Hello,
[tex]f(x)=2x^4-x^3-18x+9x\\\\=x(2x^3-x^2-18x+9)\\\\=x(x^2(2x-1)-9(2x-1))\\\\=x(2x-1)(x^2-9)\\=x(2x-1)(x-3)(x+3)\\[/tex]
Zeros are : 0; 1/2; -3; 3.
The zeros of the function are -3, 0, 1/2 and 3.
The given function is [tex]f(x)=2x^{4} -x^{3} -18x^{2} +9x[/tex].
What are the zeros of a function?Zeros of a function are the points where the graph of the function meets the X-axis i.e., at the solutions of f(x) = 0.
Now, factorise the given function, that is f(x)=x(2x³-x²-18x+9).
=x[x²(2x-1)-9x(2x-1)]
=x(2x-1)(x²-9)
=x(2x-1)(x+3)(x-3)
= -3, 0, 1/2, 3
Therefore, the zeros of the function are -3, 0, 1/2 and 3.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Consider the equation below. The value of x in terms of b is . The value of x when b is 3 is .
Answer: x=-3/3=-1
Step-by-step explanation:
To solve for x in terms of b, simply treat b as a number, and solve for x as usual: first of all, we expand the left hand side:
-2bx+10=16
Subtract 10 from both sides:
-2bx=6
Divide both sides by -2b:
x=6/-2b=-3/b
This means that in particular, if we set b=3 , we have
x=-3/3=-1
i need helpp !!!!!!!!!!!
Answer:
In descending order, 1, 4, 3
I forgot how to solve these and it won't let me go to the tutor
9514 1404 393
Answer:
see attached
Step-by-step explanation:
I find a graphing calculator to be the quickest way to create a graph of a system of equations. That result is attached.
__
If you want to graph the equations by hand, you need to know a couple of points on each line. When the equations are in slope-intercept form, the y-intercept is often a good place to start. Another point is usually easy to find based on the slope of the line, starting at the y-intercept.
__
Here, the equations are not in that form, but are in the form ax+by=c. In this form, it is often easy to find both the x- and y-intercepts and use those points to plot the line. Each intercept is found by setting the other variable to zero.
x-intercept: c/a
y-intercept: c/b
__
For the given lines, the first equation has intercepts (2, 0) and (0, 2). The line has a slope of -1 and makes an isosceles triangle with the axes in the first quadrant.
The second equation has intercepts (-1, 0) and (0, 2). This line has a slope of +2 and makes a triangle with the axes in the second quadrant.
How do I make people brainliest
Answer:
you have to wait until two people answer then you click their answer to make them brainliest
Step-by-step explanation:
i dont know
blah blah blah blah blah blah blah blah blah blah blah blah
The total number of students enrolled in MATH 123 this semester
is 5,780. If it increases by 0.28% for the next semester, what will
be the enrollment next semester? Round to a whole person.
Answer:
5796 people
Step-by-step explanation:
.28 percent of 5780 is 16.184 so added 5,780+16.184=5,796.184 but rounded to a whole person is 5,796!
What fraction of the total number of students are boys?
Step-by-step explanation:
total number of students are :4x 3 = 12
Fraction that's boys are : 3÷12
DE is tangent to Circle C at point D.
What is the measure of
Enter your answer in the box.
Answer:
39°
Step-by-step explanation:
A radius of a circle (segment CD) drawn to the point of tangency (D) intersects the tangent (line DE) at a 90-deg angle.
That makes m<D = 90.
m<D + m<C + m<E = 180
90 + 51 + m<E = 180
m<E = 39
What is the slope of a line perpendicular to the line whose equation is 2x+4y=-642x+4y=−64. Fully simplify your answer.
9514 1404 393
Answer:
2
Step-by-step explanation:
Solving the given equation for y, you have ...
2x +4y = -64
4y = -2x -64
y = -1/2x -16
The coefficient of x is the slope of the given line: -1/2. The slope of the perpendicular line is the opposite reciprocal of this:
-1/(-1/2) = 2
The slope of the perpendicular line is 2.
In a survey, 30 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $35 and standard deviation of $17. Construct a confidence interval at a 95% confidence level.
Answer:
CI 95 % = ( 28.92 ; 41.08 )
Step-by-step explanation:
Sample Information:
sample size n = 30
sample mean = 35 %
sample standard deviation s = 17
To construct a CI 95 %
significance level is α = 5 % α = 0.05 α/2 = 0.025
z critical for α/2 from z- table is : z (c) = 1.96
CI 95 % = ( x ± z(c) * s/√n )
CI 95 % = ( 35 ± 1.96 * 17/√30 )
CI 95 % = ( 35 ± 6.08 )
CI 95 % = ( 28.92 ; 41.08 )
Question
The sum of three consecutive even integers is -312. Find the Integers.
Answer:
-105, -104, -103
Step-by-step explanation:
lets the numbers be:
x
x+1
x+2
so:
x+(x+1)+(x+2)=-312
x+x+x+1+2=-312
3x+3=-312
3x=-312-3=-315
x=-315/3=-105
15.18. Find the area of the region bounded by
TC
the curve y = cosx, x=0, x= pi/
2 and x-axis.
Answer:
please mark me brainlist
Step-by-step explanation:
Components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). The first inspector detects 83% of all defectives that are present, and the second inspector does likewise. At least one inspector does not detect a defect on 34% of all defective components. What is the probability that the following occur
Complete question is;
Components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). The first inspector detects 83% of all defectives that are present, and the second inspector does likewise. At least one inspector does not detect a defect on 34% of all defective components. What is the probability that the following occurs?
(a) A defective component will be detected only by the first inspector?
b) A defective component will be detected by exactly one of the two inspectors?
(c) All three defective components in a batch escape detection by both inspectors (assuming inspections of different components are independent of one another)?
Answer:
A) 0.17
B) 0.34
C) 0
Step-by-step explanation:
a) We are told that the first inspector(A) detects 83% of all defectives that are present, and the second inspector(B) also does the same.
This means that;
P(A) = P(B) = 83% = 0.83
We are also told that at least one inspector does not detect a defect on 34% of all defective components.
Thus;
P(A' ⋃ B') = 0.34
Also, we now that;
P(A ⋂ B) = 1 - P(A' ⋃ B')
P(A ⋂ B) = 1 - 0.34
P(A ⋂ B) = 0.66
Probability that A defective component will be detected only by the first inspector is;
P(A ⋂ B') = P(A) - P(A ⋂ B)
P(A ⋂ B') = 0.83 - 0.66
P(A ⋂ B') = 0.17
B) probability that a defective component will be detected by exactly one of the two inspectors is given as;
P(A ⋂ B') + P(A' ⋂ B) = P(A) + P(B) - 2P(A ⋂ B)
P(A) + P(B) - 2P(A ⋂ B) ; 0.83 + 0.83 - 2(0.66) = 0.34
C) Probability that All three defective components in a batch escape detection by both inspectors is written as;
P(A' ⋃ B') - (P(A ⋂ B') + P(A' ⋂ B))
Plugging in the relevant values, we have;
0.34 - 0.34 = 0
What is the range of g?
y
--
.
9
7.
6+
5+
4+
3+
2+
1+
.
3
{4}}
-7 -6 -5 -4 -3 -2
+++
2 3 4 5 6 7
-2
-3
-4+
-5
-6+
7
7
Answer:
y 9 5 473648
Step-by-step explanation:
PLEASE HELP WILL MARK BRAINLIEST
Answer:
AB
Step-by-step explanation:
From the question given above, we were told that triangle ABC is similar to triangle PTG.
Since both triangles are similar, the following assumptions hold:
PG / AC = PT / AB = TG / BC
Comparing the equation above with those given in the question, the missing part of the equation is AB
Find the solution of the differential equation that satisfies the given initial condition. (dP)/(dt)
Answer:
[tex]P = (\frac{1}{3}t^\frac{3}{2} + \sqrt 2 - \frac{1}{3})^2[/tex]
Step-by-step explanation:
Given
[tex]\frac{dP}{dt} = \sqrt{Pt[/tex]
[tex]P(1) = 2[/tex]
Required
The solution
We have:
[tex]\frac{dP}{dt} = \sqrt{Pt[/tex]
[tex]\frac{dP}{dt} = (Pt)^\frac{1}{2}[/tex]
Split
[tex]\frac{dP}{dt} = P^\frac{1}{2} * t^\frac{1}{2}[/tex]
Divide both sides by [tex]P^\frac{1}{2}[/tex]
[tex]\frac{dP}{ P^\frac{1}{2}*dt} = t^\frac{1}{2}[/tex]
Multiply both sides by dt
[tex]\frac{dP}{ P^\frac{1}{2}} = t^\frac{1}{2} \cdot dt[/tex]
Integrate
[tex]\int \frac{dP}{ P^\frac{1}{2}} = \int t^\frac{1}{2} \cdot dt[/tex]
Rewrite as:
[tex]\int dP \cdot P^\frac{-1}{2} = \int t^\frac{1}{2} \cdot dt[/tex]
Integrate the left hand side
[tex]\frac{P^{\frac{-1}{2}+1}}{\frac{-1}{2}+1} = \int t^\frac{1}{2} \cdot dt[/tex]
[tex]\frac{P^{\frac{-1}{2}+1}}{\frac{1}{2}} = \int t^\frac{1}{2} \cdot dt[/tex]
[tex]2P^{\frac{1}{2}} = \int t^\frac{1}{2} \cdot dt[/tex]
Integrate the right hand side
[tex]2P^{\frac{1}{2}} = \frac{t^{\frac{1}{2} +1 }}{\frac{1}{2} +1 } + c[/tex]
[tex]2P^{\frac{1}{2}} = \frac{t^{\frac{3}{2}}}{\frac{3}{2} } + c[/tex]
[tex]2P^{\frac{1}{2}} = \frac{2}{3}t^\frac{3}{2} + c[/tex] ---- (1)
To solve for c, we first make c the subject
[tex]c = 2P^{\frac{1}{2}} - \frac{2}{3}t^\frac{3}{2}[/tex]
[tex]P(1) = 2[/tex] means
[tex]t = 1; P =2[/tex]
So:
[tex]c = 2*2^{\frac{1}{2}} - \frac{2}{3}*1^\frac{3}{2}[/tex]
[tex]c = 2*2^{\frac{1}{2}} - \frac{2}{3}*1[/tex]
[tex]c = 2\sqrt 2 - \frac{2}{3}[/tex]
So, we have:
[tex]2P^{\frac{1}{2}} = \frac{2}{3}t^\frac{3}{2} + c[/tex]
[tex]2P^{\frac{1}{2}} = \frac{2}{3}t^\frac{3}{2} + 2\sqrt 2 - \frac{2}{3}[/tex]
Divide through by 2
[tex]P^{\frac{1}{2}} = \frac{1}{3}t^\frac{3}{2} + \sqrt 2 - \frac{1}{3}[/tex]
Square both sides
[tex]P = (\frac{1}{3}t^\frac{3}{2} + \sqrt 2 - \frac{1}{3})^2[/tex]
Find the length of the arc to 2 decimals places
Answer:
Step-by-step explanation:
The formula for arc length is
[tex]AL=\frac{\theta}{360}*2\pi r[/tex] where theta is the measure of the central angle and r is the radius. We have both of those pieces of info; filling in:
[tex]AL=\frac{30}{360}*2(3.14) (4)[/tex] and simplifying a bit:
[tex]AL=\frac{1}{12}(8)(3.14)[/tex] and a bit more:
[tex]AL=\frac{25.12}{12}[/tex] and finally, to
AL = 2.09 m
the perimeter of a rectangle parking lot is 322M if the width of the parking lot is 74M what is its length
Step-by-step explanation:
Perimeter of rectangle = 2( l+b)
Ie, P = 2( L+B )
In substituting,
322 = 2( L + 74)
Ie, 322 = 2L + 148
Re - arrange
Hence,
2L = 322 - 148
2L = 174
Thus, L = 174/2
L = 87M
haydenkyletoddhaydenkyletodd
The measure of each interior angle of reglar convex polygon is 150 How many sides it does have
Step-by-step explanation:
Since an interior angle is 150 degrees, its adjacent exterior angle is 30 degrees. Exterior angles of any polygon always add up to 360 degrees. With the polygon being regular, we can just divide 360 by 30 to get 12 sides.
5. En una fábrica se producen 3,500
plumas por 6 trabajadores, si se
suman tres más, ¿cuál será la
producción de plumas? *
Answer:
Si se suman 3 trabajadores la producción será 5250 plumas.
Step-by-step explanation:
Inicialmente tenemos 6 trabajadores, al añadir 3 trabajadores más tendríamos ahora 9 trabajadores:
[tex] 6 + 3 = 9 [/tex]
Entonces, la producción de plumas (P) sería ahora:
[tex] P = \frac{3500}{6}*9 = 5250 [/tex]
Por lo tanto, si se suman 3 trabajadores la producción será 5250 plumas.
Espero que te sea de utilidad!
What is the missing term in the factorization?
12x2 – 75 = 3 (2x+?)(2x – 5)
Answer:
12x2 – 75 = 3 (2x+5)(2x – 5)
Step-by-step explanation:
Which angle is complementary to angle CFD ?
Answer:
∠DFE
Step-by-step explanation:
Complementary angles are angles that have a sum of 90°. Since there is a box on angle ∠CFB, we can infer that ∠CFE is also 90°. This is because the two are supplementary (equal 180°). Therefore, ∠DFE is the other part of ∠CFD that would complete the 90° pair.
Find the value of the variable y, where the sum of the fractions 6/(y+1) and y/(y-2) is equal to their product.
PLEASE HELP NEED ASAPPPPPP WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWERRRRR
Answer:
The answer is
[tex]y = 3[/tex]
[tex]y = - 4[/tex]
Step-by-step explanation:
We must find a solution where
[tex] \frac{6}{y + 1} + \frac{y}{y - 2} = \frac{6}{y + 1} \times \frac{y}{y - 2} [/tex]
Consider the Left Side:
First, to add fraction multiply each fraction on the left by it corresponding denomiator and we should get
[tex] \frac{6}{y + 1} \times \frac{y - 2}{y - 2} + \frac{y}{y - 2} \times \frac{y + 1}{y + 1} [/tex]
Which equals
[tex] \frac{6y - 12}{(y -2) (y + 1)} + \frac{ {y}^{2} + y }{(y - 2)(y + 1)} [/tex]
Add the fractions
[tex] \frac{y {}^{2} + 7y - 12 }{(y - 2)(y + 1)} = \frac{6}{y + 1} \times \frac{y}{y - 2} [/tex]
Simplify the right side by multiplying the fraction
[tex] \frac{6y}{(y + 1)(y + 2)} [/tex]
Set both fractions equal to each other
[tex] \frac{6y}{(y + 1)(y - 2)} = \frac{ {y}^{2} + 7y - 12}{(y + 1)(y - 2)} [/tex]
Since the denomiator are equal, we must set the numerator equal to each other
[tex]6y = {y}^{2} + 7y - 12[/tex]
[tex] = {y}^{2} + y - 12[/tex]
[tex](y + 4)(y - 3)[/tex]
[tex]y = - 4[/tex]
[tex]y = 3[/tex]
Answer:
Step-by-step explanation:
[tex]\frac{6}{y+1}+\frac{y}{y-2}=\frac{6}{y+1} \times \frac{y}{y-2} \\multiply ~by~(y+1)(y-2)\\6(y-2)+y(y+1)=6y\\6y-12+y^2+y=6y\\y^2+y-12=0\\y^2+4y-3y-12=0\\y(y+4)-3(y+4)=0\\(y+4)(y-3)=0\\y=-4,3[/tex]
what is the formula for triangle
Answer:
A = 1/2 b × h
Step-by-step explanation:
hope it helps !!!!
Answer:
The formula for the area of a triangle is 1/2bh.
why was it difficult for the woman to cross the road
A real estate agent has 12 properties that she shows. She feels that there is a 30% chance of selling any one property during a week. The chance of selling any one property is independent of selling another property. Compute the probability of selling no more than 2 properties in one week. Round your answer to four decimal places.
Answer:
0.2528 = 25.28% probability of selling no more than 2 properties in one week.
Step-by-step explanation:
For each property, there are only two possible outcomes. Either they are sold, or they are not. The chance of selling any one property is independent of selling another property, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A real estate agent has 12 properties that she shows.
This means that [tex]n = 12[/tex]
She feels that there is a 30% chance of selling any one property during a week.
This means that [tex]p = 0.3[/tex]
Compute the probability of selling no more than 2 properties in one week.
2 or less sold, which is:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,0}.(0.3)^{0}.(0.7)^{12} = 0.0138[/tex]
[tex]P(X = 1) = C_{12,1}.(0.3)^{1}.(0.7)^{11} = 0.0712[/tex]
[tex]P(X = 2) = C_{12,2}.(0.3)^{2}.(0.7)^{10} = 0.1678[/tex]
Then
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0138 + 0.0712 + 0.1678 = 0.2528[/tex]
0.2528 = 25.28% probability of selling no more than 2 properties in one week.
Examine the two normal probability curves and complete the statements.
The mean of the shorter normal curve is ["equal to", "greater than", "less than"] the mean of the taller normal curve.
The standard deviation of the shorter normal curve is ["less than", "greater than", "equal to"] the standard deviation of the taller normal curve.
The area under the shorter normal curve is ["equal to", "greater than", "less than"] the area under the taller normal curve.
Answer: hello the two normal probability curves are missing
answer:
a) equal to
b) greater than
c) equal to
Step-by-step explanation:
a) The mean of the shorter normal curve is equal to The mean of the taller normal curve is
b) The standard deviation of the shorter normal curve is greater than the standard deviation of the taller normal curve
c) The area under the shorter normal curve is equal to the area under the taller normal curve
What is the scale factor from ALMN to AOPQ?
M
P
3
3
3
3
2
4
N
0
4
A. 4
(
B. 0
c
C. 3
D. 1
Answer:
D
Step-by-step explanation:
There 2 ways to interpret this problem.
From the info given:
These two triangles are congruent by SSS and congruent triangles have congruent or equal side lengths so the answer have to be 1.
If the triangles are similar, the side lengths form a proportion of that
[tex] \frac{3}{3} = \frac{3}{3} [/tex]
So the ratio or scale factor is 1.
The scale factor in the figure is 1.
What is a scale factor?A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.
Given that two triangles, LMN and OPQ, we need to find the scale factor,
We can see triangles are congruent, and we know that
Two triangles are congruent, by the SSS congruence criterion, if they are similar and the scale factor happens to be 1,
Hence, the scale factor in the figure is 1.
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6(5x/3 -4/3 - 2)= 6 (3 - 6x/6 +4/6)
Answer:
21/8x
Step-by-step explanation:
10x -20 = -6x+22
+6x-20 = 22
16x-20 = 22
16x +20= +20
16x/16x = 42/16x
x = 21/8x
Which equation has the least steep graph?
9514 1404 393
Answer:
C. y = 1/2x +2
Step-by-step explanation:
The magnitude of the slope is the measure of "steepness." The slope is the coefficient of x in these equations. Here those values are ...
4, 3/4, 1/2, 10
Of these, 1/2 is the smallest (least steep). 1/2 is the slope in the equation ...
y = 1/2x +2