Answer:
[tex]\textsf{Factored function}: \quad f(x)=(x+2)(3x-5)(x-1)[/tex]
[tex]\textsf{Zeros}: \quad x=-2, \quad x=\dfrac{5}{3},\quad x=1[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=3x^3-2x^2-11x+10[/tex]
If (x + 2) is a factor then:
[tex]\implies f(x)=(x+2)(ax^2+bx+c)[/tex]
Expand:
[tex]\implies f(x)=ax^3+bx^2+cx+2ax^2+2bx+2c[/tex]
[tex]\implies f(x)=ax^3+2ax^2+bx^2+2bx+cx+2c[/tex]
[tex]\implies f(x)=ax^3+(2a+b)x^2+(2b+c)x+2c[/tex]
To find a, compare the coefficients of x³:
[tex]\implies a=3[/tex]
To find b, substitute the found value of a into the coefficient for x² and compare:
[tex]\implies 2a+b=-2[/tex]
[tex]\implies 2(3)+b=-2[/tex]
[tex]\implies b=-8[/tex]
To find c, compare the constants:
[tex]\implies 2c=10[/tex]
[tex]\implies c=5[/tex]
Therefore:
[tex]\implies f(x)=(x+2)(3x^2-8x+5)[/tex]
Now factor (3x²-8x+5):
[tex]\implies 3x^2-3x-5x+5[/tex]
[tex]\implies 3x(x-1)-5(x-1)[/tex]
[tex]\implies (3x-5)(x-1)[/tex]
Therefore the factored function is:
[tex]\implies f(x)=(x+2)(3x-5)(x-1)[/tex]
Zero Product Property
[tex]\boxed{\text{If \; $a \cdot b = 0$ \; then either \; $a = 0$ \;or \;$b = 0$ (or both)}.}[/tex]
To find the zeros, set each factor equal to zero and solve for x:
[tex]\implies x+2=0 \implies x=-2[/tex]
[tex]\implies 3x-5=0 \implies x=\dfrac{5}{3}[/tex]
[tex]\implies x-1=0 \implies x=1[/tex]
Therefore, the zeros of the function are:
[tex]x=-2, \quad x=\dfrac{5}{3},\quad x=1[/tex]
Select all of the solutions for the linear inequality graphed below:
The solutions to the inequality whose graph is as represented in the attached image are;
A) (-4, 0)C) (0, 0)E) (-2,0)Graphical solution of inequalities.It follows from the task content that the graphical solutions for the inequality are represented on the graph and the points which are solutions for the inequality are to be identified.
Therefore, the points which are solutions for the inequality are points which are located in the shaded region of the graph.
Hence, such points include;
A) (-4, 0)C) (0, 0)E) (-2,0)The answer choices B, D and F represents points on the border line of the inequality graph and since the line is broken, they are not solutions to the inequality.
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How long is 10:00am to 5:00 pm
Answer:
7 hours.
Step-by-step explanation:
Use a clock and count forward.
A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 4 points with 99% confidence assuming S=13.8 based on earlier studies? Suppose the doctor would be content with 90 confidence. How does the decrease in confidence affect the sample size required?
The way the decrease in confidence affect the sample size required is: A. Decreasing the confidence level decreases the sample size needed.
How to find the sample size ?Using this formula to find the decrease in sample size
n = [zs/E]^2
Where:
n = Sample size
zs = z-score
E= margin of error
Confidence coefficient for 99% = 2.58
Hence,
2.58 × 13.8/sqrt(n) = 0.04
2.598 × 13.4 /0.04 = sqrt(n)
( 2.598× 13.8 /0.04)^2 = n
n=803,371.6
So,
Confidence coefficient for 90% = 1.64
n= (1.64× 13.8/0.04)^2
n =320,129.64
Therefore the correct option is A.
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The complete question is:
A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 4 points with 99% confidence assuming S=13.8 based on earlier studies? Suppose the doctor would be content with 90 confidence. How does the decrease in confidence affect the sample size required?
How does the decrease in confidence affect the sample size required
A. Decreasing the confidence level decreases the sample size needed.
B. The sample size is the same for all levels of confidence.
C. Decreasing the confidence level increases the sample size needed.
Write equations of the horizontal and vertical lines that pass through (2,3).
horizontal line:
vertical line:
Answer:
horizontal: y = 3vertical: x = 2Step-by-step explanation:
You want the equations of the horizontal and vertical lines that pass through (2, 3).
Horizontal lineA horizontal line has an equation of the form ...
y = c . . . . . for some constant c
The value of y is the same for every value of x.
To make such a line go through the point (2, 3), we must have ...
y = 3
Vertical lineA vertical line has an equation of the form ...
x = c . . . . . for some constant c
The value of x is the same for every value of y.
To make such a line go through the point (2, 3), we must have ...
x = 2
Bimpe rues 5km per hour faster thean she walk- If she runs for 45 minute and walks for 3 hour.
! BE A GOOD NAJM/ NAJMAH, AL
Answer:
See below
Step-by-step explanation:
I think you may have left some info out of your question post, but here is something that may help you:
x = walk speed km/hr
x + 5 = run speed km/hr
45 min = 3/4 hr = .75 hr
(.75)(x+5) + 3 * x = total distance in km
3.75x + 3.75 = total distance
Mr. Carson drove 1,027 miles in April. He drove 988 miles in May. Mr. Carson used the expression below to find how many more miles he drove in April than in May -> 1,027 - 988. How many more miles did Mr. Carson drive in April than in May?
Answer:
Mr. Carson drove 39 more miles in April than in May
Step-by-step explanation:
1027-988=39
The box plot shows the times for sprinters on a track team.
(A horizontal number line starting at 40 with tick marks every one unit up to 59. The values of 42, 44, 50, 54, and 56 are all marked by the box plot. The graph is titled Sprinters' Run Times, and the line is labeled Time in Seconds.)
Which of the following lists the range and IQR for this data?
The five number from the box plot is presented as follows:
Minimum value: 42.First quartile: 44.Median: 50.Third quartile: 54.Maximum value: 56.What does a box-and-whisker plot shows?A box and whisker plot shows five things of a distribution, listed as follows:
The data set's lowest value.The value that 75% of the measures are larger than is found in the first quartile, which is the median of the data set's lowest 50% of measurements.
50% of the data set is less than the median and 50% is more than the median, which is the midpoint value of the data set.The third quartile, which is the median of the data set's top 50% of measurements, is the value that 75% of the measures fall below.The data set's maximum value.
These numbers, which make up the five number summary, are the values highlighted on the box plot from left to right, from the minimum value to the greatest value, passing through the first quartile, the median, and the third quartile.
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A gallon of water contains 128 fluid ounces. A rain barrel can hold 6,400 ounces of rainwater.
Estimate how many gallons of water can the barrel hold?
Answer:
50 gallons
Step-by-step explanation:
6400 ÷ 128
= 50
Which input value produces the same output value for the two functions on the graph?
f(x) equals negative StartFraction 2 Over 3 EndFraction x plus 1. g(x) equals StartFraction 1 Over 3 EndFraction x minus 2. A coordinate grid with two lines. One line labeled f(x) passes through (negative 3, 3), (0, 1), and point (3, negative 1). The second line is labeled g(x) and passes through (negative 3, negative 3), (0, negative 2), and point (3, negative 1).
x = –3
x = –1
x = 1
x = 3
An input value that would produce the same output value for the first functions on the graph is 0. Also, an input value that would produce the same output value for the second functions on the graph is 3.
How to determine the correct input value?In this exercise, you are required to determine the input value that would produce the same output value for the two functions on the graph. This ultimately implies that, the two functions would be equated as shown below.
From the information provided above, the two functions include the following:
f(x) = -2/3(x + 1)
g(x) = 1/3(x - 2)
Equating the two equations, we have:
f(x) = g(x)
-2/3(x + 1) = 1/3(x - 2)
-2x/3 -2/3 = x/3 - 2/3
-2x/3 - x/3 = - 2/3 + 2/3
x = 0.
For the second function on the graph, the coordinates are as follows:
f(x) = (-3, 3), (0, 1), (3, -1)
g(x) = (-3, -3), (0, -2), (3, -1)
Therefore, the above function produces the same input value (x) at point 3.
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Answer:
D
Step-by-step explanation:
edge 23
F(n)= 3n -4 find term 3 of the explicit arithmetic sequence
The third term will be 5 in the explicit arithmetic sequence.
What is an arithmetic sequence?An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.
The formula to find the general term of an arithmetic sequence is,
aₙ = a₁ + (n-1)d
The explicit formula of an arithmetic sequence is given in the question as:
F(n) = 3n -4 ....(i)
To determine the term 3.
Substitute the value of n = 3 in equation (i),
T₃ = 3(3) - 4
T₃ = 9 - 4
Apply the subtraction operation,
T₃ = 5
Therefore, the third term will be 5 in the explicit arithmetic sequence.
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Find the formula, in standard form
y=ax2+bx+c , for a quadratic, that has roots at x=5+4√10 and x=5−4√10 , and has a leading coefficient of 1.
The quadratic equation in standard form that contains the roots 5 + 4√10 and 5 - 4√10 is y = x² - 10 · x - 135.
How to determine quadratic formula in standard form
In this question we must derive a quadratic equation in standard form, that is, a polynomial of the form:
y = a · x² + b · x + c
Where b / a = - r₁ - r₂ and c / a = r₁ · r₂ and r₁ and r₂ are the roots of the polynomial. If we know that a = 1, r₁ = 5 + 4√10 and r₂ = 5 - 4√10, then the quadratic equation is:
y = a · [x² + (b / a) · x + (c / a)]
y = x² + (- 5 - 4√10 - 5 + 4√10) · x + (5 + 4√10) · (5 - 4√10)
y = x² - 10 · x + 25 - 160
y = x² - 10 · x - 135
y = x² - 10 · x - 135 is the quadratic equation in standard form.
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1.) Ace wanted to buy a gift for his mother
worth $18.60. He has $7.40 in Savings
and another $6.30 Saved from his
allowance for the past two weeks. How much more
does he need to save this week?
Answer:
$4.90
Step-by-step explanation:
He already has $13.70 (7.40+6.30) saved up so you have to subtract that from 18.60 to find the total Ace needs to save up.
18.60-13.70=4.90
To check your answer, you can add 7.40, 6.30, and 4.90 and see if you get a total of 18.60.
Check: 7.40+6.30+4.90=18.60
WILL GIVE BRAINLIEST PLEASE HELP!!!!
A cat runs 10 meters north, sees a dog and runs 2 meters back south. It then runs 6 meters west. What is the displacement of the cat and the total distance it ran?
Answer:
The cat is at at 8 north 6 west
Step-by-step explanation:
The cat ran a total of 14 meters
The table and corresponding frequency polygon show information about the
waiting times of some patients at a dentist.
What fraction of patients waited for more than 7 minutes?
Frequency
10
5
5
Waiting time (a minutes)
10
P
Waiting time
(a minutes)
5< x≤6
6<257
7<#58
8< x≤9
9< x≤ 10
The fraction of the patients that have a waiting time of more than 7 minutes found by using the area under the curve is 269/312
What is a fraction in mathematics?A fraction indicates the quantitative comparison showing the number of times one quantity is contained in another quantity.
The area under the frequency curve is found as follows;
Dividing the area into composite shapes of a rectangle, triangle and trapezoid, we get;
(9.2 - 5.5) × 4 + (4 + 2)×3/2 + (2.5 + (9.2 - 5.5)) × 1/2 + (2.5 + 1.2) × 2/2 + 1.2 × 1/2 = 31.2
The area for those that have a waiting time of more than 7 minutes is therefore;
(9.2 - 5.5) × 4 + (4 + 2)×3/2 + (2.5 + (9.2 - 5.5)) × 1/2 = 26.9
The fraction that have a waiting time of more than 7 minutes is therefore;
26.9/31.2 = 269/312 ≈ 0.862
The fraction of the patients that have a waiting time of more than 7 minutes is 269/312
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If x = 2 and t = 4, what is the value of 1/8(x^3− 4)(t² + 8)?
Answer:
64
Step-by-step explanation:
you need to plug the number in subtract and add then multiply the number from the first pair of parenthesis into the main number and after multiply the second pair into it.
1. Kevin took $45 with him to spend on snack for himself and his friends at the movie theater. The price for each bucket of popcorn was $4. The price of each drink was half the price of a bucket of popcorn.
(a) Sketch the graph that represents the situation and label the intercepts. Use one axis to represent the number of buckets of popcorn and the other axis to represent the number of drinks.
(b) Explain your graph.
The equation of the relationship is 2x + 4y = 45 and the graph is attached
How to sketch the graph?From the question, we have the following parameters:
Amount = $45Price of each bucket of popcorn = $4Price of each drink = Half the price of each bucket of popcornThis means that
Price of each drink = Half $4
Evaluate
Price of each drink = $2
Represent the number of drinks with x and the number of bucket of popcorn with y
So, we have the following representation
Total amount of popcorn + Total amount of drinks = Total amount
This gives
2x + 4y = 45
Next, we sketch the graph
See attachment for the graph of the equation
The explanation of the graphThe graph is represented by a straight line
This means that it is a linear equation
Also, the graph touches the axes at (0, 11.25) and (22.5, 0)
This means that the highest number of drinks and buckets are 11.25 and 22.5 respectively
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15. Given the following measurements in
parallelogram ABCD, find the PERIMETER of
CED
AC 34 in. AB = 26 in. BD = 28 in.
P =
20 points for whoever answers
The Perimeter of CED AC is 34 in. AB is 26 in. BD is 28 in. P is 57 in.
Explain about the parallelogram?A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.
Having two sets of parallel sides makes a quadrilateral a parallelogram. A parallelogram has opposite sides that are the same length and angles that are the same size. Additionally, the internal angles on the same transverse side are supplementary. 360 degrees are equal to the total of all internal angles.
Two parallel pairs of sides make up a parallelogram, a quadrilateral. Four right angles form a parallelogram called a rectangle. Rhombus: An equal-length parallelogram with four sides.
The diagonals of a parallelogram bisect each other AC = 2 CE
Substitute AC= 34 into AC = 2 CE 34 = 2CE
Calculate 34 = 2 CE CE = 17
The diagonals of a parallelogram bisect each other BD = 2DE
Substitute BD= 28 into BD = 2DE 28 = 2DE
Calculate 28 = 2 DE DE = 14
Opposite sides of parallelogram are congruent AB = CD
Substitute AB = 26 into AB = CD CD = 26
Perimeter of a triangle PΔCDE = CE + CD + DE
Substitute CE = 17 DE = 14 CD = 26 PΔCDE = CE + CD + DE
PΔCDE = 17+ 26 + 14
PΔCDE = 57
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enter an expression in the box to write the equation of a line that passes through the point (-6,2) and is perpendicular to the line y= 3/2x + 4
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{3}{2}}x+4 \qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{3}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{3}}}[/tex]
so we're really looking for the equation of a line whose slope is -2/3 and that it passes through (-6 , 2)
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{2}{3}}(x-\stackrel{x_1}{(-6)}) \implies y -2= -\cfrac{2}{3} (x +6) \\\\\\ y-2=-\cfrac{2}{3}x-4\implies {\Large \begin{array}{llll} y=-\cfrac{2}{3}x-2 \end{array}}[/tex]
I need the answer quick
The burner is the engine of the balloon. What is the role of a resistor in an engine?
A ballast resistor is utilized inside the ignition system of automobile engines or balloons. it acts as a resistor for the ignition ballast.
Between the main source of both the ignition coil & the coil stud, there's an ignition ballast resistor. It lowers the ignition coil's risk of failure.
An ignition ballast resistance assists in lowering the coil voltage & coil current when the generator revs the engine.
Minimal current consequently results in a low-temperature increase. Additionally, the ignition coil lives a long time as a result.
However, an ignition system requires a greater voltage that is also the same as the power source's voltage. Therefore, a resistor for the ignition ballast is connected to the jumper wire. The jumper wire additionally supplies the ignition with the necessary voltage when starting the engine.
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Need help please is do tomorrow
Answer: 39
Step-by-step explanation:
it starts at 11 and adds 7 everytime, assuming its linear (meaning it has a constant rate of change) u would add 7 to 32 to get your 5th value
Answer: y = 39
Step-by-step explanation:
Since the line is linear, the y increases 7 every time x increases 1
Add 7 to 32 and it equals 39
2
Select the correct answer from each drop-down menu.
Julia and Kellen are participating in a read-a-thon to raise money for charity. The money each of them raises will be a mix of fixed and per-page
donations.
Function / models the total amount, in dollars, that Julia will raise if she reads x pages:
j(x) = 1.65x + 17.31.
Function k models the total amount, in dollars, that Kellen will raise if he reads x pages:
k(x) = 0.90x+9.28.
The function
If they both re
h(x)=0.75x+26.59
h(x) = 0.75x+8.03
h(x) = 2.55x+8.03
h(x) = 2.55x+26.59
represents the difference between the amounts Julia and Kellen will raise when they both read x pages.
ence will be $
Reset
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Hey so basically I'm having trouble understanding this problem so if someone can help me with the answer that'd be great thx <3
Two poles of heights 9 m and 14 m stand on a plane ground. If the distance between their feet is 12 m,
then what will be the distance between their tops?
Answer:
The distance would be 13m.
Answer:
13 m
Step-by-step explanation:
this can be looked at like a triangle sorry for the bad drawing I’m in the car lol
But we know the base is 12m and the height of this triangle is 5 since the secon pole is 5m taller hence 14-9=5
So we use the Pythagorean theorem
a^2+b^2=c^2
12^2+5^2=c^2
144+25=c^2
169=c^2
Now find the square root of 169 to get the answer
13 m is the distance between the tops
Hopes this helps please mark brainliest
Please help ASAP will mark brainliest
Plot the points ( -3, 7 ) and ( 9, 0)
Find the distance between the points and the midpoint of the line segment joining the points.
Answer: 13.89 units
PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!
Which is the best first step when solving the following system of equations?
x+y=3
4x-y=7
O Multiply the first equation by 4.
Add the first equation to the second equation.
Multiply the second equation by -1.
Subtract the second equation from the first equation.
The best first step to solve equations, x+y = 3 and 4x-y = 7, is to add the first equation to the second equation.
According to the question,
We have the following system of equations:
x+y = 3 .....(1)
4x-y = 7 ....(2)
Now, these equations can be easily solved by adding the first equation to the second equation because we will only then have one variable which is x and y when added to -y will result in zero.
We can solve these equations by adding as follows:
x-y+4x+y = 3+7
5x = 10
x = 10/5
x = 2
Now, we can put the value of x in equation 1 to find the value of y:
2+y = 3
y = 3-2
y = 1
Hence, the correct option is B.
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2
Linda paid $5.50 for 4 pounds of
strawberries. How much did she pay
per pound of strawberries?
Answer:
$ 1.38
Step-by-step explanation:
5.50 ÷ 4 = 1.375. rounded to 2 dp: 1.38
Helppp!!! I need help I don’t know how to do this pleasee
Answer:10.85
Step-by-step explanation:
First you have to multiply a, 3 5/6, by b, 5 2/3. Which is 21.7222222, if you simplify it, you would get 21.7. Then you divide the total by 2 and you get 10.85.
Answer:
10 31/36 m
Step-by-step explanation:
formula for area of a triangle base times height times 1/2
we turn the height and base into improper fractions
3 5/6= 23/6
5 2/3=17/3
Now we multiply together to find area
23/6x17/3= 391/18
391/18x1/2=391/36
10 31/36
hopes this helps please mark brainliest
The sUm of the measures
of the interior angles of
polygon is 2,880°. How
many sides does the
polygon have?
A store owner buys sweatshirts for $16 and marks them up 20% to make a profit. The sales tax where his store is located is 7.5%. A customer considers buying one or two sweatshirts from the store. Select all the statements that apply.
One sweatshirt before tax costs $19.20.
One sweatshirt before tax costs $12.80.
The sales tax for two sweatshirts is $1.92.
The sales tax for two sweatshirts is $2.88.
Total cost for two sweatshirts is $41.28.
Total cost for two sweatshirts is $27.52.
Answer: The correct statements are:
1 SS before tax costs $19.20
Sales tax for 2 SS is $2.88
Total cost for 2 SS is $41.28
Step-by-step explanation:
$16 x 1.20 = $19.20 cost before tax
$19.20 x 0.075 = $1.44 sales tax, one shirt
Sales tax for 2 shirts = $1.44 x 2 = $2.88
Total cost of a shirt = $19.20 + $1.44 = $20.64
Total cost for 2 shirts = $20.64 x 2 = $41.28
Mrs. Reed is buying seeds to start a vegetable garden. She purchases 12 packets of bean seeds, 15
packets of carrot seeds, and 2 packets of corn seeds. Choose Yes or No to tell if each statement about
the purchase is correct.
Step-by-step explanation:
Mrs. Reed is buying seeds to start a vegetable garden. She purchases 12 packets of bean seeds, 15
packets of carrot seeds, and 2 packets of corn seeds. Choose Yes or No to tell if each statement about
the purchase is correct.