The most appropriate choice for Distance will be given by:
The ball takes [tex]3s[/tex] to reach a height of [tex]45[/tex] [tex]m[/tex].
What is Distance?
The length of the path an object takes without taking into account the direction of motion of the object is known as distance.
If [tex]s[/tex] is the speed of the object and [tex]t[/tex] is the time, then
Distance = [tex]s \times t[/tex]
Here,
[tex]H(t) = 30t - 5t^2[/tex], [tex]t[/tex] is the time in seconds
For finding the time taken by the ball to reach a height of [tex]45[/tex][tex]m[/tex], we need to substitute [tex]H(t) = 45[/tex]
Now putting [tex]H(t) = 45[/tex]
[tex]45 = 30t - 5t^2\\5t^2 - 30t+45 = 0\\ 5(t^2 -6t + 9)=0\\t^2 -6t+9=0\\t^2-3t-3t+9=0\\t(t-3)-3(t-3)=0\\(t-3)(t-3)=0\\t-3 = 0\\t = 3s[/tex]
So the ball takes [tex]3s[/tex] to reach a height of [tex]45[/tex] [tex]m[/tex].
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What is x^3 pls help
Answer:
its x^3 or 1
Step-by-step explanation:
there's nothing else you can do with it
also it might be 1 because x by itself is 1 so x^3 is considered 1^3
2. Each year a certain amount of money is deposited in an account which pays an
annual interest rate of r so that at the end of each year the balance in the account is
multiplied by a growth factor of x = 1+r. $500 is deposited at the start of the first
year, an additional $200 is deposited at the start of the next year, and $600 at the
start of the following year.
a. Write an expression for the value of the account at the end of three years in
terms of the growth factor x.
b. What is the amount (to the nearest cent) in the account at the end of three
years if the interest rate is 2%?
3. Consider the polynomial function p given by p(x) = 5x³ + 8x²-3x + 1. Evaluate the
function at x = -2.
Answer:
2a. ((500x +200)x +600)x
2b. $1350.68
3. -1
Step-by-step explanation:
2. You want to know the balance in an account at the end of 3 years with deposits at the beginning of successive years being $500, $200, and $600, and with deposits having an annual growth factor of x. You want (a) an expression for the balance in terms of x, and (b) the balance when x=1+2%.
3. You want the value of p(-2) for p(x) = 5x³ +8x² -3x + 1.
2. Account Balancea. Expression$500 is deposited at the beginning of the first year. The problem statement tells us that this has been multiplied by growth factor x by the end of the year, so the balance at that point is 500x.
At the beginning of the second year, $200 is added to the account, and the entire amount is multiplied by the growth factor for the year. That makes the balance at the end of the second year be ...
(500x +200)x
Then $600 is added, and again the account grows by a factor of x. At the end of the third year, the balance is ...
balance = ((500x +200)x +600)x
b. Balance for r=2%The growth factor is given as x = 1 +r. When r = 2%, this becomes x = 1.02. Then the balance at the end of year 3 is ...
((500·1.02 +200)·1.02 +600)·1.02 = 1350.68
The amount in the account at the end of three years is $1350.68.
__
3. Polynomial valueThe value of p(x) = 5x³ +8x² -3x +1 for x=-2 is found by substituting -2 where x is found. Evaluation can be easier by rewriting the polynomial to Horner form:
p(x) = ((5x +8)x -3)x +1
p(-2) = ((5(-2) +8)(-2) -3)(-2) +1 = ((-2)(-2) -3)(-2) +1 = (1)(-2) +1 = -1
The value of the function for x=-2 is -1.
__
Additional comment
You will note that the expression in problem 2 is also written in Horner form. If it were expanded, it would be 500x³ +200x² +600x. Evaluation takes fewer steps when Horner form is used.
HELP PLS 60 POINTS , Math Law Identification.
The first law is called the Law of Detachment. The law states that if p → q and p is true, then q is true.
The second law is the Law of Syllogism. It states that If p → r and q → r, then p → r is true.
What is the use of the Law of Detachment?It is to be noted that the Law of Detachment is the most often employed deductive reasoning theory.
In other words, if a conditional statement and its hypothesis are true, the conclusion is likewise true. In other words, the conclusion may be "separated" from the conditional.
In the above instance, p is synonymous with having a cat; while q is synonymous with it chasing a rat.
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Ellos ____ en la casa. (To express location)
Answer: Estan
Step-by-step explanation: I know spanish
Question 4 (10 point)
Answer:
25
Step-by-step explanation:
25 is the square root of 625
Answer:
25
Step-by-step explanation:
[tex]\sqrt{625} = \sqrt{25^{2} } = 25[/tex]
Write an algebraic expression that matches Six less than a number
ANSWER
x - 6
EXPLANATION
We want to write an algebraic expression that matches the statement:
Six less than a number.
First, let that unknown number be x.
So, 6 less than x.
Since it means that we are taking 6 from x, we subtract 6 from x.
That will be:
x - 6
Is a triangle with vertices G(3, 2), H(8, 5), and K(0, 10) a right triangle? Justify your answer.
First you need to ubicate those vertices in a plane as follow:
Then you link the vertices with lines to form the triangle:
Knowing that a right triangle must have one angle of 90º
The answer is that yes, it is a right triangle because it has an angle of 90º in the vertice H(8,5)
Sanjay a is making punch. he uses 1/3 c of pineapple juice for every 3/4 c of orange juice. how many cups of pineapple juice does he need if he uses 3 c of orange
Sanjay a is making punch. he uses 1/3 c of pineapple juice for every 3/4 c of orange juice Then 4/3 cups of pineapple juice does he need if he uses 3 c of orange
equation of direct proportion between x and y
x1/y1 = x2/y2
as per given ,
let x= quantity of pineapple juice and y= quantity of orange juice
x1= 1/3 , y1 = 3/4
x2 = ? and y2 =3
x1/y1 = x2/y2
(1/3)/ (3/4) = x2/3
4/9= x2 /3
4/3 = x2
Hence ,Sanjay a is making punch. he uses 1/3 c of pineapple juice for every 3/4 c of orange juice Then 4/3 cups of pineapple juice does he need if he uses 3 c of orange
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the average life of a certain type of small motor is 10 years with a standard deviation of 2 years. the manufacturer replaces free of charge any motor that fails during a warranty period. if she is willing to replace only 3% of the motors that fail, how long should should the warranty period last? assume that the lifetime of a motor follows a normal distribution.
using the normal distribution, the warranty period of motor last at 6.24 years.
According to given question , the average life of motor = 10 years and standard deviations = 2 years .
let X be the time period in which the warranty period of motor last . X ~ N( μ, σ²) where u is mean and s is standard deviations. X ~ N( 10, 2²) ⁼ N(μ, σ²)
it is given that only 3% number of motors are replaced and 3% = 0.03
Using normal distribution , P( X≤ x)= P(( X - μ )/ σ ≤ (x- μ)/σ ) = P ( Z ≤ (x- μ ) / σ ) =0.03
Z = (X- μ) / σ => X = Z (σ) + μ
p (Z ≤ -1.88) = 0.03 so, Z-value is - 1.88..
put all the value of variables in above formula we get , -1.88 ( 2) + 10 = X => X = - 3.76 + 10
=> X = 6.24
Thus , the motor's warranty period lasted about 6.24 years.
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Select the correct answer.
This graph represents a quadratic function.
Answer:
a = - 1
Step-by-step explanation:
given the zeros of a parabola x = a and x = b , then the factors are
(x - a) and (x - b) , then the equation is
y = a(x - a)(x - b) ← a is a multiplier
here the zeros are x = - 3 and x = 3 , then factors are
(x - (- 3) ) and (x - 3) , that is (x + 3) and (x - 3) and the equation is
y = a(x - 3)(x + 3)
to find a substitute any other point on the curve into the equation
using (0, 9 ) , then
9 = a(0 - 3)(0 + 3) = a(- 3)(3) = - 9a ( divide both sides by - 9 )
- 1 = a
what is an equation of the line that passes through the point (8,-7) and is parallel to the line x+2y=18
Answer: The equation of line parallel to given line passing through (8,-7) is:
Step-by-step explanation:
Given line is:
5x+4y=16
first of all, we have to convert the equation of given line in slope-intercept form
Dividing both sides by 4
Slope intercept form is:
The slope of given line is:
Let m1 be the slope of line parallel to given line
"The slopes of two parallel lines are equal"
The equation of line parallel to given line will be:
Putting the value of slope
Putting the point (8,-7) in the equation
Putting the value of b
Hence,
The equation of line parallel to given line passing through (8,-7) is:
Shelley's cup of tea cooled down
1
2
of a degree in 10 minutes. At what rate is her tea cooling down?
Shelley's cup of tea is cooling down at the rate of 1.2 degree per minute.
According to the question,
We have the following information:
Shelley's cup cooled down 12 degrees in 10 minutes.
In order to find the rate of cooling down of the cup of tea, we will divide the degrees of the cooling by the total number of minutes.
So, we have the following expression:
Rate of cooling down of Shelley's cup = Total degrees the cup cooled down/total time taken
Rate of cooling down of Shelley's cup = 12/10
Rate of cooling down of Shelley's cup = 1.2 degree per minute
Hence, the rate of cooling down of Shelley's cup is 1.2 degree per minute.
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Answer:
1/20
Step-by-step explanation:
Find the rate in degrees per minute. Divide
1
2
of a degree by 10 minutes.
To divide by 10, multiply by its reciprocal,
1
10
.
1
2
÷10
=
1
2
1
10
=
1
20
Shelley's tea is cooling down at a rate of
1
20
of a degree per minute.
What is an equation of the line that passes through the point (-4,8)(−4,8) and is parallel to the line x+y=6x+y=6?
The equation of the line that passes through the point; (-4, 8) and is parallel to x + y = 6 as required in the task content is; x + y = 4.
What is the equation of the line that passes through the given point and is parallel to the given line?It follows that the equation of the line that passes through the given point and is parallel to the given line is to be determined.
By expressing the given linear equation in slope-intercept form; it follows that we have;
x + y = 6
y = -x + 6
Hence, the slope of the equation by comparison with; y = mx + c is; -1.
Therefore, the slope of the required equation is same as the two lines are said to be parallel.
Ultimately, the required equation from point-slope form of an equation is;
( y - 8) = -1 ( x - (-4))
y - 8 = -x - 4
x + y = -4 +8
x + y = 4.
Ultimately, the required equation is; x + y = 4.
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Determine which integer will make the inequality 4x + 6 < 2x + 12 false.
S:{1}
S:{−1}
S:{4}
S:{−4}
Answer:
s:{4}
Step-by-step explanation:
4(4)+6<2(4)+12
16+6<8+12
32<20
which is the only false one
To win a trivia game, Nevan must score 90 points.
Each correct answer is worth 1 3/4 points, and each incorrect answer is worth −1/4 points.
If he gets 58 questions correct and 22 questions incorrect, does Nevan win? How many points does he score?
Answer: no he does not win he got 67 points not 90 or more
Step-by-step explanation:
Janell is standing on a set of bleacher and throws a ball in the air at an initial velocity of 35 ft/s. The height of the ball, h, at t seconds is modeled by the equation h=-16t^2+35t+6. How many seconds will it take the ball to reach the ground?
The time taken by the ball to reach the ground is 0.067 seconds
Given,
The initial velocity of the ball (speed) = 35 feet/second
The height of the ball (distance), h = -16t² + 35t + 6
We have to find the time, (t in seconds) taken by the ball to reach the ground.
Speed = distance/time
So, Time = distance/speed
Here,
Time = (-16t² + 35t + 6) / 35
We have to solve the equation first.
-16t² + 35t + 6 = 0 is in quadratic form. So, we can solve this by using quadratic formula.
Quadratic formula = [tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]
Here,
a = -16, b = 35, c = 6
Now,
[tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]
= [tex]\frac{-35(+-)\sqrt{35^{2}-4(-16)(6) } }{2(-16)}[/tex]
= [tex]\frac{-35(+-)\sqrt{1225 +384} }{-32}[/tex]
= (-35±√1609) / -32
= (-35±40.11) / -32
Now,
Solve for:
(-35 + 40.11) / -32 = 5.11/-32 = -0.15
Solve for
(-35 - 40.11) / -32 = -75.11 / -32 = 2.35
Lets take the height as 2.35 feet.
Now,
Time = distance/speed
Time = 2.35/35 = 0.067
Therefore, the time taken by the ball to reach the ground is 0.067 seconds.
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Prove the identity.
(csc²x - 1) secx = cosx csc x
Solve z3 = 8.
answers are
z = −4
z = 4
z = ±2
z = 2
Answer:
I'll assume z3 is actually z^3
z = 2
Step-by-step explanation:
z*z*z = 8
(2)*(2)*(2) = 8
You want to sample our class. You split the class by gender and select 5 students of each gender. What type of sample is this?
this type of sample is called fractions
Step-by-step explanation:
Hi can anyone help with this question? I have been stuck on this for hours
Answer:
ab = - 1
Step-by-step explanation:
GivenEquations:
1 - a tan θ = sec θ,b - cot θ = cosec θ.To find The value of abSolutionRecall the identities:
tan θ = sin θ / cos θsec θ = 1 / cos θ cot θ = cos θ/ sin θcosec θ = 1 / sin θsin² θ + cos² θ = 1(a + b)(a - b) = a² - b²Now find a and b, then find their product.
1 - a tan θ = sec θ1 - a sin θ / cos θ = 1 / cos θ cos θ - a sin θ = 1a sin θ = cos θ - 1a = (cos θ - 1) / sin θb - cot θ = cosec θb - cos θ/ sin θ = 1 / sin θb = cos θ/ sin θ + 1 / sin θb = (cos θ + 1) / sin θab = (cos θ - 1) / sin θ × (cos θ + 1) / sin θ = (cos² θ - 1) / sin² θ = - sin² θ / sin² θ = - 1Joshua has 245 feet of fence. His rectangular yard is 54 feet by 78 feet. Does Joshua have enough fence for his yard?
We can calculate the perimeter of the rectangular yard to find out how much fence Joshua needs:
[tex]P=2(78+54)=2(132)=264ft[/tex]since the perimeter of the yard is 264 yards, then Joshua does not have enough fence for his yard, since he only has 245 t of fence, and he needs 264ft
Find the equation of the line that goes through the points (2, 10) and (-1, -2).
Answer:
y=4x+1
Step-by-step explanation:
Step 1: plot your points
Step 2: draw a line through them
Step 3: find the slope (RISE/RUN) = 12/3 = 4
Step 4: find the y-int = 1
y=mx+b where x and y are variables, m is the slope and b is the y-int
y = 4x + 1
Hope that helps
help needed with show work. trigonometry
Answer:
16.4 cm
Step-by-step explanation:
In a right triangle :
cosine 43 = adjacent leg / hypotenuse = 12/x
SO:
cosine 43 = 12/x then x = 12 / cos 43 = 16.4 cm
What is the value of -3/15-s+ 25³ when s=-3?
Answer:
=[tex]\frac{78139}{5}[/tex]
Step-by-step explanation:
[tex]-\frac{3}{15}-(-3)+25^{3} \\=\frac{78139}{5}[/tex]
find the volume of this triangular prism
Answer:
The volume would be [tex]396cm^3[/tex].
Step-by-step explanation:
Answer:
792 cm
Step-by-step explanation:
99*8
Fred earns $16.50 an hour for overtime. He worked overtime on Monday and Thursday this week. On Monday, he worked 4 hours of overtime. His total
overtime pay for the week was $123.75.
Write and solve an equation to find the number of overtime hours, h, Fred worked on Thursday.
Fred's overtime pay is $16.50 an hour. He put in extra time this week on Monday and Thursday. The equation is $123.75-4 times the x value =h and h value is 57.75 and the working hours are 3.5 hours.
Given that,
Fred's overtime pay is $16.50 an hour. He put in extra time this week on Monday and Thursday. He put in four hours of extra on Monday. He received $123.75 in overtime compensation in total for the week.
We have to determine how many overtime hours, h, Fred worked on Thursday, write an equation and solve it.
We can write the equation as
$123.75-4 times the x value =h
Here,
x value is $16.50
We get,
$123.75-4×$16.50=h
h=57.75
To check hours working
57.75/16/50
=3.5 hours.
Therefore, the equation is $123.75-4 times the x value =h and h value is 57.75 and the working hours are 3.5 hours.
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helpppp meeee pleaseee
Please do number one please thank you
Answer:
Step-by-step explanation:
Hypothesis: you live in a state that borders California
:]
Write a story about temperatures that this expression could represent: 27+(-11)
Draw a number line diagram and write an expression to represent this situation: “On Tuesday at lunchtime, it was 29ºC. By sunset, the temperature had dropped to 16ºC.”
(this is summit learning btw)
The temperature “On Tuesday at lunchtime, it was 29ºC
i.e., 29 - 16.
Given,
Write a story about temperatures that this expression could represent:
27+(-11)
Now, According to the question:
1. The temperature is 27 degree C in the morning and reduced 11 degree C in the evening , the difference in temperature is 27 + (-11)
2. “On Tuesday at lunchtime, it was 29ºC. By sunset, the temperature had dropped to 16ºC.”
Again, Similarly
= 29 - 16
About Number line,
Draw a number line and allocate a point 16 degree C on the left side
and, 29 allocate a point on the right side.
Hence, The temperature “On Tuesday at lunchtime, it was 29ºC
i.e., 29 - 16.
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HI NEED THIS ASAPP GRAOHS OF INVERSE FUNCTIONS
Answer: D (last bubble)
Step-by-step explanation:
slope of f is 2/3
inverse of 2/3 is 3/2
that is graph h
these graphs are symmetrical around the line y = x