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KATRIN_1 [288]
3 years ago
14

Solve. y=x - 7 5+2y=7

Mathematics
2 answers:
lesantik [10]3 years ago
8 0

Answer:

\huge\boxed{x=8;\ y=1\to(8;\ 1)}

Step-by-step explanation:

\left\{\begin{array}{ccc}y=x-7&(1)\\5+2y=7&(2)\end{array}\right\\\\\text{Substitute (1) to (2) and solve for x:}\\\\5+2(x-7)=7\qquad\text{use the distributive property}\\\\5+(2)(x)+(2)(-7)=7\\\\5+2x-14=7\\\\2x+(5-14)=7\\\\2x-9=7\qquad\text{add 9 to both sides}\\\\2x-9+9=7+9\\\\2x=16\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{16}{2}\\\\\boxed{x=8}

\text{Substitute it to (1):}\\\\y=8-7\\\\\boxed{y=1}

Illusion [34]3 years ago
4 0

Answer:

(8, 1).

Step-by-step explanation:

y = x - 7

5 + 2y = 7

5 + 2(y) = 7

5 + 2(x - 7) = 7

5 + 2x - 14 = 7

Subtract 5 from both sides

2x - 14 = 2

Add 14 to both sides

2x = 16

Divide both sides by 2

x = 8

Since x = 8...

y = x - 7

y = 8 - 7

y = 1.

To check our work...

5 + 2y = 7

5 + 2 * 1 = 7

5 + 2 = 7

7 = 7

Since it works out, your answer is (8, 1).

Hope this helps!

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Given a two-digit number, make a three digit number by putting a 6 as the rightmost digit. Then, add 6 to the resulting three di
VladimirAG [237]
By working backwards, 
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<span>76x </span>
<span>(x stands for the rightmost digit, because we don't know what the rightmost digit is) </span>

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5 0
3 years ago
Consider the function f(x)=x2e4x. f(x) has two inflection points at x = C and x = D with C≤D where C is and D is Finally for eac
fredd [130]

Answer:

the inflection points are

x = -0.85, -0.14

So,

C = -0.85 \\D = -0.14

It is concave down at the intervals

(-\infty , -0.85] \cup [-0.14,\infty)

And it would be concave up at

(-0.85 , -0.14)

Step-by-step explanation:

Remember that to find inflection points you need to find where

f''(x) = 0

Since

f(x) = x^2 e^{4x}

Then using the product and the chain rule you have that

f'(x) = 2e^{4x} x(2x+1)

And then, using again the chain rule and the product rule you have that

f''(x) = 2e^{4x} (8x^2 +8x+1)

Therefore you have to solve the equation

8x^2 +8x+1 = 0

Using the quadratic equation you get that there are two solutions, so the inflection points are

x = -0.85, -0.14

So,  

C = -0.85 \\D = -0.14

Now remember that a function is concave up if the derivative is greater than zero and concave down if the derivative is less than zero. Therefor you have to solve these inequalties

8x^2 +8x+1  < 0 \\8x^2 +8x+1 \geq 0

And you would get that is concave down at the intervals

(-\infty , -0.85] \cup [-0.14,\infty)

And it would be concave up at

(-0.85 , -0.14)

8 0
3 years ago
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