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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.

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.

Line 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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Answer: (-1,4) is the answer

Answer:

[tex]5 \sqrt{5 \: } is \: \: the \: \: answer \: \: of \: \: this \: \: question[/tex]

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

y=5x+12

hope i could help!

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°.

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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Answer:

I think my calculator broke and it gave me 1e49

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

Answer:

Step-by-step explanation:

16×2/3

32/3

104

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°.

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

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

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

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.

Answer:

14

Step-by-step explanation:

Answer:

1/12

Step-by-step explanation:

i did 3x4=12 so you only need 1/12

Answer:

The answer is 6

Step-by-step explanation:

Answer:

3x

Step-by-step explanation:

Answer:

3x

Step-by-step explanation:

1+2=3

so 1X+2x=3x

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.

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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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

Answer:

D

Step-by-step explanation:

hope this helps

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

The given parameters are:

Calculate 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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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.

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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