Find three consecutive even integers such that five times the second is six more than twice the sum
of the first and third integers

The answer you are looking for is x=-2.

Solution/Explanation:

60x+153=9x+51

Subtract 9x from both sides,

60x-9x+153=51

Simplifying this part of the equation,

51x+153=51

Now, subtracting 153 from both sides,

51x+153-153=51-153

Simplifying this part of the equation,

51x=-102

Finally, dividing 51 from both sides,

So, therefore, the final answer is x=-2. I hope this helped answer your question for you. Enjoy your day, and take care!

x = -2 is the solution to the equation 60x + 153 = 9x + 51.

Here, we have,

To solve the equation 60x + 153 = 9x + 51,

follow these steps:

Step 1:

Start with the given equation: 60x + 153 = 9x + 51.

Step 2:

Simplify the equation by combining like terms.

To do this, subtract 9x from both sides of the equation:

60x + 153 - 9x = 9x + 51 - 9x.

Simplifying further:

51x + 153 = 51.

Step 3:

Subtract 153 from both sides of the equation to isolate the variable term:

51x + 153 - 153 = 51 - 153.

Simplifying further:

51x = -102.

Step 4:

Divide both sides of the equation by the coefficient of x, which is 51, to solve for x:

51x / 51 = -102 / 51.

Simplifying further:

x = -2.

Step 5:

Check the solution by substituting x = -2 back into the original equation:

60(-2) + 153 = 9(-2) + 51.

Simplifying:

-120 + 153 = -18 + 51.

33 = 33.

Since the left side of the equation equals the right side after substituting x = -2,

we can conclude that x = -2 is the solution to the equation 60x + 153 = 9x + 51.

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Answer:

C

Step-by-step explanation:

the typical form of line equation is

y = ax + b

a = the slope of the line (expressed as y/x ratio telling us how many units y changes when x changes a certain number of units).

b = the intercept on the y-axis (when x = 0).

we know, a = -4

and we use the point (x = -2, y = 1) to get b

y = -4x + b

1 = -4×-2 + b = 8 + b

b = -7

=>

y = -4x - 7

only the points of option C are all fulfilling this equation.

e.g. x = 0, y = -7

-7 = -4×0 - 7 = -7, true, -7 = -7

and so on.

Answer:

See below

Step-by-step explanation:

22. 30 = 2 * 3 * 5

23. 126 = 2 * 3 * 3 * 7

24. 4900 = 2 * 2 * 5 * 5 * 7 * 7

25. 39204 = 2 * 2 * 3 * 3 * 3 * 3 * 11 * 11

26. There's no square number

27. The highest common factor are

   30 is 5

   126 is 7

  4900 is 7

 39204 is 11

28. The lowest common factor are

 30 is 2

 126 is 2

 4900 is 2

 39204 is 2

What about you? What did you get?

Answer:

i dont know

Step-by-step explanation:

Answer:

ADF

Step-by-step explanation:

AD and DF intersect at Angle ADF. It's in the picture.

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Explanation:

Hakim and Aziz have savings in the ratio 3:5. This means that Hakim has 3x dollars while Aziz has 5x dollars. The x is some positive real number.

We're then told that Hakim saved another $82, which means it goes from 3x to 3x+82

At the same time, Aziz spent $110 which means the 5x decreases to 5x-110

At this point, the two people have the same amount of money. Set the expressions we found equal to one another and solve for x.

3x+82 = 5x-110

3x-5x = -110-82

-2x = -192

x = -192/(-2)

x = 96

Then use this x value to compute each expression like so

Both have $370 after Hakim saved that additional $82 and after Aziz spent that $110.

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Extra info:

If we rewind things a bit, Hakim would have 3*x = 3*96 = 288 dollars while Aziz would have 5x = 5*96 = 480 dollars. This is before any additional saving or spending.

Then note how the ratio 288:480 fully reduces to 3:5 after dividing both parts by the GCF 96.

Answer:

52.5 km

Step-by-step explanation:

the info about the trip from Malim to Petani is irrelevant and only there to confuse us.

but from the return trip info we get all we need.

for x km it took then 30 minutes at an average speed of 105 km/h.

to get km out of km/h, we need to multiply the speed number by the hours traveled. that removed the "h" and leaves us with km.

n km/h × a h = a×n km

so, now, in our example we have 105 km/h, and 30 minutes = 1/2 h.

so, we have

x = 105 km/h × 1/2 h = 105/2 km = 52.5 km

Answer:

x = 30

Step-by-step explanation:

These angles are supplementary which means they add up to 180:

2x + 50 + 5x - 80 = 180

7x - 30 = 180

7x = 180 + 30

7x = 210

x = 30

Answer:

Step-by-step explanation:

We know that the perimeter is the sum of side lengths.

Substitute the values and solve for x:

Answer:

[tex]perimeter = h + l + b \\ = x + 2x - 2 + 3x + 1.5 = 11.5 \\ x \: terms \: togather \\ x + 2x + 3 x- 2 + 1.5 = 11.5 \\ 6x - .5 = 11.5 \\ 6x = 11.5 + .5 \\ 6x = 12 \\ x = \frac{12}{6} \\ x = 2 \\ thank \: you[/tex]

Answer:

x = -16

Step-by-step explanation:

given:

[tex]h(x) = -2x - 4[/tex]

solve for x, when:

[tex]h(x) = 6[/tex]

~~~~~~~~~~~~

➡️ [tex] x = -2(6) - 4 [/tex]

➡️ [tex] x = -12 - 4[/tex]

➡️ [tex] x = -16 [/tex]

The solution of x when the function h ( x ) = 6 is x = -5

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as h ( x )

Now , the value of h ( x ) is given by

h ( x ) = -2x - 4   be equation (1)

On simplifying the function rule , we get

when h ( x ) = 6

Substitute the value of h ( x ) = 6 , we get

6 = -2x - 4

Adding 4 on both sides , we get

-2x = 10

Divide by -2 on both sides , we get

x = 10 / -2

x = -5

Therefore , the value of x is -5

Hence , the equation is x = -5

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Explanation:

And so on.

We'll have this countdown: 16, 15, 14, ..., 3, 2, 1, 0. By the time we get to the 17th player, they won't have anyone to kick the ball to. This is because they've already been counted in the previous scenarios. This is to avoid double-counting.

So the problem simply boils down to us adding up the numbers 0,1,2,...14,15,16.

This is an arithmetic sequence with first term a = 0 and common difference d = 1. The sum of the first n = 17 terms is...

Sn = (n/2)*(a + d(n-1))

S17 = (17/2)*(0 + 1(17-1))

S17 = (17/2)*(16)

S17 = 17*8

S17 = 136 is the final answer

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An alternative method:

Consider we have two slots A and B

For slot A, we have 17 choices because we have 17 players.

Then for slot B, we have 17-1 = 16 choices since we don't want to reselect whoever goes in slot A.

If order mattered, then we'd have 17*16 = 272 different permutations.

However, order doesn't matter. A sequence like {player1,player4} is identical to {player4,player1}. All that matters is the overall group rather than the order of it. Both of those examples say the same thing: they connect player 1 to player 4.

In short, the value 272 is too large and it double-counts the true answer. We need to divide by 2 to correct for this.

272/2 = 136

We arrive at the same answer as before. There are 136 kicks required so that each player kicks the ball to every other player.

The minimum Number of kicks required in other to ensure that each player kicks the ball to every other atleast once is 136 kicks.

The Number of kicks could be related to the sum of the nth term of an arithmetic series

[tex]S_n = \frac{n}{2} (2a_1 + (n-1)d)[/tex]

n = number of terms = 17 players

First term,

[tex]a_1 = 0[/tex]

Common difference, d = 1

Inputting the Values into the equation :

[tex]S_n = \frac{17}{2} (2(0) + 16 \times 1)[/tex]

[tex]S_n = 8.5(0 + 16)[/tex]

[tex]S_n = 0 + 136[/tex]

[tex]S_n = 136[/tex]

Hence, the minimum number of kicks which would be taken by the players in other to ensure that each player kicks to ball to every other atleast once is 136 kicks.

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16 dozen

Step-by-step explanation:

a dozen=12

x=(40×12)/2

=240 rolls : are sold by noon

y=240×(80/100)

=192 rolls after noon

192/12= 16 dozen left

Answer:

Equation is 4y = -3x + 12

Step-by-step explanation:

General equation of a line:

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

for the slope:

[tex]slope = \frac{y_{2} - y_{1} }{x _{2} - x_{1} } [/tex]

consider points: (4, 0) and (0, 3)

[tex]slope = \frac{3 - 0}{0 - 4} \\ \\ slope = - \frac{3}{4} [/tex]

for y-intercept, c :

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

consider point (0, 3):

[tex]3 = ( - \frac{3}{4} \times 0) + c \\ \\ c = 3 \\ c = 3[/tex]

Equation is:

[tex]y = - \frac{3}{4} x + 3 \\ \\ 4y = - 3x + 12[/tex]

Answer:

BC = 22

Step-by-step explanation:

BD = 67

Bc = 3x - 2

CD = 4x + 13

BC + CD = BD (Given)

3x - 2 + 4x + 13 = 67

3x + 4x -2 + 13 = 67

7x + 11 = 67

7x = 67 - 11

7x = 56

x = 56 ÷ 7

x = 8

now instead of x put 8

Bc = 3x - 2

BC = 3(8) -2

BC = 24 -2

BC = 22

Answer:

-3

Step-by-step explanation:

What this tells you is that where you see an x on the right hand side of the equation, you put -1.

h(-1) = 2(-1) - 1

h(-1) = -2 - 1

h(-1) = - 3

Answer:

answer is 19.1

Step-by-step explanation:

answer is 19.1

Step-by-step explanation:

f(x) =14x+4

h(x)=7x

f(x)-h(x)=14x+4-7x

=7x+4

Hey there! I'm happy to help!

Imagine the line that is created when you connect the two points (the distance between the two points).

You can create a right triangle where this distance is the hypotenuse where the two legs are the change in x and y. So, if you take those changes in x and y, you can use the Pythagorean Theorem (a²+b²=c²) to find the distance between the two points, which is the hypotenuse.

Our change in x is 9 because 9-0 is 9.

We square it

9²=81

Our change in y is 5 as -1-(-6) or -1+6 is 5.

5²=25

We add these.

81+25=106

We square root and round to the nearest tenth.

√106≈10.3

So, our distance is 10.3.

This Pythagorean Theorem method actually gives us a formula called the distance formula that you can use to find the distance between points.

[tex]\sqrt{(x_{2} -x_{1})^2+(y_{2}-y_{1})^2}[/tex]

Have a wonderful day and keep on learning! :D

Answer:

C

Step-by-step explanation:

y and 67 are alternate exterior angles and are congruent , then

y = 67° → C

Answer:

k = 5/6

Step-by-step explanation:

The √ can be rewrite as a power, and this power is 1/2

So √a = a^1/2, and it is multiplying a, so we add the powers: a¹•a^1/2 = a^(1+1/2) = a^3/2

And the ³√ can be rewrite as the power 1/3, but the a inside the ³√ is to the power of 2, so we can rewrite it like this: (a²)^1/3

And to evaluate this we have to multiply the powers, so we will have: a^2/3

Now we have this fraction:

[tex] \frac{ {a}^{ \frac{3}{2} } }{ {a}^{ \frac{2}{3} } } [/tex]

A fraction with powers in the same base can be rewrite like a subtraction of the powers, so let's do that:

[tex] \frac{ {a}^{ \frac{3}{2} } }{ {a}^{ \frac{2}{3} } } = {a}^{ \frac{3}{2} - \frac{2}{3} } = {a}^{ \frac{5}{6} } [/tex]

y= 3x –4

3x + y = –4

3x + (3x –4) = –4

3x+3x – 4 = – 4

6x = – 4 +4

6x=0 —> x= 0/6 —> x=0

y = 3x – 4 —> y = 3(0) – 4 = – 4

I hope I helped you^_^

Answer:

(0,-4)

Step-by-step explanation:

3x + y = -4

3x + (3x - 4) = -4

3x + 3x - 4 = -4

6x = 0

x = 0

y = 3(0) - 4

y = -4

Answer:

9m + 6

Step-by-step explanation:

Maria has half as many sweets as Yenny , that is

[tex]\frac{1}{2}[/tex] (6m + 4) ← multiply each term in the parenthesis by [tex]\frac{1}{2}[/tex]

= 3m + 2

Total sweets = 6m + 4 + 3m + 2 ← collect like terms

                      = 9m + 6

Answer:

[tex]2*y^{2}[/tex]

Step-by-step explanation:

The product of 2 is multiplication and the second power of y is just y squared

Answer:

1/32 people responded for Tampa.

Step-by-step explanation:

Answer:

left

Step-by-step explanation:

a=15

b=23

Step-by-step explanation:

a+8=b

2a=b+7

2a=(a+8)+7

2a=a+15

a=15

Answer:

7 and 15

Step-by-step explanation:

Let the numbers be x and y

[tex]x + y = 22[/tex]

[tex]x - y = 8[/tex]

On adding both

[tex]x + y + x - y = 22 + 8[/tex]

[tex]2x = 30[/tex]

[tex]x = \dfrac{30}{2} [/tex]

[tex]x = 15[/tex]

From 1

[tex]15 + y = 22[/tex]

[tex]y = 22 - 15[/tex]

[tex]y = 7[/tex]

Answer:

[tex]take \: numbers \: xand \: y \\ given \: that \: x + y = 22 .....(1)\\ x - y = 8.....(2) \\ x = 8 + y \\ put \: this \: in \: (1) \\ 8 + y + y = 22 \\ 8 + 2y = 22 \\ 2y = 22 - 8 \\ 2y = 14 \\ y = \frac{14}{2} \\ y = 7 \\ pt \: y = 7in \: eqution \: (2) \\ then \: \\ x - 7 = 8 \\ x = 7 + 8 \\ x = 15 \\ therefore \: x = 15 \\ y = 7 \\ thank \: you[/tex]