Answer:
Vertex of the quadratic function y = (x - h)² + k is:
point (h, k)Given function:
y = (x + 2)² − 3h = -2, k= -3Its vertex is (-2, -3)
The y-intercept is the point with x = 0:
y = (0 + 2)² − 3 = 4 - 3 = 1The y-intercept is (0, 1)
Answer:
Vertex: (-2, -3)
y intercept: 1
Step-by-step explanation:
A train is spotted 10 miles south and 8 miles west of an observer at 2:00 pm. At 3:00 pm the train is spotted 5 miles north and 16 miles east of the observer. a. How far did the train travel in the first hour? b. If the train continues at this pace where will it be in relation to the observer at 5:00 pm? Write a function that will give the train's position at any given time c. d. At 2:00 pm a cyclist is traveling due east and is next to the observer. If the cyclist is traveling at 10 mph, do they collide with the train when the bike goes over the train tracks?
Answer:
a. The distance the train travelled in the first hour is approximately 28.3 miles
b. The location of the train at 5:00 p.m. is 53 miles east, and 46 miles west
c. The location of the train at any given time by the function, f(t) = (-8 + 24·t, -10 + 15·t)
d. The train does not collide with the cyclist when the bike goes over the train tracks
Step-by-step explanation:
a. The given information on the train's motion are;
The location south the train is spotted = 10 miles south and 8 miles west
The time the observer spotted the train = 2:00 pm
The location the train is spotted at 3:00 p.m. = 5 miles north and 16 miles east
Therefore, the difference between the two times the train was spotted, t = 3:00 p.m. - 2:00 p.m. = 1 hour
Making use of the coordinate plane for the two locations the train was spotted, we have;
The initial location of the train = (-10, -8)
The final location of the train = (5, 16)
Therefore the distance the train travelled in the first hour is given by the formula for finding the distance, 'd', between two points, (x₁, y₁) and (x₂, y₂) as follows;
[tex]d = \sqrt{\left (x_{2}-x_{1} \right )^{2}+\left (y_{2}-y_{1} \right )^{2}}[/tex]
Therefore;
[tex]d = \sqrt{\left (5-(-10) \right )^{2}+\left (16-(-8) \right )^{2}} = 3 \cdot\sqrt{89}[/tex]
The distance the train travelled in the first hour, d = 3·√89 ≈ 28.3 miles
b. The speed of the train, v = (Distance travelled by the train)/Time
∴ v ≈ 28.3 miles/(1 hour) = 28.3 miles per hour
The speed of the train in the first hour, v ≈ 28.3 mph
The direction of the train, θ, is given by the arctangent of the slope, 'm', of the path of the train;
[tex]\therefore The \ slope \ of \ the \ path \ of \ the \ train, \, m =tan(\theta) = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
∴ m = tan(θ) = (5 - (-10))/(16 - (-8)) = 0.625
c. Distance = Velocity × Time
At 5:00 p.m., we have;
The time difference, Δt = 5:00 p.m. - 3:00 p.m. = 2 hours
The distance, d₁ = (28.3 mph × 2 hours = 56.6 miles
Using trigonometry, we have the horizonal distance travelled, 'Δx', in the 2 hours is given as follows;
Δx = d₁ × cos(θ)
∴ Δx = 56.6 × cos(arctan(0.625)) ≈ 48
The increase in the horizontal position of the train, relative to the point (5, 16), Δx ≈ 48 miles
The vertical distance increase in the two hours, Δy is given as follows;
Δy = 56.6 × sin(arctan(0.625)) ≈ 30
The increase in the vertical position of the train, relative to the point (5, 16), Δy ≈ 30 miles miles
Therefore; the location of the train at 5:00 p.m. = ((5 + 48), (16 + 30)) = (53, 46)
The location of the train at 5:00 p.m. = 53 miles east, and 46 miles west
c. The function, 'f', that would give the train's position at time-t is given as follows;
The P = f(28.3·t, θ)
Where;
28.3·t = √(x² + y²)
θ = arctan(y/x)
Parametric equations
y - 5 = 0.625·(x - 16)
∴ y = 0.625·x - 10 + 5
The equation of the train's track is therefore, presented as follows;
y = 0.625·x - 5
d = 28.3·t
The y-component of the velocity, [tex]v_y[/tex] = 3*√89 mph × sin(arctan(0.625)) = 15 mph
Therefore, we have;
y = -10 + 15·t
The x-component of the velocity, vₓ = 3*√89 mph × cos(arctan(0.625)) = 24 mph
Therefore, we have;
x = -8 + 24·t
The location of the train at any given time, 't', f(t) = (-8 + 24·t, -10 + 15·t)
d. The speed of the cyclist next to the observer at 2:00 p.m., v = 10 mph
The distance of the cyclist from the track = The x-intercept = 5/0.625 = 8
The distance of the cyclist from the track = 8 miles
The time it would take the cyclist to react the track, t = 8 miles/10 mph = 0.8 hours
The location of the train in 0.8 hours, is f(0.8) = (-8 + 24×0.8, -10 + 15×0.8)
∴ f(0.8) = (11.2, 2)
At the time the cyclist is at the track along the east-west axis, at the point (8, 0), the train is at the point (11.2, 2) therefore, the train does not collide with the cyclist when the bike goes over the train tracks.
If the cyclist is travelling at 10 mph the train does not collide with the cyclist when the bike goes over the train tracks.
The location south the train is spotted = 10 miles south and 8 miles west
The time the observer spotted the train = 2:00 pm
The location of the train is spotted at 3:00 p.m. = 5 miles north and 16 miles east
Thus, the difference between the two times the train was spotted,
t = 3:00 p.m. - 2:00 p.m. = 1 hour
What is the distance?The distance is the product of velocity and time.
Distance = Velocity × Time
The initial location of the train = (-10, -8)
The final location of the train = (5, 16)
Therefore the distance the train travelled in the first hour
[tex]d = \sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} } \\d = \sqrt{(5 -(-10) )^{2} +(16-(-8) )^{2} }[/tex]
d = 3√89
The distance the train travelled in the first hour, d = 28.3 miles
b. The speed of the train, v = (Distance travelled by train)/Time
∴ v ≈ 28.3 miles/(1 hour) = 28.3 miles per hour
The speed of the train in the first hour, v ≈ 28.3 mph
The direction of the train, θ, is given by the arc tangent of the slope, 'm', of the path of the train;
∴ m = tan(θ) = (5 - (-10))/(16 - (-8))
m = 0.625
c. Distance = Velocity × Time
At 5:00 p.m., we have;
The time difference, Δt = 5:00 p.m. - 3:00 p.m. = 2 hours
The distance, d₁ = (28.3 mph × 2 hours = 56.6 miles
Using trigonometry, we have the horizontal distance travelled, 'Δx', in the 2 hours is given as follows;
Δx = d₁ × cos(θ)
∴ Δx = 56.6 × cos(arctan(0.625)) ≈ 48
The increase in the horizontal position of the train, relative to the point (5, 16), Δx ≈ 48 miles
The vertical distance increase in the two hours, Δy is given as follows;
Δy = 56.6 × sin(arctan(0.625)) ≈ 30
The increase in the vertical position of the train, relative to the point (5, 16), Δy ≈ 30 miles miles
Therefore; the location of the train at 5:00 p.m. = ((5 + 48), (16 + 30)) = (53, 46)
The location of the train at 5:00 p.m. = 53 miles east, and 46 miles west
c. The function, 'f', that would give the train's position at time-t is given as follows;
The P = f(28.3·t, θ)
28.3·t = √(x² + y²)
θ = arctan(y/x)
Parametric equations
y - 5 = 0.625·(x - 16)
∴ y = 0.625·x - 10 + 5
The equation of the train's track is, therefore, presented as follows;
y = 0.625·x - 5
d = 28.3·t
The y-component of the velocity,
= 3 × √89 mph × sin(arctan(0.625)) = 15 mph
Therefore, we have
y = -10 + 15·t
The x-component of the velocity,
vₓ = 3 × √89 mph × cos(arctan(0.625))
= 24 mph
Therefore, we have;
x = -8 + 24·t
The location of the train at any given time, 't',
f(t) = (-8 + 24·t, -10 + 15·t)
d. The speed of the cyclist next to the observer at 2:00 p.m., v = 10 mph
The distance of the cyclist from the track = The x-intercept
= 5/0.625 = 8
The distance of the cyclist from the track = 8 miles
The time it would take the cyclist to reach the track, t = 8 miles/10 mph = 0.8 hours
The location of the train in 0.8 hours, is f(0.8)
= (-8 + 24×0.8, -10 + 15×0.8)
∴ f(0.8) = (11.2, 2)
therefore, If the cyclist is travelling at 10 mph the train does not collide with the cyclist when the bike goes over the train tracks.
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I need this question really badly
Answer:
yeah same for me but with ice cream
Solve. 382.04 – 6,3 *
I need help
Kevin knit scarves for his friends. Altogether, the scarves had a total length of
442.8 in. If he knit 9 scarves, and each scarf was the same length, how long
was each scarf? Write your answer in feet.
Kevin knit 9 scarves, and each scarf was 49.2 inches long.
Converting this length to feet, we find that each scarf is 4.1 feet long.
Let's use the variable "L" to represent the length of each scarf in inches. Since Kevin knit 9 scarves, we can write the equation for the total length of all scarves as:
[tex]\(L_{\text{total}} = L \times 9\)[/tex]
We are given that the total length of all scarves is 442.8 inches. So, we can write:
[tex]\(442.8 \text{ inches} = L \times 9\)[/tex]
To find the length of each scarf, we need to isolate "L" on one side of the equation. To do that, we can perform the following steps:
Divide both sides of the equation by 9 to get:
[tex]\(\frac{{442.8 \text{ inches}}}{{9}} = \frac{{L \times 9}}{{9}}\)[/tex]
Simplifying, we get:
[tex]\(49.2 \text{ inches} = L\)[/tex]
Now, we have found the length of each scarf in inches (49.2 inches). To convert this length to feet, we know that 1 foot is equal to 12 inches. So, to find the length in feet, we divide the length in inches by 12:
[tex]\(L_{\text{feet}} = \frac{{L_{\text{inches}}}}{{12}}\)[/tex]
Substituting the value of [tex]\(L_{\text{inches}}\)[/tex] with 49.2 inches:
[tex]\(L_{\text{feet}} = \frac{{49.2 \text{ inches}}}{{12}}\)[/tex]
Now, let's perform the division:
[tex]\(L_{\text{feet}} = 4.1 \text{ feet}\)[/tex]
So, each scarf is 4.1 feet long.
Kevin knit 9 scarves, and each scarf was 49.2 inches long.
Converting this length to feet, we find that each scarf is 4.1 feet long.
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Watch ne
The diameter of a circle is 4 m. Find its area to the nearest tenth.
m
Answer A=
Answer:
area = 12.6 m²
Step-by-step explanation:
r = 4/2 = 2
area = πr² = (3.14)(2²) = 12.56 m²
HELP ... answer correctly pls
Use the expression below to answer the question.
-3/4 x 2/5
Which situation can be modeled by the expression?
A. Zach owes 3/4 of the original price of his car. Each month he pays 2/5 of the original price. How many months will it take Zach to pay off his car?
B. Zach owes 3/4 of the original price of his car. Each month he pays 2/5 of how much he still owes on the car. What fraction of the original price does Zach owe after this month’s payment?
C. Abdi owes Kim 3/4 of a dollar. He needs to borrow more money from Kim. Abdi then borrows 2/5 of how much he owes. By what fraction of a dollar does the amount Abdi owes Kim change?
D. Abdi owes Kim 3/4 of a dollar. He pays her 2/5 of how much he owes. What fraction of a dollar does Kim receive from Abdi?
Answer:
D.
Step-by-step explanation:
The situation that can be modeled by the expression -3/4 x 2/5 is:
Abdi owes Kim 3/4 of a dollar. He pays her 2/5 of how much he owes.
The expression -3/4 x 2/5 gives us the fraction of a dollar that Kim receives from Abdi, which is -3/10 of a dollar.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The expression -3/4 x 2/5 means that we multiply -3/4 by 2/5.
Multiplying two fractions involves multiplying their numerators together and their denominators together. So,
-3/4 x 2/5 = (-3 x 2) / (4 x 5) = -6/20 = -3/10
Therefore,
The situation that can be modeled by the expression -3/4 x 2/5 is:
Abdi owes Kim 3/4 of a dollar. He pays her 2/5 of how much he owes.
The expression -3/4 x 2/5 gives us the fraction of a dollar that Kim receives from Abdi, which is -3/10 of a dollar.
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6x+2y=0 3x+y=24 using elimination
-9+3y=24 write an equivalent equation in slope intercept form
ig hanganaahajssislaalalla
I WAS IN THE HOSPITAL AND MISSED A MATH LESSON HELP PLZZZ
Answer:
30 ft
Step-by-step explanation:
[tex]C=\frac{n^2}{5} +175\\\\355=\frac{n^2}{5} +175\\\\180=\frac{n^2}{5}\\\\n^2=900\\\sqrt{n^2} =\sqrt{900} \\n=30[/tex]
rekitha arekitha kandaralu
Answer:
khing chong
Step-by-step explanation:
i don't understand this can someone help me please
Answer:
Total interest to be paid: $210
Total amount to be repaid: $3,710
Step-by-step explanation:
You can ignore the monthly payment for this problem.
For simple interest, the formula is I = PRT where I = interest earned, P = principal amount borrowed/deposited, R = rate as a decimal, and T = time in years.
I = (3,500)(0.06)(1)
I = 210
Then add that to the amount borrowed ($3,500) and you're done.
3,500 + 210 = $3,710
Please let me know if you have questions.
What is mU?
A. 17
B. 29
C. 46
D. 134
Answer:
I think its A
Step-by-step explanation:
because it's a tighter angle than 29,46,and 134 degrees i might not be right but i hope it is :)
Thalia's next class is 8 units to the right and 5 units down on the map from where she is now. In what room is Thalia's next class? Find the ordered pair that represents the location of that room.
Answer: (6,-4) music
Step-by-step explanation:
The dot plot shows the number of hours that students spent watching TV. A dot plot titled hours students spend watching T V per week. The dot plot goes from 3 to 20 and is labeled hours. The data is as follows. 16 dots above 3, 13 dots above 4, 14 dots above 5, 2 dots above 6, 7, 8, 9, and 10, 8 dots above 11, 11 dots above 12 and 13, 3 dots above 14, 15, and 16, 0 dots above 17, 18, and 19, and 1 dot above 20. Select all the statements that are true. A typical student from this group spends more than 10 hours watching television each week. More students watch 3 hours of television than watch more than 3 hours of television. All students watch 20 or fewer hours of television each week. The most common answer for the number of hours that a student watches per week was 3. Some students do not watch any TV during the week.
Answer:
The answer is , More students watch 3 hours of television than watch more than 3 hours of television.
Step-by-step explanation:
Answer: The most common number of hours that a student watches per week is 3.
Step-by-step explanation:
With 3 having 16 dots and others having lower than these dots that are 16 we can notice that 3 is the most common number and that's the simplest way I can put it.
Hope this helped!!
Find the surface area of a number cube if the height is 3cm.
I'll give brainliest
Answer:
54 unit sq
Step-by-step explanation:
Answer:
54 i think
Step-by-step explanation:
3x^2=20-7x
factor step by step please?
Answer:
x=5/3 or x=-4
Step-by-step explanation:
PLEASE HELP I NEED IT NOW
Liam puts $60 in savings in March and 150% of this amount in savings in April. How much does Liam put in savings in April? Round to the nearest whole dollar. *
Answer:
Savings in March: $60
Savings in April: $60 + 150% of $60=$60 +$90=$150
Step-by-step explanation:
Liam adds another 150% of the original amount to his savings. So, his total amount does not change but the amount increases by $90 (150% of $60).
Let K and T be the current ages of siblings, Katie and Thomas. Katie is currently twice the age of Thomas. In 6 years, Katie will be 4 times Thomas’s current age. How old are Katie and Thomas?
(a) Write a system of equations to describe the situation.
(b) Find the solution to the system and answer the question.
WILL MARK FIRST ANSWER AS BRAINLIEST!!!
Answer:
(a) K = 2T
K + 6 = 4T
(b) 2T + 6 = 4T
6 = 4T - 2T
6 = 2T
6/2 = 2T/2
T = 3
When T = 3, K = 6
Probability that the next baby born at a hospital will be a boy
evaluate the expression 6n2 when n=5
Answer:
652
Step-by-step explanation:
Answer: 60
Step-by-step explanation:
6n2
n=5
6(5)2
6×10 = 60
Mr. Thomsen is buying two types of gift
cards to give as prizes to employees at a
company meeting. He will buy restaurant
gift cards that each cost $50. He will also
buy movie theater gift cards that each
cost $20. He has $450 to buy a total of
15 gift cards. How many of each type of gift cards can he buy?
Answer:
he can buy 6 gift cards, 7 theatre cards with a remainder of $10.
Step-by-step explanation:
URGENT!!!!!!!! PLEASE HELP ASAP TIMED!!!!!!!!!!!!!!! HELP!!!!!!!!!!!!!!!!!
Answer:
Height of building = 86.9 ft
Step-by-step explanation:
I've drawn a triangle image to depict this question and I have attached it.
From the attached image, we can see that ABC is the height of the building.
We can see the distance from your eye to the ground indicated and also the distance from the horizontal distance from the building to you indicated.
We can use pythagoras theorem to find AB.
AB/57 = tan 55°
AB = 57 × 1.4281
AB = 81.4 ft
Now, total height of the building is AB + BC.
BC = 5.5 ft since B is parallel to your eye and height from there to the ground is 5.5 ft.
Thus;. Height of building = 81.4 + 5.5 = 86.9 ft
Round your answer to the nearest tenth if necessary. Use 3.14 for it.
A drum has a diameter of 26 inches and is 19 inches deep. Find the volume of his drum.
The volume of this drum is approximately
in.
Answer:
volume = 10,082.5 in³
Step-by-step explanation:
radius = 26/2 = 13
volume = πr²L = (3.14)(13²)(19) = 10,082.54 in³
Jenya graphed a scatter plot of number of potholes (y) and length of a road in miles (x). She drew the trend line and calculated its equation to be y = 3x +5. What is the predicted number of potholes for a road that is 10 miles long?
Answer: 35
Step-by-step explanation:
3•10=30, 30+5=35
The doctors had never seen anything like it. She was a perfectly healthy little girl who just happened to have two hearts. The only explanation they could offer was...
Continue the story 3-4 sentences long
Ill give brainliest
Answer:
that somehow the supposed 'twin' sister has now been integrated into one. The parents looked at the girl, and the girl blinked back. Could it be that their soul has somehow been conjoined? "Oh Lord have Mercy" prayed the mother, while the father looked at the little girl with disgust. He had already wanted a son, but to have a two-hearted freak with them? Your daughter could be one of them. And what will you do, then. You knew this would happen. The father shook off the thought. He WILL NOT let Okani know.
Step-by-step explanation:
what is the answer????
Answer:
40 m
Step-by-step explanation:
(=^w^=) woof
Answer:
40 [tex]m^2[/tex]
Step-by-step explanation:
the formula for a rectangular prism is:
A=2(wl+hl+hw)
so when you fill in the numbers, you get 40 because l = 2 and w and h are 2
2·(2·4+2·4+2·2)=40
The radius of a circle is 44 centimeters. What is the circle's circumference?
Answer:
276
Step-by-step explanation:
Circumference = 2πr
= 276
help with this nth term homework please answer true of false
I cant do this please help me i will give brainliest
Answer:
Here, I graphed this especially for you.
Check attachment.
3(x+4)=-18 Please go step by step!
Answer:
hi
Step-by-step explanation:
3(x+4)=-18
3 × X + 3× 4=-18
3x+12=-18
3x=-18-12
3x= -30
x= -30/3
x= -10
hope it helps
have a nice day