Andrei wants to fill a glass tank with marbles, and then fill the remaining space with water. WWW represents the volume of water

Answer:

The solution yields a number equal to -136.

Step-by-step explanation:

Let x represent the number, leading to the following equation:

x + 2 = 7/8 x - 15

Rearranging gives:

x - 7/8 x = -15 - 2

1/8 x = -17

x = -17 * 8 resulting in -136.

Answer:

£700,000

Detailed explanation:

Let x represent the original price of the house. Keeping in mind that

Upon a 7% increase in the house value, it is now set at £749,000. We can express this as

We can solve for x now:

Thus, the initial valuation of the house was

£700,000

Answer:

The total capacity of the tank is 14 1/2 gallons or 29/2.

The size of bucket is 1 1/4 gallons, equal to 5/4.

The expression representing this situation can be

29/2 divided by 5/4.

Therefore, the number of buckets applied equals 29/2 multiplied by 4/5.

Answer:

1) E(-3, -4), F(1, -3), G(3, -6), and H(1, -6)   reflects across the x-axis

2) E(-3, -1), F(1, -2), G(3, 1), and H(1, 1)     translates 5 units downward

3) E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6)    reflects across the y-axis

4) E(4, 4), F(8, 3), G(10, 6), and H(8, 6)    translates 7 units to the right

Step-by-step explanation:

The vertices of quadrilateral ABCD are A(-3, 4), B(1, 3), C(3, 6), and D(1, 6).

1) E(-3, -4), F(1, -3), G(3, -6), and H(1, -6)

   A(-3, 4), B(1, 3), C(3, 6), and D(1, 6)

In this instance, the vertices share the same x-coordinates while their y-coordinates are opposites, indicating a reflection across the x-axis.

2) E(-3, -1), F(1, -2), G(3, 1), and H(1, 1)

   A(-3, 4), B(1, 3), C(3, 6), and D(1, 6)

In this case, the x-coordinates of the vertices remain constant, while the y-coordinates of EFGH are reduced by 5 units, indicative of a downward translation of 5 units.

3) E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6)

   A(-3, 4), B(1, 3), C(3, 6), and D(1, 6)

Here, the vertices share the same y-coordinates while the x-coordinates are opposites, representing a reflection across the y-axis.

4) E(4, 4), F(8, 3), G(10, 6), and H(8, 6)

   A(-3, 4), B(1, 3), C(3, 6), and D(1, 6)

For this case, the y-coordinates for EFGH remain the same while the x-coordinates have increased by 7 units, showing a rightward translation of 7 units.

To solve this problem, I would add 7 to obtain...

... 2x² = 16

Next, I would divide by 2 to yield

... x² = 8

I would then take the square root, noting that both positive and negative solutions exist.

... x = ±√8

This root can be simplified to give...

... x = ±2√2

_____

This method appeared to be the most straightforward to me. Although one could apply the quadratic formula, that entails more steps.

... 2x² -16 = 0.... continuing by subtracting 9

... x = (-0 ± √(0² -4·2·(-16)))/(2·2).... inserting the coefficients into the formula

... x = ±(√128)/4 = ±√8 = ±2√2..... simplifying the final expression