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3 years ago

How many solutions can be found for the equation 2 + x = 6? (4 points)

Mathematics

2 answers:

Kryger [21]3 years ago

4 0

Answer:

one

Step-by-step explanation:

2 + x = 6

x=6-2

x=4

rewona [7]3 years ago

4 0

Zebra being in a size small box and a box size box and a box for the size small box

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A rancher wishes to build a fence to enclose a 2250 square yard rectangular field. Along one side the fence is to be made of hea

Bess [88]

Answer:

The least cost of fencing for the rancher is $1200

Step-by-step explanation:

Let x be the width and y the length of the rectangular field.

Let C the total cost of the rectangular field.

The side made of heavy duty material of length of x costs 16 dollars a yard. The three sides not made of heavy duty material cost $4 per yard, their side lengths are x, y, y. Thus

$C=4x+4y+4y+16x\\C=20x+8y$

We know that the total area of rectangular field should be 2250 square yards,

$x\cdot y=2250$

We can say that $y=\frac{2250}{x}$

Substituting into the total cost of the rectangular field, we get

$C=20x+8(\frac{2250}{x})\\\\C=20x+\frac{18000}{x}$

We have to figure out where the function is increasing and decreasing. Differentiating,

$\frac{d}{dx}C=\frac{d}{dx}\left(20x+\frac{18000}{x}\right)\\\\C'=20-\frac{18000}{x^2}$

Next, we find the critical points of the derivative

$20-\frac{18000}{x^2}=0\\\\20x^2-\frac{18000}{x^2}x^2=0\cdot \:x^2\\\\20x^2-18000=0\\\\20x^2-18000+18000=0+18000\\\\20x^2=18000\\\\\frac{20x^2}{20}=\frac{18000}{20}\\\\x^2=900\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{900},\:x=-\sqrt{900}\\\\x=30,\:x=-30$

Because the length is always positive the only point we take is $x=30$ . We thus test the intervals $(0, 30)$ and $(30, \infty)$

$C'(20)=20-\frac{18000}{20^2} = -25 < 0\\\\C'(40)= 20-\frac{18000}{20^2} = 8.75 >0$

we see that total cost function is decreasing on $(0, 30)$ and increasing on $(30, \infty)$ . Therefore, the minimum is attained at $x=30$ , so the minimal cost is

$C(30)=20(30)+\frac{18000}{30}\\C(30)=1200$

The least cost of fencing for the rancher is $1200

Here’s the diagram:

3 0

2 years ago

Two number have a sum of 71 and a difference of 37

larisa86 [58]

The right answer for the question that is being asked and shown above is that:

Two numbers have a sum of 71 and a difference of 37
x + y = 71
x - y = 37

So in order to get the two numbers, here it is:
x + y = 71
x - y = 37
------------
2x = 108
x = 54
y = 71 - 54
y = 17

So the two numbers are 54 and 17

6 0

2 years ago

Read 2 more answers

The length of the rectangle is 19 less than 3 times the width. If the width of the rectangle is 9 cm, what would the length of t

Delicious77 [7]

Step-by-step explanation:

Given,

width = 9cm

so a/q length of the rectangle will be 19 - ( 9×3) = 19 - 27 = 8 cm

hope this answer helps you dear...take care!

5 0

2 years ago

Read 2 more answers

Given u = LeftAngleBracket StartRoot 3 EndRoot, negative 1 RightAngleBracket and v = ⟨3, –4⟩, what is u · v?

Evgesh-ka [11]

Answer:

3√3+4

Step-by-step explanation:

Given the vectors u = <√3, -1> and v = <3, -4>

u · v = <√3, -1> *<3, -4>

u · v = 3√3 + (-1*-4)

u · v = 3√3+(4)

u · v = 3√3+4

Hence the dot product is 3√3+4

5 0

3 years ago

Read 2 more answers

You pick 7 digits (0-9) at random without replacement, and write them in the order picked. What is the probability that you have

Pie

Answer:

= .0000001

Step-by-step explanation:

The odds of getting 1 number of out the 10 possible number (0-9) equal 10 is 1/10

There are 7 numbers to pick

P(xxx-xxxx) = 1/10 * 1/10 *1/10 * 1/10 * 1/10 * 1/10 *1/10

= .0000001

7 0

3 years ago