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il63 [147K]
3 years ago
14

Solve each inequality. Click Submit to check your solution.

Mathematics
1 answer:
labwork [276]3 years ago
7 0

Answer:

x > 10

Step-by-step explanation:

Add 3 to both sides.

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What does it mean to determine the two positive integers that each value is between??? I'm confused ​
KIM [24]

Answer:

  11. {7, 8}

  12. {8, 9}

  13. {8, 9}

  14. {4, 5}

Step-by-step explanation:

You want consecutive integers that bracket each of the given irrational roots.

<h3>Square roots</h3>

A square root of an integer will be rational only if the integer is a perfect square. The first few perfect squares are ...

  • 1² = 1
  • 2² = 4
  • 3² = 9
  • 4² = 16
  • 5² = 25
  • 6² = 36
  • 7² = 49
  • 8² = 64
  • 9² = 81

You know these because you know your multiplication tables.

The square root of a number between these perfect squares will lie between the roots of the squares.

<h3>11. √50</h3>

50 lies between the squares 49 = 7² and 64 = 8². That means √50 lies between 7 and 8.

Your calculator tells you that √50 ≈ 7.0710678, which is a number that lies between the integers 7 and 8.

<h3>12. √72</h3>

72 lies between the squares 64 = 8² and 81 = 9². That means √72 lies between 8 and 9.

<h3>13. √65</h3>

65 lies between the squares 64 = 8² and 91 = 9². That means √65 lies between 8 and 9.

<h3>14. √23</h3>

23 lies between the squares 16 = 4² and 25 = 5². That means √23 lies between 4 and 5.

__

<em>Additional comment</em>

The purpose of questions like this appears to be to have you make use of your knowledge of integer perfect squares to guess an approximation of a square root.

A calculator can answer these questions immediately. Of course the two consecutive integers are the integer part of the root, and the next higher integer.

The question is not well-posed. The answer to "integers each value is between" could be 1 < √50 < 50. For integers greater than 1, the square root is always smaller than the integer being rooted. We've seen questions like this enough times that we can guess the intention is for you to identify <em>consecutive</em> integers.

<em>Extra credit</em>

Knowing the integer part of the root and the difference between the number and its next lower perfect square, you can approximate the root as follows:

For integer n = a² +b, the root √n lies between a +b/(2a+1) and a +b/(2a).

For example, 65 = 8²+1, so √65 lies between 8 1/17 and 8 1/16.

7 0
1 year ago
6. If you can run 1 mile in 8 minutes, how long will it take to run 4 miles (assuming you can maintain
Flauer [41]

Answer:

32 minutes

Step-by-step explanation:

all you have to do is know that the unit rate is 4 so multiply 8 and 4 to get 32

8 0
2 years ago
Read 2 more answers
What is the equation of a quadratic graph with a focus of (-4,17/8) and a detric of y=15/8 answer
Nonamiya [84]

keeping in mind that the vertex is between the focus point and the directrix, in this cases we have the focus point above the directrix, meaning is a vertical parabola opening upwards, Check the picture below, which means the "x" is the squared variable.

now, the vertical distance from the focus point to the directrix is \bf \cfrac{17}{8}-\cfrac{15}{8}\implies \cfrac{2}{8} , which means the distance "p" is half that or 1/8, and is positive since it's opening upwards.

since the vertex is 1/8 above the directrix, that puts the vertex at \bf \cfrac{15}{8}+\stackrel{p}{\cfrac{1}{8}}\implies \cfrac{16}{8}\implies 2 , meaning the y-coordinate for the vertex is 2.

\bf \textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill

\bf \begin{cases} h=-4\\ k=2\\ p=\frac{1}{8} \end{cases}\implies 4\left(\frac{1}{8} \right)(y-2)=[x-(-4)]^2\implies \cfrac{1}{2}(y-2)=(x+4)^2 \\\\\\ y-2=2(x+4)^2\implies \blacktriangleright y = 2(x+4)^2+2 \blacktriangleleft

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3 years ago
Mean , median, mode of 3,5,7,2,3,7,9,2
jarptica [38.1K]
Mean= 4.75
Median= 4
Mode= 3,7, and 2
3 0
3 years ago
Which expression(s) are greater than 0? Select all that apply.
MakcuM [25]

Answer:

1234567891011121314151617181920

4 0
2 years ago
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