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4 years ago

Which system of inequalities is represented by the graph?

Mathematics

2 answers:

sergey [27]4 years ago

7 0

I believe the correct answer is the third answer.

Hope this helps! :)

QveST [7]4 years ago

6 0

Answer:

$y$

Step-by-step explanation:

We observe in the graph that one line is horizontal, and its solution is the area above. Such line intercepts y-axis at $y=-1$ , and the solutions are all numbers more than -1, that means its inequality is

$y\geq -1$

The sign $\geq$ is the right one for this line, because the graph shows a solid line, which means that -1 is part of the solution.

If you observe all the options, you would see that the third choice is the only one that has $y\geq -1$ included.

Therefore, the answer is

$y$

You might be interested in

1-What is the sum of the series? ∑j=152j Enter your answer in the box.

tangare [24]

Answer:

Please see the Step-by-step explanation for the answers

Step-by-step explanation:

∑ $\left \ {{5} \atop {j=1}} \right.$ 2j

The sum of series from j=1 to j=5 is:

∑ = 2(1) + 2(2) + 2(3) + 2(4) + 2(5)

= 2 + 4 + 6 + 8 + 10

∑ = 30

This question is not given clearly so i assume the following series that will give you an idea how to solve this:

∑ $\left \ {{4} \atop {k=1}} \right.$ 2k²

The sum of series from k=1 to j=4 is:

∑ = 2(1)² + 2(2)² + 2(3)² + 2(4)²

= 2(1) + 2(4) + 2(9) + 2(16)

= 2 + 8 + 18 + 32

∑ = 60

∑ $\left \ {{4} \atop {k=1}} \right.$ (2k)²

∑ = (2*1)² + (2*2)² + (2*3)² + (2*4)²

= (2)² + (4)² + (6)² + (8)²

= 4 + 16 + 36 + 64

∑ = 120

∑ $\left \ {{4} \atop {k=1}} \right.$ (2k)²- 4

∑ = (2*1)²-4 + (2*2)²-4 + (2*3)²-4 + (2*4)²-4

= (2)²-4 + (4)²-4 + (6)²-4 + (8)²-4

= (4-4) + (16-4) + (36-4) + (64-4)

= 0 + 12 + 32 + 60

∑ = 104

∑ $\left \ {{4} \atop {k=1}} \right.$ 2k²- 4

∑ = 2(1)²-4 + 2(2)²-4 + 2(3)²-4 + 2(4)²-4

= 2(1)-4 + 2(4)-4 + 2(9)-4 + 2(16)-4

= (2-4) + (8-4) + (18-4) + (32-4)

= -2 + 4 + 14 + 28

∑ = 44

∑ $\left \ {{6} \atop {k=3}} \right.$ (2k-10)

∑ = (2×3−10) + (2×4−10) + (2×5−10) + (2×6−10)

= (6-10) + (8-10) + (10-10) + (12-10)

= -4 + -2 + 0 + 2

∑ = -4

1+1/2+1/4+1/8+1/16+1/32+1/64

This is a geometric sequence where first term is 1 and the common ratio is 1/2 So

a = 1

This can be derived as

1/2/1 = 1/2 * 1 = 1/2

1/4/1/2 = 1/4 * 2/1 = 1/2

1/8/1/4 = 1/8 * 4/1 = 1/2

1/16/1/8 = 1/16 * 8/1 = 1/2

1/32/1/16 = 1/32 * 16/1 = 1/2

1/64/1/32 = 1/64 * 32/1 = 1/2

Hence the common ratio is r = 1/2

So n-th term is:

$ar^{n-1}$ = $1(\frac{1}{2})^{n-1}$

So the answer that represents the series in sigma notation is:

∑ $\left \ {{7} \atop {j=1}} \right.$ $(\frac{1}{2})^{j-1}$

−3+(−1)+1+3+5

This is an arithmetic sequence where the first term is -3 and the common difference is 2. So

a = 1

This can be derived as

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

1 - (-1) = 1 + 1 = 2

3 - 1 = 2

5 - 3 = 2

Hence the common difference d = 2

The nth term is:

a + (n - 1) d

= -3 + (n−1)2

= -3 + 2(n−1)

= -3 + 2n - 2

= 2n - 5

So the answer that represents the series in sigma notation is:

∑ $\left \ {{5} \atop {j=1}} \right.$ (2j−5)

6 0

4 years ago

The product of a number t and 6 increased by 1 is equal to 43

Flura [38]

6*7=42 42+1=43 therefore the number you are looking for is 7

5 0

3 years ago

72kg in a ratio of 1:3:5

skad [1K]

first of all you add all of the ratios together so it would be 1+3+5 That equals 9 then divide 72 by 9 which gets you 8. Then you times 8 by all of the ratios to get the answer 8:24:40

4 0

3 years ago

Read 2 more answers

A baseball player reaches first base 30% of the time he is at bat.out of 50 times at bat,about how many times will the player re

SOVA2 [1]

Answer:

15 times

Step-by-step explanation:

If he bats 50 times, he will be expected to reach first base "30% of the time".

We simply need to find "what is 30% of 50?"

We first need to convert the percentage (30%) to decimal and then multiply that with 50 to get our answer.

Converting percentage to decimal is very simple! We divide by 100. That's it!

So, we have:

30% = 30/100 = 0.3

Now we do the multiplication:

0.3 * 50 = 15

So, the player would reach first base 15 times (out of 50 times of batting)

6 0

3 years ago

Sally invests £8000 in a savings account. The account pays 2.8% compound interest per year work out the value of her investment

Alborosie

Answer: the value of her investment after 4 years is £8934.3

Step-by-step explanation:

The formula for determining compound interest is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount invested.

t represents the duration of the investment in years.

From the information given,

P = 8000

r = 2.8% = 2.8/100 = 0.028

n = 1 because it was compounded once in a year.

t = 4 years

Therefore,

A = 8000(1+0.028/1)^1 × 4

A = 8000(1+0.028)^4

A = 8000(1.028)^4

A = £8934.3 to the the nearest penny

6 0

4 years ago