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Goryan [66]
3 years ago
5

What is the solution of the system defined by y= -x+5 and 5x + 2y = 14?

Mathematics
1 answer:
telo118 [61]3 years ago
5 0
          y = -x + 5
5x + 2y = 14

     5x + 2(-x + 5) = 14
5x + 2(-x) + 2(5) = 14
       5x - 2x + 10 = 14
              3x + 10 = 14
                    - 10  - 10
                      3x = 4
                       3     3
                        x = 1¹/₃
      y = -x + 5
      y = -1¹/₃ + 5
      y = 3²/₃
(x, y) = (-1¹/₂, 3²/₃)
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According to a human modeling​ project, the distribution of foot lengths of women is approximately Normal with a mean of 23.4 ce
stiv31 [10]

Answer: 22.0.6%

Step-by-step explanation:

Given : According to a human modeling​ project, the distribution of foot lengths of women is approximately Normal with \mu=23.3\ cm and \sigma=1.3\ cm.

In the United​ States, a​ woman's shoe size of 6 fits feet that are 22.4 centimeters long.

Then, the probability that women in the United States will wear a size 6 or​ smaller :-

P(x\leq22.4)=P(z\leq\dfrac{22.4-23.4}{1.3})\ \ [\because z=\dfrac{x-\mu}{\sigma}]\\\\\approx P(z\leq-0.77)\\\\=1-P(z\leq0.77)\\\\=1-0.77935=0.2206499\approx0.2206=22.06\%

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4 0
3 years ago
Short Response
garik1379 [7]

Answer:

(a)2(89x+84)

(b)2(89x+84-x^2\pi)

Step-by-step explanation:

The dimensions of the larger rectangular field are:

  • Length=5x + 12; Width = 9x + 14.

The dimensions of the smaller rectangular soccer field are:

  • Length=5x; Width = 9x.

(a)Area of the part of the field that is outside the soccer field

=Area of the larger rectangular field - Area of the Soccer Field

=(5x+12)(9x+14)-5x(9x)

=(5x)(9x)+70x+108x+168-5x(9x)

=178x+168

=2(89x+84)

(b)Radius of the Semicircular Fountain =2x

From Part (a),

Area of the larger rectangular field - Area of the Soccer Field=178x+168

Area of the Semicircular Fountain =\dfrac{\pi r^2}{2} =\dfrac{\pi (2x)^2}{2} =\dfrac{4x^2\pi}{2} =2x^2\pi

Area of the Field that does not include the soccer  field or the fountain.

=Area of the larger rectangular field - Area of the Soccer Field-Area of the Semicircular Fountain

=178x+168-2x^2\pi\\=2(89x+84-x^2\pi)

8 0
3 years ago
Is 5p+5c equal to 5(p+c)
melisa1 [442]
When using distributive properties yes.
8 0
2 years ago
Read 2 more answers
Which statement could be used to prove to provide that the function f(x)= -4x+6 grows by equal differences over any x-interval o
Ivahew [28]

Find the Greatest Common Factorthe largest number that divides evenly into <span>4x<span>4x</span></span> and <span>-6<span>−6</span></span>?
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the highest degree of <span>xx</span> that divides evenly into <span>4x<span>4x</span></span> and <span>-6<span>−6</span></span>?
It is 1, since <span>xx</span> is not in every term.Multiplying the results above,
The GCF is <span>22</span>.

<span><span>2(<span><span>​2</span>​<span>​<span>4x</span></span><span>​​</span></span>−<span><span>​2</span>​<span>​6</span><span>​​</span></span>)

</span>
<span>−2(2x−3)</span>
</span>

3 0
2 years ago
HELP PLS’ Suppose you roll a die. Find the probability of the given event. Simplify your answer.
NikAS [45]

The answer is 2) 2/3

7 0
3 years ago
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