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sladkih [1.3K]
3 years ago
6

Look at the table. Make a conjecture about the sum of the first 10 positive even numbers.

Mathematics
2 answers:
Kazeer [188]3 years ago
7 0

Answer:

The sum of the first 10 positive even numbers is 10\times 11=110

Step-by-step explanation:

From the table, we see that,

Sum of the numbers 2+4+6+8+10=30=5\times 6=5(5+1)

That is, when there are 5 terms in the sequence, the sum is given by 5\times 6.

Then, in general, when there are 'n' terms in the sequence, the sum is given by n(n+1)

We are required to find the sum of 10 even terms.

Therefore, when there are 10 terms in the sequence, the sum will be 10(10+1)=10\times 11

<h3>Hence, the sum of the first 10 positive even numbers is 10\times 11=110</h3>
inysia [295]3 years ago
6 0
The answer is 10•11, if you look at the pattern, you don't have to solve the addition.

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Graph a line that contains the point (4,3) and has a slope 1/2
Roman55 [17]

Answer: The graph is attached.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

y=mx+b

Where "m" is the slope and "b" is the y-intercept.

We can find "b" substituting the slope and coordinates of the (4,3) into thte equation  y=mx+b, and then solving for "b":

3=\frac{1}{2}(4)+b\\\\3-2=b\\\\b=1

By definition, the line intersects the x-axis when "y" is zero.

Then, we need to substitute the y-intercept and y=0 into  y=mx+b and then solve for "x" in order to find the x-intercept:

0=\frac{1}{2}x+1\\\\-1(2)=x\\\\x=-2

Knowing the x-intercept and the y-intercept, we can graph the line (The graph is attached)

6 0
3 years ago
Read 2 more answers
**50 Points Possible** I NEED URGENT HELP <br>please provide a graph
Elina [12.6K]

Answer:

See below.

Step-by-step explanation:

1)

For Ben's social media post, we are told that it was initially shared to only 2 people. However, each of those shares it with 3 people. In other words, Ben's post triples every day. This means that the rate of growth is 3. Thus, Ben's post as an exponential function is:

f(x)=2(3)^x

The 2 represents the initial amount at day 0, and the 3 represents the rate at which the post grows each day.

2)

Similarly, Carter's post was originally sent to 10 people. However, each of the 10 shares it with two others. Therefore, it doubles each day. Thus, the rate is 2. So, Carter's exponential function is:

f(x)=10(2)^x

The 10 represents the initial amount while the 2 represents the rate.

3)

I've use Desmos to graph the functions. Refer to the picture attached. Red is Amber, blue is Ben, and green is Carter.

4)

To find out the number of shares each student's post will receive on day 3 and day 10, simply plug the numbers into the functions. Therefore:

For Amber:

Day 3:

f(3)=3(4)^3=192

Day 10:

f(10)=3(4)^{10}=3,145,728

For Ben:

Day 3:

f(3)=2(3)^3=54

Day 10:

f(10)=2(3)^{10}=118,098

And for Carter:

Day 3:

f(3)=10(2)^3=80

Day 10:

f(10)=10(2)^{10}=10,240

5)

Amber's new graph of:

f(x)=3(4)^x+45

will be a shifted version of her original graph. The new graph will be shifted upwards by 45 units. However, since the 45 is not affected by the x in any way, the change will be minuscule. For instance, her number of shares on day 10 of the old graph is 3,145,728. Even with the additional 45, it will just be: 3,145,773. With enough days, the additional number becomes trivial.

6)

On the 10th day, Amber's post was shared almost 3 million times, while Ben's was shared "only" 118,098 times and Carter's with 10,240. Undoubtedly, Amber's post was the fastest.

7)

If you want to most shares as possible, choose Amber with fewer friends initially but more shares. This is because the exponential potential of a number even just a bit higher is insane. For instance, 3^10 (Ben's rate at 10th day) is only 59,049 while Amber's rate will be 4^10 which is 1,048,576. Amber's number is almost 18 times higher than Ben's. Even if Ben's initial number was say 1,000 or even 1,000,000, Amber would catch up rather quickly. Therefore, the rate is the quintessential part of an exponential growth function.

5 0
3 years ago
Supplementary angles measure _____ degrees?​
Oliga [24]

my answer

90°to 180°degrees

4 0
3 years ago
What is the solution to the system of equations?
Dovator [93]

Answer:

<h2>(-10, 2, 6)</h2>

Step-by-step explanation:

\left\{\begin{array}{ccc}x+3y+2z=8&(1)\\3x+y+3z=-10&(2)\\-2x-2y-z=10&(3)\end{array}\right\qquad\text{subtract both sides of the equations (1) from (2)}\\\\\underline{-\left\{\begin{array}{ccc}3x+y+3z=-10\\x+3y+2z=8\end{array}\right }\\.\qquad2x-2y+z=-18\qquad(4)\qquad\text{add both sides of the equations (3) and (4)}\\\\\underline{+\left\{\begin{array}{ccc}-2x-2y-z=10\\2x-2y+z=-18\end{array}\right}\\.\qquad-4y=-8\qquad\text{divide both sides by (-4)}\\.\qquad\qquad y=2\qquad\text{put the value of y to (1) and (3)}

\left\{\begin{array}{ccc}x+3(2)+2z=8\\-2x-2(2)-z=10\end{array}\right\\\left\{\begin{array}{ccc}x+6+2z=8&\text{subtract 6 from both sides}\\-2x-4-z=10&\text{add 4 to both sides}\end{array}\right\\\left\{\begin{array}{ccc}x+2z=2&\text{multiply both sides by 2}\\-2x-z=14\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2x+4z=4\\-2x-z=14\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad3z=18\qquad\text{divide both sides by 3}\\.\qquad\qquad z=6\qquad\text{put the value of z to the first equation}

x+2(6)=2\\x+12=2\qquad\text{subtract 10 from both sides}\\x=-10

4 0
3 years ago
A fish tank that is 5 feet long by 3 feet wide by 3 feet high has a 2 foot cubic stone placed in the bottom how much water will
maks197457 [2]

Answer:

37ft³

Step-by-step explanation:

Volume of the fish tank = length × width × height = 5ft × 3ft × 3ft = 45ft³

Volume of the cubic stone = length × length × length = (2ft)³ = 8ft³

Volume of the water = volume of the fish tank - volume of the cubic stone

i.e Volume of the water = 45ft³ - 8ft³ = 37ft³

4 0
3 years ago
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