the number of roots of the polynomial 7 + 5 x⁴ - 3 x² is 4.
We are given a polynomial:
7 + 5 x⁴ - 3 x²
We need to tell the number of roots that the polynomial has.
a polynomial is an expression consisting of indeterminates and coefficients.
It is the one that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Example: x² − 4x + 7.
We know that:
Number of roots = highest power of the variable of the polynomial
Here, the number of roots will be:
roots = 4
Therefore, we get that, the number of roots of the polynomial 7 + 5 x⁴ - 3 x² is 4.
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The function g(x) shown in the table below is a linear function. Find its slope, y-intercept, and formula in
slope-intercept form.
Answer:
see explanation
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 9, 31) and (x₂, y₂ ) = (15, - 41) ← 2 ordered pairs from the table
m = [tex]\frac{-41-31}{15-(-9)}[/tex] = [tex]\frac{-72}{15+9}[/tex] = [tex]\frac{-72}{24}[/tex] = - 3
the y- intercept is the value of g(x) when x = 0 , then from the table
y- intercept = 4
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept ) , then equation is
y = - 3x + 4
Which statement is true of this function?
ƒ(x) = (²) — 2
O A. As the value of x increases, the value
B. The domain of the function is (-2, 00).
OC. The function has a y-intercept at (0,-2).
OD. The function is increasing.
The statement "As the value of x increases, the value of f(x) moves toward a constant." is true. Option A
What is the function?A relation between a collection of inputs and one output for each of those inputs is the definition of a function.
The given function is;
F(x)=(1/5)^x-2
The statement that is true of this function is as follows;
As the value of x increases, the value of f(x) moves toward a constant.
The domain of the function is (-∞, ∞).The function has a y-intercept at (0,-1).The function is decreasing.Therefore, the assertion that is true about this function is that when the value of x rises, the value of f(x) advances toward a constant. This is because of the way that the function works.
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CQ
Select the correct answer. Which statement is true of this function?
f(x)=(1/5)^x-2
A.
As the value of x increases, the value of f(x) moves toward a constant.
B.
The domain of the function is (-2, ∞).
C.
The function has a y-intercept at (0,-2).
D.
The function is increasing.
Suppose that x and y vary inversely. Write a function that models the inverse variation.
x=13 when y=17
According to the question, to calculate the relationship function model of the given equations which are as follows:
[tex]x=13[/tex] and [tex]y=17[/tex]
And the condition is the function is inverse in nature that means they vary inversely. And it can be represented as:
Equation: [tex]y = \frac{k}{x}[/tex]
[tex]17 = \frac{k}{13}[/tex]
[tex]k = 221[/tex]
Substituting the values to get the final expression:
[tex]y = \frac{221}{x}[/tex]
[tex]xy = 221[/tex]
Substitute the value of 'k' in the original equation. And the final expression is: [tex]xy =221[/tex]
What is function?
In mathematics, function can be defined as an expression or the rule or the law. It defines the relationship between dependent variable and the independent variable.
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Identify the percentage of growth or decay for the exponential function y = 104(2.05) x
The percentage of decay for the exponential function: y = 104(2.05) x is 105%.
How to illustrate the information?This equation represents exponential decay. Whenever the base is less than 1, the function represents decay. When the base is greater than 1, the function represents growth. In this case, the base is 2.05 which is 1.05 than 1, representing growth.
The formula for exponential decay is y=a(1-r)x.
r is the decay rate, expressed as a decimal.
In this case, r = 2.05 - 1 = 1.05 which represents 105%.
Therefore, the percentage of decay for the exponential function is 105%.
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Write the decimal expansion for 2/33
Answer:
0.0606060606 hope that's right if not I'm sorry
what is -3 to the -3 power
Answer:
-0.03
Step-by-step explanation:
[tex]3^{-3}=\frac{1}{3^3}\\=-\frac{1}{3^3}\\3^3=27\\=-\frac{1}{27}\\= -0.03[/tex]
$750, annual rate:10 1/2% what is the time to double & the amount after 10 years?
well, let's start like the crab, from the back, what would the amount be after 10 years, with a 10.5% annual rate, compounding annually of course.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$750\\ r=rate\to 10.5\%\to \frac{10.5}{100}\dotfill &0.105\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases} \\\\\\ A=750\left(1+\frac{0.105}{1}\right)^{1\cdot 10} \implies A=750(1.105)^{10}\implies \boxed{A \approx 2035.56}[/tex]
when will it double? well, hmmm 750 doubled will be 1500, so
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$1500\\ P=\textit{original amount deposited}\dotfill &\$750\\ r=rate\to 10.5\%\to \frac{10.5}{100}\dotfill &0.105\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years \end{cases}[/tex]
[tex]1500=750\left(1+\frac{0.105}{1}\right)^{1\cdot t} \implies \cfrac{1500}{750}=(1.105)^t\implies 2=1.105^t \\\\\\ \log(2)=\log(1.105^t)\implies \log(2)=t\log(1.105) \\\\\\ \cfrac{\log(2)}{\log(1.105)}=t\implies 6.94\approx t\qquad \textit{about 6 years and 344 days}[/tex]
solve the simultaneous equation
2x + 3y = 7
3x + 2y = 8
Answer:
(2, 1 )
Step-by-step explanation:
2x + 3y = 7 → (1)
3x + 2y = 8 → (2)
multiplying (1) by 3 and (2) by - 2 and adding will eliminate x
6x + 9y = 21 → (3)
- 6x - 4y = - 16 → (4)
add (3) and (4) term by term to eliminate x
0 + 5y = 5
5y = 5 ( divide both sides by 5 )
y = 1
substitute y = 1 into either of the 2 equations and solve for x
substituting into (1)
2x + 3(1) = 7
2x + 3 = 7 ( subtract 3 from both sides )
2x = 4 ( divide both sides by 2 )
x = 2
solution is (2, 1 )
Carlo, having a mass of 50kg, running to the next classroom for his next subject. If his running speed is 10m/s, what is his kinetic energy?
Answer:
Kinetic energy = 2500 J
Step-by-step explanation:
To calculate the kinetic energy of an object, we can use the following formula:
[tex]\boxed{E_k = \frac{1}{2}mv^2}[/tex],
where:
[tex]E_k[/tex] = kinetic energy
m = mass of the object
v = speed of the object
In this question, we are told that Carlo's mass is 50 kg and his speed is 10 m/s. Using this information and the formula above, we can calculate Carlo's kinetic energy:
[tex]E_k = \frac{1}{2} \times 50 \times (10)^2[/tex]
[tex]= \frac{1}{2} \times 50 \times 100[/tex]
[tex]= \bf 2500 \: J[/tex]
Therefore, Carlo's kinetic energy is 2500 J.
Find two rational numbers between −7/2 and 4/3
Two rational numbers between −7/2 and 4/3 are -20/6 and 7/6.
The two given rational numbers are −7/2 and 4/3.
What are rational numbers?A rational number is a number that is of the form p/q where p and q are integers and q is not equal to 0.
Now, two rational numbers between −7/2 and 4/3 can be found as follows:
Make denominators the same by taking the LCM of denominators.
LCM of 2 and 3 is 6.
Change denominators of both the rational numbers to 6 by multiplying the same number by numerator and denominator.
So, the rational numbers become −21/6 and 8/6.
Now, two rational numbers between −21/6 and 8/6 are -20/6 and 7/6.
Therefore, two rational numbers between −7/2 and 4/3 are -20/6 and 7/6.
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Mackenzie bought a 10-pound bag of flour. She used some of the flour to bake loaves
of bread.
How can Mackenzie find the amount of flour she used?
Mackenzie can find the amount of flour used by using subtraction. She should subtract the flour left in the bag from 10 pounds.
Subtraction is one of the four basic mathematical operations.
It is used to calculate the amount left after a quantity is reduced.
When two variables are subtracted we use the following notation '-' .
Let us consider two variables x and y such that x is subtracted from y then mathematically it is denoted by y - x .
Mackenzie used some flour to bake bread. To calculate the amount she used from 10 pound bag , first she will have to find the amount of flour left in the bag.
Let a pounds of flour is left (a<10).
So to calculate the amount of flour used by her we simply subtract a from 10 pound.
Hence flour left is (10 - a) pounds.
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Round this number to the
nearest thousandth.
1.9541
Answer:
1.954
Step-by-step explanation:
4 is the thousandth and we wouldn’t round up because of 1
Answer: 1.954
1.9541 is to low to round up to the thousandths so it needs to be rounded down, giving the answer 1.954.
99999999999999999999999999999999999999999999999999999999999999999999999x0
Answer:
Stop please. You use brainly for answering and asking questions.
PLEASE HELP Mr. Ingram asked his students to construct an equilateral triangle inscribed in a circle.
The sequences of steps Euna and Jason used in their constructions are shown below.
Answer Choices: Only Euna, Only Jason, Both Jason and Euna, Neither Jason nor Euna, It is impossible to determine who
The correct was done by Jason
what is construction?Geometric construction is a process of constructing geometric figures using geometric tools such as a straightedge (ruler), a compass, and a pencil.
Given:
We have some sequence to construct an equilateral triangle
So, Jason are more relatable in constructing an equilateral triangle.
1. Use a compass to draw circle O
2. Use a straightedge to draw a diameter of the circle. Label the endpoints P and S.
3. Without changing the compass width draw a full circle centered at S
4. Label the points of intersection of the two circles R and Q
5. Use a straightedge to draw segments joining points P, Q, and R to form the equilateral triangle PQR.
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Please help me please help me
11. How many dots are in the nth term of the following sequence? term: 3,5,7,9 n+2 n²+2 2n+1 n+3
The nth term of the sequence is 2n + 1
The formula known as the nth term allows us to locate any term in a series. The letter n stands for number. By changing the term number's value, we can create a series that uses the nth term (n).
The sequence 3,5,7,9.....
n =1
3 = 1 + 2
3 = 1 + (2×1)
n = 2
5 = 1 + 4
5 = 1 + (2×2)
n = 3
7 = 1 + 6
5 = 1 + (2×3)
n = 4
9 = 1 + 8
9 = 1 + (2×4)
9 = 1 + 8
Therefore, the expression for the Nth is 1+ 2n or 2n + 1
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please help!. i'll give 50 brainly points
Daniel’s parents were planning a big birthday party for him.
His parents spent $2.29 on each of 8 goodie bags. How much did they spend on goodie bags? Show your work.
They spent $160 to rent a bounce house for 8 hours. How much is the hourly rate for the rental? Show your work.
If the parents spent a total of $209.48 on the party, how much more did they spend than what was spent in parts (a) and (b)? Show your work.
show your work on each questions please!
Answer: A. 18.32
B. 20
C. 31.16
Step-by-step explanation:
2.29 times 8=18.32 dollars spent on goodie bags
160 divided by 8=20 dollars per hour
160+18.32=178.32
1209.48-178.32= 31.16 more than what was spent in parts a and b.
The telephone company offers two billing plans for local calls. Plan 1 charges $33 per month for unlimited calls and Plan 2 charges $16 per month plus $0.05 per call.
A use an inequality to find the number of monthly calls for which Plan 1 is more economical than plan 2
B. Explain the meaning of the answer to part A
Answer:
Part A
Plan 1
33
Plan 2
0.05x+16
0.05x+16=33
0.05x=17
17/0.05=340
341 calls would be enough.
Part B
AN easy way of doing this is by setting the equations equal to each other and then adding a variable to one side that would be the amount of calls made on plan B. Once you get rid of the initial price of 16 dollars, then you have 17 dollars to be set equal to plan B. You divide 17 by 0.05, which gives you 340, meaning that to make both plans equal to each other, you would have to make 340 calls. To make Plan 1 more economical, you would have to add 1 more call to set plan 2 0.05 cents more than Plan 2.
Step-by-step explanation:
1. In each of the following, express x in terms of the other variables.
(i) 3x - 2y = 4
(ii) 2x-b-4c
(iv) 5(x-3)= 2y
(v) 3y=-2
(iii) 5x -4 = I
(vi) xy = xz + yz
'x' in each expression is as follows:
x = (4+2y)/3x = (b + 4c)/2x = (2y + 15)/5y = -2/3x = (l + 4)/5xy/xz = yzWhat are variables?A variable in mathematics is an alphabet or term that stands in for an unknown quantity, unknowable value, or unknowable number. Particularly in the case of algebraic expressions or algebra, the variables are used. As an illustration, the linear equation x+9=4 has the variables x and 9 as constants. Typically, it is a letter like x or y. Example: The variable in x + 2 = 6 is x. We can find x = 4 by solving the x + 2 = 6 situation.So, the value of 'x' in each expression:
(i) 3x - 2y = 4 ⇒ 3x = 4+2y ⇒ x = (4+2y)/3(ii) 2x-b-4c ⇒ 2x = b + 4c ⇒ x = (b + 4c)/2(iii) 5(x-3)= 2y ⇒ 5x = 2y + 15 ⇒ x = (2y + 15)/5(iv) 3y = -2 ⇒ y = -2/3(v) 5x -4 = I ⇒ 5x = l + 4 ⇒ x = (l + 4)/5(vi) xy = xz + yz ⇒ xy/xz = yzTherefore, 'x' in each expression is as follows:
x = (4+2y)/3x = (b + 4c)/2x = (2y + 15)/5y = -2/3x = (l + 4)/5xy/xz = yzKnow more about variables here:
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If KL = 8x - 5 and LM = 6x + 3, what is KL?
KL = LM To find the measures of KL
8x-5 = 6x+3
-6x -6x 8(4) - 5
___ ___ 32 - 5
2x - 5 = 3 27
+5 +5
__ __ To find the measure of LM
2x = 8 6(4) + 3
--- --- 24 + 3
x = 4 27
10. Justin goes to the mall with $120. He spends $54.67 on clothes. $13.49 on school supplies, and $8.14 on lunch. How much does he have left?
Answer:$43.70
Step-by-step explanation:
120−54.67−13.49−8.14
=$43.70
Answer:
43.7
Step-by-step explanation:
120-54.67-13.49-8.14=43.7$
We can go to the amusement park or the library. the amusement park is too expensive, so we must go to the library.
Based on the logical fallacy given by saying that they can either go to the amusement park or the library, the category is False dilemma.
What is a false dilemma?A False dilemma is a logical fallacy where the speaker makes it seem as though there are no other options to be considered. The possibility of there being other options is therefore ignored.
In the above thought, the speaker says that they can either go to the amusement part or to the library. They then pick the library because the amusement park is too expensive.
This is a logical fallacy because there were other places they could have gone to that were not even considered.
In conclusion, the statement above that presents only two choices of places to go which were the library or the amusement park is an example of a false dilemma.
Rest of the question:
Identify the logical fallacy in the given statement.
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which is bigger 35.7 or 35.68
Condensing Logarithms:
[tex]\frac{log2}{2} + \frac{log4}{3} =[/tex]
[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{\log(2)}{2}+\cfrac{\log(4)}{3}\implies \cfrac{1}{2}\log(2)+\cfrac{1}{3}\log(4)\implies \log(2^{\frac{1}{2}})+\log(4^{\frac{1}{3}}) \\\\\\ \log(2^{\frac{1}{2}})+\log( ~~ (2^2)^{\frac{1}{3}} ~~ )\implies \log(2^{\frac{1}{2}})+\log(2^{\frac{2}{3}})\implies \log( ~~ 2^{\frac{1}{2}}\cdot 2^{\frac{2}{3}}~~) \\\\\\ \log( ~~ 2^{\frac{1}{2}+\frac{2}{3}} ~~ )\implies \log( ~~ 2^{\frac{3+4}{6}} ~~ )\implies \log (~~ 2^{\frac{7}{6}} ~~ )\implies {\LARGE \begin{array}{llll} \log(\sqrt[6]{128}) \end{array}}[/tex]
Help what are the answers to monster challenge puzzle 34!!!
odd Answer:
make icecubes then drop them in hydrochloric acid
Step-by-step Step-by-step Step-by-step Step-by-step explanation
Kelly has 306 stars she sells 56 how many are left?
Answer:
250
Step-by-step explanation:
Take 56 away from 306
306 - 56
=250
what do i write in the blank boxes?
Answer:
the answer
Step-by-step explanation:
you got to write the answer in the blank boxes
3.18 + 2m = 12.7 how do you do this?
Answer:
Step-by-step explanation:
If you're solving for m:
3.18 + 2m = 12.7
-3.18 -3.18
Therefore making the new equation: 2m = 9.52
Divide- [tex]\frac{2m}{2\\} =\frac{9.52}{2}[/tex]
m = 4.76
The area of a rectangle with a length 2 feet less than 3 times its width.
Write a function rule for the area.
What is the area of the rectangle when its width is 2 feet?
The area of the given rectangle is 6ft².
What is a rectangle?A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can also be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.So, length 2 feet less than 3 times its width:
When the width is 2ft.Then function: L = 3w - 2
L = 3w - 2L = 3(2) - 2L = 6 - 2L = 4 ftNow, the area of the rectangle: l × w
l × w4 × 26ft²Therefore, the area of the given rectangle is 6ft².
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f(x)=10 x-10 . Find each value.
(f⁻¹ ⁰ f)(0.2)
An inverse function is one that reverses the action of another function.
The value of this function is y = 0.2.
What is meant by inverse ?Inverse operations are mathematical manipulations in which one operation reverses the action of the other, such as addition and subtraction, multiplication and division. In most cases, the inverse of a number is its reciprocal, i.e. [tex]x ^{- 1[/tex] = 1 / x. A number and its inverse (reciprocal) product equals one.
An inverse function is one that reverses the action of another function. A function g is the inverse of a function f if and only if y = f(x) and x = g. In other words, using f and then g is equivalent to doing nothing.
Let the given function be f(x) = 10x - 10
substitute the value of x = 0.2, then we get
f(0.2) = 10(0.2) - 10
simplifying the above equation be
f(0.2) = -8
y = 1/10(-8) +1
y = 0.2
Therefore, the value of y = 0.2.
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