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3 years ago

Find the sum: 2 + 9 + 16 + ... + 37

Mathematics

1 answer:

iris [78.8K]3 years ago

7 0

Step-by-step explanation:

Sum of arithmetic terms = n/2 × [2a + (n - 1)×d], where 'a' is the first term, 'd' is the common difference between two numbers, and 'n' is the number of terms.

this is the same as n/2 × (a1 + an), because

an = a1 + (n-1)×d

so, for the series above :

a or a1 = 2

d = 7, as every new term is the previous term plus 7.

for n

37 = a1 + (n-1)×d = 2 + (n-1)×7

and now solve for n

35 = 7n - 7

42 = 7n

n = 6

so, the sum of all terms is

6/2 × (2+37) = 3×39 = 117

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Marty and Ethan both wrote a function, but in different ways.

marishachu [46]

Question:

Marty and Ethan both wrote a function, but in different ways.

Marty

y+3=1/3(x+9)

Ethan

x y

-4 9.2

-2 9.6

0 10

2 10.4

Whose function has the larger slope?

1. Marty’s with a slope of 2/3

2. Ethan’s with a slope of 2/5

3. Marty’s with a slope of 1/3

4. Ethan’s with a slope of 1/5

Answer:

Marty’s with a slope of 1/3 has the larger slope

Solution:

Given that Marty equation is:

$y + 3 = \frac{1}{3}(x+9)$

The point slope form is given as:

$y - y_1 = m(x-x_1)$

Where, "m" is the slope of line

On comapring both equations,

$m = \frac{1}{3}$

Ethan wrote a function:

Consider any two values from the table we have;

(0, 10) and (2, 10.4)

The slope is given by formula:

$m = \frac{y_2-y_1}{x_2-x_1}$

From above two points,

$(x_1, y_1) = (0, 10)\\\\(x_2, y_2) = (2, 10.4)$

Therefore,

$m = \frac{10.4-10}{2-0}\\\\m = \frac{0.4}{2} \\\\m = 0.2$

Thus we get,

$\text{Slope of Ethan} < \text{Slope of Marty}$

Therefore, Marty’s with a slope of 1/3 has the larger slope

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Answer:

Step-by-step explanation:

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a = 48

b= 30

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Mrs. Synder must choose two of her homeroom students to be class representatives. The class consists of 13 girls and 9 boys. App

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How do you Graph y-3=1/3(x+1)

jekas [21]

Answer:

You can find the point of intersection of the line with the y-axis and the the point of intersection of the line with the x-axis. See the graph attached.

Step-by-step explanation:

Find the intersection with the y-axis. Substitute $x=0$ into the equation and solve for y:

$y-3=\frac{1}{3}(x+1)\\\\y-3=\frac{1}{3}(0+1)\\\\y-3=\frac{1}{3}(1)\\y=\frac{1}{3}+3\\\\y=\frac{10}{3}$

$y$ ≈3.33

Find the intersection with the x-axis. Substitute $y=0$ into the equation and solve for x:

$y-3=\frac{1}{3}(x+1)$

$0-3=\frac{1}{3}(x+1)\\(-3)(3)=x+1\\-9-1=x\\x=-10$

Now, you know that the line passes through the point (0,3.33) and (-10,0). Now you can graph the function. (Observe the graph attached)

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