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DerKrebs [107]
2 years ago
7

The following inequalities are equivalent

Mathematics
1 answer:
forsale [732]2 years ago
6 0

Answer:

c )

Step-by-step explanation:

To find equivalent inequalities, we are looking to isolate x on the left side.

a) x < 4 ✅

b) x -1 < 3 <u>add</u> 1 to both sides  x -1 +1 < 3 +1 result x < 4 ✅

c) x + 1 < 4 <u>subtract</u> 1 from both sides x + 1 -1 < 4 -1 result x < 3 ❌

d) x - 2 < 2 <u>add</u> 2 to both sides x - 2 +2 < 2+2 result x < 4 ✅

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The sum of two consecutive odd integers is 28. What are the integers?
Fantom [35]
The correct option is B): "<span>Let x = 1st integer. Let x + 2 = 2nd integer.</span><span>"
Given that "The sum of two consecutive odd integers is 28."
 
Now the difference between two odd numbers is 2. So this means that one odd number has to be greater than the other by 2.

Let the smaller number be 'X' therefore the bigger number will be 'x+2' thus x + (x+2) = 28
 
therefore, x + x + 2 = 28 now we subtract "2" from both the sides
therefore, 2x = 26 now dividing throughout by 2 we get:

x = 13 therefore, x + 2 = 13+2
                                    = 15
 
therefore, the numbers are 13 AND 15</span>
4 0
4 years ago
A parabola is given by the equation y2 = -24x. The equation of the directrix of the parabola is
LiRa [457]
<span>Find the focus and directrix of the parabola with the given equation. Then graph the parabola. 
y^=-12x
**
y^2=-12x
This is an equation of a parabola with a horizontal axis of symmetry. 
Its standard form: (y-k)^2=4p(x-h), with (h,k) being the (x,y) coordinates of the vertex.
For given equation:

Vertex(0,0) 
4p=12
p=3
Focus:(-3,0)
Directrix: x=3
see the graph below as a visual check on the answers:
..
y=±(-12x)^.5</span>
7 0
3 years ago
Read 2 more answers
A parallelogram has sides of length 16 units and 10 units. The shorter diagonal is 11 units. Find the measure of the longer diag
lord [1]

The measure of the longer diagonal is 24.31 units

<h3>How to determine the longer diagonal?</h3>

The side lengths are given as;

a = 16

b = 10

The shorter diagonal is represented as d1, and it is given as

d1 = 11

The longer diagonal is represented as d2, and it is calculated using

d1^2 + d2^2 = 2 * (a^2 + b^2)

Substitute the known values in the above equation

11^2 + d2^2 = 2 * (16^2 + 10^2)

Evaluate the sum

121 + d2^2 =2 * 356

Evaluate the product

121 + d2^2 = 712

Subtract 121 from both sides

d2^2 = 591

Take the square root of both sides

d2 = 24.31

Hence, the measure of the longer diagonal is 24.31 units

Read more about parallelograms at:

brainly.com/question/970600

#SPJ1

4 0
2 years ago
1. Given GH = 7x + 3, HI= 3x - 5,<br> and GI= 9x + 5.<br> H<br> G<br> A. Find x:<br> B. Find GH:
blsea [12.9K]

Answer:

\boxed{\bf x=7}

\boxed{\bf GH= 52}

Step-by-step explanation:

In the line segment..

\bf 7x+3+3x-5=9x+5

Combine like terms.

  • \bf 10x-2=9x+5

Add -2 to both sides.

  • \bf 10x-2+2=9x+5+2
  • \bf 10x=9x+7

Subtract 9x from both sides.

  • \bf 10x-9x=9x+7-9x
  • \boxed{\bf x=7}

\bf GH=7x+3

  • \bf 7(7)+3
  • \bf 49+3
  • \boxed{\bf 52}
<h3>__________________</h3>
6 0
3 years ago
A family worked all day building a sandcastle on the beach. As they were building the castle they recorded the number of pails o
LiRa [457]

Answer:

15708 cubic inches

Step-by-step explanation:

The formula for a cylandir is V=πr^2h, substitute in your known factors and multiply by 20 for the 20 pails used and you get your answer.

5 0
3 years ago
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