According to the Rational Root Theorem, the potential rational roots of the equation 9x^3 + 14x^2 - x + 18 = 0 are ±1/3 and ±3. The values ±1/8 and ±1/2 are not valid since their denominators are not factors of the leading coefficient, which is 9.
Explanation:The possible rational roots of the polynomial equation 9x^3 + 14x^2 - x + 18 = 0 can be determined using the Rational Root Theorem. This theorem states that any rational solution, expressed in the form of a fraction p/q, where p is a factor of the constant term and q is a factor of the leading coefficient, must be among these possible roots.
The constant term in this equation is 18, and its factors are ±1, ±2, ±3, ±6, ±9, ±18. The leading coefficient is 9, with factors of ±1, ±3, ±9. According to the Rational Root Theorem, we take each factor of the constant term and divide by each factor of the leading coefficient to find the possible rational roots. Thus, the potential rational roots are ±1/1, ±1/3, ±1/9, ±2/1, ±2/3, ±2/9, ±3/1, ±3/3, ±3/9, and so forth, including their negative counterparts.
From the options provided in the question, the potential rational roots that fit the criteria set by the theorem are: ±1/3, and ±3. The other options, ±1/8, ±1/2, do not satisfy the theorem as their denominators are not factors of the leading coefficient.
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What is -14+6b+7-2b=1+5b show your work
-14+6b+7-2b=1+5b
step 1: simplify the equation
-7+4b=1+5b
step 2: collect your variables
-7=1+b
step 3: collect your whole numbers
-8=b
Which of the following is NOT true about the following equation? y=−5 It is perpendicular to the equation y=15x−3. Its slope is zero. The line does not cross the x-axis. It is the equation of a horizontal line.
Can someone explain how to answer this? Thanks in advance.
Alright, so before we can answer this problem we need to go over some basics! For this problem, you'll need to know:
The Triangle Sum theorem states that the interior angles of every triangle must add up to 180 degrees.
Also, corresponding angles are angles that have the same relative position when 2 lines intersect. Therefore, angle I and angle K are corresponding (and as an example, angle J and angle H are corresponding). When lines are parallel (Line HI and Line JK), corresponding angles are equal.
Now that we've covered that, we can use that information to find x!
Let's start with finding angle I since we know it'll be equal to angle X. We also now know that angle H + angle A + angle I = 180. So, plug it in.
56 + 66 + I = 180.
122 + I = 180
Then subtract on both sides:
I = 58.
Since I = X we now know that angle x = 58 degrees.
What fraction is halfway between 9/10 and 10/10. Question 8
[tex]\frac{-9.5}{10}[/tex] is halfway between [tex]\frac{-9}{10}[/tex] and [tex]\frac{10}{10}[/tex].
hope that helps :)
Which rule transforms quadrilateral ABCD to quadrilateral A'B'C'D'?
A. (x,y)---->(x,-y-4)
B. (x,y)---->(x+6,-y)
C. (x,y)---->(x+6,y-4)
D. (x,y)---->(-x,y-4)
Answer:
The rule transforms the quadrilateral ABCD to quadrilateral A'B'C'D' is given by
D.(-x,y-4).
Step-by-step explanation:
Given quadrilateral ABCD transform into new quadrilateral A'B'C'D.
The transformation is a special rule by which to determine the coordintae of image point of any coordinate of given point . The transformation can be rotation, reflection, dialtion etc.
In given figure of qudrilateral ABCD
Coordinate of A (-5,4)
Coordinate of B(0,1)
Coordinate of C (-4,0)
Coordinate of D (-6,2)
In II figure of quadrilateral A'B'C'D
Coordinate of A' (5,0)
Coordinate of B' (0,-3)
Coordinate of C' (4,-4)
Coordinate of D' (6,-2)
Then we can see that coordinate of A (-5,4) change into A' (5,0)
It means x change into -x and y change into y-4
Similarly in same way B (0,1) change into B'(0,-3)
C(-4,0) change into C'(4,-4) and D( -6,2) change into D'(6,-2)
Hence, the correct transformation (x,y) into (-x,y-4).You bought 5 pounds of hamburger meat, and you want to make quarter pounders (each weigh .25 of a pound). How many quarter pounders can you make? Show your work and explain your reasoning. Katie’s answer: To determine how many .25 pound burgers I can make, I have to divide 5 by .25. The quotient of 5 divided by .25 will tell me how many groups of .25 there are in 5. I followed the procedure to divide and my quotient is 2, so I can make exactly 2 quarter pound burgers with 5 pounds of meat. 0.25 5.0 = 25 50 Is Katie correct? If not, what was her mistake? Justify your answer
Final answer:
Katie's mistake was in her division calculation. The correct way to find out how many quarter pounders can be made from 5 pounds of meat involves converting pounds to ounces, because you can make 20 quarter pounders when you multiply 5 by 16 to convert to ounces and then divide by 4.
Explanation:
Katie's strategy to divide the total weight of the hamburger meat by the weight of one quarter pounder is a correct approach, but her calculation is incorrect. When you want to determine how many quarter pounders you can make from 5 pounds of hamburger meat, you need to divide the total pounds of hamburger meat by the weight of one quarter pounder, which is 0.25 pounds.
To correct Katie's mistake, you should multiply the weight in pounds by the unit equivalence to get the weight in ounces since we are dealing with a conversion from a larger unit (pounds) to a smaller unit (ounces). Considering the fact that 1 pound equals 16 ounces, the calculation should be:
5 pounds imes 16 ounces/pound = 80 ounces
After converting the weight to ounces, now compare it to the weight of a quarter pounder in ounces:
0.25 pounds imes 16 ounces/pound = 4 ounces per quarter pounder
Finally, divide the total number of ounces of hamburger meat by the number of ounces in a quarter pounder to determine how many quarter pounders you can make:
80 ounces/4 ounces per quarter pounder = 20 quarter pounders
Therefore, you can make 20 quarter pounders from 5 pounds of hamburger meat.
How do I get the answer what is the answer
The answer is 0.75 Hope this Helps
PICKING BRAINLIEST ANSWER!!!!!!!!!! Which graph shows a dilation?
Answer:
The last graph.
Step-by-step explanation:
In the first graph, the darker triangle has one side that is 1/3 of the corresponding side of the other triangle, and one side that is 2/5 of the corresponding side of the other triangle. This is not proportional for all sides, so this is not a dilation.
In the second graph, the darker triangle has one side that is 1/2 of the corresponding side of the other triangle, and one side that is 3/5 of the corresponding side of the other triangle. This is not proportional for all sides, so this is not a dilation.
In the third graph, the darker triangle has one side that is 1/3 of the corresponding side of the other triangle, and one side that is 1/2 of the corresponding side of the other triangle. This is not proportional for all sides, so this is not a dilation.
In the fourth graph, the darker triangle has one side that is 2/3 of the corresponding side of he other triangle, and another side that is 4/6=2/3 of the corresponding side of the other triangle. Since these are both right triangles, this means the other side, the hypotenuse, will have the same ratio. Since it is proportional for all sides, this is a dilation.
Answer:
Last GRaph
Step-by-step explanation:
What's the equation for 5.2 more than the quotient of h and 3 is w
h/3 + 5.2 = w
"More" stands for adding, and "quotient" stand for division.
Hope this helps!
The equation for '5.2 more than the quotient of h and 3 is w' is 'h/3 + 5.2 = w'. This means h divided by 3, plus 5.2, equals w.
Explanation:The subject of this question is Mathematics and it involves the creation of a mathematical equation. When the question states 'the quotient of h and 3', it means 'h divided by 3'. So, that part of the equation would be written as 'h/3'.
When the question says '5.2 more than', that indicates you are adding 5.2 to the previous value. So, the whole left side of the equation would be 'h/3 + 5.2'.
Finally, the question states 'is w', which means 'equals w'. So, the entire equation would be written as 'h/3 + 5.2 = w'.
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How much is 6 yards in inches
36*6= 216 inches in a yard
(Easy)+(20 points)
insert parenthesis in expression 2 so that it has a value of 19. then show why your expression has a value of 19.
I've already done the work:
(5+4)*2+6-2*2-1=19 (i added the parenthesis)
but i dont know how to show why it makes 19 so yeah could someone put an explanation or something
The reasoning behind why it equals 19 is because you use PEMDAS (aka: Order Of Operations). When you solve, you solve in the same order PEMDAS, so you first solve the parenthesis. Next, you'd solve exponents, but in this case, there are none. So, you solve the multiplication and/or division (from left to right). Finally you'd solve completely, by adding and subtracting (from left to right). Doing all these steps would give you your answer of 19.
I hope this helps!
Which of the following is an example of a run-on sentence?
7 + 7 + (–1) =
Run on sentences is a sentence that doesn't have proper punctuation
Ex: I love to write papers I would write one every day if I had the time.
this is a run-on sentence because you need a comma or a period between them.
7 + 7 = 14, 14 - 1 = 13
hope this helps :)
Answer: 13
Step-by-step explanation:
[tex]14+(-1)[/tex] Add [tex]7[/tex] to [tex]7[/tex]
[tex]14-1[/tex] Take the parentheses off
[tex]13[/tex] Subtract [tex]14[/tex] to [tex]1[/tex]
Additional Information: A runoff sentence is where a sentence have no cut off and continues.
Example: I have a car and the car has black on it and is very shiny with a clean engine and more and it can drive very fast.
*This is an example more examples can vary*
Angela is going on vacation to Mexico. She needs to buy new shirts for her trip. She buys 10 new shirts that cost her a total of $222. Some are casual shirts that cost her $18 each. The other are dressy shirts that cost her $25. How many of each did she purchase?
Angela bought 4 casual shirts, and 6 dressy shirts.
To find this, I used the equation ($18c) + ($25d) = $222, and filled in for c (casual) and d (dressy) until the outcomes were the same. Filling in for c and d, you'll get ($18 * 4) + ($25 * 6) = $222. Solving both sides, you'll get $72 + $150 = $222 or $222 = $222. Thus meaning she bought 4 casual shirts and 6 dressy shirts,
I hope this helps!
please help solve
|y|=-18
Answer:
Step-by-step explanation:
+y = -18
-y = -18
If my dad gets home at 5:30 and it is 4:22 how many more minutes do we wait
when steve woke up. his temperature was 102° F. two hours later it was 3° lower. what was his temperature then?
A lower temperature suggests a subtraction.
Wake up temperature: 102° F
Temperature two hours later: 3° F lower, or -3° F
Temperature two hours later: 102° F - 3° F = 99° F
Answer: 99° F
A number (A) is 50% larger than (C). Another number (B) is 25% larger than (C) How many percent bigger is (A) than (B)?
A is twice ( 200%) lager than b
PLEASE SHOW WORK Joanne removed 8 1/3 yards of material from a roll that contained 24 1/2 yards. how much material was left on the roll
First, you need to have a similar denominator! so the closest would be 1/6th
put 8 and 24 back into the percentages to get 24/3 and 48/2
then multiply everything by 2 or 3 to make it sixths getting 48/6 and 144/6
these two simplify to 8 and 24 ( Look it didnt change!)
so to answer 1/3 of it is left or 16
the amount of medicine in Elizabeth blood is modeled by the function M(t)= -t2+10t where t is the number of hours of
We are given function : [tex]M(t)=-t^2+10t[/tex], where t is the number of hours of after she takes the madicine.
We need to find, how many hours after Elizabeth takes her madicine is the amount of madicine in her blood is highest.
Note: The given function is a quadratic function and a quadratic function represents a parabolic shape.
The highest point on the parabola is the vertex of the parabola.
The x-coordinate of the vertex of the parabola would represent the number hours after Elizabeth takes her madicine is the amount of madicine in her blood is highest.
We know, x-coordinate of the vertex = [tex]\frac{-b}{2a}[/tex]
For the given quadratic function a= -1 and b=10.
Plugging values of a and b in x-coordinate of the vertex formula, we get
[tex]\frac{-10}{2(-1)}=\frac{-10}{-2}=5[/tex]
Therefore, after 5 hours Elizabeth takes her madicine is the amount of madicine in her blood is highest.
Tameka plans to run 84 miles in four weeks if she continues the pattern how many miles will she run in one year explain
Answer:
1092 miles/year
Step-by-step explanation:
84/4=21
21 miles/week
21*52=1092
1 year = 52 weeks.
Divide total weeks in a year by 4:
52 / 4 = 13
Multiply 84 miles by 13 = 1092 total miles in a year.
Samantha has 40 minutes to complete both a Math quiz and a spelling quiz. She completes the spelling quiz in 9 minutes. It takes her 3 times as long to complete the Math quiz. How much time does she have left over?
If her spelling quiz was 9 minutes and her math quiz was 3 times as long you find that answer by doing the following math.
9x3=27 minutes (time for her math quiz)
27 minutes + 9 minutes = 36 minutes
40 minutes - 36 minutes = 4 minutes
what is 14÷426 this is to help me for my hw
14 / 426 = 0.09389
Hope this helps!
7/213 in fraction and 0.03286384977 in decimal form
Puala and kelly are comparing their ruining times.
Puala completed a 10-mile run in 65 minuets.
Kelly completed 10-kilometre run in 40 minuets.
Given that 8 kilometre are equal to 5 miles, whch girl has the greatest average speed?
Kelly's average speed is greater. Paula: ~0.026 miles per minute, Kelly: ~0.156 miles per minute. Kelly's average speed is higher.
To compare their average speeds, let's first convert their distances to the same unit. Since 8 kilometers is equal to 5 miles, we can use this conversion to make both distances consistent.
Kelly ran 10 kilometers, which is [tex]\( \frac{10}{8} \times 5 = \frac{25}{4} \)[/tex] miles.
Now we can compare their average speeds:
Paula's average speed = [tex]\( \frac{10 \text{ miles}}{65 \text{ minutes}} \)[/tex]
Kelly's average speed = [tex]\( \frac{\frac{25}{4} \text{ miles}}{40 \text{ minutes}} \)[/tex]
Now, let's calculate both:
Paula's average speed:
[tex]$\begin{aligned} & \text { Paula's average speed }=\frac{10 \text { miles }}{65 \text { minutes }} \times \frac{1 \text { hour }}{60 \text { minutes }} \\ & =\frac{10}{65} \times \frac{1}{60} \text { miles per minute } \\ & \approx \frac{1}{39} \text { miles per minute }\end{aligned}$[/tex]
Kelly's average speed:
[tex]$\begin{aligned} & \text { Kelly's average speed }=\frac{\frac{23}{4} \text { miles }}{40 \text { minutes }} \times \frac{1 \text { hour }}{60 \text { minutes }} \\ & =\frac{\frac{25}{4}}{40} \text { miles per minute } \\ & =\frac{25}{4} \times \frac{1}{40} \text { miles per minute } \\ & =\frac{25}{160} \text { miles per minute }\end{aligned}$[/tex]
Now, we can compare the two speeds. Since both speeds are in miles per minute, we can directly compare them.
[tex]\[ \frac{1}{39} \text{ miles per minute} \approx 0.0256 \text{ miles per minute} \][/tex]
[tex]\[ \frac{25}{160} \text{ miles per minute} \approx 0.15625 \text{ miles per minute} \][/tex]
Kelly's average speed is greater than Paula's average speed.
Therefore, Kelly has the greater average speed.
The complete question is here:
Paula and Kelly are comparing their running times. Paula completed a 10-mile run in 65 minutes. Kelly completed a 10-kilometre run in 40 minutes. Given that 8 kilometres are equal to 5 miles, which girl has the greater average speed?
What is the value of t?
3.5(t+6)=7
A. −4
B. −0.25
C. 0.25
D. 4
3.5(t+6)=7
Use Distributive Property:
3.5t + 21 = 7
Subtract 21 from both sides:
3.5t = -14
Divide both sides by 3.5:
t = -14 / 3.5
t = -4
The answer is A.
To solve for the value of t in the equation 3.5(t+6)=7, we divide both sides by 3.5 and then subtract 6 from both sides, resulting in t = -4.
To find the value of t, we need to solve the equation 3.5(t+6)=7. To do this, we start by dividing both sides of the equation by 3.5 to isolate the t term:
3.5(t+6) / 3.5 = 7 / 3.5t + 6 = 2Next, we subtract 6 from both sides to solve for t:
t + 6 - 6 = 2 - 6t = -4Therefore, the value of t is -4, which corresponds to option A.
There are two connected gears. One has 60 teeth and it makes 50 complete revolutions in a minute. How many complete revolutions will the second gear complete, if it has 40 teeth?
The Second gear will complete 75 revolutions.
Hope this helps. I tried using my past knowledge.
60 teeth = 50 revolutions
40 teeth = x revolutions
To figure this out, you can multiply 60 and 50 together to get 3000, and 40 and x to get 40x.
If you solve this equation, 40x = 3000,
x = 75
Hope this helped!
It takes 1 cup of a liquid fertility to make 7 1/2 gallons of spray. How much liquid fertilizer Ian needed to make 80 gallons of spray?
it would take 10 3/5 cups of liquid fertilizer
By setting up a proportion and solving, we find that it takes approximately 10.67 cups of liquid fertilizer to make 80 gallons of spray.
Explanation:The problem deals with a simple rate, or ratio. In this case, the rate is 1 cup of fertilizer per 7.5 gallons of spray. We need to find out how much fertilizer is needed for 80 gallons of spray.
To do this, we need to set up a proportion. On one side of the equation, we'll have the original ratio (1 cup fertilizer : 7.5 gallons spray). On the other side, we'll set up a ratio with the quantity we're trying to find (x cups fertilizer : 80 gallons spray).
So, our equation looks like this:
1 cup / 7.5 gallons = x cups / 80 gallons
To solve for x, we can cross-multiply:
1 cup * 80 gallons = x cups * 7.5 gallons
Which simplifies to:
80 = 7.5x
To isolate x, we divide both sides of the equation by 7.5:
x = 80 / 7.5
Through this, we get that it takes approximately 10.67 cups of liquid fertilizer to make 80 gallons of spray.
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The table below shows measurements (in inches) from cubes with different side lengths.
Which pairs of variables have a linear relationship? Check all that apply.
side length and perimeter of 1 face
perimeter of 1 face and area of 1 face
surface area and volume
area of 1 face and surface area
side length and volume
Answer:
Only side length and perimeter of one face
Step-by-step explanation:
Given is a cube with measures given in inches.
For a cube
Volume = s^3 where s = side
Hence volume and side are not having linear relation
Perimeter of 1 face = 4s and area =s^2
Obviously 4s and s^2 cannot have linear relationship as degree is diferent
Surface area of cube = 6s^2 but volume = s^3 both have different degrees of s and hence cannot have linear relation
Area of 1 face = s^2 and surface area = 6s^2
THus we get Surface area = 6(area of 1 face) hence can have linear relationship
side length =s and volume = s^3 so cannot have linear relaionship
Side length =s and perimeter = 4s thus having linear relation.
Hence answers are
side length and perimeter of 1 face
area of 1 face and surface area
A linear relationship is represented by [tex]y = mx + b[/tex], where [tex]m \ne 0[/tex]. The linear relationships are:
Side length and perimeter of 1 face Area of 1 face and surface area
Let
[tex]x \to[/tex] side length of the cube
A. Side length and perimeter of 1 face
The perimeter (P) of one face is:
P = 4 x Side length
[tex]P =4 \times x[/tex]
[tex]P = 4x[/tex]
Compare the above equation to [tex]y = mx + b[/tex].
We can conclude that (a) is a linear relationship
B. Perimeter of 1 face and area of 1 face
We have:
[tex]P = 4x[/tex]
Make x the subject
[tex]x= \frac{P}{4}[/tex]
The area of 1 face is:
[tex]A = x^2[/tex]
Substitute [tex]x= \frac{P}{4}[/tex]
[tex]A = (\frac P4)^2[/tex]
[tex]A = \frac{P^2}{16}[/tex]
Compare the above equation to [tex]y = mx + b[/tex].
We can conclude that (b) is not a linear relationship
C. Surface area and volume
The surface area is:
[tex]S=6x^2[/tex]
The volume is:
[tex]V = x^3[/tex]
Make [tex]x^2[/tex] the subject in [tex]S=6x^2[/tex]
[tex]x^2 = \frac S6[/tex]
So, we have:
[tex]V = x^3[/tex]
[tex]V = \frac S6x[/tex]
Compare the above equation to [tex]y = mx + b[/tex].
We can conclude that (c) is not a linear relationship
D. Area of 1 face and surface area
The surface area is:
[tex]S=6x^2[/tex]
The area of 1 face is:
[tex]A = x^2[/tex]
Substitute [tex]A = x^2[/tex]
[tex]S = 6A[/tex]
Compare the above equation to [tex]y = mx + b[/tex].
We can conclude that (d) is a linear relationship
E. Side length and volume
The volume is:
[tex]V = x^3[/tex]
Compare the above equation to [tex]y = mx + b[/tex].
We can conclude that (e) is a not linear relationship
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SOMEONE HELP
plz and thank you
Answer: 60 mph
=================================================================
Explanation:
R*T = D is the same as D = R*T
The D value is unknown, but it is the same for both cars since each car traveled the same distance.
The rate or R value for car A is some unknown x. For car B, R = x+15 because it traveled 15 mph faster than car A.
For car A, T = 2. For car B, T = 1.5
---------------------------------
The equation for car A is going to be D = x*2 or D = 2x. Note how I replaced R and T with x and 2 respectively.
The equation for car B is D = (x+15)*1.5 which distributes and simplifies to D = 1.5x+22.5
Because we're dealing with the same D value for both equations, we can equate the two right hand sides and solve for x
D = 2x
1.5x+22.5 = 2x ..... replace D with 1.5x+22.5
22.5 = 2x-1.5x
22.5 = 0.5x
0.5x = 22.5
x = 22.5/0.5
x = 45
So car A's speed was 45 mph. Add on 15 to get
x+15 = 45+15 = 60
which is car B's speed
side note: car A travels a distance of D = R*T = 45*2 = 90 miles; while car B travels a distance of D = R*T = 60*1.5 = 90 miles. Both cars traveling the same distance helps us confirm we have the right answer.
---------------------------------
So this is why the final answer is 60 mph
how many lines of symmetry are there in a regular decagon
Answer: In a regular decagon, there are 10 lines of symmetry.
Step-by-step explanation:
Line of symmetry divides a figure into two equal halves so that if you flip the half image over the line of symmetry , the figure will look unchanged.
A regular decagon has 10 vertices and 10 edges.
To draw line of symmetry :
1.Draw lines to meet the exactly opposite point [shown by red color in the picture attached with the answer].
∴ 10 vertices will form 5 lines of symmetry.
2.Draw lines from the mid points of all the edges to the midpoint of the exactly opposite edge [shown by blue color in the picture attached with the answer].
∴ 10 edges will form 5 lines of symmetry.
⇒Total lines of symmetry in a decagon =5+5= 10
what percent of 80 is 10
I believe that the answer is 12.5%
Reason 100% of 80= 80,
So if 80=100%,
then that means 10=x%
Fore it means that, [tex]x=(\frac{10}{80} )*100[/tex]%=12.5%
Answer:
Let the required percentage be x%.
Atq,
[tex] \: \: \: \: \: \: \: x\% \: of80 = 10 \\ = > \frac{x}{100} \times 80 = 10 \\ = > \frac{4x}{5} =1 0 \\ = > 4x = 5 \times 10 \\ = > x = \frac{5 \times 10}{4} \\ = > x = \frac{5 \times 5}{2} \\ = > x = \frac{25}{2} \\ = > x = 12.5[/tex]
Hence, required percentage = 12.5%