Mr. Donley drove 504 km in each direction on a vacation
trip. The average rate going was 14 km/h faster than the
rate returning. The total time for the entire trip was 21
hours. Find the average rate for each direction.
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.
Find the slope of the line that passes through (4,7) and (1,8)
Consider the diagram.
Lines AC and RS can best be described as
intersecting.
parallel.
perpendicular.
skew.
Answer:
Scew option D
Step-by-step explanation:
I have the same test
When lines are not parallel, and they do not intersect, such lines are said to be skewed.
Line AC and RS are skew.
From the diagram, we have two planes.
Plane x Plane yLine AC is on plane x, while line RS is on plane y.
This means that both lines are non-coplanar
Planes x and y are not parallel; so lines AC and RS are not parallel.
Using the condition of skewness stated above, we can conclude that line AC and RS are skew.
See attachment for plane x and plane y
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Six friends shared 79 trading cards and kept a record of how they did it. What does 13 represent? the answers are- The number of trading cards each friend ended up with The number of trading cards left after each friend got the same amount The number of trading cards left after each friend got 10 The number of friends sharing trading cards
Answer: The number of trading cards each friend ended up with
Step-by-step explanation:
Given that:
Total Number of trading cards = 79
Number of friends = 6
Number of trading cards each friend got of shared equally :
Total Number of trading cards / number of friends
= 79 / 6
= 13.166
Highest number of cards got by each = 13
Number left : 79 - (13 * 6) = 1
Hence, 13 represents the number of trading cards each friend ended up with
What is the probability he takes a yellow jellybean?
Answer: 3/20
Step-by-step explanation:
12/80 is simplified to 3/20
Answer: The answer is D
Step-by-step explanation: Add them all up and you get 80 then 12/80 divided by 4 is 3/20
what is the sum of the 18 and 42 as a product of their GCF.
Answer:
The answer is 6
Step-by-step explanation:
PLEASE HELP ME ANSWER DIRECTIONS ARE IN THE PIC PLEASE HELP ASAP!
How many cupcakes can I make with 16 cups of batter if I pour 2/3 Cup of batter into each cake?
Answer:
Step-by-step explanation:
16×2/3
32/3
104
A regular hexagon is inscribed in a circle with radius 9 cm. Find the area
Answer:
121.5sqrt(3)
Step-by-step explanation:
Ok, so all regular hexagons are made out of 6 equilateral triangles. If the hexagon is inscribed in the circle, the radius lines up with a side of one of the 6 equilateral triangles and you get 6 equilateral triangles with a side length of 9.
The formula for an equilateral triangle's area is (a/2)^2 * sqrt(3) where a = side length. That means we just plug in 9 to find the area of one of these six triangles. We get 20.25sqrt(3).
We multiply this by 6 (to find the sum of the areas of 6 equilateral triangles) and get 121.5sqrt(3)
The area of the hexagon will be 210.4 cm².
What is a hexagon?The definition of a hexagon in mathematics and geometry is a polygon with six straight sides that is closed in two dimensions.
Given, a circle with a radius of 9 cm. which have a regular hexagon whose all corner touch the circle. If we draw a radius of a circle at the corner of the hexagon. then we get six equilateral triangles.
A regular hexagon is 6 equilateral triangles of side r and area
Area of triangle = (r/2)(√3r/2)
so the total area is
A(hex ) = (6/4) √3r² = 3√3(r²)/2
r = 9m so
A = 210.4m²
Hence the Area of the given hexagon is 210.4 square meters.
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Which of the equations shown will have infinitely many solutions? Select the TWO that apply. A 3x−1=3x+13 x minus 1 is equal to 3 x plus 1 B 2x−1=1−2x2 x minus 1 is equal to 1 minus 2 x C 3(x−1)=3x−33 times open paren x minus 1 close paren is equal to 3 x minus 3 D 2x+2=2(x+1)2 x plus 2 is equal to 2 times open paren x plus 1 close paren E 3(x−2)=2(x−3)
Answer:
Step-by-step explanation:
Am equation with infinite number of solution means that the equation has uncountable solutions.
Let's analyse each options
For the expression 3x-1 = 3x+1
Collect like terms
3x-3x = 1+1
0x = 2
Divide both sides by 0
x = 2/0
x = infinity
This shows that the expression 3x-1 = 3x+1 has infinite number of solution
Also considering the third expression
3(x-1) = 3x+3
Open the parenthesis
3x-3 = 3x+3
Collect like terms
3x-3x = 3+3
0x = 6
x = 6/0.
x = infinity
Thus also shows that expression 3(x-1) = 3x+3 has infinite number of solution.
3x-1 = 3x+1
3(x-1) = 3x+3
Please help
8 square root 5 minus square root 45
Answer:
[tex]5 \sqrt{5 \: } is \: \: the \: \: answer \: \: of \: \: this \: \: question[/tex]
The mean and standard deviation for number of battery crimes in the U.S. from 1985 to 2000 are X = 326,845 and sx = 27,569. The mean and standard deviation for number of property crimes in the U.S. for the same time period are y = 634,235 and Sy = 42,268. The correlation coefficient is r = 0.92. Find the equation for the least- squares regression line for number of property crimes compared with number of battery crimes.
A: y = 1.41 + 173,214.37x
B: y = 173,214.37 + 1.41x
C: y = 421,052.69 + 0.65x
D: y = 0.65 + 421,052.69x
E: Unable to determine the equation
Answer:
The correct answer is: A
Step-by-step explanation:
The value of the slope and intercept is:
=0.92(42268/27569)
=1.410518
a=y-bx
=634235-1.410518×326845
=173214.3716
The eququation for the least-square regression line is:
y=173214.3716 + 1.4105518x
Round to the 2 decimal place:
=173,214.37 +1.41x
The equation for the least squares regression line for number of property crimes compared with number of battery crimes is (b) y = 141x + 173214.37
How to determine the least square regression equation?The given parameters are:
Mean x, μ = 326,845 Standard deviation of x, σ = 27,569Mean y, μ = 634,235 Standard deviation of y, σ = 42,268Correlation coefficient, r = 0.92Calculate the slope (m) using:
m = r * Sy/Sx
This gives
m = 0.92 * 42268/27569
Evaluate
m =1.41051761036
Approximate
m = 1.41
The y-intercept (c) is calculated using:
c = μy -m * μx
So, we have:
c = 634235 - 1.41051761036 * 326845
Evaluate
c = 173214.371642
Approximate
c =173214.37
The least-square regression line equation is represented as:
y = mx + c
So, we have:
y = 141x + 173214.37
Hence, the equation for the least squares regression line for number of property crimes compared with number of battery crimes is (b) y = 141x + 173214.37
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what is the midpoint between point A and B
Answer: (-1,4) is the answer
Does anyone know this?? Tysm
Answer:
D
Step-by-step explanation:
hope this helps
Plz help me
Last year, 75 new houses were built in a neighborhood. So far this year, 5/8 of them have been sold. How many new houses have been sold this year? Write your answer in simplest form.
152
Find the x of the angle
Intro:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
So first we will do 180-152 to get the measure of the angle besides the angle. That'll give us 28, then we know that those base angles of this mini triangle are congruent so we will do 28+28 to get 56. Now we will do 180-56 to get the last angle of the triangle, which is 124. And this angle is the same as the angle with x because they are corresponding angles so x is 124°.
Lines AB and CD are parallel. Find the measures of the three angles in triangle ABF.
What is the angle measurement for A, B, and F. (Make sure they are degrees)
Can you help me with this math question?
A = 42°
B= 23°
F = 115°
Step-by-step explanation:
The required measures of the three angles in triangle ABF are A = 23°, B = 42°, and F = 115°.
What are Alternate Interior Angles?Alternate Interior Angles are defined as the pair of angles created on the inner side of the parallel lines
Given that Lines AB and CD are parallel.
To determine the measures of the three angles in triangle ABF.
For finding ∠F,
∠CDF = 180° - 157° = 23°
∠F = 180° - ∠C - ∠CDF
∠F = 180° - 42° - 23°
∠F = 115°
However, if a transversal intersects two parallel lines, then each pair of alternate interior angles is equal.
So ∠A = ∠CDF = 23°
And ∠B = ∠C = 42°
Thus, the required measures of the three angles in triangle ABF are A = 23°, B = 42°, and F = 115°.
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A tape diagram. There are 65 students out of 100 students who ride the bus. There are question mark students out of 800 students who ride the bus. 65% of the 800 students at North High School ride the bus. How many students ride the bus? 100 multiplied by is equal to 800. 65 multiplied by is equal to . out of students ride the bus.
Answer:
answer one is 8
answer two is 8
answer three is 520
answer four is 520
answer five is 800
Step-by-step explanation:
There are 520 students out of 800 ride the bus,
65% of 800 is 520,
100 multiplied by 8 is 800.
What are ratios and proportions?The majority of the explanations for ratios and proportions use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion.
Given,
1: There are 65 students out of 100 students who ride the bus. There are question mark students out of 800 students who ride the bus.
let x student out of 800 rides the bus
so both conditions 65/100 and x/800 are in proportions,
65/100 = x/800
x = 800*65/100
x = 520
2: 65% of the 800 students at North High School ride the bus.
65% of 800 = 65/100 x 800
65% of 800 = 520
3: 100 multiplied by is equal to 800.
let x multiplied by 100 is 800
x*100 = 800
x = 800/100
x = 8
Hence 520 students out of 800 ride the bus,
65% of 800 is 520,
100 multiplied by 8 is 800.
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whats 1000000000000000000000000x10000000000000000000000000
Answer:
I think my calculator broke and it gave me 1e49
4(m+3)=36 what’s the value of m
Answer:
m=6
Step-by-step explanation:
4(m+3) = 36
4m + 12 = 36
4m + (12 -12) = (36 -12)
4m = 24
4m/4 = 24/4
m = 6
Mr. Brooks has $14.20 in his checking account, he uses
his debit card to buy four Sonic meal deals for $4.25 each. His
bank charges him a $20 overdraft fee for insufficient funds.
What is the new balance in Mr. Brooks’ checking account?
Answer:
-$22.80.
Step-by-step explanation:
The 4 meals cost 4.25 * 4 = $17 which gives him a new balance of
14.20 - 17 -20
= -$22.80.
1x+2x = what?
Will mark brainiest whatever that mean
Answer:
3x
Step-by-step explanation:
Answer:
3x
Step-by-step explanation:
1+2=3
so 1X+2x=3x
Is -6 greater than, less than, of equal too -4
Answer:
-6 in less than -4.
Answer:
-6 less than -4
Step-by-step explanation:
-6 is less because on the number line it will look like it's before -4
Hope this helps!!!
If y varies drectly with x
and y= 4.5 when x= 2.5,
what is y when x= 12?
$19.39÷12 I just need the answer asap
Answer:
$1.62
Step-by-step explanation:
(Why not use a calculator for this?)
Answer:
19.39 divided by 12 is
1.615 or 1.61583333
Mrs. Van and her family went bowling. The total cost of the shoes was $12 and the cost to bowl was $5 per game. Write an equation y, the cost of bowling and x the number of games they played.
y=5x+12
hope i could help!
Alecia placed the numbers 0, 2, 14, -8, and -11 on the number line. Which of the numbers is furthest from zero?
Answer:
14
Step-by-step explanation:
Write the equation of the line that passes through the given points.
(0,1) and (7,5)
It costs $7.20 for 6 large candy bars. How many candy bars can you buy for $13.20?
Answer:
11
Step-by-step explanation:
I divided 7.20 and 6 and got 1.2 so i did 13.20 divided by 1.2 and got 11
Answer: You can buy 11 candy bars.
Step-by-step explanation:
$7.20 =6
$7.20/6 =$1.20
$13.20/$1.20=11
what is 96-4.5y-3.2y=5.6y+42.80
PLEASE HELP!!!!