Rational root theorem is used to determine the possible root of a function.
Rational root theorem provides a complete list of all roots of [tex]\mathbf{(a)\ f(x)= 4x^2 - 25}[/tex]Rational root theorem does not provide a complete list of all roots of [tex]\mathbf{(b)\ g(x)= 4x^2 + 25}[/tex]Rational root theorem does not provide a complete list of all roots of [tex]\mathbf{(c)\ h(x)= 3x^2 - 25}[/tex][tex]\mathbf{(a)\ f(x)= 4x^2 - 25}[/tex]
Set to 0
[tex]\mathbf{4x^2 - 25 = 0}[/tex]
Add 25 to both sides
[tex]\mathbf{4x^2 = 25}[/tex]
Divide both sides by 4
[tex]\mathbf{x^2 = \frac{25}{4}}[/tex]
Take square roots
[tex]\mathbf{x = \pm\frac{5}{2}}[/tex]
The function has rational roots.
This means that: rational root theorem provides a complete list of all roots
[tex]\mathbf{(b)\ g(x)= 4x^2 + 25}[/tex]
Set to 0
[tex]\mathbf{4x^2 + 25 = 0}[/tex]
Add -25 to both sides
[tex]\mathbf{4x^2 = -25}[/tex]
Divide both sides by 4
[tex]\mathbf{x^2 = -\frac{25}{4}}[/tex]
Take square roots
[tex]\mathbf{x = \pm \sqrt{-\frac{25}{4}}}[/tex]
The function has complex roots.
This means that: rational root theorem does not provide a complete list of all roots
[tex]\mathbf{(c)\ h(x)= 3x^2 - 25}[/tex]
Set to 0
[tex]\mathbf{3x^2 - 25 = 0}[/tex]
Add -25 to both sides
[tex]\mathbf{3x^2 = 25}[/tex]
Divide both sides by 4
[tex]\mathbf{x^2 = 8.333}[/tex]
Take square roots
[tex]\mathbf{x = \pm 2.89}[/tex]
The function has irrational roots.
This means that: rational root theorem does not provide a complete list of all roots
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Explanation of the Rational Root Theorem and its application to polynomial functions f(x), g(x), and h(x).
The Rational Root Theorem provides a list of possible rational roots for a polynomial function. However, it does not guarantee that all roots will be rational. Let's examine the given polynomial functions:
For f(x) = 4x² - 25: The rational root theorem suggests possible rational roots, but the roots could also be irrational.For g(x) = 4x² + 25: As this polynomial has no real roots (due to the presence of complex numbers under the square root), the rational root theorem won't provide all roots.For h(x) = 3x² - 25: Again, the rational root theorem gives possible rational roots, but not the complete list of roots.I need help with number 14 please
Which inequality is represented by the number line graph?
A) x > -6
B) x < -6
C) x ≥ -6
D) x ≤ -6
The correct answer is option (D).
What is inequality?Inequality shows relation between two expression which are not equal to each others.
The graph shows an open circle at -6,
which implies that -6 is not a solution to the inequality.
The shaded arrow on all values shows that values are smaller than -6 and x < -6 is the inequality that represented on the line graph.
The required inequality is x < -6.
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Will give lots of points/write a rule to describe each transformation
Step-by-step explanation:
What number(s)?
Solve for x
3x-xy=4z-5y
Is it no solutionn????
From algebra1
HELP PLZZZZZZ
Answer:
x = (4z -y)/(3 – y); y ≠ 3
Step-by-step explanation:
3x – xy = 4z - 5y Factor
x(3-y) = 4z - y Divide each side by 3-y
x = (4z -y)/(3 – y); y ≠ 3
x is undefined when y = 3, so we must include the condition that y ≠ 3.
Evaluate (precalculus)
Answer:
Option 4 which is 1,430.
Step-by-step explanation:
Step 1
In this this step we will break up the terms in the summation symbol using the rules for manipulation summations.
[tex]\sum_{i=1}^{n}(aX^2_i+k)=\sum_{i=1}^{n}(aX)+\sum_{i=1}^{n}k\\\\\sum_{i=1}^{n}(aX^2_i+k)=a\sum_{i=1}^{n}X^2+nk.[/tex]
This means that for our case, the sum can be simplified to be,
[tex]\sum_{i=1}^{11}(3i^2_i-8)=3\sum_{i=1}^{11}i^2+11\times(-8)\\\\\sum_{i=1}^{11}(3i^2_i-8)=3\sum_{i=1}^{11}i^2-88[/tex]
Step 2
In this step we use the formula for the sum of the first n squares to evaluate the first part of the sum in step 2. The formula for the sum of the first n squares is,
[tex]\sum_{i=1}^{n}n^2=\frac{n(n+1)(2n+1)}{6} \\\\\implies\sum_{i=1}^{11}i^2=\frac{11(11+1)(2\times 11+1)}{6} =506[/tex]
Step 3
In this step we use the result from step 1 to evaluate the sum.[tex]3\sum_{i=1}^{11}i^2-88=3(506)-88=1,430.[/tex]
The correct answer is Option 4,which is 1,430.
Answer:
[tex]\boxed{\boxed{\sum_{i=1}^{11}(3i^2-8)=1430}}[/tex]
Step-by-step explanation:
The given expression is,
[tex]\sum_{i=1}^{11}(3i^2-8)[/tex]
[tex]=\sum_{i=1}^{11}(3i^2)-\sum_{i=1}^{11}(8)[/tex]
[tex]=3\sum_{i=1}^{11}(i^2)-\sum_{i=1}^{11}(8)[/tex]
we know that,
[tex]\sum_{i=1}^{n}i^2=\dfrac{n(n+1)(2n+1)}{6}[/tex] and
[tex]\sum_{i=1}^{n}c=cn,\text{ Where c is a constant}[/tex]
Hence,
[tex]3\sum_{i=1}^{11}(i^2)-\sum_{i=1}^{11}(8)=3\left(\dfrac{11(11+1)(2(11)+1)}{6}\right)-8(11)[/tex]
[tex]=3\left(\dfrac{11(12)(23)}{6}\right)-8(11)[/tex]
[tex]=3\left(506}\right)-8(11)[/tex]
[tex]=1518-88[/tex]
[tex]=1430[/tex]
Jim earns $140 during the summer doing chores. He bought 2 sets of pens worth $25 each using his chore money. How much money was left after he bought the pen sets?
A.) $58
B.)$90
C.)$190
D.)$255
Answer:
B) $90!
I hope this helped :D
Answer:
90 is the answer
Step-by-step explanation:
90+50=140
140-50=90
Luz reads for 1/4 hours every night. After 8 nights, how much total time has she been reading?
Answer:
2 hours
Step-by-step explanation:
To find out how much she has read, we multiply the number of nights by how much read per night
time read = 8 nights * 1/4 hours per night
time read = 8/4 hours
time read = 2 hours
Answer: 2 weeks?
Step-by-step explanation: 1/4 x 8= 2
at a farmers market two vendors sell fresh milk. one vendor sells 2 liters for $3.80, and another vendor sells 1.5 liters for $2.70. which is the better deal?
Answer:
The second dealer is better.
Step-by-step explanation:
To figure this out we need to divide the price by the amount of milk. Lets do both at the same time.
3.8/2= 2.7/1.5=
3.8/2=1.9 2.7/1.5=1.8
The second dealer is better.
Price per unit is the cost of the sing unit or measure of goods or the service provided.The second vendor sells 1 liter of fresh milk at $1.80 which is $0.10 less than the first vendor. Therefore the second vendor gives the better deal.
Given information-
First vendor sells 2 liters for $3.80.
Second vendor sells 1.5 liters for $2.70.
What is price per unit?Price per unit is the cost of the sing unit or measure of goods or the service provided.
Price per unit helps to compare the two product with there cost. The less will be the price per unit of a product the product will be more cheaper.
Price per unit is the ratio of the total cost to the number of units.
The vendor which provide more milk in less rate will be the better deal.
As first vendor sells 2 liters for $3.80. Thus the price of milk per liter is,
[tex]P_1=\dfrac{3.80}{2} \\P_1=1.90[/tex]
Hence the first vendor sells the 1 liter milk in $1.90.
As Second vendor sells 1.5 liters for $2.70. Thus the price of milk per liter is,
[tex]P_2=\dfrac{2.70}{1.5} \\P_2=1.80[/tex]
Hence the second vendor sells the 1 liter milk in $1.80.
Hence the second vendor sells 1 liter of fresh milk at $1.80 which is $0.10 less than the first vendor. Therefore the second vendor gives the better deal.
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What is 341/1000 in words
a 33 m tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 36m Find the length of the shadow
Answer:
14.39
Step-by-step explanation:
a^2 + b^2 = c^2
33^2 + b^2 = 36^2
1089 + b^2 = 1296
1089 - 1089 + b^2 = 1296 - 1089
b^2 = 207
b = 14.39
3+2(2p+4t) some one plz HELP ME.
Answer:
3+4p+8t
Step-by-step explanation:
We have been given an expression:
3+2(2p+4t)
We will simplify the equation:
Firstly, we will open the parenthesis by multiplying it with the 2 given outside of the parenthesis we get:
3+4p+8t
Since, we have two variables so it can not be further solved therefore,
This is the maximum simplification of the given expression.
a ferris wheel can accumulate 75 people in 30 minutes how many people could ride the ferris wheel in 4 hours what was that rate per hour
Answer:
600 people
Step-by-step explanation:
We can use ratios to solve this problem.
Change the 30 minutes in to hours
30 minutes = .5 hours
75 people x people
---------------- = -----------------------
.5 hours 4 hours
Using cross products
75*4 = .5 *x
300 = .5x
Divide each side by .5
300/.5 = .5x/.5
600 =x
The angle bisector of a triangle divides the triangle into two similar triangles
-always
-sometimes
-never
The angle bisector of a triangle divides the triangle into two similar triangles sometimes true and sometimes not true. Because the sum of the angle of the triangle is 180 degrees. But all three angles are not equal.
TriangleTriangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.
Given
Angle bisector of the triangle.
To find
The angle bisector of a triangle divides the triangle into two similar triangles always, sometimes, or never.
How to show the condition?The angle bisector of a triangle divides the triangle into two similar triangles sometimes true and sometimes not true. Because the sum of the angle of the triangle is 180 degrees. But all three angles are not equal.
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The angle bisector divides a triangle into two similar triangles Option B) sometimes, specifically when the triangle is isosceles.
1. Isosceles Triangle: In an isosceles triangle, two sides are equal in length. When the angle bisector of the vertex angle is drawn, it also bisects the base, creating two congruent triangles (by the Angle Bisector Theorem). Congruent triangles are always similar, so in this case, the statement holds true.
2. Scalene Triangle: In a scalene triangle, none of the sides are equal. When you draw the angle bisector of one of the angles, it won't necessarily bisect any other side into two equal lengths. Hence, the resulting triangles formed by the angle bisector won't necessarily be similar.
So, the angle bisector divides the triangle into two similar triangles sometimes (when it's an isosceles triangle) but not always (when it's a scalene triangle).
What is the value of cos 0 given that (-2,9) is a point on the terminal side of 0?
Answer:
The value of cos 0 = - 2 sqrt(85) / 85 = - 0.216930458
Step-by-step explanation:
cos 0 = ?
Point on the terminal side of 0 : (-2,9)=(x,y)→x=-2, y=9
cos 0 = x/r
r=sqrt(x^2+y^2)
Replacing the known values:
r=sqrt( (-2)^2+(9)^2)
r=sqrt(4+81)
r=sqrt(85)
cos 0 = x/r
cos 0 = -2 / sqrt(85) = -2/9.219544457 = -0.216930458
Rationalizing:
cos 0 = -[2 / sqrt(85)] [sqrt(85) / sqrt(85)]
cos 0 = - 2 sqrt(85) / [sqrt(85)]^2
cos 0 = - 2 sqrt(85) / 85
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 18 N acts on a certain object, the acceleration of the object is 6 /ms2 . If the acceleration of the object becomes 5 /ms2 , what is the force?
Answer: [tex]F=15N[/tex]
Step-by-step explanation:
1. You know that the force acting on the object varies directly with the object's acceleration. Then, by definition, you have:
[tex]F=ka[/tex]
Where [tex]F[/tex] is the force acting on the object, [tex]a[/tex] is the object's acceleration and [tex]k[/tex] is the constant of proportionality.
2. Keeping this on mind, you can calculate the constant of proportionality by substituting [tex]F=18[/tex] and [tex]a=6[/tex] into the equation and solving for [tex]k[/tex]:
[tex]18=k6\\k=\frac{18}{6}\\k=3[/tex]
3. Now, you can calculate the force when the acceleration of the object becomes 5 m/s², as following:
[tex]F=3(5)\\F=15[/tex]
3. The result is:
[tex]F=15N[/tex]
The acceleration that an objects gains is given by the mass of the object.
If the acceleration of the object becomes 5 m/s² the force is 15 N.Reason:
The given parameters are;
The acting force ∝ The acceleration of the object.
The acceleration given by an amount of force, F, of 18 N = 6 m/s²
Required:
The force acting on the object acceleration, a, is 5 m/s².
Solution:
According to Newton's Second Law of motion, we have;
F = m·a
Where;
m = The mass of the object
Therefore, we have;
[tex]Mass, \, m = \dfrac{F}{a}[/tex]
From the conditions, F = 18 N, when a = 6 m/s², we have, the mass of the
given object is given as follows;
[tex]Mass \ of \ the \ object, \, m = \dfrac{18 \, N}{6 \ m/s^2} = 3 \, kg[/tex]
The force acting when the the acceleration, a = 5 m/s², is therefore;
F = 3 kg × 5 m/s² = 15 N
If the acceleration of the object becomes 5 m/s² the force is 15 N.
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Layla and Carson work at the same store. Last week, Layla worked 8.75 hours, which was 25% of the amount of the time that Carson worked. How many hours did Carson work last week
Divide 8.75 by 35 and multiply the result by 100 to get 25 hours.
Which equation represents the following word sentence? The opposite of g times the quantity 2 plus 5.
Answer:
-g * (2+5)
Step-by-step explanation:
The opposite of g times the quantity 2 plus 5
Opposite means put a negative sign
times means multiply
Quantity means parenthesis
plus means addition
-g * (2+5)
The problem 'The opposite of g times the quantity 2 plus 5' translates into the mathematical equation -g*(2+5) or -g*7 in which g is multiplied by 7, and the result is negated.
Explanation:The word sentence 'The opposite of g times the quantity 2 plus 5' can be represented by the equation -g*(2+5) or -g*7, where * denotes multiplication, + denotes addition, and - denotes opposite or negation. Therefore, the interpretation of the sentence is 'multiply g by 7 and then take the opposite or negative of the result'. The use of parentheses ( ) in the equation ensures we first perform the addition within, according to the order of operations in math, most commonly known as BIDMAS/BODMAS or PEMDAS rules.
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Denise’s rock sample weighs 684 grams Pauline’s rock sample weighs 29,510 centimeters how much heavier is Denise’s sample than Pauline’s
Answerenise's rock sample has
38
,
890
centigrams more mass than that of Pauline
:
Step-by-step explanation:
Look at the table below showing an example of a checkbook ledger. Adrienne has several receipts from recent transactions that she entered in her records. The receipts include an ATM receipt for a $60.00 withdrawal (plus a $2.00 transaction fee), a grocery store receipt for $32.50, and a $1,200 paycheck deposit slip. When she finishes entering her transactions, Adrienne realizes that her balance is incorrect. Assuming that Adrienne’s beginning account balance was $320.00, why is her balance incorrect?
I think it's "Adrienne did not enter her ATM withdrawal correctly"
Answer:
" Adrienne did not enter her ATM withdrawal correctly."
D.
Step-by-step explanation: <3
There are 3.79 L in every gallon how many liters of gas does a 13.6 gallon tank hold
Answer:
51.544 L in our tank
Step-by-step explanation:
We have a 13.6 gallon tank
Our conversion factor is 3.79 L = 1 gallon. We want liters on top since that is where we want to end up
3.79 L /1 gallon is what we want to use
13.6 * 3.79L/1 gallon = 51.544 L in our tank
Given f(x)=5x+5, find f(-4)
f(-4) This means that x is -4, so you can plug in -4 for "x" in the equation
f(x) = 5x + 5
f(-4) = 5(-4) + 5
f(-4) = -20 + 5
f(-4) = -15
What is median of this histogram
Answer: You take the 2 middle columns in this case the purple gray looking one and the brown one and add them together divide them by 2
Step-by-step explanation:
Someone please help!!!!!
I'm bad at math!!!
(5b - 9) - 3(8 - 2b)
Also, could you give me tips on how to solve these kind of problems?
Thanks.
- A Math Disaster
Emma,brandy,and Damian will cut a rope that is 29.8 feet long into 3 jump ropes. Each of the 3 ropes will be the same length.Write a division sentence using compatible numbers to estimate the length of each rope
Answer:
30 ÷ 3 = 10 ft each
hope it helps :)))
Step-by-step explanation:
29.8 you can estimate it to 30
so you would divide 30 ÷ 3 = 10
what is the name of the angle formed by the rays please show the work
Answer:
∠RQP
Step-by-step explanation:
What is the coefficient of the fourth term in the expression? 5 − 10x + 15y − 20xy
A) −
B) 20
C) −20
D) −20xy
Answer:
C
Step-by-step explanation:
the coefficient of a term is the numeric value including the sign in front of the variable/ s
the fourth term in the expression is - 20xy
The coefficient of this term is - 20 → C
What is the diameter of a circle that has a circumference of 56.52 feet? Round your answere to the nearest whole number
Answer:
18 = diameter
Step-by-step explanation:
What is the value of arcsin (0) in degrees
Answer:
0
Step-by-step explanation:
full answer guide attached
Please help I don’t know how to do this at all!
Answer:
16 times the square root of 6
Step-by-step explanation:
2 radical54 simplifies:
2(radical6 x radical9), which is 6 radical6
and 5 radical24 simplifies:
5(radical6 x radical4), which is 10 radical6,
10 radical6 + 6 radical6=
16 radical6
The cost of a car rental is twenty-five dollars a day plus ten cents a mile. What is the total cost, in dollars, if the car is rented for three days and driven a total of six hundred and sixty miles? A) 86 B) 91 C) 97 D) 141
Answer:
The total cost is D) $141
Step-by-step explanation:
To solve we can use the equation: [tex]y=25d+0.10m[/tex]
d= number of days m= number of miles
We know both of these values so we can plug them in and solve.
y= 25(3) + 0.10(660)
y= 75 + 66
y = 141