Find three consecutive even integers such that the sum of twice the smallest and three times the largest is 42

This line is already in slope-intercept form.

The slope of the line is 9, and the y-intercept is 0.

Because of this, we can find every y value for any x value simply by replacing x with the value of the x coordinate.

By replacing x with 2, we can see what the y coordinate would be when x is 2.

9(2) = 18

The y value would be 18, which is not 10, meaning (2, 10) is not a solution to the equation.

The point (2,10) is not a solution to the equation y = 9x because when x is substituted into the equation, it results in y = 18, not y = 10 as in the point.

To determine if the point (2,10) is a solution to the equation y = 9x, we need to substitute the x-value from the point into the equation and see if the corresponding y-value matches the one in the point. Let's substitute x = 2 into the equation:

y = 9 x 2

y = 18

For the point (2,10), the y-value is 10, which does not equal the calculated y-value of 18. Therefore, the point (2,10) is not a solution to the equation y = 9x.

Applying the concept of Algebra, the toll collector processed 40 cars and 5 buses during a 4-hour period. This is found by checking each option against the equations 8c + 9b = 368 and c + b = total number of vehicles (where c = cars and b = buses).

To solve this problem, we need to find the number of cars and buses that make up the total toll collected, which is $368. We can set up a system of equations to solve for the two variables: number of cars (c) and number of buses (b).

So, we have two equations: 8c + 9b = 368 and c + b = total number of vehicles. By checking each option, only 40 cars and 5 buses match these equations, because 8*40 + 9*5 = 368.

So, the toll collector processed 40 cars and 5 buses during the 4 hour period.

Learn more about Algebra here:

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Domain is the set of x values

so answer is D) {2, 4, 6, 8}

Hope it helps

The average is 18m/s.

The average acceleration of the roller coaster car is [tex]\( 6\, \text{m/s}^2 \)[/tex].

The average acceleration of the roller coaster car is calculated using the formula:

[tex]\[ a = \frac{{v_f - v_i}}{{\Delta t}} \][/tex]

where [tex]\( v_f \)[/tex] is the final velocity, [tex]\( v_i \)[/tex]  is the initial velocity, and [tex]\( \Delta t \)[/tex] is the time interval over which the acceleration occurs.

Given:

[tex]- Initial velocity (\( v_i \)) = 4 m/s \\- Final velocity (\( v_f \)) = 22 m/s\\ - Time interval (\( \Delta t \)) = 3 s[/tex]

Plugging in the values:

[tex]\[ a = \frac{{22\, \text{m/s} - 4\, \text{m/s}}}{{3\, \text{s}}} \] \[ a = \frac{{18\, \text{m/s}}}{{3\, \text{s}}} \] \[ a = 6\, \text{m/s}^2 \][/tex]

Answer:

9 feet will the cat cover on 24 steps.

Step-by-step explanation:

Given: A dog takes 3 steps to walk the same distance for which a cat takes 4 steps.

⇒ 3 steps of dog=4 steps of Cat

If 1 step of the dogs cover [tex]\frac{1}{2}[/tex] feet

then,

4 steps of cat=3 steps of dog

24 steps of cat=[tex]\frac{3}{4}\times(24)[/tex]=18 steps of dog

Also, 1 step of the dogs cover=[tex]\frac{1}{2}[/tex] feet

18 steps of the dogs cover=9 feet

therefore, 24 steps of cat will cover 9 feet .

9z + 10 = 1 - 3(5 - 3z)    use distributive property

9z + 10 = 1 + (-3)(5) + (-3)(-3z)

9z + 10 = 1 - 15 + 9z

9z + 10 = -14 + 9z     subtract 9z from both sides

10 = -14   FALSE

NO SOLUTION

Answer: zero solutions.

Answer:

[tex] \sf \: z = no \: solution[/tex]

Step-by-step explanation:

Given equation,

→ 9z + 10 = 1 - 3(5 - 3z)

Now the value of z will be,

→ 9z + 10 = 1 - 3(5 - 3z)

→ 9z + 10 - 1 = -15 + 9z

→ 9z + 9 = -15 + 9z

→ 9z - 9z = -15 - 9

→ 0 = -24

→ [ z = no solution ]

Hence, there is no solution.

To solve the given system of equations by substitution, 'y' from the first equation is substituted into the second, resulting in x = 4/3. Substituting this into the first equation yields y = 5/3. Therefore, the solution to the system is x = 4/3, y = 5/3.

To solve the given system of equations by substitution, we will start with the first equation y = 2x - 1 and substitute it into the second equation 6x - 3y = 7.

Substituting 'y' from the first equation into the second, we get: 6x - 3(2x - 1) = 7.

Solving this, we find 'x': 6x - 6x + 3 = 7 => x = 7/3 = 4/3.

Next, we substitute 'x' into the first equation to find 'y': y = 2(4/3) - 1 = 8/3 - 1 = 5/3.

So, the solution to the system of equations is x = 4/3, y = 5/3.

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Answer:

4 umbrellas

Step-by-step explanation:

Number of Umbrellas              Total Money

                1                                            $12                

                2                                           $24

                3                                           $36

                4                                           $48

She can't go over $48 because $48 + $12 is $60, which is more than she has ($54). So the max amount of umbrellas she can buy is 4.

Here is your equation:

[tex]12x-5=127[/tex]

You're trying to find x, and to do that, the variable must be alone. That means you need to cancel out everything with it. The only thing with the variable 12x is -5. To cancel that out, you have to do the opposite of it, which is +5. Add 5 to both sides.

[tex]12x-5+5=127+5 \\12x=132[/tex]

12x(12 times x) is equal to 132. You need to find x. You have to do the opposite of times 12, which is divide by 12. Divide both sides by 12.

[tex]\frac{12x}{12} = \frac{132}{12} \\ \\x=11[/tex]

Your answer is x is equal to 11 ; x = 11

If you have any questions, feel free to ask in the comments! :)

the key is to write [tex]n^2 + n[/tex] as [tex]n(n+1)[/tex] which can be easily seen as an area of a rectangle with one side length n and the other (n+1). That explains the rectangle made of dots - 3 x 4

Now you only have half of them because of the 1/2. So that explains the lower "triangle" of dots being greyed out - they do not count in  the area (upper triangle). So the count of the dark dots corresponds to the original expression.

For n=5 you can draw a similar rectangular matrix with 5 x 6 dots. And count only the upper triangular part.  

I’m pretty sure you are

Answer:

#1. (6n) to the second power = (6^2) * (n^2)

n^2 means n to the second power, by the way

#2. (1+7n) to the second power = 1+14n+49n^2

Step-by-step explanation: You would just seperated square for the first one, since it involves the multiplication of squares, which is the same as squaring the product.

For the second one, you would expand the product to a^2+2ab+b^2, which is the same as 1^2 + 2(1*7n)+7n^2, which simplifies to 1+14n+49n^2

D) 209 with a remainder of 4

The question is about the division of 1467 by 7. The answer is '209 with a remainder of 4'.

This question is about division in mathematics. To solve this, we will divide 1467 by 7. Division is really repeated subtraction. You subtract 7 from 1467 as many times as you can until you get a number smaller than 7. That number is called the 'remainder', and the number of times you could subtract is the 'result' of the division.

After the division, the quotient is 209 and the remainder is 4. Therefore, the correct option is 'D) 209 with a remainder of 4'.

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           Today          2 years ago

Chris:   x + 3            (x + 3) - 2   = x + 1

Nathan: 18               (18) - 2       = 16

Jacob:   x                (x) - 2          = x - 2

Chris + Nathan + Jacob = sum

x + 1  +     16     +   x - 2   = 59

                            2x - 15 = 59   added like terms (x and x) and (1, 16, and -2)

                                   2x = 74   added 15 to both sides

                                     x = 37    divided both sides by 2

Answer: Jacob is 37 yrs old

The slope is -22/9. Use the formula (y2-y1)/(x2-x1)

(-1/3 +4)/(-1/3-7/6)

Answer:

37.5%

Step-by-step explanation:

subtract 80 by 50 to find the increase of money

80-50=30

then divide the number you got by the increase of price Wich is 80

30÷80=0.375

then multiply 0.375 by 100 to put it in percentage form

0.375x100=37.5%

Hey there!!

Recursive formula :

... a( n ) = a ( n - 1 ) + 7

The first term is 12

To find the second term, we will need to substitute 2 in place of ' n '

2 term :

... a( 2 ) = a ( 2 - 1 ) + 7

... a( 2 ) = a( 1 ) + 7

We know a( 1 ) = 12

... a( 2 ) = 12 + 7

... 19 is the second term and we will need to use this to find the other terms.

Hope my answer helps!

5x - 3 = 7

Add 3 to both sides.

5x = 10

Divide both sides by 5.

x = 2

The value of x is 2.

hello there this one was tricky i looked at it for sevrel minutes and solve dit

the answer is 50%

To obtain the same annual interest on both accounts, $3,600 should be invested at 9%, and $2,400 should be invested at 6%.

To solve this problem, we need to use the formula for simple interest, which is I = PRT, where P is the principal amount (the initial amount of money), R is the annual interest rate in decimal form, and T is the time the money is invested for in years. Here, we want both accounts to earn the same annual interest, so we'll let x be the amount of money invested at 9%, and 6000 - x be the amount of money invested at 6%. The annual interest for both should be the same, so:

x × 0.09 = (6000 - x) × 0.06

Solving for x, we get x = $3,600. So, $3,600 should be invested at 9%, and $2,400 ($6,000 - $3,600) should be invested at 6% to obtain the same annual interest.

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we can see that

For x is 0, 1, 2, 3 ,4

f(x) is  0 , 1 ,  4, 9 , 16

g(x) is -2 , -1 , 1 , 5 , 13

so, g(x) is greater than f(x) for x is 0, 1, 2, 3 ,4

It means that f(x) exceeds g(x) on [0,4]

But for x=5

f(x) is 25

g(x) is 29

Here, we can see that g(x) exceeds f(x) at x=5

so, there must be intersection point between x=4 and x=5

so, option-C.........Answer

Each option describes different behaviors and relationships between the two functions over the interval [0, 5]. Without further details, we can only conceptualize the scenarios provided.

To compare the graphs of f(x) and g(x) over the interval [0, 5], we can evaluate the options provided:

Without the exact equations or a graph to analyze, we cannot definitively determine which option is correct. However, we can conceptualize the scenarios described:

Option A suggests f(x) is consistently greater than g(x) throughout the interval. Option B suggests the opposite. Option C introduces an intersection point, where f(x) transitions from being greater to less than g(x). Option D indicates g(x) is initially greater, with a reversal after an intersection between 4 and 5.

If we had the graphs or more specific information, we could more precisely identify the correct statement.

Not sure if I am right but I looked online for you and it said divide the numerator and the denominator by the given rate so I guess you do 46 divided  by 5 I'm sorry if I am wrong nd let me know

The unit rate of $46 for 5 toys is calculated by dividing the total cost by the number of toys, resulting in $9.20 per toy.

This question demands complete basic understanding of mathematical concepts in general and division in particular.

To find the unit rate of $46 for 5 toys, you divide the total cost by the number of toys. This calculation will give you the cost of one toy. Here's how it's done step-by-step:

So, as per the above explaination, the unit rate is $9.20 per toy.

The two points on a line such that it has a slope 5/8 is:

             (0,0) and (8,5)

We know that the slope of a line is the ratio of the change in the y-coordinates to the change in the x-coordinates.

Now, let us assume that the equation of a line with slope 5/8 be given by:

        [tex]y=\dfrac{5}{8}x[/tex]

Hence, the point (0,0) lie on the line.

(  since, when x=0 we have:

[tex]y=\dfrac{5}{8}\times 0\\\\y=0[/tex]  )

and also the point (8,5) lie on the line.

(  when x=8 we have:

[tex]y=\dfrac{5}{8}\times 8\\\\y=5[/tex]  )

[tex]6f-12=-4f+6\qquad|\text{add 12 to both sides}\\\\6f=-4f+18\qquad|\text{add 4f to both sides}\\\\10f=18\qquad|\text{divide both sides by 10}\\\\\boxed{f=1.8}[/tex]

Given  Kruger National Park in Skukuza coordinate : (-24.98,31.58).

Nelson Mandela Musuem in Mpumalanga coordinate : (-29.82,31.58).

We need to find exactly in between given coordinates.

We know, mid - point formula :  

[tex]\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right).[/tex]

[tex]\left(x_1,\:y_1\right)=\left(-24.98,\:31.58\right),\:\left(x_2,\:y_2\right)=\left(-29.82,\:31.58\right)[/tex]

[tex]=\left(\frac{-29.82-24.98}{2},\:\frac{31.58+31.58}{2}\right)[/tex].

[tex]=\left(-27.4,\:31.58\right)[/tex].

Therefore, will be meeting at (-27.4, 31.58).

In order to use the elimination method, you have to create variables that have the same coefficient—then you can eliminate them. Next add the equations, and solve for y or x. Once you find out the value of either y or x you can substitute into one of the original equations to find x or y.

We calculate the volume of the sphere to find the amount of gas it can hold, then we multiply this volume by the price per cubic foot to get the total cost of the gas, which is $3216.96.

The problem is asking us to determine the total value of gas in a spherical container given the radius of the sphere (container) and the cost of gas per cubic foot.

Firstly, we need to calculate the volume of the sphere using the formula: V = 4/3 * pi * r^3, where r is the radius of the sphere. Substituting the given radius, V = 4/3 * pi * 4^3 = 268.08 cubic feet

Then, we find the total value of the gas by multiplying the volume of the gas by the cost per cubic foot. So, the total value = volume * cost = 268.08 * 12 = $3216.96

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The total value of the gas in the container is $3216.96.

To find the total value of the gas in the container, we first need to calculate the volume of the gas.

The formula to find the volume of a sphere is V = (4/3) * π * r^3, where r is the radius of the sphere.

Plugging in the given radius of 4 ft, we get V = (4/3) * π * (4^3) = 268.08 ft^3.

Next, we multiply the volume of the gas by the cost per cubic foot to find the total value.

Multiplying 268.08 ft^3 by $12/ft^3, we get a total value of $3216.96.

Therefore, the total value of the gas in the container is $3216.96.

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Final answer:

To solve the equation 3/8 + b/3 = 5/12 for b, we find a common denominator, combine the fractions, and then isolate and solve for b. The solution for b is 1/8.

Explanation:

The equation presented by the student is 3/8 + b/3 = 5/12. To solve for b, we must first get a common denominator for the fractions to combine them. In this case, the common denominator is 24, since it is the least common multiple of 8 and 3. Multiplying each term by 24 yields:

(3/8)*24 + (b/3)*24 = (5/12)*24

9 + 8b = 10

Next, we isolate the variable b by subtracting 9 from both sides of the equation:

8b = 10 - 9

8b = 1

Finally, divide both sides by 8 to solve for b:

b = 1/8

Thus, the value of b that satisfies the given equation is 1/8.