Answers
Answer:
See belowStep-by-step explanation:
speed = distance / timetime = distance / speeda)
i)
Time taken at the first part:
105 / xii)
Time taken at the second part:
(190 - 105) / (x + 12) = 85/(x + 12)b)
If time is 3 hours and 15 minutes = 3 1/4 hours = 13/4 hours, the equation is:
105/x + 85/(x + 12) = 13/44(x + 12)*105 + 4(85x) = 13x(x + 12)13x² - 604x - 5040 = 0c)
Solve the equation:
13x² - 604x - 5040 = 0x = [604 ± √((-604)² + 4*13*5040) ]/26 = [604 ± √626896]/26 = [604 ± 791.77]/26x = (604 + 791.77)/26 = 53.68 km/h (taking positive root only)d)
105/x = 105/53.68 h = 1.956 h = 1 h 0.956*60 min = 1 h 57 min (rounded)85/(53.68 + 12) = 85/65.68 = 1.294 h = 1 h 0.294*60 min = 1 h 18 min (rounded)Answer:
see below
Step-by-step explanation:
Let t = time (in hours)
a) i) First 105 km of journey
[tex]\mathsf{speed=\dfrac{distance}{time}}[/tex]
[tex]\implies x=\dfrac{105}{t_1}[/tex]
[tex]\implies t_1=\dfrac{105}{x}[/tex]
ii) Rest of journey
distance = 190 - 105 = 85 km
speed = [tex]x+12[/tex] km/h
[tex]\mathsf{speed=\dfrac{distance}{time}}[/tex]
[tex]\implies x+12=\dfrac{85}{t_2}[/tex]
[tex]\implies t_2=\dfrac{85}{x+12}[/tex]
b) 3 hours 15 minutes = 3.25 hours
[tex]\implies[/tex] total time = [tex]t_1+t_2=3.25[/tex]
[tex]\implies \dfrac{105}{x}+\dfrac{85}{x+12} =3.25[/tex]
[tex]\implies \dfrac{105(x+12)+85x}{x(x+12)} =3.25[/tex]
[tex]\implies 105(x+12)+85x =3.25x(x+12)[/tex]
[tex]\implies 105x+1260+85x =3.25x^2 +39x[/tex]
[tex]\implies 3.25x^2-151x-1260=0[/tex]
multiply by 4:
[tex]\implies 13x^2-604x-5040=0[/tex]
c)
[tex]\textsf{quadratic formula} \ x=\dfrac{-b \pm\sqrt{b^2-4ac} }{2a}}[/tex]
[tex]\implies x=\dfrac{604 \pm\sqrt{(-604)^2-4(13)(-5040)} }{2(13)}}[/tex]
[tex]\implies x=\dfrac{604 \pm\sqrt{626896} }{26}}[/tex]
[tex]\implies x = 53.68, x=-7.22[/tex]
(to 2 decimal places)
d) time ≥ 0, therefore, x = 53.68 only
Substitute x = 53.68 into the expression for [tex]t_1[/tex] and solve for [tex]x[/tex]:
[tex]\implies t_1=\dfrac{105}{53.68}=1.955912... \textsf{hours}=\textsf{1 hr 57 min}[/tex]
Related Questions
Please help!!! What is the equation of the function given the following table of values?
Answers
Answer:
C
Step-by-step explanation:
if you plug in the X values, you get the corresponding Y values.
PLEASE HELP WILL MARK BRAINLIEST FOR BEST ANSWER If you reflect (-2, -8) across both axes, which quadrant will it be in? Justify your reasoning. Please no links or files
Answers
Answer:
I
Step-by-step explanation:
Reflecting the point across both axes changes the signs of both coordinates. The reflected point will be (2, 8). Both coordinates are positive for points in Quadrant I.
If im going 30 km per hour and i need to go 500 metres how long would it take
Answers
Answer:
1 minute
Step-by-step explanation:
1km = 1000m
30km = 30000m
30km ÷ 60 = 500m
it takes one hour to go 30km or a ratio of 30km to 1hour. 1hour is also 60minutes. 30:60
divide both sides by 60 gets 500m and the amount of time to go that distance 1 minute
Answer:
1/60 hr or 1 minute
Step-by-step explanation:
30 km per hour
30 km : 1 hr
convert 500 metres to km
1 km = 1000 metres
500 ÷ 1000 = 0.5 km
using ratios
30 km : 1 hr
0.5 km : x hr
to get from 30 to 0.5 multiply by 1/60 ( we got this from doing 0.5 ÷ 30) , so do the same to the other side
1 hr × 1/60 = 1/60 hr
you can convert to minutes = 1/60 × 60 = 1 minute
A car dealership increased the price of a certain car by 3%. The original price was $31,800.
Answers
Please help me figure these out!
Answers
Step-by-step explanation:
just u have to put the values of sin and cos and you will get the answer
hope u get help
The magic number is -15. Combine each statement with the magic number and determine if it will result in zero. _______ a. An elevator rises 15 floors. _______ b. $15 is withdrawn out of your account. _______ c. The temperature rises 15 degrees.
Answers
Answer:
A. is 0
B. is -30
C. is 0
Step-by-step explanation:
Hope this helps!
The correct answers are:
0-300CalculationsWe are asked to combine the magic number -15 with the given statements.
Hence, if we combine the magic number with the given statements, we would have:
a. -15 + 15 = 0
b. -15 + (-15)= -30.
c. -15 + 15 = 0.
Hence, the answers are 0, -30 and 0 respectively.
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PLEASE HELP ITS DUE TODAY PLEASE HELP ASAP 15 POINTS PLEASE HELP
Answers
Answer:
210 cm³
Step-by-step explanation:
volume = W x L x H
(where W = width, L = length and H = height)
By inspection of the diagram,
W = 6 cm
L = 7 cm
H = 5 cm
Therefore, volume = 6 x 7 x 5 = 210 cm³
Answer:
210 cm³
Work:
6×7=42
42×5=210
Step-by-step explanation:
When finding volume of a cube or rectangular prism you do the same thing as when you find the area of a square or rectangle, which is multiply the dimensions.
We see it is 7 cubes long, 6 cubes wide, and 5 cubes tall. To find the volume multiply all of these values together.
7×6×5=210
So, the volume of the prism is 210 cubes. Sense each cube is 1 cm³ the answer to the problem is 210 cm³
What is the probability that amber could pull a red 9 out of a deck of cards, replace it, then pull out a black 5?
Answers
Answer:
Try looking it up
Step-by-step explanation:
sorry i tried! Dont get mmad i tried the best i could to work this out..
please help I realy need help HHHHEEELLLPPPP
Answers
Answer: 63/100
Step-by-step explanation: it is in its most simplified form
Bamboo plants grow rapidly. A bamboo plant is 121 inches tall. Tomorrow it will be 134 inches tall, the next day it will be 147 inches tall, and on the next day it will be 160 inches tall. Write an explicit formula to represent the height of the bamboo plant as an arithmetic sequence. How tall will the plant be in 15 days?
Answers
The height of the bamboo plant after 15 days is 316 inches.
What is the height of the plant in 15 days?
In order to determine the formula that represents the rate of growth of the bamboo plant, we have to determine the inches of growth per day.
Rate of growth per day = 134 - 121 = 13 inches
The height of the bamboo plant = 121 + 13h
Where h is the number of days
Height in 15 days = = 121 + (13 x 15)
= 316 inches
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Antonio has $330 to spend on a hover board. Decide which description of a
price and discount, represents a pair of skis that Antonio can purchase with
the money he has.
25% off $450
20% off $385
20% off $360
Answers
Casey walked diagonally, from one corner to the opposite corner, across a square garden whose sides are 25 feet. How far did he walk?
Answers
Answer:
25m
Step-by-step explanation:
A square is a parallelogram having all sides equal. Hence, if Casey walked diagonally, she should have gone 25m as the rules of square states.
please mark brainliest
Round your answer to the nearest hundredth.
Answers
Given b=4 and ∠β=20°,
a = 10.98991
c = 11.69522
∠α = 70° = 1.22173 rad = 7/18π
h = 3.75877
area = 21.97982
perimeter = 26.68513
inradius = 1.64735
circumradius = 5.84761
a
b
c
Calculation Steps
The following is one way to perform the calculation. It may not be the best way.
c =
b
sin(β)
= 11.69522
a = √c2 - b2
= √11.6952176006522 - 42
= √120.77811472661
= 10.98991
∠α = 90° - ∠β
= 70° = 1.22173 rad = 7/18π
area =
a × b
2
=
10.989909677818 × 4
2
= 21.97982
perimeter = a + b + c
= 10.989909677818 + 4 + 11.695217600652
= 26.68513
inradius =
a × b
a + b + c
=
43.959638711274
26.685127278471
= 1.64735
circumradius =
c
2
=
11.695217600652
2
= 5.84761
- ror
sonny has $76to spend. The purchase he wants to make requires $93. If he borrow the extra money that he needs, how much dos he need to borrow
Answers
Answer:
$17
Step-by-step explanation:
$93 minus $76 equals $17 which is how much sonny needs to borrow.
Answer: he will need to borrow $17
to make his purchase that cost $93
Step-by-step explanation: $93 - $76 = $17
5x+15+10x+7
5(x+3)+2x+7
Answers
Step-by-step explanation:
1. Combine Like Terms (Add):
[tex]5x+15+10x+7[/tex]
[tex]15x+22[/tex]
2. Use Distributive Property:
[tex]5(x+3)+2x+7[/tex]
[tex]5x+15+2x+7[/tex]
Combine Like Terms:
[tex]7x+22[/tex]
this may sound like an easy question to some people but which fraction is 11/10 or 7/8 is greater than 1
Answers
Answer:
11/10 is greater than 1
Step-by-step explanation:
For reference, 10/10 = 1, 8/8 = 1. So when looking at these:
11/10 is 1 and 1/10
7/8 is less than 1
help me with geometry please
Answers
Answer:
y= 95.
180°-120°=60° (adding 120° with x should give you 180°)
x=60°
25°+60°=85°
180°-85°=95
Answer:
y=95
Step-by-step explanation:
we know that the triangle angles sum is 180°
to find Y you should find x
we are going to find x, we know that a straight angle is 180, to find the x you should:
[tex]120+x=180[/tex]
move 120 to the other side with a negative sign:
[tex]x=180-120\\x=60[/tex]
angle [tex]x=60[/tex]
now we know enough angles to find y:
[tex]25+60+y=180[/tex]
25 is given in the picure and 60 is the x angle while 180 is the sum of a triangle angles, we have to flip the equaton to find y:
[tex]25+60+y=180\\85+y=180\\y=180-85\\y=95[/tex]
write an exponential function in the form y=ab^x that goes through the points (0,14) and (6,896)
Answers
Answer:
y = 14 [tex](2)^{x}[/tex]
Step-by-step explanation:
Find a and b by substituting the points into the equation
using (0, 14 ) , then
14 = a[tex]b^{0}[/tex] [ [tex]b^{0}[/tex] = 1 ] , then
14 = a × 1 ⇒ a = 14
y = 14 [tex]b^{x}[/tex]
using (6, 896 )
896 = 14 [tex]b^{6}[/tex] ( divide both sides by 14 )
64 = [tex]b^{6}[/tex] ( take the sixth root of both sides )
b = [tex]\sqrt[6]{64}[/tex] = 2
Then
y = 14 [tex](2)^{x}[/tex] ← is the exponential function
Write the slope-intercept form of
the equation of the line described
through: (2.0), perp. to y=-2x+2
Answers
Answer: Y= 1/2X+5
Step-by-step explanation: Equation of the line
The slope-intercept form of a line is given by:
Being:
m = the slope of the line
b = the y-intercept
We can also use the point-slope form of the line:
Being:
(h,k) = A point that belongs to the line
Two lines of slopes m1 and m2 are perpendicular if:
We are given the line:
Whose slope is m1=-2
Thus, the perpendicular line has a slope of:
The required line contains the point (-8,1), thus the equation is:
Removing the parentheses:
Adding 1:
Operating:
A boat is heading towards a lighthouse, whose beacon-light is 107 feet above the water. From point AA, the boat’s crew measures the angle of elevation to the beacon, 13°
, before they draw closer. They measure the angle of elevation a second time from point BB at some later time to be 22°
. Find the distance from point AA to point BB. Round your answer to the nearest tenth of a foot if necessary.
Answers
Answer:
198.6
Step-by-step explanation:
see pic
Help me please I really need help
Answers
Answer:
37
Step-by-step explanation:
I'm having trouble explaining this one, sorry
Answer:
The team is measuring 333 feet below the surface.
Step-by-step explanation:
Step 1. Write the function out
P = 14 +(8d/9)
Step 2. Plug in the (P )ounds [310]
310 = 14 + (8d/9)
Step 3. Remove 14 from the right side of the equation (Subtract 14 from everything)
296 = 8d/9
Step 4. Remove 9 from the right side of the equation (Multiply everything by 9)
2664 = 8d
Step 5. Remove 8 from the right side of the equation (Divide everything by 8)
333 = d
Final Answer: The team is measuring 333 feet below the surface.
What is the image of (-4, 2) after a reflection over the y-axis?
Answers
Answer:
(4,2)
Step-by-step explanation:
x,y > -x, y
What is the ratio for 128 eggs per 72 strips of bacon
Answers
Answer:
128:72
Or
16:9 (simplified)
Hope this helps!
Madaly was extremely excited to go on vacation. HELP!!!!
The underlined part of the sentence can best be described as a/an...
adjective phrase.
prepositional phrase.
adverbial phrase.
noun phrase.
Answers
The underlined part of the sentence can best be described as an adjective phrase.
Parts of speechIn formation of sentences in English language, the words that are used usually include the following parts of speech:
nounspronounsverbsadjectivesadverbsprepositionsconjunctionsinterjectionsAn Adjective is a word that describes or modifies a noun or a pronoun. While adjective phrase is the phrase that can be used to modify or describe a noun in a sentence.
From the sentence given, extremely excited is adverbial phrase used to modify the noun vacation.
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find the mean of 12 ,10,12,14,8,15,8,9,6,5
Answers
Answer:9.9
Step-by-step explanation:
Add up the scores and dividing the total by the number of scores.
Answer:
9.9
Step-by-step explanation:
12+10+12+14+8+15+8+9+6+5 =99
99÷10=9.9
Please help. I'll give Brainliest to the correct answer!
Answers
Answer:
A) x = 0, y = 14
Step-by-step explanation:
Line A: y = 6x + 14
Therefore, the slope of line A = 6
If Line B is perpendicular to Line A, then the product of their slopes is -1.
⇒ slope of Line B = [tex]-\dfrac16[/tex]
Given Line B passes through point (2, 13 2/3).
Use slope-point form of linear equation to find equation for Line B:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-13 \frac23=-\dfrac16(x-2)[/tex]
[tex]\implies y=-\dfrac16x+14[/tex]
Solution of system is the point where the lines intersect.
From inspection of the equations of the lines, the point of intersection is (0, 14)
help asap! brainlist will be given!
Answers
for b, the answer would be 15 because as i explained before, the bigger segment is double the size of the smaller segment inside the figure
for c and d, i’m not so sure on the results
Jamar just got hired for a new job and will make $ 48 , 000 $48,000 in his first year. Jamar was told that he can expect to get raises of $ 3 , 500 $3,500 every year going forward. How much money in salary would Jamar make in his 18th year working at this job?
Answers
The amount of money Jamar will make in his 18th year working at this job is = $107,500
Calculation of yearly salary outcomeThe amount of money Jamar made in his first year= $48,000
The salary rise per year = $3,500
The amount of money he will make for the extra 17 years is = 17 × $3,500
= $59,500
Therefore the amount he will receive as his salary in the 18th year working at this job = $48,000 + $59,500
= $107,500
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Image attached! Please help, and explain because I don’t understand!
Answers
Answer:
64 (2) ^ n-1
I hope that this helps!
The admission fee at a water park is $9 for children and $15 for adults. On a certain day, 220
people entered the park, and the admission fees collected totaled $2640. How many children and
how many adults were admitted? Let x represent the number of children and y represent the
number of adults.
Total Equation:
Cost Equation:
The number of children admitted was
The number of adults admitted was
Answers
hope this helps :)