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mars1129 [50]
3 years ago
10

8. For all pairs of real numbers P and Q where P = 2Q + 9, Q = ?

Mathematics
1 answer:
Gnom [1K]3 years ago
5 0

Answer:

Q = (P-9)/2

Step-by-step explanation:

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What is the justification for each step in the solution of the equation?
Alexandra [31]

For this case we have the following equation:

\frac{2}{3}x-\frac{1}{3}= 2 (x + 2)\\

If we multiply both sides of the equation by 3 we get:

2x-1 = 6 (x + 2) ---> Multiplication Property of Equality

Applying the distributive property we have:

2x-1 = 6x + 12 ---> Distributive Property

Adding 1 on both sides of equality we have:

2x-1 + 1 = 6x + 12 + 1\\

2x = 6x + 13 ---> Addition Property of Equality

Subtracting 6x on both sides we have:

-6x + 2x = 6x-6x + 13\\

-4x = 13 ---> Subtraction Property of Equality

Finally, dividing by -4 on both sides we have:

\frac{-4x}{-4}= \frac{13}{-4}\\

x = -\frac{13}{4}---> Division Property of Equality


5 0
3 years ago
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What is the reference angle for 225° and what is a reference angle?
sertanlavr [38]
<span> the angle that the Main Angle is called reference angle
</span><span>Given angle - 180
</span><span> 225° -180
</span>=45
eference angle for 225° is 45 
6 0
3 years ago
Line d has a slope of –7 4 . Line e is perpendicular to d . What is the slope of line e ? Simplify your answer and write it as a
Anna [14]

Answer:

4/7

Step-by-step explanation:

If the slope of line d is -7/4, then the slope of a perpendicular is 4/7.

Given a slope, to find the slope of a perpendicular, flip the fraction and change the sign.

Flip -7/4 to get -4/7. Then change the sign of -4/7 to get 4/7.

Answer: 4/7

4 0
3 years ago
Help please!<br><br> | 2x^2 + 5x + 3 | &gt; 0<br> solve the inequality
vovikov84 [41]

Factorize the quadratic.

2x^2 + 5x + 3 = (2x + 3) (x + 1)

We have |ab| = |a||b|, so

|2x^2 + 5x + 3| = |2x + 3| |x + 1| > 0

Now, both |2x+3|\ge0 and |x+1|\ge0 (since the absolute value of any number cannot be negative), so we just need to worry about when the left side is exactly zero. This happens for

(2x + 3) (x + 1) = 0 \implies 2x+3 = 0\text{ or }x+1 = 0 \\\\ \implies x = -\dfrac32 \text{ or } x = -1

So the solution to the inequality is the set

\left\{x \in \Bbb R \mid x\neq-\dfrac32 \text{ and } x\neq-1\right\}

3 0
2 years ago
Use compatible numbers to estimate the quotient 358/3
sweet-ann [11.9K]

Compatible numbers are known as numbers that are the closest value to the actual numbers- this makes mental arithmetic to be performed better. The quotient of 358/3 is equal to 119.333 therefore the compatible number of the quotient of 358/3 is 119.

6 0
3 years ago
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