Rational root theorems are used to determine the potential roots of a polynomial function
The actual roots are 3 and -4The potential roots are [tex]\pm0.5, \pm1, \pm 1.5, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24[/tex]The function is given as:
[tex]f(x) = 2x^2 + 2x - 24[/tex]
Expand
[tex]f(x) = 2x^2 + 8x - 6x - 24[/tex]
Expand
[tex]f(x) = 2x(x + 4) - 6(x + 4)[/tex]
Factor out x + 4
[tex]f(x) = (2x -6)(x + 4)[/tex]
Set to 0
[tex](2x -6)(x + 4) = 0[/tex]
Split
[tex](2x -6) = 0\ or\ (x + 4) = 0[/tex]
Make x the subject in both cases
[tex]2x = 6\ or\ x= -4[/tex]
Solve for x
[tex]x = 3\ or\ x= -4[/tex]
So, the actual roots are 3 and -4
Recall that, the function is:
[tex]f(x) = 2x^2 + 2x - 24[/tex]
For a function,
[tex]f(x) = px^n + ax^{n-1} +.......+q[/tex]
According to rational root theorem, the roots of f(x) are:
[tex]Roots = \pm \frac{Factors\ of\ q}{Factors\ of\ p}[/tex]
The roots of 24 are:
[tex]24 = \pm1, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24[/tex]
The roots of 2 are:
[tex]2 = \pm1, \pm2[/tex]
So, the possible roots are:
[tex]Roots = \frac{\pm1, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24}{\pm 1, \pm 2}[/tex]
This gives:
[tex]Roots = \pm1, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24,\pm0.5, \pm1, \pm 1.5, \pm 2, \pm 3, \pm 4, \pm6\pm 12[/tex]
Remove repetitions
[tex]Roots = \pm0.5, \pm1, \pm 1.5, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24[/tex]
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3 and -4 dudes and dudettes
edg2022
solve pls brainliest
Answer:
a) 45 minutes
b) 2 miles
c) 8 miles per hour
d) 7.5 minutes per mile
Step-by-step explanation:
a) (150/20) x 6 = 45 minutes
b) (20/150)(15) = 2 miles
c) (20/150)(60) = 8 miles per hour
d) 150/20 = 7.5 minutes per mile
20 miles in 150 minutes = 20/150 miles per minute = 2/15 miles per minute
distance/speed = time
6 miles / (2/15) miles per minute = 45 -> 45 minutes
time*speed=distance
15 minutes * 2/15 miles per minute = 2 miles
Her speed, 2/15 is in miles per minute. To convert to miles per hour, you multiply by 60 (60 minutes in an hour). 2/15*60=8 miles per hour
minutes per mile = 150 minutes for 20 miles = 150/20=15/2 minutes per mile
15/2=7.5
7.5 minutes per mile
rewrite expression as a single power. 5^3/5^6
Answer:
1/125
Step-by-step explanation:
Simply subtract the exponents
in this case 6 - 3 so then its now 5 / 5^3
now just make the numerator a 1
1 / 5^3
5x5x5 = 125
1/125
Answer:
0.008
Step-by-step explanation:
i did 5 to the 3rd power which is 125
Then i did 5 to the 6 power and got 15625
finally I divided the answers and got 0.008 or in 125
johan earns $650 per week and works 48 hours a week. if he gets a free tax allowance of $8000, pays tax at a rate of 10% on the next $10000 and 20% on the rest. how much tax will he pay in a year?
Answer:
follow me on the gram (andrewa223) also the answer is a
Step-by-step explanation:
Determine what type of model best fits the given situation: A $500 raise in salary each year. A. exponential B. quadratic C. none of these D. linear
Answer:
A - Exponential
Step-by-step explanation:
Exponential is the best fitting model because there's a $500 raise in salary each year, so $500 is added to the salary of the previous year.
urgent !!
<1 and <5 are what kind of angles
Answer:
Obtuse Angles are
1, 3, 5, 7, 9, 11
Acute angles are
2, 4, 6, 8, 10, 12
Step-by-step explanation:
15 minutes how many students read the book in an hour
Answer:
Your reading speed will increase if you're reading a book you're familiar with than one you barely know. So, on average, you can read 40 to 50 pages of a book in an hour.
Step-by-step explanation:
One spinner has three equally sized sectors labeled R, S, and T. A second spinner has two equally sized sectors labeled 3 and 5. Each
spinner is spun once.
What is the sample space of outcomes?
Answer:
3rd option
Step-by-step explanation:
The sample space of outcomes, when two spinners, one with three equally sized sectors labeled R, S, and T and the other with two equally sized sectors labeled 3 and 5 spun once, is {R3, R5, S3, S5, T3, T5}.
What is sample space?Sample space is the set of all the possible values or the outcomes of an event.
Let suppose the coin is tossed two times. Then the set of possible outcomes or sample space of it can be given as,
[tex]S=\{HH,HT,TH,TT\}[/tex]
Here, H denotes the head and T denotes the tail part of the coin.
In the given problem,
One spinner has three equally sized sectors labeled R, S, and T. A second spinner has two equally sized sectors labeled 3 and 5. Each spinner is spun once.
The sample space when are {R3, R5, S3, S5, T3, T5}. Thus, there is a total of 6 outcomes of the event.
Hence, the sample space of outcomes, when two spinners, one with three equally sized sectors labeled R, S, and T and the other with two equally sized sectors labeled 3 and 5 spun once, is {R3, R5, S3, S5, T3, T5}.
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A recipe calls for cup
3/4of milk to make 4
cookies. If Sarah wants to
cut the recipe in, 1/2how
much milk would she
need?
3/ 8
of a cup.
Explanation:
You want half of the recipe, so you want half of
3/4
of a cup.
Of means multiplication when it comes to fractions, so multiply
3/4 by 1/2 to get 3/4 ⋅ 1/2 = 3/8
I need help with this. I'm so lost..
Answer:
1. Answer Is 33
2. Answer Is 25
3. Answer Is 33
HELP PLZ!!!!
1) Which rigid motion will verify that rectangle ABCD is congruent to rectangle A'B'C’D’ ?
A) A reflection over x-axis.
B) A reflection over y-axis.
C) A 270° clockwise rotation about the origin.
D) A 90° counterclockwise rotation about the origin.
2) Which rigid motion will verify that rectangle A'B'C'D' is congruent to rectangle A"B"C"D"?
A) A reflection over x-axis.
B) A reflection over y-axis.
C) A translation 8 units to the right.
D) A 90° counterclockwise rotation about the origin.
Answer:
reflection over x-axis
hope that helps!!!
Rewrite using a single positive exponent..-
7^2
——
7^-4
Answer:
7 ^2 ⋅ 7 ^4 = 49^6
Step-by-step explanation:
7² / 7 ⁻⁴
= 7²⁻⁽⁻⁴⁾
= 7 ⁽²⁺⁴⁾
= 7⁶
= 117649
Remember :-
xᵃ / xᵇ = xᵃ⁻ᵇ
___
Hope it helps ⚜
⁽
The world’s two highest dams are both in Tajikistan. The Rogun dam is 35 meters taller than the Nurek dam. Together they are 635 meters tall. Find the height of the Nurek dam
Answer: Rogun dam is 335m tall and Nurek dam is 300m tall
Step-by-step explanation:
I will use [tex]r[/tex] to represent the height of the Rogun dam and [tex]n[/tex] to represent the height of the Nurek dam.
The system of equations is as follows:
[tex]r+n=635[/tex]
[tex]r-n=35[/tex]
From the second equation, we can rearange it to be:
[tex]r=35+n[/tex]
Then take this new value of [tex]r[/tex] and plug it into our first equation to find [tex]n[/tex]
[tex](35+n)+n=635[/tex]
[tex]35+2n=635[/tex]
[tex]2n=600[/tex]
[tex]n=300[/tex]
This means that the Nurek dam is 300m tall, and the Rogun dam is 335m tall, found by pluggin the value into our first equation:
[tex]r+300=635[/tex]
[tex]r=335[/tex]
Question 25 of 55
Compare 5 and - 8. Which of the following is true?
O A. 15| > |-81 and 5 > -8
B. 151 > T-81 and 5<-8
O C. 151 = 1-8) and 5 >-8
O D. 151 < |-81 and 5 >-8
Plz answer it will be nice thanks
hlo math genius plz help no spam !!! (*°*°)
the area of a rectangle field 1800 m2 .If the ratio of length and breadth is 5:4, find itz perimeter
Let
Length=5xBreadth=4xATQ
[tex]\\ \sf{:}\longrightarrow Area=1800[/tex]
[tex]\\ \sf{:}\longrightarrow Length(Breadth)=1800[/tex]
[tex]\\ \sf{:}\longrightarrow 5x(4x)=1800[/tex]
[tex]\\ \sf{:}\longrightarrow 20x^2=1800[/tex]
[tex]\\ \sf{:}\longrightarrow x^2=900[/tex]
[tex]\\ \sf{:}\longrightarrow x=30[/tex]
Length=L=5(30)=150mBreadth=B=4(30)=120m[tex]\\ \sf{:}\longrightarrow Perimeter=2(L+B)[/tex]
[tex]\\ \sf{:}\longrightarrow Perimeter=2(150+120)[/tex]
[tex]\\ \sf{:}\longrightarrow Perimeter=2(270)[/tex]
[tex]\\ \sf{:}\longrightarrow Perimeter=540m[/tex]
13. Write the equation of the line perpendicular to
5y = 3x + 25 but passing through (-4,-1)
Answer:
y = -[tex]\frac{5}{3}[/tex]x - -[tex]\frac{23}{3}[/tex]
Step-by-step explanation:
First, let's divide both sides by 5 to get the first equation into the form y = mx + b. We get y = [tex]\frac{3}{5}[/tex]x + 5. The m value, [tex]\frac{3}{5}[/tex], is the slope and the b value, 5, is the y-intercept of this line.
When a line is perpendicular to another line, the slopes must multiply to get -1. In other words, the slopes must be a negative reciprocal of each other. Since the slope of the original line is [tex]\frac{3}{5}[/tex], we know that the slope of the line perpendicular to that is -[tex]\frac{5}{3}[/tex].
Then, since we know x, y, and m of the second equation, we can substitute those three values into the equation, y = mx + b, to find the y-intercept (b).
-1 = (-[tex]\frac{5}{3}[/tex])(-4) + b
-1 = [tex]\frac{20}{3}[/tex] + b
b = -[tex]\frac{23}{3}[/tex]
After plugging in the values of m and b we calculated, we get the equation for the line perpendicular to the original line: y = -[tex]\frac{5}{3}[/tex]x -[tex]\frac{23}{3}[/tex].
Which pair of triangles must be similar?
Triangle 5 has a 30∘ angle and a 90∘ angle. Triangle 6 has a 30∘ angle and a 70∘ angle.
Triangles 1 and 2 each have a 35∘ angle.
Triangle 7 has a 50∘ angle and a 25∘ angle. Triangle 8 has a 50∘ angle and a 105∘ angle.
Triangles 3 and 4 are both isosceles. They each have a 40∘ angle.
1 – 2x + 3y for when X = – 2 and y = – 5
Answer:
-12
Step-by-step explanation:
1-2x+3y
1-2(-2)+ 3(-5)
1-4-9
= -12
A bag only contains 4 red and 6 blue marbles. What is the probability of drawing a green marble?
NO LINKS OR TROLL
THIS IS YOUR WARNING
Answer:
0% chance
Step-by-step explanation:
there are no green marbles
Marbles no
red=4blue=6green=0There is no green marbles
So it will never occur(impossible event)
Probability is 0Can someone help me please
Answer:
D
Step-by-step explanation:
Sarafina Ltd is considering two new investment projects, project A and project B. Each project would require an immediate cash outlay of Ksh. 10 million. The company expects to have available enough resources to undertake only one of the projects.The company management believe that return from existing activities and from the new projects will depend on economic environment that will prevail during the coming year. The estimated returns and probabilities of the possible economic environments are as follows:Economic environmentGoodFairBadProbability0.30.40.3Return from project A (Ksh "000")12,50012,5009,500Return from Project B (Ksh "000")10,00011,75013,000Aggregate return from existing portfolio of projects. (Ksh "000")90,000120,000130,000The company has a current market value of Ksh. 100 million. The management believe that the risks and returns per shilling of market value of their existing activities are similar to those of the stock market as a whole, including their dependence on whichever economic environment prevails. The return on treasury bills is 8% per annum.Using CAPM, advise the management of the company on which of the two projects should be accepted.
X, Y, and Z are collinear and Y is between X and Z. If XY = 3x – 1, YZ = 5, and XZ = 5x – 8,
what is the value of x?
a. 6
b. 4
c. 10
d. 8
Answer:
6
Step-by-step explanation:
XY = 3x – 1, YZ = 5, and XZ = 5x – 8,
We know that XY + YZ = XZ, so
3x - 1 + 5 = 5x - 8
3x + 4 = 5x - 8
3x + 12 = 5x
12 = 2x
6 = x
The value of x from the given line segment XZ is 6. Therefore, the correct answer is option A.
Given that, X, Y, and Z are collinear and Y is between X and Z.
Collinear points are those that are on the same straight line or in the same plane. In Euclidean geometry, two or more points on a line that are close to or far from each other are said to be collinear.
So, here [tex]XZ=XY+YZ[/tex]
[tex]5x-8=3x-1+5[/tex]
[tex]5x-8=3x+4[/tex]
[tex]5x-3x=4+8[/tex]
[tex]2x=12[/tex]
[tex]x=6[/tex]
Therefore, the correct answer is option A.
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equation where slope = 7/2 and y-intercept is -15
Answer:
y = 7/2x - 15
Step-by-step explanation:
y = mx + b
if slope is 7/2, m= 7/2
y = 7/2x + b
if y-intercept is -15, y = -15, x = 0
-15 = 7/2(0) + b
b = -15
then
y = 7/2x - 15
Express each ratio as a fraction in simplest form.
2 gallons to 27 quarts
The ratio 2 gallons to 27 quarts as a fraction in its simplest form is 4/27
The given ratio is:
2 gallons to 27 quarts
This can also be written as:
2 gallons : 27 quarts
Convert 27 quarts to gallons so that both items in the ratio can be of equal unit
Note that:
1 quart = 0.25 gallons
27 quarts = 0.25 x 27
27 quarts = 6.75 gallons
The ratio can therefore be re-written as:
2 gallons : 6.75 gallons
In fraction form:
2 gallons : 27 quarts = 2/6.75
Multiply the numerator and denominator by 4
2 gallons : 27 quarts = 4/27
The ratio 2 gallons to 27 quarts as a fraction in its simplest form is 4/27
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What is the constant of this polynomial? 3x9 + 4x + 129
Answer:
129
Step-by-step explanation:
When referring to the constant in a polynomial, we're generally referring to the term that has no variables in it. Here, that term is 129.
The constant is 129.
How does a value that is greater
than 100% of the original value or less than
1% of the original value compare to the original
value?
[tex] \: \: \: \: \: \: [/tex]
If a value is greater than 100% of the original value, then it is larger than the original value. For example, 150% of 6 is 6 150% = 61.5 =9> 6. -
If a value is greater than 100% of the original value, then it is larger than the original value. For example, 150% of 6 is 6 150% = 61.5 =9> 6. -If the value is less than 1% of the original value, then it is smaller than the original value. For example, 0.1% of 6 is 6 0.1% = 6 0.001 0.006 < 6.
hope it helps
A movie-theater employee notes an inverse relationship between the theater's popcorn sales and its nacho sales. On a given night, the theater makes $1,540 from popcorn sales and $1,330 from nacho sales. If on the next night the employees sell $1,672 of popcorn, how much is earned from nachos?
Using proportions, it is found that $1,225 is earned from nachos.
This question is solved by proportions, using a rule of three.The measures have an inverse relationship, hence line multiplication is applied instead of cross multiplication.When the theater makes $1,540 from popcorn sales, it makes $1,330 from nacho sales. How much is earned from nachos when $1,672 is earned from popcorn?The rule of three is:
$1,540 - $1,330
$1,672 - $x
Applying line multiplication:
[tex]1672x = 1540 \times 1330[/tex]
[tex]x = \frac{1540 \times 1330}{1672}[/tex]
[tex]x = 1225[/tex]
$1,225 is earned from nachos.
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x over 3 is less then or equal to 5
Answer:
x/3 ≤ 5
I'm not sure if this is what you were looking for. If not, please be more specific in your questions!
Given h(x)=4x-1, solve for x when h(x)=-9
Step-by-step explanation:
h(x) = 4x - 1
given,
h(x) = -9
now,
h(-9) = 4(-9) - 1
→ -36 - 1
→ -37
hope this answer helps you dear, take care!
Answer:
x = - 2
Step-by-step explanation:
Given h(x) = 4x - 1 and h(x) = - 9, then equating right sides gives
4x - 1 = - 9 ( add 1 to both sides )
4x = - 8 ( divide both sides by 4 )
x = - 2
Translate the phrase into an expression with integers: negative 13. Do not simplify your expression.
Answer:
-13
Step-by-step explanation:
negative 13 = -13
The price of an item has been reduced by 45%. The original price was $43. What is the price of the item now?
Thank you!
Answer:
23.65
Step-by-step explanation: