Answer:
Data that we know:
He drove 504km in each direction.
Going, the average speed was 14km/h more than returning.
The total trip lasted 21 hours.
Ok, to solve this first:
Let's define the variables:
Sg = Average speed when going.
Sr = Average speed when returning.
Then we can write one of our relationships as:
Sg = Sr + 14km/h.
Now, you can recall the relation:
Time = Distance/speed.
Then we can write the equation that represents the total time of the travel as:
504km/Sg + 504km/Sr = 21h
Now we can replace the Sg by Sr + 14km/h, and get:
504km/(Sr + 14km/h) + 504km/Sr = 21h.
Now we must multiplacate by each denominator, in order to remove them:
504km*Sr + 504km*(Sr + 14km/h) = 21h*Sr*(Sr + 14km/h)
Sr*1008km + 7056km^2/h = 21h*Sr^2 + 294km*Sr
Now we can write a cuadratic equation, where i will ignore the units so it is easier to read, as:
21*Sr^2 -714*Sr - 7056 = 0
The solutions are given by the Bhaskara formula:
[tex]Sr = \frac{714 +- \sqrt{714^2 - 4*21*(-7056)} }{2*21} = \frac{714 +- 1050}{42}[/tex]
We have two solutions, one negative and one positive, and because Sr represents an average speed, it must be a positive number, then we choose the positive solution:
Sr = (714 + 1050)/42 km/h = 42km/h
Now we have the average speed for the returning, with this we can find Sg.
Sg = Sr + 14km/h = 42km/h + 14km/h = 56km/h.
if the roof building is 46 feet off the ground and the floor of the basement is 15 feet under ground what is the total distance from roof to basement floor
Answer:
61
Step-by-step explanation:
46 then you have to add another 15 feet for underground and you get 61 because it is asking form the roof to the basement floor
hope this helps
When x = -3, then y = ?
Step-by-step explanation:
the answer is y=-6 when x=-3
If Hector is 8 years old and Mary is 3 years old, how old will Mary be when Hector is 16? Can I use proportional reasoning in here
Answer: Mary will be 11, and yes you can
Step-by-step explanation: hector will be 16 in 8 years so you just add the 8 on to the 3
Which expression is equivalent to 16.8 - 18.616.8−18.616, point, 8, minus, 18, point, 6? Choose 1 answer: Choose 1 answer: (Choice A) A 16.8-(-18.6)16.8−(−18.6)16, point, 8, minus, left parenthesis, minus, 18, point, 6, right parenthesis (Choice B) B -18.6+(-16.8)−18.6+(−16.8)minus, 18, point, 6, plus, left parenthesis, minus, 16, point, 8, right parenthesis (Choice C) C 18.6-16.818.6−16.818, point, 6, minus, 16, point, 8 (Choice D) D 16.8+(-18.6)16.8+(−18.6)
Given:
The expression is
[tex]16.8-18.6[/tex]
To find:
The expression which is equivalent to the given expression.
Solution:
We have,
[tex]16.8-18.6=-1.8[/tex]
In option A,
[tex]16.8-(-18.6)=16.8+18.6[/tex]
[tex]=35.4\neq -1.8[/tex]
In option B,
[tex]-18.6+(-16.8)=-18.6-16.8[/tex]
[tex]=-35.4\neq -1.8[/tex]
In option C,
[tex]18.6-16.8=1.8\neq -1.8[/tex]
In option D,
[tex]16.8+(-18.6)=16.8-18.6=-1.8[/tex]
Only the value of the expression in option D is equal to the value of given expression.
Therefore, correct option is D.
Please help me with this
Answer:
B.
[tex](x + 2) ^{3} - 9 [/tex]
help me answer this slope problem (10 points)
Find the equation of line b described below, in slope-intercept form
Line a is perpendicular to line b
Line a passes through the points (1,-8) and (9,-12)
Line b passes through the point (-8, -16)
The equation of line b is y= ______
Given:
Line a is perpendicular to line b .
Line a passes through the points (1,-8) and (9,-12) .
Line b passes through the point (-8, -16).
To find:
The equation of b.
Solution:
Line a passes through the points (1,-8) and (9,-12) . So, slope of line a is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m_a=\dfrac{-12-(-8)}{9-1}[/tex]
[tex]m_a=\dfrac{-12+8}{8}[/tex]
[tex]m_a=\dfrac{-4}{8}[/tex]
[tex]m_a=-\dfrac{1}{2}[/tex]
Product of slopes of two perpendicular lines is -1.
[tex]m_a\times a_b=-1[/tex]
[tex]-\dfrac{1}{2}\times a_b=-1[/tex]
[tex]b=2[/tex]
Slope of line b is 2.
If a line passing through a point [tex](x_1,y_1)[/tex] with slope m, then equation of line is
[tex]y-y_1=m(x-x_1)[/tex]
Line b passing through (-8,-16) with slope 2. So, equation of line b is
[tex]y-(-16)=2(x-(-8))[/tex]
[tex]y+16=2(x+8)[/tex]
[tex]y+16=2x+16[/tex]
Subtract 16 from both sides.
[tex]y=2x[/tex]
Therefore, the equation of line b is [tex]y=2x[/tex].
Jackson was solving the problem below for k. However, he made a mistake.
19 - 2k = 3k - 1
+3k +3k
19 +1k = -1
-19 -19
k = -20
Part A: Identify the FIRST mistake Jackson made.
Part B: Solve for k.
At the zoo, the ratio of elephants to hippos is 1.2. So for every elephant, there
are hippos
Answer:
2 hippos
Step-by-step explanation:
Answer:
For every elephant, there are 2 hippos.
Students surveyed boys and girls separately to determine which sport was enjoyed the most. After completing the boy survey, it was determined that for every 3 boys who enjoyed soccer, 5 boys enjoyed basketball. The girl survey had a ratio of the number of girls who enjoyed soccer to the number of girls who enjoyed basketball of 7: 1. If the same number of boys and girls were surveyed, and 90 boys enjoy soccer, how many girls enjoy each sport?
Ratio of boys who liked soccer to boys who liked basketball = 3:5
Given :-
Number of boys who enjoyed soccer :-
[tex]\color{hotpink} = \color{hotpink}90 \: \: \color{hotpink}boys[/tex]
Total number of boys who were surveyed were equal to the total number of girls who were surveyed .
Which means :-
Let the total number of boys who were surveyed be x .
Total number of boys =
[tex] = \frac{3}{8} \times x = 90[/tex]
[tex] = x = 90 \div \frac{3}{8} [/tex]
[tex] = x = 90 \times \frac{8}{3} [/tex]
[tex] = x = \frac{720}{3} [/tex]
[tex]\color{hotpink}x =\color{hotpink} 240[/tex]
Which means a total of 240 boys were surveyed .
Number of boys who liked basketball :-
[tex] = \frac{5}{8} \times 240[/tex]
[tex] = \frac{1200}{8} [/tex]
[tex]\color{hotpink} = 150 \: \: boys[/tex]
Which means a total of 150 boys liked basketball .
Number of girls who liked soccer :-
[tex] = \frac{7}{8} \times 240[/tex]
[tex] = \frac{1680}{8} [/tex]
[tex]\color{hotpink} = 210 \: \: girls[/tex]
A total of 210 girls enjoyed soccer .
Number of girls who enjoyed basketball :-
[tex] = \frac{1}{8} \times 240[/tex]
[tex] = \frac{240}{8} [/tex]
[tex]\color{hotpink} = 30 \: \: girls[/tex]
A total of 30 girls like basketball .
Therefore , 210 girls enjoyed soccer and 30 girls enjoyed basketball .
Ryan is taking a survey to find out how many people prefer soda A over soda B. He surveyed 100 people and forty-nine preferred soda A. Seven percent had no preference for soda A or soda B. What percentage of peoples surveyed preferred soda B?
Answer:
44%
Step-by-step explanation:
Please help me with this one I rly need it.ill give you Brainly if I can. 567/9
Answer:
66.3333333333 depending on the decimal point you'd go to
Which of the following expression are equivalent to -11/4?
Answer:
B
Step-by-step explanation:
The equivalent expression to - 11/4 is, - (-11/-4).
Option B is true.
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
Given that;
The fraction is,
⇒ - 11/4
Now, By option B;
The number is,
⇒ - (- 11/ - 4)
Multiply by - 1 in denominator and numerator,
⇒ - (- 1 × - 11 / - 1 × - 4)
⇒ - (11/4)
⇒ - 11/4
Thus, The equivalent expression is, - (-11/-4).
Learn more about the fraction visit:
https://brainly.com/question/5454147
#SPJ2
The complete question is this,
Which of the following expression are equivalent to -11/4?
A) - (11/ - 4)
B) - (-11/-4)
C) None of these
select all of the following expressions that are equivalent to 9 1/2
(1) 3 1/2 * 3 1/2 (2) sqrt[6]{27} (3) 27 1/3 * 3 1/2 (4) 81 1/2 * 81 1/2 (5) 729 1/6 (6) 81 1/3 * 81 1/3 (7) 81 1/4 * 81 1/4
(1)
(3)
(4)
I think im sorry if im wrong too
Solve for x when 4x+x+2=10x−13
Answer:
x = 3
Step-by-step explanation:
First lets add 4x + x so that we can get one x value on that side of the equation.
4x + x + 2 = 10x - 13
5x + 2 = 10x - 13
Then we can solve for x from there
5x + 2 = 10x - 13
-5x + 2 = -13 [Subtract 10x from both sides of the equation]
-5x = -15 [Subtract 2 from both sides of the equation]
-x = -3 [Simplify]
x = 3 [Simplify]
Hope this helps! I apologize if I got this incorrect
Answer: x = 3
Steps: 4x + x + 2 = 10x - 13
Combine like terms: 5x + 2 = 10x - 13
Subtract 2 from both sides: 5x + 2 - 2 = 10x - 13 - 2
Simplify: 5x = 10x - 15
Subtract 10x from both sides: 5x - 10x = 10x - 15 - 10x
Simplify: -5x = -15
Divide both sides by -5: -5x ÷ -5 = -15 ÷ -5
Simplify: x = 3
Plz mark brainliest:)
a and b are positive numbers.
a is inversely proportional to b.
when a=4,b=36
find value of a when b=a
Answer:
a = 12
Step-by-step explanation:
Given that a is inversely proportional to b then the equation relating them is
a = [tex]\frac{k}{b}[/tex] ← k is the comstant of proportion
To find k use the condition when a = 4, b = 36, then
4 = [tex]\frac{k}{36}[/tex] ( multiply both sides by 36 )
144 = k
a = [tex]\frac{144}{b}[/tex] ← equation of proportion
When b = a , then
a = [tex]\frac{144}{a}[/tex] ( multiply both sides by a )
a² = 144 ( take square root of both sides )
a = ± [tex]\sqrt{144}[/tex] = ± 12
However a is a positive number, thus a = 12
Lines s, t, and u are perpendicular bisectors of the sides of APGH and meet at J. If JG - 2x+ 2, JH - 2y-4, JF-8 and
HI - 32-3, find x, y, and z.
Ox= 5, y = 2, z = 2
O x = 2, y = 7,2 = 2
x = 3, y = 6,2 = 4
x = 6.) = 3,2 = 4
Answer:
x = 3, y = 6, z = 4
Step-by-step explanation:
If lines s, t, and u are perpendicular bisectors of the sides of APGH and meet at J, then JG = JH = JF = HI
Given
JG - 2x+ 2
JH - 2y-4
JF-8 a
HI - 3z-3,
Hence 2x+2 = 2y-4 = 3z-3 = 8
This means that
2x+2 = 8
2x = 8-2
2x = 6
x = 3
Also, 2y-4 = 8
2y = 8+4
2y = 12
y = 6
And 3z-3 = 8
3z = 8+3
3z = 11
z = 11/3
z = 3.67 ≈ 4
Hence x = 3, y = 6,z = 4
what is the slope of the line y= 20x
Answer: The Slope is 20
Step-by-step explanation:
M A T H W A Y . C o M
(2a-b-c)³+(2b-c-a)³+(2c-a-b)³ factorise
Answer:
Sowy but try Mathwa y
Step-by-step explanation:
helpppp!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! pleaseeeeeee
Answer:
Step-by-step explanation:
y= money earned , x is the number of hours
k is the constant=y/x=12
a- y=12 xb- if she worked 18 hours:
y=12(18)
y=216 dollarsc- if she earned 330 dollars:
330=12x
x=330/12
x=27.5 hours5x + 8 - 7x = -4x + 1
Choose 1 answer:
А
No solutions
Exactly one solution
Infinitely many solutions
Step-by-step explanation:
5x+8-7x=4x+1
5x+7x-4x=8+1
8x=9
HELPS ME SOLVE THIS PROBLEM PLEASE
Answer:
The third answer, y = 4x + 1
Step-by-step explanation:
Let's take the pair x = 2, and y = 9.
We know what x is, and what the result, y, is now.
Let's plug x into the third equation, y = 4x + 1
y = 4 * 2 + 1
y = 8 + 1
y = 9
We already know that y = 9, so this equation is correct.
Hope this helps!
(Let me know if you want to know why it's not any of the others.)
A group of people were asked if Marilyn Monroe had an affair with JFK. 184 responded "yes", and 387 responded "no". Find the probability that if a person is chosen at random, the person does NOT believes Marilyn Monroe had an affair with JFK.
Probability (round to 4 decimal places)
Answer:
0.6778 to 4 dec. places.
Step-by-step explanation:
That is 387 / (184+387)
= 387 / 571
= 0.677758
Which ordered pair is a solution to the system of inequalities
Y<3x-1
Y>|x-2|
A. (-2,0)
B. ( 0,1)
C. (4,4)
D. (3,-1)
Find the measures of the interior angles and please tell me all angles
Ryan and his brother are at a carnival. They separate from each other at the ferris wheel at 1:00 PM, and they agree that they will each meet back at the ferris wheel from time to time to see whether the other is ready to leave. Ryan checks the ferris wheel every 15 minutes. His brother checks in every 24 minutes. At what time will they meet at the ferris wheel again. (Hint: Don't forget you're looking for a time)
Answer:
3:00pmStep-by-step explanation:
The idea hear is to find the least common multiples of 15 and 24
Given that they separated at exactly 1:00pm
the multiples are
15= 15,30,45,60,75,90,105,120
24= 24, 48,72,96,120
the multiples common is 120
Therefore they will meet in 120minute, which is 2 hours time \
hence the time will be 3:00pm
An atom is neutral. Its nucleus contains two protons and two neutrons. How
many electrons does the atom have?
Answer:
2 electrons
Step-by-step explanation:
An atom is neutral if it has no charge. That means the positive and negative charge balance each other out.
There are two protons, so that is a charge of +2. To make the charge 0, there needs to be a charge of -2. -2= 2 electrons.
Answer:
Answer is 2
Step-by-step explanation:
Jimmy deposits $5000 into an account that pays 4.5% interest compounded weekly. How much would he have when he goes to withdraw his funds? There is not enough information to complete this problem. What part is missing if you are using the formula given below?
Answer: TIME
Step-by-step explanation: I cant see the formula, but I think the one you are using is Interest = (principal)(interest rate)(time). You have the interest rate and principal, but you need the amount of time to figure out how much he has earned.
please help me with this
Answer:
its yes
I'm fighting ransome cuz I need at least 20 characters
Find the rate of change from the given table