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Over [174]
2 years ago
14

Solve (x - 2 < 5) ∩ (x + 7 > 6).

Mathematics
2 answers:
WITCHER [35]2 years ago
5 0

For this case we must solve the following expression:

x-2 intersected x + 7> 6

We have:

x-2

Adding 2 to both sides of the inequality:

x

The solution is given by all values of x less strict than 7.

Now we have:

x + 7> 6

Subtracting 7 from both sides of the inequality:

x> 6-7\\x> -1

The solution is given by all values of x higher than -1.

If we intersect the solutions we have:

The solution is given by all values of x between -1 and 7. That is:

(-1,7)

Answer:

-1

Scrat [10]2 years ago
3 0

Answer:

-1<x<7

Step-by-step explanation:

We need to solve each inequality and then from the interval of numbers they both have in common (doing this because of the 'and').

x-2<5

Add 2 on both sides:

x<5+2

Simplify:

x<7

These are values of x that are less than 7.

x+7>6

Subtract 7 on both sides:

x>6-7

Simplify:

x>-1

These are values of x greater than -1.

So the values they have in common are the numbers in between -1 and 7.

That is x<7 and x>-1.

You can also write it as -1<x<7.

Maybe you need a graph to convince you more.

○~~~~~~~~~~~~~~~~~~~~~~~~~~~

~~~~~~~~~~~~~~~~~~~~~~~~~○

‐-------------(-1)------------------------(7)-----------------

So where you see both graphs is the solution:

○~~~~~~~~~~~~~~○

‐-------------(-1)------------------------(7)-----------------

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Solve the given differential equation by separation of variables. dy dx = xy + 5x − y − 5 xy − 2x + 6y − 12
Solnce55 [7]

solution:

Consider the differential equation DE

Dy/dx = xy + 5x –y -5 /xy -2x + 6y -12

Write the DE as the follows.

Dy/dx = x(y+5) -1(y+5)/x(y-2) +6(y-2)

Dy/dx = (x-1) (y+5)/(x+6)(y-2)

Separate the variables.

y-2/y+5 dy = x-1/x+6 dx

integrate on the both sides,

∫y-2/y+5 dy = ∫x-1/x+6 dx

7in(x+6) -7in(y+5) = x-y+c

In(x+6)∧7 –in(y+5)∧7 = x-y+c , using bIna =Inab

In [(x+6)∧7/(y+5)∧7] = x-y+c   ,using Ina – Inb = In(b/a)

eIn[(x+6)∧7/(y+5)∧7] = ex-y+c    , taking exponents on both sides

(x+6)∧7/(y+5)∧7 = ec.ex-y       ,use eInx = x

(x+6)∧7/(y+5)∧7 = c1ex-y , take ec =c1

Hence, the solution of the DE is (x+6)∧7/(y+5)∧7 = c1ex-y


3 0
3 years ago
Please help me with this math question
natta225 [31]

ANSWER

x   = 54\degree

EXPLANATION

The diameter meets the tangent to the circle at right angles.

The sum of interior angles of a triangle is 180°.

This implies that

x + 36 \degree + 90 \degree = 180 \degree

Group the constant terms

x   = 180 \degree -  36 \degree -  90 \degree

We simplify to obtain,

x   = 54\degree

7 0
3 years ago
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Alik [6]
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so
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Arturiano [62]

Answer: d

Step-by-step explanation:

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3 years ago
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kenny6666 [7]

Step-by-step explanation:

because because that would be subtracting positive 10 by -10. not adding -10 + -10 which would be 20

5 0
3 years ago
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