To find potential rational roots, we make use of the rational root theorem
How to determine potential rational root?From the question, we have the following parameters that can be used in our computation:
Task: How the potential rational root is calculated
To make use of the potential rational root, we use the rational root theorem using the following steps
Get the constant term and its factors (p)Get the leading coefficient and its factors (q)Find each possible value of p/q Remove duplicates from the possible rational zeros aboveRead more about rational root theorem at
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A ball is thrown upward from a height of 15 feet with an initial velocity of 64 feet per second. Use indefinite integrals to write the position function of the ball at time t.
Answer:
The equation of the position at time t will be:
[tex]y(t)=-\frac{1}{2}9.81t^{2}+64t+15[/tex]
Step-by-step explanation:
We can start by saying that the acceleration here is g = -9.81 m/s². The minus sign is because the gravity acceleration is a vector downward (negative value), and the ball is going upward (positive value).
And we know that acceleration can be written as a second derivative:
[tex]g=\frac{d^{2}y}{dt^{2}}=y''[/tex] (1)
Now, we can take the integral in each side:
[tex]\int gdt=\int y''dt[/tex]
[tex]\int y''dt=\int -9.81dt[/tex] (2)
Solving the integral in each side we have:
[tex]y'(t)=-9.81t+C[/tex] (3)
Where y'(t) is the velocity at t time (v = dy/dt = y' ) and c is a constant value.
Now, the initial conditions are:
initial height y(0) = 15 feet
initial velocity y'(0) = v(0) = 64 feet/s
Using this condition we can find C. Let's evaluate equation (3) at t = 0.
[tex]y'(0)=-9.81(0)+C[/tex]
[tex]C=64\: feet/s[/tex]
So we have:
[tex]y'(t)=-9.81t+64[/tex] (4)
Now, we need to take the integral of equation (4) to get the position function:
[tex]\int y'(t)dt=\int (-9.81t+64)dt[/tex]
Solving this new integral we have:
[tex]y(t)=-\frac{1}{2}9.81t^{2}+64t+D[/tex] (5)
Using the same method above, we can find D evaluating (5) at t = 0, we have:
[tex]y(0)=-\frac{1}{2}9.81(0)^{2}+64(0)+D[/tex]
[tex]D=y(0)[/tex]
[tex]D=15\: feet[/tex]
Finally, the equation of the position at time t will be:
[tex]y(t)=-\frac{1}{2}9.81t^{2}+64t+15[/tex]
I hope it helps you!
A farm stand sells apples pies and jars of applesauce. The table shows the number of apples needed to
make a pie and a jar of applesauce. Yesterday, the farm picked 245 Granny Smith apples and 133 Golden
Delicious apples. How many pies and jars of applesauce can the farm make if every apple is used?
Type of apple Granny Smith Golden Delicious
Needed for a pie
9
5
Needed for a jar of applesauce 4
2
The farm can make
pies and jars of applesauce.
A student stated that x = - 5 and
x= -2 are the solutions to the quadratic
equation x2 – 7x + 10 = 0 because the
equation factors to (x - 5)(x - 2) = 0.
Is the student correct or incorrect?
Explain
Answer:
Student is incorrect
Step-by-step explanation:
x^2-7x+10=0
x^2+2x-5x+10=0
x(x-2)-5(x-2)=0
(x-5)(x-2)=0
x-5=0 , x-2=0
x=5 , x=2
So the correct solutions of given equation is 2 and 5
The factors of the equation [tex]x^2- 7x + 10 = 0[/tex] is [tex]x=2,5[/tex] so the students are incorrect.
What is the equation?
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Here given equation is:-
[tex]x^2-7x+10=0\\\\x^2-2x-5x+10=0\\\\x(x-2)-5(x-2)=0\\\\(x-5)(x-2)=0\\\\x-5=0\\\\x=5\\\\x-2=0\\\\x=2[/tex]
Hence, the factors of the equation [tex]x^2- 7x + 10 = 0[/tex] is [tex]x=2,5[/tex] so the students are incorrect.
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Cone is formed from 3200 ft of gravel, if the height of the cone is 24 ft what is the radius in feet of the base of the cone
Question :
Cone is formed from 3200 ft³ of gravel, if the height of the cone is 24 ft what is the radius in feet of the base of the cone
Answer:
11.3 feet
Step-by-step explanation:
The volume of a cone = πr²h/3
We are asked to find the radius
The formula is given as:
r = √3V/πh
V = 3200 ft³
h = 24 ft
r = √3 × 2400/π × 24
r = 11.28379 ft
Approximately = 11.3 ft
The radius in feet = 11.3 ft
Match the statements to the correct ratios. 6 : 5 1 : 3 3 : 4 1 : 4 1 : 2 3 : 1 There are 12 boys and 8 girls in a class. If 2 more girls join the class, what is the new ratio for the number of boys to the number of girls in the class? arrowRight Joshua is 11 years old, and his dad is 33 years old. What is the ratio of Joshua's age to his dad's age? arrowRight Jemma has 24 balls. Out of the 24 balls, 12 are yellow, 4 are pink, and the rest are red. What is the ratio of the number of red balls to the number of balls that are either yellow or pink? arrowRight A box contains 84 chocolates, of which 63 are dark chocolates. The rest are milk chocolates. What is the ratio of milk chocolates to the total number of chocolates in the box? arrowRight
Answer:
Step-by-step explanation:
The one about the boys and girls are 3:1
The one about the balls no h0m0 is 1:4
The one about the chocolates is 1:3
The one about the Joshua and his dad is 3:4
If you be so kind mark me as brainliest
Answer:
A box contains 84 chocolates - 1 : 3
Jemma has 24 balls - 1 : 4
There are 12 boys - 3 : 1
Joshua is 11 years old - 3 : 4
Step-by-step explanation:
This is the correct answer for edmentum
In ATUV, the measure of V=90°, TU = 5.4 feet, and VT = 1.6 feet. Find the measure
of ZT to the nearest degree.
U
5.4
хо
V
1.6
Answer:
Submit Ang
Answer:73
Step-by-step explanation:
The Scale on a map shows that 1 inch represents 18 miles. The distance on the map between Olivia's town and her grandmother's town is 4-5 inches.
Answer:
(20 miles/inch) * (3.5 inches) = 70 miles
Step-by-step explanation:
Answer:
72-90 mile
OlivOliviOlivia‘s grandmother Town is 72 to 90 miles away
As an estimation we are told €4 is $5. What is the conversation rate from euros to dollars? Give your answer rounded to 2 decimal places?
Which inequality represents the stated situation :
A bus is made to carry a maximum of 85 passengers.
p ≤ 85
p > 85
p < 85
p ≥ 85
Answer: p ≤ 85
Step-by-step explanation: The value of p cannot be greater than 85 but can be equal to or less than 85.
daily limit on the videos for free answers ....completely and utterly st up id.
Answer:
I was not aware of the "daily limit" thing for answers
Step-by-step explanation:
Help me please thank you
Answer:
h=18.68
Step-by-step explanation:
V=( [tex]\pi[/tex] h r² )/ 3
h = 3V / r²·[tex]\pi[/tex] = 18.68
Answer:
V=3,14×6
=18,68
A.16,68 feet
Please help, points are (-6, -2) and (-3, -7)
Answer:
-1/3
Step-by-step explanation:
-6+3=-3
2 and -7 is 9
Answer:
the correct answer is B
Step-by-step explanation:
go it right!!!
DO NOT guess just answer the question correctly.
In the equation, 3x-6y=18, what is the x-intercept?
What is the following product
Answer:
the answer is 7x^2-12x square root of 14 +72 (option 2)
Step-by-step explanation:
The growth rate of Las Vegas is about 3.5% per year. If the population in 2010 was 1.35 million, what would be the expected population in 2020?
Answer:
Expected population= 1,904,308 people
Step-by-step explanation:
Giving the following information:
Present Value (PV)= 1,350,000
Number of periods (n)= 10 years
Growth rate (g)= 0.035 per year
To calculate Future Value (FV), we need to use the following formula:
FV= PV*(1 + i)^n
FV= 1,350,000*(1.035^10)
FV= 1,904,308 people
I need help with this question, please answer quickly.
Answer:
Flowers: 5
Vegetables: 25
Step-by-step explanation:
Carrie is on Shark Tank and is offering 40% of her company for $100,000. What is the value of Carrie's company?
Answer:
I think the answer is $40,000
Step-by-step explanation:
Answer:40,000
Step-by-step explanation:
from birth to 6 months, babies gain 6 ounces every week. How many ounces does a baby gain in 11 weeks ?
Answer:
156oz
Step-by-step explanation:
Hope this help and have wonderful day!!!
Write an expression to find the amount of money you will earn in a day if you are paid $10.25 an hour and spend $4.00 round trip to get to and from work.
A. 10.25h − 4
B. 10.25h + 4
C. 10.25h(4)
D. 10.25h / 4
Answer:
A. 10.25h − 4
Step-by-step explanation:
Hope this helps
For which equation does it make the most sense to solve by using the zero product property? 4x2−2=15 2x2+2x−9=0 x² + 11x +30 = 0 x² + 2x = 119
Answer:
It makes more sense to apply the zero product property on x² + 11x + 30 = 0.
Step-by-step explanation:
The zero product property simply states that if ab = 0, then a = 0 or b = 0 or both are zeros.
Given 4x² – 2 = 15, 2x² + 2x – 9 = 0, x² + 11x + 30 = 0, x² + 2x = 119; let's see which of the above is easiest to apply the zero product property.
1. 4x² – 2 = 15
4x² – 2 – 15 = 0
4x² – 17 = 0
It's not so easy to express the result as a product equal to zero.
2. 2x² + 2x – 9 = 0
This is not factorisable easily and can't be expressed as a product equal to zero easily.
3. x² + 11x + 30 = 0
This is factorisable easily. On factorising we have:
x² + 5x + 6x + 30 = 0
(x + 5)(x + 6) = 0. The zero product property can be applied here easily since x = 5 or x = 6 or both.
4. x² + 2x = 119
x² + 2x – 119 = 0
This is not easily factorisable and cannot be expressed easily as a product equal to zero.
Therefore, it makes more sense to apply the zero product property on
x² + 11x + 30 = 0
4х² – 2(x² — 3х+2)
combine like terms to write a polynomial in standard form.
Step-by-step explanation:
[tex]4 {x}^{2} - 2( {x}^{2} - 3x + 2) \\ = 4 {x}^{2} - 2 {x}^{2} + 6x - 4 \\ = 2 {x}^{2} + 6x - 4 = \\ {x}^{2} + 3x - 2[/tex]
can someone help me with this... also can you do this on paper...
here you go hope this helps!
heyy dude just wanted points. so yeah.
Which fractions have a LCD of 84? A. 3/14 1/42 1/6 B. 2/84 1/16 1/42 C. 2/21 1/4 1/3 D. 2/3 1/6 1/7
Answer:
D.)
2/3 1/6 1/7
Step-by-step explanation:
Given the fractions :
A. 3/14 1/42 1/6 B. 2/84 1/16 1/42 C. 2/21 1/4 1/3 D. 2/3 1/6 1/7
We need ot Obtian the set of fractions whose L. C. M of denominator multiplied by the numerator gives an of 84 for all its values.
A.)
L. C. M of 14, 42 and 6 = 42
42 * 3 = 126 ( not true)
B.)
L. C. M of 84, 16, 42 = 336
Can't be true
C.)
L. C. M of 21, 4, 3 = 84
84 * 2 = 168 (not true)
D.)
L.C.M of 3, 6, 7 = 42
Answer:
d
Step-by-step explanation:
All of these have to be estimated using the chart shown^
1- 11% of 507
2-26% of 91
3-34% of 91
4-48% of 124
5-20% of 66
6- 47% of 80
7-48% of 202
8-74% of 39
9-30% of 118
10-20% of 42
11-arnold ate breakfast at a restaurant. The total cost of his food, juice, and coffee was $6.45. If the sales tax rate is 8% and Arnold wants to leave a 20% tip. how much should he pay
12- rodneys weekly gross pay is $91. He must pay 32% of taxes and deductions. estimate rodneys weekly take home after deductions.
what is the slope of the line that contains the points (13,2) and (3,-2)
Answer:
⅖
Step-by-step explanation:
please like my answer and brainliest me... hshshshshs
Can you please help me I am in a rush
Can someone please help me?
Answer:
It is C i believe
Step-by-step explanation:
-8x+14≥60 or -4x+50<58
Answer: x ≤ −23/4 or x> -2
Step-by-step explanation:
Find the surface area of the composite figure.
Answer The answer is c.
Step-by-step explanation:
cause i said it was
Sarah was thinking of a number. Sarah divides by 7, then adds 9 to get an answer of 3. What was the original number?
Answer:
-42
Step-by-step explanation:
x/7 = y
y + 9 = 3
3 - 9 = y
y = -6
-6 * 7 = x
x = -42
Answer:
-42
Step-by-step explanation:
Do it backwards
Start with 3
SUBTRACT 9 to get -6
MULTIPLY by 7 to get -42.
Check:
Start: -42
Divide by 7: -6
Add 9: 3
Ding Ding!