5
Drag the tiles to the correct boxes to complete the pairs.
Luke is driving from his house to the store. After driving 16 miles at a constant speed of 0.8 mile/minute, he realizes that he forgot his wallet. So,
he turns around and drives all the way back to his house at the same speed. The equation below models Luke's distance, in miles, from home as
he drives for t minutes.
d = -0.8t - 20 + 16
Using the given equation, match the number of minutes since Luke started driving from his house to his distance from the house.
12 minutes
27 minutes
31 minutes
7 minutes
10.4 miles on his return trip
5.6 miles on his trip to the restaurant
9.6 miles his trip to the restaurant
7.2 miles on his return trip
Answers
Answer:
10.4 miles on his return trip → 27 minutes
5.6 miles on his trip to the restaurant → 7 minutes
9.6 miles on his trip to the restaurant → 12 minutes
7.2 miles on his return trip → 31 minutes
Step-by-step explanation:
When solving, we note that on his trip to the restaurant, [tex]\left |t - 20 \right |[/tex] is a negative number, while it is a positive number on his return trip
1) At 10.4 miles on his return trip, we have;
[tex]d = 10.4 = -0.8 \cdot \left |t - 20 \right |+ 16[/tex]
Therefore;
(10.4 - 16)/(-0.8) = 7 = [tex]\left |t - 20 \right |[/tex]
t = 20 + 7 = 27
The number of minutes since Luke started driving from his house, t = 27 minutes
2) At 5.6 miles on his trip to the restaurant, we have;
[tex]d = 5.6 = -0.8 \cdot \left |t - 20 \right |+ 16[/tex]
Therefore;
(5.6 - 16)/(-0.8) = 13 = [tex]\left |t - 20 \right |[/tex]
Here, t is less than 20 (minutes), therefore, t - 20 is negative, we get
t - 20 = -13
∴ t = 20+ (-13) = 7
The number of minutes since Luke started driving from his house when he is 5.6 miles on his trip to the restaurant, t = 7 minutes
3) At 9.6 miles on his trip to the restaurant, we have;
[tex]d = 9.6 = -0.8 \cdot \left |t - 20 \right |+ 16[/tex]
Therefore;
(9.6 - 16)/(-0.8) = 8 = [tex]\left |t - 20 \right |[/tex]
[tex]\left |t - 20 \right |[/tex] is negative on his trip to the restaurant, therefore;
- [tex]\left |t - 20 \right |[/tex] = 8
t - 20 = -8
t = 20 - 8 = 12
The number of minutes since he started driving from his house to when he is 9.6 miles on the his trip to the restaurant, t = 12 minutes
4) At 7.2 miles on his return trip, we have;
[tex]d = 7.2 = -0.8 \cdot \left |t - 20 \right |+ 16[/tex]
Therefore;
(7.2 - 16)/(-0.8) = 11 = [tex]\left |t - 20 \right |[/tex]
t = 20 + 11 = 31
At 7.2 miles from his house on the return trip, t = 31 minutes
Related Questions
5. In the triangle ABC, M is the midpoint of [AB] and N is the midpoint of [CM].
Find the coordinates of N. Given that A(-1,3), B(7.-3) and C(1,6).
Answers
Answer:
The coordinates of the point N is (2,3)
Step-by-step explanation:
For us to find the midpoint between two points
We use the midpoint formula which is;
(x,y) = (x1 + x2)/2, (y1 + y2)/2
We start by finding the midpoint of AB to get the coordinates of the point M
A(-1,3) and B(7,-3)
(x,y) = (-1 + 7)/2, (3-3)/2 = (6/2,0/2) = (3,0)
Now that we have the coordinate of M, we can find the midpoint of CM to get the coordinates of N
C(1,6) and M (3,0)
(x,y) = (1 + 3)/2, (6+0)/2 = (4/2, 6/2) = (2,3)
rewrite the following linear equations in general form
can someone help explain how to do this?
Answers
Answer:
5y = x +15
Step-by-step explanation:
here you have to multiply both sides with 5 to make it a general form ,
5(y) = 5(1/5x) + 5(3)
5y = x + 15
Got a little help from app called Gauthmath. It got concept videos and tutors. You can check it on Play Store and App Store. Really good app in my opinion.
Hope this helps. :)
Amanda works as a hostess at Red Robin on weekday nights and at the Pix movie theatre on the weekends. Amanda’s pay at Red Robin is 11.50ℎ+0.25+10and her pay at the Pix is 10.50ℎ+0.5−20. Find the polynomial that would represent Amanda’s total earnings from her two jobs.
Answers
Answer:
22h−9.25
Step-by-step explanation:
Lucas suele gastar $150 en gaseosas al mes, pero, para cuidar su salud decidió dejar de consumir gaseosas ¿cuánto dinero a dejado de gastar en cinco meses?
Answers
Answer:
$750
Step-by-step explanation:
Primero, Lucas gastaba $150 cada mes en gaseosas.
Al decidir cuidar su salud, deja de comprar gaseosas, entonces ya no gasta esos $150 al mes.
Es decir, a dejado de gastar $150 al mes.
Nosotros queremos saber:
¿cuánto dinero a dejado de gastar en cinco meses?
Bueno, si en un solo mes a dejado de gastar $150
En 5 meses a dejado de gastar 5 veces esa cantidad, que es:
5*$150 = $750
The expression \sqrt[3]{3}\cdot \sqrt[5]{3^6}
3
3
⋅
5
3
6
is equivalent to
Answers
By simplifying the given expression, the expression [tex]\sqrt[3]{3}[/tex] * [tex]\sqrt[5]{3^6}[/tex] is equivalent to [tex]3^(23/15).[/tex]
How to find equivalent valueTo simplify the given expression, combine the two radicals using the property of exponentiation.
First, simplify the expression inside the second radical:
√[5]{[tex]3^6[/tex]}
Since the index is 5, rewrite the expression as:
[tex](3^6)^(1/5)[/tex]
Using the property of exponentiation, multiply the exponents:
[tex]3^(6/5)[/tex]
Now combine this result with the first radical:
[tex]3\sqrt3 * 3^(6/5)[/tex]
Since ∛3 can be written as [tex]3^(1/3)[/tex], rewrite the expression as:
[tex]3^(1/3) * 3^(6/5)[/tex]
To multiply two numbers with the same base, add the exponents:
[tex]3^(1/3 + 6/5)[/tex]
To simplify further, we need a common denominator for the fractions:
[tex]3^(5/15 + 18/15)[/tex]
Combining the fractions:
[tex]3^(23/15)[/tex]
Therefore, the given expression is equivalent to [tex]3^(23/15).[/tex]
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Hihi , please help if able.
Answers
Answer:
Option c
Step-by-step explanation:
multiply the expression in the parentheses by 4 and you get 12x+16
a doesn't fit, x³ is x*x*x, not plus
b 14x-2x is 12x, not 16x
d got a 5x expression with no correspondence on the other side and 12x² isn't 17x²
Anyone know this answer?
Answers
Answer:
56 degrees
Step-by-step explanation:
The tangent of any angle in a right triangle is equal to its opposite side divided by its adjacent side.
Therefore, we have the equation:
[tex]\tan x^{\circ}=\frac{15}{10}[/tex]
To isolate [tex]x[/tex], take the inverse tangent of both sides:
[tex]\tan^{-1}(\tan (x^{\circ}))=\tan^{-1}(\frac{15}{10}),\\x^{\circ}=\arctan(\frac{15}{10})=56.30993247\approx \boxed{56^{\circ}}[/tex]
*Recall [tex]\tan^{-1}(\tan x)=x, x\in (-\frac{\pi}{2}, \frac{\pi}{2})[/tex]
Find x in circle O. Figure is not drawn to scale. HURRY PLEASE
Answers
Answer:
B. 23,5
Step-by-step explanation:
Question 7 of 10
Classify the following triangle. Check all that apply.
109
15
14
D A. Right
B. Equilateral
O C. Acute
D D. Scalene
O E. Isosceles
M F Obtuse
Answers
Answer:
A & D
Step-by-step explanation:
A. acute because all angles are less than 90 degrees
D. scale because all sides have different
if you look up the definition of the properties you will see they don't apply
Answer:
F.Obtuse angle
because the angles are between 90-180
The equation C = 20n + 35 represents the relationship between the cost of school volleyball uniforms,
C, in dollars, and the number of uniforms ordered, n.
The uniform company requires that the school order a minimum of 15 uniforms.
The school has a maximum of $600 to spend on the uniforms.
Determine the possible values for n and C in this situation
.
Answers
Answer:
Given the equation
C = 20n + 35We need:
n ≥ 15 and C ≤ 600following
20n + 35 ≤ 60020n ≤ 565n ≤ 565/20n ≤ 28 (rounded to the whole number)Considering that n ≥ 15, we have:
15 ≤ n ≤ 28And the cost is going to be:
20*15 + 35 ≤ C ≤ 20*28 + 35335 ≤ C ≤ 595Cho hình chóp SABCD. Lấy I thuộc SA, J thuộc SB sao cho IJ không song song với AB. Lấy điểm K trong miền tứ giác ABCD. Tìm đường cao tuyến của I, J, K với các mặt sau đây: ABCD, SBC, SAD, SCD
Answers
Answer:
Step-by-step explanation:
ABCD is a square. Square A B C D is shown. The length of A B is x + 6 and the length of B C is 2 x minus 1. What is the length of line segment DC? 5 units 7 units 11 units 13 units
Answers
Answer:
DC = 13units
Step-by-step explanation:
For a square, all the sides are equal, hence;
AB = BC
x+6 = 2x-1
x-2x = -1-6
-x = -7
x =7
Also DC =AB
DC = x+6
DC = 7+6
DC = 13units
Hence the length of DC is 13units
Answer: 13 units
Step-by-step explanation:
DC = 13 units
Step-by-step explanation:
For a square, all the sides are equal, hence;
AB = BC
x+6 = 2x-1
x-2x = -1-6
-x = -7
x =7
Also DC =AB
DC = x+6
DC = 7+6
DC = 13 units
Hence the length of DC is 13 units
harlie is a hotel manager. Their responsibilities include renting rooms for conferences. The hotel charges $250 per day plus $15 per person for the grand ballroom.
Create a formula for the cost, C, in dollars, to rent the ballroom for any number of people for 1 day.
Hint: Use C for cost and n for the number of people. C = ________
How much should Charlie charge to rent the hall for 50 people? What about 100 people?
Rearrange your formula to express n in terms of C (rewrite your formula to solve for n)
How many people could attend a wedding reception if the planners have a budget of:
$4000
$2000
Answers
Answer:
Formula: C= $15n + $250
50 People: $1000
100 People: $1750
Formula: n= (C- $250)/ 15
$4000 Budget: 250 Guests
$2000 Budget: 116.67 Guests
Step-by-step explanation:
Since the rental is $250 with an additional charge of $15 per person, we write this as C = $250 + $15n.
With the given equation, simply substitute n for the amount of guests.
C = $250 + $15(50) = $1000
C = $250 + $15(100) = $1750
To solve for n, everything would need to be moved to isolate n. This can be achieved by first subtracting $250 from each side: C- 250= 15n
Then divide both sides by 15, making the new equation: (C-250)/15 = n
Again, substitute C with allowed cost to find the amount of guests allowed.
n = ($4000- 250)/ 15 = 250 People
n = ($2000-250)/15 = 116.67 People
During a game of pool near hit a ball and it follow the path from B to C and then to de- the angles formed by the path of congruent to the nearest 10th of an inch which of the following represents the total distance the ball travels before it stopped at point D
Answers
Answer:
please mark me as brainleast
Please, can I get help?
Answers
Answer:
a- 14,11
b-13,63
Step-by-step explanation:
how do i calculate an enlargement
Answers
Answer: The formula involves the dimension of the space available divided by the size of the original. In this case, that is 94 divided by 72. The answer is 1.31. Move the decimal point and that is a 131 percent enlargement.
Step-by-step explanation:
2 consecutive postive nos are such that the sum of their squares is 113. Find the 2 numbers
Answers
Answer:
7,8
Step-by-step explanation:
n^2+(n+1)^2=113; this is the information we are provided in the question.
n^2+n^2+2n+1=113 ; just expanding the numbers
2n^2+2n-112=0 ; moving everything to the same side
n^2+n - 56= 0 ; divide everything by two
(n-7)(n+8)=0 : factor the polynomial
so answers for n are: 7 and -8. since the questions asks for positive numbers -8 cannot be correct.
so n=7
n+1 = 8
Nina and Jo both ran an 8 km race. Nina took 55 minutes to run the whole race. Jo started the race 3 minutes later than Nina but caught up when they had both travelled 6 km. If Nina and Jo both ran at constant speeds, what is Jo's speed to 2 dp?
Answers
Answer:
Step-by-step explanation:
First we figure out how fast Nina can run. If Nina can run 8 km in 55 minutes, then her rate is
[tex]\frac{8km}{55min}=.145\frac{km}{min}[/tex] and we can use that in a d = rt table:
d = r * t
Nina .145
Jo
Now we can fill in the distance which is 6 for both, since that is the distance where they met:
d = r * t
Nina 6 = .145
Jo 6 =
Now we go to the info given about the time. If Jo started the race 3 minutes after Nina, that means that Nina is running 3 minutes longer than Jo. Filling in the time info:
d = r * t
Nina 6 = .145 * t + 3
Jo 6 = r * t
As you can see, right now we have 2 unknowns in Jo's row. But we don't have to! We will go to Nina's row where the only unknown is time and solve for t. If d = rt, then
6 = .145(t + 3) and
6 = .145t + .435 and
5.55 = .145t so
t = 38.379 minutes. This means that Jo was running 38.379 minutes when she caught up to Nina (it took Nina 3 minutes longer than that to go 6 km since she was already running for 3 minutes when Jo started the race). If Jo's time is 38.379, we can use that in her row for t and solve for r. If d = rt, then
6 = r(38.379) and
r = .16 km/min
Let's check it without the rounding (rounding takes away from the accuracy). If 6 = .145(t + 3) and Nina's rate not rounded is .145454545 and t = 38.37931034, then, rewriting without rounding:
6 should equal .145454545( 38.37931034 + 3)
6 ?=? .145454545(41.37931034)
6 ?=? 6.0 so
Jo's rate is .16 km/min rounded
A rectangle has a perimeter of 54 cm. It has a length of 15 cm. What is its area? *
Answers
the area is 180 cm. to find the perimeter you would do 15+15+14+14 to get 54 cm. So for area you do (l×w) which is 15×14=180.
Each pair of figures is similar find the missing sie
Answers
Answer:
x = 3
Step-by-step explanation:
since they are similar use these ratios
x/9 = 1/3
do cross multiplication
9*1 = 3*x
9/3 = x
3 = x
A car travels 22 miles for every gallon of gasoline used. The table below represents this relationship
Answers
Answer:
the answer would be 1/22 = x/3
Step-by-step explanation:
because 1 gallon of gasoline got him to travel 22 miles so your trying to solve for x for 3 gallons
need help asap!!!!!! Marcel is performing the first test on his company’s new electric car. During the test, the electric car reaches a maximum speed of 81 mph.
The performance test results of the electric car can be modeled by the following table, where x represents time, in seconds at the start of the test, and y represents the speed, in miles per hour.
Answers
For this case we have the following variables:
x: represents time, in seconds at the start of the test.
y: represents the speed, in miles per hour.
We have then that:
x = 0 ---> y = 0
x = 12 ---> y = 0
Answer:
the electric car is not moving at 0 seconds and 12 seconds
I hope this helps!
the electric car is not moving at 0 seconds and 12 seconds
I hope this helps!
tìm các giá trị của tham số m để hàm số y = (m-1)x^3 - 3(m-1)x^2 + 3(2m-3)x + m nghịch biến trên R
Answers
Answer:
3
Step-by-step explanation:
Please help I’ll give brainliest
Answers
Answer:
Option A
Step-by-step explanation:
Please Mark me brainliest
Expand and simplify (x - 1)(x + 2)(x - 1)
Answers
Answer:
[tex](x - 1)(x + 2)(x - 1)=(x-1)^{2}(x+2)[/tex]
Step-by-step explanation:
Use the product rule [tex]x^{a} x^{b}=x^{a+b}[/tex]
Answer:
x^3 -3x + 2
Step-by-step explanation:
(x - 1)(x - 1) =
x^2 -2x + 1 (x+2) =
x^3 + 2x^2
-2x^ - 4x
x + 2
----------------------------
x^3 -3x + 2
YALL REALLY NEED TO
HELP MEEEE
determine if the triangles are similar. Why are they similar or not similar ?
please show work
Answers
Answer:
Not similar
Step-by-step explanation:
In triangle MLN & WXY,
Right angles - > 1
There is nothing common in these 2 triangles other than (1)
Therefore,
Not similar
Find the volume of a right circular cone that has a height of 18.8 m and a base with a
radius of 19.3 m. Round your answer to the nearest tenth of a cubic meter.
Answers
Step-by-step explanation:
Height of the right circular cone = 18.8 metres
And base is 19.3 metres
Volume of the right circular cylinder is given by,
= πr²h
= 3.14 × (19.3)² × 18.8
= 21999.98(approx.) cubic metre
Rounding off nearest tenth
= 21999 cubic metres
The volume of the right circular cone is 280,199.5 m³
What is a right circular cone?
'A right circular cone is a cone where the axis of the cone is the line meeting the vertex to the midpoint of the circular base.'
According to the given problem,
Height = 18.8 m
Radius = 19.3 m
Volume of right circular cone = [tex]\frac{\pi r^{2}h }{3}[/tex]
= [tex]\frac{\pi * 19.3^{2} * 18.8}{3}[/tex]
= 280199.499 m³
= 280199.5 m³
Hence, we can conclude that the volume of the right circular cone is 280199.5 m³.
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SAT A bag contains 3 red marbles, 2 green
marbles, and 4 blue marbles. One marble is
randomly drawn and replaced. Then a second marble
is drawn. Find the probability of drawing three blue
marbles.
Answers
Answer:
[tex] \frac{1}{21} [/tex]
Step-by-step explanation:
refer to solution in picture
Classify the following triangle. Check all that apply.
Answers
Answer:
A, E, F
Step-by-step explanation:
A: the angles are less than 90 degrees
E: all sides have equal lengths
F: has at least 2 sides equivalent in length
please answer this !!!
You toss a coin 83 times. The coin lands 40 times on heads and 43 times on tails. If you define a fails as a success, what is the relative frequency of tails?
Answers
Answer:
to do this we have to divide 43 by 83
0.51807228915
so the frequency is about 51.8%