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Shtirlitz [24]
3 years ago
13

What is the sum of the series? Write in expanded form making sure to show all steps used to find the sum.

Mathematics
1 answer:
rjkz [21]3 years ago
6 0

Given:

$\sum_{k=3}^{6}(-2 k+5)

To find:

The sum of the series.

Solution:

$\sum_{k=3}^{6}(-2 k+5)

Substitute k = 3.

-2 (3)+5=-6+5=-1

Substitute k = 4.

-2 (4)+5=-8+5=-3

Substitute k = 5.

-2 (5)+5=-10+5=-5

Substitute k = 6.

-2 (6)+5=-12+5=-7

$\sum_{k=3}^{6}(-2 k+5)=(-1)+(-3)+(-5)+(-7)

Apply minus plus rule: +(-a)=-a

                    =-1-3-5-7

                    =-16

$\sum_{k=3}^{6}-2 k+5=-16

Therefore the sum of the series is -16.

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A ferry is travelling at a constant speed back to the dock, as shown in the graph. Which
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Answer:

<h2>y = -35x + 105</h2>

Step-by-step explanation:

The given graph represents a function between hours and miles.

To determine the equation that belong to this graph, first we need to find the slope using two points from the graph: (0, 105) and (3, 0).

The definition of slope is

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5 0
3 years ago
Write each fraction as a decimal. round to the nearest hundredth if necessary.
SashulF [63]

Answer:

0.375

1.4

3

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Step-by-step explanation:

Divide the numerator (top number) by the denominator (bottom).

3 0
3 years ago
Read 2 more answers
Kylie buys cranberries and raspberries in the ratio of 8:9 to prepare mock tails. If she buys 64 ounces of cranberries what is t
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Answer: 136 ounces

Step-by-step explanation:

Given: The ratio of cranberries and raspberries is 8:9 .

Let quantity of cranberries= 8x , quantity of raspberries = 9x

If quantity of cranberries = 64 ounces

\Rightarrow\ 8x=64\\\\\Rightarrow\ x=\dfrac{64}{8}\\\\\Rightarrow\ x=8

Quantity of raspberries = 9(8) = 72 ounces

Total quantity = 64 ounces  +  72 ounces =  136 ounces

Hence, the total weight of berries purchased=  136 ounces

6 0
2 years ago
Copy DEF to the line so that S is the vertex. This task will be complete when you have constructed an angle with vertex S that i
tino4ka555 [31]

Explanation:

There are numerous videos and web sites that can show you the process of copying an angle. Some are animated. The best we can do here is show you a diagram with instructions. Of course, your curriculum materials already provide that.

__

1. Set the compass to a convenient radius. Use that to draw an arc through rays ED and EF, using point E as the center.

2. Without changing the compass setting, draw a similar arc using S as the center, making sure it crosses the line containing S and extends far enough to accommodate the following steps. (In the attached, we show a full circle, because the tool we used won't draw an arc with a specific radius.)

3. Mark the points where the arc crosses ED as G, and where it crosses EF as H. Mark the point where the arc crosses the line containing S as I.

4. Set the compass radius to the distance GH. Using I as the center draw an arc with that radius so that it crosses the one made in step 2. Call that intersection point J. (Again, we have shown a circle because of the limitations of the tool being used for our diagram.)

5. Draw ray SJ to complete the angle copy.

4 0
3 years ago
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