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4 years ago

Solve −5x−3≥2 and 4x−2≥5 and write the solution in interval notation. If there is no solution, type ∅.

Mathematics

1 answer:

denis23 [38]4 years ago

6 0

Answer:

Step-by-step explanation:

Given the set of inequalities

−5x−3≥2 and 4x−2≥5

We are to write the solution in interval notation. We need to solve them individually first as shown;

For −5x−3≥2

add 3 to both sides

−5x−3+3≥2+3

-5x ≥5

divide both sides by -5 (note that dividing by a negative value will change the sense of the inequality sign)

-5x/-5 ≤5/-5

x ≤ -1

For the inequality 4x−2≥5;

add 2 to both sides

4x−2+2≥5+2

4x≥7

divide both sides by 4;

4x/4 ≥ 7/4

x≥7/4 or 7/4≤x

Combining 7/4≤x and x ≤ -1, the solution in interval notation is expressed as 7/4≤x ≤-1

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Combine like terms.<br> (x+6)(x+6)

ycow [4]

Answer:

(x+6)(x+6)

(x+6)^2

Always remember this identity

(a+b)^2 = a^2 + b^2 + 2ab

So, Now take x=a , 6 =b

Substitute above values

x^2 + 36 +2(x)(6)

=x^2 +36 +12x

=x(x+12) +36

5 0

3 years ago

Read 2 more answers

Last HW Mr Thompson! Please Help!

TiliK225 [7]

Answer:

B, D, D, B, C

Step-by-step explanation:

1) The part of the equation that tells us the graph would open downward would be B, the negative coefficient of $x^{2}$ .

We know this because, if we reorganize the equation into the standard form y = mx + b, we get y = -(x²) + 1. This means that for any value we substitute for x, y will always be negative. The answer is B.

2) To find the zeroes of this function, we just have to see which answer makes the function, well, zero.

We have the equation y = (-16t - 2) (t - 1)

We set the equation equal to zero like this:

0 = (-16t - 2) (t - 1)

We also know that anything multiplied <em>by</em> zero will <em>equal</em> zero, so:

0 = (-16t - 2) and 0 = (t - 1)

Now we just solve for t in both equations:

0 = -16t - 2

-16t = 2

t = 2/-16 or -1/8

0 = t - 1

t = 1

So our answer will be D.

3) This time, we are given the same equation but the variable t represents time and y represents the height.

The zeroes are when y = 0, so the zeroes (which are 1 and -1/8 from the last problem) mean that the height is also at zero (which is the ground).

Furthermore, time cannot be negative, so the correct answer choice would be D.

4) We are given the same equation and story problem, but instead we are asked to find the height when the ball was thrown. In other words, we need to find the y-intercept.

The y-intercept is when t = 0, so:

y = (-16t - 2) (t - 1)

y = (-16(0) - 2) (0 - 1)

y = (-2) (-1)

y = 2

So, the correct answer is B, 2 feet.

5) This problem is a simple theoretical question. We know that the constant c will represent the vertical translation or y-intercept, so the correct answer is C.

8 0

3 years ago

Find the coordinates of a point in Quadrant 3 that makes the following triangles congruent. Triangle GHJ: G(1,−6), H(2,−5), J(2,

Jobisdone [24]

Answer:

(-6, -5)

Step-by-step explanation:

<u>Plot the points first:</u>

Triangle GHJ: G(1,−6), H(2,−5), J(2,1)

Triangle NOP: N(−6,1), O(−5,2)

Missing Point P is in quadrant 3and its coordinates are (-6, -5) as per symmetry with triangle GHJ.

4 0

3 years ago

Please help

ValentinkaMS [17]

A) 324

I divided 240 by 20 to get how much it would cost per kg. For each KG the cost is $12. So then I multiplied 12 by what was asked of you (27) which lead me to the answer of 324.

B) 512
Same concept as A. Divide to get how much gasoline is used per mile. That was 4 miles per 1 gas. Multiply 4 by whatever you have been asked for (128). That leads you to 512.

C) 648

Same concept as above.

D) 5,445

3 0

3 years ago

Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the range, interquartile range, variance, and

Valentin [98]

So we have a set of integers,

$X=\{15,20,25,25,27,28,30,34\}$

And we need to compute some stats.

First the range,

The range of data set is difference between the maximum and the minimum of the data set.

So the minimum is 15 and maximum is 34 therefore the range is 34 - 15 = 19.

Second the interquartile range,

The interquartile range of data set is the difference of the first and third quartiles.

First quartile is the value separating the lower quarter and higher three - quarters of the set. The first quartile is computed by taking median of the lower half of the sorted set. This is 15, 20, 25, 25 and it's median is 22.5

Third quartile is therefore the median of 27, 28, 30, 34 which is 29.

Next up, variance.

The variance of set measures how much data is spread out. For data set $x_1,\dots, x_n$ with an average $a$ ,