3(x+5) = -6x+6 two column proof

Answer:

10

Step-by-step explanation:

Remember that the formula for the sum of an arithmetic series is:

[tex]S=\frac{k}{2}(a+x_k)[/tex]

Where k is the number of terms, a is the initial term, and x_k is the last term of the series.

We essentially want to find k, the number of terms, given that the sum S is equal to 105. So, substitute 105 into our equation:

[tex]105=\frac{k}{2}(a+x_k)[/tex]

To do so, we need to final term x_k. We don't know what it is yet, but that doesn't matter. All we need to do is to write it in terms of k. First, remember that the standard form for the explicit formula of an arithmetic sequence is:

[tex]x_n=a+d(n-1)[/tex]

Where a is the first term, d is the common difference, and n is the nth term.

From our sequence, we can see that the first term is -3.

Also, we can determine that our common difference is +3, since each subsequent term is 3 more than the previous one. -3+3 is 0, 0+3 is 3, 3+3 is 6, and so on.

Therefore, our explicit formula is:

[tex]x_n=-3+3(n-1)[/tex]

Therefore, our final term, x_k, will be if we substitute k for n. So, we can acquire the equation:

[tex]x_k=-3+3(k-1)[/tex]

Now that we know what x_k is, we can substitute that into our original equation:

[tex]105=\frac{k}{2}(a+x_k)[/tex]

Substitute the equation into x_k. Also, let's substitute -3 (our first term) for a. So:

[tex]105=\frac{k}{2}(-3+(-3+3(k-1)))[/tex]

And now, all we have to do is to solve for k.

First, distribute the 3:

[tex]105=\frac{k}{2}(-3+(-3+3k-3))[/tex]

Add within the parentheses:

[tex]105=\frac{k}{2}(3k-9)[/tex]

Multiply both sides by 2. This removes the fraction on the right:

[tex]210=k(3k-9)[/tex]

Distribute. We will get a quadratic:

[tex]210=3k^2-9k[/tex]

So, let's solve for k. Let's divide everything by 3:

[tex]70=k^2-3k[/tex]

Subtract 70 from both sides:

[tex]0=k^2-3k-70[/tex]

Factor. We can use -10 and 7. So:

[tex]0=(k-10)(k+7)[/tex]

Zero Product Property:

[tex]k-10=0\text{ or } k+7=0[/tex]

Solve for k for each equation:

[tex]k=10\text{ or } k=-7[/tex]

-7 doesn't make sense (we can't have -7 terms). Remove that solution. So, we are left with:

[tex]k=10[/tex]

Therefore, the number of terms we have in our series for our sum to be 105 is 10.

And we're done!

Step-by-step explanation:

this is your answer.........

Answer:

conditional equation

Step-by-step explanation:

Collecting terms on both sides, we get

6x−10−86x−18=9+4x−4x=9

Adding 18 to both sides of the equation, we get

6x=27

This can be solved by dividing by 6 on both sides of the equation, which gives a unique solution of 92. So, this is a conditional equation.

Answer:

x<3/4 and x>0

for graphs, refer to the images attached.

Step-by-step explanation:

-1-4x > -4 AND -1-4x <-1

Answer:

The value is [tex]w = 6.7 \%[/tex]

Step-by-step explanation:

Generally the productivity rate is mathematically represented as

[tex]P_r = K * Z[/tex]

Here K is the ha the farmer could harvest in an hour and Z is a typical yield of corn in kg/ha

Now considering 1970

The productivity rate is

[tex]P_r = 0.75 *5000[/tex]

=> [tex]P_r = 3750 \ kg/h [/tex]

Now considering 1940

The productivity rate is given as [tex]P_R = 250 \ kg/h [/tex]

Generally the productivity ratio is mathematically ration is mathematically represented as

[tex]w = \frac{P_R}{P_r} * 100[/tex]

=> [tex]w =  \frac{250}{3750}  * 100[/tex]

=> [tex]w = 6.7 \%[/tex]

The correct answer is (-7/2,-1/2) or (-3.5,-0.5)  To find the midpoint of a segment, add both "x" coordinates, divide by 2.  Then add both "y" coordinates, and divide by 2

Answer:

Hello

Step-by-step explanation:

yUh GeT iNtO iT

Answer:

Reflection over y axis, and translate right 1

Step-by-step explanation:

Answer: The probability that no women are chosen to be in the committee is 2/5 or 0.40.

Step-by-step explanation:

We have two positions, and we have 6 options for those positions, 3 are men, and 3 are women.

If we want to see the probability where no women are chosen, then this means that in the first selection a man is chosen.

If all the 6 nominees have the same probability of being chosen, then the probability that in the first selection a man is chosen is equal to the number of men divided the total number of nominees, this is:

p1 = 3/6 = 1/2.

Now the same happens for the second selection, but now we have 5 total nominees and 2 are men, so the probability now is:

p2 = 2/5

And the joint probability will be the product of the individual probabilities, then we have:

P = p1*p2 = (1/2)*(2/5)  = 2/5.

The probability that no women are chosen to be in the committee is 2/5 or 0.40.

The probability that no woman is chosen to be on the committee is 0.40.

A club is choosing 2 members to serve on a committee.

The club has nominated 3 women and 3 men.

The number of ways to select two persons from 6 will be:

[tex]\rm = ^6C_2[/tex]

Therefore,

The probability that no woman is chosen to be on the committee is;

[tex]= \dfrac{1}{2} \times \dfrac{2}{5}\\\\= \dfrac{1}{5}\\\\=0.40[/tex]

Hence, the probability that no woman is chosen to be on the committee is 0.40.

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Answer:

38 and 40

Step-by-step explanation:

Hope this helps you :)

Answer:

39 would fall between 38 and 40

Step-by-step explanation:

Answer:

y=5x

Step-by-step explanation:

Answer:

y=5x

Step-by-step explanation:

Answer: none of thoses

Step-by-step explanation:

Answer: The train station is located at point (5,1).

Step-by-step explanation:

Given: On a grid, information center is located at (1,4) and the bus is located at (-3,7).

A tourist information center is between bus station and train station.

i.e.  tourist information center is a mid point  of line joining bus station and  train station.

Midpoint between (a,b) and (c,d) is given by :-

[tex](x,y)=(\dfrac{a+c}{2},\dfrac{b+d}{2})[/tex]

Let (a,b) be the coordinates of train station , then

[tex](1,4)=(\dfrac{-3+a}{2},\dfrac{7+b}{2})\\\\\Rightarrow\ 1=\dfrac{-3+a}{2}\ \ \ , 4=\dfrac{7+b}{2}\\\\\Rightarrow\ 2=-3+a\ \ \ , 8=7+b\\\\\Rightarrow\ 2+3=a\ \ \ , 8-7=b\\\\\Rightarrow a= 5,\ \ b=1[/tex]

Hence, the train station is located at point (5,1).

Answer:

60° =19π/3

288°=22π/9

315°=23π/4

80°=18π/5

Step-by-step explanation:

The question is incomplete. Find the completed question in the attachment.

We are to convert the radian values to the corresponding degrees that are less than 360°

Since π rad = 180°

For 23π/4:

If π rad = 180°

23π/4 = x

Cross multiply:

πx = 23π/4 × 180

x = 23π/4π × 180

x = (23×180)/4

x = 1035°

Next is to scale down 1035° to a degree less than 360 and to do this we will be subtracting multiples of 360° from the value gotten.

x = 1035 - (360×2)

x = 1035 - 720

x = 315°

Hence 23π/4 = 315°

For 18π/5:

If π rad = 180°

18π/5 = y

Cross multiply:

πy = 18π/5 × 180

y = 18π/5π × 180

y = (18×180)/5

y = 648°

In scaling down:

y = 648°-360°

y = 288°

Hence 18π/5 = 288°

For 22π/9:

If π rad = 180°

22π/9 = t

Cross multiply:

πt = 22π/9 × 180

t = 22π/9π × 180

t = (22×180)/9

t = 440°

In scaling down:

t = 440-360°

t = 80°

Hence 22π/9 = 80°

For 19π/3:

If π rad = 180°

19π/3 = y

Cross multiply:

πy = 19π/3 × 180

y = 19π/3π × 180

y = (19×180)/3

y = 3420/3

y = 1140°

In scaling down:

y = 1140°-(3×360)°

y = 1140-1080

y = 60°

Hence 19π/3 = 60°

Answer:

the other person was almost right except they mixed up 2 of them. this is the right answer, i hope this helps :)

60° =19π/3

288°=18π/5

315°=23π/4

80°=22π/9

have a great day :))

Answer:

Hi there!

An inequality to demonstrate this is:

105.5 + 7.5x >= 250

Hope this helps

Answer:

it is terminating

Step-by-step explanation:

Answer:

first option

Step-by-step explanation:

There is a common ratio r between consecutive terms in the sequence, that is

r = - 15 ÷ 3 = 75 ÷ - 15 = - 375 ÷ 75 = - 5

The recursive formula allows a term in the sequence to be found by multiplying the previous term by r , thus

f(n) = - 5f(n - 1) if n > 1

with f(1) = 3 ← first term

Answer:

D . f(n)=f(1)=3

            f(n)= -5f(n-1)if n >1

Step-by-step explanation:

i hope this help  got it right on test

Answer:

it is a square

because

as we can see in the graph the

distance from A to B is 5 cm

distance from B to C is 5 cm

distance from C to D is 5 cm

distance from D to A is 5 cm

please mark me as the brainliest I really need it

Answer: 50,400

Step-by-step explanation: 180 times 280 is like multiplying 180 by 280 times.

We can write 180 times 280 like this; 180 x 280.

180 x 280 = 50,400

Answer:

50,400

Step-by-step explanation:

180×280=50,400

Answer:

13

Step-by-step explanation:

you plug in 3 for n

4n+1

4(3)+1

12+1

13

Answer:

95

Step-by-step explanation:

5+5 = 10 x 10 = 100 - 5 = 95

Have a good day!!

Answer:11

Step-by-step explanation:

Answer:

  5 months

Step-by-step explanation:

We assume that y represents production capacity, rather than increase in production capacity. Then we want to solve the 6th-degree equation ...

  x^6 -25x^4 +199x^2 -4975 = 0

This can be factored in groups as ...

  x^4(x^2 -25) + 199(x^2 -25) = 0

  (x^4 +199)(x^2 -25) = 0

This has 4 complex solutions and 2 real solutions.

  x^2 = 25

  x = ±5

The duration required for capacity to reach 4975 units is 5 months.

Answer:

-22

Step-by-step explanation:

You have to add -32+10

and you will get the answer -22

Answer:

-22

Step-by-step explanation:

On a number line, negative numbers go left and posative numbers go right. So on a numberline, if you find -32 and jump ten spaces to the right, you land on -22

0 because anything below sea level will be in the negatives and anything above will be and positive number higher than 0 :D

Hope this helped

Answer: 8b and 80

Step-by-step explanation: H3h3

The Area of Rectangle is 80 unit².

The Area of rectangle is the product of its length to its width.

Area of rectangle = length x width

Given:

Expression that represents the area of this rectangle is 8b.

Now, b = 10

As, area of rectangle = l x w

area of rectangle = 8b

area of rectangle = 8 x 10

area of rectangle = 80 unit².

Hence, the area is 80 unit².

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Answer:

Remember that:

Speed = distance/time.

Then we can calculate the average speed in any segment,

Let's make a model where the average speed at t = t0 can be calculated as:

AS(t0) = (y(b) - y(a))/(b - a)

Where b is the next value of t0, and a is the previous value of t0. This is because t0 is the middle point in this segment.

Then:

if t0 = 100s

AS(100s) = (400ft - 0ft)/(200s - 0s) =   2ft/s

if t0 = 200s

AS(200s) = (1360ft - 50ft)/(300s - 100s) = 6.55 ft/s

if t0 = 300s

AS(300s) = (3200ft - 400ft)/(400s - 200s) =  14ft/s

if t0 = 400s

AS(400s) = (6250s - 1360s)/(500s - 300s) = 24.45 ft/s

So for the given options, t = 400s is the one where the velocity seems to be the biggest.

And this has a lot of sense, because while the distance between the values of time is constant (is always 100 seconds) we can see that the difference between consecutive values of y(t) is increasing.

Then we can conclude that the rocket is accelerating upwards, then as larger is the value of t, bigger will be the average velocity at that point.

Speed is simply the rate of change of distance over time.

The greatest speed is at [tex]t = 400[/tex]

To calculate the time of the greatest speed, we simply calculate the slope between each interval.

The slope (m) of a line is:

[tex]m = \frac{y_2 - y_1}{t_2 - t_1}[/tex]

When [tex]t = 100[/tex]

[tex](t_1,y_1) = (0,0)[/tex]

[tex](t_2,y_2) = (200,400)[/tex]

So, we have:

[tex]m = \frac{400-0}{200 -0}[/tex]

[tex]m= \frac{400}{200}[/tex]

[tex]m = 2[/tex]

When [tex]t = 200[/tex]

[tex](t_1,y_1) = (100,50)[/tex]

[tex](t_2,y_2) = (300,1360)[/tex]

So, we have:

[tex]m = \frac{1360-50}{300 -100}[/tex]

[tex]m = \frac{1310}{200}[/tex]

[tex]m = 6.55[/tex]

When [tex]t = 300[/tex]

[tex](t_1,y_1) = (200,400)[/tex]

[tex](t_2,y_2) = (400,3200)[/tex]

So, we have:

[tex]m = \frac{3200-400}{400 -200}[/tex]

[tex]m = \frac{2800}{200}[/tex]

[tex]m = 14[/tex]

When [tex]t = 400[/tex]

[tex](t_1,y_1) = (300,1360)[/tex]

[tex](t_2,y_2) = (500,6250)[/tex]

So, we have:

[tex]m = \frac{6250-1360}{500-300}[/tex]

[tex]m = \frac{4890}{200}[/tex]

[tex]m = 24.45[/tex]

From the above computation, the greatest speed (i.e. slope) is

[tex]m = 24.45[/tex]

The corresponding time at [tex]m = 24.45[/tex] is [tex]t = 400[/tex]

Hence, the greatest speed is at [tex]t = 400[/tex]

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Hi there!

~

The coefficient of x in -7xyz2 is -7.

❀Hope this helped you!❀

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