value of left node must be smaller than the parent node, and the value of right node must be greater than the parent node.
Given,
Here we have to plot the optimal binary search tree for the following words, where the frequency of occurrence is in parentheses: a (0.18), and (0.19), I (0.23), it (0.21), or (0.19).
In order to plot the binary search tree, we have to do the following steps,
First, we have to insert 0.18 into the tree as the root of the tree.Now, then read the next element; if it is smaller than the root node, insert it as the root of the left subtree, and move to the next element.Whereas, if the element is larger than the root node, then insert it as the root of the right subtree.Then we get the binary search tree like the following.
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b) On the grid draw the graph of x + y = 6
for values of x between -2 and 3.
Answer:
x=1 y=6
Step-by-step explanation:
???
What are the zeros of this function?
Answer:
B. x = 0 and x = 5
Step-by-step explanation:
The zeros of this function are x = 0 and x=5
_________________
Have a great day!
Write the following equation in slope-intercept form and identify the slope and y-intercept.
6x - 4y = 11
Answer:
Step-by-step explanation:
This in standard form (Ax + By = C.) In order to make this slope-intercept form, you need to isolate y.
y = -1.5x + 2.75
y=mx + b is slope intercept, where m is the slope and b is the y-intercept.
In this case, -1.5 is the slope and 2.75 is the y-intercept.
Hope this helps!!
Is the following statement linear or exponential?
Lalo's hair is also known to grow rapidly. It began at a length of 6 in and grew at a constant rate of 1 in per month. HELP PLEASE Nobody is helping me :(
Answer:
Step-by-step explanation:
exponential
Your business has conducted five market research surveys in the past year. The cost per survey is as follows: Survey 1: $725 Survey 2: $850, Survey 3: $1,250, Survey 4: $1,350, Survey 5: $900. What is the median cost of the market research surveys?
a) $900
b) $1,015
c) $1,092
d) $1,250
The median cost of the market research surveys is $900 so option (a) is correct.
What are the mode and median?Mode is the highest frequency number while the median is the middle value of a data set after writing in either an increasing or decreasing manner.
As per the given surveys,
Survey 1: $725 Survey 2: $850, Survey 3: $1,250, Survey 4: $1,350, Survey 5: $900.
Write the surveys in the increasing format as
$175,$850,$900,$1250,$1350
The median will be the middle value thus $900 will be correct.
Hence "The median price of the surveys for market research is $900".
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Two people receive an e-mail. Every day, the number of people who receives the e-mail triples. If people continue to receive the e-mail at this rate, how long will it take until 4,374 people receive the e-mail?
Choose the equation for the number of people who receive the e-mail, E, in terms of the number of days since the first e-mail was sent, d, and the correct solution.
PLS HELP
Answer:
Step-by-step explanation:
First, you will multiply 2 times 4,374 and get 8,748 then you will divide 8748 by 7 which is a week, and get 1249.7 then you will divide it by 356 which is a year approximate, and get 10.51 days.
find the mean weight and variance of the following students in kilograms 50,70,58,62,66,53 and 76
Answer:
The answer is 62 and 86
Step-by-step explanation:
Mean
(50 + 70 + 58 + 62 + 66 + 53 + 76) ÷ 7
435/7 = 62.1 ≈ 62
Variance
(50 - 62)² + (70 - 62)² + (58 - 62)² + (62 - 62)² + (66 - 62)² + (53 - 62)² + (76 - 62)²
(144 + 64 + 16 + 0 + 16 + 81 + 196)/(7 - 1)
517/6 = 86
Thus, The mean of the given data is 62 and Variance is 86
Any help on this question
Using trigonometric relations we will see that:
a = 5*√3
b = 5
The correct option is the one you marked.
How to get the values of a and b?For a right triangle with a known hypotenuse H and a known angle x, we can use the trigonometric relations:
cos(x)= (adjacent cathetus)/h
sin(x) = (opposite cathetus)/h
Here the hypotenuse measures 10 units, and the known angle is x = 30°.
The adjacent cathetus to that angle is a, so we can write:
cos(30°) = a/10
a = cos(30°)*10 = 10*√3/2 = 5*√3
And b is the opposite cathetus:
sin(30°) = b/10
b = 10*sin(30°) = 5
Then the correct option is the one you marked.
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Consider the function f(x)=x³+7 x²-36
1. Consider the function f(x)=x³+7 x²-36.
a. [1 pts] Find f(2).
b. [4 pts] Factor f(x). Show all your work. (Hint: You can use the fact that if f(a)=0, then the f(x) must have (x-a) as a factor.
2. Miguel decided to invest some of his money in an account gaining $3 % interest compounded semiannually. He ultimately would like to purchase a 560,000 car.
a. [5 pts] How much would he have to invest initially to have the necessary money in 4 years? Round your answer to the nearest whole dollar
By using the concept of factorization and compound interest, it can be calculated that-
1a) f(2) = 0
b) f(x) = (x - 2)(x + 6)(x + 3)
2) Miguel must initially invest 497118.23
What is factorization and compound interest?
Factorization is the reduction of an algebraic expression into two or more algebraic expressions of smaller degree
If the interest on a certain principal at a certain rate over a certain period of time increases exponentially rather than linearly, the interest earned is called compound interest.
1) a) f(x) = x³+7 x²-36
f(2) = 2³+7(2)²-36
f(2) = 36 - 36 = 0
b) Since f(2) = 0, (x - 2) is a factor of f(x)
f(x) = x²(x - 2) + 9x(x - 2) + 18(x - 2)
f(x) = (x - 2)(x² + 9x + 18)
f(x) = (x - 2)(x² + 6x + 3x + 18)
f(x) = (x - 2){x(x + 6) + 3(x + 6)}
f(x) = (x - 2)(x + 6)(x + 3)
c) Let the principal be $p
Rate = 3%
Time = 4 years
[tex]560000 = p(1 + \frac{3}{200})^{4 \times 2}\\\\560000 = p(\frac{203}{200})^8\\\\\\p = 560000 \times (\frac{200}{203})^8\\\\p = 497118.23[/tex]
Miguel must initially invest 497118.23
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SUPER URGENT!
20 points!!
picture required
Find the angle between 0 and 2π in radians that is coterminal with the angle -25π/6
Hi,
I hope you and your family are doing well!
An angle is coterminal with another angle if it has the same terminal side as the other angle, but may have a different degree measure. In other words, coterminal angles are angles that are measured around the same point on the unit circle, but may start at different points.
To find the angle between 0 and 2π in radians that is coterminal with the angle -25π/6, we can add or subtract multiples of 2π to -25π/6 until we get an angle between 0 and 2π.
For example, adding 2π to -25π/6 gives us:
-25π/6 + 2π = -π/6 + 2π = 7π/6
This angle is between 0 and 2π, so it is coterminal with -25π/6.
Alternatively, subtracting 4π from -25π/6 gives us:
-25π/6 - 4π = -29π/6 = -π/2
This angle is also between 0 and 2π, so it is coterminal with -25π/6.
Therefore, the angle between 0 and 2π in radians that is coterminal with -25π/6 is either 7π/6 or -π/2.
Please give this answer 5 stars and brainliest if you find it helpful.
Happy Holidays & New Year!
Where, if anywhere, does h(x) = m(x) when h(x) = (x+2)^2-9 and m(x) = x-10
Answer:
Where, if anywhere, does h(x) = m(x) when h(x) = (x+2)^2-9 and m(x) = x-10
wut do i have to find
Step-by-step explanation:
John drew a triangle with side lengths of 5, 12 and 13. His friend, Bryan, looked at it and asked John if it is a right triangle. John’s response was yes. Explain or show how John can prove to Bryan that the triangle is a right triangle
It's a right angle as 13² is the addition of 5² and 12².
How to prove the right angle?A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly known as a rectangled triangle, is a triangle with one right angle, i.e. two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.
In this case, the values given are 5, 12 and 13. This will be illustrated thus:
5² + 12² = 13²
25 + 144 = 169
169 = 169
This was done based on Pythagoras theorem.
Therefore, it's a right angle.
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A diver starts out at 426 feet below the surface (or -426 feet). She then swims upward 212 feet. Use a signed number to represent the diver's current depth
Step-by-step explanation:
this is a college question ?
oh, my dear ...
we start at -426 ft.
swimming upwards reduces depth by adding hight.
so,
-426 + 212 = -214 ft
basically the same method is used as if we would subtract 212 from 426.
so, the diver is currently at -214 ft (214 ft below the surface).
fill in the blank so that the equation is a prefect square trinomial
A cookie recipe calls for 4 cups of flour for every 1 cup of sugar. If you want to make multiple batches of the cookies and you use 8 cups of sugar, how much flour will you use?
Answer:
8x4=32
Step-by-step explanation:
I hope I helped you
What is the correct to this answer ???? ( answers only)
Answer:
x>9
Step-by-step explanation:
2x-5>13
2x>13+5
2x>18
x>18/2
x>9
Answer:
x > 9
Step-by-step explanation:
To find the solution to this inequality we need to follow these steps:
2x - 5 > 13
add 5 to both sides2x > 18 (-5 will be eliminated by +5 on the left side while 13 will be 18 when 5 added to it)
divide both sides by 2x > 9
consider the following method. public int pick(boolean test, int x, int y) { if (test) return x; else return y; }
If P is the minimum number of tests to achieve full statement coverage for f(x) and Q is the minimum number of tests to achieve full branch coverage for f(x), then (P,Q) =(3, 4)
Branch coverage: During program testing, every branch in a statement must be run at least once.
Coverage of the statement:
This means that during testing, every statement in the computer code must be run at least once.
All of the statements must be executed in order to obtain complete statement coverage.
Statement coverage is calculated as (statement executions divided by total statement executions).
To obtain complete statement coverage in the code above, two test cases are necessary.
Case 1: If the if condition is satisfied,
{
int res=0;
if(m<0) {res=n-m;}
return res;
}
These commands will be carried out.
Case 2: All remaining statements will also be put into effect when the other two cases of else do. Full statement coverage is attained after three tests.
Branch coverage: It includes both true and false situations and is decision-based.
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3y^2 + 3(4y^2 - 2) please help
The roots of the quadratic equation 3y² + 3(4y² - 2) is ± √(1/7).
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, 3y² + 3(4y² - 2).
3y² + 12y² - 2.
14y² - 2.
Let 14y² - 2 = 0.
14y² = 2.
y² = (2/14).
y = ± √(2/14) Or ± √(2/2×7) Or ± √(1/7).
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5/6 q - 1/3 q = 2/5
Please explain step by step on how I could get this answer
Answer:
4/5
Step-by-step explanation:
5/6q-1/3q=2/5
We change the coefficient’s denominators to 6 so we can subtract them
5/6q-2/6q=2/5
3/6q=2/5
1/2q=2/5
Now divide both sides by 1/2 or multiply both sides by 2
1/2q=2/5
/1/2. /1/2
q=2/5/1/2
q=2/5*2/1
q=4/5
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K
Problem Solving
X 4.3.PS-7
Simplify the expression.
-2.6f+0.2f-15-9
-2.6f+0.2f-15-9=
(Simplify your answer. Use integers or decimals for any numbers in the
Answer:
(23x+4.2)
Step-by-step explanation:
Which is equivalent to 64 1/4 ?
O24^4
04
O 16
O 1644
Help me pls !! Being timed !
The value equivalent to [tex](64)^{1/4}[/tex] is [tex]2\sqrt[4]{4}[/tex].
What is meant by an expression?An expression or mathematical expression is a finite arrangement of symbols that are well-formed in line with context-dependent criteria. To help define the logical grammar and order of operations, mathematical symbols can be used to represent variables, operations, functions, brackets, punctuation, and grouping.
A formula and an expression are often distinguished by authors, with the former designating a mathematical entity and the latter a statement about such a thing.
But in contemporary mathematics, and particularly in computer algebra, formulas are seen as expressions that can be evaluated as true or false, depending on the values given to the variables present in the expressions.
Given expression is [tex](64)^{1/4}[/tex]
The number 64 can be written as 2 × 2 × 2 × 2 × 2× 2 =2⁶
So, the above given expression becomes,
[tex](64)^{1/4}[/tex]=[tex](2^{6}) ^{1/4}[/tex]
2⁶=2⁴.2²
So,
[tex](2^{6}) ^{1/4}[/tex]=[tex](2^{4} 2^{2})^{1/4}[/tex]
By simplifying we get,
[tex](64)^{1/4}[/tex]=[tex]2\sqrt[4]{4}[/tex]
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