The only option that meets the root theorem is option b.
which of the following is a possible root of the polynomial function below?
The polynomial function is:
[tex]f(x) = 2x^2 - 4x + 9[/tex]
The rational root theorem says that if a root is a rational number, then the leading coefficient must be divisible by the denominator of the rational number and the constant term must be divisible by the numerator.
In this case, the constant is 9, and the only option such that the constant is divisible by the numerator is option b: 3
Where 3 is a rational number:
3 = 3/1
The numerator is 3 (which divides 9) and the denominator is 1 (which divides the leading coefficient 9. (notice that it meets the theorem, but it is not an actual root).
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Which choice is equivalent to the fraction below when x is an appropriate
value? Hint: Rationalize the denominator and simplify.
2
2-√6x
A.
2+√6x
2-6x
B. 2+√6x
4-3x
C. 2+√6x
2-3x
D. 2+√6x
4-6x
A fraction is a way to describe a part of a whole. The correct option is C.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
The choice that is equivalent to the fraction can be found by rationalizing the denominator of the fraction. Therefore, we can write,
[tex]\dfrac{2}{2-\sqrt{6x}}\\\\\\=\dfrac{2}{2-\sqrt{6x}} \times \dfrac{2+\sqrt{6x}}{2+\sqrt{6x}}\\\\\\= \dfrac{4+2\sqrt{6x}}{4-6x}\\\\\\=\dfrac{2(2+\sqrt{6x})}{2(2-3x)}\\\\\\= \dfrac{2+\sqrt{6x}}{2-3x}[/tex]
Hence, the correct option is C.
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Find the surface area of the cone in terms of 1.
15 cm
3 cm
In terms of l?
TSA
πr²+πrlπr(l+r)π(3)(3+l)9.42(3+l) cm²LSA
πrl9.42l cm²Answer:
[tex]\sf SA=54\pi\:\:\:cm^2[/tex]
Step-by-step explanation:
Surface Area of a Cone
[tex]\sf SA=\pi r l+\pi r^2[/tex]
where:
r is the radiusl is the slant heightGiven:
r = 3 cml = 15 cmSubstitute the given values into the formula and solve for SA:
[tex]\implies \sf SA=\pi (3)(15)+\pi (3)^2[/tex]
[tex]\implies \sf SA=45\pi+ 9 \pi[/tex]
[tex]\implies \sf SA=54\pi\:\:cm^2[/tex]
Therefore, the surface area of the cone in terms of pi is:
[tex]\sf SA=54 \pi\:\:\:cm^2[/tex]
Out of 475 applicants for a job, 240 have 10 years experience and 83 have over 10 years experience and a graduate degree. what is the probability that a randomly chosen applicant has a graduate degree given that they have over 10 years of experience?
Answer:
1
Step-by-step explanation:
Could this be a tricky question? See the point:
240 have 10 years experience (exactly)and 83 have over 10 years experience and a graduate degreeCombining 1 and 2 the answer is 1Though it's inlikely that the first 240 people have only 10 years. Don't take this answer very seriously
Pls answer thissssssss
Answer:
Area of room = 21 * 16
= 336 m²
Area of Carpet = (21 - 1)* (16-1)
= 20*15
= 300
Area of border = Area of room - Area of carpet
= 336 - 300
= 36 m².
Which of the following is calculated by finding the product of the length,
width, and height of a prism?
A. Perimeter
B. Surface area
C. Lateral area
D. Volume
vulume of the following is calculte by finding the product of the lenth,width,and height of a prism
Volume and surface area rectangular prism
13 in 7in 7in
The Volume and Surface Area of Prism is 462 in² and 637 in³.
What is Prism?
Prism is a three-dimensional solid object in which the two ends are identical. It is the combination of the flat faces, identical bases and equal cross-sections.
Surface area of rectangular prism,
= 2( lb +bh +lh)
= 2 ( 13*7 + 7*7+ 13*7)
=2*231
= 462 in²
Now, Volume,
= bhl
= 13*7*7
= 637 in³
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select the most appropriate measurement for each of the following
Answer:The following what
Step-by-step explanation:
what is the following and there is no questions.
Complete the steps in solving the quadratic function 7x – 9 = 7x2 – 49x by completing the square.
answer below:
–9 = 7x2 –
⇒ 56 x
–9 +
⇒ 112 = 7(x2 – 8x +
⇒ 16 )
56, 112, 16 in that order
Answer:
it's actually 28+/-√721/7
Step-by-step explanation:
What are the domain and range of f(x) = 2x - 41?
O domain: x < 2; range: (-00,00)
O domain: (-00,00); range: f(x) > 0
O domain: (-0,00); range: f(x) ≤0
O domain: x ≥ 2; range: (-00,00)
Answer:
X intercepts (41/2, 0), Y intercepts (0, -41)
Step-by-step explanation:
I hope this helps, if it doesn't then just message me, and ill be more than happy to help :)
The domain and range of function f(x) = 2x - 41 is domain (-∞,∞) and range is (0,∞).
What is a function?A relation is a function if it has only One y-value for each x-value.
The domain of a function is the set of values that we are allowed to plug into our function.
This set is the x values in a function such as f(x).
The range of a function is the set of values that the function assumes.
The function f(x) = 2x - 41 is a linear function.
As a linear function, the domain is all real numbers, and the range is also all real numbers.
So the domain is (-∞,∞) and range is (0,∞)
Hence, the domain and range of function f(x) = 2x - 41 is domain (-∞,∞) and range is (0,∞).
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The nth term of a sequence is -2n-4. Work out the 50th term of the sequence
Answer:
-104
Step-by-step explanation:
Completed by plugging 50 in the equation:
-2(50) - 4 =
-100 - 4 =
-104
Given parallelogram STUV, what is the length of TV?
The length of TV would be [tex]y^{2}[/tex] + 2y -1.
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
Given parallelogram STUV,
The length of TW = [tex]y^{2}[/tex]
WV = 2y - 1
The length of TV = TW + WV
= [tex]y^{2}[/tex] + 2y -1
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It's very urgent plss answer
The solution of the equation 4p – [(2p – 3) / 2] = 6 with variable p will be 1.5.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
The equation is given below.
4p – [(2p – 3) / 2] = 6
On simplifying, we have
(8p – 2p + 3) / 2 = 6
6p + 3 = 12
6p = 9
p = 1.5
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When a patient with hypertension takes a particular type of blood pressure medication, the effects on the systolic pressure, S(t), can be measured by the following piecewise defined function: S of t is equal to the piecewise function of 140 minus 6 times t if 0 is less than or equal to t is less than or equal to 4 and 116 if 4 is less than t is less than 8 and 96 plus 8 times t if 8 is less than or equal to t is less than or equal to 12 where t is the time, in hours, since taking the medication. Based on the graph of the piecewise function, if the patient takes the blood pressure medication at 8 a.m., in which interval will their systolic pressure be lowest?
Based on the graph, the interval will their systolic pressure be lowest is 4pm to 5pm.
What is the interval in blood pressure ?The lowest systolic pressure can be seen from 5 and 8 hours after taken the medication.
If we look at the time details then this will fall inbetween the interval of 2pm to 5pm.
According to question, the time range is 4pm to 5pm.
Hence, the interval will their systolic pressure be lowest is 4pm to 5pm.
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Answer:
The answer is B - 12 P.M to 2 P.M
Step-by-step explanation:
Is augmented matri invertible if linear system has a unique solution
An augmented matrix is invertible if the linear system has a unique solution.
What is an augmented matrix?
The augmented matrix is known as a rectangular matrix.
The properties of an augmented matrix includes:
The number of columns is equal to the number of variables in the linear equations. The number of rows is the same as the number of linear equations.The rows of the augmented matrix can be also be interchanged.Note that the inverse of a matrix must be unique
And If A is invertible, then its inverse is unique.
If the linear system is unique, then the augmented matrix is invertible.
Thus, an augmented matrix is invertible if the linear system has a unique solution.
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please evaluate the equation
Step-by-step explanation:
[tex] = \sum \limits_{n = 1}^{7} ( - 2. {6}^{n - 1} )[/tex]
[tex] = \sum \limits_ {n = 1}^{n_{ \text{max}}} (a_1. {r}^{n - 1} )[/tex]
[tex] \: [/tex]
[tex]a_1 = - 2[/tex]
[tex]n = 7[/tex]
[tex]r = 6 \to r >1[/tex]
[tex] \: [/tex]
• Find S7.
[tex]s_n = a_1.( \frac{ {r}^{n} - 1}{r - n} )[/tex]
[tex]s_7 = - 2.( \frac{ {6}^{7} - 1 }{6 - 1} )[/tex]
[tex]s_7 = - 2.( \frac{279.936 - 1}{5} )[/tex]
[tex]s_7 = - 2.( \frac{279.935}{5} )[/tex]
[tex]s_7 = - 2 \: . \: 55.987[/tex]
[tex]s_7 = - 111.974[/tex]
The answer is B.
what are the zero of f(x)=x(x-8)
The zeroes of the function f(x) = x (x – 8) will be 0 and 8.
What is a factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The function is given below.
f(x) = x (x – 8)
The zeroes of the function f(x) is given by the factor equals to zero.
Then we have
f(x) = 0
x(x – 8) = 0
x = 0, 8
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Suppose you flip two coins. What is the probability of getting at most one heads? give your answer as a reduced fraction.
The probability of getting at most one heads is 1/2
How to determine the probability?Let H represents Head and T represents Tail.
The sample space of two coin is:
S=(H,T),(T,T),(T,H),(H,H).
In the above sample, we have:
At most one head = 2
Total = 2
The required probability is then calculated as:
P = 2/4
Simplify
P = 1/2
Hence, the probability of getting at most one heads is 1/2
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On a coordinate plane, the x-axis is labeled minutes and the y-axis is labeled Blocks. Line A goes through points (10, 4), (15, 12), and (20, 20). Line B goes through points (5, 8), (10, 16), (15, 24). Line C goes through points (5, 24), (15, 16), (20, 12).
The table shows Jose’s rate of bicycle riding.
A 2-column table with 3 rows. Column 1 is labeled Minutes with entries 5, 10, 15. Column 2 is labeled Blocks with entries 8, 16, 24.
Which line on the graph shows the proportional relationship in the table?
Line
on the graph shows the proportional relationship.
The proportional relationship given in the table is y = 1.6x, and line B shows this relationship.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
The constant of proportionality, considering the points on the table, is given as follows:
[tex]k = \frac{24}{15} = \frac{16}{10} = \frac{8}{5} = 1.6[/tex].
Hence the equation is:
y = 1.6x.
Line B gives the same points as the table, hence it shows the proportional relationship.
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A pair of dice is rolled. What is the probability that the sum is 9 or that the first number is a 2?
Answer:
9/2 or 6/2
Step-by-step explanation:
The sum of nine should be amended by adding 6 + 2 +1 = 9
so when adding these numbers you will get the sum of 9
The graph represents a pair of equations. What point represents the solution to the pair of equations?
Answer:
if I'm correct it's where the 2 lines meet, which would mean the answer to be (-3,2)
Sylvia bought 4 bananas for 50 cents each and 1 apple for 80 cents. Write a numerical expression to represent this situation and then find the total cost.
Answer: 280
Step-by-step explanation:
50 cents for each banana so: 4* 50= 200
200+80
Answer is 280
Assuming no air resistance, how long would it
take a skydiver to fall 180 feet? (Estimate
your answer to one decimal place. Hint: Use the
equation d = 16+²)
Using the given equation, the time it would take for the skydiver to fall 180 feet is of 3.35 seconds.
What is the height considering no air resistance?The height in feet that a person has fallen after t seconds is given by:
d = 16t².
In this problem, we want the time for a fall of 180 feet, hence.
[tex]16t^2 = 180[/tex]
[tex]t = \sqrt{\frac{180}{16}}[/tex]
t = 3.35
The time it would take for the skydiver to fall 180 feet is of 3.35 seconds.
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find the ratio of 4 days to 2 weeks
Which expression is represented by the diagram?
-6 - (-1)
-6 - 1
-5 - (-1)
-5 -1
Answer:
C
Step-by-step explanation:
Answer:
Please review the question. I don't see a diagram. And the "expressions" are just numbers.
Step-by-step explanation:
The expressions aren't really expressions. There are no variables (x or y).
-6 - (-1) is -5
-6 - 1 is -7
-5 - (-1) is -4
-5 -1 is -6
We don't know if these are values of x or y, so the diagram could only be a series of dots on a number line.
f(x)=12(x-10)2+18
What is the "a" value of this function?
Answer:
12
Step-by-step explanation:
Assuming that the 2 actually represents square, the equation is
[tex]f(x) = 12(x-2)^2 + 18[/tex]
[tex](x-2)^2 = x^2 - 4x + 4\\\\12(x-2)^2 + 18 = 12( x^2 - 4x + 4) + 18 = 12x^2 -48x + 48 + 18 = 12x^2 -48x + 66\\[/tex]
This equation is of the form
[tex]ax^2 + bx + c[/tex]
[tex]a = 12, b = -48, c = 66[/tex]
Note
Since the question is only asking for the a value which is the coefficient of x² it is clear that 12 is the coefficient without expanding (x-2)² but it is always better to proceed as above in case you are asked for b and c values also
Value of the function at x=a is [tex]12a^{2} -240a +1218[/tex].
Given function f(x)=[tex]12(x-10)^{2} +18[/tex]
We have to find the value of function at x=a.
For this we have to just put x=a in the function f(x)=[tex]12(x-10)^{2}+18[/tex]
f(a)=12[tex](a-10)^{2} +18[/tex]
we have to expand (x-10) to the power 2 to get the value of function.
f(a)=[tex]12(a^{2} +10^{2} -20a)+18[/tex]
=[tex]12a^{2}+1200-240a+18\\[/tex]
=[tex]12a^{2} -240a+1218[/tex]
Hence the value of function at x=a is [tex]12a^{2} -240a+1218[/tex] means f(a)=[tex]12a^{2} -240a+1218[/tex].
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In the figure, all, and both lines are intersected by transversal & Complete the statements to prove that m≤1 = m25.
allo (given)
m1+m3=180° (Linear Pair Theorem)
m5+ m6=180° (Linear Pair Theorem)
m1+m3= 5+ 6()
m3=m6()
m1 m5 (Subtraction Property of Equality)
First blank: Substitution or transitive property of equality
Second blank: Subtraction property of equality
A sample of 40 11th graders were asked to select a favorite pattern out of 6
choices. the following display shows what their favorite color patterns were.
the counts have been recorded in the accompanying table according to
pattern and the number of students who selected that pattern. what is the
missing value in the table?
color pattern
frequency
blue on gray
4
green
6
pink polka dots
?
purple
8
red and orange
stripes
7
yellow
3
the answer is 12
Step-by-step explanation:
Jaime makes the following claim.
An angle with a measure of π/3 radians in a circle with a radius of 3 inches is smaller than an angle with a measure of π/3 radians in a circle with a radius of 6 inches. This is because the radian measure is based on the length of the radius of the circle and a radius of 3 inches is smaller than a radius of 6 inches.
1. Review Jaime’s statement and what you know about angles and radians.
a. Explain whether you agree with Jaime’s statement or not.
b. Provide examples to support your whether you agree or disagree.
In the case above, Jaime claim is true.
The explanation to agree with Jaime’s statement or not is that the longer the length of the radius, the longer the length of the arc.What is the claim about?1. Note that radian measure:
= [tex]\frac{60° }{360°}[/tex] x 2π x 3
= 1/6 x 6π
= π
2. Note that radian measure:
= [tex]\frac{60° }{360°}[/tex] x 2π x 6
= 1/6 x 2π x 6
=2π
So we can write it as:
π/3 x 180°/π = 60°
Therefore, via the solution above, Jaime claim is true.
3. Note that: Radian measures: the percentage of arc measures x 2π x radius and so one can say that The explanation to agree with Jaime’s statement or not is that the longer the length of the radius, the longer the length of the arc.
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Find the highest common factor of 12 and 40
To find the highest common factor (HCF) between two numbers , first to take HCF of both the numbers.
[tex] \purple {\Large\begin{array}{r | l}2&\underline{12}\\3& \underline{6}\\2&\underline{2}\\&\underline{1}\\\end{array}} \: \: \: \: \: \: \: \: \: \: \: \: \purple {\Large\begin{array}{r | l}2&\underline{40}\\2& \underline{20}\\5&\underline{10}\\2&\underline{2} \ \\ &\underline{1}\\\end{array}}[/tex]
Take every common prime factor between 12 and 40[tex] \red {\large \implies} \large \: 12 \: = \: 2 \: \times \: 3 \: \times \: 2 \: \: \: \: \: \: \: \: \: \: \\ \\ \red {\large \implies} \large \:40 \: = \: 2 \: \times \: 2 \: \times \: 5 \: \times \: 2 \: [/tex]
Finally, identify the factors common to each number and multiply those common factors together.
[tex] \rm\orange {\large \implies} \large \:Common \: factors \: = \: 2 \: \times \: 2[/tex]
[tex]\rm\orange {\large \implies} \large \:HCF = 4[/tex]
Bearing a to b is 280 what is bearing b to A
Answer:
please see photo attached for detailed analysis.
