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alekssr [168]
3 years ago
10

5x + 4y = 11 2x + 6y = -7

Mathematics
1 answer:
olga55 [171]3 years ago
8 0

\left\{\begin{array}{ccc}5x+4y=11&|\cdot2\\2x+6y=-7&|\cdot(-5)\end{array}\right\\\underline{+\left\{\begin{array}{ccc}10x+8y=22\\-10x-30y=35\end{array}\right}\ \ \ \ |add\ both\ sides\ of\ the\ equations\\.\ \ \ \ \ \ \ \ \ \ \ -22y=57\ \ \ \ |:(-22)\\.\ \ \ \ \ \ \ \ \ \ \ y=-\dfrac{57}{22}\\\\substitute\ the\ value\ of\ y\ to\ the\ first\ equation\\\\5x+4\left(-\dfrac{57}{22}\right)=11\\\\5x-2\cdot\dfrac{57}{11}=11\ \ \ \ |\cdot11\\\\55x-114=121\ \ \ \ |+114\\\\55x=135\ \ \ \ |:55

x=\dfrac{135}{55}\\\\x=\dfrac{27}{11}\\\\Answer:\ x=\dfrac{27}{11}\ and\ y=-\dfrac{57}{22}\to\left(\dfrac{27}{11},\ -\dfrac{57}{22}\right)

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Find a function f such that f '(x) = 5x3 and the line 40x + y = 0 is tangent to the graph of f.
Alex17521 [72]

The function that is a  tangent to the graph of f is f(x) = (5/4)x^4+60

<h3>What is the concept of integral?</h3>

The definite integral can be interpreted as the resulting area of a region. In addition, it is a value in its result, that is, it does not depend on the variable x, which can be exchanged for any other variable without changing the value of the integral.

Knowing that :

  • 40x + y = 0 is tangent of f(x)
  • slope of the line = -40

therefore, f'(x)|x=a = -40, so only look for a we have:

5a^3 = -40\\a^3 = -8\\a = -2

if, x = -2, then y = 80 (since, 40x + y = 0), therefore, f(x) passes through (-2,80), so in the equation:

f'(x) = 5x^3\\f(x) = (5/4)x^4 + c\\80 = (5/4)(-2)^4 + c\\c = 60

Therefore,

f(x) = (5/4)x^4+60

See more about tangent at brainly.com/question/401236

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4 0
2 years ago
The temperature in degrees Celsius, c, can be converted to degrees Fahrenheit, f, using the equation f-c+32. Which
Basile [38]

It is a function because every Celsius temperature is associated with only one Fahrenheit temperature. Therefore, option B is true.

<h3>How to convert Celsius into Fahrenheit ?</h3>

We are given that the temperature in degrees Celsius C can be converted to degrees Fahrenheit F

We know that the formula

\dfrac{C}{5} = \dfrac{F - 32}{9}

If we are substituting c = -40

Then, we get

\dfrac{C}{5} = \dfrac{F - 32}{9}\\\\\dfrac{-40}{5} = \dfrac{F - 32}{9}\\\\-8 \times 9 = F - 32\\\\F = -72 + 32\\\\F = -40

For every Celsius temperature, we get only one value of Fahrenheit.

The function is one-one because for every value of Celsius we get a unique value of Fahrenheit.

Hence, it is a function because every Celsius temperature is associated with only one Fahrenheit temperature.

Therefore, option B is true.

Learn more about temperature scale here:

brainly.com/question/2919967

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7 0
3 years ago
Write an equation for the line parallel to the line 24x+8y=7 through the point (-5, -8).
nikdorinn [45]
Paralelll ines have same slope
in form
ax+by=c
slope=-a/b

point slope form
the equtaiotn of a line that passes through the point (x1,y1) and has a slope of m is
y-y1=m(x-x1)
so
find slope

24x+8y=7
slope=-24/8=-3

a point is (-5,-8)

m=-3


y-(-8)=-3(x-(-5))
y+8=-3(x+5)
y+8=-3x-15
y=-3x-23
8 0
3 years ago
A swimming pool is in the shape of a right triangle. One leg has a length of 10 feet and one leg has a length of 15 feet. Estima
sasho [114]

Answer:

5√13 = c  OR 18. 0

Step-by-step explanation:

Using the Pyhtagorean Theorem, we will solve for x (in this case our hypothenuse)

a2 + b2 = c2

10(square) + 15(square)= c2  .....10*10 = 100  and   15* 15= 225

100 + 225 = c2

325= c2

√325 = c

5√13 = c  OR 18. 0

5 0
3 years ago
An equation is given.
svp [43]

Answer:

option A is correct answer

divide both sides with 2

hope it helps

6 0
3 years ago
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