Question:
The function D(t) defines a traveler’s distance from home, in miles, as a function of time, in hours.
[tex]D(t) = \left \{ {{300t + 125,\ 0 \le t < 2.5} \atop {880,\ 2.5 \le t \le 3.5}} \right.[/tex]
[tex]75t + 612.5,\ 3.5 < t \le 6[/tex]
Which times and distances are represented by the function?
(a)The starting distance, at 0 hours, is 300 miles.
(b) At 2 hours, the traveler is 725 miles from home.
(c) At 2.5 hours, the traveler is 875 miles from home.
(d) At 3 hours, the distance is constant, at 880 miles.
(e) The total distance from home after 6 hours is 1,062.5 miles.
Answer:
At 2 hours, the traveler is 725 miles from home. At 3 hours, the distance is constant, at 880 miles. The total distance from home after 6 hours is 1,062.5 miles.Step-by-step explanation:
Given
[tex]D(t) = \left \{ {{300t + 125,\ 0 \le t < 2.5} \atop {880,\ 2.5 \le t \le 3.5}} \right.[/tex]
[tex]75t + 612.5,\ 3.5 < t \le 6[/tex]
Required
Select the right options
(a) t = 0 hours, d(t) = 300 miles.
To check this, we make use of:
[tex]D(t) = 300t + 125, 0 \le t < 2.5[/tex]
So, we have:
[tex]D(0) = 300*0 + 125[/tex]
[tex]D(0) = 0+125[/tex]
[tex]D(0) = 125[/tex]
(a) is incorrect
(b) t =2 hours, d(t) = 725 miles
To check this, we make use of:
[tex]D(t) = 300t + 125, 0 \le t < 2.5[/tex]
[tex]D(2) = 300 *2 + 125[/tex]
[tex]D(2) = 600 + 125[/tex]
[tex]D(2) = 725[/tex]
(b) is correct
(c) t = 2.5 hours, d(t) = 875 miles
To check this, we make use of:
[tex]D(t) = 800, 2.5 \le t \le 3.5[/tex]
So, we have:
[tex]D(2.5) = 800[/tex]
(c) is incorrect
(d) t = 3 hours, d(t) = 880 miles constant
To check this, we make use of:
[tex]D(t) = 800, 2.5 \le t \le 3.5[/tex]
So, we have:
[tex]D(3) = 800[/tex]
(d) is correct
(e) t = 6 hours d = 1,062.5 miles.
To check this, we make use of:
[tex]D(t) =75t + 612.5,\ 3.5 < t \le 6[/tex]
So, we have:
[tex]D(6) =75*6 + 612.5[/tex]
[tex]D(6) =450 + 612.5[/tex]
[tex]D(6) =1062.5[/tex]
(e) is correct
please help me with this
Answer:5,2,4,8
Step-by-step explanation:hope it helped
Please help someone I need an answer
Answer:
Step-by-step explanation:
Right Isosceles Triangle
Side a = 9
Side b = 9
Side c = 12.72792 = 9√2
Angle ∠A = 45° = 0.7854 rad = π/4
Angle ∠B = 45° = 0.7854 rad = π/4
Angle ∠C = 90° = 1.5708 rad = π/2
hope you pass your retest ;)
Jason jumped off a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h ( t ) = − 16 t 2 + 16 t + 480 h(t)=−16t 2 +16t+480, where t is the time in seconds and h is the height in feet. What is the maximum height that Jason reaches?
Answer:
484feet
Step-by-step explanation:
If the height as a function of time could be modeled by the function h(t)=−16t^2 +16t+480, where t is the time in seconds and h is the height in feet.
The maximum height of Jason occurs when dh/dt = 0 (velocity is zero)
dh/dt = -32t + 16
0 = -32t + 16
32t = 16
t = 16/32
t = 1/2
t = 0.5secs
Get the maximum height
Recall that h(t)=−16t^2 +16t+480
Substitute t = 0.5
h(0.5)=−16(0.5)^2 +16(0.5)+480
h(0.5) = -4 + 8 + 480
h(0.5) = 4 + 480
h(0.5) = 484
Hence the maximum height reached by Jason is 484feet
The maximum height that Jason reaches is h = 484 feet and it will be reached at t = 0.5 sec.
How to find the maximum of a polynomial function?Let the function be denoted by [tex]y = f(x)[/tex]
If it is twice differentiable, then, firstly, we differentiate it with respect to x and equate with 0 to find the critical values.
Let the obtained critical values be [tex]x_1, x_2, ... x_n[/tex]
The second derivative of that function is then evaluated on those critical values.
The [tex]i^{th}[/tex] critical value has got the maximum if [tex]f''(x_i) < 0[/tex]
That means, if at [tex]x = x_i[/tex] , we get
[tex]f'(x-i) = 0\\and\\f''(x_i) < 0[/tex]
Then that point is where function will have maximum.
If [tex]f''(x_i) > 0[/tex], then the point where the function will have minimum
If value of second rate at point [tex]x_i[/tex] is 0, then we go for third rate of function and check the same facts so on for upper rate(if they exist).
For the given case, we're given the height function as:
[tex]h(t) = - 16t^2 + 16t + 480[/tex]
The function is infinitely differentiable as its polynomial(by a theorem).
Its first and second rate with respect to 't', we get;
[tex]h(t) = - 16t^2 + 16t + 480\\h'(t) = -32t + 16\\h''(t) = -32 < 0[/tex]
Thus, all critical points will be maximum points.
The critical points are evaluated by [tex]h'(t) = 0[/tex]
They are calculated as:
[tex]h'(t) = 0\\-32t + 16 = 0\\t = 0.5 \: \rm sec[/tex]
The height at t = 0.5 s is evaluated as:
[tex]h(0.5) = - 16(0.5)^2 + 16(0.5) + 480 = 484 \: \rm feet[/tex]
Thus, at time 0.5, the height function will be at its maximum value(484 feet). That means, the height of Jason will be maximum when time will be 0.5 seconds from initial time.
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Ayden rents skates at the skate park for
$1.25. He also spends $1.75 on snacks
and a drink each time he goes. If Ayden
has $20, which expression shows how
much money Ayden will have left over if
he visits the skate park a times?
A $20 + [($1.25 + $1.75) X a]
B $20 + ($1.25 + $1.75 X a)
c $20 - [($125 + $1.75) X aj
D $20- ($1.25 + $1.75 X a)
Answer:
C
Step-by-step explanation:
(4,6) rotated 90 degree
Answer:
(6,-4)
Step-by-step explanation:
when you have (x,y) and you want to rotate it 90 degrees, you would switch the x and the y and then make the x negative. So (4,6) would switch to (6,4) and then the 4 would become negative.
The Garcia family drives 3/4 of the distance to their. grandparents house in 3/4 hour. How many hours will it take to drive to their grandparents house at the same rate? A-9/16 B-1. C- 1 7/9
Answer:
B
Step-by-step explanation:
Can u find the value of the x.
Answer:x=8
Step-by-step explanation:
x²-3x=-3x+64
- Add 3x to both sides
x²-3x+3x=-3x+3x+64
= x²=64
- Square both sides
√x²=√64
x=±8
- Since the question is asking for the positive value of x, the answer is 8.
I completely forgot how to do this, so if you can answer and give an explanation, I’d really appreciate it!
Answer:
C
Step-by-step explanation:
Well to do this we can eliminate answers that seem unreasonable and just calculate the ones we think might be it
We know it can't be the first one or the second since its perimeter isn't 32
It could be the third one so we can check the perimeter
3+3+16+16=38
so it is the third one
Find the mean of the weight of rocks: 4 lbs, 6 lbs, 4 lbs, 5 lbs, 9 lbs, 8 lbs
3
Answer:
5.6 (rounded)
Step-by-step explanation:
add all the numbers, then divide by how many numbers u added :)
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Ellen is drawing two polygons. One of the polygons has 3 more angels then the other. What shapes could she be drawing?
Answer:
Step-by-step explanation:
This is quite and easy one, but also vague at the same time.
A polygon is a shape with 5 or more sides, so, if she were drawing a pentagon, then the second polygon has to be an octagon. A pentagon has 5 sides, and an octagon has 5 + 3 sides
In the same vein, if she were drawing a hexagon, with 6 sides, the other polygon has to be monsoon, with 6 + 3 sides.
A heptagon also gives us a 7 + 3 polygon, in decagon.
All in all, it depends on the first polygon she's drawing as the question is vague in that aspect.
Remove the brackets using the distributive law for the following: 5(4x - 3y) - 4(4x - 3y)
Answer:
4x - 3yStep-by-step explanation:
5(4x - 3y) - 4(4x - 3y)
= 5 × 4x - 5 × 3y - 4 × 4x + 4 × 3y
= 20x - 15y - 16x + 12y
= 20x - 16x - 15y + 12y
= 4x - 3y (Ans)
Find the Circumference and Area of the circle with a diameter of 3 inches.
Answer:
Circumference-18.84956, rounded, 18.85
Area- 28.27433, rounded-38.27
Answer:
C≈9.42in
A≈7.07in²
Step-by-step explanation:
C=2πr
d=2r
C=πd=π·3≈9.42478in
A=πr2
d=2r
A=1
4πd2=1
4·π·32≈7.06858in²
Hope this helps!
Factor.
11x2+35x+6
Enter your answer in the box.
Answer:
[tex]\displaystyle [x + 3][11x + 2][/tex]
Step-by-step explanation:
[tex]\displaystyle 11x^2 + 35x + 6 \\ [11x^2 + 2x] + [33x + 6] \\ x[11x + 2]\:\:\:\:\:3[11x + 2] \\ \\ \boxed{[x + 3][11x + 2]}[/tex]
I am joyous to assist you at any time.
Answer: i took the test
Step-by-step explanation:
The difference between 3 1/2 and 1 4/6 is _____.
A. 1 4/5
B. 2 4/5
C. 2 7/10
D. 1 7/10
Answer:
1 5/6.
Step-by-step explanation:
3 1/2 - 1 4/6
= 3 1/2 - 1 4/6
= 7/2 - 10/6 The LCM of 2 and 6 is 6 so:
= 21/6 - 10/6
= 11/6
= 1 5/6.
Given DE || BC, find the length of BD.
Answer:
BD = 12.5
Step-by-step explanation:
Full answer in the attachment!!
To find the volume of a figure you need to use which of the following formulas?
Answer:
l x w x h
Step-by-step explanation:
volume is usually length x width x height
What is 10% of 30 plz help I am stuck in this answer
Answer:
it's 3
Step-by-step explanation:
Matthew was modeling an activity to the class. In a brown paper bag, he had 3 red marbles, 2 blue, and 5 green marbles. What is the probability of Matthew choosing a red marble, NOT replacing the marble, and then selecting a blue marble from the bag?
The value of a new car depreciates over time. Felicia purchased a new car in August 2019. The value, V, of her car after t years can be modeled by the equation image. If you wanted to know the specific value of the car after t years, how could you rewrite the equation?
Answer: V=17,000 times (0.8)^t
Step-by-step explanation:
Si se llenan 45 frascos de 200 gramos de mayonesa cuantos frascos de 150 gramos se puede llenar con la misma cantidad
Answer:
45x200gr/150gr= 60
Step-by-step explanation:
y = x + 5
y = -2x - 4
what are the y and x values please
Answer:
x=-3, and y=2
Step-by-step explanation:
Since both equations are equal to y, set them equal to each other and solve for x, that way you can solve for y:
x+5=-2x-4
3x+5=-4
3x=-9
x=-3
Plugging in x=-3 into one of the original equations:
y = x + 5
y = -3 + 5
y = 2
Therefore, x=-3 and y=2. You can also write as the ordered pair (-3,2) since that's where the two equations would intercept on a graph.
What choice below best explains why two Hydrogen atoms below would bond together?
Answer:
QUESTION:
What choice below best explains why two Hydrogen atoms below would bond together?
ANSWER:
covalent bond
The bond joining two hydrogen atoms in a hydrogen gas molecule is a classic covalent bond. The bond is easy to analyze because the hydrogen atoms only have one proton and one electron each. The electrons are in the hydrogen atom's single electron shell, which has room for two electrons.
Step-by-step explanation:
Hope that this helps you out! :)
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Have a great rest of your day/night!
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Q4) Identify which of the following are geometric sequences and which are
not
(i) 2, 6, 18, 54.....
(ii) 25,5, 1,
(iii) 1, 4, 9, 16
Answer:
(i) and (ii)
Step-by-step explanation:
For a sequence to be geometric then the ratio r between consecutive terms must be common.
(1)
2, 6, 18, 54
6 ÷ 2 = 3
18 ÷ 6 = 3
54 ÷ 18 = 3
Here there is a common ratio r = 3 , then sequence is geometric
(ii)
25, 5, 1
[tex]\frac{5}{25}[/tex] = [tex]\frac{1}{5}[/tex] and [tex]\frac{a_{3} }{a_{2} }[/tex] = [tex]\frac{1}{5}[/tex]
There is a common ratio r = [tex]\frac{1}{5}[/tex] , then sequence is geometric
(iii)
1, 4, 9, 16
4 ÷ 1 = 4
9 ÷ 4 = 2.25
16 ÷ 9 = 1.777..
There is no common ratio, then sequence is not geometric
PLS HELP IVE BEEN ASKING FOR 4 HOURS NOT A SINGLE PERSON HAS BEEN RIGHT ITS PAST DUE :( JUST TROLLS I WILL GIVE BRAINLIEST JUST PLS HELP
Answer:
Answer is in attachment. I am really sorry if I'm wrong.
Step-by-step explanation:
Finding the height:Greatest common factor (GCF) is the highest number that is a factor of 2 numbers. Not sure if that makes sense.
For example, GCF of 8 and 4 is 4, because 4 is the highest factor that fits into both numbers. 4x2=8 and 4x1=4.
In this case, the height is 7, because that's the GCF of 21 and 70. There's no bigger common factor than that. 7x3=21 and 7x10=70
Finding the length and area:Now that we know the "height", even though there's no such thing as height when calculating the area, we know the length.
The area of something is length x width. Your assignment calls it height for some reason so we'll use height x length.
Area of the 2 shapes is already given, which is 21n for the first shape. Length of the first shape is 3n because 3nx7=21n. Recall that 7 is what we found earlier.
As we can see, the "height" of the 2nd shape is the same as the first, therefore it should also be 7.
Since we are given the area of the 2nd shape, we now know its length. Length of 2nd shape is 10, because 7x10=70.
Simplify the following expression by combining like terms: *
-2g - 8 +5g - 5
Answer:
3g -13
Step-by-step explanation:
Identify the place of the
3
in 24.936
Answer:
hundredths place
Step-by-step explanation:
When using decimals we determine by
Tens,ones.Hundredths,Thousandths, etc
Answer:
Hundredths Place
Step-by-step explanation:
Adam jogs at an average speed of 10km/h from his house to the airport. The airport is 7km away from his house. At what time must Adam leave his house in order for him to reach the airport at 7:20 am.
Answer:
6:38am
Step-by-step explanation:
From the question we are told that
Average speed [tex]V_{avg}=10km/h[/tex]
Distance traveled [tex]d=7km[/tex]
Generally the velocity across a distance is mathematically given given as [tex]V=d/t[/tex]
[tex]10=\frac{7}{t}[/tex]
[tex]t=0.7h\\t=42minutes[/tex]
Therefore
7:20-42 minutes =6:38am
The interior angles of a triangle have measures 90°, 48°, and xº.
What is the value of x?
Answer:
42°
Step-by-step explanation:
The interior angles of a triangle always add to 180 degrees.
90+48+x=180
x=180-90-48
=42
x is 42°
PLS HELP!!
In the following diagram, L || M. (i think that's an L, i dont know)
Solve for each of the variables w, x, y, and z. For each solution, explain, in complete sentences which special angles allowed you to create an equation in order to find a solution.
Answer:
Un sistema de ecuaciones es un conjunto de ecuaciones con las mismas incógnitas. Un
sistema de ecuaciones lineales es un sistema de ecuaciones en el que cada ecuación es lineal. Una solución de un sistema es una asignación de valores para las incógnitas que hace
verdadera cada una de las ecuaciones. Resolver un sistema signifi ca hallar todas las soluciones del sistema.
Step-by-step explanation:
Does the quadratic function
f(x) = 4x2 + 5x – 29 have one,
two, or no real zeros? Utilize the
quadratic formula to determine
the answer.
The quadratic function is negative meaning there is no real zeros.
We have given,
The quadratic function
f(x) = 4x^2 + 5x – 29
have one, two, or no real zeros.
What is the form of a quadratic equation?
The general form of a quadratic equation is,
ax^2+bx+c
Compare the given equation with the given equation we get,
a=4, b=5 and c=-29
We can use b^2-4ac which is 25-16*29.
We know that is negative meaning there is no real zeros.
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