Complete question :
Mr. Sawyer drove his car from his home to New York at the rate of 45 mph and returned over the same road at the rate of 40 mph. If his time returning exceeded his time going by 30 min, find his time going and his time returning.
Answer:
T1 = 4
T2 = 4.5
Step-by-step explanation:
Difference in time = 0.5 hour
Time = distance / speed
Let distance = d
Time, T1 = d / 45
Time, T2 = d / 40
d/40 - d /45 = 1/2
(45d - 40d) / 100 = 2
45d - 40d = 900
5d = 900
d = 180
T1 = 180 /45 = 4 hours
T2 = 180 / 40 = 4.5 hours
SYSTEMS OF EQUATIONS WORD PROBLEM: The members of the city cultural center have decided to put on a play once a night for a week. Their auditorium holds 500 people. By selling tickets, the members would like to raise $3,350 every night to cover all expenses. Let d represent the number of adult tickets sold at $8.50. Let s represent the number of student tickets sold at $5.50 each. If all 500 seats are filled for a performance, how many of each type of ticket must have been sold for the members to raise exactly $3,350? At one performance there were two times as many student tickets sold as adult tickets. If there were 360 tickets sold at that performance, how much below the goal of $3,350 did ticket sales fall?
first question: Number of student's ticket(s) = 400
And number of adult's ticket(d) = 100
Second question: The goal of $3050 fell by $710
6) Two boats set off from X at the same
time (below). Boat A sets off on a bearing of 325° and with a velocity of
14 km/h. Boat B sets off on a bearing of 2350 with a velocity of 18 km/h.
Calculate the distance between the boats after they have been travelling
for 2.5 hours. Give your answer to the nearest metre.
A
N
X Х
B
Answer:
The distance between the two boats after 2.5 hours is 57 m.
Step-by-step explanation:
The distance covered by each boat after 2.5 hours are:
speed = [tex]\frac{distance}{time}[/tex]
distance = speed x time
For boat A, speed = 14 km/h and time = 2.5 hrs.
So that,
distance = 14 x 2.5
= 35 km
For boat B, speed = 18 km/h and time = 2.5 hrs.
So that,
distance = 18 x 2.5
= 45 km
The distance between the two boats after travelling 2.5 hours can be determined by applying the cosine rule. Let the distance be represented by x, so that:
[tex]a^{2}[/tex] = [tex]b^{2}[/tex] + [tex]c^{2}[/tex] - 2bc Cos A
[tex]x^{2}[/tex] = [tex]45^{2}[/tex] + [tex]35^{2}[/tex] - 2(45 x 35) Cos [tex]90^{o}[/tex]
= 2025 + 1225 - 3150 (0)
= 3250
x = [tex]\sqrt{3250}[/tex]
= 57.0088
x = 57.0 m
The distance between the two boats after 2.5 hours is 57 m.
Solve the system by substitution.
y =
-4x
y = x - 5
Answer:
x=-1
Step-by-step explanation:
thanks I'm done pls
Answer: 1,-4
Step-by-step explanation: I noticed there are no steps for this one so I will go ahead and put them.
-4x+x=x-5+-x
combine:
-5x/5=-5/-5
x=1
Substitute:
y=-4x(1)
y=-4
so we get 1,-4
PLEASE HELP THIS IS DUE TODAY!!
Answer:
254 in
Step-by-step explanation:
1 yard = 36 in
7 yards = 36 (7)
7 yards = 252
add 2
254 in
:)
Answer: 254 inches
Step-by-step explanation:
1 yard= 36 inches x 7 (yards) + 2 inches= 254 inches
The total cost of a vase of spring flowers at a flower shop depends on the number of flowers ordered. Each flower costs $2.50. Which equation represents the relationship between the total cost, y, to the number of flowers, x?
Answer:
D. y=2.50x
Step-by-step explanation:
Since the equation asks for the total cost of a vase of flowers (y) that goes on the left side. Each flower costs 2.50 and the flower shop depends on the number of flowers ordered, which makes it a variable. Therefore C is wrong because it has 2.50 as a constant.
The ending equation will be y = 2.50x
Written in context this means that the total cost of a vase of flowers is equal to the cost of each flower (2.50) by how many flowers are ordered.
I hope this helps!!
- Kay :)
I need help with this question
Answer:
it's 324
Step-by-step explanation:
divide 72 by 4 to get one side, then multiply the side by itself, 18 times 18
Graph the solution of the inequality on a number line. 2(x - 3) - 5x < x-2
Answer:
good luck with this, i have got a good mark in this lesson back then and i would gladly like to help you miss gilr
Step-by-step explanation:
Option D is representing the inequality 2(x - 3) - 5x < x-2 on the number line.
What is a number line?A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R."
It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.
Given that the inequality is 2(x - 3) - 5x < x-2. The inequality will be solved as,
2(x - 3) - 5x < x-2
2x - 6 - 5x < x - 2
-3x - 6 < x - 2
-3x - x < 6 - 2
-4x < 4
x > -1
The number line of the inequality is attached with the answer below.
To know more about number lines follow
https://brainly.com/question/28516910
#SPJ2
John and Tom invited 27 friends to make popcorn and watch an outdoor movie. Tom invited twice as many friends as John. How many did each brother invite? nice step by step work pls
Answer:
Step-by-step explanation:
Remark
You can do this with just 1 unknown.
John = x
Tom = 2x
Solution
x + 2x = 27 Combine the left
3x = 27 Divide by 3
3x/3 = 27/3
x = 9
Conclusion
John invited 9
Tom invited 18
Finding which number supports the idea that the rational numbers are dense in the real numbers?
Answer:
an integer between –11 and –10
a whole number between 1 and 2
a terminating decimal between –3.14 and –3.15
Step-by-step explanation:
Find the missing length of the triangle.
A = 3.4 cm
C = 1.6 cm
B = ?
Answer: b = 3
Step-by-step explanation:
1. a^2 + b^2 = c^2
2. 1.6^2 + b^2 = 3.4^2
3. 2.56 + b^2 = 11.56
4. 11.56-2.56 = b^2
5. 9 = b^2
6. 3 = b
Find x, the angle of depression from the top of a lighthouse that is 199 ft above water level to the waterline of a ship 1104 ft off shore. Round your answer to the nearest tenth of a degree.
Answer:
10.2°
Step-by-step explanation:
I'm not sure if my answer is correct and I'm not too good at explaining but I'll try.
The height of the triangle would be 199 ft and it's length would be 1104 ft. Since were looking for the angle of depression, the angle would obviously be outside of our triangle (as shown in the picture). The height and length wouldn't change at all so we can just label the imaginary lines with their corresponding measurements.
The angle that we're looking for is marked in the picture. Since we are given the opposite and the adjacent side, we can use the inverse of tan to figure out our angle, which is 10.2°.
You can also use the "Z" rule and our angle would be where it's shown in the third picture. Nothing would change because our opposite side would still be 199 ft and our adjacent side would still be 1104 ft.
I JUST NEED SOMEONE TO ANSWER THIS ONE QUESTION PLEASE!
Can a set of data have more than one line of best fit? Why or why not?
2 Answers. It is certainly possible (in mostly silly cases). For example, suppose you sample the same x value twice and get two experimental y values that differ. One such case might be getting the points (0,−1) and (0,1) if we sample x=0 twice.
Answer:
yes because for data you need more than one line.
Step-by-step explanation:
Brett needed to repair a window that sat 12 feet
high on a house. He has a 15 foot ladder. How far away
must he set the ladder from the base of the house for it
to reach the window exactly?
3 ft
65 ft
© 9 ft D 6 ft
the nth term of 17,29,41,53,65
Answer:
12n+5
Step-by-step explanation:
The difference is 12 so that means n is 12 and the +5 is what the number in the sequence is before 17
What is Ac Brainliest
Answer:
Ac is hypotenuse as c=90
Answer:
6
Step-by-step explanation:
let us call dc x
root(16+x2) =ac
root(25+x2)=bc
using the pytogoren theroum for traingle ABC we get
41+2x2=9 squared
41+2x2=81
2x2=40
x2=20
x=2 root 5
so then plugging the values in
you know ac=root(16+x2)
=root(36)
=6
Cole buys a new laptop for $335. He makes a down payment of $50 and pays the rest in 6 equal monthly payments, p. What equation represents the relationship between the cost of the laptop and Cole’s payments?
The measure of the sides of a triangle are 43, 72, and 91. Use the Pythagorean theorem to classify the triangles as acute, obtuse or right.
Answer:
i tjink its obtuse im not quite sure though im so sorty if its wrong.
find the 41st term of the arithmetic sequence
87, 89, 91
Answer:
167
Step-by-step explanation:
Its simple
2. ∠F and ∠S are supplementary angles, and ∠S is 99°. What is ∠F?
71°
The sum of supplementary angles is 180°.
=> < F+<S=180°
Given: <S=99°
•
•• <F+99°= 180°
<F= 180°-99°
<F= 81°
We have 6 face red cards (JQK x 2) and 16 black cards, so a total of 22 cards.The red face cards and the black cards numbered 2-9 are put into a bag. Four cardsare drawn at random without replacement. Find the following probabilities:
a) All 4 cards are red
b) 2 cards are red and two cards are black
c) At least one of the red cards is red.
d) All four cards are black
Answer:
I dont know
Step-by-step explanation:
only doing it for points
How many solutions will this equation have? 2(x + 4) = 2x + 8
Answer:
None
Step-by-step explanation:
This type of equation is a tautology, it will always be true
We want to see how many solutions does the given equation has.
We will see that the equation has infinite solutions.
The given equation is:
2(x + 4) = 2x + 8
To find how many solutions it has, we need to solve it, we first can distribute the product at the left to get:
2(x + 4) = 2x + 8
2x + 2*4 = 2x + 8
2x + 8 = 2x + 8
Note that we have the exact same thing in both sides, so the value of x can be any real number, and the equation will still be true.
This means that there are infinite solutions for the given equation.
If you want to learn more, you can read:
https://brainly.com/question/16797952
HELP ASAP 10) Determine the volume; just answer without the units
B
9.5 in.
3.75 in.
8 in.
Answer:
Volume is 285
Step-by-step explanation:
We start by calculating the area of the base
Mathematically, we have a rectangle as the base
So, the area of the base will be;
3.75 * 8 = 30
We now multiply this by the height to get the volume
we have this as:
30 * 9.5 = 285
3 friends want to go for a hike. (Level 4)They pack enough water to last for 6 hours. 3 more people join the hike.How long will their water last now?
Answer:
3 hours
Step-by-step explanation:
Because first 3 friends have water that last 6 hours when you double the amount of people you get less water, I don't speak good English to explain but you have to subtract 3 from 6 because 3 is amount of people that need water that lasts 6 hours and when you have more people you get less water sooooo you subtract 3 from 6.
Hope you understand!
What is the circumference of the following circle?
diameter=9cm
Answer:
The circumference of the following circle is 9π (around 28.274)
Step-by-step explanation:
The circumference can be found by using the following formula, where d is the diameter of the circle...
dπ = 9π ≈ 28.274
Prove that
cos 9°+sin 9°/cos9°-sin9° =cot 36°
plzz fasstttt i need to writw this!!!!!!!!!
Answer:
Step-by-step explanation:
LHS = (Cos9° + Sin9°) / (Cos9° - Sin9°)
Divide by Numerator and Denominator by Cos9°
LHS = (1 + Tan9°) / (1 - Tan9°)
= (Tan 45° + Tan 9°) / (1 - Tan 45° * Tan 9°)
= Tan (45°+9°)
= Tan 54°
= Cot 36°
hope it helps :)
Question 9 options:
Review the diagram below.
Apply the properties of angles to solve for the missing angles.
Angle x is
Answer:
Angle X is 122°
Step-by-step explanation:
Because it's a 180° line (supplementary angle thm):
180°-58°=122°
Answer:
y = 62
x = 122
Step-by-step explanation:
58 + 60 = 118
118 - 180 = y
118 - 180 = 62
y = 62
x = 180 - 58 = 122
the image is the problem:
ty :P
Write down the next two terms in this number pattern
2, 5, 9, 14, 20,0
Answer:
+3,+4,+5,+6,-20
Step-by-step explanation:
its:
2+3=5
5+4=9
9+5=14
14+6=20
20- 20=0
i believe so
peter weighs 8kg heavier than Ailen.If 5/7 of Peter weight is 35kg,what is their total weight?
5/7 = 35 kg
1/7 = 7 kg
Peter weighs 49 kg
49 - 8 = 41 kg
Ailen weighs 41 kg
49 + 41 = 90kg
Their total weight is 90 kg
Dustin Ambrose is married and claims 3 allowances. His gross weekly pay is $628.00. Each week he pays federal, Social Security, and Medicare taxes, $52.00 for medical insurance, and $23.50 toward his retirement fund.
Answer:
еиниемксцчуиетнмкчеимусцсуиеи