Train A traveled 173 miles in five hours. For Train B, y = 31.35x represents its rate of speed over the same five hours. Analyze the date to determine which train traveled at a faster rate and by what factor? (round to nearest tenth)

Answer: [tex]27a^6[/tex]

Step-by-step explanation:

The question is not clear. So, assuming that the expression you need to simplify is this one:

[tex](3a^2)^3[/tex]

You need to remember a property called "Power of a power property". This property states the following:

[tex](b^m)^n=b^{(m*n)}=b^{(mn)}[/tex]

Therefore, you need to apply the Power of a power property explained before, in order to simplify the expression provided in the exercise, multiplying the exponents inside the parentheses by the exponent outside of the parentheses. Then:

[tex](3a^2)^3=3^{(1*3)}a^{(2*3)}=3^3a^6[/tex]

Now, you must remember that:

[tex]3^3=3*3*3=27[/tex]

Finally, you get:

[tex]=27 a^6[/tex]

Answer:

D

Step-by-step explanation:

Please look at the attached picture for full solution.

Method 1 is using the shoelace method to find the area of the rectangle. Shoelace method can be used to find the areas of any polygons given their coordinates. The coordinates have to be taken in an anticlockwise order and ending with the first coordinate.

Method 2 is making use of the distance formula of two points. The formula is as shown below:

[tex] \sqrt{(x1 - x2) ^{2} + (y1 - y2)^{2} } [/tex]

Having found the distance of the length and breadth of the rectangle, you can now find its area since area of rectangle= length × breadth.

Answer:

V=(4/3)πr^3

Step-by-step explanation:

This is the equation to find the volume of a sphere

V=(4/3)πr^3

than plug in 6 for x, and solve

The volume of a sphere with a radius of 6 units is represented by the expression [tex]\frac{4}{3}[/tex] πr³, which calculates to V = [tex]\frac{4}{3}[/tex] π(6)³, cubic units. If two such spheres combine, the volume doubles, and the new radius is the cube root of the new volume.

The expression that represents the volume of a sphere with a given radius in cubic units is given by the formula V = [tex]\frac{4}{3}[/tex] πr³. For a sphere with a radius of 6 units, you can substitute the value of the radius into this formula to calculate the volume.

The calculated volume V would be V = [tex]\frac{4}{3}[/tex] π(6)³, which simplifies to V = [tex]\frac{4}{3}[/tex] π(216), or V = 288π cubic units. Therefore, the volume of the sphere is 288 times π cubic units.

x will represent the number of tickets.

y will represent the fixed fee given by the ticket agency

6x + y = 135

3x + y = 75

To solve, we can use the process of elimination by multiplying the second equation by -2 so that 6y will cancel:

-6x - 2y = -150

+6y + y = 135

Now we simplify by adding/subtracting:

-y = -15 or y = 15

Plug the value of y into any of the two equations and solve for x. I will use the second equation:

3x + 15 = 75

3x = 60

x = 20

To set this up in slope intercept form (y = mx + b), we need to identify what m and b are.

m is x because it is not a fixed number, and b is y because it is a fixed number (price of “fixed” fee). This brings us to y = 20x + 15

Answer: [tex]=24+(1+92)[/tex]

Step-by-step explanation:

For this exercise you need to remember a property called "Associative Property".

The Associative Property states that it does not matter how you group the numbers, because you will always obtained the same result.

For Additiion, the Associentive property states the following:

[tex]a + (b + c) = (a + b) + c[/tex]

Where "a", "b" and "c" are Real numbers.

In this case you have:

[tex](24+1)+92[/tex]

As you can notice, the number 24 and the number 1 are grouped inside the parentheses, but you can also regroup the numbers 1 and 92 using parentheses and you will have the same result.

Therefore, based on the Associative Property explained before, you can conclude that:

[tex](24+1)+92=24+(1+92)[/tex]

Answer:

Equation: [tex]8.5t+6.5=57.5[/tex]

Solution: [tex]t=6[/tex]

Step-by-step explanation:

Let be "t" the number of movie tickets bought by the group of friends.

According to the information given in the exercise, the price of each movie ticket is: $8.50.

Then, you can represent the amount (in dollars) the group of friends spent in movie tickets, with this expression:

[tex]8.5t[/tex]

You know that one person spent $6.50, then the expression that represents the total amount (in dollars) the group of friends spent in food and movie tickets, is:

[tex]8.5t+6.5[/tex]

Since that total amount spent is given in the exercise, you can write the following equation to determine how many tickets were bought:

[tex]8.5t+6.5=57.5[/tex]

Finally, you can solve for "t" in order to find the solution of the equation. This is:

[tex]8.5t=57.5-6.5\\\\t=\frac{51}{8.5}\\\\t=6[/tex]

Final answer:

The group purchased 6 movie tickets. The equation formulated to determine this is t × $8.50 + $6.50 = $57.50, where t stands for the number of tickets. Subtracting the food cost and dividing the remainder by the ticket cost gives us the answer.

Explanation:

To determine how many movie tickets were bought by the group, we can set up the following equation:

t × $8.50 + $6.50 = $57.50

Here, t represents the number of tickets. The cost of one movie ticket is $8.50 and the cost of the food is $6.50. The total amount spent by the group is $57.50.

To solve for t, subtract the cost of the food from the total amount:

$57.50 - $6.50 = $51

Now divide the remaining amount by the cost of one ticket to find the number of tickets:

$51 ÷ $8.50 = 6

Therefore, the group purchased 6 movie tickets.

Answer:

i) the value of a = 0 is non-permissible

ii) the value of b = 0 is non-permissible

Step-by-step explanation:

i) the given expression is [tex]\frac{5a^{2} + 80a }{50ab^{2} }[/tex]

ii) if a = 0 then the expression will become infinity hence the value of a = 0 cannot be used

iii) if b = 0 then the expression will become infinity, hence the value of b = 0 also cannot be used.

iv) In the numerator of the expression if it is factorized we get 5a[tex]\times[/tex] ( a + 16)

    if a = -16 then the value of the expression becomes zero.

Answer:

The answer is the first choice: 10x - 12 + x + 10x - 12 + x

Step-by-step explanation:

Let the length of a table 2.5x - 3 and let the width of the table be x.

Four tables with identical dimensions are placed together.

So we can say that width of the new table formed by placing the four tables side to side will be the same as the width of one table, that is x.

And the two sides of the new table which will represent the width will be the width of one table at one end and the width of the table at the other end, that is x + x.length

Now as we saw before there are are two widths which are part of the perimeter there are also two lengths which are part of the perimeter.

The perimeter of a table is given by (2 × length) + (2 × width).

Now one length of the new table will be equal to (4 × length of one table) = 4 × (2.5 x - 3) = 10x -12

Therefore perimeter of the new table is given from the formula of the perimeter = Length + width + Length + width

     =   10x - 12  + x  +  10x -12 + x

Answer:

Last one is your answer

Step-by-step explanation:

It is equal to 0..... it is

Step-by-step explanation:

yes

Final answer:

Demand is considered inelastic when the elasticity of demand is less than one, signifying that consumers are less responsive to price changes.

Explanation:

When discussing the elasticity of demand, it is important to understand how demand responds to changes in price. If the elasticity of demand is less than one, this is known as inelastic demand. In this scenario, a 1 percent increase in the price that consumers pay will lead to a less than 1 percent change in the quantity purchased, showing a low responsiveness to price changes.

Conversely, demand is considered elastic when elasticity is greater than one, showing high responsiveness to price changes. If elasticity is exactly one, it is referred to as unitary elasticity, indicating that the percentage change in quantity demanded is equal to the percentage change in price.

Answer:

The answer is 9 on edgggggggggggg

Step-by-step explanation:

Based on the information given, the value of h is 9.

Firstly, it should be noted that the sum of the angles that are on a straight line is 180°.

In this case, we'll have to equate both values that are given and this will be:

3h + 18° + 15h = 180°

Collect like terms

3h + 15h = 180° - 18°

18h = 162°

Divide both sides by 18

18h/18 = 162°/18

h = 9

Therefore, the value of h will be 9

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Answer:

3x-5y

Step-by-step explanation:

Combine like terms

To simplify the expression 13x + 2y - 10x - 7y, combine the like terms together. The simplified expression is 3x - 5y.

To simplify the expression 13x + 2y - 10x - 7y, combine the like terms together. Start by combining the x terms and then combine the y terms.

13x - 10x = 3x

2y - 7y = -5y

Therefore, the simplified expression is "3x - 5y."

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Answer:

A function and its inverse

Step-by-step explanation:

The property (fg)(x)= x holds for a function and its inverse.

For instance:

Let

[tex]f(x) = 2x[/tex]

and

[tex]g(x) = \frac{x}{2} [/tex]

These two functions are inverse of each other.

[tex]f(g(x)) = 2( \frac{x}{2} ) = x[/tex]

The correct pair is B: [tex]\(f(x)=\frac{2}{x}\) and \(g(x)=\frac{2}{c}\)[/tex], satisfying [tex]\((f \circ g)(x)=x\).[/tex]

To find which pairs of functions satisfy the condition [tex]\((f \circ g)(x) = x\),[/tex] let's compute [tex]\(f(g(x))\)[/tex] for each pair of functions and see if it equals [tex]\(x\).[/tex]

A. [tex]\(f(x) = x^2\) and \(g(x) = \frac{1}{x}\):[/tex]

[tex]\[f(g(x)) = f\left(\frac{1}{x}\right) = \left(\frac{1}{x}\right)^2 = \frac{1}{x^2}\][/tex]

[tex]\(f(g(x)) \neq x\),[/tex] so option A is not correct.

B. [tex]\(f(x) = \frac{2}{x}\) and \(g(x) = \frac{2}{c}\):[/tex]

[tex]\[f(g(x)) = f\left(\frac{2}{c}\right) = \frac{2}{\frac{2}{c}} = c\][/tex]

[tex]\(f(g(x)) = x\)[/tex] if [tex]\(c = x\).[/tex] So, option B is correct.

C. [tex]\(f(x) = \frac{x - 2}{3}\) and \(g(x) = 2 - 3x\):[/tex]

[tex]\[f(g(x)) = f(2 - 3x) = \frac{(2 - 3x) - 2}{3} = \frac{-3x}{3} = -x\][/tex]

[tex]\(f(g(x)) \neq x\)[/tex], so option C is not correct.

D. [tex]\(f(x) = \frac{1}{2x - 2}\) and \(g(x) = \frac{1}{2x + 2}\):[/tex]

[tex]\[f(g(x)) = f\left(\frac{1}{2x + 2}\right) = \frac{1}{2\left(\frac{1}{2x + 2}\right) - 2}\][/tex]

[tex]\[= \frac{1}{\frac{1}{x + 1} - 2}\][/tex]

[tex]\[= \frac{1}{\frac{1 - 2(x + 1)}{x + 1}}\][/tex]

[tex]\[= \frac{1}{\frac{-2x - 1}{x + 1}}\][/tex]

[tex]\[= \frac{x + 1}{-2x - 1}\][/tex]

[tex]\(f(g(x))\)[/tex] does not simplify to [tex]\(x\)[/tex], so option D is not correct.

Thus, the correct answer is option B: [tex]\(f(x) = \frac{2}{x}\) and \(g(x) = \frac{2}{c}\).[/tex]

Complete Question:

For which pairs of functions is (fg)(x)=x?

A. f(x)=x^2 and g(x)=1/x

B.f(x)=2/x and g(x)=2/c

C. f(x)=x-2/3 and g(x)=2-3x

D. f(x)=1/2x-2 and g(x)=1/2x+2

Answer:

=5x+3

Step-by-step explanation:

Hope this helps!

Answer:

annnnnnn

Step-by-step explanation:

u r wronggggggggggggggggggggggggggg

Nina makes 11.25 per hour.

Step-by-step explanation:

Given,

Number of hours worked by Nina = 32 hours

Amount earned by Nina = 360

Let,

x represent the amount earned by Nina per hour.

Amount per hour * Number of hours = Amount earned

[tex]32*x=360\\32x=360[/tex]

Dividing both sides by 32

[tex]\frac{32x}{32}=\frac{360}{32}\\x=11.25[/tex]

Nina makes 11.25 per hour.

Keywords: variable, equation

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The perimeter of triangle ABC can be calculated by adding the distance between points A and B, B and C, and A and C. The respective distances are roughly 5, 4.12, and 5.1, thus, the estimated perimeter of the triangle is 14.22.

To calculate the approximate perimeter of a triangle given its vertices, one should first calculate the distance between each pair of vertices. In the context of the triangle △ABC with vertices at A(3,4), B(−1,1), and C(−2,5), the distance formula, which stems from the Pythagorean Theorem, is applied. The formula is as follows: D = √[(x2-x1)² + (y2-y1)²].

For the distance between A and B, the formula would play out as follows: D = √[((-1)-3)² + (1-4)²] = √[16 + 9] = √25 = 5.

For AB to C, the calculation would be: D = √[((-2)-(-1))² + (5-1)²] = √[1+16] = √17 ≈ 4.12

For AC: D = √[((-2)-3)² + ((5-4)²] = √[25 + 1]= √26 ≈ 5.1.

Essentially, you sum these distances up to get the perimeter, which in this case is approximately: 5 + 4.12 + 5.1 = 14.22

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To find the approximate perimeter of triangle ABC, we use the distance formula to calculate the lengths of the sides.

To find the approximate perimeter of triangle ABC, we need to calculate the distances between its vertices. Using the distance formula, we can calculate the length of each side.

Side AB: sqrt((3-(-1))^2 + (4-1)^2) = sqrt(16+9) = sqrt(25) = 5

Side BC: sqrt((-1-(-2))^2 + (1-5)^2) = sqrt(1+16) = sqrt(17)

Side AC: sqrt((3-(-2))^2 + (4-5)^2) = sqrt(25+1) = sqrt(26)

The perimeter of triangle ABC is approximately 5 + sqrt(17) + sqrt(26).

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Answer:

I believe the answer to this question is: 1 x 10^21 equal to 1000000000000000000000.

Answer:

Slope [tex]\dfrac{20}{3}[/tex]

y-intercept [tex]\dfrac{10}{3}[/tex]

Equation [tex]y=\dfrac{20}{3}x+\dfrac{10}{3}[/tex]

150 miles traveled

Step-by-step explanation:

The line shown on the diagram passes through the points (4,30) and (7,50). Find the slope of the line:

[tex]\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{50-30}{7-4}=\dfrac{20}{3}[/tex]

The equation of the line is

[tex]y-30=\dfrac{20}{3}(x-4)\\ \\y=\dfrac{20}{3}x+\dfrac{10}{3}[/tex]

Hence, y-intercept is [tex]\dfrac{10}{3}[/tex]

When [tex]x=22,[/tex] then

[tex]y=\dfrac{20}{3}\cdot 22+\dfrac{10}{3}=\dfrac{440+10}{3}=150\ miles[/tex]

The diameter of hemisphere is 61.4 units

Solution:

Given that, volume of hemisphere is 60570 cubic units

To find: Diameter of hemisphere

The formula for volume of hemisphere is given as:

[tex]V = \frac{2}{3} \pi r^3[/tex]

Where, "r" is the radius of hemisphere

Substituting the values we get,

[tex]60570 = \frac{2}{3} \times 3.14 \times r^3\\\\60570 = 2.093 \times r^3\\\\r^3 = \frac{60570}{2.093}\\\\r^3 = 28939.32\\\\\text{Take cube root on both sides }\\\\r = \sqrt[3]{28939.32} \\\\r = 30.7017248 \approx 30.7[/tex]

We know diameter is twice of radius

[tex]Diameter = 2 \times radius\\\\Diameter = 2 \times 30.7\\\\Diameter = 61.4[/tex]

Thus diameter of hemisphere is 61.4 units

The diameter of the hemisphere is [tex]\( 60.2 \, \text{cm} \)[/tex].

To find the diameter of a hemisphere with a volume of [tex]\( 60,570 \, \text{cm}^3 \)[/tex], we can follow these steps:

Step 1: Write a hemisphere's volume formula.

A hemisphere's volume (V) is determined by:

[tex]\[ V = \frac{2}{3} \pi r^3 \][/tex]

where ( r ) is the radius.

Step 2: Set up the equation with the given volume

Given [tex]\( V = 60,570 \, \text{cm}^3 \)[/tex], we substitute into the formula:

[tex]\[ 60,570 = \frac{2}{3} \pi r^3 \][/tex]

Step 3: Find the value of [tex]\( r^3 \)[/tex]

First, isolate [tex]\( r^3 \)[/tex]:

[tex]\[ r^3 = \frac{60,570 \times 3}{2 \pi} \][/tex]

Step 4: Calculate the value inside the equation

[tex]\[ r^3 = \frac{181,710}{2 \pi} \approx \frac{181,710}{6.2832} \approx 28,931.89 \][/tex]

Step 5: Solve for ( r )

Take the cube root of both sides to find ( r ):

[tex]\[ r = \sqrt[3]{28,931.89} \approx 30.1 \][/tex]

Step 6: Calculate the diameter

Two times the radius is the diameter (D):

[tex]\[ D = 2r \approx 2 \times 30.1 = 60.2 \][/tex]

Thus, the diameter of the hemisphere is [tex]\( 60.2 \, \text{cm} \)[/tex].

Complete Question:

What is the diameter of a hemisphere with a volume of 60570 [tex]cm^{3}[/tex] , to the nearest tenth of a centimeter?

Answer:5y+5

Step-by-step explanation:

2+y+y+y+y+y+3

Collect like terms

y+y+y+y+y+3+2

5y+5

Answer:

TV is 3 inches tall.

Step-by-step explanation:

Given: Diagonal length of TV is 5 inch

            Width of TV is 4 inches.

Considering TV to be in rectangle shape.

Lets assume the TV height to be "x"

Diagonal form a right angle triangle as shown on picture attached.

∴ using pathagorean theoram to find the height of TV.

[tex]h^{2} = a^{2} + b^{2}[/tex], where h is hypotenous, a is width or adjacent and b is height or opposite side.

∴ [tex]5^{2} = 4^{2} + x^{2}[/tex]

⇒[tex]25= 16+x^{2}[/tex]

subtracting both side by 16

⇒[tex]25-16= x^{2}[/tex]

⇒[tex]x^{2} = 9[/tex]

Taking sqaure root on both side.

Remember, √a²= a

⇒[tex]x= \sqrt{9}[/tex]

∴[tex]x= 3[/tex]

Hence, the height of TV is 3 inches.

Answer:

5 is greater

Step-by-step explanation:

Answer:

12:45

Step-by-step explanation:

quik maths

Answer:12:45

Step-by-step explanation:

Answer:

Therefore the slope of

[tex]y= -3.2x + 9.7[/tex]

is

[tex]Slope =-3.2[/tex]

Step-by-step explanation:

Given:

A regression line was calculated as

[tex]y= -3.2x + 9.7[/tex]

To Find:

Slope = ?

Solution:

General Slope-Point Form is given as

[tex]y=mx+c[/tex]

Where,

[tex]m=Slope\\c=y-intercept[/tex]

On Comparing with given Regression line we get

[tex]Slope = m = -3.2[/tex]

Therefore the slope of

[tex]y= -3.2x + 9.7[/tex]

is

[tex]Slope =-3.2[/tex]

Answer:

[tex]c\leq \$17[/tex]

Step-by-step explanation:

Let

c -----> the additional amount (in dollars) David will spend

we know that

The word " at most" in this context means "less than or equal to"

The amount David has spent plus possible additional amounts he will spend must be less than or equal to $39

so

The inequality that represent this situation is

[tex]22+c\leq 39[/tex]

solve for c

subtract 22 both sides

[tex]c\leq 39-22[/tex]

[tex]c\leq \$17[/tex]

The maximum amount he could spend is $17