Complete question is;
Zac and Lynn are each traveling on a trip. So far, Zac has traveled 123.75 miles in 2.25 hours. Lynn leaves half an hour after Zac. So far
she has traveled 105 miles in 1.75 hours. Assume Zac and Lynn travel at constant rates.
Let a represent the number of hours that have elapsed since Zac started traveling. Let y represent the number of miles traveled. Write a system of linear equations that represents the distance each of them has traveled since Zac left on his trip.
Assume Zac and Lynn continue to travel at the same constant rates and make no stops.
Determine the solution of the system of linear equations.
Answer:
Zac: y = 55a
Lynn: y = 60(a - ½)
6 hours after Zac started traveling, both Zac and Lynn would have covered 330 miles each.
Step-by-step explanation:
Zac has traveled 123.75 miles in 2.25 hours. Since he travels at constant speed, we can say;
zac's speed = 123.75/2.25 = 55 mi/hr
Similarly, Lynn traveled 105 miles in 1.75 hours. Thus, since she travels at a constant speed;
Lynn's speed = 105/1.75 = 60 mi/hr
Now, we are told that a represents the number of hours that have elapsed since Zac started traveling and y represents the number of miles traveled.
Thus;
a hours after Zac started travelling, his distance covered will be;
Zac: y = 55a
Now,for Lynn, since she started ½ an hour after Zac, it means a hours after Zac started, she had traveled (a - ½) hours.
Thus, Lynn's distance traveled after Zac started = 60(a - ½)
Lynn: y = 60(a - ½)
The solution will be when they have travelled equal distances a hours after Zac started. Thus;
55a = 60(a - ½)
55a = 60a - 30
60a - 55a = 30
5a = 30
a = 30/5
a = 6 hours
Putting 6 for a in y = 55a, we have;
y = 55 × 6
y = 330 miles
The graph shows the relationship between the distance a car is driven and the number of gallons of gasoline used. Identify the value in d in the point (1, d). What does that point represent?
A. d=25; the unit rate is 25 miles per gallon
B. d=25; the unit rate is 25 gallons per mile
C. d=50; the unit rate is 50 miles per gallon
D. d=50; the unit rate is 50 gallons per mile
Answer:
A. d = 25; the unit rate is 25 miles per gallon
Step-by-step explanation:
The point (1, d) on the graph represents (x, y), where,
x = gasoline used = 1 gallon
y = distance = d = 25 miles
That is, (1, d) represents when x = 1, y = 25.
Thus, (1, 25) is the unit rate which is 25miles per gallon.
Simplify: (3y^4 - 2y^2 + 3y - 2) - (-4y^4 - 2y^2+ 3)
Answer:
7y^4+3y-5
Step-by-step explanation:
What is the solution to the inequality 7x + 2 < -3x + 1?
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Answer:
and DJ ssksb did did isbn dhe9susaew7s ene 8th box hcm box bro sb d
Step-by-step explanation:
ishdbd works zjsbdjs s nsie djsid
The first second and fourth terms of a proportion are 6, 18 and 25 respectively. Find
its third term.
Answer:
The third term is 25/3
Explanation:
According to the given proportion,
→ First term : second term : : third term : fourth
→ 6 : 18 : : third term : 25
→ 6/18 = third term/25
→ 6*25/18 = third term [multiplying both sides by 25]
→ 1*25/3 = third term
→ 25/3 = third term.
150% as a simplified fraction
Answer:
It would be 3/2 as 1/2 is 50%, 2/2 or 1 is 100% and 3/2 is 150%
Step-by-step explanation:
The weight of the load varies
directly with the number of boxes
in the load. A load of 18 boxes
weighs 600 lbs. What does a load
of 12 boxes weigh?
The weight varies directly with the number of boxes, so this means every box weighs the same amount.
Find the weight of a box by dividing the known weight by the number of boxes:
600 pounds / 16 boxes = 37.5 pounds per box.
Now multiply the weight per box by the number of boxes:
37.5 pounds x 12 boxes = 450 pounds
12 boxes weigh 450 pounds
factor 3a^5-18a^3+6a^2, I know the answer is 3a^2(a^3-6a+2) but I am so lost on how to get the factor of 3a^2..How in the world do you get the exponent for the factor
Answer:
[tex]\huge\boxed{3a^2(a^3-6a+2)}[/tex]
Step-by-step explanation:
[tex]\sf 3a^5-18a^3+6a^2\\\\HCF = 3a^2\\\\Take \ 3a^2 \ common\\\\= 3a^2(a^3-6a+2)\\\\\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Find the nth term of the following arithmetic sequence.
f(1) = -7, d=3, n = 17
Answer:
f(n)=17+3(n-1)
f(17)=65
Step-by-step explanation:
arithmetic sequences are in form:
f(n)=f(o)+d(n-1)
f(1)=17=f(0)
f(n)=17+3(n-1)
f(17)=17+3(16)=65
Help pls! Need by 2 pm est time. Just do number 2 pls
Answer:
7 feet
Step-by-step explanation:
I hope my answer is correct!
A woman wishes to rent a house within 9 miles of her work. If she lives x miles from her work, her transportation cost will be cx dollars per year, while her rent will be 4c/( x + 1) dollars per year, where c is a constant taking various situational factors into account. How far should she live from work to minimize her combined expenses for rent and transportation? Use the methods outlined in this section to find the minimum.
Answer:
the woman has to live 1 mile from work to minimize the expenses
Step-by-step explanation:
Given the data in the question;
the distance within 9 miles ⇒ 0 < x > 9
Total costs Q = cx + 4c/( x + 1)
costs should be minimum ⇒ dQ/dx = 0
⇒ d/dx [ cx + 4c/( x + 1) ] = 0
⇒ ( x + 1)² = 4
take square root of both side
√[ ( x + 1)² ] = √4
x + 1 = 2
x = 2 - 1
x = 1
Therefore, the woman has to live 1 mile from work to minimize the expenses
If triangle ABC is similar to triangle PQR, find the value of x and y.
Answer:
x = 9
y = 6
Step-by-step explanation:
ΔABC ~ ΔPQR
Therefore, corresponding sides of these similar triangles will be in the proportional.
[tex]\frac{AB}{PQ}=\frac{BC}{QR}= \frac{AC}{PR}[/tex]
[tex]\frac{6}{x}= \frac{4}{y}= \frac{8}{12}[/tex]
[tex]\frac{6}{x}= \frac{8}{12}[/tex]
x = [tex]\frac{12\times 6}{8}[/tex]
x = 9
Similarly, [tex]\frac{4}{y}= \frac{8}{12}[/tex]
y = [tex]\frac{12\times 4}{8}[/tex]
y = 6
Someone please help me answer this
Answer:
2^10
Step-by-step explanation:
When multipying indices, if the base is the same then just add the indices.
A partially completed equation for a line is shown below. If the line passes through the point (-4, 6). Write the equation for the line.
y=-3x+by=−3x+b
Answer:
Nice
Step-by-step explanation:
Karma..... ;)
Write a positive or negative integer that represents the situation.
The temperature falls 14 degrees.
An integer that represents the situation is what?
Answer:
im not sure sorry! lol
Step-by-step explanation:
sorry!
Divide using long division.
8x3 - 18x2 + 21x - 20 = 2x - 3
Answer:
[tex] \frac{29}{19} [/tex]
Step-by-step explanation:
Hopefully that is correcr
The area of the triangle below is 8.91 square inches. What is the length of the base?
2.2 in is the height will mark BRAINLIEST!!!!!!
Find the length of the third side. If necessary, round to the nearest tenth.
24
14
Answer:
The answer is 19.49
Step-by-step explanation:
Hope this help you
Answer:
19.5
Step-by-step explanation:
19.49= 19.5
because of the nearest tenth
I need help please it’s due tomorrow
Answer:
<E(it is obtuse), <C, <D
The angle opposite to the longer side is greater than the angle opposite to the shorter side
^^for the second one use the same logic <C, <B, <A
A 12-sided die is rolled. The set of equally likely outcomes is \ 1.2.3.4.5.6.7.8.9.10.11.12) . Find the probability of rolling a 9
Answer:
1/12
Step-by-step explanation:
Calvin paints pictures and sells them at art shows. The charges $56.25 for a large painting. He charges $25.80 for a small painting. Last month he sold six large paintings and three small paintings. How much did he make in all?
Answer:
He made $414.90 in all.
Step-by-step explanation:
56.25 * 6 = $337.50
25.80 * 3 = $77.40
77.40 + 337.50 = $414.90
My little cousin took a STAR math test and she wanted to know if her score is good she got a 923 score on her STAR math test and she is in 8th grade did she do good or? She was really curious and wanted me to answer this question lol
I guesse she did pretty good lol :D
Extra Example 3: Hazel has $23.28 in her purse. She has $5.60 more than Nixon.
Paul says that Nixon has $28.88. Yolanda says that Nixon has $17.68. Who is
correct?
Answer:
Yolanda is correct.
Step-by-step explanation:
If Hazel has $23.28 and $5.60 more than Nixon, then Nixon will have $17.68 because 23.28-5.60 is 17.68.
The only way Paul would be right is if Nixon has $5.60 more than Hazel because 23.28+5.60 is 28.88.
Pls help me pls i will mark brainliest
Answer:
The line cannot be extended to any point since we are trying to graph a zero that is equivalent to absolutely nothing
Step-by-step explanation:
choose as brainliest
I need help, this is homework due in a few minutes
The y-intercept is -6
It opens down.
Insert 4 geometric means between 6
and 92
Answer:
6 23.2 40.4 57.6 74.8 92
Step-by-step explanation:
92-6 = 86
86/5 spaces = 17.2 each
can somebody plllllzzzzzzzzzzz help me with this-2 (x + 4 + 5y)
Answer:
-2x -8-10y
Step-by-step explanation:
-2 (x + 4 + 5y)
distribute
-2x -8-10y
A line's graph is shown. Write an equation for the line.
Answer:
Step-by-step explanation:
the equation for the line is y = 4
Which one, please?!
Quickly!
Answer:
c) FJ and GH
Step-by-step explanation:
Radius of sphere js 6 centimeters what is volume
the equation for volume of sphere is 4/3 x π x r^3
so just put the numbers in
4/3 x π x 6^3
= 288 π cm^3
Answer:
The volume of a sphere is given as
4/3 πr^3
There is only one variable, the radius, which we are given in the problem.
since the radius is 6 cm, we can plug that in to the formula
4/3 π6^3
Put this into the calculator, and we see that the volume is 904.8cm rounded to the nearest tenth.
Step-by-step explanation:
Hope it is helpful....
cogenuity Quiz
Find the value of 6^3.
OA) 6
ОВ) 36
OC) 72
OD) 216
Answer: OD) 216
Step-by-step explanation: 6^3 multiple it three times 6x6x6=216