Using quadratic function concepts, it is found that the system that models the height of the tennis ball and the height of the dog's mouth over time is given by:
h(t) = -16t² + 18t + 4.5 and h(t) = -16t² + 21t + 1.5.
What is the quadratic function for the height of a projectile?It is given by:
h(t) = -16t² + v(0)t + h(0)
In which:
v(0) is the initial velocity.h(0) is the initial height.For the tennis ball, we have that v(0) = 18, h(0) = 4.5, hence the equation is:
h(t) = -16t² + 18t + 4.5.
For the dog jump, we have that v(0) = 21, h(0) = 1.5, hence:
h(t) = -16t² + 21t + 1.5.
Hence, the system is given by:
h(t) = -16t² + 18t + 4.5 and h(t) = -16t² + 21t + 1.5.
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Answer:
D) h = -16t2 + 18t + 4.5 and h = -16t2 + 21t + 1.5
Step-by-step explanation:
The next answer is, "the time at which the ball and the dog's mouth are at the same height"
3. The number of home phones Best Bytes sold
decreased by 14% each year after 1987. Write
a function to represent the number of home
phones sold x years after 1987.
Step-by-step explanation:
Let the number of phones sold in 1987 is k.
The rate of decrease is
1 - 14% = 1 - 0.14 = 0.86The function to represent the number of phones P sold after x years after 1987 is
P(x) = k(0.86ˣ)Answer:
[tex]f(x)=a(0.86)^x[/tex]
where:
a is the number of phones sold in 1987x is the number of years after 1987Step-by-step explanation:
General form of an exponential function:
[tex]f(x)=ab^x[/tex]
where:
a is the initial valueb is the growth/decay factor in decimal formx is the independent variablef(x) is the dependent variableIf b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
Given:
f(x) = number of home phones sold after 1987x = years after 1987a = number of phones sold in 1987If the number of phones decreased by 14% each year, then each year the number of phones will be 86% of the previous year
(100% - 14% = 86%)
Therefore, b = 86% = 0.86
Substitute the given and found values into the general form of the function to create a function to represent the number of home phones sold:
[tex]f(x)=a(0.86)^x[/tex]
where:
a is the number of phones sold in 1987x is the number of years after 1987can someone help me super quick?
subject is stretching/reflecting quadratic functions
If you know what y = x², you can make the parabola more narrow by scaling this by some constant greater than 1 or smaller than -1. For example, y = 2x² or y = -5x². Note that if you pick a negative constant, you would end up reflecting the parabola across the horizontal axis.
To get a wider graph, you would instead scale by some constant between -1 and 1. For example, y = -1/2 x² (scaling by -1/2, or equivalently scaling by 1/2 and reflecting).
Taking the aformentioned details together, you can (1) reflect and (2) narrow the graph by multiplying y = 3x² by a negative constant larger than 1 in magnitude. For example, y = -15x², where we scale by -5.
Which statement is true for all real values of theta?
Answer:
(a) sec²(θ) -tan²(θ) = 1
Step-by-step explanation:
The identity relation between sec(θ) and tan(θ) is ...
tan²(θ) +1 = sec²(θ)
__
When tan²(θ) is subtracted from both sides of this equation, the result matches the first choice:
sec²(θ) -tan²(θ) = 1
_____
Additional comment
This is a variation of the "Pythagorean" relationship between sine and cosine. There is a similar relation between cot²(θ) and csc²(θ).
[tex]\sin^2\theta+\cos^2\theta=1\\\\\dfrac{\sin^2\theta}{\cos^2\theta}+\dfrac{\cos^2\theta}{\cos^2\theta}=\dfrac{1}{\cos^2\theta}\qquad\text{divide by $\cos^2\theta$}\\\\\tan^2\theta+1=\sec^2\theta[/tex]
Choose the inequality represented in the graph.
A. y ≤ x + 9
B. y ≥ -x + 9
C. y < -x + 9
D. y ≤ -x + 9
Answer:
D
Step-by-step explanation:
The solid line is y = -x + 9, and everything below it is shaded, so the correct sign is less than or equal to.
Putting the two pieces of information together, the equation you get is:
D. y ≤ -x + 9
Luisa sells stuffed animals. She sells a stuffed elephant for $34.90, and the sales tax is 9% of the sale price. About how much is the sales tax on the elephant?
Step-by-step explanation:
Topic :- Percentage Increase
Percentage Increase Formula= Cost price × Rate/one hundred
⇒ 34.90 × 9/100
⇒ 314.1/100
⇒ 3.141
Therefore, the sale tax of the elephant would be $3.141
Answer:
3.15
Step-by-step explanation:
Show that the set a = (1, 2, 1); b = (0, 1, 0); c = (-2, 0, 2) is linearly dependent.
By definition of linear independence, the vectors in the set {a, b, c} are independent if
[tex]k_1\vec a+k_2\vec b+k_3\vec c=\vec0[/tex]
can only be obtained with the choice of k₁ = k₂ = k₃ = 0.
This vector equation corresponds to the system of linear equations
[tex]\begin{cases}k_1 - 2k_3 = 0 \\ 2k_1 + k_2 = 0 \\ k_1 + 2k_3 = 0\end{cases}[/tex]
The first equation says k₁ = 2 k₃, while the third one says k₁ = -2 k₃. This can only be possible if k₁ = k₃ = 0, and from the second equation it follows that k₂ = 0. So the given set is linearly independent (and *not* dependent).
Establish the identity.
sin theta * sec theta = tan theta
Answer:
In the picture is how to solve it
Step-by-step explanation:
Answer:
We are multiplying sin theta by sec theta, so we first start with valuing sec theta. Re-evaluate sec theta as sec(theta), and get the reciprocal.
[tex]sin(theta) * \frac{1}{cos(theta)}[/tex] <-- reciprocal
Combine sin() with the reciprocal of sec theta.
[tex]\frac{sin(theta)}{cos(theta)}[/tex]
Rewrite this combination as tan(theta)
[tex]tan(theta)[/tex]
Since the sides are equal, they count as an identity.
[tex]sin(theta) * sec(theta) = tan(theta)[/tex]
That said, sin(theta) × sec(theta) = tan(theta) is an identity.
The hopper bin in the picture below is modeled by the two-dimensional figure beside it. The hopper bin is
composed of a cylinder, and 2 EQUAL cones. Let d be the center of the base of the cone.
52° cylinder cones
The diameter of the hopper is 36 ft and the height of the cylindrical portion is 20 ft. The measure of the acute
angle formed by the slant height of the cone and its base is 52°, determine and state, to the nearest cubic foot,
the volume of the hopper bin.
The hopper bin was constructed to hold a maximum of 500,000 pounds of feed. If feed weighs 22 pounds per cubic foot, can the carnival tent be filled to 85% of its volume and not exceed the weight limit? Justify your
answer.
The volume of the hopper bin is the amount of feed in it
The volume of the hopper bin is 35974 cubic feetThe carnival tent can be filled to 85% of its volume and not exceed the weight limitThe volume of the hopper bin
The given parameters are:
Height of cylinder, H = 20 ftDiameter of cylinder, D = 36 feetAngle, θ = 52°Start by calculating the radius (r) of the cones.
r = D/2 -------- because the cones and the cylinder have equal diameters.
So, we have:
r = 36/2 = 18
The height (h) of the cones is:
tan(θ) = h/r
This gives
tan(52) = h/18
Make h the subject
h = 18 * tan(52)
Evaluate
h = 23.04
The volume is then calculated as:
Volume = Volume of cylinder + 2 * Volume of cone
This gives
Volume = πr^2H + 2 * 1/3πr^2h
Volume = πr^2H + 2/3πr^2h
Factor out πr^2
Volume = πr^2(H + 2/3h)
Substitute known values
Volume = 3.14 * 18^2 * (20 + 2/3 * 23.04)
Evaluate
Volume = 35973.85 cubic feet
Hence, the volume of the hopper bin is 35974 cubic feet
The weight limit of the hopper binThe given parameters are:
Maximum weight = 500000 poundsFeed weight = 22 pounds per cubic feetFor a feed that weighs 22 pounds per cubic feet, the weight of the hopper bin would be:
Weight = 22 * 35974 pounds
Weight = 791428 pounds
At 85% full, the weight wuld be:
Weight = 85% * 791428 pounds
Weight = 672713.8 pounds
672713.8 pounds is greater than the weight limit of 500000 pounds.
Hence, the carnival tent can be filled to 85% of its volume and not exceed the weight limit
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Karen makes $6 per hour baby-sitting and $13 per hour giving music lessons. One
weekend, she worked a total of 8 hours and made $55. How many hours did she spend
baby-sitting?
a. 9
b. 1
C. 2
D.7
The total hours that Karen spent baby-sitting on the weekend is 7 hours.
What are the equations that represent the question?a + b = 8 hours equation 1
6a + 13b = 55 equation 2
Where:
a = hours spent baby-sitting b = hours spent giving music lessonsHow many hours was spent babysitting?Multiply equation 1 by 13
13a + 13b = 104 equation 3
Subtract equation 2 from equation 3
7a = 49
a = 7 hours
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What is the LCD of 1/9,1/27,8/45
HELP ASAP PLEASE
to get the LCD we should start by doing a quick prime factoring of each denominator, as you see in the picture below.
the factors in red are the common factors to all values, and they are used in the LCD only once, the other not common factors in blue, they're used in the LCD.
If the probability that a person will die in the next year is 782/100000, what is the probability that the person will not die in the next year?
A. 0.00365
B. 99635
C. 0.99635
D. 0.99218
The answer is D) 0.99218
The probability that the person will not die in the next year is approximately 0.99218.
Option D is the correct answer.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
The probability that a person will die in the next year is 782/100000.
To find the probability that the person will not die in the next year, we can subtract the probability of dying from 1, since the sum of the probabilities of dying and not dying is always 1.
1 - 782/100000 = 99218/100000
This fraction can be simplified by dividing both the numerator and the denominator by their greatest common factor, which is 2:
99218/100000
= 49609/50000
This fraction can be converted to a decimal by dividing the numerator by the denominator:
= 49609/50000
= 0.99218
Therefore,
The probability that the person will not die in the next year is approximately 0.99218.
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If you travel 20 kilometers in 29 minutes, how fast are you going in meters per second?
Answer:
~12 meters per second is your answer
Step-by-step explanation:
You need to do these specific things in order to convert.
Kilometers to meters - Multiply by 1000
Minutes to Seconds - Multiply by 60.
_______________________________________________________
First, do 20 kilometers multiplied by 1000
20 x 1000 = 20,000 meters
Do 29 minutes multiplied by 60.
29 x 60 = 1,740 seconds
_______________________________________________________
Now that we have everything converted, you need to divide it to find the speed.
Speed is Distance over Time.
20,000 meters / 1,740 seconds = Speed
Do 20,000 divided by 1,740
11.494252873563218390804597701149 That is your number.
You need to round that to the nearest whole number.
~12 meters per second is your answer
2/3 of a number is 18 work out 5/9 of the number
Answer:
15
Step-by-step explanation:
let the number=x
⅔x=18
2x=54
x=27
Now 5/9 of the number=5/9×27
=5×3=15
The area of a triangle is 273 square centimeters. If the base is 21 centimeters what is the height?
Th anwse is d) :B k .............
Help hemp help math math
According to Boyle's law, PV = k, what was the pressure to the nearest tenth at the time of the first measurement given the following information? V1 = 7,450 mL
The pressure to the nearest tenth at the time of the first measurement for this case was 1.82 atm approximately.
What is Boyle's law?According to the Boyle's law, the pressure of a gas tends to drop as the capacity of the container increases. We can write it symbolically as:
[tex]P_1V_1 = P_2V_2[/tex]
where we have:
[tex]P_1[/tex] and [tex]V_1[/tex] are first pressure and first volume, and:
[tex]P_2[/tex] and [tex]V_2[/tex] are second pressure and second volume.
The complete question is:
" According to Boyle's law, PV = k, what was the pressure to the nearest tenth at the time of the first measurement given the following information?
V₁ = 7,450 mL, P₂ = 8.25 atm, V₂ = 1,645 mL"
So, using the Boyle's rule, we get:
[tex]P_1V_1 = P_2V_2\\\\P_1 = \dfrac{P_2V_2}{V_1}\\\\P_1 = \dfrac{8.25 \times 1645}{7450} \approx 1.82 \: \rm atm[/tex]
Thus, the pressure to the nearest tenth at the time of the first measurement for this case was 1.82 atm approximately.
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Help me please i’ll mark u as brainliest:(
Answer:
It's X=3y = -9
Step-by-step explanation:
helping!!!
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS PLEASE AND PLEASE EXPLAIN WHY THAT IS THE ANSWER
Answer:
X and 127 are co-interior angles and X and Y are straight angle
Answer:
Y=127°
X=53°
Step-by-step explanation:
Y is 127 bcs it is correspoding to the 127° it has given u in the question. But you know that half a circle is 180° now that you have 127 as y u minus 180- 127 which equals X that is 53 hope u understood
12 less than the product of what number and 3 is 36
Answer:
16
Step-by-step explanation:
3x - 12 = 36
3x = 48
x = 16
Problem Situation: Gabi buys tickets to the movies.
She buys 1 adult ticket for $14 and 3 youth tickets.
She pays a total of $35.
What is the cost of each youth ticket?
Complete the equation to represent this situation.
The letter t represents the cost of a youth ticket.
iti
t + 14 =
Answer:
each youth ticket costs $7
Explanation:
Let the cost of each youth ticket be "y"
Solve for y:
$14 + 3y = $353y = $35 - $143y = $21y = $7Answer:
t = 7
Step-by-step explanation:
total cost = 35
price per adult = 14x -> only 1 adult so 14(1) = 14
35 = 14(1) +3t
35-14 = 3t
21 = 3t
t=7
Josh calculated the mean absolute deviation of the points he earned throughout the year in four of his classes: science math Spanish and art. Science: MAD of 1.14, Math: of 1.6, Spanish: MAD of 1.2 Art: MAD of 1.93 In which class were his scores the closest together?
Answer:B
Step-by-step explanation: Because the science math Spanish and art. Science: MAD of 1.14, Math: of 1.6, Spanish: MAD of 1.2 Art: MAD of 1.93 In which class were his scores the closest together
Answer:
spanish
Step-by-step explanation:
Easy functions giving brainlest
Please solve with explanation high points
Answer:
Step-by-step explanation:
(x+y)/2 - (x-y)/6 = 16
x/3 + (x+2y)/3 = 14
Multiply first equation by 6
3(x+y) - (x - y) = 96
2x + 4y = 96
x + 2y = 48 (A)
Multiply second equation by 3
x + x + 2y = 42
x + y = 21 (B)
Subtract A - B:-
y = 27
So:
x + 27 = 21
x = -6.
The quadratic relation
is f(x) = a(x - 27)(x + 6)
= a(x^2 - 21x - 162) where a is some constant
Vertex form:
f(x) = a[(x - 10.5)^2 - 110.25 - 162]
f(x) = a[(x - 10.5)^2 - 272.25]
f(x) = a[(x - 10.5)^2 - 272.25a.
Write the equation for each translation of the graph of y=|1/2x-2| +3.
one unit to the right
An equation is formed of two equal expressions. The equation of the new graph will be y=|1/(2x-4)|+3.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The equation given is [tex]y=\left|\dfrac{1}{2x-2}\right|+3[/tex], which is needed to be translated 1 unit to the right therefore, the value of x should be decreased by 1. Therefore, the equation of the new graph will be,
[tex]y=\left|\dfrac{1}{2(x-1)-2}\right|+3\\\\\\y=\left|\dfrac{1}{2x-2-2}\right|+3\\\\\\y=\left|\dfrac{1}{2x-4}\right|+3[/tex]
Hence, the equation of the new graph will be y=|1/(2x-4)|+3.
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Please explain how to solve these!
Step-by-step explanation:
11.
As all the exterior angles of a pentagon add up to 360, [ because exterior angle of a polygon = n(360/n) where n = no. Of sides, As the number of sides in a pentagon is 5, n=5. Thus, the sum of exterior angles of a pentagon = 5(360°/5) = 360°.]
THEN,
56 + 2x + 85 + 57 + 4x = 360
6x + 198 = 360
6x = 360 - 198
X = 162/6 = 27
Ans : x = 27
12.
Let the missing angle be x,
As we know that all exterior angles in a pentagon add up to 360 ( Write the same thing written above),
Then,
83 + 83 + 26 + 46 + x = 360
238 + x = 360
X= 360 - 238
X = 122
Answer : the fifth exterior angle = 122°
Hope this helps
PLEASE ANSWER AS SOON AS POSSIBLE WILL GIVE "Brainliest" TO THE FIRST CORRECT PERSON!!!
Find the area of the figure. Round your answer to the nearest tenth.
The area is about ___square meters.
Answer:
17.3
Step-by-step explanation:
area of paralellogram=base x height
height=sin(60) x 4= [tex]2\sqrt{3}[/tex]
area = 5 x [tex]2\sqrt{3}[/tex]
= [tex]10\sqrt{3}[/tex] = 17.3(to nearest tenth)
In a class of 28 students, 16 play an instrument and 11 play a sport. There are
7 students who do not play an instrument or a sport. What is the probability
that a student plays an instrument given that they play a sport?
Answer: 6/11
Step-by-step explanation:
28 - 7 = 21
16 + 11 - 21 = 6
11 - 6 = 5
16-6 = 10
10 + 5 15
P (a) = 16/28
p (b) = 11/28
A I B = 6/28/11/28 = 6/11
The circumference of the Earth is roughly forty thousand kilometres. Use this value to calculate the distance from the surface to the centre of the Earth.
Answer:
The distance to the center of the earth from the equator is 6,378 km or 33,963 miles, whereas the distance to the center of the earth from a pole is 6,357km or 3,950 miles. Complete answer: The average distance from the surface of the earth to its center is 6,371 km or 3,959 miles.
Hayden went to the park to play for an hour. He spent one-fourth of the hour
swinging. How many minutes did Hayden swing?
Answer:
15 minutes.
Step-by-step explanation:
One hour is equal to 60 minutes. Since you're asking for 1/4, or a quarter, of that amount of time, we should divide 60 by four.
Using a calculator, you'd get 15 asap. Without one, if you can divide 60 in half (that equals 30), then divide that half in half again (that equals 15), you'll have divided it into quarters and gotten your answer.
Match the verbal expression (term) with its algebraic expression (definition).
Match Term Definition
Four less than an unknown value A) y − 4
Quotient of a variable and four B) b + 4
Some number to the power of four C) a4
Four times an unknown value D) 4x
Four more than some number E) z ÷ 4
A) y − 4
Four less than an unknown value
B) b + 4
Four more than some number
C) a^4
Some number to the power of four
D) 4x
Four times an unknown value
E) z ÷ 4 =
Quotient of a variable and four