Answer:
x = 4 is the only real zeroStep-by-step explanation:
Find the zero's of f(x)
2x³ - 12x² + 20x - 16 = 0x³ - 6x² + 10x - 8 = 0x³ - 4x² - 2x² + 8x + 2x - 8 = 0x²(x - 4) - 2x(x - 4) + 2(x - 4) = 0(x - 4)(x² - 2x + 2) = 0(x - 4)(x² - 2x + 1 + 1) = 0(x - 4)[(x - 1)² + 1] = 0x - 4 = 0 ⇒ x = 4, we already know this(x - 1)² + 1 = 0 ⇒ (x - 1)² = - 1, no real solution as the square is never negativeAnswer:
[tex]x=4, \quad x=1+i,\quad x=1-i[/tex]
(one real zero and 2 complex zeros)
Step-by-step explanation:
Given polynomial:
[tex]f(x)= 2x^3-12x^2+20x-16[/tex]
According to the Factor Theorem, if f(4) = 0 then (x - 4) is a factor of the given polynomial.
[tex]\implies f(x)=(x-4)(ax^2+bx+c)[/tex]
Expand the brackets:
[tex]\implies f(x)=ax^3+bx^2+cx-4ax^2-4bx-4c[/tex]
[tex]\implies f(x)=ax^3+(b-4a)x^2+(c-4b)x-4c[/tex]
Compare coefficients with the given polynomial:
[tex]\implies a=2[/tex]
[tex]\implies -4c=-16 \implies c=4[/tex]
[tex]\implies (b-4a)=-12 \implies b-8=-12 \implies b=-4[/tex]
Substitute the found values of a, b and c:
[tex]\implies f(x)=(x-4)(2x^2-4x+4)[/tex]
To find the zeros of f(x), set the function to zero and solve for x:
[tex]\implies (x-4)(2x^2-4x+4)=0[/tex]
[tex]\textsf{Therefore},\: (x - 4) = 0\: \textsf{ and }\: (2x^2-4x+4)=0[/tex]
[tex]\textsf{To solve}\: (2x^2-4x+4)=0\: \textsf{ use the quadratic formula}[/tex]
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore:
[tex]\implies x=\dfrac{-(-4) \pm \sqrt{(-4)^2-4(2)(4)} }{2(2)}[/tex]
[tex]\implies x=\dfrac{4 \pm \sqrt{-16}}{4}[/tex]
[tex]\implies x=\dfrac{4 \pm \sqrt{16 \cdot -1}}{4}[/tex]
[tex]\implies x=\dfrac{4 \pm \sqrt{16}\sqrt{-1}}{4}[/tex]
[tex]\implies x=\dfrac{4 \pm 4i}{4}[/tex]
[tex]\implies x=1 \pm i[/tex]
Therefore, the zeros of the function are:
[tex]x=4, \quad x=1+i,\quad x=1-i[/tex]
(one real zero and 2 complex zeros)
What is the volume of this triangular prism?
Answer:
The volume is 288 ft^3
Answer:
288
Step-by-step explanation:
The formula for finding the volume is to find the side and then multiplying it by the width. (half of the base times length times width) So, you first find the area of the triangle.
9x4=36, 36/2=18.
Then, 16x18=288.
PLS HELP
1.
Seats in a theater are curved from the front row to the back. The front row has 18 chairs, the second has 26
and the third has 34, and so on.
a.
Write a recursive rule for this series (2 points):
b. Write an explicit rule in simplified form for this series:
Show the steps to simplify. (2 points)
c. Using the explicit formula, find the number of chairs in row 7 (show work) (3 points):
on Voy bob ochote
bu ma'isto
d. The auditorium can hold 12 rows of chairs. Write a sigma notation for this series, and then use either series
formulas to calculate how many chairs can fit in the auditorium. Show all work. (5 points)
The chairs in the auditorium illustrates an arithmetic sequence
The recursive rule is: an = an-1 + 8; a1 = 26The explicit rule is: an = 18 + 8nThere are 74 seats in the 7th row840 chairs can fit the auditoriumThe recursive ruleFrom the question, we have the following sequence:
Seats: 18, 26, 34
Rewrite as:
26 = 18 + 8
34 = 26 + 8
The above means that:
The number of seats on a row is 8 added to the the number of seats on the previous row.
Hence, the recursive rule is:
an = an-1 + 8; a1 = 26
The explicit ruleIn (a), we have:
a1 = 26 and d = 8
The explicit rule is calculated using:
an = a1 + (n -1) * d
This gives
an = 26 + (n - 1) * 8
Expand
an = 26 - 8 + 8n
Evaluate the difference
an = 18 + 8n
Hence, the explicit rule is:
an = 18 + 8n
The number of seats in the row 7This means that n = 7.
So, we have:
a7 = 18 + 8 * 7 = 74
Hence, there are 74 seats in the 7th row
The sigma notationWe have the maximum number of rows to be 12.
So, the sigma notation would be:
[tex]\sum\limits^{12}_{n=1} {18 + 8n}[/tex]
The total number of seats is:
Sn = n/2(2a + (n -1) * d)
This gives
S12 = 12/2(2 * 26 + (12 -1) * 8)
S12 = 840
Hence, 840 chairs can fit the auditorium
Read more about arithmetic sequence at:
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Aiko types at a rate of 50 words per minute.
After typing at the same rate for 3 minutes, he has typed a total of 150
words.
This situation can be represented with a linear equation written in point- slope form, where x represents the number of minutes and y represents the number of words.
Use this information to complete each statement about the linear equation.
Answer:
Slope: 50x
One point will be: (1,50)
Equation: y = 50x
Step-by-step explanation:
Answer:
The slope of the linear equation is *50
One point on the graph of the linear equation will be *(3, 150)
This linear equation can be written as *y – 150 = 50(x – 3)
Step-by-step explanation:
ttm
The cost to mail a package is $8 for the first 4 pounds and 25 cents for each additional ounce. Which of the following functions represents the cost to mail a package if x is the number of ounces over 4 pounds?
f( x) = 32 + 0.25 x
f( x) = 0.25( x + 4)
f( x) = 0.25+ 8 x
f( x) = 8 + 0.25 x
Answer:
f(x) = 8 + 0.25x
Step-by-step explanation:
The minimum cost is $8, for up to 4 pounds.
The added cost is ($0.25/oz)(x), where x is trhe ounces over 4 pounds
The total cost is the sum of these two:
f(x) = 8 + 0.25x
Simplify. (In the problems where you combine fractions with unlike denominators leave the denominators in factored form.)
Answer:
[tex] \dfrac{a}{a - 4} [/tex]
Step-by-step explanation:
You are subtracting fractions, so as usual with fraction subtraction, you need a common denominator. To get a common denominator, you need to factor each denominator.
[tex] \dfrac{3a}{a + 4} - \dfrac{2a^2 - 16a}{a^2 - 16} = [/tex]
Factor the right denominator. It is a difference of two squares.
[tex] = \dfrac{3a}{a + 4} - \dfrac{2a^2 - 16a}{(a - 4)(a + 4)} [/tex]
The left denominator is (a + 4). The right denominator is (a - 4)(a + 4). The LCD is (a - 4)(a + 4), so multiply the left fraction by (a - 4)/(a - 4).
[tex] = \dfrac{3a}{a + 4} \times \dfrac{a - 4}{a - 4} - \dfrac{2a^2 - 16a}{(a - 4)(a + 4)} [/tex]
[tex] = \dfrac{3a^2 - 12a}{(a - 4)(a + 4)} - \dfrac{2a^2 - 16a}{(a - 4)(a + 4)} [/tex]
Be careful when you do the subtraction of the numerators, 3a² - 12a minus 2a² - 16a. 3a² - 12a - (2a² - 16a). The minus of the subtraction changes each sign inside the parentheses, so you end up with 3a² - 12a - 2a² + 16a. Be especially careful with the +16a.
[tex] = \dfrac{3a^2 - 12a - (2a^2 - 16a)}{(a - 4)(a + 4)} [/tex]
[tex] = \dfrac{3a^2 - 12a - 2a^2 + 16a}{(a - 4)(a + 4)} [/tex]
[tex] = \dfrac{a^2 + 4a}{(a - 4)(a + 4)} [/tex]
[tex] = \dfrac{a(a + 4)}{(a - 4)(a + 4)} [/tex]
[tex] = \dfrac{a}{a - 4} [/tex]
What is the value of y in the equation 6 + y = −3? (1 point) Group of answer choices −3 −9 3 9
Answer:
y= -9
Step-by-step explanation:
y+6=-3
subtract 6 from both sides
y=-9
y=-9
Solution:First, subtract 6 from both sides.6+y=-3Ory+6=-3Why subtract? Because 6 is added to y, and we need to use the opposite operation. Remember, our goal is to find the value of y.Subtract:y=-3-6y=-9We have found the value of y; it's equivalent to -9.Hope it helps.
Do comment if you have any query.
Please explain someone!!!
Answer: 1 and 2
Step-by-step explanation: 1 and 2 because if you are graphing this the formula to find the slope / the line is y = x + some number. In the formula x is how much the line goes from the x axis and the number is how much it is from the y axis. On #2 the problem is 3y = 2x + 4 so to follow the formula you need to divide both sides by 3 to get y = 2/3x + 4. For #3 you do the same thing to get y = -3/2x -5. Finally for #1 the equation is 2x + 3y = 7 so to get the slope / line you need to put x on the other side so now it is 3y = 7-2x then you divide both sides by 3 and get y = -2/3x + 7 and on 1 and 2 there x is 2/3 (the negative doesn't matter and the random number) so they are parallel.
Bella baked a two layer cake.The bottom layer has dimensions of 4 inch x 6inch x 8inch.The dimensions of the top layer are half bottom.What is the volume of the top layer.
Answer:
30 is the answer because you need to multiple 4 and 6
A=2.3,b=3.9,c=5,9 I do not know how to do this
Answer:
put the cords on a chart
Step-by-step explanation:
h(t)=50− 5th, left parenthesis, t, right parenthesis, equals, 50, minus, start fraction, t, divided by, 5, end fraction
h(35)=h(35)=
Answer:
H(t) = 50 - t/5
h(35)=50-35/5
=50-7
=43
h(35) = 43
I need help with this
Answer:
75%
Step-by-step explanation:
It's over 50% and it's definitely not 100%
You send an email with a file size of 4 kilobytes. one kilobyte is 2-0 bytes. what is the file size of your email in bytes? write your answer as a power.
The file size sent in kilobytes was converted to bytes, the 4 kilobytes is equivalent to 80 bytes
Unit ConversionGiven Data
File Size = 4 kilobytesWe are told that 1 kilobytes = is equivalent to 20 bytes
hence 4 kilobytes will be equivalent to x bytes
cross multiplying we have
4*20 = x
x = 80 bytes
Therefore, the file size is 80 bytes
Learn more about unit conversion here:
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Please help pleeaassee!! >_<.
Answer:
Slope intercept form does not dictate whether or not a function is linear. What determines if a function is linear is if there is one independent variable, one dependent variable, and it makes a STRAIGHT line. This function is linear because there are only 2 variables and a horizontal line.
Levi could have determined that the graph was linear by checking the conditions stated above or graphing it out. Then, he would see that y = 2 is a straight horizontal line with an independent and dependent variable.
Hope this helps!
Cedar Point amusement park has some of the tallest roller coasters in the United States. The Mantis is 165 feet shorter than the Millennium Force.
Write and solve an equation that can be used to find the height x of the Mantis.
(4x - 3)
Find the value of 'x'.
(2x + 9)
A. 53
B. 14
C. 16
D. 37
Answer:
please the question is not clear
which statement uses words to represent 5+8×3-2
Answer:
A
Step-by-step explanation:
You should always multiply before adding or subtracting. By saying "a product of 8 and 3," it means we multiplied them together first.
You should then add and subtract in the order in which they appear. Saying "five more" before "minus 2" means we did it in the right order.
please help i need help
Answer:
the answer is 14
Step-by-step explanation:
so first you subtract 8- 2 over 2 then =1 over 8 then subract 2 over 2
8 x 2 - 2 = 16 - 2 = 14 = 2 x 7 = 7
1 x 2 - 2 = 2 = 2 = 2 x 1
then 1 x 2 = 2 = 7 over 1 next add 21 over 3 + 7 = 21 over 3 + 7 over 1 = 21 over 3 + 21 over 3 = 21 +21 over 3 = 42 over 3 = 3 X 14 over 3 x 1 = 14
hope this helps you have a good day
What is the multiplier for a 58% decrease
Answer:
A. 0.58
Step-by-step explanation:
HCF or LCM
294 blue smarties, 252 pink smarties, and 210 yellow smarties are shared equally among some students with none left over. What is the largest possible number of students?
In a number of identical boxes of chocolates, there are 90 dark ginger, 198 white, and 126 hazelnut. What is the largest possible number of boxes of chocolates?
HCF for both I believe!
Complete the calculations so that each shows the correct sum of difference (GIVING 30 POINTS)
Answer:
See below ↓↓↓
Step-by-step explanation:
a) 2 . 1 4 0 b) 2 9 . 9 9 c) 6 . 1 5 7
+ 1 . 7 2 5 + 1 . 4 2 - 1 . 0 0 9
3 . 8 6 5 3 1 . 4 1 5 . 1 4 8
a. Convert 5x^2 + 55x + 140 from standard to vertex form
b. Describe the transformation.
Answer:
The transformation will be 5
Step-by-step explanation:
Answer:
See below.
Step-by-step explanation:
5x^2 + 55x + 140 ---> required
Coefficients a=5, b=55, c=140 yield
[tex]h=\frac{-h}{2*a} =\frac{-(55)}{2*5} =\frac{-55}{10} =-5.5[/tex]
Thus, the x-coordinate of the vertex is [tex]\boxed{h = -5.5 }[/tex]
Plugging x=-5.5 into the given equation yields:
[tex]k=5*(-5.5)^{2} +55*-5.5+140=-11.25[/tex]
Thus, the y-coordinate of the vertex is [tex]\boxed{k = -11.25 }[/tex]
Altogether, the vertex of the given parabola is
[tex]\boxed{ (h,k)=(-5.5,-11.25) }[/tex]
Plugging (h,k)=(−5.5,−11.25) into the vertex formula
[tex]\boxed{ y=(x-h)^2+k }[/tex]
yields the vertex form of the parabola
[tex]\boxed{ y=(x+5.5)^2-11.25 }[/tex]
To find the vertex of a parabola in standard form, first, convert it to the vertex form y=a(x−h)2+k y = a ( x − h ) 2 + k .10)Find the mean of the following data?
0 1 2 3 4 5 6 7
Answer:
3.5
Step-by-step explanation:
The mean, or average, is calculated by adding up the scores and dividing the total by the number of scores
How many like terms are in the expression a3+3a2b-4ab-11b+7
Answer:
There are five terms.
Terms in an expression contains variables and numbers. They are separated by any operators like addition and subtraction.
In this expression the terms are:
a^3, 3a^2b , -4ab, -11b and 7
As you can see, there are five terms in the expression
Find the length of the third side. If necessary, round to the nearest tenth
Pythagorean Theorem (Rounding)
By using the Pythagorean Theorem, we will see that the length of the missing side is 4 units.
How to find the length of the third side?
We need to remember the Pythagorean Theorem, the sum of the squares of the cathetus is equal to the square of the hypotenuse.
In this case, the cathetus are x and 3, and the hypotenuse is 5, then we have:
x^2 + 3^2 = 5^2
x^2 = 25 - 9 = 16
x = √16 = 4
So the length of the missing side is 4 units.
If you want to learn more about right triangles, you can read:
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Find the perimeter of the semicircular region. Round your answer to the nearest hundredth.
The perimeter is about
meters.
Answer:
23.14
Step-by-step explanation:
The semi circular region's diagram looks as if it is half of a circle, cut in half by its diameter.
So the circumference of a circle is 2πr or πd
This is half a circle, so the formula is πd/2
π9/2 = 14.137
However, that's only half of the circumference. That does not contain the diameter that is also included.
So if you add 9m to that you get 23.137
On a standardized exam, the scores are normally distributed with a mean of 300 and a standard deviation of 20. Find the z-score of a person who scored 270 on the exam.
Answer:
z = -1.5
Step-by-step explanation:
To Find z-score
z = (X - μ) / σX = Test scoreμ = Mean σ = Standard DeviationGiven
X = 270μ = 300σ = 20Solving
z = 270 - 300 / 20z = -30/20z = -1.5Under his cell phone plan, Adrian pays a flat cost of $59.50 per month and $5 per gigabyte. He wants to keep his bill under $70 per month. Write and solve an inequality which can be used to determine x x, the number of gigabytes Adrian can use while staying within his budget.
The cell phone plan is an illustration of a linear inequality
Adrian gigabyte usage must be less than 2.1 to spend under $70.
How to determine the number of gigabytes within budget?The given parameters are:
Base cost = $59.50
Rate = $5 per gigabyte
Let the number of gigabyte be x.
So, the total amount is:
Total = 59.50 + 5x
Adrian wants to spend under $70.
So, we have:
59.50 + 5x < 70
Evaluate the like terms
5x < 10.5
Divide both sides by 5
x < 2.1
Hence, the number of gigabyte must be less than 2.1
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helppp please been stuck for so long
Answer:
Floating point(Decimal) is 0.1
Fraction is [tex]\frac{1}{10}[/tex]
This is because...10^-1 is going to be 0.1 in this case. This is because 10^-1 is the same as [tex]\frac{1}{10^1}[/tex], which is the same as [tex]\frac{1}{10}[/tex], because anything times 1 remains the same.
[tex]\frac{1}{10}[/tex] is the same as 0.1
We get a 2-in-1 answer, which is perfect for this scenario!
Hence, the correct answers are [tex]\frac{1}{10}[/tex] and 0.1
Paul bought 4 DVDs for $9.95 each. What was his total cost?
$39.90
$40.80
$39.80
$38.80
Answer:
$39.80
Step-by-step explanation:
just 9.95 x 4
factor each completely
n^2 - 11n + 10
[tex] {n}^{2} - 11n + 10 = [/tex]
[tex](n - 1)(n - 10)[/tex]
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