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1 year ago

Nine times the sum of a number and 3 is 6 .

Mathematics

1 answer:

Rufina [12.5K]1 year ago

7 0

Answer: -2 1/3

Step-by-step explanation:

First, change the word into equation

9*x+3=6

Do division first, so 6/9, simplify into 2/3 then subtract it by 3 which is -2 1/3

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For every integer k from 1 to 10, inclusive the "k"th term of a certain sequence is given by (−1)(k+1)∗(12k). If T is the sum of

Katena32 [7]

Answer:

Option D. is the correct option.

Step-by-step explanation:

In this question expression that represents the kth term of a certain sequence is not written properly.

The expression is $(-1)^{k+1}(\frac{1}{2^{k}})$ .

We have to find the sum of first 10 terms of the infinite sequence represented by the expression given as $(-1)^{k+1}(\frac{1}{2^{k}})$ .

where k is from 1 to 10.

By the given expression sequence will be $\frac{1}{2},\frac{(-1)}{4},\frac{1}{8}.......$

In this sequence first term "a" = $\frac{1}{2}$

and common ratio in each successive term to the previous term is 'r' = $\frac{\frac{(-1)}{4}}{\frac{1}{2} }$

r = $-\frac{1}{2}$

Since the sequence is infinite and the formula to calculate the sum is represented by

$S=\frac{a}{1-r}$ [Here r is less than 1]

$S=\frac{\frac{1}{2} }{1+\frac{1}{2}}$

$S=\frac{\frac{1}{2}}{\frac{3}{2} }$

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

Now we are sure that the sum of infinite terms is $\frac{1}{3}$ .

Therefore, sum of 10 terms will not exceed $\frac{1}{3}$

Now sum of first two terms = $\frac{1}{2}-\frac{1}{4}=\frac{1}{4}$

Now we are sure that sum of first 10 terms lie between $\frac{1}{4}$ and $\frac{1}{3}$

Since $\frac{1}{2}>\frac{1}{3}$

Therefore, Sum of first 10 terms will lie between $\frac{1}{4}$ and $\frac{1}{2}$ .

Option D will be the answer.

3 0

3 years ago

What is pie^2<br><br>________________________________________

mrs_skeptik [129]

Pi^2 = 9.86960440109

8 0

3 years ago

Read 2 more answers

in Mrs. Dawson's class, 16 out of 24 students made at least an 80% on the last math test. Write a ratio in simplest form compari

Thepotemich [5.8K]

16:24 students made at least 80% on the test. The question is what is the ratio of students who scored below an 80% to the total number of students. 8:24 would be the right answer, but since it is asking for the answer in the simplest form, it would be 1:3.

4 0

3 years ago

Read 2 more answers

whole milk is 4% butterfat how much skim milk with 0% butterfat should be added to 32 ounces of whole milk to obtain a mixture t

vivado [14]

Answer:

whole milk 4 ---------------- 32 ounces

skim milk 0 ---------------- x ounces

Mixture 2.5 ---------------- 32 + x ounces

4*32+0x =2.5(32 +x)

128+0x= 80+2.5 x

0 x + -2.5 x = 80 - -128

-2.5 x = -48

/ -2.5

x = 19.2

19.2 ounces of 0 % fat skim milk

4 0

3 years ago

If point A is located at (-3,-1) and there are 10 points between A and B, what could be the possible coordinates for point B?

Nataly [62]

Answer:

Step-by-step explanation:

By drawing the point (-3,-1) in the coordinate plane we find the graph shown below. Since there are 10 points between points A and B, we need to start at point A and then we have to move 11 units either to the right, to the left, up, or down .

1. MOVING TO THE RIGHT:

From point A, move 11 units horizontally to the right to come to point B:

(-3+11, -1) = (8, -1)

2. MOVING TO THE LEFT:

From point A, move 11 units horizontally to the left to come to point B:

(-3-11, -1) = (-14, -1)

3. MOVING UPWARD:

From point A, move 11 units vertically upward to come to point B:

(-3, -1+11) = (-3, 10)

4. MOVING DOWNWARD:

From point A, move 11 units vertically downward to come to point B:

(-3, -1-11) = (-3, -12)

So this are the basic movements you can get to find point B. You also can move diagonally upwards or downwards in whose case you would find other four points. The graph below shows a red point which is A, and the other points are in black color and represent B.

7 0

3 years ago